pax_global_header00006660000000000000000000000064145460112670014520gustar00rootroot0000000000000052 comment=b1bbdbefc400229f35163cd8c9e31a47258d75c7 golang-github-cloudflare-circl-1.3.7/000077500000000000000000000000001454601126700174675ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/.etc/000077500000000000000000000000001454601126700203205ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/.etc/action.awk000066400000000000000000000001511454601126700222760ustar00rootroot00000000000000!/^#/{split($0, a, ":"); print "::error file="a[1]",line="a[2]",col="a[3]"::"a[4]} END{if(NR!=0) exit 1} golang-github-cloudflare-circl-1.3.7/.etc/all_imports.go000066400000000000000000000017441454601126700232020ustar00rootroot00000000000000//go:build ignore // +build ignore // Generates a Go program with all the public imports of CIRCL. It is used to // test compilation using static (buildmode=default) and dynamic linking // (buildmode=plugin). package main import ( "flag" "fmt" "io/fs" "os" "strings" ) func main() { outputFileName := flag.String("out", "circl.go", "name of the output file.") flag.Parse() f, err := os.Create(*outputFileName) if err != nil { panic(err) } defer f.Close() skipDirs := []string{".", "testdata", "internal", "templates"} circl := "github.com/cloudflare/circl/" fmt.Fprintln(f, "package main") err = fs.WalkDir(os.DirFS("."), ".", func(path string, d fs.DirEntry, err error) error { if err != nil { panic(err) } if d.IsDir() { for _, sd := range skipDirs { if strings.Contains(path, sd) { return nil } } fmt.Fprintf(f, "import _ \"%v%v\"\n", circl, path) } return nil }) if err != nil { panic(err) } fmt.Fprintln(f, "func main() {}") } golang-github-cloudflare-circl-1.3.7/.etc/golangci.yml000066400000000000000000000017701454601126700226330ustar00rootroot00000000000000--- linters: disable-all: true enable: # - lll # - gocritic # - gocognit # - gci (deprecated since v1.30.0) # - interfacer (deprecated since v1.38.0) # - scopelint (deprecated since v1.39.0) # - golint (deprecated since v1.41.0) # - structcheck (deprecated since v1.49.0) # - varcheck (deprecated since v1.49.0) # - deadcode (deprecated since v1.49.0) - bodyclose - depguard - dogsled - errcheck - exportloopref - forbidigo - funlen - goconst - gocyclo - gofmt - gofumpt - goimports - gosec - gosimple - govet - ineffassign - misspell - nakedret - staticcheck - stylecheck - typecheck - unconvert - unparam - unused - whitespace linters-settings: funlen: lines: 120 statements: 80 nestif: min-complexity: 6 govet: check-shadowing: true issues: max-issues-per-linter: 0 max-same-issues: 0 output: format: github-actions golang-github-cloudflare-circl-1.3.7/.etc/icon.png000066400000000000000000022166551454601126700217770ustar00rootroot00000000000000PNG  IHDRbKGD pHYsu} IDATxzW IDAT A"    _ R2   n ~    2N } e    8HG8u  IDAT   8HG8 h x ~B8    8?x   ux   t $ IDAT?8~ 88  uy   C8  ~  9 IDATv  z8Hq 88|  88o  88o  88R IDATe 'F qu @yt77,E ,? 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IDAT/   *( # $#2 p z88@!87[ 6Af IDATT   ,) p#  *' #  T 88  8H, IDATq x   *( y& (P   Xo8xb{!] IDAT x~x    bhx    ?8 M* x  xs#i IDAT x   M3,S   M3 y   M3 r   Bp~ ['   ? IDAT 3C  SIDAT>]OIENDB`golang-github-cloudflare-circl-1.3.7/.github/000077500000000000000000000000001454601126700210275ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/.github/workflows/000077500000000000000000000000001454601126700230645ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/.github/workflows/ci-actions.yml000066400000000000000000000072731454601126700256510ustar00rootroot00000000000000--- name: CIRCL on: push: branches: - main pull_request: branches: - main jobs: amd64_job: name: Go-${{matrix.GOVER}}/amd64 runs-on: ubuntu-22.04 strategy: matrix: GOVER: ['1.21.1', '1.20.8'] steps: - name: Setup Go-${{ matrix.GOVER }} uses: actions/setup-go@v3 with: go-version: ${{ matrix.GOVER }} - name: Checkout uses: actions/checkout@v3 - name: Linting uses: golangci/golangci-lint-action@v3 with: version: v1.51.2 args: --config=./.etc/golangci.yml ./... - name: Check shadowing run: | go install golang.org/x/tools/go/analysis/passes/shadow/cmd/shadow@latest go vet -vettool=$(which shadow) ./... 2>&1 | awk -f .etc/action.awk shell: bash - name: Verifying Code run: | go generate -v ./... test -z "$(git status --porcelain)" go vet ./... shell: bash - name: Building run: go build -v ./... - name: Testing run: go test -v -count=1 ./... exotic_job: name: Go-${{matrix.CFG[2]}}/${{matrix.CFG[0]}} needs: [amd64_job] runs-on: ubuntu-22.04 strategy: matrix: CFG: [[arm64, arm64v8, '1.21.1']] steps: - uses: actions/checkout@v3 - name: Enabling Docker Experimental run: | echo $'{\n "experimental": true\n}' | sudo tee /etc/docker/daemon.json sudo service docker restart - name: Pulling Images run: | docker pull -q multiarch/qemu-user-static docker pull -q --platform linux/${{matrix.CFG[0]}} ${{matrix.CFG[1]}}/golang:${{matrix.CFG[2]}} docker run --rm --privileged multiarch/qemu-user-static --reset -p yes - name: Testing run: | docker run --rm -v `pwd`:`pwd` -w `pwd` ${{matrix.CFG[1]}}/golang:${{matrix.CFG[2]}} go test -v ./... build_modes: needs: [amd64_job] runs-on: ubuntu-22.04 name: Testing Build Modes steps: - name: Checkout uses: actions/checkout@v3 - name: Setup Go uses: actions/setup-go@v3 with: go-version: '1.21.1' - name: Build as Static run: make circl_static - name: Build as Plugin run: make circl_plugin coverage_amd64_job: needs: [amd64_job] if: github.event_name == 'push' runs-on: ubuntu-22.04 name: amd64/coverage steps: - name: Checkout uses: actions/checkout@v3 - name: Setup Go uses: actions/setup-go@v3 with: go-version: '1.21.1' - name: Produce Coverage run: go test -coverprofile=./coverage.txt ./... - name: Upload Codecov uses: codecov/codecov-action@v2 with: file: ./coverage.txt osCompat: runs-on: ${{ matrix.os }} needs: [amd64_job] name: Running on ${{ matrix.os }} strategy: matrix: os: [macos-11, windows-2019] steps: - name: Checkout uses: actions/checkout@v3 - name: Setup Go uses: actions/setup-go@v3 with: go-version: '1.21.1' - name: Building run: go build -v ./... - name: Testing run: go test -v -count=1 ./... analyze: name: Analyze with CodeQL runs-on: ubuntu-latest permissions: actions: read contents: read security-events: write steps: - name: Checkout repository uses: actions/checkout@v3 - name: Initialize CodeQL uses: github/codeql-action/init@v2 with: languages: go - name: Perform CodeQL Analysis uses: github/codeql-action/analyze@v2 with: category: "/language:go" golang-github-cloudflare-circl-1.3.7/CITATION.cff000066400000000000000000000017371454601126700213710ustar00rootroot00000000000000--- cff-version: 1.2.0 version: 1.3.7 title: "Introducing CIRCL: An Advanced Cryptographic Library" license: BSD-3-Clause abstract: > CIRCL (Cloudflare Interoperable, Reusable Cryptographic Library) is a collection of cryptographic primitives written in Go. The goal of this library is to be used as a tool for experimental deployment of cryptographic algorithms targeting Post-Quantum (PQ) and Elliptic Curve Cryptography (ECC). authors: - family-names: Faz-Hernández given-names: Armando affiliation: Cloudflare, Inc. orcid: "https://orcid.org/0000-0001-5502-8666" - family-names: Kwiatkowski given-names: Kris orcid: "https://orcid.org/0000-0003-2363-317X" date-released: "2019-07-10" keywords: - cryptography - crypto - post-quantum - golang repository-code: "https://github.com/cloudflare/circl/" type: software message: "Available at https://github.com/cloudflare/circl. v1.3.7 Accessed Dec, 2023." contact: - name: "Cloudflare, Inc." golang-github-cloudflare-circl-1.3.7/LICENSE000066400000000000000000000057241454601126700205040ustar00rootroot00000000000000Copyright (c) 2019 Cloudflare. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of Cloudflare nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ======================================================================== Copyright (c) 2009 The Go Authors. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of Google Inc. nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. golang-github-cloudflare-circl-1.3.7/Makefile000066400000000000000000000033201454601126700211250ustar00rootroot00000000000000# I'm sure there is better way. But I would need to find it first MK_FILE_PATH = $(lastword $(MAKEFILE_LIST)) PRJ_DIR = $(abspath $(dir $(MK_FILE_PATH))) GOPATH_BUILD = $(PRJ_DIR)/build COVER_DIR = $(GOPATH_BUILD)/coverage TOOLS_DIR ?= $(GOPATH)/bin ETC_DIR = $(PRJ_DIR)/.etc OPTS ?= NOASM ?= GO ?= go GOLANGCILINT ?= golangci-lint # -run="^_" as we want to avoid running tests by 'bench' and there never be a test starting with _ BENCH_OPTS ?= -bench=. -run="^_" -benchmem V ?= 1 GOARCH ?= BUILD_ARCH = $(shell $(GO) env GOARCH) ifeq ($(NOASM),1) OPTS+=--tags noasm endif ifeq ($(V),1) OPTS += -v # Be verbose endif all: build lint: $(GOLANGCILINT) run --config $(ETC_DIR)/golangci.yml ./... lint-fix: $(GOLANGCILINT) run --config $(ETC_DIR)/golangci.yml --fix ./... build: $(GO) build ./... test: clean $(GO) vet ./... $(GO) test $(OPTS) ./... bench: clean $(GO) test $(BENCH_OPTS) $(OPTS) ./... cover: clean mkdir -p $(COVER_DIR) $(GO) test -race -coverprofile=$(COVER_DIR)/coverage.txt -covermode=atomic $(OPTS) ./... $(GO) tool cover -html $(COVER_DIR)/coverage.txt -o $(COVER_DIR)/coverage.html generate: clean $(GO) generate -v ./... bootstrap: curl -sfL https://install.goreleaser.com/github.com/golangci/golangci-lint.sh | sh -s -- -b $(TOOLS_DIR) v1.18.0 clean: rm -rf $(GOPATH_BUILD) .INTERMEDIATE: circl.go circl_static.exe circl_plugin.so circl_static: circl_static.exe circl_static.exe: circl.go go clean -cache -modcache go build -buildmode=default -o $@ $^ circl_plugin: circl_plugin.so circl_plugin.so: circl.go go clean -cache -modcache go build -buildmode=plugin -o $@ $^ circl.go: go run .etc/all_imports.go -out $@ golang-github-cloudflare-circl-1.3.7/README.md000066400000000000000000000163421454601126700207540ustar00rootroot00000000000000 # CIRCL [![GitHub release](https://img.shields.io/github/release/cloudflare/circl.svg)](https://GitHub.com/cloudflare/circl/releases/) [![CIRCL](https://github.com/cloudflare/circl/workflows/CIRCL/badge.svg)](https://github.com/cloudflare/circl/actions) [![GoDoc](https://godoc.org/github.com/cloudflare/circl?status.svg)](https://pkg.go.dev/github.com/cloudflare/circl?tab=overview) [![Go Report Card](https://goreportcard.com/badge/github.com/cloudflare/circl)](https://goreportcard.com/report/github.com/cloudflare/circl) [![codecov](https://codecov.io/gh/cloudflare/circl/branch/main/graph/badge.svg)](https://codecov.io/gh/cloudflare/circl) **CIRCL** (Cloudflare Interoperable, Reusable Cryptographic Library) is a collection of cryptographic primitives written in Go. The goal of this library is to be used as a tool for experimental deployment of cryptographic algorithms targeting Post-Quantum (PQ) and Elliptic Curve Cryptography (ECC). ## Security Disclaimer 🚨 This library is offered as-is, and without a guarantee. Therefore, it is expected that changes in the code, repository, and API occur in the future. We recommend to take caution before using this library in a production application since part of its content is experimental. All security issues must be reported, please notify us immediately following the instructions given in our [Security Policy](https://github.com/cloudflare/circl/security/policy). ## Installation You can get CIRCL by fetching: ```sh go get -u github.com/cloudflare/circl ``` Alternatively, look at the [Cloudflare Go](https://github.com/cloudflare/go/tree/cf) fork to see how to integrate CIRCL natively in Go. ## List of Algorithms [RFC-7748]: https://doi.org/10.17487/RFC7748 [RFC-8032]: https://doi.org/10.17487/RFC8032 [RFC-8235]: https://doi.org/10.17487/RFC8235 [RFC-9180]: https://doi.org/10.17487/RFC9180 [RFC-9380]: https://doi.org/10.17487/RFC9380 [RFC-9474]: https://doi.org/10.17487/RFC9474 [RFC-9496]: https://doi.org/10.17487/RFC9496 [RFC-9497]: https://doi.org/10.17487/RFC9497 [FIPS 202]: https://doi.org/10.6028/NIST.FIPS.202 [FIPS 186-5]: https://doi.org/10.6028/NIST.FIPS.186-5 [BLS12-381]: https://electriccoin.co/blog/new-snark-curve/ [ia.cr/2015/267]: https://ia.cr/2015/267 [ia.cr/2019/966]: https://ia.cr/2019/966 ### Elliptic Curve Cryptography | Diffie-Hellman Protocol | |:---:| - [X25519](./dh/x25519) and [X448](./dh/x448) functions. ([RFC-7748]) - [Curve4Q](./dh/curve4q) function based on FourQ curve. ([draft-ladd-cfrg-4q](https://datatracker.ietf.org/doc/draft-ladd-cfrg-4q/)) | Digital Signature Schemes | |:---:| - [Ed25519](./sign/ed25519) and [Ed448](./sign/ed448) signatures. ([RFC-8032]) | Prime Groups | |:---:| - [P-256, P-384, P-521](./group). ([FIPS 186-5]) - [Ristretto](./group) group. ([RFC-9496]) - [Bilinear pairings](./ecc/bls12381): with the [BLS12-381] curve, and hash to G1 and G2. - [Hash to curve](./group), hash to field, XMD and XOF [expanders](./expander). ([RFC-9380]) | High-Level Protocols | |:---:| - [HPKE](./hpke): Hybrid Public-Key Encryption ([RFC-9180]) - [VOPRF](./oprf): Verifiable Oblivious Pseudorandom functions. ([RFC-9497]) - [RSA Blind Signatures](./blindsign/blindrsa). ([RFC-9474]) - [Partilly-blind](./blindsign/blindrsa/partiallyblindrsa/) Signatures. ([draft-cfrg-partially-blind-rsa](https://datatracker.ietf.org/doc/draft-amjad-cfrg-partially-blind-rsa/)) - [CPABE](./abe/cpabe): Ciphertext-Policy Attribute-Based Encryption. ([ia.cr/2019/966]) - [OT](./ot/simot): Simplest Oblivious Transfer ([ia.cr/2015/267]). - [Threshold RSA](./tss/rsa) Signatures ([Shoup Eurocrypt 2000](https://www.iacr.org/archive/eurocrypt2000/1807/18070209-new.pdf)). ### Post-Quantum Cryptography | KEM: Key Encapsulation Methods | |:---:| - [CSIDH](./dh/csidh): Post-Quantum Commutative Group Action ([CSIDH](https://csidh.isogeny.org/)). - [Kyber KEM](./kem/kyber): modes 512, 768, 1024 ([KYBER](https://pq-crystals.org/kyber/)). - [FrodoKEM](./kem/frodo): modes 640-SHAKE. ([FrodoKEM](https://frodokem.org/)) - (**insecure, deprecated**) ~~[SIDH/SIKE](./kem/sike)~~: Supersingular Key Encapsulation with primes p434, p503, p751 ([SIKE](https://sike.org/)). | Digital Signature Schemes | |:---:| - [Dilithium](./sign/dilithium): modes 2, 3, 5 ([Dilithium](https://pq-crystals.org/dilithium/)). ### Zero-knowledge Proofs - [Schnorr](./zk/dl): Prove knowledge of the Discrete Logarithm. ([RFC-8235]) - [DLEQ](./zk/dleq): Prove knowledge of the Discrete Logarithm Equality. ([RFC-9497]) ### Symmetric Cryptography | XOF: eXtendable Output Functions | |:---:| - [SHAKE128 and SHAKE256](./xof) ([FIPS 202]). - [BLAKE2X](./xof): BLAKE2XB and BLAKE2XS ([Blake2x](https://www.blake2.net/blake2x.pdf)) - [KangarooTwelve](./xof/k12): fast hashing based on Keccak-p. ([KangarooTwelve](https://keccak.team/kangarootwelve.html)). - SIMD [Keccak](https://keccak.team/keccak_specs_summary.html) f1600 Permutation. | LWC: Lightweight Cryptography | |:---:| - [Ascon v1.2](./cipher/ascon): Family of AEAD block ciphers ([ASCON](https://ascon.iaik.tugraz.at/index.html)) ### Misc | Integers | |:---:| - Safe primes generation. - Integer encoding: wNAF, regular signed digit, mLSBSet representations. | Finite Fields | |:---:| - Fp25519, Fp448, Fp511, Fp434, Fp503, Fp751. - Fp381, and its quadratic, sextic and twelveth extensions. - Polynomials in monomial and Lagrange basis. | Elliptic Curves | |:---:| - P-384 Curve - [FourQ](https://eprint.iacr.org/2015/565) - [Goldilocks](https://eprint.iacr.org/2015/625) - [BLS12-381](https://electriccoin.co/blog/new-snark-curve/) ## Testing and Benchmarking Library comes with number of make targets which can be used for testing and benchmarking: - ``test`` performs testing of the binary. - ``bench`` runs benchmarks. - ``cover`` produces coverage. - ``lint`` runs set of linters on the code base. ## Contributing To contribute, fork this repository and make your changes, and then make a Pull Request. A Pull Request requires approval of the admin team and a successful CI build. ## How to Cite To cite CIRCL, use one of the following formats and update the version and date you accessed this project. APA Style ``` Faz-Hernández, A. and Kwiatkowski, K. (2019). Introducing CIRCL: An Advanced Cryptographic Library. Cloudflare. Available at https://github.com/cloudflare/circl. v1.3.7 Accessed Dec, 2023. ``` Bibtex Source ```bibtex @manual{circl, title = {Introducing CIRCL: An Advanced Cryptographic Library}, author = {Armando Faz-Hern\'{a}ndez and Kris Kwiatkowski}, organization = {Cloudflare}, abstract = {{CIRCL (Cloudflare Interoperable, Reusable Cryptographic Library) is a collection of cryptographic primitives written in Go. The goal of this library is to be used as a tool for experimental deployment of cryptographic algorithms targeting Post-Quantum (PQ) and Elliptic Curve Cryptography (ECC).}}, note = {Available at \url{https://github.com/cloudflare/circl}. v1.3.7 Accessed Dec, 2023}, month = jun, year = {2019} } ``` CFF Style See attached [CITATION.cff](CITATION.cff) file. ## License The project is licensed under the [BSD-3-Clause License](./LICENSE). golang-github-cloudflare-circl-1.3.7/abe/000077500000000000000000000000001454601126700202165ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/abe/cpabe/000077500000000000000000000000001454601126700212705ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/abe/cpabe/doc.go000066400000000000000000000001411454601126700223600ustar00rootroot00000000000000// Package cpabe provides Ciphertext-Policy Attribute-based Encryption algorithms. package cpabe golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/000077500000000000000000000000001454601126700222265ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/bench_test.go000066400000000000000000000143351454601126700247010ustar00rootroot00000000000000package tkn20 import ( "crypto/rand" "crypto/rsa" "crypto/x509" "fmt" "strconv" "strings" "testing" "golang.org/x/crypto/nacl/box" ) type abeTestCase struct { desc string attrs Attributes policy Policy msk SystemSecretKey pk PublicKey } var testCases []abeTestCase var ( msg = []byte("drink your ovaltine now") longMsg = []byte(strings.Repeat("a", 10000)) ) func generateAttrs() Attributes { benchableAttrs := make(map[string]string, 50) for i := 0; i < 50; i++ { benchableAttrs["k"+strconv.Itoa(i)] = "v" + strconv.Itoa(i) } attrs := Attributes{} attrs.FromMap(benchableAttrs) return attrs } func generatePolicy() string { var policyBuilder strings.Builder for i := 0; i < 50; i++ { policyBuilder.WriteString("k") policyBuilder.WriteString(strconv.Itoa(i)) policyBuilder.WriteString(":v") policyBuilder.WriteString(strconv.Itoa(i)) if i != 49 { if i%2 == 0 { policyBuilder.WriteString(" and ") } else { policyBuilder.WriteString(" or ") } } } return policyBuilder.String() } func init() { smallPolicy := Policy{} _ = smallPolicy.FromString("(k1:v1 or k1:v2) and not k2:v3") smallAttrs := Attributes{} smallAttrs.FromMap(map[string]string{"k1": "v2", "k2": "v4"}) longPolicy := Policy{} _ = longPolicy.FromString(generatePolicy()) testCases = []abeTestCase{ { desc: "smallPolicy/Attrs", attrs: smallAttrs, policy: smallPolicy, }, { desc: "longPolicy/Attrs", attrs: generateAttrs(), policy: longPolicy, }, } var err error for i := range testCases { testCases[i].pk, testCases[i].msk, err = Setup(rand.Reader) if err != nil { panic(err) } } } func BenchmarkTKN20KeyGen(b *testing.B) { for _, tc := range testCases { b.Run(fmt.Sprintf("keygen:%s", tc.desc), func(b *testing.B) { b.ResetTimer() for i := 0; i < b.N; i++ { _, err := tc.msk.KeyGen(rand.Reader, tc.attrs) if err != nil { b.Fatal(err) } } }) } } func BenchmarkRSAKeyGen(b *testing.B) { for i := 0; i < b.N; i++ { _, err := rsa.GenerateKey(rand.Reader, 2048) if err != nil { b.Fatal(err) } } } func BenchmarkX25519KeyGen(b *testing.B) { for i := 0; i < b.N; i++ { _, _, err := box.GenerateKey(rand.Reader) if err != nil { b.Fatal(err) } } } func BenchmarkTKN20Encrypt(b *testing.B) { for _, tc := range testCases { b.Run(fmt.Sprintf("encrypt:%s", tc.desc), func(b *testing.B) { b.ResetTimer() for i := 0; i < b.N; i++ { _, err := tc.pk.Encrypt(rand.Reader, tc.policy, msg) if err != nil { b.Fatal(err) } } }) } } func BenchmarkRSAEncrypt(b *testing.B) { privKey, err := rsa.GenerateKey(rand.Reader, 2048) if err != nil { b.Fatal(err) } pubKey := privKey.PublicKey b.ResetTimer() for i := 0; i < b.N; i++ { _, err := rsa.EncryptPKCS1v15(rand.Reader, &pubKey, msg) if err != nil { b.Fatal(err) } } } func BenchmarkX25519Encrypt(b *testing.B) { pubKey, _, err := box.GenerateKey(rand.Reader) if err != nil { b.Fatal(err) } b.ResetTimer() for i := 0; i < b.N; i++ { _, err := box.SealAnonymous(nil, msg, pubKey, rand.Reader) if err != nil { b.Fatal(err) } } } func BenchmarkTKN20Decrypt(b *testing.B) { for _, tc := range testCases { b.Run(fmt.Sprintf("decrypt:%s", tc.desc), func(b *testing.B) { userKey, err := tc.msk.KeyGen(rand.Reader, tc.attrs) if err != nil { b.Fatal(err) } ciphertext, err := tc.pk.Encrypt(rand.Reader, tc.policy, msg) if err != nil { b.Fatal(err) } keyBytes, _ := userKey.MarshalBinary() pubKeyBytes, _ := tc.pk.MarshalBinary() // longCt is only benchmarked to measure size overhead longCt, err := tc.pk.Encrypt(rand.Reader, tc.policy, longMsg) if err != nil { b.Fatal(err) } b.ResetTimer() for i := 0; i < b.N; i++ { _, err = userKey.Decrypt(ciphertext) if err != nil { b.Fatal(err) } } b.ReportMetric(float64(len(pubKeyBytes)), "public_key_size") b.ReportMetric(float64(len(keyBytes)), "attribute_secret_key_size") b.ReportMetric(float64(len(ciphertext)-len(msg)), "ciphertext_bytes_overhead_32b_msg") b.ReportMetric(float64(len(longCt)-len(longMsg)), "ciphertext_bytes_overhead_10kb_msg") }) } } func BenchmarkRSADecrypt(b *testing.B) { privKey, err := rsa.GenerateKey(rand.Reader, 2048) if err != nil { b.Fatal(err) } pubKey := privKey.PublicKey ct, err := rsa.EncryptPKCS1v15(rand.Reader, &pubKey, msg) if err != nil { b.Fatal(err) } // longCt is only benchmarked to measure size overhead longCt, err := rsaEncrypt(longMsg, &privKey.PublicKey) if err != nil { b.Fatal(err) } b.ResetTimer() for i := 0; i < b.N; i++ { _, err := rsa.DecryptPKCS1v15(rand.Reader, privKey, ct) if err != nil { b.Fatal(err) } } b.ReportMetric(float64(privKey.PublicKey.Size()), "public_key_size") b.ReportMetric(float64(len(x509.MarshalPKCS1PrivateKey(privKey))), "secret_key_size") b.ReportMetric(float64(len(ct)-len(msg)), "ciphertext_bytes_overhead") b.ReportMetric(float64(len(longCt)-len(longMsg)), "ciphertext_bytes_overhead_10kb_msg") } func BenchmarkX25519Decrypt(b *testing.B) { pubKey, privKey, err := box.GenerateKey(rand.Reader) if err != nil { b.Fatal(err) } ct, err := box.SealAnonymous(nil, msg, pubKey, rand.Reader) if err != nil { b.Fatal(err) } // longCt is only benchmarked to measure size overhead longCt, err := box.SealAnonymous(nil, longMsg, pubKey, rand.Reader) if err != nil { b.Fatal(err) } b.ResetTimer() for i := 0; i < b.N; i++ { _, ok := box.OpenAnonymous(nil, ct, pubKey, privKey) if !ok { b.Fatal(err) } } b.ReportMetric(float64(len(pubKey)), "public_key_size") b.ReportMetric(float64(len(privKey)), "secret_key_size") b.ReportMetric(float64(len(ct)-len(msg)), "ciphertext_bytes_overhead_32b_msg") b.ReportMetric(float64(len(longCt)-len(longMsg)), "ciphertext_bytes_overhead_10kb_msg") } func rsaEncrypt(data []byte, pubKey *rsa.PublicKey) ([]byte, error) { chunkSize := 245 // Max chunk size for 2048 bit key with PKCS1v15 padding var ct []byte for len(data) > 0 { if len(data) < chunkSize { chunkSize = len(data) } chunk := data[:chunkSize] data = data[chunkSize:] encryptedChunk, err := rsa.EncryptPKCS1v15(rand.Reader, pubKey, chunk) if err != nil { return nil, err } ct = append(ct, encryptedChunk...) } return ct, nil } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/example_test.go000066400000000000000000000065061454601126700252560ustar00rootroot00000000000000package tkn20_test import ( "bytes" "crypto/rand" "fmt" "log" "strconv" cpabe "github.com/cloudflare/circl/abe/cpabe/tkn20" ) func checkPolicy(in map[string][]string) bool { possiblePairs := map[string][]string{ "occupation": {"wizard", "doctor", "ghost"}, "country": {"US", "croatia"}, "age": {}, } isValid := func(key string, value string) bool { vs, ok := possiblePairs[key] if !ok { return false } if key == "age" { age, err := strconv.Atoi(value) if err != nil { return false } if age < 13 || age > 100 { return false } } else { for _, v := range vs { if value == v { return true } } } return false } for k, v := range in { for _, value := range v { if !isValid(k, value) { return false } } } return true } func Example() { policyStr := `(occupation: doctor) and (country: US)` invalidPolicyStr := `(title: doctor) and (country: pacific)` msgStr := `must have the precious 🎃` wrongAttrsMap := map[string]string{"occupation": "doctor", "country": "croatia"} rightAttrsMap := map[string]string{"occupation": "doctor", "country": "US", "age": "16"} publicKey, systemSecretKey, err := cpabe.Setup(rand.Reader) if err != nil { log.Fatalf("%s", err) } policy := cpabe.Policy{} err = policy.FromString(policyStr) if err != nil { log.Fatal(err) } if !checkPolicy(policy.ExtractAttributeValuePairs()) { log.Fatalf("policy check failed for valid policy") } fmt.Println(policy.String()) invalidPolicy := cpabe.Policy{} err = invalidPolicy.FromString(invalidPolicyStr) if err != nil { log.Fatal(err) } if checkPolicy(invalidPolicy.ExtractAttributeValuePairs()) { log.Fatalf("policy check should fail for invalid policy") } // encrypt the secret message for a given policy ct, err := publicKey.Encrypt(rand.Reader, policy, []byte(msgStr)) if err != nil { log.Fatalf("%s", err) } // generate secret key for certain set of attributes wrongAttrs := cpabe.Attributes{} wrongAttrs.FromMap(wrongAttrsMap) rightAttrs := cpabe.Attributes{} rightAttrs.FromMap(rightAttrsMap) wrongSecretKey, _ := systemSecretKey.KeyGen(rand.Reader, wrongAttrs) rightSecretKey, _ := systemSecretKey.KeyGen(rand.Reader, rightAttrs) wrongSat := policy.Satisfaction(wrongAttrs) if wrongSat { log.Fatalf("wrong attributes should not satisfy policy") } rightSat := policy.Satisfaction(rightAttrs) if !rightSat { log.Fatalf("right attributes should satisfy policy") } // wrong attrs should not satisfy ciphertext wrongCtSat := wrongAttrs.CouldDecrypt(ct) if wrongCtSat { log.Fatalf("wrong attrs should not satisfy ciphertext") } rightCtSat := rightAttrs.CouldDecrypt(ct) if rightCtSat == false { log.Fatalf("right attrs should satisfy ciphertext") } // attempt to decrypt with wrong attributes should fail pt, err := wrongSecretKey.Decrypt(ct) if err == nil { log.Fatalf("decryption using wrong attrs should have failed, plaintext: %s", pt) } pt, err = rightSecretKey.Decrypt(ct) if err != nil { log.Fatalf("decryption using right attrs should have succeeded, plaintext: %s", pt) } if !bytes.Equal(pt, []byte(msgStr)) { log.Fatalf("recovered plaintext: %s is not equal to original msg: %s", pt, msgStr) } fmt.Println("Successfully recovered plaintext") // Output: (occupation:doctor and country:US) // Successfully recovered plaintext } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/format_test.go000066400000000000000000000027051454601126700251100ustar00rootroot00000000000000package tkn20 import ( "os" "testing" ) func TestPublicKeyFormat(t *testing.T) { paramsData, err := os.ReadFile("testdata/publicKey") if err != nil { t.Fatalf("Unable to read public key") } pp := &PublicKey{} err = pp.UnmarshalBinary(paramsData) if err != nil { t.Fatalf("unable to parse public key") } } func TestSystemSecretKeyFormat(t *testing.T) { secret, err := os.ReadFile("testdata/secretKey") if err != nil { t.Fatalf("Unable to read secret key") } sk := &SystemSecretKey{} err = sk.UnmarshalBinary(secret) if err != nil { t.Fatalf("unable to parse system secret key") } } func TestAttributeKeyFormat(t *testing.T) { attributeKey, err := os.ReadFile("testdata/attributeKey") if err != nil { t.Fatalf("Unable to read secret key") } sk := &AttributeKey{} err = sk.UnmarshalBinary(attributeKey) if err != nil { t.Fatalf("unable to parse secret key") } } func TestCiphertext(t *testing.T) { ciphertext, err := os.ReadFile("testdata/ciphertext") if err != nil { t.Fatalf("Unable to read ciphertext data") } policyKey, err := os.ReadFile("testdata/attributeKey") if err != nil { t.Fatalf("Unable to read secret key") } sk := AttributeKey{} err = sk.UnmarshalBinary(policyKey) if err != nil { t.Fatalf("unable to parse secret key") } msg, err := sk.Decrypt(ciphertext) if err != nil { t.Fatal("unable to decrypt message") } if string(msg) != "Be sure to drink your ovaltine!" { t.Fatal("message incorrect") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/gen_testdata.go000066400000000000000000000026311454601126700252210ustar00rootroot00000000000000//go:build ignore // +build ignore // Generates golden files for tests. package main import ( "encoding" mrand "math/rand" "os" "path/filepath" cpabe "github.com/cloudflare/circl/abe/cpabe/tkn20" ) func writeToFile(name string, data []byte) { err := os.WriteFile("testdata/"+name, data, 0o644) if err != nil { panic(err) } } func dumpToFile(name string, m encoding.BinaryMarshaler) { data, err := m.MarshalBinary() if err != nil { panic(err) } writeToFile(name, data) } func main() { // Using fixed PRNG for reproducibility, fixedSeed := int64(0xC1C1C1C1) prng := mrand.New(mrand.NewSource(fixedSeed)) if prng == nil { panic("failed to create PRNG") } err := os.MkdirAll(filepath.Join(".", "testdata"), 0o755) if err != nil { panic(err) } publicParams, secretParams, err := cpabe.Setup(prng) if err != nil { panic(err) } dumpToFile("publicKey", &publicParams) dumpToFile("secretKey", &secretParams) attrs := cpabe.Attributes{} attrs.FromMap(map[string]string{"country": "NL", "EU": "true"}) policy := cpabe.Policy{} err = policy.FromString("EU: true") if err != nil { panic(err) } msg := []byte("Be sure to drink your ovaltine!") ciphertext, err := publicParams.Encrypt(prng, policy, msg) if err != nil { panic(err) } writeToFile("ciphertext", ciphertext) key, err := secretParams.KeyGen(prng, attrs) if err != nil { panic(err) } dumpToFile("attributeKey", &key) } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/000077500000000000000000000000001454601126700240425ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/000077500000000000000000000000001454601126700246245ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/ast.go000066400000000000000000000033261454601126700257460ustar00rootroot00000000000000package dsl import ( "fmt" "github.com/cloudflare/circl/abe/cpabe/tkn20/internal/tkn" ) var operators = map[string]int{ "and": tkn.Andgate, "or": tkn.Orgate, } type attrValue struct { value string positive bool } type attr struct { key string id int } type gate struct { op string in1 attr in2 attr out attr } type Ast struct { wires map[attr]attrValue gates []gate } func (t *Ast) RunPasses() (*tkn.Policy, error) { inputs, err := t.hashAttrValues() if err != nil { return nil, fmt.Errorf("attribute values could not be hashed: %s", err) } gates, err := t.transformGates() if err != nil { return nil, fmt.Errorf("gates could not be converted into a formula: %s", err) } return &tkn.Policy{ Inputs: inputs, F: tkn.Formula{Gates: gates}, }, nil } func (t *Ast) hashAttrValues() ([]tkn.Wire, error) { wires := make([]tkn.Wire, len(t.wires)) for k, v := range t.wires { value := tkn.HashStringToScalar(AttrHashKey, v.value) if value == nil { return nil, fmt.Errorf("error on hashing") } wire := tkn.Wire{ Label: k.key, RawValue: v.value, Value: value, Positive: v.positive, } wires[k.id] = wire } return wires, nil } func (t *Ast) transformGates() ([]tkn.Gate, error) { lenGates := len(t.gates) gates := make([]tkn.Gate, lenGates) for i, g := range t.gates { class, ok := operators[g.op] if !ok { return nil, fmt.Errorf("invalid operator %s", g.op) } wireIDs := [3]int{g.in1.id, g.in2.id, g.out.id} for j, wireID := range wireIDs { if wireID < 0 { wireIDs[j] = -1*wireID + lenGates } } gate := tkn.Gate{ Class: class, In0: wireIDs[0], In1: wireIDs[1], Out: wireIDs[2], } gates[i] = gate } return gates, nil } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/dsl.go000066400000000000000000000005711454601126700257400ustar00rootroot00000000000000package dsl import "github.com/cloudflare/circl/abe/cpabe/tkn20/internal/tkn" var AttrHashKey = []byte("attribute value hashing") func Run(source string) (*tkn.Policy, error) { l := newLexer(source) err := l.scanTokens() if err != nil { return nil, err } p := newParser(l.tokens) ast, err := p.parse() if err != nil { return nil, err } return ast.RunPasses() } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/dsl_test.go000066400000000000000000000107721454601126700270030ustar00rootroot00000000000000package dsl_test import ( "errors" "testing" "github.com/cloudflare/circl/abe/cpabe/tkn20/internal/dsl" "github.com/cloudflare/circl/abe/cpabe/tkn20/internal/tkn" ) var testCases = []struct { input string output *tkn.Policy err error }{ { input: "", err: errors.New("expected parentheses or literal"), }, { input: "&", err: errors.New("unexpected character(s): '&'"), }, { input: "country: north korea", err: errors.New("unexpected token korea, expected logical operator \"and\" or \"or\""), }, { input: "(country: congo", err: errors.New("expected ')' after expression"), }, { input: "(country: china or taiwan)", err: errors.New("expected parentheses or literal"), }, { input: "not (planet: arakis", err: errors.New("expected ')' after expression"), }, { input: "ocean: indian and ship: rms titanic", err: errors.New("unexpected token titanic, expected logical operator \"and\" or \"or\""), }, { input: "not (spice: saffron and region: persia)", output: &tkn.Policy{ Inputs: []tkn.Wire{ {Label: "spice", RawValue: "saffron", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "saffron"), Positive: false}, {Label: "region", RawValue: "persia", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "persia"), Positive: false}, }, F: tkn.Formula{ Gates: []tkn.Gate{ {Class: tkn.Orgate, In0: 0, In1: 1, Out: 2}, }, }, }, }, { input: "not (spice: mace or spice: nutmeg)", output: &tkn.Policy{ Inputs: []tkn.Wire{ {Label: "spice", RawValue: "mace", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "mace"), Positive: false}, {Label: "spice", RawValue: "nutmeg", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "nutmeg"), Positive: false}, }, F: tkn.Formula{ Gates: []tkn.Gate{ {Class: tkn.Andgate, In0: 0, In1: 1, Out: 2}, }, }, }, }, { input: "((region: caribean)) or (not (((fruit: stonefruit and not flower: hibiscus) or spice: mace) and not (family: extracts or family: chilis)))", output: &tkn.Policy{ Inputs: []tkn.Wire{ {Label: "region", RawValue: "caribean", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "caribean"), Positive: true}, {Label: "fruit", RawValue: "stonefruit", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "stonefruit"), Positive: false}, {Label: "flower", RawValue: "hibiscus", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "hibiscus"), Positive: true}, {Label: "spice", RawValue: "mace", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "mace"), Positive: false}, {Label: "family", RawValue: "extracts", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "extracts"), Positive: true}, {Label: "family", RawValue: "chilis", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "chilis"), Positive: true}, }, F: tkn.Formula{ Gates: []tkn.Gate{ {Class: tkn.Orgate, In0: 1, In1: 2, Out: 6}, {Class: tkn.Andgate, In0: 3, In1: 6, Out: 7}, {Class: tkn.Orgate, In0: 4, In1: 5, Out: 8}, {Class: tkn.Orgate, In0: 7, In1: 8, Out: 9}, {Class: tkn.Orgate, In0: 0, In1: 9, Out: 10}, }, }, }, }, { input: "(9country8: france)", output: &tkn.Policy{ Inputs: []tkn.Wire{ {Label: "9country8", RawValue: "france", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "france"), Positive: true}, }, F: tkn.Formula{ Gates: []tkn.Gate{}, }, }, }, { input: "((country : afghanistan) or (country: bactria)) and (not (king: alexander))", output: &tkn.Policy{ Inputs: []tkn.Wire{ {Label: "country", RawValue: "afghanistan", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "afghanistan"), Positive: true}, {Label: "country", RawValue: "bactria", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "bactria"), Positive: true}, {Label: "king", RawValue: "alexander", Value: tkn.HashStringToScalar(dsl.AttrHashKey, "alexander"), Positive: false}, }, F: tkn.Formula{ Gates: []tkn.Gate{ {Class: tkn.Orgate, In0: 0, In1: 1, Out: 3}, {Class: tkn.Andgate, In0: 3, In1: 2, Out: 4}, }, }, }, }, } func TestDsl(t *testing.T) { for _, test := range testCases { t.Run("TestDsl:"+test.input, func(t *testing.T) { a, err := dsl.Run(test.input) if test.err == nil { if err != nil { t.Fatal(err) } if !a.Equal(test.output) { t.Fatalf("incorrect attributes: expected %v, received: %v", test.output, a) } } else { if err == nil { t.Fatalf("this should fail") } if test.err.Error() != err.Error() { t.Fatalf("incorrect error: expected: %v, received: %v", test.err, err) } } }) } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/expr.go000066400000000000000000000015031454601126700261300ustar00rootroot00000000000000package dsl type Expr interface { Accept(ExprVisitor) } type ExprVisitor interface { visitBinary(binary Binary) visitUnary(unary Unary) visitGrouping(grouping Grouping) visitLiteral(literal Literal) } // Binary is used for And, Or type Binary struct { Left Expr Operator Token Right Expr Output attr } func (b Binary) Accept(visitor ExprVisitor) { visitor.visitBinary(b) } // Unary is used for Not type Unary struct { Operator Token Right Expr } func (u Unary) Accept(visitor ExprVisitor) { visitor.visitUnary(u) } // Grouping is used for LeftParen, RightParen type Grouping struct { Expr Expr } func (g Grouping) Accept(visitor ExprVisitor) { visitor.visitGrouping(g) } type Literal struct { Key attr Value attrValue } func (l Literal) Accept(visitor ExprVisitor) { visitor.visitLiteral(l) } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/interpreter.go000066400000000000000000000006451454601126700275230ustar00rootroot00000000000000package dsl type Interpreter struct { Literal } func (i *Interpreter) Evaluate(expr Expr) Literal { expr.Accept(i) return i.Literal } func (i *Interpreter) visitBinary(b Binary) { i.Literal.Key = b.Output } func (i *Interpreter) visitUnary(u Unary) { i.Evaluate(u.Right) } func (i *Interpreter) visitGrouping(g Grouping) { g.Expr.Accept(i) } func (i *Interpreter) visitLiteral(at Literal) { i.Literal = at } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/lexer.go000066400000000000000000000025441454601126700262770ustar00rootroot00000000000000package dsl import ( "fmt" "strings" ) var keywords = map[string]string{ "and": And, "or": Or, "not": Not, } type Lexer struct { source string tokens []Token start int curr int line int hadError bool } func newLexer(source string) Lexer { return Lexer{ source: source, tokens: nil, start: 0, curr: 0, line: 1, hadError: false, } } func (l *Lexer) scanTokens() error { errMsg := "unexpected character(s): " for l.curr < len(l.source) { l.start = l.curr c := l.source[l.curr] l.curr++ switch c { case '(': l.addToken(LeftParen) case ')': l.addToken(RightParen) case ':': l.addToken(Colon) case ' ', '\r', '\t': case '\n': l.line++ default: if isAlphaNumeric(c) { l.identifier() } else { errMsg += fmt.Sprintf("'%s' ", string(c)) l.hadError = true } } } l.addToken(EOF) if l.hadError { return fmt.Errorf(strings.TrimSpace(errMsg)) } return nil } func (l *Lexer) addToken(tokenType string) { token := Token{ tokenType, l.source[l.start:l.curr], l.line, } l.tokens = append(l.tokens, token) } func (l *Lexer) identifier() { for l.curr < len(l.source) { if isAlphaNumeric(l.source[l.curr]) { l.curr++ } else { break } } tokenType, ok := keywords[l.source[l.start:l.curr]] if !ok { tokenType = Identifier } l.addToken(tokenType) } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/lexer_test.go000066400000000000000000000020031454601126700273240ustar00rootroot00000000000000package dsl import ( "errors" "testing" ) func TestLexerErr(t *testing.T) { l := newLexer("sleep: @)") err := l.scanTokens() expectedErr := errors.New("unexpected character(s): '@'") if err == nil { t.Fatalf("missing expected err %v", expectedErr) } if expectedErr.Error() != err.Error() { t.Fatalf("incorrect error: expected %v, received %v", expectedErr, err) } } func TestLexer(t *testing.T) { l := newLexer("(sleep \n: \nnice\n)") err := l.scanTokens() if err != nil { t.Fatal(err) } types := []string{LeftParen, Identifier, Colon, Identifier, RightParen, EOF} if len(l.tokens) != len(types) { t.Fatalf("expected %d tokens, received: %v", len(types), len(l.tokens)) } for i, typ := range types { if typ != l.tokens[i].Type { t.Fatalf("expected token %s, received: %s", typ, l.tokens[i].Type) } } if l.tokens[2].Line != 2 { t.Fatalf("expected line 2, received: %d", l.tokens[2].Line) } if l.tokens[3].Line != 3 { t.Fatalf("expected line 3, received: %d", l.tokens[3].Line) } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/parser.go000066400000000000000000000071141454601126700264520ustar00rootroot00000000000000package dsl import ( "fmt" ) type Parser struct { tokens []Token curr int wires map[attr]attrValue gates []gate negative bool } func newParser(tokens []Token) Parser { return Parser{ tokens: tokens, curr: 0, wires: make(map[attr]attrValue), gates: make([]gate, 0), negative: false, } } func (p *Parser) parse() (Ast, error) { _, err := p.expression() if err != nil { return Ast{}, err } return Ast{ wires: p.wires, gates: p.gates, }, nil } func (p *Parser) expression() (Expr, error) { return p.or() } func (p *Parser) or() (Expr, error) { expr, err := p.and() if err != nil { return nil, err } for p.tokens[p.curr].Type == Or { orToken := p.tokens[p.curr] p.curr++ right, err := p.and() if err != nil { return nil, err } in1 := extractAttr(expr) in2 := extractAttr(right) newGate := gate{ op: Or, in1: in1, in2: in2, out: attr{ key: "", id: -(len(p.gates) + 1), }, } if p.negative { newGate.op = And } p.gates = append(p.gates, newGate) expr = Binary{ Left: expr, Operator: orToken, Right: right, Output: p.gates[len(p.gates)-1].out, } } return expr, nil } func (p *Parser) and() (Expr, error) { expr, err := p.not() if err != nil { return nil, err } for p.tokens[p.curr].Type == And { andToken := p.tokens[p.curr] p.curr++ right, err := p.not() if err != nil { return nil, err } in1 := extractAttr(expr) in2 := extractAttr(right) newGate := gate{ op: And, in1: in1, in2: in2, out: attr{ key: "", id: -(len(p.gates) + 1), }, } if p.negative { newGate.op = Or } p.gates = append(p.gates, newGate) expr = Binary{ Left: expr, Operator: andToken, Right: right, Output: p.gates[len(p.gates)-1].out, } } return expr, nil } func (p *Parser) not() (Expr, error) { if p.tokens[p.curr].Type == Not { p.curr++ currWires := make(map[attr]int) for wire := range p.wires { currWires[wire] = 1 } p.negative = !p.negative right, err := p.not() p.negative = !p.negative if err != nil { return nil, err } for k, v := range p.wires { _, ok := currWires[k] if !ok { v.positive = !v.positive p.wires[k] = v } } return Unary{ Operator: p.tokens[p.curr-1], Right: right, }, nil } return p.primary() } func (p *Parser) primary() (Expr, error) { if p.tokens[p.curr].Type == LeftParen { p.curr++ expr, err := p.expression() if err != nil { return nil, err } if !(p.tokens[p.curr].Type == RightParen) { return nil, fmt.Errorf("expected ')' after expression") } p.curr++ return Grouping{ Expr: expr, }, nil } if p.tokens[p.curr].Type == Identifier { if p.tokens[p.curr+1].Type == Colon { if p.tokens[p.curr+2].Type == Identifier { nextToken := p.tokens[p.curr+3].Type if (nextToken == Identifier) || (nextToken == Colon) || (nextToken == LeftParen) || (nextToken == Not) { return nil, fmt.Errorf( "unexpected token %s, expected logical operator \"and\" or \"or\"", p.tokens[p.curr+3].Lexeme) } key := p.tokens[p.curr] value := p.tokens[p.curr+2] currAttr := attr{ key: key.Lexeme, id: len(p.wires), } attrVal := attrValue{ value: value.Lexeme, positive: true, } p.wires[currAttr] = attrVal p.curr += 3 return Literal{ Key: currAttr, Value: attrVal, }, nil } } } return nil, fmt.Errorf("expected parentheses or literal") } func extractAttr(expr Expr) attr { i := Interpreter{} expr.Accept(&i) return i.Literal.Key } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/tokens.go000066400000000000000000000003701454601126700264560ustar00rootroot00000000000000package dsl const ( LeftParen = "(" RightParen = ")" Colon = ":" And = "and" Or = "or" Not = "not" Identifier = "identifier" EOF = "eof" ) type Token struct { Type string Lexeme string Line int } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/dsl/util.go000066400000000000000000000003721454601126700261320ustar00rootroot00000000000000package dsl func isDigit(c uint8) bool { return c >= '0' && c <= '9' } func isAlpha(c uint8) bool { return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') || c == '_' } func isAlphaNumeric(c uint8) bool { return isAlpha(c) || isDigit(c) } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/000077500000000000000000000000001454601126700246365ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/bk.go000066400000000000000000000136411454601126700255660ustar00rootroot00000000000000package tkn import ( "crypto/subtle" "fmt" "io" pairing "github.com/cloudflare/circl/ecc/bls12381" "golang.org/x/crypto/blake2b" ) // This file is based on the techniques in // https://www.iacr.org/archive/pkc2011/65710074/65710074.pdf that // apply the Boneh-Katz transform to Attribute based encryption. // Seed size is chosen based on the proof for BK transform // (https://eprint.iacr.org/2004/261.pdf - page 12, theorem 2) to maintain the // statistical hiding property. Their input is 448 bits -> 128 bits, // whereas we require a seed size of 576 bits to ensure a 2^(-65) statistical difference // for our output size of 256 bits. const macKeySeedSize = 72 func blakeEncrypt(key []byte, msg []byte) ([]byte, error) { xof, err := blake2b.NewXOF(blake2b.OutputLengthUnknown, key) if err != nil { return nil, err } keystream := make([]byte, len(msg)) _, err = io.ReadFull(xof, keystream) if err != nil { return nil, err } for i := 0; i < len(msg); i++ { keystream[i] ^= msg[i] } return keystream, nil } func blakeDecrypt(key []byte, msg []byte) ([]byte, error) { return blakeEncrypt(key, msg) } func blakeMac(key []byte, msg []byte) (tag []byte, err error) { mac, err := blake2b.New256(key) if err != nil { return nil, err } mac.Write(msg) tag = mac.Sum(nil) return } func expandSeed(seed []byte) (id []byte, macKey []byte, err error) { h1, err := blake2b.New256(nil) if err != nil { return nil, nil, err } h1.Write([]byte("id computation hash")) h2, err := blake2b.New256(nil) if err != nil { return nil, nil, err } h2.Write([]byte("key computation hash")) h1.Write(seed) h2.Write(seed) id = h1.Sum(nil) macKey = h2.Sum(nil) return } func DeriveAttributeKeysCCA(rand io.Reader, sp *SecretParams, attrs *Attributes) (*AttributesKey, error) { realAttrs := transformAttrsBK(attrs) return deriveAttributeKeys(rand, sp, realAttrs) } func EncryptCCA(rand io.Reader, public *PublicParams, policy *Policy, msg []byte) ([]byte, error) { seed := make([]byte, macKeySeedSize) _, err := io.ReadFull(rand, seed) if err != nil { return nil, err } id, macKey, err := expandSeed(seed) if err != nil { return nil, err } numid := &pairing.Scalar{} numid.SetBytes(id) encPolicy := policy.transformBK(numid) header, encPoint, err := encapsulate(rand, public, encPolicy) if err != nil { return nil, err } // Send the policy that was not enhanced. The receiver will recover with the ID. // This avoids a bug where we omit the check that the ID is correct header.p = policy C1, err := header.marshalBinary() if err != nil { return nil, err } env := make([]byte, len(seed)+len(msg)) copy(env[0:len(seed)], seed) copy(env[len(seed):], msg) encKey, err := encPoint.MarshalBinary() if err != nil { return nil, err } hashedEncKey := blake2b.Sum256(encKey) env, err = blakeEncrypt(hashedEncKey[:], env) if err != nil { return nil, err } macData := appendLenPrefixed(nil, C1) macData = appendLenPrefixed(macData, env) tag, err := blakeMac(macKey, macData) if err != nil { return nil, err } ret := appendLenPrefixed(nil, id) ret = appendLenPrefixed(ret, macData) ret = appendLenPrefixed(ret, tag) return ret, nil } func DecryptCCA(ciphertext []byte, key *AttributesKey) ([]byte, error) { id, rest, err := removeLenPrefixed(ciphertext) if err != nil { return nil, err } macData, rest, err := removeLenPrefixed(rest) if err != nil { return nil, err } tag, _, err := removeLenPrefixed(rest) if err != nil { return nil, err } C1, envRaw, err := removeLenPrefixed(macData) if err != nil { return nil, err } env, _, err := removeLenPrefixed(envRaw) if err != nil { return nil, err } header := &ciphertextHeader{} err = header.unmarshalBinary(C1) if err != nil { return nil, err } numid := &pairing.Scalar{} numid.SetBytes(id) header.p = header.p.transformBK(numid) encPoint, err := decapsulate(header, key) if err != nil { return nil, fmt.Errorf("error in decryption: %w", err) } encKey, err := encPoint.MarshalBinary() if err != nil { return nil, err } hashedEncKey := blake2b.Sum256(encKey) // Decrypt the envelope decEnv, err := blakeDecrypt(hashedEncKey[:], env) if err != nil { return nil, err } if len(decEnv) < macKeySeedSize { return nil, fmt.Errorf("envelope too short") } seed := decEnv[0:macKeySeedSize] ptx := make([]byte, len(decEnv)-macKeySeedSize) compID, macKey, err := expandSeed(seed) if err != nil { return nil, err } compTag, err := blakeMac(macKey, macData) if err != nil { return nil, err } // Now check that compTag = tag and compID = id // We don't want to distinguish which fails. tagMatch := subtle.ConstantTimeCompare(compTag, tag) idMatch := subtle.ConstantTimeCompare(compID, id) check := tagMatch & idMatch if check == 1 { copy(ptx, decEnv[macKeySeedSize:]) return ptx, nil } return nil, fmt.Errorf("failure of decryption") } func CouldDecrypt(ciphertext []byte, a *Attributes) bool { id, rest, err := removeLenPrefixed(ciphertext) if err != nil { return false } macData, _, err := removeLenPrefixed(rest) if err != nil { return false } C1, _, err := removeLenPrefixed(macData) if err != nil { return false } header := &ciphertextHeader{} err = header.unmarshalBinary(C1) if err != nil { return false } numid := &pairing.Scalar{} numid.SetBytes(id) header.p = header.p.transformBK(numid) realAttrs := transformAttrsBK(a) _, err = header.p.Satisfaction(realAttrs) return err == nil } func (p *Policy) ExtractFromCiphertext(ct []byte) error { _, rest, err := removeLenPrefixed(ct) if err != nil { return fmt.Errorf("invalid ciphertext") } macData, _, err := removeLenPrefixed(rest) if err != nil { return fmt.Errorf("invalid ciphertext") } C1, _, err := removeLenPrefixed(macData) if err != nil { return fmt.Errorf("invalid ciphertext") } header := &ciphertextHeader{} err = header.unmarshalBinary(C1) if err != nil { return fmt.Errorf("invalid ciphertext") } *p = *header.p return nil } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/bk_test.go000066400000000000000000000135541454601126700266300ustar00rootroot00000000000000package tkn import ( "crypto/rand" "testing" ) var encTestCases = []TestCase{ { &Policy{ Inputs: []Wire{ {"a", "", ToScalar(0), true}, }, F: Formula{ Gates: []Gate{}, }, }, &Attributes{ "a": { wild: false, Value: ToScalar(0), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "", ToScalar(1), true}, {"b", "", ToScalar(2), true}, {"c", "", ToScalar(3), true}, }, F: Formula{ Gates: []Gate{ {Andgate, 0, 1, 3}, {Andgate, 2, 3, 4}, }, }, }, &Attributes{ "d": { wild: false, Value: ToScalar(4), }, "c": { wild: false, Value: ToScalar(3), }, "b": { wild: false, Value: ToScalar(2), }, "a": { wild: false, Value: ToScalar(1), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "", ToScalar(1), false}, {"b", "", ToScalar(2), true}, {"c", "", ToScalar(3), true}, }, F: Formula{ Gates: []Gate{ {Andgate, 0, 1, 3}, {Andgate, 2, 3, 4}, }, }, }, &Attributes{ "d": { wild: false, Value: ToScalar(4), }, "c": { wild: false, Value: ToScalar(3), }, "b": { wild: false, Value: ToScalar(2), }, "a": { wild: false, Value: ToScalar(2), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "", ToScalar(1), false}, {"c", "", ToScalar(4), true}, }, F: Formula{ Gates: []Gate{ {Andgate, 0, 1, 2}, }, }, }, &Attributes{ "d": { wild: false, Value: ToScalar(4), }, "c": { wild: true, Value: ToScalar(3), }, "b": { wild: false, Value: ToScalar(2), }, "a": { wild: true, Value: ToScalar(2), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "", ToScalar(1), true}, {"b", "", ToScalar(2), true}, {"c", "", ToScalar(3), true}, }, F: Formula{ Gates: []Gate{ {Andgate, 0, 1, 3}, {Orgate, 2, 3, 4}, }, }, }, &Attributes{ "d": { wild: false, Value: ToScalar(4), }, "c": { wild: false, Value: ToScalar(3), }, "b": { wild: false, Value: ToScalar(2), }, "a": { wild: false, Value: ToScalar(1), }, }, }, { &Policy{ Inputs: []Wire{ {"blocked", "", ToScalar(1), false}, {"secure", "", ToScalar(1), true}, {"eu", "", ToScalar(1), true}, {"us", "", ToScalar(1), true}, }, F: Formula{ Gates: []Gate{ {Orgate, 2, 3, 4}, {Andgate, 0, 4, 5}, {Andgate, 1, 5, 6}, }, }, }, &Attributes{ "blocked": { wild: false, Value: ToScalar(0), }, "secure": { wild: false, Value: ToScalar(1), }, "us": { wild: false, Value: ToScalar(1), }, "irrelevantAttr": { wild: false, Value: ToScalar(1), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "", ToScalar(1), true}, {"a", "", ToScalar(2), true}, }, F: Formula{ Gates: []Gate{ {Orgate, 0, 1, 2}, }, }, }, &Attributes{ "a": { false, ToScalar(1), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "", ToScalar(1), true}, {"a", "", ToScalar(2), true}, }, F: Formula{ Gates: []Gate{ {Orgate, 0, 1, 2}, }, }, }, &Attributes{ "a": { false, ToScalar(2), }, }, }, } func TestEncryptionBk(t *testing.T) { msg := []byte("drink your ovaltine") for _, suite := range encTestCases { public, secret, err := GenerateParams(rand.Reader) if err != nil { t.Fatalf("error generating parameters: %s", err) } userKey, err := DeriveAttributeKeysCCA(rand.Reader, secret, suite.a) if err != nil { t.Fatalf("error generating Attribute keys: %s", err) } ciphertext, err := EncryptCCA(rand.Reader, public, suite.p, msg) if err != nil { t.Fatalf("error encrypting: %s", err) } recovered, err := DecryptCCA(ciphertext, userKey) if err != nil { t.Fatalf("error decrypting: %s", err) } if string(recovered) != string(msg) { t.Fatalf("expected: %s, got %s", string(recovered), string(msg)) } } } var benchPolicy = &Policy{ Inputs: []Wire{ {"blocked", "", ToScalar(1), false}, {"secure", "", ToScalar(1), true}, {"eu", "", ToScalar(1), true}, {"us", "", ToScalar(1), true}, }, F: Formula{ Gates: []Gate{ {Orgate, 2, 3, 4}, {Andgate, 0, 4, 5}, {Andgate, 1, 5, 6}, }, }, } var benchAttrs = &Attributes{ "blocked": { wild: false, Value: ToScalar(0), }, "secure": { wild: false, Value: ToScalar(1), }, "us": { wild: false, Value: ToScalar(1), }, "irrelevantAttr": { wild: false, Value: ToScalar(1), }, } func BenchmarkTkDecryption(b *testing.B) { msg := []byte("drink your ovaltine") public, secret, err := GenerateParams(rand.Reader) if err != nil { b.Fatalf("error generating parameters: %s", err) } userKey, err := DeriveAttributeKeysCCA(rand.Reader, secret, benchAttrs) if err != nil { b.Fatalf("error generating Attribute keys: %s", err) } ciphertext, err := EncryptCCA(rand.Reader, public, benchPolicy, msg) if err != nil { b.Fatalf("error encrypting: %s", err) } b.ResetTimer() for i := 0; i < b.N; i++ { _, err = DecryptCCA(ciphertext, userKey) if err != nil { b.Fatalf("mismatch: %s", err) } } } func BenchmarkTkEncryption(b *testing.B) { msg := []byte("drink your ovaltine") public, _, err := GenerateParams(rand.Reader) if err != nil { b.Fatalf("error generating parameters: %s", err) } b.ResetTimer() for i := 0; i < b.N; i++ { _, err := EncryptCCA(rand.Reader, public, benchPolicy, msg) if err != nil { b.Fatalf("error encrypting: %s", err) } } } func BenchmarkTkDerivation(b *testing.B) { _, secret, err := GenerateParams(rand.Reader) if err != nil { b.Fatalf("error generating parameters: %s", err) } b.ResetTimer() for i := 0; i < b.N; i++ { _, err := DeriveAttributeKeysCCA(rand.Reader, secret, benchAttrs) if err != nil { b.Fatalf("error generating Attribute keys: %s", err) } } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/formula.go000066400000000000000000000201431454601126700266320ustar00rootroot00000000000000package tkn import ( "encoding/binary" "fmt" "io" ) const ( Andgate = iota Orgate ) // Gate is a Gate in a monotone boolean formula. type Gate struct { Class int // either Andgate or Orgate In0 int // numbering of wires In1 int Out int } func (g Gate) operator() string { switch g.Class { case Andgate: return "and" case Orgate: return "or" default: return "unknown" } } // Formula represents a monotone boolean circuit with Inputs not // repeated. The representation is as follows: for n Gates there n+1 // input wires, 1 output Wire, and n-1 intermediate wires. That's // because there are 2n Inputs to all Gates and n outputs since every // Gate is 2:1. // // The wires are conceptually in an array. Wires 0 through n are // the input wires, and Wire 2n is the output Wire. If there are wires // between n and 2n they are intermediate wires. // // All intermediate and input wires must be used exactly once as Inputs. type Formula struct { Gates []Gate } func (g Gate) Equal(g2 Gate) bool { if (g.Class != g2.Class) || (g.Out != g2.Out) { return false } if g.In0 == g2.In0 && g.In1 == g2.In1 { return true } if g.In0 == g2.In1 && g.In1 == g2.In0 { return true } return false } func (f *Formula) MarshalBinary() ([]byte, error) { n := len(f.Gates) ret := make([]byte, 2+7*n) binary.LittleEndian.PutUint16(ret, uint16(len(f.Gates))) for i := 0; i < n; i++ { ret[7*i+2] = byte(f.Gates[i].Class) binary.LittleEndian.PutUint16(ret[7*i+2+1:], uint16(f.Gates[i].In0)) binary.LittleEndian.PutUint16(ret[7*i+2+3:], uint16(f.Gates[i].In1)) binary.LittleEndian.PutUint16(ret[7*i+2+5:], uint16(f.Gates[i].Out)) } return ret, nil } func (f *Formula) UnmarshalBinary(data []byte) error { if len(data) < 2 { return fmt.Errorf("too short data") } n := int(binary.LittleEndian.Uint16(data[0:2])) f.Gates = make([]Gate, n) for i := 0; i < n; i++ { f.Gates[i].Class = int(data[7*i+2]) f.Gates[i].In0 = int(binary.LittleEndian.Uint16(data[7*i+2+1:])) f.Gates[i].In1 = int(binary.LittleEndian.Uint16(data[7*i+2+3:])) f.Gates[i].Out = int(binary.LittleEndian.Uint16(data[7*i+2+5:])) } return nil } func (f *Formula) wellformed() error { // Check every Wire used once n := len(f.Gates) inputs := make([]bool, 2*n) // n+1 already, n-1 intermediates outputs := make([]bool, n) for i, gate := range f.Gates { if gate.In0 > 2*n-1 || gate.In0 < 0 { return fmt.Errorf("Gate %d has an Out of range In0", i) } if inputs[gate.In0] { return fmt.Errorf("Gate %d has In0 that is already used", i) } inputs[gate.In0] = true if gate.In1 > 2*n-1 || gate.In1 < 0 { return fmt.Errorf("Gate %d has an Out of range In1", i) } if inputs[gate.In1] { return fmt.Errorf("Gate %d has In1 that is already used", i) } inputs[gate.In1] = true if gate.Out > 2*n || gate.Out < n+1 { return fmt.Errorf("Gate %d has an Out of range Out", i) } outputs[gate.Out-(n+1)] = true } for i, wire := range inputs { if !wire { return fmt.Errorf("unused input Wire %d", i) } } for i, wire := range outputs { if !wire { return fmt.Errorf("unused output Wire %d", i+(n+1)) } } return nil } // Sort the Gates so that Inputs are set before outputs. func (f *Formula) toposort() error { err := f.wellformed() if err != nil { return err } n := len(f.Gates) if n == 0 { return nil } // Intermediate wires are indexed after subtracting n+1 outputGate := make([]int, n) // the Gate that sets this Wire inputGate := make([]int, n) // the Gate that uses this intermediate Wire. counts := make([]int, n) // the number of Inputs no yet output queue := make([]int, 0, n) reordered := make([]Gate, 0, n) inputGate[n-1] = -1 // No Gate uses the output as input for i, gate := range f.Gates { outputGate[gate.Out-(n+1)] = i if gate.In0 > n { inputGate[gate.In0-(n+1)] = i counts[i]++ } if gate.In1 > n { inputGate[gate.In1-(n+1)] = i counts[i]++ } } for i := 0; i < n; i++ { if counts[i] == 0 { queue = append(queue, i) } } if len(queue) == 0 { return fmt.Errorf("no starting gates") } for len(queue) > 0 { reordered = append(reordered, f.Gates[queue[0]]) next := inputGate[f.Gates[queue[0]].Out-(n+1)] if next >= 0 { counts[next]-- if counts[next] == 0 { queue = append(queue, next) } } queue = queue[1:] } if len(reordered) != n { return fmt.Errorf("not all gates were extracted. check for loops") } f.Gates = reordered return nil } // Given a set of possible Inputs (not necessarily in order!) // return a subset that satisfy the formula with no extras. func (f *Formula) satisfaction(available []match) ([]match, error) { err := f.toposort() if err != nil { return nil, err } n := len(f.Gates) assignments := make([][]int, 2*n+1) for _, match := range available { assignments[match.wire] = []int{match.wire} } for _, gate := range f.Gates { switch gate.Class { case Andgate: if assignments[gate.In0] == nil || assignments[gate.In1] == nil { assignments[gate.Out] = nil } else { assignments[gate.Out] = make([]int, 0, len(assignments[gate.In0])+len(assignments[gate.In1])) assignments[gate.Out] = append(assignments[gate.Out], assignments[gate.In0]...) assignments[gate.Out] = append(assignments[gate.Out], assignments[gate.In1]...) } case Orgate: if assignments[gate.In0] == nil && assignments[gate.In1] == nil { assignments[gate.Out] = nil } else { assignments[gate.Out] = assignments[gate.In0] if assignments[gate.Out] == nil { assignments[gate.Out] = assignments[gate.In1] } if (len(assignments[gate.In1]) < len(assignments[gate.Out])) && assignments[gate.In1] != nil { assignments[gate.Out] = assignments[gate.In1] } } default: return nil, fmt.Errorf("unmatched case") } } if assignments[2*n] == nil { return nil, fmt.Errorf("no satisfying assignment") } ret := make([]match, 0) for _, wire := range assignments[2*n] { for _, match := range available { if match.wire == wire { ret = append(ret, match) } } } return ret, nil } // share distributes an input into shares for a secret sharing system // for the formula: the original vector can be recovered from shares // that satisfy the formula, by adding them all up. func (f *Formula) share(rand io.Reader, k *matrixZp) ([]*matrixZp, error) { err := f.toposort() if err != nil { return nil, err } n := len(f.Gates) shares := make([]*matrixZp, 2*n+1) // Reverse order: we want to set the share of the output ahead of the Inputs shares[2*n] = k for i := len(f.Gates) - 1; i >= 0; i-- { gate := f.Gates[i] switch gate.Class { case Andgate: shares[gate.In0], err = randomMatrixZp(rand, k.rows, k.cols) if err != nil { return nil, err } shares[gate.In1] = newMatrixZp(k.rows, k.cols) shares[gate.In0].sub(shares[gate.Out], shares[gate.In1]) case Orgate: shares[gate.In0] = newMatrixZp(k.rows, k.cols) shares[gate.In0].set(shares[gate.Out]) shares[gate.In1] = newMatrixZp(k.rows, k.cols) shares[gate.In1].set(shares[gate.Out]) } } return shares[0 : n+1], nil } // insertAnd adds and Gate for a new input func (f *Formula) insertAnd() Formula { // Let n=3 // The old Inputs are 0, 1, 2, 3. // Old intermediates 4, 5, // Old output 6. // The old Inputs are Inputs 0,1,2,3 and new input 4 // Intermediates are all shifted up by 1: 5, 6 // Old output is also shifted up but is the intermediate 7 // New output 8. n := len(f.Gates) gates := make([]Gate, len(f.Gates)+1) newInput := func(in int) int { if in > n { return in + 1 } else { return in } } for i := 0; i < n; i++ { gates[i].Class = f.Gates[i].Class gates[i].In0 = newInput(f.Gates[i].In0) gates[i].In1 = newInput(f.Gates[i].In1) gates[i].Out = f.Gates[i].Out + 1 } gates[n].Class = Andgate // if there were zero gates, then In0 = 0, In1 = 1, Out = 2 if n == 0 { gates[n].In0 = n } else { gates[n].In0 = n + 1 } gates[n].In1 = 2*n + 1 gates[n].Out = 2*n + 2 return Formula{ Gates: gates, } } func (f *Formula) Equal(g Formula) bool { if len(f.Gates) != len(g.Gates) { return false } for i := 0; i < len(f.Gates); i++ { if !f.Gates[i].Equal(g.Gates[i]) { return false } } return true } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/formula_test.go000066400000000000000000000017031454601126700276720ustar00rootroot00000000000000package tkn import ( "crypto/rand" "testing" ) func TestShare(t *testing.T) { f := Formula{ Gates: []Gate{ {Andgate, 2, 3, 4}, {Andgate, 0, 1, 3}, }, } k, err := randomMatrixZp(rand.Reader, 1, 17) if err != nil { t.Fatalf("error generating vector: %s", err) } res, err := f.share(rand.Reader, k) if err != nil { t.Fatalf("error sharing: %s", err) } if len(res) != 3 { t.Errorf("res wrong size") } acc := newMatrixZp(1, 17) for i := 0; i < len(res); i++ { acc.add(acc, res[i]) } if !acc.Equal(k) { t.Errorf("incorrect share") } } func TestFormulaMarshal(t *testing.T) { f := Formula{ Gates: []Gate{ {Andgate, 0, 1, 3}, {Andgate, 2, 3, 4}, }, } data, err := f.MarshalBinary() if err != nil { t.Fatalf("error marshalling: %s", err) } g := &Formula{} err = g.UnmarshalBinary(data) if err != nil { t.Fatalf("error unmarshalling: %s", err) } if !f.Equal(*g) { t.Fatal("failure to recover formula") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixG1.go000066400000000000000000000136471454601126700266740ustar00rootroot00000000000000package tkn import ( "encoding/binary" "fmt" "io" pairing "github.com/cloudflare/circl/ecc/bls12381" ) // matrixG1 represents a matrix of G1 elements. They are stored in row-major order. type matrixG1 struct { rows int cols int entries []pairing.G1 } func (m *matrixG1) marshalBinary() ([]byte, error) { ret := make([]byte, 4+pairing.G1Size*m.rows*m.cols) binary.LittleEndian.PutUint16(ret[0:], uint16(m.rows)) binary.LittleEndian.PutUint16(ret[2:], uint16(m.cols)) for i := 0; i < m.rows*m.cols; i++ { pt := m.entries[i].Bytes() if !m.entries[i].IsOnG1() { return nil, fmt.Errorf("matrixG1: illegal serialization attempt") } if len(pt) != pairing.G1Size { panic("matrixG1: incorrect assumption of size") } copy(ret[pairing.G1Size*i+4:], pt) } return ret, nil } func (m *matrixG1) unmarshalBinary(data []byte) error { if len(data) < 4 { return fmt.Errorf("matrixG1 deserialization failure: input too short") } m.rows = int(binary.LittleEndian.Uint16(data[0:])) m.cols = int(binary.LittleEndian.Uint16(data[2:])) data = data[4:] if len(data) != pairing.G1Size*m.rows*m.cols { return fmt.Errorf("matrixG1 deserialization failure: invalid entries length: expected %d, actual %d", pairing.G1Size*m.cols*m.rows, len(data)) } m.entries = make([]pairing.G1, m.rows*m.cols) var err error for i := 0; i < m.rows*m.cols; i++ { err = m.entries[i].SetBytes(data[pairing.G1Size*i : pairing.G1Size*(i+1)]) if err != nil { return fmt.Errorf("matrixG1 deserialization failure: error from bytes %v: %w", data[pairing.G1Size*i:pairing.G1Size*(i+1)], err) } } return nil } // We write addition for each of these, multiplication by scalars, and action on both // sides? // exp computes the naive matrix exponential of a with respect to the basepoint. func (m *matrixG1) exp(a *matrixZp) { basepoint := pairing.G1Generator() m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].ScalarMult(&a.entries[i], basepoint) } } // resize only changes the matrix if we have to func (m *matrixG1) resize(r int, c int) { if m.rows != r || m.cols != c { m.rows = r m.cols = c m.entries = make([]pairing.G1, m.rows*m.cols) } } // clear sets a matrix to the all zero matrix func (m *matrixG1) clear() { for i := 0; i < len(m.entries); i++ { m.entries[i].SetIdentity() } } // conformal returns true iff m and a have the same dimensions. func (m *matrixG1) conformal(a *matrixG1) bool { return a.rows == m.rows && a.cols == m.cols } // Equal returns true if m == b. func (m *matrixG1) Equal(b *matrixG1) bool { if !m.conformal(b) { return false } for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { if !m.entries[i*m.cols+j].IsEqual(&b.entries[i*b.cols+j]) { return false } } } return true } // set sets m to a. func (m *matrixG1) set(a *matrixG1) { m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i] = a.entries[i] } } // add sets m to a+b. func (m *matrixG1) add(a *matrixG1, b *matrixG1) { if !a.conformal(b) { panic(errBadMatrixSize) } m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].Add(&a.entries[i], &b.entries[i]) } } // sub sets m to a-b. func (m *matrixG1) sub(a *matrixG1, b *matrixG1) { if !a.conformal(b) { panic(errBadMatrixSize) } m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { t := b.entries[i] t.Neg() m.entries[i].Add(&a.entries[i], &t) } } // leftMult multiples a*b with a matrixZp, b matrixG1. func (m *matrixG1) leftMult(a *matrixZp, b *matrixG1) { if a.cols != b.rows { panic(errBadMatrixSize) } if b == m { c := newMatrixG1(0, 0) c.set(b) b = c } m.resize(a.rows, b.cols) m.clear() var t pairing.G1 t.SetIdentity() for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { for k := 0; k < a.cols; k++ { t.ScalarMult(&a.entries[i*a.cols+k], &b.entries[k*b.cols+j]) m.entries[i*m.cols+j].Add(&m.entries[i*m.cols+j], &t) } } } } // rightMult multiplies a*b with a matrixG1, b matrixZp. func (m *matrixG1) rightMult(a *matrixG1, b *matrixZp) { if a.cols != b.rows { panic(errBadMatrixSize) } if a == m { c := newMatrixG1(0, 0) c.set(a) a = c } m.resize(a.rows, b.cols) m.clear() var t pairing.G1 t.SetIdentity() for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { for k := 0; k < a.cols; k++ { t.ScalarMult(&b.entries[k*b.cols+j], &a.entries[i*a.cols+k]) m.entries[i*m.cols+j].Add(&m.entries[i*m.cols+j], &t) } } } } // scalarMult sets m to c*a where c is a Scalar, func (m *matrixG1) scalarMult(c *pairing.Scalar, a *matrixG1) { m.resize(a.rows, a.cols) for i := 0; i < len(a.entries); i++ { m.entries[i].ScalarMult(c, &a.entries[i]) } } // copy creates and returns a new matrix that shares no storage with m func (m *matrixG1) copy() *matrixG1 { ret := new(matrixG1) ret.resize(m.rows, m.cols) for i := 0; i < m.rows*m.cols; i++ { ret.entries[i] = m.entries[i] } return ret } func newMatrixG1(r int, c int) *matrixG1 { ret := new(matrixG1) ret.resize(r, c) ret.clear() return ret } func randomMatrixG1(rand io.Reader, r int, c int) (*matrixG1, error) { a, err := randomMatrixZp(rand, r, c) if err != nil { return nil, err } ret := newMatrixG1(r, c) ret.exp(a) return ret, nil } // oracle generates 3x2 matrices via the random oracle func oracle(input []byte) (*matrixG1, *matrixG1) { a := newMatrixG1(3, 2) b := newMatrixG1(3, 2) for i := 0; i < 3; i++ { for j := 0; j < 2; j++ { a.entries[i*a.cols+j].Hash(input, []byte(fmt.Sprintf("a matrix entry [%d, %d]", i, j))) b.entries[i*b.cols+j].Hash(input, []byte(fmt.Sprintf("b matrix entry [%d, %d]", i, j))) } } return a, b } // transpose sets m to the transpose of a. // Not aliasing safe func (m *matrixG1) transpose(a *matrixG1) { if m == a { c := newMatrixG1(0, 0) c.set(a) a = c } m.resize(a.cols, a.rows) for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { m.entries[i*m.cols+j] = a.entries[j*a.cols+i] } } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixG1_test.go000066400000000000000000000131301454601126700277160ustar00rootroot00000000000000package tkn import ( "crypto/rand" "testing" ) func TestRightMultLinearityG1(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 2, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 2, 3) if err != nil { t.Fatal(err) } zpMat1p2 := newMatrixZp(2, 3) zpMat1p2.add(zpMat1, zpMat2) a, err := randomMatrixG1(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG1(3, 3) u := newMatrixG1(3, 3) r := newMatrixG1(3, 3) tmp := newMatrixG1(3, 3) r.rightMult(a, zpMat1) s.rightMult(a, zpMat2) u.rightMult(a, zpMat1p2) tmp.add(r, s) if !tmp.Equal(u) { t.Fatal("failure of linearity") } } func TestLeftMultLinearityG1(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat1p2 := newMatrixZp(3, 3) zpMat1p2.add(zpMat1, zpMat2) a, err := randomMatrixG1(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG1(0, 0) u := newMatrixG1(0, 0) r := newMatrixG1(0, 0) tmp := newMatrixG1(0, 0) r.leftMult(zpMat1, a) s.leftMult(zpMat2, a) u.leftMult(zpMat1p2, a) tmp.add(r, s) if !tmp.Equal(u) { t.Fatal("failure of linearity") } } func TestLeftMultActionG1(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2m1 := newMatrixZp(3, 3) zpMat2m1.mul(zpMat2, zpMat1) a, err := randomMatrixG1(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG1(0, 0) u := newMatrixG1(0, 0) r := newMatrixG1(0, 0) r.leftMult(zpMat1, a) s.leftMult(zpMat2, r) u.leftMult(zpMat2m1, a) if !s.Equal(u) { t.Fatal("failure of action") } } func TestRightMultActionG1(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } zpMat1m2 := newMatrixZp(2, 2) zpMat1m2.mul(zpMat1, zpMat2) a, err := randomMatrixG1(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG1(0, 0) u := newMatrixG1(0, 0) r := newMatrixG1(0, 0) r.rightMult(a, zpMat1) s.rightMult(r, zpMat2) u.rightMult(a, zpMat1m2) if !s.Equal(u) { t.Fatal("failure of action") } } func TestExpG1(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } b, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } ab := newMatrixZp(2, 2) ab.mul(a, b) aexp := newMatrixG1(0, 0) aexp.exp(a) abexp := newMatrixG1(0, 0) abexp.exp(ab) bexp := newMatrixG1(0, 0) bexp.exp(b) abres := newMatrixG1(0, 0) abres.rightMult(aexp, b) if !abres.Equal(abexp) { t.Fatal("action and exp failure") } abres.leftMult(a, bexp) if !abres.Equal(abexp) { t.Fatal("left action and exp failure") } } func TestMarshalG1(t *testing.T) { a, err := randomMatrixG1(rand.Reader, 7, 9) if err != nil { t.Fatal(err) } data, err := a.marshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } b := newMatrixG1(0, 0) err = b.unmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(b) { t.Fatal("failure to roundtrip") } // deserialize into non-empty struct c, err := randomMatrixG1(rand.Reader, 1, 2) if err != nil { t.Fatal(err) } err = c.unmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(c) { t.Fatal("failure to roundtrip") } } func TestOracle(t *testing.T) { a, b := oracle([]byte("kalliste")) for i := 0; i < len(a.entries); i++ { if !a.entries[i].IsOnG1() { t.Fatalf("failure to be in group from oracle") } } for i := 0; i < len(a.entries); i++ { if !b.entries[i].IsOnG1() { t.Fatalf("failure to be in group from oracle") } } } func TestAliasLeftMult(t *testing.T) { a, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG1(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.leftMult(b, a) res := newMatrixG1(0, 0) res.leftMult(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of leftMult to be alias safe") } } func TestAliasRightMult(t *testing.T) { a, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG1(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.rightMult(a, b) res := newMatrixG1(0, 0) res.rightMult(aCopy, bCopy) if !res.Equal(a) { t.Fatalf("failure of rightMult to be alias safe") } } func TestAliasAdd(t *testing.T) { a, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG1(4, 4) aCopy.set(a) bCopy := newMatrixG1(4, 4) bCopy.set(b) a.add(b, a) res := newMatrixG1(0, 0) res.add(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of add to be alias safe") } } func TestAliasSub(t *testing.T) { a, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG1(4, 4) aCopy.set(a) bCopy := newMatrixG1(4, 4) bCopy.set(b) a.sub(b, a) res := newMatrixG1(0, 0) res.sub(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of sub to be alias safe") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixG2.go000066400000000000000000000104051454601126700266620ustar00rootroot00000000000000package tkn import ( "encoding/binary" "fmt" "io" pairing "github.com/cloudflare/circl/ecc/bls12381" ) // matrixG2 represents a matrix of G2 elements. They are stored in row-major order. type matrixG2 struct { rows int cols int entries []pairing.G2 } func (m *matrixG2) marshalBinary() ([]byte, error) { ret := make([]byte, 4+pairing.G2Size*m.rows*m.cols) binary.LittleEndian.PutUint16(ret[0:], uint16(m.rows)) binary.LittleEndian.PutUint16(ret[2:], uint16(m.cols)) for i := 0; i < m.rows*m.cols; i++ { pt := m.entries[i].Bytes() if len(pt) != pairing.G2Size { return nil, errBadMatrixSize } copy(ret[pairing.G2Size*i+4:], pt) } return ret, nil } func (m *matrixG2) unmarshalBinary(data []byte) error { if len(data) < 4 { return fmt.Errorf("matrixG2 deserialization failure: input too short") } m.rows = int(binary.LittleEndian.Uint16(data[0:])) m.cols = int(binary.LittleEndian.Uint16(data[2:])) data = data[4:] if len(data) != pairing.G2Size*m.rows*m.cols { return fmt.Errorf("matrixG2 deserialization failure: invalid entries length: expected %d, actual %d", pairing.G2Size*m.cols*m.rows, len(data)) } m.entries = make([]pairing.G2, m.rows*m.cols) var err error for i := 0; i < m.rows*m.cols; i++ { err = m.entries[i].SetBytes(data[pairing.G2Size*i : pairing.G2Size*(i+1)]) if err != nil { return fmt.Errorf("matrixG2 deserialization failure: error from bytes %v: %w", data[pairing.G2Size*i:pairing.G2Size*(i+1)], err) } } return nil } // exp computes the naive matrix exponential of a with respect to the basepoint. func (m *matrixG2) exp(a *matrixZp) { basepoint := pairing.G2Generator() m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].ScalarMult(&a.entries[i], basepoint) } } // clear sets m to the zero matrix func (m *matrixG2) clear() { for i := 0; i < len(m.entries); i++ { m.entries[i].SetIdentity() } } // resize only changes the matrix if we have to func (m *matrixG2) resize(r int, c int) { if m.rows != r || m.cols != c { m.rows = r m.cols = c m.entries = make([]pairing.G2, m.rows*m.cols) } } // conformal returns true iff m and a have the same dimensions. func (m *matrixG2) conformal(a *matrixG2) bool { return a.rows == m.rows && a.cols == m.cols } // Equal returns true if m == b. func (m *matrixG2) Equal(b *matrixG2) bool { if !m.conformal(b) { return false } for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { if !m.entries[i*m.cols+j].IsEqual(&b.entries[i*b.cols+j]) { return false } } } return true } // set sets m to a. func (m *matrixG2) set(a *matrixG2) { m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i] = a.entries[i] } } // add sets m to a+b. func (m *matrixG2) add(a *matrixG2, b *matrixG2) { if !a.conformal(b) { panic(errBadMatrixSize) } m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].Add(&a.entries[i], &b.entries[i]) } } // leftMult multiples a*b with a matrixZp, b matrixG2. func (m *matrixG2) leftMult(a *matrixZp, b *matrixG2) { if a.cols != b.rows { panic(errBadMatrixSize) } if m == b { c := newMatrixG2(b.rows, b.cols) c.set(b) b = c } m.resize(a.rows, b.cols) m.clear() var tmp pairing.G2 for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { for k := 0; k < a.cols; k++ { tmp.ScalarMult(&a.entries[i*a.cols+k], &b.entries[k*b.cols+j]) m.entries[i*m.cols+j].Add(&m.entries[i*m.cols+j], &tmp) } } } } // rightMult multiplies a*b with a matrixG1, b matrixZp. func (m *matrixG2) rightMult(a *matrixG2, b *matrixZp) { if a.cols != b.rows { panic(errBadMatrixSize) } if m == a { c := newMatrixG2(a.rows, a.cols) c.set(a) a = c } m.resize(a.rows, b.cols) m.clear() var tmp pairing.G2 for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { for k := 0; k < a.cols; k++ { tmp.ScalarMult(&b.entries[k*b.cols+j], &a.entries[i*a.cols+k]) m.entries[i*m.cols+j].Add(&m.entries[i*m.cols+j], &tmp) } } } } func newMatrixG2(r int, c int) *matrixG2 { ret := new(matrixG2) ret.resize(r, c) ret.clear() return ret } func randomMatrixG2(rand io.Reader, r int, c int) (*matrixG2, error) { a, err := randomMatrixZp(rand, r, c) if err != nil { return nil, err } ret := newMatrixG2(r, c) ret.exp(a) return ret, nil } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixG2_test.go000066400000000000000000000111421454601126700277200ustar00rootroot00000000000000package tkn import ( "crypto/rand" "testing" ) func TestRightMultLinearityG2(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 2, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 2, 3) if err != nil { t.Fatal(err) } zpMat1p2 := newMatrixZp(2, 3) zpMat1p2.add(zpMat1, zpMat2) a, err := randomMatrixG2(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG2(3, 3) u := newMatrixG2(3, 3) r := newMatrixG2(3, 3) tmp := newMatrixG2(3, 3) r.rightMult(a, zpMat1) s.rightMult(a, zpMat2) u.rightMult(a, zpMat1p2) tmp.add(r, s) if !tmp.Equal(u) { t.Fatal("failure of linearity") } } func TestLeftMultLinearityG2(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat1p2 := newMatrixZp(3, 3) zpMat1p2.add(zpMat1, zpMat2) a, err := randomMatrixG2(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG2(0, 0) u := newMatrixG2(0, 0) r := newMatrixG2(0, 0) tmp := newMatrixG2(0, 0) r.leftMult(zpMat1, a) s.leftMult(zpMat2, a) u.leftMult(zpMat1p2, a) tmp.add(r, s) if !tmp.Equal(u) { t.Fatal("failure of linearity") } } func TestLeftMultActionG2(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2m1 := newMatrixZp(3, 3) zpMat2m1.mul(zpMat2, zpMat1) a, err := randomMatrixG2(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG2(0, 0) u := newMatrixG2(0, 0) r := newMatrixG2(0, 0) r.leftMult(zpMat1, a) s.leftMult(zpMat2, r) u.leftMult(zpMat2m1, a) if !s.Equal(u) { t.Fatal("failure of action") } } func TestRightMultActionG2(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } zpMat1m2 := newMatrixZp(2, 2) zpMat1m2.mul(zpMat1, zpMat2) a, err := randomMatrixG2(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixG2(0, 0) u := newMatrixG2(0, 0) r := newMatrixG2(0, 0) r.rightMult(a, zpMat1) s.rightMult(r, zpMat2) u.rightMult(a, zpMat1m2) if !s.Equal(u) { t.Fatal("failure of action") } } func TestExpG2(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } b, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } ab := newMatrixZp(2, 2) ab.mul(a, b) aexp := newMatrixG2(0, 0) aexp.exp(a) abexp := newMatrixG2(0, 0) abexp.exp(ab) abres := newMatrixG2(0, 0) abres.rightMult(aexp, b) if !abres.Equal(abexp) { t.Fatal("action and exp failure") } } func TestMarshalG2(t *testing.T) { a, err := randomMatrixG2(rand.Reader, 7, 9) if err != nil { t.Fatal(err) } data, err := a.marshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } b := newMatrixG2(0, 0) err = b.unmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(b) { t.Fatal("failure to roundtrip") } c := newMatrixG2(0, 0) err = c.unmarshalBinary(append(data, 0)) if err == nil { t.Fatalf("data has excess bytes, deserialization should fail") } } func TestAliasLeftMultG2(t *testing.T) { a, err := randomMatrixG2(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG2(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.leftMult(b, a) res := newMatrixG2(0, 0) res.leftMult(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of leftMult to be alias safe") } } func TestAliasRightMultG2(t *testing.T) { a, err := randomMatrixG2(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG2(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.rightMult(a, b) res := newMatrixG2(0, 0) res.rightMult(aCopy, bCopy) if !res.Equal(a) { t.Fatalf("failure of rightMult to be alias safe") } } func TestAliasAddG2(t *testing.T) { a, err := randomMatrixG2(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixG2(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG2(4, 4) aCopy.set(a) bCopy := newMatrixG2(4, 4) bCopy.set(b) a.add(b, a) res := newMatrixG2(0, 0) res.add(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of add to be alias safe") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixGT.go000066400000000000000000000104741454601126700267320ustar00rootroot00000000000000package tkn import ( "encoding/binary" "fmt" "io" pairing "github.com/cloudflare/circl/ecc/bls12381" ) // matrixGT represents a matrix of GT elements. They are stored in row-major order. type matrixGT struct { rows int cols int entries []pairing.Gt } func (m *matrixGT) marshalBinary() ([]byte, error) { ret := make([]byte, 4+pairing.GtSize*m.rows*m.cols) binary.LittleEndian.PutUint16(ret[0:], uint16(m.rows)) binary.LittleEndian.PutUint16(ret[2:], uint16(m.cols)) for i := 0; i < m.rows*m.cols; i++ { pt, err := m.entries[i].MarshalBinary() if err != nil { return nil, err } if len(pt) != pairing.GtSize { panic("matrixGT: incorrect assumption of size") } copy(ret[pairing.GtSize*i+4:], pt) } return ret, nil } func (m *matrixGT) unmarshalBinary(data []byte) error { if len(data) < 4 { return fmt.Errorf("matrixGT deserialization failure: input too short") } m.rows = int(binary.LittleEndian.Uint16(data[0:])) m.cols = int(binary.LittleEndian.Uint16(data[2:])) data = data[4:] if len(data) != pairing.GtSize*m.rows*m.cols { return fmt.Errorf("matrixGT deserialization failure: invalid entries length: expected %d, actual %d", pairing.GtSize*m.cols*m.rows, len(data)) } m.entries = make([]pairing.Gt, m.rows*m.cols) var err error for i := 0; i < m.rows*m.cols; i++ { err = m.entries[i].UnmarshalBinary(data[pairing.GtSize*i : pairing.GtSize*(i+1)]) if err != nil { return fmt.Errorf("matrixGT deserialization failure: error from bytes %v: %w", data[pairing.GtSize*i:pairing.GtSize*(i+1)], err) } } return nil } // exp computes the naive matrix exponential of a with respect to the basepoint. func (m *matrixGT) exp(a *matrixZp) { basepoint := gtBaseVal m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].Exp(basepoint, &a.entries[i]) } } // resize sets up m to be r x c func (m *matrixGT) resize(r int, c int) { if m.rows != r || m.cols != c { m.rows = r m.cols = c m.entries = make([]pairing.Gt, m.rows*m.cols) } } // clear sets m to be the "zero" matrix func (m *matrixGT) clear() { for i := 0; i < len(m.entries); i++ { m.entries[i].SetIdentity() } } // conformal returns true iff m and a have the same dimensions. func (m *matrixGT) conformal(a *matrixGT) bool { return a.rows == m.rows && a.cols == m.cols } // Equal returns true if m == b. func (m *matrixGT) Equal(b *matrixGT) bool { if !m.conformal(b) { return false } for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { if !m.entries[i*m.cols+j].IsEqual(&b.entries[i*b.cols+j]) { return false } } } return true } // set sets m to b. func (m *matrixGT) set(b *matrixGT) { m.resize(b.rows, b.cols) copy(m.entries, b.entries) } // add sets m to a+b. func (m *matrixGT) add(a *matrixGT, b *matrixGT) { if !a.conformal(b) { panic(errBadMatrixSize) } m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].Mul(&a.entries[i], &b.entries[i]) } } // leftMult multiples a*b with a matrixZp, b matrixGT. func (m *matrixGT) leftMult(a *matrixZp, b *matrixGT) { if a.cols != b.rows { panic(errBadMatrixSize) } if m == b { c := newMatrixGT(a.rows, a.cols) c.set(b) b = c } m.resize(a.rows, b.cols) m.clear() tmp := &pairing.Gt{} for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { for k := 0; k < a.cols; k++ { tmp.Exp(&b.entries[k*b.cols+j], &a.entries[i*a.cols+k]) m.entries[i*m.cols+j].Mul(&m.entries[i*m.cols+j], tmp) } } } } // rightMult multiplies a*b with a matrixG1, b matrixZp. func (m *matrixGT) rightMult(a *matrixGT, b *matrixZp) { if a.cols != b.rows { panic(errBadMatrixSize) } if m == a { c := newMatrixGT(a.rows, a.cols) c.set(a) a = c } m.resize(a.rows, b.cols) m.clear() tmp := &pairing.Gt{} // to transpose can index bt[i,j] as b.entries[j*b.rows+i] for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { for k := 0; k < a.cols; k++ { tmp.Exp(&a.entries[i*a.cols+k], &b.entries[k*b.cols+j]) m.entries[i*m.cols+j].Mul(&m.entries[i*m.cols+j], tmp) } } } } func newMatrixGT(r int, c int) *matrixGT { ret := new(matrixGT) ret.resize(r, c) ret.clear() return ret } func randomMatrixGT(rand io.Reader, r int, c int) (*matrixGT, error) { a, err := randomMatrixZp(rand, r, c) if err != nil { return nil, err } ret := newMatrixGT(r, c) ret.exp(a) return ret, nil } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixGT_test.go000066400000000000000000000130151454601126700277630ustar00rootroot00000000000000package tkn import ( "crypto/rand" "testing" pairing "github.com/cloudflare/circl/ecc/bls12381" ) func TestRightMultLinearityGT(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 2, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 2, 3) if err != nil { t.Fatal(err) } zpMat1p2 := newMatrixZp(3, 2) zpMat1p2.add(zpMat1, zpMat2) a, err := randomMatrixGT(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixGT(3, 3) u := newMatrixGT(3, 3) r := newMatrixGT(3, 3) tmp := newMatrixGT(3, 3) r.rightMult(a, zpMat1) s.rightMult(a, zpMat2) u.rightMult(a, zpMat1p2) tmp.add(r, s) if !tmp.Equal(u) { t.Fatal("failure of linearity") } } func TestLeftMultLinearityGT(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat1p2 := newMatrixZp(3, 3) zpMat1p2.add(zpMat1, zpMat2) a, err := randomMatrixGT(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixGT(0, 0) u := newMatrixGT(0, 0) r := newMatrixGT(0, 0) tmp := newMatrixGT(0, 0) r.leftMult(zpMat1, a) s.leftMult(zpMat2, a) u.leftMult(zpMat1p2, a) tmp.add(r, s) if !tmp.Equal(u) { t.Fatal("failure of linearity") } } func TestLeftMultActionGT(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 3, 3) if err != nil { t.Fatal(err) } zpMat2m1 := newMatrixZp(3, 3) zpMat2m1.mul(zpMat2, zpMat1) a, err := randomMatrixGT(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixGT(0, 0) u := newMatrixGT(0, 0) r := newMatrixGT(0, 0) r.leftMult(zpMat1, a) s.leftMult(zpMat2, r) u.leftMult(zpMat2m1, a) if !s.Equal(u) { t.Fatal("failure of action") } } func TestRightMultActionGT(t *testing.T) { zpMat1, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } zpMat2, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } zpMat1m2 := newMatrixZp(2, 2) zpMat1m2.mul(zpMat1, zpMat2) a, err := randomMatrixGT(rand.Reader, 3, 2) if err != nil { t.Fatal(err) } s := newMatrixGT(0, 0) u := newMatrixGT(0, 0) r := newMatrixGT(0, 0) r.rightMult(a, zpMat1) s.rightMult(r, zpMat2) u.rightMult(a, zpMat1m2) if !s.Equal(u) { t.Fatal("failure of action") } } func TestExpGT(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } b, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } ab := newMatrixZp(2, 2) ab.mul(a, b) aexp := newMatrixGT(0, 0) aexp.exp(a) abexp := newMatrixGT(0, 0) abexp.exp(ab) abres := newMatrixGT(0, 0) abres.rightMult(aexp, b) if !abres.Equal(abexp) { t.Fatal("action and exp failure") } } func TestExpGTLinearity(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } b, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatal(err) } ab := newMatrixZp(2, 2) ab.add(a, b) aexp := newMatrixGT(0, 0) aexp.exp(a) bexp := newMatrixGT(0, 0) bexp.exp(b) abexp := newMatrixGT(0, 0) absum := newMatrixGT(0, 0) absum.add(aexp, bexp) abexp.exp(ab) if !abexp.Equal(absum) { t.Fatal("linearity of exponentiation broken") } } func TestExpKnownAnswer(t *testing.T) { a := eye(2) b := newMatrixGT(0, 0) b.exp(a) one := &pairing.Gt{} one.SetIdentity() if !b.entries[0].IsEqual(gtBaseVal) { t.Fatal("failure of 0") } if !b.entries[1].IsEqual(one) { t.Fatal("failure of 1") } if !b.entries[2].IsEqual(one) { t.Fatal("failure of 2") } if !b.entries[3].IsEqual(gtBaseVal) { t.Fatal("failure of 3") } } func TestMarshalGt(t *testing.T) { a, err := randomMatrixGT(rand.Reader, 7, 9) if err != nil { t.Fatal(err) } data, err := a.marshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } b := newMatrixGT(0, 0) err = b.unmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(b) { t.Fatal("failure to roundtrip") } c := newMatrixGT(0, 0) err = c.unmarshalBinary(data[0 : len(data)-2]) if err == nil { t.Fatalf("data is too short, deserialization should fail") } } func TestAliasLeftMultGT(t *testing.T) { a, err := randomMatrixGT(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixGT(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.leftMult(b, a) res := newMatrixGT(0, 0) res.leftMult(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of leftMult to be alias safe") } } func TestAliasRightMultGT(t *testing.T) { a, err := randomMatrixGT(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixGT(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.rightMult(a, b) res := newMatrixGT(0, 0) res.rightMult(aCopy, bCopy) if !res.Equal(a) { t.Fatalf("failure of rightMult to be alias safe") } } func TestAliasAddGt(t *testing.T) { a, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixG1(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixG1(4, 4) aCopy.set(a) bCopy := newMatrixG1(4, 4) bCopy.set(b) a.add(b, a) res := newMatrixG1(0, 0) res.add(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of add to be alias safe") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixZp.go000066400000000000000000000217331454601126700270110ustar00rootroot00000000000000package tkn import ( "encoding/binary" "fmt" "io" pairing "github.com/cloudflare/circl/ecc/bls12381" "golang.org/x/crypto/blake2b" ) // matrixZp represents a matrix of mod grouporder elements. They are stored in row-major order. // The name is a gesture toward the paper. type matrixZp struct { rows int cols int entries []pairing.Scalar } func (m *matrixZp) marshalBinary() ([]byte, error) { ret := make([]byte, 4+pairing.ScalarSize*m.rows*m.cols) binary.LittleEndian.PutUint16(ret[0:], uint16(m.rows)) binary.LittleEndian.PutUint16(ret[2:], uint16(m.cols)) for i := 0; i < m.rows*m.cols; i++ { pt, err := m.entries[i].MarshalBinary() if err != nil { return nil, err } if len(pt) != pairing.ScalarSize { panic("matrixZp: incorrect assumption of size") } copy(ret[pairing.ScalarSize*i+4:], pt) } return ret, nil } func (m *matrixZp) unmarshalBinary(data []byte) error { if len(data) < 4 { return fmt.Errorf("matrixZp deserialization failure: input too short") } m.rows = int(binary.LittleEndian.Uint16(data[0:])) m.cols = int(binary.LittleEndian.Uint16(data[2:])) data = data[4:] if len(data) != pairing.ScalarSize*m.rows*m.cols { return fmt.Errorf("matrixZp deserialization failure: invalid entries length: expected %d, actual %d", pairing.ScalarSize*m.cols*m.rows, len(data)) } m.entries = make([]pairing.Scalar, m.rows*m.cols) var err error for i := 0; i < m.rows*m.cols; i++ { err = m.entries[i].UnmarshalBinary(data[pairing.ScalarSize*i : pairing.ScalarSize*(i+1)]) if err != nil { return fmt.Errorf("matrixZp deserialization failure: error from bytes %v: %w", data[pairing.ScalarSize*i:pairing.ScalarSize*(i+1)], err) } } return nil } // sampleDlin samples from the distribution Dk. // See section 3.2 of the paper for details. func sampleDlin(rand io.Reader) (*matrixZp, error) { var ret matrixZp ret.rows = 3 ret.cols = 2 ret.entries = make([]pairing.Scalar, 6) err := ret.entries[0].Random(rand) if err != nil { return nil, err } ret.entries[1].SetUint64(0) ret.entries[2].SetUint64(0) err = ret.entries[3].Random(rand) if err != nil { return nil, err } ret.entries[4].SetOne() ret.entries[5].SetOne() return &ret, nil } func randomMatrixZp(rand io.Reader, r int, c int) (*matrixZp, error) { ret := newMatrixZp(r, c) for i := 0; i < r*c; i++ { err := ret.entries[i].Random(rand) if err != nil { return nil, err } } return ret, nil } // We adopt the interface that math.Big uses // Receivers get set to the results of operations, and return themselves. // All aliases are allowed. // Now recall that G1, G2, GT are acted on by Zp. // So we don't have all products, just left and right with Zp. // Zp doesn't need this distinction. // Errors are signalled by returning nil, which propagates. // initialize sets up m to be r x c func (m *matrixZp) resize(r int, c int) { if m.rows != r || m.cols != c { m.rows = r m.cols = c m.entries = make([]pairing.Scalar, m.rows*m.cols) } } // clear makes m an all 0 func (m *matrixZp) clear() { for i := 0; i < len(m.entries); i++ { m.entries[i] = pairing.Scalar{} } } func newMatrixZp(r int, c int) *matrixZp { ret := new(matrixZp) ret.resize(r, c) ret.clear() return ret } // eye returns the k by k identity matrix. func eye(k int) *matrixZp { ret := newMatrixZp(k, k) for i := 0; i < k; i++ { ret.entries[i*k+i].SetUint64(1) } return ret } // conformal returns true iff m and a have the same dimensions. func (m *matrixZp) conformal(a *matrixZp) bool { return a.rows == m.rows && a.cols == m.cols } // Equal returns true iff m == a. func (m *matrixZp) Equal(a *matrixZp) bool { if !m.conformal(a) { return false } for i := 0; i < m.rows*m.cols; i++ { if m.entries[i].IsEqual(&a.entries[i]) == 0 { return false } } return true } // set sets m to a. func (m *matrixZp) set(a *matrixZp) { m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].Set(&a.entries[i]) } } // add sets m to a+b. func (m *matrixZp) add(a *matrixZp, b *matrixZp) { if !a.conformal(b) { panic(errBadMatrixSize) } m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].Add(&a.entries[i], &b.entries[i]) } } // sub sets m to a-b. func (m *matrixZp) sub(a *matrixZp, b *matrixZp) { if !a.conformal(b) { panic(errBadMatrixSize) } m.resize(a.rows, a.cols) for i := 0; i < m.rows*m.cols; i++ { m.entries[i].Sub(&a.entries[i], &b.entries[i]) } } // mul sets m to a*b. func (m *matrixZp) mul(a *matrixZp, b *matrixZp) { if a.cols != b.rows { panic(errBadMatrixSize) } if m == a { c := newMatrixZp(a.rows, a.cols) c.set(a) a = c } if m == b { c := newMatrixZp(b.rows, b.cols) c.set(b) b = c } m.resize(a.rows, b.cols) m.clear() t := &pairing.Scalar{} for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { for k := 0; k < a.cols; k++ { t.Mul(&a.entries[i*a.cols+k], &b.entries[k*b.cols+j]) m.entries[i*m.cols+j].Add(&m.entries[i*m.cols+j], t) } } } } // transpose sets m to the transpose of a. func (m *matrixZp) transpose(a *matrixZp) { if m == a { c := newMatrixZp(a.rows, a.cols) c.set(a) a = c } m.resize(a.cols, a.rows) for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { m.entries[i*m.cols+j].Set(&a.entries[j*a.cols+i]) } } } // swaprows swaps two rows. func (m *matrixZp) swapRows(i int, j int) { t := &pairing.Scalar{} for k := 0; k < m.cols; k++ { t.Set(&m.entries[i*m.cols+k]) m.entries[i*m.cols+k].Set(&m.entries[j*m.cols+k]) m.entries[j*m.cols+k].Set(t) } } // scalerow scales a row. func (m *matrixZp) scaleRow(alpha *pairing.Scalar, i int) { for k := 0; k < m.cols; k++ { m.entries[i*m.cols+k].Mul(&m.entries[i*m.cols+k], alpha) } } // addscaledrow takes alpha * row i and adds it to row j. func (m *matrixZp) addScaledRow(alpha *pairing.Scalar, i int, j int) { tmp := &pairing.Scalar{} for k := 0; k < m.cols; k++ { tmp.Mul(alpha, &m.entries[i*m.cols+k]) m.entries[j*m.cols+k].Add(tmp, &m.entries[j*m.cols+k]) } } // inverse sets m to the inverse of a. If a is not invertible, // the result is undefined and an error is returned. // Aliasing safe func (m *matrixZp) inverse(a *matrixZp) error { if a.rows != a.cols { panic(errBadMatrixSize) } // Any way we slice it we need additional storage. y := newMatrixZp(a.rows, 2*a.cols) for i := 0; i < a.rows; i++ { for j := 0; j < a.cols; j++ { y.entries[i*y.cols+j].Set(&a.entries[i*a.cols+j]) } y.entries[i*y.cols+y.rows+i].SetUint64(1) } tmp := &pairing.Scalar{} // Gaussian elimination with pivoting begins here. for i := 0; i < y.rows; i++ { pivoted := false pivot: for j := i; j < y.rows; j++ { if y.entries[i*y.cols+j].IsZero() == 0 { y.swapRows(i, j) pivoted = true break pivot } } if !pivoted { return errMatrixNonInvertible } tmp.Inv(&y.entries[i*y.cols+i]) y.scaleRow(tmp, i) for j := i + 1; j < y.rows; j++ { tmp.Set(&y.entries[j*y.cols+i]) tmp.Neg() y.addScaledRow(tmp, i, j) } } // At this point the matrix is in reduced row echelon form. // The next step is to substitute back. for i := y.rows - 1; i >= 0; i-- { for j := i - 1; j >= 0; j-- { tmp.Set(&y.entries[j*y.cols+i]) tmp.Neg() y.addScaledRow(tmp, i, j) } } m.resize(a.rows, a.cols) for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { m.entries[i*m.cols+j].Set(&y.entries[i*y.cols+m.cols+j]) } } return nil } // prf computes a prf with output in pairs of 3x2 matrices func prf(key []byte, input []byte) (*matrixZp, *matrixZp, error) { xof, err := blake2b.NewXOF(blake2b.OutputLengthUnknown, key) if err != nil { return nil, nil, err } if _, err = xof.Write(input); err != nil { return nil, nil, err } m1 := newMatrixZp(3, 2) m2 := newMatrixZp(3, 2) for i := 0; i < m1.rows; i++ { for j := 0; j < m1.cols; j++ { local := xof.Clone() if _, err = local.Write([]byte(fmt.Sprintf("m1 matrix entry (%d, %d)", i, j))); err != nil { return nil, nil, err } err = m1.entries[i*m1.cols+j].Random(local) if err != nil { return nil, nil, err } local = xof.Clone() if _, err = local.Write([]byte(fmt.Sprintf("m2 matrix entry (%d, %d)", i, j))); err != nil { return nil, nil, err } err = m2.entries[i*m2.cols+j].Random(local) if err != nil { return nil, nil, err } } } return m1, m2, nil } // scalarmul sets m to a matrix a*B func (m *matrixZp) scalarmul(a *pairing.Scalar, b *matrixZp) { m.resize(b.rows, b.cols) for i := 0; i < b.rows*b.cols; i++ { m.entries[i].Mul(a, &b.entries[i]) } } // colsel sets m to a matrix with the selected columns. func (m *matrixZp) colsel(a *matrixZp, cols []int) { if m == a { c := newMatrixZp(a.rows, a.cols) c.set(a) a = c } m.resize(a.rows, len(cols)) for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { m.entries[i*m.cols+j].Set(&a.entries[i*a.cols+cols[j]]) } } } func (m *matrixZp) String() string { var s string for i := 0; i < m.rows; i++ { for j := 0; j < m.cols; j++ { s += fmt.Sprintf("%v ", m.entries[i*m.cols+j].String()) } s += "\n" } return s } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/matrixZp_test.go000066400000000000000000000132471454601126700300510ustar00rootroot00000000000000package tkn import ( "crypto/rand" "testing" pairing "github.com/cloudflare/circl/ecc/bls12381" "github.com/cloudflare/circl/ecc/bls12381/ff" ) func TestSampleDlin(t *testing.T) { _, err := sampleDlin(rand.Reader) if err != nil { t.Errorf("failure of dlin: %s", err) } } func TestAdditionAndTranspose(t *testing.T) { a, err := sampleDlin(rand.Reader) if err != nil { t.Errorf("failure of dlin: %s", err) } b, err := sampleDlin(rand.Reader) if err != nil { t.Errorf("failure of dlin: %s", err) } at := new(matrixZp) bt := new(matrixZp) aplusb := new(matrixZp) atplusbt := new(matrixZp) lhs := new(matrixZp) at.transpose(a) bt.transpose(b) aplusb.add(a, b) atplusbt.add(at, bt) lhs.transpose(atplusbt) if !aplusb.Equal(lhs) { t.Errorf("failure of equality") } } func TestMultiplication(t *testing.T) { a, err := sampleDlin(rand.Reader) if err != nil { t.Errorf("failure of diln: %s", err) } b, err := sampleDlin(rand.Reader) if err != nil { t.Errorf("failure of diln: %s", err) } bta := new(matrixZp) atb := new(matrixZp) tmp := new(matrixZp) tmp.transpose(b) bta.mul(tmp, a) tmp.transpose(a) atb.mul(tmp, b) tmp.transpose(atb) if !tmp.Equal(bta) { t.Errorf("failure of multiplication") } } func TestInverse(t *testing.T) { a, err := sampleDlin(rand.Reader) if err != nil { t.Errorf("failure of diln: %s", err) } aa := new(matrixZp) at := new(matrixZp) ainv := new(matrixZp) res := new(matrixZp) at.transpose(a) aa.mul(at, a) err = ainv.inverse(aa) if err != nil { t.Errorf("failure to compute inverse") } res.mul(ainv, aa) expected := eye(res.cols) if !expected.Equal(res) { t.Errorf("failure of inverse value: expected:\n%v\n got:\n%v", expected, res) t.Errorf("inversion was of %v\n", aa) } res.mul(aa, ainv) if !expected.Equal(res) { t.Errorf("failure of reversed mult: got\n%v\n", res) } } func TestInverse2x2(t *testing.T) { A, err := randomMatrixZp(rand.Reader, 2, 2) if err != nil { t.Fatalf("failure of random: %v", err) } B := newMatrixZp(2, 2) C := newMatrixZp(2, 2) err = C.inverse(A) if err != nil { t.Fatalf("ah, we have a problem: try again") } var a pairing.Scalar var b pairing.Scalar var c pairing.Scalar var d pairing.Scalar var det pairing.Scalar var tmp pairing.Scalar a.Set(&A.entries[0]) b.Set(&A.entries[1]) c.Set(&A.entries[2]) d.Set(&A.entries[3]) det.Mul(&a, &d) tmp.Mul(&b, &c) det.Sub(&det, &tmp) tmp.Inv(&det) B.entries[0].Set(&d) B.entries[1].Set(&b) B.entries[1].Neg() B.entries[2].Set(&c) B.entries[2].Neg() B.entries[3].Set(&a) B.scalarmul(&tmp, B) if !C.Equal(B) { t.Errorf("failure to agree with explicit formula: got:\n%v, wanted\n%v\n", B, C) } expected := eye(2) res := newMatrixZp(0, 0) res.mul(B, A) if !res.Equal(expected) { t.Errorf("explicit formula wrong: got:\n%v\n as inverse of\n%v\n", B, A) } } func TestPRF(t *testing.T) { m1, m2, err := prf([]byte("test key do not use"), []byte("some input")) if err != nil { t.Errorf("failure of prf: %s", err) } if m1.Equal(m2) { t.Errorf("prf fails to have distinct outputs") } m3, _, err := prf([]byte("test key do not use"), []byte("some other input")) if err != nil { t.Errorf("failure of prf: %s", err) } if m1.Equal(m3) { t.Errorf("prf ignores input Value") } m4, _, err := prf([]byte("test key"), []byte("some input")) if err != nil { t.Errorf("failure of prf: %s", err) } if m1.Equal(m4) { t.Errorf("prf ignores key") } } func TestColsel(t *testing.T) { m1, err := randomMatrixZp(rand.Reader, 17, 17) if err != nil { t.Fatal(err) } res := new(matrixZp) res.colsel(m1, []int{0, 1, 2}) if res.rows != m1.rows { t.Errorf("wrong number of rows") } if res.cols != 3 { t.Errorf("wrong number of columns") } } func TestAliasMul(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixZp(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.mul(b, a) res := newMatrixZp(0, 0) res.mul(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of mul to be alias safe") } } func TestAliasAddZp(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixZp(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.add(b, a) res := newMatrixZp(0, 0) res.add(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of add to be alias safe") } } func TestAliasSubZp(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } b, err := randomMatrixZp(rand.Reader, 4, 4) if err != nil { t.Fatalf("error: %v", err) } aCopy := newMatrixZp(4, 4) aCopy.set(a) bCopy := newMatrixZp(4, 4) bCopy.set(b) a.sub(b, a) res := newMatrixZp(0, 0) res.sub(bCopy, aCopy) if !res.Equal(a) { t.Fatalf("failure of sub to be alias safe") } } func TestMarshalZp(t *testing.T) { a, err := randomMatrixZp(rand.Reader, 7, 9) if err != nil { t.Fatal(err) } data, err := a.marshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } b := newMatrixZp(0, 0) err = b.unmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(b) { t.Fatal("failure to roundtrip") } // test failure to set entry bytes scOrder := ff.ScalarOrder() scOrder[len(scOrder)-1] += 1 copy(data[4:pairing.ScalarSize+4], scOrder[:]) d := newMatrixZp(0, 0) err = d.unmarshalBinary(data) if err == nil { t.Fatal("deserialization of matrixZp with entry larger than scalar order must fail") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/pairAccum.go000066400000000000000000000012371454601126700270740ustar00rootroot00000000000000package tkn import ( "fmt" pairing "github.com/cloudflare/circl/ecc/bls12381" ) type pairAccum struct { as []*pairing.G1 bs []*pairing.G2 scalars []int } func (pairs *pairAccum) addDuals(m1 *matrixG1, m2 *matrixG2, n int) { if m1.cols != 1 || m2.cols != 1 { panic(fmt.Sprintf("misuse of addDuals: m1: %d x %d m2: %d x %d\n", m1.rows, m1.cols, m2.rows, m2.cols)) } for k := 0; k < m1.rows; k++ { pairs.as = append(pairs.as, &m1.entries[k]) pairs.bs = append(pairs.bs, &m2.entries[k]) pairs.scalars = append(pairs.scalars, n) } } func (pairs *pairAccum) eval() *pairing.Gt { return pairing.ProdPairFrac(pairs.as, pairs.bs, pairs.scalars) } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/policy.go000066400000000000000000000212361454601126700264700ustar00rootroot00000000000000package tkn import ( "encoding/binary" "fmt" pairing "github.com/cloudflare/circl/ecc/bls12381" ) const ( bkAttribute = "internal-boneh-katz-transform-attribute" attributeSize = pairing.ScalarSize + 1 ) type Wire struct { Label string RawValue string Value *pairing.Scalar Positive bool } func (w *Wire) String() string { if w.Positive { return fmt.Sprintf("%s:%s", w.Label, w.RawValue) } return fmt.Sprintf("not %s:%s", w.Label, w.RawValue) } type Policy struct { Inputs []Wire F Formula // monotonic boolean formula } type Attribute struct { wild bool // false if tame Value *pairing.Scalar } func (a *Attribute) marshalBinary() ([]byte, error) { ret := make([]byte, 1) if a.wild { ret[0] = 1 } aBytes, err := a.Value.MarshalBinary() if err != nil { return nil, err } return append(ret, aBytes...), nil } func (a *Attribute) unmarshalBinary(data []byte) error { if len(data) != attributeSize { return fmt.Errorf("unmarshalling Attribute failed: invalid input length, expected: %d, received: %d", attributeSize, len(data)) } a.wild = false if data[0] == 1 { a.wild = true } a.Value = &pairing.Scalar{} err := a.Value.UnmarshalBinary(data[1:]) if err != nil { return fmt.Errorf("unmarshalling Attribute failed: %w", err) } return nil } func (a *Attribute) Equal(b *Attribute) bool { return a.wild == b.wild && a.Value.IsEqual(b.Value) == 1 } type Attributes map[string]Attribute func (a *Attributes) marshalBinary() ([]byte, error) { ret := make([]byte, 2) binary.LittleEndian.PutUint16(ret[0:], uint16(len(*a))) aBytes, err := marshalBinarySortedMapAttribute(*a) if err != nil { return nil, fmt.Errorf("marshalling Attributes failed: %w", err) } ret = append(ret, aBytes...) return ret, nil } func (a *Attributes) unmarshalBinary(data []byte) error { if len(data) < 2 { return fmt.Errorf("unmarshalling Attributes failed: data too short") } n := int(binary.LittleEndian.Uint16(data)) data = data[2:] *a = make(map[string]Attribute, n) for i := 0; i < n; i++ { labelBytes, rem, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("unmarshalling Attributes failed: %w", err) } if len(rem) < attributeSize { return fmt.Errorf("unmarshalling Attributes failed: data too short") } attr := Attribute{} err = attr.unmarshalBinary(rem[:attributeSize]) if err != nil { return fmt.Errorf("unmarshalling Attributes failed: %w", err) } (*a)[string(labelBytes)] = attr data = rem[attributeSize:] } if len(data) != 0 { return fmt.Errorf("unmarshalling Attributes failed: excess bytes remain in data") } return nil } func (a *Attributes) Equal(b *Attributes) bool { if len(*a) != len(*b) { return false } for k := range *a { v := (*a)[k] if v2, ok := (*b)[k]; !(ok && v2.Equal(&v)) { return false } } return true } func (w *Wire) MarshalBinary() ([]byte, error) { strBytes := []byte(w.Label) valBytes := []byte(w.RawValue) intBytes, err := w.Value.MarshalBinary() if err != nil { return nil, err } totalLen := len(strBytes) + len(valBytes) + len(intBytes) + 2 + 2 + 2 + 1 ret := make([]byte, totalLen) where := 0 binary.LittleEndian.PutUint16(ret[where:], uint16(len(strBytes))) where += 2 where += copy(ret[where:], strBytes) binary.LittleEndian.PutUint16(ret[where:], uint16(len(valBytes))) where += 2 where += copy(ret[where:], valBytes) binary.LittleEndian.PutUint16(ret[where:], uint16(len(intBytes))) where += 2 where += copy(ret[where:], intBytes) if w.Positive { ret[where] = 1 } else { ret[where] = 0 } return ret, nil } func (w *Wire) UnmarshalBinary(data []byte) error { where := 0 if len(data) < 2 { return fmt.Errorf("data not long enough") } strLen := int(binary.LittleEndian.Uint16(data[where:])) where += 2 if len(data[where:]) < strLen { return fmt.Errorf("data not long enough") } w.Label = string(data[where : where+strLen]) where += strLen if len(data[where:]) < 2 { return fmt.Errorf("data not long enough") } valLen := int(binary.LittleEndian.Uint16(data[where:])) where += 2 if len(data[where:]) < valLen { return fmt.Errorf("data not long enough") } w.RawValue = string(data[where : where+valLen]) where += valLen if len(data[where:]) < 2 { return fmt.Errorf("data not long enough") } intLen := int(binary.LittleEndian.Uint16(data[where:])) where += 2 if len(data[where:]) < intLen { return fmt.Errorf("data not long enough") } w.Value = &pairing.Scalar{} w.Value.SetBytes(data[where : where+intLen]) where += intLen if len(data[where:]) < 1 { return fmt.Errorf("data not long enough") } if data[where] == 1 { w.Positive = true } else { w.Positive = false } return nil } func (w *Wire) Equal(w2 *Wire) bool { return w.Label == w2.Label && w.RawValue == w2.RawValue && w.Positive == w2.Positive && w.Value.IsEqual(w2.Value) == 1 } func (p *Policy) MarshalBinary() ([]byte, error) { ret := make([]byte, 2) fBytes, err := p.F.MarshalBinary() if err != nil { return nil, err } binary.LittleEndian.PutUint16(ret[0:2], uint16(len(fBytes))) ret = append(ret, fBytes...) ret = append(ret, 0, 0) binary.LittleEndian.PutUint16(ret[len(ret)-2:], uint16(len(p.Inputs))) for i := 0; i < len(p.Inputs); i++ { input, err := p.Inputs[i].MarshalBinary() if err != nil { return nil, err } ret = append(ret, 0, 0) binary.LittleEndian.PutUint16(ret[len(ret)-2:], uint16(len(input))) ret = append(ret, input...) } return ret, nil } func (p *Policy) UnmarshalBinary(data []byte) error { // Extract formula if len(data) < 2 { return fmt.Errorf("data not long enough") } fLen := uint(binary.LittleEndian.Uint16(data)) data = data[2:] err := p.F.UnmarshalBinary(data) if err != nil { return err } data = data[fLen:] // Extract wires if len(data) < 2 { return fmt.Errorf("data not long enough") } nWires := int(binary.LittleEndian.Uint16(data)) data = data[2:] p.Inputs = make([]Wire, nWires) for i := 0; i < nWires; i++ { wireLen := uint(binary.LittleEndian.Uint16(data)) data = data[2:] err = p.Inputs[i].UnmarshalBinary(data) data = data[wireLen:] if err != nil { return fmt.Errorf("data not long enough") } } return nil } func (p *Policy) Equal(p2 *Policy) bool { if len(p.Inputs) != len(p2.Inputs) { return false } if !p.F.Equal(p2.F) { return false } for i := range p.Inputs { if !p.Inputs[i].Equal(&p2.Inputs[i]) { return false } } return true } func (p *Policy) String() string { // gateAssign takes n wires (intermediates and outputs) and maps to the gate // that set them. For details, refer to [Formula]. offset := len(p.F.Gates) + 1 gateAssign := make([]int, len(p.F.Gates)) for i, gate := range p.F.Gates { gateAssign[gate.Out-offset] = i } return p.printWire(gateAssign, 2*len(p.F.Gates)) } func (p *Policy) printWire(gateAssign []int, wire int) string { n := len(p.F.Gates) if wire < n+1 { return p.Inputs[wire].String() } gate := p.F.Gates[gateAssign[wire-n-1]] return fmt.Sprintf("(%s %s %s)", p.printWire(gateAssign, gate.In0), gate.operator(), p.printWire(gateAssign, gate.In1)) } type match struct { wire int label string } type Satisfaction struct { matches []match } func (p *Policy) pi() []int { ret := make([]int, len(p.Inputs)) counts := make(map[string]int) for i := 0; i < len(p.Inputs); i++ { // Paper would have us put a +1 here // we change the indexing instead ret[i] = counts[p.Inputs[i].Label] counts[p.Inputs[i].Label]++ } return ret } func (p *Policy) Satisfaction(attr *Attributes) (*Satisfaction, error) { // For now its all of the wires, so we don't need to look at the formula. var matches []match for i := 0; i < len(p.Inputs); i++ { wire := p.Inputs[i] at, ok := (*attr)[wire.Label] if !ok { continue // missing Attribute might not be needed } if wire.Positive { if (wire.Value.IsEqual(at.Value) == 1) || at.wild { matches = append(matches, match{i, wire.Label}) } } else { if (wire.Value.IsEqual(at.Value) == 0) || at.wild { matches = append(matches, match{i, wire.Label}) } } } matches, err := p.F.satisfaction(matches) if err != nil { return nil, err } return &Satisfaction{ matches, }, nil } // Carry Out the augmentation under the BK transform func (p *Policy) transformBK(val *pairing.Scalar) *Policy { ret := new(Policy) for i := 0; i < len(p.Inputs); i++ { ret.Inputs = append(ret.Inputs, p.Inputs[i]) } ret.Inputs = append(ret.Inputs, Wire{ Label: bkAttribute, Value: val, Positive: true, }) ret.F = p.F.insertAnd() return ret } func transformAttrsBK(attr *Attributes) *Attributes { ret := make(map[string]Attribute) for name, val := range *attr { ret[name] = val } ret[bkAttribute] = Attribute{ wild: true, Value: &pairing.Scalar{}, } return (*Attributes)(&ret) } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/policy_test.go000066400000000000000000000106521454601126700275270ustar00rootroot00000000000000package tkn import ( "testing" ) var AttrHashKey = []byte("attribute value hashing") func TestWireSerialization(t *testing.T) { in := &Wire{"a", "0", HashStringToScalar(AttrHashKey, "0"), true} data, err := in.MarshalBinary() if err != nil { t.Fatalf("error in marshaling: %s", err) } out := &Wire{} err = out.UnmarshalBinary(data) if err != nil { t.Fatalf("error in unmarshaling: %s", err) } if !in.Equal(out) { t.Fatalf("failure to round trip") } } func TestPolicySerialization(t *testing.T) { in := Policy{ Inputs: []Wire{ {"a", "1", HashStringToScalar(AttrHashKey, "1"), true}, {"b", "xx", HashStringToScalar(AttrHashKey, "xx"), true}, {"c", "3", HashStringToScalar(AttrHashKey, "3"), true}, }, F: Formula{ Gates: []Gate{ {Andgate, 0, 1, 3}, {Andgate, 2, 3, 4}, }, }, } data, err := in.MarshalBinary() if err != nil { t.Fatalf("error in marshalling: %s", err) } out := Policy{} err = out.UnmarshalBinary(data) if err != nil { t.Fatalf("error in unmarshaling: %s", err) } if !in.F.Equal(out.F) { t.Fatalf("formulas do not match") } for i, input := range in.Inputs { if !input.Equal(&out.Inputs[i]) { t.Fatal("failure to round trip: inputs do not match") } } } type TestCase struct { p *Policy a *Attributes } func TestSatisfaction(t *testing.T) { testCases := []TestCase{ { &Policy{ Inputs: []Wire{ {"a", "0", ToScalar(0), true}, }, F: Formula{ Gates: []Gate{}, }, }, &Attributes{ "a": { wild: false, Value: ToScalar(0), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "1", ToScalar(1), true}, {"b", "2", ToScalar(2), true}, {"c", "3", ToScalar(3), true}, }, F: Formula{ Gates: []Gate{ {Andgate, 0, 1, 3}, {Andgate, 2, 3, 4}, }, }, }, &Attributes{ "d": { wild: false, Value: ToScalar(4), }, "c": { wild: false, Value: ToScalar(3), }, "b": { wild: false, Value: ToScalar(2), }, "a": { wild: false, Value: ToScalar(1), }, }, }, { &Policy{ Inputs: []Wire{ {"a", "1", ToScalar(1), false}, {"b", "2", ToScalar(2), true}, {"c", "3", ToScalar(3), true}, }, F: Formula{ Gates: []Gate{ {Andgate, 0, 1, 3}, {Andgate, 2, 3, 4}, }, }, }, &Attributes{ "d": { wild: false, Value: ToScalar(4), }, "c": { wild: false, Value: ToScalar(3), }, "b": { wild: false, Value: ToScalar(2), }, "a": { wild: false, Value: ToScalar(2), }, }, }, } for _, args := range testCases { sat, err := args.p.Satisfaction(args.a) if err != nil { t.Fatalf("no satisfaction found for valid program: %s", err) } for i := 0; i < len(sat.matches); i++ { match := sat.matches[i] if args.p.Inputs[match.wire].Positive { if args.p.Inputs[match.wire].Value.IsEqual((*args.a)[match.label].Value) == 0 || match.label != args.p.Inputs[match.wire].Label { t.Errorf("mismatch of Attribute name or Value") } } else { if match.label != args.p.Inputs[match.wire].Label { t.Errorf("mismatch of Attribute name") } } } } } func TestMarshalAttribute(t *testing.T) { in := Attribute{true, ToScalar(1)} data, err := in.marshalBinary() if err != nil { t.Fatalf("error in marshaling: %s", err) } out := Attribute{} err = out.unmarshalBinary(data) if err != nil { t.Fatalf("error in unmarshaling: %s", err) } if !in.Equal(&out) { t.Fatal("failure to roundtrip") } } func TestMarshalAttributes(t *testing.T) { in := Attributes{ "cat": { wild: true, Value: ToScalar(0), }, "bree": { wild: false, Value: ToScalar(2), }, "a": { wild: true, Value: ToScalar(2), }, } data, err := in.marshalBinary() if err != nil { t.Fatalf("error in marshaling: %s", err) } // check if deserializing into non-empty struct works out := &Attributes{ "evil": { wild: true, Value: ToScalar(0), }, "bree": { wild: false, Value: ToScalar(2), }, "a": { wild: true, Value: ToScalar(2), }, } if in.Equal(out) { t.Fatalf("shouldn't be equal") } err = out.unmarshalBinary(data) if err != nil { t.Fatalf("error in unmarshaling: %s", err) } if !in.Equal(out) { t.Fatal("failure to roundtrip") } err = out.unmarshalBinary(append(data, 0)) if err == nil { t.Fatalf("data has excess bytes, deserialization should fail") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/tk.go000066400000000000000000000471721454601126700256160ustar00rootroot00000000000000// Implements the scheme of https://eprint.iacr.org/2019/966 package tkn import ( "crypto/subtle" "encoding/binary" "fmt" "io" pairing "github.com/cloudflare/circl/ecc/bls12381" ) type PublicParams struct { b2 *matrixG2 wb1 *matrixG1 btk *matrixGT } func (p *PublicParams) MarshalBinary() ([]byte, error) { b2Bytes, err := p.b2.marshalBinary() if err != nil { return nil, fmt.Errorf("PublicParams serializing failed: %w", err) } ret := appendLenPrefixed(nil, b2Bytes) wb1Bytes, err := p.wb1.marshalBinary() if err != nil { return nil, fmt.Errorf("PublicParams serializing failed: %w", err) } ret = appendLenPrefixed(ret, wb1Bytes) btkBytes, err := p.btk.marshalBinary() if err != nil { return nil, fmt.Errorf("PublicParams serializing failed: %w", err) } ret = appendLenPrefixed(ret, btkBytes) return ret, nil } func (p *PublicParams) UnmarshalBinary(data []byte) error { b2Bytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("PublicParams deserialization failure: %w", err) } p.b2 = newMatrixG2(0, 0) err = p.b2.unmarshalBinary(b2Bytes) if err != nil { return fmt.Errorf("PublicParams deserialization failure: %w", err) } wb1Bytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("PublicParams deserialization failure: %w", err) } p.wb1 = newMatrixG1(0, 0) err = p.wb1.unmarshalBinary(wb1Bytes) if err != nil { return fmt.Errorf("PublicParams deserialization failure: %w", err) } btkBytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("PublicParams deserialization failure: %w", err) } p.btk = newMatrixGT(0, 0) err = p.btk.unmarshalBinary(btkBytes) if err != nil { return fmt.Errorf("PublicParams deserialization failure: %w", err) } if len(data) != 0 { return fmt.Errorf("PublicParams deserialization failed: excess bytes remain in data") } return nil } func (p *PublicParams) Equal(p2 *PublicParams) bool { return p.b2.Equal(p2.b2) && p.wb1.Equal(p2.wb1) && p.btk.Equal(p2.btk) } type SecretParams struct { a *matrixZp wtA *matrixZp bstar *matrixZp bstar12 *matrixZp k *matrixZp // vectors are represented as 1 x n matrices prfKey []byte } func (s *SecretParams) MarshalBinary() ([]byte, error) { aBytes, err := s.a.marshalBinary() if err != nil { return nil, fmt.Errorf("SecretParams serializing failed: %w", err) } wtABytes, err := s.wtA.marshalBinary() if err != nil { return nil, fmt.Errorf("SecretParams serializing failed: %w", err) } bstarBytes, err := s.bstar.marshalBinary() if err != nil { return nil, fmt.Errorf("SecretParams serializing failed: %w", err) } bstar12Bytes, err := s.bstar12.marshalBinary() if err != nil { return nil, fmt.Errorf("SecretParams serializing failed: %w", err) } kBytes, err := s.k.marshalBinary() if err != nil { return nil, fmt.Errorf("SecretParams serializing failed: %w", err) } bufs := [][]byte{ aBytes, wtABytes, bstarBytes, bstar12Bytes, kBytes, s.prfKey, } ret := appendLenPrefixed(nil, bufs[0]) for _, buf := range bufs[1:] { ret = appendLenPrefixed(ret, buf) } return ret, nil } func (s *SecretParams) UnmarshalBinary(data []byte) error { aBytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } s.a = newMatrixZp(0, 0) err = s.a.unmarshalBinary(aBytes) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } wtABytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } s.wtA = newMatrixZp(0, 0) err = s.wtA.unmarshalBinary(wtABytes) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } bstarBytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } s.bstar = newMatrixZp(0, 0) err = s.bstar.unmarshalBinary(bstarBytes) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } bstar12Bytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } s.bstar12 = newMatrixZp(0, 0) err = s.bstar12.unmarshalBinary(bstar12Bytes) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } kBytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } s.k = newMatrixZp(0, 0) err = s.k.unmarshalBinary(kBytes) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } prfBytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("SecretParams deserialization failure: %w", err) } s.prfKey = prfBytes if len(data) != 0 { return fmt.Errorf("SecretParams deserialization failed: excess bytes remain in data") } return nil } func (s *SecretParams) Equal(s2 *SecretParams) bool { return s.a.Equal(s2.a) && s.wtA.Equal(s2.wtA) && s.bstar.Equal(s2.bstar) && s.bstar12.Equal(s2.bstar12) && s.k.Equal(s2.k) && subtle.ConstantTimeCompare(s.prfKey, s2.prfKey) == 1 } type AttributesKey struct { a *Attributes k1 *matrixG2 k2 *matrixG1 k3 map[string]*matrixG1 k3wild map[string]*matrixG1 // only contains wildcards } func (a *AttributesKey) MarshalBinary() ([]byte, error) { aBytes, err := a.a.marshalBinary() if err != nil { return nil, fmt.Errorf("AttributesKey serializing failed: %w", err) } ret := appendLenPrefixed(nil, aBytes) k1Bytes, err := a.k1.marshalBinary() if err != nil { return nil, fmt.Errorf("AttributesKey serializing failed: %w", err) } ret = appendLenPrefixed(ret, k1Bytes) k2Bytes, err := a.k2.marshalBinary() if err != nil { return nil, fmt.Errorf("AttributesKey serializing failed: %w", err) } ret = appendLenPrefixed(ret, k2Bytes) ret = append(ret, 0, 0) binary.LittleEndian.PutUint16(ret[len(ret)-2:], uint16(len(a.k3))) k3Bytes, err := marshalBinarySortedMapMatrixG1(a.k3) if err != nil { return nil, fmt.Errorf("AttributesKey serializing failed: %w", err) } ret = append(ret, k3Bytes...) ret = append(ret, 0, 0) binary.LittleEndian.PutUint16(ret[len(ret)-2:], uint16(len(a.k3wild))) k3wildBytes, err := marshalBinarySortedMapMatrixG1(a.k3wild) if err != nil { return nil, fmt.Errorf("AttributesKey serializing failed: %w", err) } ret = append(ret, k3wildBytes...) return ret, nil } func (a *AttributesKey) UnmarshalBinary(data []byte) error { aBytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } a.a = &Attributes{} err = a.a.unmarshalBinary(aBytes) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } k1Bytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } a.k1 = newMatrixG2(0, 0) err = a.k1.unmarshalBinary(k1Bytes) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } k2Bytes, data, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } a.k2 = newMatrixG1(0, 0) err = a.k2.unmarshalBinary(k2Bytes) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } if len(data) < 2 { return fmt.Errorf("AttributesKey deserialization failure: data too short") } n := int(binary.LittleEndian.Uint16(data)) data = data[2:] a.k3 = make(map[string]*matrixG1, n) for i := 0; i < n; i++ { sBytes, rem, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } mBytes, rem, err := removeLenPrefixed(rem) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } m := newMatrixG1(0, 0) err = m.unmarshalBinary(mBytes) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } a.k3[string(sBytes)] = m data = rem } if len(data) < 2 { return fmt.Errorf("AttributesKey deserialization failure: data too short") } n = int(binary.LittleEndian.Uint16(data)) data = data[2:] a.k3wild = make(map[string]*matrixG1, n) for i := 0; i < n; i++ { sBytes, rem, err := removeLenPrefixed(data) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } mBytes, rem, err := removeLenPrefixed(rem) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } m := newMatrixG1(0, 0) err = m.unmarshalBinary(mBytes) if err != nil { return fmt.Errorf("AttributesKey deserialization failure: %w", err) } a.k3wild[string(sBytes)] = m data = rem } if len(data) != 0 { return fmt.Errorf("AttributesKey deserialization failed: excess bytes remain in data") } return nil } func (a *AttributesKey) Equal(b *AttributesKey) bool { if !a.a.Equal(b.a) || !a.k1.Equal(b.k1) || !a.k2.Equal(b.k2) { return false } if len(a.k3) != len(b.k3) || len(a.k3wild) != len(b.k3wild) { return false } for k, v := range a.k3 { if !b.k3[k].Equal(v) { return false } } for k, v := range a.k3wild { if !b.k3wild[k].Equal(v) { return false } } return true } type ciphertextHeader struct { p *Policy c1 *matrixG2 c2 []*matrixG2 c3 []*matrixG1 c3neg []*matrixG1 // additional vector for negated attributes } func (hdr *ciphertextHeader) marshalBinary() ([]byte, error) { pBytes, err := hdr.p.MarshalBinary() if err != nil { return nil, err } ret := appendLenPrefixed(nil, pBytes) c1Bytes, err := hdr.c1.marshalBinary() if err != nil { return nil, fmt.Errorf("c1 serializing: %w", err) } ret = appendLenPrefixed(ret, c1Bytes) // Now we need to indicate how long c2, c3, c3neg are. // Each array will be the same size (or nil), so with more work we can specialize // but for now we will ignore that. c2Len := len(hdr.c2) ret = append(ret, 0, 0) binary.LittleEndian.PutUint16(ret[len(ret)-2:], uint16(c2Len)) for i := 0; i < c2Len; i++ { c2dat, errM := hdr.c2[i].marshalBinary() if errM != nil { return nil, fmt.Errorf("c2 serializing %d: %w", i, errM) } ret = appendLenPrefixed(ret, c2dat) } c3Len := len(hdr.c3) ret = append(ret, 0, 0) binary.LittleEndian.PutUint16(ret[len(ret)-2:], uint16(c3Len)) for i := 0; i < c3Len; i++ { c3dat, errM := hdr.c3[i].marshalBinary() if errM != nil { return nil, fmt.Errorf("c3 serializing %d: %w", i, errM) } ret = appendLenPrefixed(ret, c3dat) } for i := 0; i < c3Len; i++ { var c3negdat []byte if hdr.c3neg[i] != nil { c3negdat, err = hdr.c3neg[i].marshalBinary() if err != nil { return nil, fmt.Errorf("c3neg serializing %d: %w", i, err) } } else { c3negdat = nil } ret = appendLenPrefixed(ret, c3negdat) } return ret, nil } func (hdr *ciphertextHeader) unmarshalBinary(data []byte) error { pBytes, data, err := removeLenPrefixed(data) if err != nil { return err } hdr.p = new(Policy) err = hdr.p.UnmarshalBinary(pBytes) if err != nil { return err } c1Bytes, data, err := removeLenPrefixed(data) if err != nil { return err } hdr.c1 = newMatrixG2(0, 0) err = hdr.c1.unmarshalBinary(c1Bytes) if err != nil { return err } c2Len := int(binary.LittleEndian.Uint16(data)) hdr.c2 = make([]*matrixG2, c2Len) data = data[2:] var c2data []byte var c3data []byte var c3negdata []byte for i := 0; i < c2Len; i++ { c2data, data, err = removeLenPrefixed(data) if err != nil { return err } hdr.c2[i] = newMatrixG2(0, 0) err = hdr.c2[i].unmarshalBinary(c2data) if err != nil { return err } } c3Len := int(binary.LittleEndian.Uint16(data)) hdr.c3 = make([]*matrixG1, c3Len) hdr.c3neg = make([]*matrixG1, c3Len) data = data[2:] for i := 0; i < c3Len; i++ { c3data, data, err = removeLenPrefixed(data) if err != nil { return err } hdr.c3[i] = newMatrixG1(0, 0) err = hdr.c3[i].unmarshalBinary(c3data) if err != nil { return err } } for i := 0; i < c3Len; i++ { c3negdata, data, err = removeLenPrefixed(data) if err != nil { return err } if len(c3negdata) != 0 { hdr.c3neg[i] = newMatrixG1(0, 0) err = hdr.c3neg[i].unmarshalBinary(c3negdata) if err != nil { return err } } } return nil } func GenerateParams(rand io.Reader) (*PublicParams, *SecretParams, error) { A, err := sampleDlin(rand) if err != nil { return nil, nil, err } Bbar, err := randomMatrixZp(rand, 4, 4) if err != nil { return nil, nil, err } W, err := randomMatrixZp(rand, 3, 4) if err != nil { return nil, nil, err } k, err := randomMatrixZp(rand, 4, 1) if err != nil { return nil, nil, err } prfKey := make([]byte, 16) _, err = io.ReadFull(rand, prfKey) if err != nil { return nil, nil, err } B := newMatrixZp(0, 0) B.colsel(Bbar, []int{0, 1}) wb := newMatrixZp(0, 0) wb.mul(W, B) Bt := newMatrixZp(0, 0) Bt.transpose(B) BtKp := newMatrixZp(0, 0) BtKp.mul(Bt, k) pp := PublicParams{} pp.b2 = newMatrixG2(0, 0) pp.b2.exp(B) pp.wb1 = newMatrixG1(0, 0) pp.wb1.exp(wb) pp.btk = newMatrixGT(0, 0) pp.btk.exp(BtKp) sp := SecretParams{} sp.a = A sp.wtA = newMatrixZp(0, 0) wt := newMatrixZp(0, 0) wt.transpose(W) sp.wtA.mul(wt, A) BbarTinv := newMatrixZp(0, 0) BbarT := newMatrixZp(0, 0) BbarT.transpose(Bbar) err = BbarTinv.inverse(BbarT) if err != nil { return nil, nil, err } sp.bstar = newMatrixZp(0, 0) sp.bstar.colsel(BbarTinv, []int{0, 1}) sp.bstar12 = newMatrixZp(0, 0) sp.bstar12.colsel(BbarTinv, []int{2, 3}) sp.k = k sp.prfKey = prfKey return &pp, &sp, nil } func max(in []int) int { max := 0 for i := 0; i < len(in); i++ { if in[i] > max { max = in[i] } } return max } // encapsulate creates a new ephemeral key and header that can be opened to it. This is // the transformation of an Elgamal like scheme to a KEM. func encapsulate(rand io.Reader, pp *PublicParams, policy *Policy) (*ciphertextHeader, *pairing.Gt, error) { pi := policy.pi() d := max(pi) + 1 ri := make([]*matrixZp, d) r, err := randomMatrixZp(rand, 2, 1) if err != nil { return nil, nil, err } for i := 0; i < d; i++ { ri[i], err = randomMatrixZp(rand, 2, 1) if err != nil { return nil, nil, err } } rshares, err := policy.F.share(rand, r) if err != nil { return nil, nil, err } tmp := newMatrixZp(2, 1) wshares := make([]*matrixG1, len(rshares)) for i := 0; i < len(rshares); i++ { wshares[i] = newMatrixG1(0, 0) wshares[i].rightMult(pp.wb1, rshares[i]) } c1 := newMatrixG2(0, 0) c1.rightMult(pp.b2, r) c2 := make([]*matrixG2, d) for i := 0; i < d; i++ { c2[i] = newMatrixG2(0, 0) c2[i].rightMult(pp.b2, ri[i]) } c4mat := newMatrixGT(1, 1) tmp.transpose(r) c4mat.leftMult(tmp, pp.btk) if c4mat.rows != 1 || c4mat.cols != 1 { panic("failure to get the encryption right") } c3 := make([]*matrixG1, len(policy.Inputs)) c3neg := make([]*matrixG1, len(policy.Inputs)) for i := 0; i < len(policy.Inputs); i++ { U0, U1 := oracle([]byte(policy.Inputs[i].Label)) if policy.Inputs[i].Positive { c3[i] = newMatrixG1(0, 0) c3[i].scalarMult(policy.Inputs[i].Value, U0) c3[i].add(c3[i], U1) c3[i].rightMult(c3[i], ri[pi[i]]) c3[i].add(c3[i], wshares[i]) c3neg[i] = nil } else { c3[i] = newMatrixG1(0, 0) c3[i].rightMult(U0, ri[pi[i]]) c3[i].sub(c3[i], wshares[i]) c3neg[i] = newMatrixG1(0, 0) c3neg[i].rightMult(U1, ri[pi[i]]) tmpmat := newMatrixG1(0, 0) tmpmat.scalarMult(policy.Inputs[i].Value, wshares[i]) c3neg[i].add(c3neg[i], tmpmat) } } return &ciphertextHeader{ p: policy, c1: c1, c2: c2, c3: c3, c3neg: c3neg, }, &c4mat.entries[0], nil } func deriveAttributeKeys(rand io.Reader, sp *SecretParams, attrs *Attributes) (*AttributesKey, error) { s, err := randomMatrixZp(rand, 2, 1) if err != nil { return nil, err } As := newMatrixZp(0, 0) k1 := newMatrixG2(0, 0) As.mul(sp.a, s) k1.exp(As) Ast := newMatrixZp(0, 0) Ast.transpose(As) k2 := newMatrixG1(0, 0) tmp := newMatrixZp(0, 0) tmp.mul(sp.wtA, s) tmp.add(tmp, sp.k) k2.exp(tmp) k3 := make(map[string]*matrixG1) k3wild := make(map[string]*matrixG1) for label, attr := range *attrs { if attr.wild { // For wild k3 is y term, k3wild is constant term U0, U1 := oracle([]byte(label)) V0, V1, err := prf(sp.prfKey, []byte(label)) if err != nil { return nil, err } k3[label] = newMatrixG1(0, 0) k3wild[label] = newMatrixG1(0, 0) left := newMatrixG1(0, 0) right := newMatrixG1(0, 0) left.transpose(U0) left.leftMult(sp.bstar, left) left.rightMult(left, As) tmp.transpose(V0) tmp.mul(sp.bstar12, tmp) tmp.mul(tmp, As) right.exp(tmp) k3[label].add(left, right) left.transpose(U1) left.leftMult(sp.bstar, left) left.rightMult(left, As) tmp.transpose(V1) tmp.mul(sp.bstar12, tmp) tmp.mul(tmp, As) right.exp(tmp) k3wild[label].add(left, right) } else { U0, U1 := oracle([]byte(label)) V0, V1, err := prf(sp.prfKey, []byte(label)) if err != nil { return nil, err } k3[label] = newMatrixG1(0, 0) left := newMatrixG1(0, 0) right := newMatrixG1(0, 0) left.scalarMult(attr.Value, U0) left.add(U1, left) left.transpose(left) left.leftMult(sp.bstar, left) left.rightMult(left, As) tmp.scalarmul(attr.Value, V0) tmp.add(tmp, V1) tmp.transpose(tmp) tmp.mul(sp.bstar12, tmp) tmp.mul(tmp, As) right.exp(tmp) k3[label].add(left, right) } } return &AttributesKey{ a: attrs, k1: k1, k2: k2, k3: k3, k3wild: k3wild, }, nil } // Decapsulate decapsulates func decapsulate(header *ciphertextHeader, key *AttributesKey) (*pairing.Gt, error) { // First we need to determine the satisfying assignment: which attributes in attr // are needed. // We use pi to determine which D to sum into pi := header.p.pi() d := max(pi) + 1 // p1, p2 are the left halves of the pairings. p1 := make([]*matrixG1, d) p2 := make([]*matrixG1, d) sat, err := header.p.Satisfaction(key.a) if err != nil { return nil, err } for k := 0; k < len(sat.matches); k++ { match := sat.matches[k] j := pi[match.wire] if p1[j] == nil { p1[j] = newMatrixG1(header.c3[match.wire].rows, header.c3[match.wire].cols) } if p2[j] == nil { p2[j] = newMatrixG1(key.k3[match.label].rows, key.k3[match.label].cols) } if header.p.Inputs[match.wire].Positive { p1[j].add(p1[j], header.c3[match.wire]) if (*key.a)[match.label].wild { if key.k3wild[match.label] == nil { return nil, fmt.Errorf("missing wildcard data for Label %s", match.label) } y := header.p.Inputs[match.wire].Value tmp1 := newMatrixG1(0, 0) tmp1.scalarMult(y, key.k3[match.label]) tmp1.add(tmp1, key.k3wild[match.label]) p2[j].add(p2[j], tmp1) } else { p2[j].add(p2[j], key.k3[match.label]) } } else { keymat := newMatrixG1(0, 0) y := &pairing.Scalar{} if (*key.a)[match.label].wild { y.Add(header.p.Inputs[match.wire].Value, ToScalar(1)) keymat.scalarMult(y, key.k3[match.label]) keymat.add(keymat, key.k3wild[match.label]) } else { y.Set((*(key.a))[match.label].Value) keymat.set(key.k3[match.label]) } diff := &pairing.Scalar{} diff.Sub(header.p.Inputs[match.wire].Value, y) diff.Inv(diff) p1add := newMatrixG1(0, 0) p1add.scalarMult(y, header.c3[match.wire]) p1add.add(p1add, header.c3neg[match.wire]) p1add.scalarMult(diff, p1add) p2add := newMatrixG1(0, 0) p2add.scalarMult(diff, keymat) p1[j].add(p1[j], p1add) p2[j].add(p2[j], p2add) } } pairs := &pairAccum{} var pTot *matrixG1 for i := 0; i < d; i++ { if p1[i] != nil { if pTot == nil { pTot = newMatrixG1(p1[i].rows, p1[i].cols) } pTot.add(pTot, p1[i]) pairs.addDuals(p2[i], header.c2[i], 1) } } pairs.addDuals(pTot, key.k1, -1) pairs.addDuals(key.k2.copy(), header.c1, 1) return pairs.eval(), nil } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/tk_test.go000066400000000000000000000102531454601126700266430ustar00rootroot00000000000000package tkn import ( "crypto/rand" "fmt" "testing" ) func TestEncryptionSimple(t *testing.T) { for i, suite := range encTestCases { t.Run(fmt.Sprintf("test %d", i), func(t *testing.T) { public, secret, err := GenerateParams(rand.Reader) if err != nil { t.Fatalf("error generating parameters: %s", err) } userKey, err := deriveAttributeKeys(rand.Reader, secret, suite.a) if err != nil { t.Fatalf("error generating attribute keys: %s", err) } header, shared, err := encapsulate(rand.Reader, public, suite.p) if err != nil { t.Fatalf("error encrypting message: %s", err) } headerSerialized, err := header.marshalBinary() if err != nil { t.Fatalf("cannot serialize: %s", err) } newHeader := &ciphertextHeader{} err = newHeader.unmarshalBinary(headerSerialized) if err != nil { t.Fatalf("unmarshaling failed: %s", err) } recovered, err := decapsulate(newHeader, userKey) if err != nil { t.Fatalf("error decrypting message: %s", err) } if !recovered.IsEqual(shared) { t.Fatalf("decryption is incorrect") } }) } } func TestMarshalPublicParams(t *testing.T) { a, _, err := GenerateParams(rand.Reader) if err != nil { t.Fatal(err) } data, err := a.MarshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } b := &PublicParams{} err = b.UnmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(b) { t.Fatal("failure to roundtrip") } } func TestMarshalSecretParams(t *testing.T) { _, a, err := GenerateParams(rand.Reader) if err != nil { t.Fatal(err) } data, err := a.MarshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } b := &SecretParams{} err = b.UnmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(b) { t.Fatal("failure to roundtrip") } } func TestMarshalAttributesKey(t *testing.T) { _, sp, err := GenerateParams(rand.Reader) if err != nil { t.Fatal(err) } attrs := &Attributes{ "d": { wild: false, Value: ToScalar(4), }, "c": { wild: true, Value: ToScalar(3), }, "b": { wild: false, Value: ToScalar(2), }, "a": { wild: true, Value: ToScalar(2), }, } a, err := deriveAttributeKeys(rand.Reader, sp, attrs) if err != nil { t.Fatalf("error generating attribute keys: %s", err) } data, err := a.MarshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } b := &AttributesKey{} err = b.UnmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(b) { t.Fatal("failure to roundtrip") } // ensure we can deserialize into non-empty struct cAttrs := &Attributes{ "evil": { wild: false, Value: ToScalar(0), }, } c, err := deriveAttributeKeys(rand.Reader, sp, cAttrs) if err != nil { t.Fatalf("error generating attribute keys: %s", err) } err = c.UnmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize into non-empty struct: %s", err) } if !a.Equal(c) { t.Fatal("failure to roundtrip") } } func TestEqualAttributesKey(t *testing.T) { _, sp, err := GenerateParams(rand.Reader) if err != nil { t.Fatal(err) } attrs := &Attributes{ "d": { wild: false, Value: ToScalar(4), }, } a, err := deriveAttributeKeys(rand.Reader, sp, attrs) if err != nil { t.Fatalf("error generating attribute keys: %s", err) } _, sp2, err := GenerateParams(rand.Reader) if err != nil { t.Fatal(err) } attrs2 := &Attributes{ "k": { wild: false, Value: ToScalar(4), }, } b, err := deriveAttributeKeys(rand.Reader, sp2, attrs2) if err != nil { t.Fatalf("error generating attribute keys: %s", err) } if a.Equal(b) { t.Fatalf("shouldnt be equal") } // deep copy data, err := a.MarshalBinary() if err != nil { t.Fatalf("failure to serialize: %s", err) } c := &AttributesKey{} err = c.UnmarshalBinary(data) if err != nil { t.Fatalf("failure to deserialize: %s", err) } if !a.Equal(c) { t.Fatalf("failure to roundtrip") } for k, v := range a.k3 { c.k3[k], err = randomMatrixG1(rand.Reader, v.rows, v.cols) if err != nil { t.Fatal(err) } break } if a.Equal(c) { t.Fatalf("shouldnt be equal") } } golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/internal/tkn/util.go000066400000000000000000000043761454601126700261540ustar00rootroot00000000000000package tkn import ( "encoding/binary" "errors" "fmt" "sort" pairing "github.com/cloudflare/circl/ecc/bls12381" "golang.org/x/crypto/blake2b" ) var gtBaseVal *pairing.Gt func init() { // This should really be a constant, but what can I do? g1 := pairing.G1Generator() g2 := pairing.G2Generator() gtBaseVal = pairing.Pair(g1, g2) } func ToScalar(n int) *pairing.Scalar { ret := &pairing.Scalar{} ret.SetUint64(uint64(n)) return ret } func HashStringToScalar(key []byte, value string) *pairing.Scalar { xof, err := blake2b.NewXOF(blake2b.OutputLengthUnknown, key) if err != nil { return nil } _, err = xof.Write([]byte(value)) if err != nil { return nil } s := &pairing.Scalar{} err = s.Random(xof) if err != nil { return nil } return s } func appendLenPrefixed(a []byte, b []byte) []byte { a = append(a, 0, 0) binary.LittleEndian.PutUint16(a[len(a)-2:], uint16(len(b))) a = append(a, b...) return a } func removeLenPrefixed(data []byte) (next []byte, remainder []byte, err error) { if len(data) < 2 { return nil, nil, fmt.Errorf("data too short") } itemLen := int(binary.LittleEndian.Uint16(data)) if (2 + itemLen) > len(data) { return nil, nil, fmt.Errorf("data too short") } return data[2 : 2+itemLen], data[2+itemLen:], nil } func marshalBinarySortedMapMatrixG1(m map[string]*matrixG1) ([]byte, error) { sortedKeys := make([]string, 0, len(m)) for key := range m { sortedKeys = append(sortedKeys, key) } sort.Strings(sortedKeys) ret := []byte{} for _, key := range sortedKeys { b, err := m[key].marshalBinary() if err != nil { return nil, err } ret = appendLenPrefixed(ret, []byte(key)) ret = appendLenPrefixed(ret, b) } return ret, nil } func marshalBinarySortedMapAttribute(m map[string]Attribute) ([]byte, error) { sortedKeys := make([]string, 0, len(m)) for key := range m { sortedKeys = append(sortedKeys, key) } sort.Strings(sortedKeys) ret := []byte{} for _, key := range sortedKeys { a := m[key] b, err := a.marshalBinary() if err != nil { return nil, err } ret = appendLenPrefixed(ret, []byte(key)) ret = append(ret, b...) } return ret, nil } var ( errBadMatrixSize = errors.New("matrix inputs do not conform") errMatrixNonInvertible = errors.New("matrix has no inverse") ) golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/testdata/000077500000000000000000000000001454601126700240375ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/testdata/attributeKey000066400000000000000000000053441454601126700264440ustar00rootroot00000000000000EU>; EF3d^SQ9wJvcountryP&p:%)ܴONU ж'internal-boneh-katz-transform-attributeDY.qA˥Z̩_2}V*ec*>;6_\5Z}FGWsy-ʗєBH|+/5 }x-Glޡ1 F&+OTdDv*s;RB7h{ 7GU|YKC\lK9 Q,?134ڹv>![/2XߺszčQdnŭٌ)BA+T\ͷWld*d%mtIlzZjO49R1o8P%>'jg*E掏Ʈ@Z^}(|!nbbBpF{;6^f9,h&nFd 2^oE-w]}MQUvbKܐW[FN> \$RMeLŋSydˁu.F6PHaAJ49 ij){2nlB#$eŀ#mH \lH~iW\<+AAAd2s״{'pE*p!~UQyjgtT9 ǕjgeziWNW'%UaX@wl .En7ۻ,( v`W?jinW(Ę|S^qR:%>uP'4~$GB3h/,&5R *7VA+K4Y Xw?onHNCW*p5`8u0"x~Cپ'N2|WG+&NtPS󂶞srAH уīFE@tȞj26^v`:;^i.,n Ҽ[+[=!vEU 2^ATG ov iZВ"-Q%BcLf}j#:-̅ Ig 6pC LUdޮ Er daT>#A4.5s_T§?ͧen7$'^C4aH!4a˯'Uzck 8DpY?i*cmFu00Mm`kNp#eiǁQwt9 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N 9l \&kqDa~KlG1Uݑ9d;fF(>펶[\>=F iN GcnO88! golang-github-cloudflare-circl-1.3.7/abe/cpabe/tkn20/testdata/secretKey000066400000000000000000000021601454601126700257170ustar00rootroot00000000000000UW_:#z6 |"|f.f# 5~kNBc&AX4e\_+PG)&(;]DmI?/ A6 ,xdCw~*Ddl\roaoN4 ^WF*k^JƮ[i:!KTjdD~:NBJ:t9ZS'A>d?%G;`.)EnD:ƧrnKGp$Fސ­u1Vs85аA~V)O%UcGY(ʂS9f^ݯEqG@d*6P?2];Klz7+]0MFCE8w?: dImt:G%fzX;jJGƠY16/$lZ ׭o8?KP{I+DA0t(Pv"MD$/圶a:7"@̝\U+L;ib7)Xn͝R2Ԅ A{o@Jc'*LbV= 0 { return nil, VerifierState{}, common.ErrInvalidBlind } rInv := new(big.Int).ModInverse(r, v.pk.N) if rInv == nil { return nil, VerifierState{}, common.ErrInvalidBlind } return fixedBlind(message, salt, r, rInv, v.pk, v.hash) } // Verify verifies the input (message, signature) pair and produces an error upon failure. func (v deterministicBRSAVerifier) Verify(message, signature []byte) error { return common.VerifyMessageSignature(message, signature, 0, keys.NewBigPublicKey(v.pk), v.cryptoHash) } // Blind initializes the blind RSA protocol using an input message and source of randomness. The // signature includes a randomly generated PSS salt whose length equals the size of the underlying // hash function. This function fails if randomness was not provided. // // See the specification for more details: // https://www.rfc-editor.org/rfc/rfc9474.html#name-blind func (v randomBRSAVerifier) Blind(random io.Reader, message []byte) ([]byte, VerifierState, error) { if random == nil { return nil, VerifierState{}, common.ErrInvalidRandomness } salt := make([]byte, v.hash.Size()) _, err := io.ReadFull(random, salt) if err != nil { return nil, VerifierState{}, err } r, rInv, err := common.GenerateBlindingFactor(random, v.pk.N) if err != nil { return nil, VerifierState{}, err } return fixedBlind(message, salt, r, rInv, v.pk, v.hash) } // FixedBlind runs the Blind function with fixed blind and salt inputs. func (v randomBRSAVerifier) FixedBlind(message, blind, salt []byte) ([]byte, VerifierState, error) { if blind == nil { return nil, VerifierState{}, common.ErrInvalidRandomness } r := new(big.Int).SetBytes(blind) if r.Cmp(v.pk.N) >= 0 { return nil, VerifierState{}, common.ErrInvalidBlind } rInv := new(big.Int).ModInverse(r, v.pk.N) if rInv == nil { return nil, VerifierState{}, common.ErrInvalidBlind } return fixedBlind(message, salt, r, rInv, v.pk, v.hash) } // Verify verifies the input (message, signature) pair and produces an error upon failure. func (v randomBRSAVerifier) Verify(message, signature []byte) error { return common.VerifyMessageSignature(message, signature, v.hash.Size(), keys.NewBigPublicKey(v.pk), v.cryptoHash) } // An VerifierState carries state needed to complete the blind signature protocol // as a verifier. type VerifierState struct { // Public key of the Signer pk *rsa.PublicKey // Hash function used in producing the message signature hash hash.Hash // The hashed and encoded message being signed encodedMsg []byte // The salt used when encoding the message salt []byte // Inverse of the blinding factor produced by the Verifier rInv *big.Int } // Finalize computes and outputs the final signature, if it's valid. Otherwise, it returns an error. // // See the specification for more details: // https://www.rfc-editor.org/rfc/rfc9474.html#name-finalize func (state VerifierState) Finalize(data []byte) ([]byte, error) { kLen := (state.pk.N.BitLen() + 7) / 8 if len(data) != kLen { return nil, common.ErrUnexpectedSize } z := new(big.Int).SetBytes(data) s := new(big.Int).Set(state.rInv) s.Mul(s, z) s.Mod(s, state.pk.N) sig := make([]byte, kLen) s.FillBytes(sig) err := common.VerifyBlindSignature(keys.NewBigPublicKey(state.pk), state.encodedMsg, sig) if err != nil { return nil, err } return sig, nil } // CopyBlind returns an encoding of the blind value used in the protocol. func (state VerifierState) CopyBlind() []byte { r := new(big.Int).ModInverse(state.rInv, state.pk.N) return r.Bytes() } // CopySalt returns an encoding of the per-message salt used in the protocol. func (state VerifierState) CopySalt() []byte { salt := make([]byte, len(state.salt)) copy(salt, state.salt) return salt } // An Signer represents the Signer in the blind RSA protocol. // It carries the raw RSA private key used for signing blinded messages. type Signer struct { // An RSA private key sk *rsa.PrivateKey } // NewSigner creates a new Signer for the blind RSA protocol using an RSA private key. func NewSigner(sk *rsa.PrivateKey) Signer { return Signer{ sk: sk, } } // BlindSign blindly computes the RSA operation using the Signer's private key on the blinded // message input, if it's of valid length, and returns an error should the function fail. // // See the specification for more details: // https://www.rfc-editor.org/rfc/rfc9474.html#name-blindsign func (signer Signer) BlindSign(data []byte) ([]byte, error) { kLen := (signer.sk.N.BitLen() + 7) / 8 if len(data) != kLen { return nil, common.ErrUnexpectedSize } m := new(big.Int).SetBytes(data) if m.Cmp(signer.sk.N) > 0 { return nil, common.ErrInvalidMessageLength } s, err := common.DecryptAndCheck(rand.Reader, keys.NewBigPrivateKey(signer.sk), m) if err != nil { return nil, err } blindSig := make([]byte, kLen) s.FillBytes(blindSig) return blindSig, nil } var ( ErrUnexpectedSize = common.ErrUnexpectedSize ErrInvalidMessageLength = common.ErrInvalidMessageLength ErrInvalidBlind = common.ErrInvalidBlind ErrInvalidRandomness = common.ErrInvalidRandomness ErrUnsupportedHashFunction = common.ErrUnsupportedHashFunction ) golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/brsa_test.go000066400000000000000000000354641454601126700255670ustar00rootroot00000000000000package blindrsa import ( "bytes" "crypto" "crypto/rand" "crypto/rsa" "crypto/x509" "encoding/hex" "encoding/json" "encoding/pem" "fmt" "io" "math/big" "os" "strings" "testing" "github.com/cloudflare/circl/internal/test" ) // 2048-bit RSA private key const testPrivateKey = ` -----BEGIN RSA PRIVATE KEY----- MIIEowIBAAKCAQEAyxrta2qV9bHOATpM/KsluUsuZKIwNOQlCn6rQ8DfOowSmTrx KxEZCNS0cb7DHUtsmtnN2pBhKi7pA1I+beWiJNawLwnlw3TQz+Adj1KcUAp4ovZ5 CPpoK1orQwyB6vGvcte155T8mKMTknaHl1fORTtSbvm/bOuZl5uEI7kPRGGiKvN6 qwz1cz91l6vkTTHHMttooYHGy75gfYwOUuBlX9mZbcWE7KC+h6+814ozfRex26no KLvYHikTFxROf/ifVWGXCbCWy7nqR0zq0mTCBz/kl0DAHwDhCRBgZpg9IeX4Pwhu LoI8h5zUPO9wDSo1Kpur1hLQPK0C2xNLfiJaXwIDAQABAoIBAC8wm3c4tYz3efDJ Ffgi38n0kNvq3x5636xXj/1XA8a7otqdWklyWIm3uhEvjG/zBVHZRz4AC8NcUOFn q3+nOgwrIZZcS1klfBrAbL3PKOhj9nGOqMKQQ8HG2oRilJD9BJG/UtFyyVnBkhuW lJxyV0e4p8eHGZX6C56xEHuoVMbDKm9HR8XRwwTHRn1VsICqIzo6Uv/fJhFMu1Qf +mtpa3oJb43P9pygirWO+w+3U6pRhccwAWlrvOjAmeP0Ndy7/gXn26rSPbKmWcI6 3VIUB/FQsa8tkFTEFkIp1oQLejKk+EgUk66JWc8K6o3vDDyfdbmjTHVxi3ByyNur F87+ykkCgYEA73MLD1FLwPWdmV/V+ZiMTEwTXRBc1W1D7iigNclp9VDAzXFI6ofs 3v+5N8hcZIdEBd9W6utHi/dBiEogDuSjljPRCqPsQENm2itTHzmNRvvI8wV1KQbP eJOd0vPMl5iup8nYL+9ASfGYeX5FKlttKEm4ZIY0XUsx9pERoq4PlEsCgYEA2STJ 68thMWv9xKuz26LMQDzImJ5OSQD0hsts9Ge01G/rh0Dv/sTzO5wtLsiyDA/ZWkzB 8J+rO/y2xqBD9VkYKaGB/wdeJP0Z+n7sETetiKPbXPfgAi7VAe77Rmst/oEcGLUg tm+XnfJSInoLU5HmtIdLg0kcQLVbN5+ZMmtkPb0CgYBSbhczmbfrYGJ1p0FBIFvD 9DiCRBzBOFE3TnMAsSqx0a/dyY7hdhN8HSqE4ouz68DmCKGiU4aYz3CW23W3ysvp 7EKdWBr/cHSazGlcCXLyKcFer9VKX1bS2nZtZZJb6arOhjTPI5zNF8d2o5pp33lv chlxOaYTK8yyZfRdPXCNiwKBgQDV77oFV66dm7E9aJHerkmgbIKSYz3sDUXd3GSv c9Gkj9Q0wNTzZKXkMB4P/un0mlTh88gMQ7PYeUa28UWjX7E/qwFB+8dUmA1VUGFT IVEW06GXuhv46p0wt3zXx1dcbWX6LdJaDB4MHqevkiDAqHntmXLbmVd9pXCGn/a2 xznO3QKBgHkPJPEiCzRugzgN9UxOT5tNQCSGMOwJUd7qP0TWgvsWHT1N07JLgC8c Yg0f1rCxEAQo5BVppiQFp0FA7W52DUnMEfBtiehZ6xArW7crO91gFRqKBWZ3Jjyz /JcS8m5UgQxC8mmb/2wLD5TDvWw+XCfjUgWmvqIi5dcJgmuTAn5X -----END RSA PRIVATE KEY-----` func loadPrivateKey() (*rsa.PrivateKey, error) { block, _ := pem.Decode([]byte(testPrivateKey)) if block == nil || block.Type != "RSA PRIVATE KEY" { return nil, fmt.Errorf("PEM private key decoding failed") } privateKey, err := x509.ParsePKCS1PrivateKey(block.Bytes) if err != nil { return nil, err } return privateKey, nil } func mustDecodeHex(h string) []byte { b, err := hex.DecodeString(h) if err != nil { panic(err) } return b } func loadStrongRSAKey() *rsa.PrivateKey { // https://gist.github.com/chris-wood/b77536febb25a5a11af428afff77820a pEnc := "dcd90af1be463632c0d5ea555256a20605af3db667475e190e3af12a34a3324c46a3094062c59fb4b249e0ee6afba8bee14e0276d126c99f4784b23009bf6168ff628ac1486e5ae8e23ce4d362889de4df63109cbd90ef93db5ae64372bfe1c55f832766f21e94ea3322eb2182f10a891546536ba907ad74b8d72469bea396f3" qEnc := "f8ba5c89bd068f57234a3cf54a1c89d5b4cd0194f2633ca7c60b91a795a56fa8c8686c0e37b1c4498b851e3420d08bea29f71d195cfbd3671c6ddc49cf4c1db5b478231ea9d91377ffa98fe95685fca20ba4623212b2f2def4da5b281ed0100b651f6db32112e4017d831c0da668768afa7141d45bbc279f1e0f8735d74395b3" NEnc := "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" eEnc := "010001" dEnc := "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" p := new(big.Int).SetBytes(mustDecodeHex(pEnc)) q := new(big.Int).SetBytes(mustDecodeHex(qEnc)) N := new(big.Int).SetBytes(mustDecodeHex(NEnc)) e := new(big.Int).SetBytes(mustDecodeHex(eEnc)) d := new(big.Int).SetBytes(mustDecodeHex(dEnc)) primes := make([]*big.Int, 2) primes[0] = p primes[1] = q key := &rsa.PrivateKey{ PublicKey: rsa.PublicKey{ N: N, E: int(e.Int64()), }, D: d, Primes: primes, } return key } func runSignatureProtocol(signer Signer, verifier Verifier, message []byte, random io.Reader) ([]byte, error) { blindedMsg, state, err := verifier.Blind(random, message) if err != nil { return nil, err } kLen := (signer.sk.N.BitLen() + 7) / 8 if len(blindedMsg) != kLen { return nil, fmt.Errorf("Protocol message (blind message) length mismatch, expected %d, got %d", kLen, len(blindedMsg)) } blindedSig, err := signer.BlindSign(blindedMsg) if err != nil { return nil, err } if len(blindedSig) != kLen { return nil, fmt.Errorf("Protocol message (blind signature) length mismatch, expected %d, got %d", kLen, len(blindedMsg)) } sig, err := state.Finalize(blindedSig) if err != nil { return nil, err } err = verifier.Verify(message, sig) if err != nil { return nil, err } return sig, nil } func TestRoundTrip(t *testing.T) { message := []byte("hello world") key, err := loadPrivateKey() if err != nil { t.Fatal(err) } verifier := NewVerifier(&key.PublicKey, crypto.SHA512) signer := NewSigner(key) sig, err := runSignatureProtocol(signer, verifier, message, rand.Reader) if err != nil { t.Fatal(err) } if sig == nil { t.Fatal("nil signature output") } } func TestDeterministicRoundTrip(t *testing.T) { message := []byte("hello world") key, err := loadPrivateKey() if err != nil { t.Fatal(err) } verifier := NewDeterministicVerifier(&key.PublicKey, crypto.SHA512) signer := NewSigner(key) sig, err := runSignatureProtocol(signer, verifier, message, rand.Reader) if err != nil { t.Fatal(err) } if sig == nil { t.Fatal("nil signature output") } } func TestDeterministicBlindFailure(t *testing.T) { message := []byte("hello world") key, err := loadPrivateKey() if err != nil { t.Fatal(err) } verifier := NewDeterministicVerifier(&key.PublicKey, crypto.SHA512) signer := NewSigner(key) _, err = runSignatureProtocol(signer, verifier, message, nil) if err == nil { t.Fatal("Expected signature generation to fail with empty randomness") } } func TestRandomSignVerify(t *testing.T) { message := []byte("hello world") key, err := loadPrivateKey() if err != nil { t.Fatal(err) } verifier := NewVerifier(&key.PublicKey, crypto.SHA512) signer := NewSigner(key) sig1, err := runSignatureProtocol(signer, verifier, message, rand.Reader) if err != nil { t.Fatal(err) } sig2, err := runSignatureProtocol(signer, verifier, message, rand.Reader) if err != nil { t.Fatal(err) } if sig1 == nil || sig2 == nil { t.Fatal("nil signature output") } if bytes.Equal(sig1, sig2) { t.Fatal("random signatures matched when they should differ") } } type mockRandom struct { counter uint8 } func (r *mockRandom) Read(p []byte) (n int, err error) { for i := range p { p[i] = r.counter r.counter = r.counter + 1 } return len(p), nil } func TestFixedRandomSignVerify(t *testing.T) { message := []byte("hello world") key, err := loadPrivateKey() if err != nil { t.Fatal(err) } verifier := NewVerifier(&key.PublicKey, crypto.SHA512) signer := NewSigner(key) mockRand := &mockRandom{0} sig1, err := runSignatureProtocol(signer, verifier, message, mockRand) if err != nil { t.Fatal(err) } mockRand = &mockRandom{0} sig2, err := runSignatureProtocol(signer, verifier, message, mockRand) if err != nil { t.Fatal(err) } if sig1 == nil || sig2 == nil { t.Fatal("nil signature output") } if !bytes.Equal(sig1, sig2) { t.Fatal("random signatures with fixed random seeds differ when they should be equal") } } type rawTestVector struct { Name string `json:"name"` P string `json:"p"` Q string `json:"q"` N string `json:"n"` E string `json:"e"` D string `json:"d"` Msg string `json:"msg"` MsgPrefix string `json:"msg_prefix"` InputMsg string `json:"input_msg"` Salt string `json:"salt"` SaltLen string `json:"sLen"` IsRandomized string `json:"is_randomized"` Inv string `json:"inv"` BlindedMessage string `json:"blinded_msg"` BlindSig string `json:"blind_sig"` Sig string `json:"sig"` } type testVector struct { t *testing.T name string p *big.Int q *big.Int n *big.Int e int d *big.Int msg []byte msgPrefix []byte inputMsg []byte salt []byte saltLen int isRandomized bool blindInverse *big.Int blindedMessage []byte blindSig []byte sig []byte } type testVectorList struct { t *testing.T vectors []testVector } func mustUnhexBigInt(number string) *big.Int { data := mustUnhex(number) value := new(big.Int) value.SetBytes(data) return value } func mustUnhex(value string) []byte { value = strings.TrimPrefix(value, "0x") data, err := hex.DecodeString(value) if err != nil { panic(err) } return data } func mustUnhexInt(value string) int { number := mustUnhexBigInt(value) result := int(number.Int64()) return result } func (tv *testVector) UnmarshalJSON(data []byte) error { raw := rawTestVector{} err := json.Unmarshal(data, &raw) if err != nil { return err } tv.name = raw.Name tv.p = mustUnhexBigInt(raw.P) tv.q = mustUnhexBigInt(raw.Q) tv.n = mustUnhexBigInt(raw.N) tv.e = mustUnhexInt(raw.E) tv.d = mustUnhexBigInt(raw.D) tv.msg = mustUnhex(raw.Msg) tv.msgPrefix = mustUnhex(raw.MsgPrefix) tv.inputMsg = mustUnhex(raw.InputMsg) tv.salt = mustUnhex(raw.Salt) tv.saltLen = mustUnhexInt(raw.SaltLen) tv.isRandomized = mustUnhexInt(raw.IsRandomized) != 0 tv.blindedMessage = mustUnhex(raw.BlindedMessage) tv.blindInverse = mustUnhexBigInt(raw.Inv) tv.blindSig = mustUnhex(raw.BlindSig) tv.sig = mustUnhex(raw.Sig) return nil } func (tvl testVectorList) MarshalJSON() ([]byte, error) { return json.Marshal(tvl.vectors) } func (tvl *testVectorList) UnmarshalJSON(data []byte) error { err := json.Unmarshal(data, &tvl.vectors) if err != nil { return err } for i := range tvl.vectors { tvl.vectors[i].t = tvl.t } return nil } func verifyTestVector(t *testing.T, vector testVector) { key := new(rsa.PrivateKey) key.PublicKey.N = vector.n key.PublicKey.E = vector.e key.D = vector.d key.Primes = []*big.Int{vector.p, vector.q} key.Precomputed.Dp = nil // Remove precomputed CRT values // Recompute the original blind rInv := new(big.Int).Set(vector.blindInverse) r := new(big.Int).ModInverse(rInv, key.N) if r == nil { t.Fatal("Failed to compute blind inverse") } signer := NewSigner(key) var verifier Verifier switch vector.name { case "RSABSSA-SHA384-PSS-Deterministic": verifier = NewVerifier(&key.PublicKey, crypto.SHA384) case "RSABSSA-SHA384-PSSZERO-Deterministic": verifier = NewDeterministicVerifier(&key.PublicKey, crypto.SHA384) case "RSABSSA-SHA384-PSS-Randomized", "RSABSSA-SHA384-PSSZERO-Randomized": t.Skipf("variant %v not supported yet", vector.name) default: t.Fatal("variant not supported") } inputMsg := prepareMsg(vector.msg, vector.msgPrefix) got := hex.EncodeToString(inputMsg) want := hex.EncodeToString(vector.inputMsg) if got != want { test.ReportError(t, got, want) } blindedMsg, state, err := fixedBlind(inputMsg, vector.salt, r, rInv, &key.PublicKey, verifier.Hash()) test.CheckNoErr(t, err, "fixedBlind failed") got = hex.EncodeToString(blindedMsg) want = hex.EncodeToString(vector.blindedMessage) if got != want { test.ReportError(t, got, want) } blindSig, err := signer.BlindSign(blindedMsg) test.CheckNoErr(t, err, "blindSign failed") got = hex.EncodeToString(blindSig) want = hex.EncodeToString(vector.blindSig) if got != want { test.ReportError(t, got, want) } sig, err := state.Finalize(blindSig) test.CheckNoErr(t, err, "finalize failed") got = hex.EncodeToString(sig) want = hex.EncodeToString(vector.sig) if got != want { test.ReportError(t, got, want) } err = verifier.Verify(inputMsg, sig) test.CheckNoErr(t, err, "verification failed") } func TestVectors(t *testing.T) { data, err := os.ReadFile("testdata/test_vectors_rfc9474.json") if err != nil { t.Fatal("Failed reading test vectors:", err) } tvl := &testVectorList{} err = tvl.UnmarshalJSON(data) if err != nil { t.Fatal("Failed deserializing test vectors:", err) } for _, vector := range tvl.vectors { t.Run(vector.name, func(tt *testing.T) { verifyTestVector(tt, vector) }) } } func BenchmarkBRSA(b *testing.B) { message := []byte("hello world") key := loadStrongRSAKey() verifier := NewVerifier(&key.PublicKey, crypto.SHA512) signer := NewSigner(key) var err error var blindedMsg []byte var state VerifierState b.Run("Blind", func(b *testing.B) { for n := 0; n < b.N; n++ { blindedMsg, state, err = verifier.Blind(rand.Reader, message) if err != nil { b.Fatal(err) } } }) var blindedSig []byte b.Run("BlindSign", func(b *testing.B) { for n := 0; n < b.N; n++ { blindedSig, err = signer.BlindSign(blindedMsg) if err != nil { b.Fatal(err) } } }) var sig []byte b.Run("Finalize", func(b *testing.B) { for n := 0; n < b.N; n++ { sig, err = state.Finalize(blindedSig) if err != nil { b.Fatal(err) } } }) err = verifier.Verify(message, sig) if err != nil { b.Fatal(err) } } func Example_blindrsa() { // Setup (offline) // Server: generate an RSA keypair. sk, err := rsa.GenerateKey(rand.Reader, 2048) if err != nil { fmt.Fprintf(os.Stderr, "failed to generate RSA key: %v", err) return } pk := &sk.PublicKey server := NewSigner(sk) // Client: stores Server's public key. verifier := NewVerifier(pk, crypto.SHA384) // Protocol (online) // Client blinds a message. msg := []byte("alice and bob") blindedMsg, state, err := verifier.Blind(rand.Reader, msg) if err != nil { fmt.Fprintf(os.Stderr, "client failed to generate blinded message: %v", err) return } // Server signs a blinded message, and produces a blinded signature. blindedSignature, err := server.BlindSign(blindedMsg) if err != nil { fmt.Fprintf(os.Stderr, "server failed to sign: %v", err) return } // Client builds a signature from the previous state and the blinded signature. signature, err := state.Finalize(blindedSignature) if err != nil { fmt.Fprintf(os.Stderr, "client failed to obtain signature: %v", err) return } // Client verifies the signature is valid. ok := verifier.Verify(msg, signature) fmt.Printf("Valid signature: %v", ok == nil) // Output: Valid signature: true } golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/internal/000077500000000000000000000000001454601126700250525ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/internal/common/000077500000000000000000000000001454601126700263425ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/internal/common/common.go000066400000000000000000000104731454601126700301660ustar00rootroot00000000000000package common import ( "crypto" "crypto/rand" "crypto/rsa" "crypto/sha256" "crypto/sha512" "crypto/subtle" "errors" "hash" "io" "math/big" "github.com/cloudflare/circl/blindsign/blindrsa/internal/keys" ) // ConvertHashFunction converts a crypto.Hash function to an equivalent hash.Hash type. func ConvertHashFunction(hash crypto.Hash) hash.Hash { switch hash { case crypto.SHA256: return sha256.New() case crypto.SHA384: return sha512.New384() case crypto.SHA512: return sha512.New() default: panic(ErrUnsupportedHashFunction) } } // EncodeMessageEMSAPSS hashes the input message and then encodes it using PSS encoding. func EncodeMessageEMSAPSS(message []byte, N *big.Int, hash hash.Hash, salt []byte) ([]byte, error) { hash.Reset() // Ensure the hash state is cleared hash.Write(message) digest := hash.Sum(nil) hash.Reset() emBits := N.BitLen() - 1 encodedMsg, err := emsaPSSEncode(digest[:], emBits, salt, hash) return encodedMsg, err } // GenerateBlindingFactor generates a blinding factor and its multiplicative inverse // to use for RSA blinding. func GenerateBlindingFactor(random io.Reader, N *big.Int) (*big.Int, *big.Int, error) { randReader := random if randReader == nil { randReader = rand.Reader } r, err := rand.Int(randReader, N) if err != nil { return nil, nil, err } if r.Sign() == 0 { r.SetInt64(1) } rInv := new(big.Int).ModInverse(r, N) if rInv == nil { return nil, nil, ErrInvalidBlind } return r, rInv, nil } // VerifyMessageSignature verifies the input message signature against the expected public key func VerifyMessageSignature(message, signature []byte, saltLength int, pk *keys.BigPublicKey, hash crypto.Hash) error { h := ConvertHashFunction(hash) h.Write(message) digest := h.Sum(nil) err := verifyPSS(pk, hash, digest, signature, &rsa.PSSOptions{ Hash: hash, SaltLength: saltLength, }) return err } // DecryptAndCheck checks that the private key operation is consistent (fault attack detection). func DecryptAndCheck(random io.Reader, priv *keys.BigPrivateKey, c *big.Int) (m *big.Int, err error) { m, err = decrypt(random, priv, c) if err != nil { return nil, err } // In order to defend against errors in the CRT computation, m^e is // calculated, which should match the original ciphertext. check := encrypt(new(big.Int), priv.Pk.N, priv.Pk.E, m) if c.Cmp(check) != 0 { return nil, errors.New("rsa: internal error") } return m, nil } // VerifyBlindSignature verifies the signature of the hashed and encoded message against the input public key. func VerifyBlindSignature(pub *keys.BigPublicKey, hashed, sig []byte) error { m := new(big.Int).SetBytes(hashed) bigSig := new(big.Int).SetBytes(sig) c := encrypt(new(big.Int), pub.N, pub.E, bigSig) if subtle.ConstantTimeCompare(m.Bytes(), c.Bytes()) == 1 { return nil } else { return rsa.ErrVerification } } func saltLength(opts *rsa.PSSOptions) int { if opts == nil { return rsa.PSSSaltLengthAuto } return opts.SaltLength } func verifyPSS(pub *keys.BigPublicKey, hash crypto.Hash, digest []byte, sig []byte, opts *rsa.PSSOptions) error { if len(sig) != pub.Size() { return rsa.ErrVerification } s := new(big.Int).SetBytes(sig) m := encrypt(new(big.Int), pub.N, pub.E, s) emBits := pub.N.BitLen() - 1 emLen := (emBits + 7) / 8 if m.BitLen() > emLen*8 { return rsa.ErrVerification } em := m.FillBytes(make([]byte, emLen)) return emsaPSSVerify(digest, em, emBits, saltLength(opts), hash.New()) } var ( // ErrUnexpectedSize is the error used if the size of a parameter does not match its expected value. ErrUnexpectedSize = errors.New("blindsign/blindrsa: unexpected input size") // ErrInvalidMessageLength is the error used if the size of a protocol message does not match its expected value. ErrInvalidMessageLength = errors.New("blindsign/blindrsa: invalid message length") // ErrInvalidBlind is the error used if the blind generated by the Verifier fails. ErrInvalidBlind = errors.New("blindsign/blindrsa: invalid blind") // ErrInvalidRandomness is the error used if caller did not provide randomness to the Blind() function. ErrInvalidRandomness = errors.New("blindsign/blindrsa: invalid random parameter") // ErrUnsupportedHashFunction is the error used if the specified hash is not supported. ErrUnsupportedHashFunction = errors.New("blindsign/blindrsa: unsupported hash function") ) golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/internal/common/pss.go000066400000000000000000000152561454601126700275070ustar00rootroot00000000000000// Copyright (c) 2009 The Go Authors. All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following disclaimer // in the documentation and/or other materials provided with the // distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived from // this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. package common // Copyright 2013 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // This file implements the RSASSA-PSS signature scheme according to RFC 8017. import ( "bytes" "crypto/rsa" "errors" "hash" ) // Per RFC 8017, Section 9.1 // // EM = MGF1 xor DB || H( 8*0x00 || mHash || salt ) || 0xbc // // where // // DB = PS || 0x01 || salt // // and PS can be empty so // // emLen = dbLen + hLen + 1 = psLen + sLen + hLen + 2 // func emsaPSSEncode(mHash []byte, emBits int, salt []byte, hash hash.Hash) ([]byte, error) { // See RFC 8017, Section 9.1.1. hLen := hash.Size() sLen := len(salt) emLen := (emBits + 7) / 8 // 1. If the length of M is greater than the input limitation for the // hash function (2^61 - 1 octets for SHA-1), output "message too // long" and stop. // // 2. Let mHash = Hash(M), an octet string of length hLen. if len(mHash) != hLen { return nil, errors.New("crypto/rsa: input must be hashed with given hash") } // 3. If emLen < hLen + sLen + 2, output "encoding error" and stop. if emLen < hLen+sLen+2 { return nil, errors.New("crypto/rsa: key size too small for PSS signature") } em := make([]byte, emLen) psLen := emLen - sLen - hLen - 2 db := em[:psLen+1+sLen] h := em[psLen+1+sLen : emLen-1] // 4. Generate a random octet string salt of length sLen; if sLen = 0, // then salt is the empty string. // // 5. Let // M' = (0x)00 00 00 00 00 00 00 00 || mHash || salt; // // M' is an octet string of length 8 + hLen + sLen with eight // initial zero octets. // // 6. Let H = Hash(M'), an octet string of length hLen. var prefix [8]byte hash.Write(prefix[:]) hash.Write(mHash) hash.Write(salt) h = hash.Sum(h[:0]) hash.Reset() // 7. Generate an octet string PS consisting of emLen - sLen - hLen - 2 // zero octets. The length of PS may be 0. // // 8. Let DB = PS || 0x01 || salt; DB is an octet string of length // emLen - hLen - 1. db[psLen] = 0x01 copy(db[psLen+1:], salt) // 9. Let dbMask = MGF(H, emLen - hLen - 1). // // 10. Let maskedDB = DB \xor dbMask. mgf1XOR(db, hash, h) // 11. Set the leftmost 8 * emLen - emBits bits of the leftmost octet in // maskedDB to zero. db[0] &= 0xff >> (8*emLen - emBits) // 12. Let EM = maskedDB || H || 0xbc. em[emLen-1] = 0xbc // 13. Output EM. return em, nil } func emsaPSSVerify(mHash, em []byte, emBits, sLen int, hash hash.Hash) error { // See RFC 8017, Section 9.1.2. hLen := hash.Size() if sLen == rsa.PSSSaltLengthEqualsHash { sLen = hLen } emLen := (emBits + 7) / 8 if emLen != len(em) { return errors.New("rsa: internal error: inconsistent length") } // 1. If the length of M is greater than the input limitation for the // hash function (2^61 - 1 octets for SHA-1), output "inconsistent" // and stop. // // 2. Let mHash = Hash(M), an octet string of length hLen. if hLen != len(mHash) { return rsa.ErrVerification } // 3. If emLen < hLen + sLen + 2, output "inconsistent" and stop. if emLen < hLen+sLen+2 { return rsa.ErrVerification } // 4. If the rightmost octet of EM does not have hexadecimal value // 0xbc, output "inconsistent" and stop. if em[emLen-1] != 0xbc { return rsa.ErrVerification } // 5. Let maskedDB be the leftmost emLen - hLen - 1 octets of EM, and // let H be the next hLen octets. db := em[:emLen-hLen-1] h := em[emLen-hLen-1 : emLen-1] // 6. If the leftmost 8 * emLen - emBits bits of the leftmost octet in // maskedDB are not all equal to zero, output "inconsistent" and // stop. var bitMask byte = 0xff >> (8*emLen - emBits) if em[0] & ^bitMask != 0 { return rsa.ErrVerification } // 7. Let dbMask = MGF(H, emLen - hLen - 1). // // 8. Let DB = maskedDB \xor dbMask. mgf1XOR(db, hash, h) // 9. Set the leftmost 8 * emLen - emBits bits of the leftmost octet in DB // to zero. db[0] &= bitMask // If we don't know the salt length, look for the 0x01 delimiter. if sLen == rsa.PSSSaltLengthAuto { psLen := bytes.IndexByte(db, 0x01) if psLen < 0 { return rsa.ErrVerification } sLen = len(db) - psLen - 1 } // 10. If the emLen - hLen - sLen - 2 leftmost octets of DB are not zero // or if the octet at position emLen - hLen - sLen - 1 (the leftmost // position is "position 1") does not have hexadecimal value 0x01, // output "inconsistent" and stop. psLen := emLen - hLen - sLen - 2 for _, e := range db[:psLen] { if e != 0x00 { return rsa.ErrVerification } } if db[psLen] != 0x01 { return rsa.ErrVerification } // 11. Let salt be the last sLen octets of DB. salt := db[len(db)-sLen:] // 12. Let // M' = (0x)00 00 00 00 00 00 00 00 || mHash || salt ; // M' is an octet string of length 8 + hLen + sLen with eight // initial zero octets. // // 13. Let H' = Hash(M'), an octet string of length hLen. var prefix [8]byte hash.Write(prefix[:]) hash.Write(mHash) hash.Write(salt) h0 := hash.Sum(nil) // 14. If H = H', output "consistent." Otherwise, output "inconsistent." if !bytes.Equal(h0, h) { // TODO: constant time? return rsa.ErrVerification } return nil } golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/internal/common/rsa.go000066400000000000000000000072611454601126700274640ustar00rootroot00000000000000// Copyright (c) 2009 The Go Authors. All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following disclaimer // in the documentation and/or other materials provided with the // distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived from // this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. package common import ( "crypto/rand" "crypto/rsa" "hash" "io" "math/big" "github.com/cloudflare/circl/blindsign/blindrsa/internal/keys" ) var ( bigZero = big.NewInt(0) bigOne = big.NewInt(1) ) // incCounter increments a four byte, big-endian counter. func incCounter(c *[4]byte) { if c[3]++; c[3] != 0 { return } if c[2]++; c[2] != 0 { return } if c[1]++; c[1] != 0 { return } c[0]++ } // mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function // specified in PKCS #1 v2.1. func mgf1XOR(out []byte, hash hash.Hash, seed []byte) { var counter [4]byte var digest []byte done := 0 for done < len(out) { hash.Write(seed) hash.Write(counter[0:4]) digest = hash.Sum(digest[:0]) hash.Reset() for i := 0; i < len(digest) && done < len(out); i++ { out[done] ^= digest[i] done++ } incCounter(&counter) } } func encrypt(c *big.Int, N *big.Int, e *big.Int, m *big.Int) *big.Int { c.Exp(m, e, N) return c } // decrypt performs an RSA decryption, resulting in a plaintext integer. If a // random source is given, RSA blinding is used. func decrypt(random io.Reader, priv *keys.BigPrivateKey, c *big.Int) (m *big.Int, err error) { // TODO(agl): can we get away with reusing blinds? if c.Cmp(priv.Pk.N) > 0 { err = rsa.ErrDecryption return } if priv.Pk.N.Sign() == 0 { return nil, rsa.ErrDecryption } var ir *big.Int if random != nil { // Blinding enabled. Blinding involves multiplying c by r^e. // Then the decryption operation performs (m^e * r^e)^d mod n // which equals mr mod n. The factor of r can then be removed // by multiplying by the multiplicative inverse of r. var r *big.Int ir = new(big.Int) for { r, err = rand.Int(random, priv.Pk.N) if err != nil { return } if r.Cmp(bigZero) == 0 { r = bigOne } ok := ir.ModInverse(r, priv.Pk.N) if ok != nil { break } } rpowe := new(big.Int).Exp(r, priv.Pk.E, priv.Pk.N) // N != 0 cCopy := new(big.Int).Set(c) cCopy.Mul(cCopy, rpowe) cCopy.Mod(cCopy, priv.Pk.N) c = cCopy } m = new(big.Int).Exp(c, priv.D, priv.Pk.N) if ir != nil { // Unblind. m.Mul(m, ir) m.Mod(m, priv.Pk.N) } return m, nil } golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/internal/keys/000077500000000000000000000000001454601126700260255ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/internal/keys/big_keys.go000066400000000000000000000025501454601126700301520ustar00rootroot00000000000000package keys import ( "crypto/rsa" "math/big" ) // BigPublicKey is the same as an rsa.PublicKey struct, except the public // key is represented as a big integer as opposed to an int. For the partially // blind scheme, this is required since the public key will typically be // any value in the RSA group. type BigPublicKey struct { N *big.Int E *big.Int } // Size returns the size of the public key. func (pub *BigPublicKey) Size() int { return (pub.N.BitLen() + 7) / 8 } // Marshal encodes the public key exponent (e). func (pub *BigPublicKey) Marshal() []byte { buf := make([]byte, (pub.E.BitLen()+7)/8) pub.E.FillBytes(buf) return buf } // NewBigPublicKey creates a BigPublicKey from a rsa.PublicKey. func NewBigPublicKey(pk *rsa.PublicKey) *BigPublicKey { return &BigPublicKey{ N: pk.N, E: new(big.Int).SetInt64(int64(pk.E)), } } // CustomPublicKey is similar to rsa.PrivateKey, containing information needed // for a private key used in the partially blind signature protocol. type BigPrivateKey struct { Pk *BigPublicKey D *big.Int P *big.Int Q *big.Int } // NewBigPrivateKey creates a BigPrivateKey from a rsa.PrivateKey. func NewBigPrivateKey(sk *rsa.PrivateKey) *BigPrivateKey { return &BigPrivateKey{ Pk: &BigPublicKey{ N: sk.N, E: new(big.Int).SetInt64(int64(sk.PublicKey.E)), }, D: sk.D, P: sk.Primes[0], Q: sk.Primes[1], } } golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/partiallyblindrsa/000077500000000000000000000000001454601126700267565ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/partiallyblindrsa/pbrsa.go000066400000000000000000000260341454601126700304210ustar00rootroot00000000000000// Package partiallyblindrsa implements a partially blind RSA protocol. package partiallyblindrsa import ( "crypto" "crypto/rand" "crypto/rsa" "encoding/binary" "errors" "hash" "io" "math/big" "github.com/cloudflare/circl/blindsign/blindrsa/internal/common" "github.com/cloudflare/circl/blindsign/blindrsa/internal/keys" "golang.org/x/crypto/hkdf" ) func encodeMessageMetadata(message, metadata []byte) []byte { lenBuffer := []byte{'m', 's', 'g', 0, 0, 0, 0} binary.BigEndian.PutUint32(lenBuffer[3:], uint32(len(metadata))) framedMetadata := append(lenBuffer, metadata...) return append(framedMetadata, message...) } // A randomizedVerifier represents a Verifier in the partially blind RSA signature protocol. // It carries state needed to produce and validate an RSA signature produced // using the blind RSA protocol. type randomizedVerifier struct { // Public key of the Signer pk *keys.BigPublicKey // Identifier of the cryptographic hash function used in producing the message signature cryptoHash crypto.Hash // Hash function used in producing the message signature hash hash.Hash } // NewVerifier creates a new PBRSAVerifier using the corresponding Signer parameters. // This corresponds to the RSAPBSSA-SHA384-PSS-Deterministic variant. See the specification for more details: // https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa#name-rsapbssa-variants func NewVerifier(pk *rsa.PublicKey, hash crypto.Hash) Verifier { h := common.ConvertHashFunction(hash) return randomizedVerifier{ pk: keys.NewBigPublicKey(pk), cryptoHash: hash, hash: h, } } // derivePublicKey tweaks the public key based on the input metadata. // // See the specification for more details: // https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa-00#name-public-key-augmentation // // See the following issue for more discussion on HKDF vs hash-to-field: // https://github.com/cfrg/draft-irtf-cfrg-hash-to-curve/issues/202 func derivePublicKey(h crypto.Hash, pk *keys.BigPublicKey, metadata []byte) *keys.BigPublicKey { // expandLen = ceil((ceil(log2(\lambda)/2) + k) / 8), where k is the security parameter of the suite (e.g., k = 128). // We stretch the input metadata beyond \lambda bits s.t. the output bytes are indifferentiable from truly random bytes lambda := pk.N.BitLen() / 2 expandLen := uint((lambda + 128) / 8) hkdfSalt := make([]byte, (pk.N.BitLen()+7)/8) pk.N.FillBytes(hkdfSalt) hkdfInput := append([]byte("key"), append(metadata, 0x00)...) hkdf := hkdf.New(h.New, hkdfInput, hkdfSalt, []byte("PBRSA")) bytes := make([]byte, expandLen) _, err := hkdf.Read(bytes) if err != nil { panic(err) } // H_MD(D) = 1 || G(x), where G(x) is output of length \lambda-2 bits // We do this by sampling \lambda bits, clearing the top two bits (so the output is \lambda-2 bits) // and setting the bottom bit (so the result is odd). newE := new(big.Int).SetBytes(bytes[:lambda/8]) newE.SetBit(newE, 0, 1) newE.SetBit(newE, lambda-1, 0) newE.SetBit(newE, lambda-2, 0) // Compute e_MD = e * H_MD(D) return &keys.BigPublicKey{ N: pk.N, E: newE, } } // deriveKeyPair tweaks the private key using the metadata as input. // // See the specification for more details: // https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa-00#name-private-key-augmentation func deriveKeyPair(h crypto.Hash, sk *keys.BigPrivateKey, metadata []byte) *keys.BigPrivateKey { // pih(N) = (p-1)(q-1) pm1 := new(big.Int).Set(sk.P) pm1.Sub(pm1, new(big.Int).SetInt64(int64(1))) qm1 := new(big.Int).Set(sk.Q) qm1.Sub(qm1, new(big.Int).SetInt64(int64(1))) phi := new(big.Int).Mul(pm1, qm1) // d = e^-1 mod phi(N) pk := derivePublicKey(h, sk.Pk, metadata) bigE := new(big.Int).Mod(pk.E, phi) d := new(big.Int).ModInverse(bigE, phi) return &keys.BigPrivateKey{ Pk: pk, D: d, P: sk.P, Q: sk.Q, } } func fixedPartiallyBlind(message, salt []byte, r, rInv *big.Int, pk *keys.BigPublicKey, hash hash.Hash) ([]byte, VerifierState, error) { encodedMsg, err := common.EncodeMessageEMSAPSS(message, pk.N, hash, salt) if err != nil { return nil, VerifierState{}, err } m := new(big.Int).SetBytes(encodedMsg) bigE := pk.E x := new(big.Int).Exp(r, bigE, pk.N) z := new(big.Int).Set(m) z.Mul(z, x) z.Mod(z, pk.N) kLen := (pk.N.BitLen() + 7) / 8 blindedMsg := make([]byte, kLen) z.FillBytes(blindedMsg) return blindedMsg, VerifierState{ encodedMsg: encodedMsg, pk: pk, hash: hash, salt: salt, rInv: rInv, }, nil } // Verifier is a type that implements the client side of the partially blind RSA // protocol, described in https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa-00 type Verifier interface { // Blind initializes the partially blind RSA protocol using an input message and source of // randomness. The signature includes a randomly generated PSS salt whose length equals the // size of the underlying hash function. This function fails if randomness was not provided. Blind(random io.Reader, message, metadata []byte) ([]byte, VerifierState, error) // FixedBlind initializes the partially blind RSA protocol using an input message, metadata, and randomness values. FixedBlind(message, metadata, salt, blind, blindInv []byte) ([]byte, VerifierState, error) // Verify verifies the input (message, signature) pair using the augmented public key // and produces an error upon failure. Verify(message, signature, metadata []byte) error // Hash returns the hash function associated with the Verifier. Hash() hash.Hash } // Blind initializes the partially blind RSA protocol using an input message and source of randomness. The // signature includes a randomly generated PSS salt whose length equals the size of the underlying // hash function. This function fails if randomness was not provided. // // See the specification for more details: // https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa-00#name-blind func (v randomizedVerifier) Blind(random io.Reader, message, metadata []byte) ([]byte, VerifierState, error) { if random == nil { return nil, VerifierState{}, common.ErrInvalidRandomness } salt := make([]byte, v.hash.Size()) _, err := io.ReadFull(rand.Reader, salt) if err != nil { return nil, VerifierState{}, err } r, rInv, err := common.GenerateBlindingFactor(random, v.pk.N) if err != nil { return nil, VerifierState{}, err } return v.FixedBlind(message, metadata, salt, r.Bytes(), rInv.Bytes()) } // FixedBlind initializes the partially blind RSA using fixed randomness as input. func (v randomizedVerifier) FixedBlind(message, metadata, salt, blind, blindInv []byte) ([]byte, VerifierState, error) { r := new(big.Int).SetBytes(blind) rInv := new(big.Int).SetBytes(blindInv) metadataKey := derivePublicKey(v.cryptoHash, v.pk, metadata) inputMsg := encodeMessageMetadata(message, metadata) return fixedPartiallyBlind(inputMsg, salt, r, rInv, metadataKey, v.hash) } // Verify verifies the input (message, signature) pair using the augmented public key // and produces an error upon failure. // // See the specification for more details: // https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa-00#name-verification-2 func (v randomizedVerifier) Verify(message, metadata, signature []byte) error { metadataKey := derivePublicKey(v.cryptoHash, v.pk, metadata) inputMsg := encodeMessageMetadata(message, metadata) return common.VerifyMessageSignature(inputMsg, signature, v.hash.Size(), metadataKey, v.cryptoHash) } // Hash returns the hash function associated with the Verifier. func (v randomizedVerifier) Hash() hash.Hash { return v.hash } // A VerifierState carries state needed to complete the blind signature protocol // as a verifier. type VerifierState struct { // Public key of the Signer pk *keys.BigPublicKey // Hash function used in producing the message signature hash hash.Hash // The hashed and encoded message being signed encodedMsg []byte // The salt used when encoding the message salt []byte // Inverse of the blinding factor produced by the Verifier rInv *big.Int } // Finalize computes and outputs the final signature, if it's valid. Otherwise, it returns an error. // // See the specification for more details: // https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa-00#name-finalize func (state VerifierState) Finalize(data []byte) ([]byte, error) { kLen := (state.pk.N.BitLen() + 7) / 8 if len(data) != kLen { return nil, common.ErrUnexpectedSize } z := new(big.Int).SetBytes(data) s := new(big.Int).Set(state.rInv) s.Mul(s, z) s.Mod(s, state.pk.N) sig := make([]byte, kLen) s.FillBytes(sig) err := common.VerifyBlindSignature(state.pk, state.encodedMsg, sig) if err != nil { return nil, err } return sig, nil } // CopyBlind returns an encoding of the blind value used in the protocol. func (state VerifierState) CopyBlind() []byte { r := new(big.Int).ModInverse(state.rInv, state.pk.N) return r.Bytes() } // CopySalt returns an encoding of the per-message salt used in the protocol. func (state VerifierState) CopySalt() []byte { salt := make([]byte, len(state.salt)) copy(salt, state.salt) return salt } // An Signer represents the Signer in the blind RSA protocol. // It carries the raw RSA private key used for signing blinded messages. type Signer struct { // An RSA private key sk *keys.BigPrivateKey h crypto.Hash } // isSafePrime returns true if the input prime p is safe, i.e., p = (2 * q) + 1 for some prime q func isSafePrime(p *big.Int) bool { q := new(big.Int).Set(p) q.Sub(q, big.NewInt(1)) q.Div(q, big.NewInt(2)) return q.ProbablyPrime(20) } // NewSigner creates a new Signer for the blind RSA protocol using an RSA private key. func NewSigner(sk *rsa.PrivateKey, h crypto.Hash) (Signer, error) { bigSk := keys.NewBigPrivateKey(sk) if !(isSafePrime(bigSk.P) && isSafePrime(bigSk.Q)) { return Signer{}, ErrInvalidPrivateKey } return Signer{ sk: bigSk, h: h, }, nil } // BlindSign blindly computes the RSA operation using the Signer's private key on the blinded // message input, if it's of valid length, and returns an error should the function fail. // // See the specification for more details: // https://datatracker.ietf.org/doc/html/draft-amjad-cfrg-partially-blind-rsa-00#name-blindsign func (signer Signer) BlindSign(data, metadata []byte) ([]byte, error) { kLen := (signer.sk.Pk.N.BitLen() + 7) / 8 if len(data) != kLen { return nil, common.ErrUnexpectedSize } m := new(big.Int).SetBytes(data) if m.Cmp(signer.sk.Pk.N) > 0 { return nil, common.ErrInvalidMessageLength } skPrime := deriveKeyPair(signer.h, signer.sk, metadata) s, err := common.DecryptAndCheck(rand.Reader, skPrime, m) if err != nil { return nil, err } blindSig := make([]byte, kLen) s.FillBytes(blindSig) return blindSig, nil } var ( // ErrInvalidPrivateKey is the error used if a private key is invalid ErrInvalidPrivateKey = errors.New("blindsign/blindrsa/partiallyblindrsa: invalid private key") ErrUnexpectedSize = common.ErrUnexpectedSize ErrInvalidMessageLength = common.ErrInvalidMessageLength ErrInvalidRandomness = common.ErrInvalidRandomness ) golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/partiallyblindrsa/pbrsa_test.go000066400000000000000000000223311454601126700314540ustar00rootroot00000000000000package partiallyblindrsa import ( "bytes" "crypto" "crypto/rand" "crypto/rsa" "encoding/hex" "encoding/json" "fmt" "io" "math/big" "os" "testing" "github.com/cloudflare/circl/blindsign/blindrsa/internal/keys" ) const ( pbrsaTestVectorOutEnvironmentKey = "PBRSA_TEST_VECTORS_OUT" pbrsaTestVectorInEnvironmentKey = "PBRSA_TEST_VECTORS_IN" ) func loadStrongRSAKey() *rsa.PrivateKey { // https://gist.github.com/chris-wood/b77536febb25a5a11af428afff77820a pEnc := "dcd90af1be463632c0d5ea555256a20605af3db667475e190e3af12a34a3324c46a3094062c59fb4b249e0ee6afba8bee14e0276d126c99f4784b23009bf6168ff628ac1486e5ae8e23ce4d362889de4df63109cbd90ef93db5ae64372bfe1c55f832766f21e94ea3322eb2182f10a891546536ba907ad74b8d72469bea396f3" qEnc := "f8ba5c89bd068f57234a3cf54a1c89d5b4cd0194f2633ca7c60b91a795a56fa8c8686c0e37b1c4498b851e3420d08bea29f71d195cfbd3671c6ddc49cf4c1db5b478231ea9d91377ffa98fe95685fca20ba4623212b2f2def4da5b281ed0100b651f6db32112e4017d831c0da668768afa7141d45bbc279f1e0f8735d74395b3" NEnc := "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" eEnc := "010001" dEnc := "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" p := new(big.Int).SetBytes(mustDecodeHex(pEnc)) q := new(big.Int).SetBytes(mustDecodeHex(qEnc)) N := new(big.Int).SetBytes(mustDecodeHex(NEnc)) e := new(big.Int).SetBytes(mustDecodeHex(eEnc)) d := new(big.Int).SetBytes(mustDecodeHex(dEnc)) primes := make([]*big.Int, 2) primes[0] = p primes[1] = q key := &rsa.PrivateKey{ PublicKey: rsa.PublicKey{ N: N, E: int(e.Int64()), }, D: d, Primes: primes, } return key } func runPBRSA(signer Signer, verifier Verifier, message, metadata []byte, random io.Reader) ([]byte, error) { blindedMsg, state, err := verifier.Blind(random, message, metadata) if err != nil { return nil, err } kLen := (signer.sk.Pk.N.BitLen() + 7) / 8 if len(blindedMsg) != kLen { return nil, fmt.Errorf("Protocol message (blind message) length mismatch, expected %d, got %d", kLen, len(blindedMsg)) } blindedSig, err := signer.BlindSign(blindedMsg, metadata) if err != nil { return nil, err } if len(blindedSig) != kLen { return nil, fmt.Errorf("Protocol message (blind signature) length mismatch, expected %d, got %d", kLen, len(blindedMsg)) } sig, err := state.Finalize(blindedSig) if err != nil { return nil, err } err = verifier.Verify(message, metadata, sig) if err != nil { return nil, err } return sig, nil } func mustDecodeHex(h string) []byte { b, err := hex.DecodeString(h) if err != nil { panic(err) } return b } func TestPBRSARoundTrip(t *testing.T) { message := []byte("hello world") metadata := []byte("metadata") key := loadStrongRSAKey() hash := crypto.SHA384 verifier := NewVerifier(&key.PublicKey, hash) signer, err := NewSigner(key, hash) if err != nil { t.Fatal(err) } sig, err := runPBRSA(signer, verifier, message, metadata, rand.Reader) if err != nil { t.Fatal(err) } if sig == nil { t.Fatal("nil signature output") } } type encodedPBRSATestVector struct { Message string `json:"msg"` Info string `json:"info"` P string `json:"p"` Q string `json:"q"` D string `json:"d"` E string `json:"e"` N string `json:"N"` Eprime string `json:"eprime"` Blind string `json:"blind"` Salt string `json:"salt"` Request string `json:"blinded_msg"` Response string `json:"blinded_sig"` Signature string `json:"sig"` } type rawPBRSATestVector struct { privateKey *rsa.PrivateKey message []byte info []byte infoKey []byte blind []byte salt []byte request []byte response []byte signature []byte } func mustHex(d []byte) string { return hex.EncodeToString(d) } func (tv rawPBRSATestVector) MarshalJSON() ([]byte, error) { pEnc := mustHex(tv.privateKey.Primes[0].Bytes()) qEnc := mustHex(tv.privateKey.Primes[1].Bytes()) nEnc := mustHex(tv.privateKey.N.Bytes()) e := new(big.Int).SetInt64(int64(tv.privateKey.PublicKey.E)) eEnc := mustHex(e.Bytes()) dEnc := mustHex(tv.privateKey.D.Bytes()) ePrimeEnc := mustHex(tv.infoKey) return json.Marshal(encodedPBRSATestVector{ P: pEnc, Q: qEnc, D: dEnc, E: eEnc, N: nEnc, Eprime: ePrimeEnc, Message: mustHex(tv.message), Info: mustHex(tv.info), Blind: mustHex(tv.blind), Salt: mustHex(tv.salt), Request: mustHex(tv.request), Response: mustHex(tv.response), Signature: mustHex(tv.signature), }) } func generatePBRSATestVector(t *testing.T, msg, metadata []byte) rawPBRSATestVector { key := loadStrongRSAKey() hash := crypto.SHA384 verifier := NewVerifier(&key.PublicKey, hash) signer, err := NewSigner(key, hash) if err != nil { t.Fatal(err) } publicKey := keys.NewBigPublicKey(&key.PublicKey) metadataKey := derivePublicKey(hash, publicKey, metadata) blindedMsg, state, err := verifier.Blind(rand.Reader, msg, metadata) if err != nil { t.Fatal(err) } blindedSig, err := signer.BlindSign(blindedMsg, metadata) if err != nil { t.Fatal(err) } sig, err := state.Finalize(blindedSig) if err != nil { t.Fatal(err) } err = verifier.Verify(msg, metadata, sig) if err != nil { t.Fatal(err) } return rawPBRSATestVector{ message: msg, info: metadata, privateKey: key, infoKey: metadataKey.Marshal(), salt: state.CopySalt(), blind: state.CopyBlind(), request: blindedMsg, response: blindedSig, signature: sig, } } func verifyTestVector(t *testing.T, vector rawPBRSATestVector) { key := loadStrongRSAKey() key.PublicKey.N = vector.privateKey.N key.PublicKey.E = vector.privateKey.E key.D = vector.privateKey.D key.Primes[0] = vector.privateKey.Primes[0] key.Primes[1] = vector.privateKey.Primes[1] key.Precomputed.Dp = nil // Remove precomputed CRT values hash := crypto.SHA384 signer, err := NewSigner(key, hash) if err != nil { t.Fatal(err) } verifier := NewVerifier(&key.PublicKey, crypto.SHA384) r := new(big.Int).SetBytes(vector.blind) rInv := new(big.Int).ModInverse(r, key.N) if r == nil { t.Fatal("Failed to compute blind inverse") } blindedMsg, state, err := verifier.FixedBlind(vector.message, vector.info, vector.salt, r.Bytes(), rInv.Bytes()) if err != nil { t.Fatal(err) } blindSig, err := signer.BlindSign(blindedMsg, vector.info) if err != nil { t.Fatal(err) } sig, err := state.Finalize(blindSig) if err != nil { t.Fatal(err) } if !bytes.Equal(sig, vector.signature) { t.Errorf("Signature mismatch: expected %x, got %x", sig, vector.signature) } } func TestPBRSAGenerateTestVector(t *testing.T) { testCases := []struct { msg []byte metadata []byte }{ { []byte("hello world"), []byte("metadata"), }, { []byte("hello world"), []byte(""), }, { []byte(""), []byte("metadata"), }, { []byte(""), []byte(""), }, } vectors := []rawPBRSATestVector{} for _, testCase := range testCases { vectors = append(vectors, generatePBRSATestVector(t, testCase.msg, testCase.metadata)) } for _, vector := range vectors { verifyTestVector(t, vector) } // Encode the test vectors encoded, err := json.Marshal(vectors) if err != nil { t.Fatalf("Error producing test vectors: %v", err) } var outputFile string if outputFile = os.Getenv(pbrsaTestVectorOutEnvironmentKey); len(outputFile) > 0 { err := os.WriteFile(outputFile, encoded, 0o600) if err != nil { t.Fatalf("Error writing test vectors: %v", err) } } } func BenchmarkPBRSA(b *testing.B) { message := []byte("hello world") metadata := []byte("good doggo") key := loadStrongRSAKey() hash := crypto.SHA384 verifier := NewVerifier(&key.PublicKey, hash) signer, err := NewSigner(key, hash) if err != nil { b.Fatal(err) } var blindedMsg []byte var state VerifierState b.Run("Blind", func(b *testing.B) { for n := 0; n < b.N; n++ { blindedMsg, state, err = verifier.Blind(rand.Reader, message, metadata) if err != nil { b.Fatal(err) } } }) var blindedSig []byte b.Run("BlindSign", func(b *testing.B) { for n := 0; n < b.N; n++ { blindedSig, err = signer.BlindSign(blindedMsg, metadata) if err != nil { b.Fatal(err) } } }) var sig []byte b.Run("Finalize", func(b *testing.B) { for n := 0; n < b.N; n++ { sig, err = state.Finalize(blindedSig) if err != nil { b.Fatal(err) } } }) err = verifier.Verify(message, metadata, sig) if err != nil { b.Fatal(err) } } golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/testdata/000077500000000000000000000000001454601126700250475ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/blindsign/blindrsa/testdata/test_vectors_rfc9474.json000066400000000000000000001031111454601126700316450ustar00rootroot00000000000000[ { "name": "RSABSSA-SHA384-PSS-Randomized", "p": "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", "q": "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", "n": "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", "e": "0x010001", "d": "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", "msg": "8f3dc6fb8c4a02f4d6352edf0907822c1210a9b32f9bdda4c45a698c80023aa6b59f8cfec5fdbb36331372ebefedae7d", "msg_prefix": "8417e699b219d583fb6216ae0c53ca0e9723442d02f1d1a34295527e7d929e8b", "input_msg": "8417e699b219d583fb6216ae0c53ca0e9723442d02f1d1a34295527e7d929e8b8f3dc6fb8c4a02f4d6352edf0907822c1210a9b32f9bdda4c45a698c80023aa6b59f8cfec5fdbb36331372ebefedae7d", "sLen": "0x30", "salt": "051722b35f458781397c3a671a7d3bd3096503940e4c4f1aaa269d60300ce449555cd7340100df9d46944c5356825abf", "is_randomized": "0x01", "inv": "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", "blinded_msg": "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", "blind_sig": "3f4a79eacd4445fca628a310d41e12fcd813c4d43aa4ef2b81226953248d6d00adfee6b79cb88bfa1f99270369fd063c023e5ed546719b0b2d143dd1bca46b0e0e615fe5c63d95c5a6b873b8b50bc52487354e69c3dfbf416e7aca18d5842c89b676efdd38087008fa5a810161fcdec26f20ccf2f1e6ab0f9d2bb93e051cb9e86a9b28c5bb62fd5f5391379f887c0f706a08bcc3b9e7506aaf02485d688198f5e22eefdf837b2dd919320b17482c5cc54271b4ccb41d267629b3f844fd63750b01f5276c79e33718bb561a152acb2eb36d8be75bce05c9d1b94eb609106f38226fb2e0f5cd5c5c39c59dda166862de498b8d92f6bcb41af433d65a2ac23da87f39764cb64e79e74a8f4ce4dd567480d967cefac46b6e9c06434c3715635834357edd2ce6f105eea854ac126ccfa3de2aac5607565a4e5efaac5eed491c335f6fc97e6eb7e9cea3e12de38dfb315220c0a3f84536abb2fdd722813e083feda010391ac3d8fd1cd9212b5d94e634e69ebcc800c4d5c4c1091c64afc37acf563c7fc0a6e4c082bc55544f50a7971f3fb97d5853d72c3af34ffd5ce123998be5360d1059820c66a81e1ee6d9c1803b5b62af6bc877526df255b6d1d835d8c840bebbcd6cc0ee910f17da37caf8488afbc08397a1941fcc79e76a5888a95b3d5405e13f737bea5c78d716a48eb9dc0aec8de39c4b45c6914ad4a8185969f70b1adf46", "sig": "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" }, { "name": "RSABSSA-SHA384-PSSZERO-Randomized", "p": "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", "q": "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", "n": "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", "e": "0x010001", "d": "0x0d43242aefe1fb2c13fbc66e20b678c4336d20b1808c558b6e62ad16a287077180b177e1f01b12f9c6cd6c52630257ccef26a45135a990928773f3bd2fc01a313f1dac97a51cec71cb1fd7efc7adffdeb05f1fb04812c924ed7f4a8269925dad88bd7dcfbc4ef01020ebfc60cb3e04c54f981fdbd273e69a8a58b8ceb7c2d83fbcbd6f784d052201b88a9848186f2a45c0d2826870733e6fd9aa46983e0a6e82e35ca20a439c5ee7b502a9062e1066493bdadf8b49eb30d9558ed85abc7afb29b3c9bc644199654a4676681af4babcea4e6f71fe4565c9c1b85d9985b84ec1abf1a820a9bbebee0df1398aae2c85ab580a9f13e7743afd3108eb32100b870648fa6bc17e8abac4d3c99246b1f0ea9f7f93a5dd5458c56d9f3f81ff2216b3c3680a13591673c43194d8e6fc93fc1e37ce2986bd628ac48088bc723d8fbe293861ca7a9f4a73e9fa63b1b6d0074f5dea2a624c5249ff3ad811b6255b299d6bc5451ba7477f19c5a0db690c3e6476398b1483d10314afd38bbaf6e2fbdbcd62c3ca9797a420ca6034ec0a83360a3ee2adf4b9d4ba29731d131b099a38d6a23cc463db754603211260e99d19affc902c915d7854554aabf608e3ac52c19b8aa26ae042249b17b2d29669b5c859103ee53ef9bdc73ba3c6b537d5c34b6d8f034671d7f3a8a6966cc4543df223565343154140fd7391c7e7be03e241f4ecfeb877a051", "msg": "8f3dc6fb8c4a02f4d6352edf0907822c1210a9b32f9bdda4c45a698c80023aa6b59f8cfec5fdbb36331372ebefedae7d", "msg_prefix": "84ea86c8cf3beedfed73beceabd792027c609d1100bf041fdd60d826a718130d", "input_msg": "84ea86c8cf3beedfed73beceabd792027c609d1100bf041fdd60d826a718130d8f3dc6fb8c4a02f4d6352edf0907822c1210a9b32f9bdda4c45a698c80023aa6b59f8cfec5fdbb36331372ebefedae7d", "sLen": "0x00", "salt": "", "encoded_msg": 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"sig": "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" }, { "name": "RSABSSA-SHA384-PSSZERO-Deterministic", "p": "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", "q": "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", "n": "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", "e": "0x010001", "d": "0x0d43242aefe1fb2c13fbc66e20b678c4336d20b1808c558b6e62ad16a287077180b177e1f01b12f9c6cd6c52630257ccef26a45135a990928773f3bd2fc01a313f1dac97a51cec71cb1fd7efc7adffdeb05f1fb04812c924ed7f4a8269925dad88bd7dcfbc4ef01020ebfc60cb3e04c54f981fdbd273e69a8a58b8ceb7c2d83fbcbd6f784d052201b88a9848186f2a45c0d2826870733e6fd9aa46983e0a6e82e35ca20a439c5ee7b502a9062e1066493bdadf8b49eb30d9558ed85abc7afb29b3c9bc644199654a4676681af4babcea4e6f71fe4565c9c1b85d9985b84ec1abf1a820a9bbebee0df1398aae2c85ab580a9f13e7743afd3108eb32100b870648fa6bc17e8abac4d3c99246b1f0ea9f7f93a5dd5458c56d9f3f81ff2216b3c3680a13591673c43194d8e6fc93fc1e37ce2986bd628ac48088bc723d8fbe293861ca7a9f4a73e9fa63b1b6d0074f5dea2a624c5249ff3ad811b6255b299d6bc5451ba7477f19c5a0db690c3e6476398b1483d10314afd38bbaf6e2fbdbcd62c3ca9797a420ca6034ec0a83360a3ee2adf4b9d4ba29731d131b099a38d6a23cc463db754603211260e99d19affc902c915d7854554aabf608e3ac52c19b8aa26ae042249b17b2d29669b5c859103ee53ef9bdc73ba3c6b537d5c34b6d8f034671d7f3a8a6966cc4543df223565343154140fd7391c7e7be03e241f4ecfeb877a051", "msg": "8f3dc6fb8c4a02f4d6352edf0907822c1210a9b32f9bdda4c45a698c80023aa6b59f8cfec5fdbb36331372ebefedae7d", "msg_prefix": "", "input_msg": "8f3dc6fb8c4a02f4d6352edf0907822c1210a9b32f9bdda4c45a698c80023aa6b59f8cfec5fdbb36331372ebefedae7d", "sLen": "0x00", "salt": "", "encoded_msg": "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", "is_randomized": "0x00", "inv": "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", "blinded_msg": "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", "blind_sig": "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", "sig": "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" } ]golang-github-cloudflare-circl-1.3.7/blindsign/doc.go000066400000000000000000000001111454601126700225250ustar00rootroot00000000000000// Package blindsign provides blind signature schemes. package blindsign golang-github-cloudflare-circl-1.3.7/cipher/000077500000000000000000000000001454601126700207415ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/cipher/ascon/000077500000000000000000000000001454601126700220445ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/cipher/ascon/ascon.go000066400000000000000000000207221454601126700235010ustar00rootroot00000000000000// Package ascon provides ASCON family of light-weight AEAD ciphers. // // This package implements Ascon128 and Ascon128a two AEAD ciphers as specified // in ASCON v1.2 by C. Dobraunig, M. Eichlseder, F. Mendel, M. Schläffer. // https://ascon.iaik.tugraz.at/index.html // // It also implements Ascon-80pq, which has an increased key-size to provide // more resistance against a quantum adversary using Grover’s algorithm for // key search. Since Ascon-128 and Ascon-80pq share the same building blocks // and same parameters except the size of the key, it is claimed the same // security for Ascon-80pq against classical attacks as for Ascon-128. package ascon import ( "crypto/subtle" "encoding/binary" "errors" "math/bits" ) const ( KeySize = 16 // For Ascon128 and Ascon128a. KeySize80pq = 20 // Only for Ascon80pq. NonceSize = 16 TagSize = 16 ) type Mode int // KeySize is 16 for Ascon128 and Ascon128a, or 20 for Ascon80pq. func (m Mode) KeySize() int { switch m { case Ascon128, Ascon128a, Ascon80pq: v := int(m) >> 2 return KeySize&^v | KeySize80pq&v default: panic(ErrMode) } } func (m Mode) String() string { switch m { case Ascon128: return "Ascon128" case Ascon128a: return "Ascon128a" case Ascon80pq: return "Ascon80pq" default: panic(ErrMode) } } const ( Ascon128 Mode = 1 Ascon128a Mode = 2 Ascon80pq Mode = -1 ) const permA = 12 type Cipher struct { key [3]uint64 mode Mode } // New returns a Cipher struct implementing the crypto/cipher.AEAD interface. // The key must be Mode.KeySize() bytes long, and the mode is one of Ascon128, // Ascon128a or Ascon80pq. func New(key []byte, m Mode) (*Cipher, error) { if (m == Ascon128 || m == Ascon128a) && len(key) != KeySize { return nil, ErrKeySize } if m == Ascon80pq && len(key) != KeySize80pq { return nil, ErrKeySize } if !(m == Ascon128 || m == Ascon128a || m == Ascon80pq) { return nil, ErrMode } c := new(Cipher) c.mode = m if m == Ascon80pq { c.key[0] = uint64(binary.BigEndian.Uint32(key[0:4])) c.key[1] = binary.BigEndian.Uint64(key[4:12]) c.key[2] = binary.BigEndian.Uint64(key[12:20]) } else { c.key[0] = 0 c.key[1] = binary.BigEndian.Uint64(key[0:8]) c.key[2] = binary.BigEndian.Uint64(key[8:16]) } return c, nil } // NonceSize returns the size of the nonce that must be passed to Seal // and Open. func (a *Cipher) NonceSize() int { return NonceSize } // Overhead returns the maximum difference between the lengths of a // plaintext and its ciphertext. func (a *Cipher) Overhead() int { return TagSize } // Seal encrypts and authenticates plaintext, authenticates the // additional data and appends the result to dst, returning the updated // slice. The nonce must be NonceSize() bytes long and unique for all // time, for a given key. // // To reuse plaintext's storage for the encrypted output, use plaintext[:0] // as dst. Otherwise, the remaining capacity of dst must not overlap plaintext. func (a *Cipher) Seal(dst, nonce, plaintext, additionalData []byte) []byte { if len(nonce) != NonceSize { panic(ErrNonceSize) } ptLen := len(plaintext) ret, out := sliceForAppend(dst, ptLen+TagSize) ciphertext, tag := out[:ptLen], out[ptLen:] var s [5]uint64 a.initialize(nonce, &s) a.assocData(additionalData, &s) a.procText(plaintext, ciphertext, true, &s) a.finalize(tag, &s) return ret } // Open decrypts and authenticates ciphertext, authenticates the // additional data and, if successful, appends the resulting plaintext // to dst, returning the updated slice. The nonce must be NonceSize() // bytes long and both it and the additional data must match the // value passed to Seal. // // To reuse ciphertext's storage for the decrypted output, use ciphertext[:0] // as dst. Otherwise, the remaining capacity of dst must not overlap plaintext. // // Even if the function fails, the contents of dst, up to its capacity, // may be overwritten. func (a *Cipher) Open(dst, nonce, ciphertext, additionalData []byte) ([]byte, error) { if len(nonce) != NonceSize { panic(ErrNonceSize) } if len(ciphertext) < TagSize { return nil, ErrDecryption } ptLen := len(ciphertext) - TagSize ret, out := sliceForAppend(dst, ptLen) plaintext := out[:ptLen] ciphertext, tag0 := ciphertext[:ptLen], ciphertext[ptLen:] tag1 := (&[TagSize]byte{})[:] var s [5]uint64 a.initialize(nonce, &s) a.assocData(additionalData, &s) a.procText(ciphertext, plaintext, false, &s) a.finalize(tag1, &s) if subtle.ConstantTimeCompare(tag0, tag1) == 0 { return nil, ErrDecryption } return ret, nil } func abs(x int) int { m := uint(x >> (bits.UintSize - 1)); return int((uint(x) + m) ^ m) } // blockSize = 8 for Ascon128 and Ascon80pq, or 16 for Ascon128a. func (a *Cipher) blockSize() int { return abs(int(a.mode)) << 3 } // permB = 6 for Ascon128 and Ascon80pq, or 8 for Ascon128a. func (a *Cipher) permB() int { return (abs(int(a.mode)) + 2) << 1 } func (a *Cipher) initialize(nonce []byte, s *[5]uint64) { bcs := uint64(a.blockSize()) pB := uint64(a.permB()) kS := uint64(a.mode.KeySize()) s[0] = ((kS * 8) << 56) | ((bcs * 8) << 48) | (permA << 40) | (pB << 32) | a.key[0] s[1] = a.key[1] s[2] = a.key[2] s[3] = binary.BigEndian.Uint64(nonce[0:8]) s[4] = binary.BigEndian.Uint64(nonce[8:16]) perm(permA, s) s[2] ^= a.key[0] s[3] ^= a.key[1] s[4] ^= a.key[2] } func (a *Cipher) assocData(add []byte, s *[5]uint64) { bcs := a.blockSize() pB := a.permB() if len(add) > 0 { for ; len(add) >= bcs; add = add[bcs:] { for i := 0; i < bcs; i += 8 { s[i/8] ^= binary.BigEndian.Uint64(add[i : i+8]) } perm(pB, s) } for i := 0; i < len(add); i++ { s[i/8] ^= uint64(add[i]) << (56 - 8*(i%8)) } s[len(add)/8] ^= uint64(0x80) << (56 - 8*(len(add)%8)) perm(pB, s) } s[4] ^= 0x01 } func (a *Cipher) procText(in, out []byte, enc bool, s *[5]uint64) { bcs := a.blockSize() pB := a.permB() mask := uint64(0) if enc { mask -= 1 } for ; len(in) >= bcs; in, out = in[bcs:], out[bcs:] { for i := 0; i < bcs; i += 8 { inW := binary.BigEndian.Uint64(in[i : i+8]) outW := s[i/8] ^ inW binary.BigEndian.PutUint64(out[i:i+8], outW) s[i/8] = (inW &^ mask) | (outW & mask) } perm(pB, s) } mask8 := byte(mask & 0xFF) for i := 0; i < len(in); i++ { off := 56 - (8 * (i % 8)) si := byte((s[i/8] >> off) & 0xFF) inB := in[i] outB := si ^ inB out[i] = outB ss := inB&^mask8 | outB&mask8 s[i/8] = (s[i/8] &^ (0xFF << off)) | uint64(ss)<>32 s[bcs/8+1] ^= a.key[1]<<32 | a.key[2]>>32 s[bcs/8+2] ^= a.key[2] << 32 } else { s[bcs/8+0] ^= a.key[1] s[bcs/8+1] ^= a.key[2] } perm(permA, s) binary.BigEndian.PutUint64(tag[0:8], s[3]^a.key[1]) binary.BigEndian.PutUint64(tag[8:16], s[4]^a.key[2]) } func perm(n int, s *[5]uint64) { x0, x1, x2, x3, x4 := s[0], s[1], s[2], s[3], s[4] for i := permA - n; i < permA; i++ { // pC -- addition of constants x2 ^= uint64((0xF-i)<<4 | i) // pS -- substitution layer // Figure 6 from Spec [DHVV18,Dae18] // https://ascon.iaik.tugraz.at/files/asconv12-nist.pdf x0 ^= x4 x4 ^= x3 x2 ^= x1 t0 := x0 & (^x4) t1 := x2 & (^x1) x0 ^= t1 t1 = x4 & (^x3) x2 ^= t1 t1 = x1 & (^x0) x4 ^= t1 t1 = x3 & (^x2) x1 ^= t1 x3 ^= t0 x1 ^= x0 x3 ^= x2 x0 ^= x4 x2 = ^x2 // pL -- linear diffusion layer x0 ^= bits.RotateLeft64(x0, -19) ^ bits.RotateLeft64(x0, -28) x1 ^= bits.RotateLeft64(x1, -61) ^ bits.RotateLeft64(x1, -39) x2 ^= bits.RotateLeft64(x2, -1) ^ bits.RotateLeft64(x2, -6) x3 ^= bits.RotateLeft64(x3, -10) ^ bits.RotateLeft64(x3, -17) x4 ^= bits.RotateLeft64(x4, -7) ^ bits.RotateLeft64(x4, -41) } s[0], s[1], s[2], s[3], s[4] = x0, x1, x2, x3, x4 } // sliceForAppend takes a slice and a requested number of bytes. It returns a // slice with the contents of the given slice followed by that many bytes and a // second slice that aliases into it and contains only the extra bytes. If the // original slice has sufficient capacity then no allocation is performed. func sliceForAppend(in []byte, n int) (head, tail []byte) { if total := len(in) + n; cap(in) >= total { head = in[:total] } else { head = make([]byte, total) copy(head, in) } tail = head[len(in):] return } var ( ErrKeySize = errors.New("ascon: bad key size") ErrNonceSize = errors.New("ascon: bad nonce size") ErrDecryption = errors.New("ascon: invalid ciphertext") ErrMode = errors.New("ascon: invalid cipher mode") ) golang-github-cloudflare-circl-1.3.7/cipher/ascon/ascon_test.go000066400000000000000000000156201454601126700245410ustar00rootroot00000000000000package ascon_test import ( "bytes" "crypto/cipher" hexa "encoding/hex" "encoding/json" "io" "os" "strconv" "sync" "testing" "github.com/cloudflare/circl/cipher/ascon" "github.com/cloudflare/circl/internal/test" ) type vector struct { Count int `json:"Count"` Key hex `json:"Key"` Nonce hex `json:"Nonce"` PT hex `json:"PT"` AD hex `json:"AD"` CT hex `json:"CT"` } type hex []byte func (h *hex) UnmarshalJSON(data []byte) error { var s string if err := json.Unmarshal(data, &s); err != nil { return err } decoded, err := hexa.DecodeString(s) if err != nil { return err } *h = hex(decoded) return nil } func readFile(t *testing.T, fileName string) []vector { jsonFile, err := os.Open(fileName) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", fileName, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", fileName, err) } var v []vector err = json.Unmarshal(input, &v) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) } return v } func TestAscon(t *testing.T) { // Test vectors generated with pyascon // https://github.com/meichlseder/pyascon/ for _, mode := range []ascon.Mode{ascon.Ascon128, ascon.Ascon128a, ascon.Ascon80pq} { name := mode.String() t.Run(name, func(t *testing.T) { vectors := readFile(t, "testdata/"+name+".json") for _, v := range vectors { a, err := ascon.New(v.Key, mode) test.CheckNoErr(t, err, "failed to create cipher") var aead cipher.AEAD = a test.CheckOk(len(v.Nonce) == aead.NonceSize(), "bad nonce size", t) got := aead.Seal(nil, v.Nonce, v.PT, v.AD) want := v.CT if !bytes.Equal(got, want) { test.ReportError(t, got, want, name, v.Count) } got, err = aead.Open(nil, v.Nonce, v.CT, v.AD) if err != nil { t.Fatal(err) } want = v.PT if !bytes.Equal(got, want) { test.ReportError(t, got, want, name, v.Count) } test.CheckOk(len(v.PT)+aead.Overhead() == len(v.CT), "bad overhead size", t) } }) } } func TestBadInputs(t *testing.T) { var key [ascon.KeySize]byte var m ascon.Mode = 0 _, err := ascon.New(key[:], m) test.CheckIsErr(t, err, "should fail due to bad mode") err = test.CheckPanic(func() { _ = m.String() }) test.CheckNoErr(t, err, "should panic due to bad mode") _, err = ascon.New(nil, ascon.Ascon128) test.CheckIsErr(t, err, "should fail due to nil key") _, err = ascon.New(key[:4], ascon.Ascon128) test.CheckIsErr(t, err, "should fail due to short key") _, err = ascon.New(key[:], ascon.Ascon80pq) test.CheckIsErr(t, err, "should fail due to short key") a, _ := ascon.New(key[:], ascon.Ascon128) err = test.CheckPanic(func() { _ = a.Seal(nil, nil, nil, nil) }) test.CheckNoErr(t, err, "should panic due to bad nonce") err = test.CheckPanic(func() { _, _ = a.Open(nil, nil, nil, nil) }) test.CheckNoErr(t, err, "should panic due to bad nonce") var nonce [ascon.NonceSize]byte _ = a.Seal(nil, nonce[:], nil, nil) _, err = a.Open(nil, nonce[:], nil, nil) test.CheckIsErr(t, err, "should panic due to empty ciphertext") pt := []byte("") ct := a.Seal(nil, nonce[:], pt, nil) ct[0] ^= 0xFF // tamper ciphertext _, err = a.Open(nil, nonce[:], ct, nil) test.CheckIsErr(t, err, "should panic due to bad ciphertext") } func TestAPI(t *testing.T) { key, _ := hexa.DecodeString("000102030405060708090A0B0C0D0E0F") nonce, _ := hexa.DecodeString("000102030405060708090A0B0C0D0E0F") c, _ := ascon.New(key, ascon.Ascon128) pt := []byte("helloworld") ct, _ := hexa.DecodeString("d4e663d29cd60a693c20f890982e167d266f940b93b586945065") t.Run("append", func(t *testing.T) { prefix := [5]byte{0x1F, 0x2F, 0x3F, 0x4F, 0x5F} prefixAndCt := c.Seal(prefix[:], nonce, pt, nil) got := prefixAndCt want := append(append([]byte{}, prefix[:]...), ct...) if !bytes.Equal(got, want) { test.ReportError(t, got, want) } ciphertext := prefixAndCt[len(prefix):] prefix = [5]byte{0x11, 0x22, 0x33, 0x44, 0x55} prefixAndPt, err := c.Open(prefix[:], nonce, ciphertext, nil) if err != nil { t.Fatal(err) } got = prefixAndPt want = append(append([]byte{}, prefix[:]...), pt...) if !bytes.Equal(got, want) { test.ReportError(t, got, want) } }) t.Run("reuse", func(t *testing.T) { ptWithCap := make([]byte, len(pt), len(pt)+100) copy(ptWithCap, pt) // reusing the input to store the ciphertext. ciphertext := c.Seal(ptWithCap[:0], nonce, ptWithCap, nil) got := ciphertext want := ct if !bytes.Equal(got, want) { test.ReportError(t, got, want) } test.CheckOk(&ptWithCap[0] == &ciphertext[0], "should have same address", t) ctWithCap := make([]byte, len(ct), len(ct)+100) copy(ctWithCap, ct) // reusing the input to store the plaintext. plaintext, err := c.Open(ctWithCap[:0], nonce, ctWithCap, nil) if err != nil { t.Fatal(err) } got = plaintext want = pt if !bytes.Equal(got, want) { test.ReportError(t, got, want) } test.CheckOk(&ctWithCap[0] == &plaintext[0], "should have same address", t) }) t.Run("parallel", func(t *testing.T) { var wg sync.WaitGroup for i := 0; i < 1_000; i++ { wg.Add(1) go func() { defer wg.Done() ciphertext := c.Seal(nil, nonce, pt, nil) plaintext, err := c.Open(nil, nonce, ciphertext, nil) if err != nil { t.Error(err) } got := plaintext want := pt if !bytes.Equal(got, want) { test.ReportError(t, got, want) } }() } wg.Wait() }) } func BenchmarkAscon(b *testing.B) { for _, mode := range []ascon.Mode{ascon.Ascon128, ascon.Ascon128a, ascon.Ascon80pq} { for _, length := range []int{64, 1350, 8 * 1024} { b.Run(mode.String()+"/Open-"+strconv.Itoa(length), func(b *testing.B) { benchmarkOpen(b, make([]byte, length), mode) }) b.Run(mode.String()+"/Seal-"+strconv.Itoa(length), func(b *testing.B) { benchmarkSeal(b, make([]byte, length), mode) }) } } } func benchmarkSeal(b *testing.B, buf []byte, mode ascon.Mode) { b.ReportAllocs() b.SetBytes(int64(len(buf))) var key []byte switch mode { case ascon.Ascon128, ascon.Ascon128a: key = make([]byte, ascon.KeySize) case ascon.Ascon80pq: key = make([]byte, ascon.KeySize80pq) } var nonce [ascon.NonceSize]byte var ad [13]byte a, err := ascon.New(key[:], mode) if err != nil { b.Fatal(err) } var out []byte b.ResetTimer() for i := 0; i < b.N; i++ { out = a.Seal(out[:0], nonce[:], buf, ad[:]) } } func benchmarkOpen(b *testing.B, buf []byte, mode ascon.Mode) { b.ReportAllocs() b.SetBytes(int64(len(buf))) var key []byte switch mode { case ascon.Ascon128, ascon.Ascon128a: key = make([]byte, ascon.KeySize) case ascon.Ascon80pq: key = make([]byte, ascon.KeySize80pq) } var nonce [ascon.NonceSize]byte var ad [13]byte a, err := ascon.New(key[:], mode) if err != nil { b.Fatal(err) } var out []byte ct := a.Seal(nil, nonce[:], buf, ad[:]) b.ResetTimer() for i := 0; i < b.N; i++ { out, _ = a.Open(out[:0], nonce[:], ct, ad[:]) } } golang-github-cloudflare-circl-1.3.7/cipher/ascon/testdata/000077500000000000000000000000001454601126700236555ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/cipher/ascon/testdata/Ascon128.json000066400000000000000000011550251454601126700260570ustar00rootroot00000000000000[ { "Count": 1, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "", "CT": "E355159F292911F794CB1432A0103A8A" }, { "Count": 2, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "00", "CT": "944DF887CD4901614C5DEDBC42FC0DA0" }, { "Count": 3, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "0001", "CT": "CE1936FBDD191058DEA8769B79319858" }, { "Count": 4, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102", "CT": "4C9450689BE3D7C23925A4219DE6B50C" }, { "Count": 5, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "00010203", "CT": "082389C8819A82BD98C04A3C64A63AA9" }, { "Count": 6, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "0001020304", "CT": "A88AF3E37EE0188B2B70A74BE1AB573F" }, { "Count": 7, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405", "CT": "4700E8F2474520FCE1DF779B496A3D43" }, { "Count": 8, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "00010203040506", "CT": "8CA228C9EA549C73A8BA27291FED88BF" }, { "Count": 9, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "0001020304050607", "CT": "E3DCF95F869752F61CD7A2DB895F918E" }, { "Count": 10, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708", "CT": "ABCDB317ECCFE67A62CF70AE974C3DBE" }, { "Count": 11, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "00010203040506070809", "CT": "4B006A400B6DFB9777BC3446C2B7DC26" }, { "Count": 12, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A", "CT": "D72C225D6BC2075163BED863186EC886" }, { "Count": 13, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B", "CT": "4ACECAA3B349728E7317D82467B2749E" }, { "Count": 14, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C", "CT": "BB6EC1A7AE8120CAD76566397C9AE920" }, { "Count": 15, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C0D", "CT": "3078530D228A443D764648F498C26CC2" }, { "Count": 16, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C0D0E", "CT": "7E4371F17406D6E5328473177A791CEE" }, { "Count": 17, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C0D0E0F", "CT": "EF5763E75FE32F96D7863410FF0B4786" }, { "Count": 18, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C0D0E0F10", "CT": "79AC0FA2BF3859D6962D0C0AF45B1D3E" }, { "Count": 19, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C0D0E0F1011", "CT": "F56840B36DEE4F7D3450762B209CD93C" }, { "Count": 20, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C0D0E0F101112", "CT": "4A55B63A5F9218829D81973135D03B10" }, { "Count": 21, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "", "AD": "000102030405060708090A0B0C0D0E0F10111213", "CT": "0B1C94E36D55C29951A74FA7E7F7349B" }, { "Count": 22, "Key": "000102030405060708090A0B0C0D0E0F", "Nonce": "000102030405060708090A0B0C0D0E0F", 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"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F", "AD": "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E", "CT": "6C459619110ADA74E585FE4424B2913E0BE9ACCADCBEFDE59C5A6792320999E6647DC2846708BA6E9B99DE058A9FCC0F" }, { "Count": 1089, "Key": "000102030405060708090A0B0C0D0E0F10111213", "Nonce": "000102030405060708090A0B0C0D0E0F", "PT": "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F", "AD": "000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F", "CT": "CC4E07E5FB13426EFFD17B0F51A6A830BF484C9651D77679971E8EB4A8EDB5A00782A94C72B2B02D87DCF4AF75DB6996" } ]golang-github-cloudflare-circl-1.3.7/cipher/doc.go000066400000000000000000000001061454601126700220320ustar00rootroot00000000000000// Package cipher provides data encryption algorithms. package cipher golang-github-cloudflare-circl-1.3.7/codecov.yml000066400000000000000000000005641454601126700216410ustar00rootroot00000000000000# Default codecoverage configuration https://docs.codecov.io/docs/codecov-yaml codecov: require_ci_to_pass: yes coverage: precision: 2 round: down range: "70...100" parsers: gcov: branch_detection: conditional: yes loop: yes method: no macro: no comment: layout: "reach,diff,flags,tree" behavior: default require_changes: no golang-github-cloudflare-circl-1.3.7/dh/000077500000000000000000000000001454601126700200625ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/csidh/000077500000000000000000000000001454601126700211545ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/csidh/consts.go000066400000000000000000000060721454601126700230210ustar00rootroot00000000000000package csidh const ( // pbits is a bitsize of prime p pbits = 511 // primeCount number of Elkies primes used for constructing p primeCount = 74 // (2*5+1)^74 is roughly 2^256 expMax = int8(5) // size of the limbs, pretty much hardcoded to 64-bit words limbBitSize = 64 // size of the limbs in bytes limbByteSize = limbBitSize >> 3 // Number of limbs for a field element numWords = 8 // PrivateKeySize is a size of cSIDH/512 private key in bytes. PrivateKeySize = 37 // PublicKeySize is a size of cSIDH/512 public key in bytes. PublicKeySize = 64 // SharedSecretSize is a size of cSIDH/512 shared secret in bytes. SharedSecretSize = 64 ) var ( // Elkies primes up to 374 + prime 587 // p = 4 * product(Elkies primes) - 1 primes = [primeCount]uint64{ 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083, 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, 0x016F, 0x0175, 0x024B, } p = fp{ 0x1B81B90533C6C87B, 0xC2721BF457ACA835, 0x516730CC1F0B4F25, 0xA7AAC6C567F35507, 0x5AFBFCC69322C9CD, 0xB42D083AEDC88C42, 0xFC8AB0D15E3E4C4A, 0x65B48E8F740F89BF, } /* Montgomery R = 2^512 mod p */ one = fp{ 0xC8FC8DF598726F0A, 0x7B1BC81750A6AF95, 0x5D319E67C1E961B4, 0xB0AA7275301955F1, 0x4A080672D9BA6C64, 0x97A5EF8A246EE77B, 0x06EA9E5D4383676A, 0x3496E2E117E0EC80, } // 2 in Montgomery domain two = fp{ 0x767762E5FD1E1599, 0x33C5743A49A0B6F6, 0x68FC0C0364C77443, 0xB9AA1E24F83F56DB, 0x3914101F20520EFB, 0x7B1ED6D95B1542B4, 0x114A8BE928C8828A, 0x03793732BBB24F40, } // -2 in Montgomery domain twoNeg = fp{ 0xA50A561F36A8B2E2, 0x8EACA7BA0E0BF13E, 0xE86B24C8BA43DAE2, 0xEE00A8A06FB3FE2B, 0x21E7ECA772D0BAD1, 0x390E316192B3498E, 0xEB4024E83575C9C0, 0x623B575CB85D3A7F, } // 4 in Montgomery domain four = fp{ 0xECEEC5CBFA3C2B32, 0x678AE87493416DEC, 0xD1F81806C98EE886, 0x73543C49F07EADB6, 0x7228203E40A41DF7, 0xF63DADB2B62A8568, 0x229517D251910514, 0x06F26E6577649E80, } // 4 * sqrt(p) fourSqrtP = fp{ 0x17895E71E1A20B3F, 0x38D0CD95F8636A56, 0x142B9541E59682CD, 0x856F1399D91D6592, 0x0000000000000002, } // -p^-1 mod 2^64 pNegInv = fp{ 0x66c1301f632e294d, } // (p-1)/2. Used as exponent, hence not in // montgomery domain pMin1By2 = fp{ 0x8DC0DC8299E3643D, 0xE1390DFA2BD6541A, 0xA8B398660F85A792, 0xD3D56362B3F9AA83, 0x2D7DFE63499164E6, 0x5A16841D76E44621, 0xFE455868AF1F2625, 0x32DA4747BA07C4DF, } // p-1 mod 2^64. Used as exponent, hence not // in montgomery domain pMin1 = fp{ 0x1B81B90533C6C879, 0xC2721BF457ACA835, 0x516730CC1F0B4F25, 0xA7AAC6C567F35507, 0x5AFBFCC69322C9CD, 0xB42D083AEDC88C42, 0xFC8AB0D15E3E4C4A, 0x65B48E8F740F89BF, } ) golang-github-cloudflare-circl-1.3.7/dh/csidh/csidh.go000066400000000000000000000162471454601126700226070ustar00rootroot00000000000000package csidh import ( "io" ) // 511-bit number representing prime field element GF(p) type fp [numWords]uint64 // Represents projective point on elliptic curve E over GF(p) type point struct { x fp z fp } // Curve coefficients type coeff struct { a fp c fp } type fpRngGen struct { // working buffer needed to avoid memory allocation wbuf [64]byte } // Defines operations on public key type PublicKey struct { fpRngGen // Montgomery coefficient A from GF(p) of the elliptic curve // y^2 = x^3 + Ax^2 + x. a fp } // Defines operations on private key type PrivateKey struct { fpRngGen // private key is a set of integers randomly // each sampled from a range [-5, 5]. e [PrivateKeySize]int8 } // randFp generates random element from Fp. func (s *fpRngGen) randFp(v *fp, rng io.Reader) { mask := uint64(1<<(pbits%limbBitSize)) - 1 for { *v = fp{} _, err := io.ReadFull(rng, s.wbuf[:]) if err != nil { panic("Can't read random number") } for i := 0; i < len(s.wbuf); i++ { j := i / limbByteSize k := uint(i % 8) v[j] |= uint64(s.wbuf[i]) << (8 * k) } v[len(v)-1] &= mask if isLess(v, &p) { return } } } // cofactorMul helper implements batch cofactor multiplication as described // in the ia.cr/2018/383 (algo. 3). Returns tuple of two booleans, first indicates // if function has finished successfully. In case first return value is true, // second return value indicates if curve represented by cofactor 'a' is // supersingular. // Implementation uses divide-and-conquer strategy and recursion in order to // speed up calculation of Q_i = [(p+1)/l_i] * P. // Implementation is not constant time, but it operates on public data only. func cofactorMul(p *point, a *coeff, halfL, halfR int, order *fp) (bool, bool) { var Q point var r1, d1, r2, d2 bool if (halfR - halfL) == 1 { // base case if !p.z.isZero() { tmp := fp{primes[halfL]} xMul(p, p, a, &tmp) if !p.z.isZero() { // order does not divide p+1 -> ordinary curve return true, false } mul512(order, order, primes[halfL]) if isLess(&fourSqrtP, order) { // order > 4*sqrt(p) -> supersingular curve return true, true } } return false, false } // perform another recursive step mid := halfL + ((halfR - halfL + 1) / 2) mulL, mulR := fp{1}, fp{1} // compute u = primes_1 * ... * primes_m for i := halfL; i < mid; i++ { mul512(&mulR, &mulR, primes[i]) } // compute v = primes_m+1 * ... * primes_n for i := mid; i < halfR; i++ { mul512(&mulL, &mulL, primes[i]) } // calculate Q_i xMul(&Q, p, a, &mulR) xMul(p, p, a, &mulL) d1, r1 = cofactorMul(&Q, a, mid, halfR, order) d2, r2 = cofactorMul(p, a, halfL, mid, order) return d1 || d2, r1 || r2 } // groupAction evaluates group action of prv.e on a Montgomery // curve represented by coefficient pub.A. // This is implementation of algorithm 2 from ia.cr/2018/383. func groupAction(pub *PublicKey, prv *PrivateKey, rng io.Reader) { var k [2]fp var e [2][primeCount]uint8 done := [2]bool{false, false} A := coeff{a: pub.a, c: one} k[0][0] = 4 k[1][0] = 4 for i, v := range primes { t := (prv.e[uint(i)>>1] << ((uint(i) % 2) * 4)) >> 4 if t > 0 { e[0][i] = uint8(t) e[1][i] = 0 mul512(&k[1], &k[1], v) } else if t < 0 { e[1][i] = uint8(-t) e[0][i] = 0 mul512(&k[0], &k[0], v) } else { e[0][i] = 0 e[1][i] = 0 mul512(&k[0], &k[0], v) mul512(&k[1], &k[1], v) } } for { var P point var rhs fp prv.randFp(&P.x, rng) P.z = one montEval(&rhs, &A.a, &P.x) sign := rhs.isNonQuadRes() if done[sign] { continue } xMul(&P, &P, &A, &k[sign]) done[sign] = true for i, v := range primes { if e[sign][i] != 0 { cof := fp{1} var K point for j := i + 1; j < len(primes); j++ { if e[sign][j] != 0 { mul512(&cof, &cof, primes[j]) } } xMul(&K, &P, &A, &cof) if !K.z.isZero() { xIso(&P, &A, &K, v) e[sign][i] = e[sign][i] - 1 if e[sign][i] == 0 { mul512(&k[sign], &k[sign], primes[i]) } } } done[sign] = done[sign] && (e[sign][i] == 0) } modExpRdc512(&A.c, &A.c, &pMin1) mulRdc(&A.a, &A.a, &A.c) A.c = one if done[0] && done[1] { break } } pub.a = A.a } // PrivateKey operations func (c *PrivateKey) Import(key []byte) bool { if len(key) < len(c.e) { return false } for i, v := range key { c.e[i] = int8(v) } return true } func (c PrivateKey) Export(out []byte) bool { if len(out) < len(c.e) { return false } for i, v := range c.e { out[i] = byte(v) } return true } func GeneratePrivateKey(key *PrivateKey, rng io.Reader) error { for i := range key.e { key.e[i] = 0 } for i := 0; i < len(primes); { _, err := io.ReadFull(rng, key.wbuf[:]) if err != nil { return err } for j := range key.wbuf { if int8(key.wbuf[j]) <= expMax && int8(key.wbuf[j]) >= -expMax { key.e[i>>1] |= int8((key.wbuf[j] & 0xF) << uint((i%2)*4)) i = i + 1 if i == len(primes) { break } } } } return nil } // Public key operations // reset removes key material from PublicKey. func (c *PublicKey) reset() { for i := range c.a { c.a[i] = 0 } } // Assumes key is in Montgomery domain. func (c *PublicKey) Import(key []byte) bool { if len(key) != numWords*limbByteSize { return false } for i := 0; i < len(key); i++ { j := i / limbByteSize k := uint64(i % 8) c.a[j] |= uint64(key[i]) << (8 * k) } return true } // Assumes key is exported as encoded in Montgomery domain. func (c *PublicKey) Export(out []byte) bool { if len(out) != numWords*limbByteSize { return false } for i := 0; i < len(out); i++ { j := i / limbByteSize k := uint64(i % 8) out[i] = byte(c.a[j] >> (8 * k)) } return true } func GeneratePublicKey(pub *PublicKey, prv *PrivateKey, rng io.Reader) { pub.reset() groupAction(pub, prv, rng) } // Validate returns true if 'pub' is a valid cSIDH public key, // otherwise false. // More precisely, the function verifies that curve // // y^2 = x^3 + pub.a * x^2 + x // // is supersingular. func Validate(pub *PublicKey, rng io.Reader) bool { // Check if in range if !isLess(&pub.a, &p) { return false } // Check if pub represents a smooth Montgomery curve. if pub.a.equal(&two) || pub.a.equal(&twoNeg) { return false } // Check if pub represents a supersingular curve. for { var P point A := point{pub.a, one} // Randomly chosen P must have big enough order to check // supersingularity. Probability of random P having big // enough order is very high, as proven by W.Castryck et // al. (ia.cr/2018/383, ch 5) pub.randFp(&P.x, rng) P.z = one xDbl(&P, &P, &A) xDbl(&P, &P, &A) done, res := cofactorMul(&P, &coeff{A.x, A.z}, 0, len(primes), &fp{1}) if done { return res } } } // DeriveSecret computes a cSIDH shared secret. If successful, returns true // and fills 'out' with shared secret. Function returns false in case 'pub' is invalid. // More precisely, shared secret is a Montgomery coefficient A of a secret // curve y^2 = x^3 + Ax^2 + x, computed by applying action of a prv.e // on a curve represented by pub.a. func DeriveSecret(out *[64]byte, pub *PublicKey, prv *PrivateKey, rng io.Reader) bool { if !Validate(pub, rng) { return false } groupAction(pub, prv, rng) pub.Export(out[:]) return true } golang-github-cloudflare-circl-1.3.7/dh/csidh/csidh_test.go000066400000000000000000000230401454601126700236330ustar00rootroot00000000000000package csidh import ( "bytes" "crypto/rand" "encoding/binary" "encoding/hex" "encoding/json" "os" "testing" . "github.com/cloudflare/circl/internal/test" ) // Possible values for "Status" const ( Valid = iota // Indicates that shared secret must be agreed correctly ValidPublicKey2 // Public key 2 must succeed validation InvalidSharedSecret // Calculated shared secret must be different than test vector InvalidPublicKey1 // Public key 1 generated from private key must be different than test vector InvalidPublicKey2 // Public key 2 must fail validation ) var StatusValues = map[int]string{ Valid: "valid", ValidPublicKey2: "valid_public_key2", InvalidSharedSecret: "invalid_shared_secret", InvalidPublicKey1: "invalid_public_key1", InvalidPublicKey2: "invalid_public_key2", } var rng = rand.Reader type TestVector struct { ID int `json:"Id"` Pk1 string `json:"Pk1"` Pr1 string `json:"Pr1"` Pk2 string `json:"Pk2"` Ss string `json:"Ss"` Status string `json:"status"` } type TestVectors struct { Vectors []TestVector `json:"Vectors"` } func TestCompare64(t *testing.T) { const s uint64 = 0xFFFFFFFFFFFFFFFF val1 := fp{0, 2, 3, 4, 5, 6, 7, 8} val2 := fp{s, s, s, s, s, s, s, s} var zero fp if !zero.isZero() { t.Errorf("isZero returned true, where it should be false") } if val1.isZero() { t.Errorf("isZero returned false, where it should be true") } if val2.isZero() { t.Errorf("isZero returned false, where it should be true") } } func TestEphemeralKeyExchange(t *testing.T) { var ss1, ss2 [64]byte var prv1, prv2 PrivateKey var pub1, pub2 PublicKey prvBytes1 := []byte{0xaa, 0x54, 0xe4, 0xd4, 0xd0, 0xbd, 0xee, 0xcb, 0xf4, 0xd0, 0xc2, 0xbc, 0x52, 0x44, 0x11, 0xee, 0xe1, 0x14, 0xd2, 0x24, 0xe5, 0x0, 0xcc, 0xf5, 0xc0, 0xe1, 0x1e, 0xb3, 0x43, 0x52, 0x45, 0xbe, 0xfb, 0x54, 0xc0, 0x55, 0xb2} prv1.Import(prvBytes1) GeneratePublicKey(&pub1, &prv1, rng) CheckNoErr(t, GeneratePrivateKey(&prv2, rng), "PrivateKey generation failed") GeneratePublicKey(&pub2, &prv2, rng) CheckOk( DeriveSecret(&ss1, &pub1, &prv2, rng), "Derivation failed", t) CheckOk( DeriveSecret(&ss2, &pub2, &prv1, rng), "Derivation failed", t) if !bytes.Equal(ss1[:], ss2[:]) { t.Error("ss1 != ss2") } } func TestPrivateKeyExportImport(t *testing.T) { var buf [37]byte for i := 0; i < numIter; i++ { var prv1, prv2 PrivateKey CheckNoErr(t, GeneratePrivateKey(&prv1, rng), "PrivateKey generation failed") prv1.Export(buf[:]) prv2.Import(buf[:]) for i := 0; i < len(prv1.e); i++ { if prv1.e[i] != prv2.e[i] { t.Error("Error occurred when public key export/import") } } } } func TestValidateNegative(t *testing.T) { pk := PublicKey{a: p} pk.a[0]++ if Validate(&pk, rng) { t.Error("Public key > p has been validated") } pk = PublicKey{a: p} if Validate(&pk, rng) { t.Error("Public key == p has been validated") } pk = PublicKey{a: two} if Validate(&pk, rng) { t.Error("Public key == 2 has been validated") } pk = PublicKey{a: twoNeg} if Validate(&pk, rng) { t.Error("Public key == -2 has been validated") } } func TestPublicKeyExportImport(t *testing.T) { var buf [64]byte eq64 := func(x, y []uint64) bool { for i := range x { if x[i] != y[i] { return false } } return true } for i := 0; i < numIter; i++ { var prv PrivateKey var pub1, pub2 PublicKey CheckNoErr(t, GeneratePrivateKey(&prv, rng), "PrivateKey generation failed") GeneratePublicKey(&pub1, &prv, rng) pub1.Export(buf[:]) pub2.Import(buf[:]) if !eq64(pub1.a[:], pub2.a[:]) { t.Error("Error occurred when public key export/import") } } } // Test vectors generated by reference implementation. func TestKAT(t *testing.T) { var tests TestVectors // Helper checks if e==true and reports an error if not. checkExpr := func(e bool, vec *TestVector, t *testing.T, msg string) { t.Helper() if !e { t.Errorf("[Test ID=%d] "+msg, vec.ID) } } // checkSharedSecret implements nominal case - imports asymmetric keys for // both parties, derives secret key and compares it to value in test vector. // Comparison must succeed in case status is "Valid" in any other case // it must fail. checkSharedSecret := func(vec *TestVector, t *testing.T, status int) { var prv1 PrivateKey var pub1, pub2 PublicKey var ss [SharedSecretSize]byte prBuf, err := hex.DecodeString(vec.Pr1) if err != nil { t.Fatal(err) } checkExpr(prv1.Import(prBuf[:]), vec, t, "PrivateKey wrong") pkBuf, err := hex.DecodeString(vec.Pk1) if err != nil { t.Fatal(err) } checkExpr(pub1.Import(pkBuf[:]), vec, t, "PublicKey 1 wrong") pkBuf, err = hex.DecodeString(vec.Pk2) if err != nil { t.Fatal(err) } checkExpr(pub2.Import(pkBuf[:]), vec, t, "PublicKey 2 wrong") checkExpr(DeriveSecret(&ss, &pub2, &prv1, rng), vec, t, "Error when deriving key") ssExp, err := hex.DecodeString(vec.Ss) if err != nil { t.Fatal(err) } checkExpr(bytes.Equal(ss[:], ssExp) == (status == Valid), vec, t, "Unexpected value of shared secret") } // checkPublicKey1 imports public and private key for one party A // and tries to generate public key for a private key. After that // it compares generated key to a key from test vector. Comparison // must fail. checkPublicKey1 := func(vec *TestVector, t *testing.T) { var prv PrivateKey var pub PublicKey var pubBytesGot [PublicKeySize]byte prBuf, err := hex.DecodeString(vec.Pr1) if err != nil { t.Fatal(err) } pubBytesExp, err := hex.DecodeString(vec.Pk1) if err != nil { t.Fatal(err) } checkExpr( prv.Import(prBuf[:]), vec, t, "PrivateKey wrong") // Generate public key CheckNoErr(t, GeneratePrivateKey(&prv, rng), "PrivateKey generation failed") pub.Export(pubBytesGot[:]) // pubBytesGot must be different than pubBytesExp checkExpr( !bytes.Equal(pubBytesGot[:], pubBytesExp), vec, t, "Public key generated is the same as public key from the test vector") } // checkPublicKey2 the goal is to test key validation. Test tries to // import public key for B and ensure that import succeeds in case // status is "Valid" and fails otherwise. checkPublicKey2 := func(vec *TestVector, t *testing.T, status int) { var pub PublicKey pubBytesExp, err := hex.DecodeString(vec.Pk2) if err != nil { t.Fatal(err) } // Import validates an input, so it must fail pub.Import(pubBytesExp[:]) checkExpr( Validate(&pub, rng) == (status == Valid || status == ValidPublicKey2), vec, t, "PublicKey has been validated correctly") } // Load test data file, err := os.Open(katFile) if err != nil { t.Fatal(err.Error()) } err = json.NewDecoder(file).Decode(&tests) if err != nil { t.Fatal(err.Error()) } // Loop over numIter test cases // The algorithm is relatively slow, so it tests a smaller number. N := len(tests.Vectors) var buf [2]byte for i := 0; i < numIter; i++ { _, _ = rand.Read(buf[:]) idx := binary.LittleEndian.Uint16(buf[:]) % uint16(N) test := tests.Vectors[idx] switch test.Status { case StatusValues[Valid]: checkSharedSecret(&test, t, Valid) checkPublicKey2(&test, t, Valid) case StatusValues[InvalidSharedSecret]: checkSharedSecret(&test, t, InvalidSharedSecret) case StatusValues[InvalidPublicKey1]: checkPublicKey1(&test, t) case StatusValues[InvalidPublicKey2]: checkPublicKey2(&test, t, InvalidPublicKey2) case StatusValues[InvalidPublicKey2]: checkPublicKey2(&test, t, InvalidPublicKey2) case StatusValues[ValidPublicKey2]: checkPublicKey2(&test, t, ValidPublicKey2) } } } var ( prv1, prv2 PrivateKey pub1, pub2 PublicKey ) // Private key generation. func BenchmarkGeneratePrivate(b *testing.B) { for n := 0; n < b.N; n++ { _ = GeneratePrivateKey(&prv1, rng) } } // Public key generation from private (group action on empty key). func BenchmarkGenerateKeyPair(b *testing.B) { for n := 0; n < b.N; n++ { var pub PublicKey _ = GeneratePrivateKey(&prv1, rng) GeneratePublicKey(&pub, &prv1, rng) } } // Benchmark validation on same key multiple times. func BenchmarkValidate(b *testing.B) { prvBytes := []byte{0xaa, 0x54, 0xe4, 0xd4, 0xd0, 0xbd, 0xee, 0xcb, 0xf4, 0xd0, 0xc2, 0xbc, 0x52, 0x44, 0x11, 0xee, 0xe1, 0x14, 0xd2, 0x24, 0xe5, 0x0, 0xcc, 0xf5, 0xc0, 0xe1, 0x1e, 0xb3, 0x43, 0x52, 0x45, 0xbe, 0xfb, 0x54, 0xc0, 0x55, 0xb2} prv1.Import(prvBytes) var pub PublicKey GeneratePublicKey(&pub, &prv1, rng) for n := 0; n < b.N; n++ { Validate(&pub, rng) } } // Benchmark validation on random (most probably wrong) key. func BenchmarkValidateRandom(b *testing.B) { var tmp [64]byte var pub PublicKey // Initialize seed for n := 0; n < b.N; n++ { if _, err := rng.Read(tmp[:]); err != nil { b.FailNow() } pub.Import(tmp[:]) } } // Benchmark validation on different keys. func BenchmarkValidateGenerated(b *testing.B) { for n := 0; n < b.N; n++ { _ = GeneratePrivateKey(&prv1, rng) GeneratePublicKey(&pub1, &prv1, rng) Validate(&pub1, rng) } } // Generate some keys and benchmark derive. func BenchmarkDerive(b *testing.B) { var ss [64]byte _ = GeneratePrivateKey(&prv1, rng) GeneratePublicKey(&pub1, &prv1, rng) _ = GeneratePrivateKey(&prv2, rng) GeneratePublicKey(&pub2, &prv2, rng) b.ResetTimer() for n := 0; n < b.N; n++ { DeriveSecret(&ss, &pub2, &prv1, rng) } } // Benchmarks both - key generation and derivation. func BenchmarkDeriveGenerated(b *testing.B) { var ss [64]byte for n := 0; n < b.N; n++ { _ = GeneratePrivateKey(&prv1, rng) GeneratePublicKey(&pub1, &prv1, rng) _ = GeneratePrivateKey(&prv2, rng) GeneratePublicKey(&pub2, &prv2, rng) DeriveSecret(&ss, &pub2, &prv1, rng) } } golang-github-cloudflare-circl-1.3.7/dh/csidh/curve.go000066400000000000000000000131211454601126700226250ustar00rootroot00000000000000package csidh // xAdd implements differential arithmetic in P^1 for Montgomery // curves E(x): x^3 + A*x^2 + x by using x-coordinate only arithmetic. // // x(PaQ) = x(P) + x(Q) by using x(P-Q) // // This algorithms is correctly defined only for cases when // P!=inf, Q!=inf, P!=Q and P!=-Q. func xAdd(PaQ, P, Q, PdQ *point) { var t0, t1, t2, t3 fp addRdc(&t0, &P.x, &P.z) subRdc(&t1, &P.x, &P.z) addRdc(&t2, &Q.x, &Q.z) subRdc(&t3, &Q.x, &Q.z) mulRdc(&t0, &t0, &t3) mulRdc(&t1, &t1, &t2) addRdc(&t2, &t0, &t1) subRdc(&t3, &t0, &t1) mulRdc(&t2, &t2, &t2) // sqr mulRdc(&t3, &t3, &t3) // sqr mulRdc(&PaQ.x, &PdQ.z, &t2) mulRdc(&PaQ.z, &PdQ.x, &t3) } // xDbl implements point doubling on a Montgomery curve // E(x): x^3 + A*x^2 + x by using x-coordinate only arithmetic. // // x(Q) = [2]*x(P) // // It is correctly defined for all P != inf. func xDbl(Q, P, A *point) { var t0, t1, t2 fp addRdc(&t0, &P.x, &P.z) mulRdc(&t0, &t0, &t0) // sqr subRdc(&t1, &P.x, &P.z) mulRdc(&t1, &t1, &t1) // sqr subRdc(&t2, &t0, &t1) mulRdc(&t1, &four, &t1) mulRdc(&t1, &t1, &A.z) mulRdc(&Q.x, &t0, &t1) addRdc(&t0, &A.z, &A.z) addRdc(&t0, &t0, &A.x) mulRdc(&t0, &t0, &t2) addRdc(&t0, &t0, &t1) mulRdc(&Q.z, &t0, &t2) } // xDblAdd implements combined doubling of point P // and addition of points P and Q on a Montgomery curve // E(x): x^3 + A*x^2 + x by using x-coordinate only arithmetic. // // x(PaP) = x(2*P) // x(PaQ) = x(P+Q) func xDblAdd(PaP, PaQ, P, Q, PdQ *point, A24 *coeff) { var t0, t1, t2 fp addRdc(&t0, &P.x, &P.z) subRdc(&t1, &P.x, &P.z) mulRdc(&PaP.x, &t0, &t0) subRdc(&t2, &Q.x, &Q.z) addRdc(&PaQ.x, &Q.x, &Q.z) mulRdc(&t0, &t0, &t2) mulRdc(&PaP.z, &t1, &t1) mulRdc(&t1, &t1, &PaQ.x) subRdc(&t2, &PaP.x, &PaP.z) mulRdc(&PaP.z, &PaP.z, &A24.c) mulRdc(&PaP.x, &PaP.x, &PaP.z) mulRdc(&PaQ.x, &A24.a, &t2) subRdc(&PaQ.z, &t0, &t1) addRdc(&PaP.z, &PaP.z, &PaQ.x) addRdc(&PaQ.x, &t0, &t1) mulRdc(&PaP.z, &PaP.z, &t2) mulRdc(&PaQ.z, &PaQ.z, &PaQ.z) mulRdc(&PaQ.x, &PaQ.x, &PaQ.x) mulRdc(&PaQ.z, &PaQ.z, &PdQ.x) mulRdc(&PaQ.x, &PaQ.x, &PdQ.z) } // cswappoint swaps P1 with P2 in constant time. The 'choice' // parameter must have a value of either 1 (results // in swap) or 0 (results in no-swap). func cswappoint(P1, P2 *point, choice uint8) { cswap512(&P1.x, &P2.x, choice) cswap512(&P1.z, &P2.z, choice) } // xMul implements point multiplication with left-to-right Montgomery // adder. co is A coefficient of x^3 + A*x^2 + x curve. k must be > 0 // // Non-constant time! func xMul(kP, P *point, co *coeff, k *fp) { var A24 coeff var Q point var j uint A := point{x: co.a, z: co.c} R := *P // Precompyte A24 = (A+2C:4C) => (A24.x = A.x+2A.z; A24.z = 4*A.z) addRdc(&A24.a, &co.c, &co.c) addRdc(&A24.a, &A24.a, &co.a) mulRdc(&A24.c, &co.c, &four) // Skip initial 0 bits. for j = 511; j > 0; j-- { // performance hit from making it constant-time is actually // quite big, so... unsafe branch for now if uint8(k[j>>6]>>(j&63)&1) != 0 { break } } xDbl(&Q, P, &A) prevBit := uint8(1) for i := j; i > 0; { i-- bit := uint8(k[i>>6] >> (i & 63) & 1) cswappoint(&Q, &R, prevBit^bit) xDblAdd(&Q, &R, &Q, &R, P, &A24) prevBit = bit } cswappoint(&Q, &R, uint8(k[0]&1)) *kP = Q } // xIso computes the isogeny with kernel point kern of a given order // kernOrder. Returns the new curve coefficient co and the image img. // // During computation function switches between Montgomery and twisted // Edwards curves in order to compute image curve parameters faster. // This technique is described by Meyer and Reith in ia.cr/2018/782. // // Non-constant time. func xIso(img *point, co *coeff, kern *point, kernOrder uint64) { var t0, t1, t2, S, D fp var Q, prod point var coEd coeff M := [3]point{*kern} // Compute twisted Edwards coefficients // coEd.a = co.a + 2*co.c // coEd.c = co.a - 2*co.c // coEd.a*X^2 + Y^2 = 1 + coEd.c*X^2*Y^2 addRdc(&coEd.c, &co.c, &co.c) addRdc(&coEd.a, &co.a, &coEd.c) subRdc(&coEd.c, &co.a, &coEd.c) // Transfer point to twisted Edwards YZ-coordinates // (X:Z)->(Y:Z) = (X-Z : X+Z) addRdc(&S, &img.x, &img.z) subRdc(&D, &img.x, &img.z) subRdc(&prod.x, &kern.x, &kern.z) addRdc(&prod.z, &kern.x, &kern.z) mulRdc(&t1, &prod.x, &S) mulRdc(&t0, &prod.z, &D) addRdc(&Q.x, &t0, &t1) subRdc(&Q.z, &t0, &t1) xDbl(&M[1], kern, &point{x: co.a, z: co.c}) // NOTE: Not constant time. for i := uint64(1); i < kernOrder>>1; i++ { if i >= 2 { xAdd(&M[i%3], &M[(i-1)%3], kern, &M[(i-2)%3]) } subRdc(&t1, &M[i%3].x, &M[i%3].z) addRdc(&t0, &M[i%3].x, &M[i%3].z) mulRdc(&prod.x, &prod.x, &t1) mulRdc(&prod.z, &prod.z, &t0) mulRdc(&t1, &t1, &S) mulRdc(&t0, &t0, &D) addRdc(&t2, &t0, &t1) mulRdc(&Q.x, &Q.x, &t2) subRdc(&t2, &t0, &t1) mulRdc(&Q.z, &Q.z, &t2) } mulRdc(&Q.x, &Q.x, &Q.x) mulRdc(&Q.z, &Q.z, &Q.z) mulRdc(&img.x, &img.x, &Q.x) mulRdc(&img.z, &img.z, &Q.z) // coEd.a^kernOrder and coEd.c^kernOrder modExpRdc64(&coEd.a, &coEd.a, kernOrder) modExpRdc64(&coEd.c, &coEd.c, kernOrder) // prod^8 mulRdc(&prod.x, &prod.x, &prod.x) mulRdc(&prod.x, &prod.x, &prod.x) mulRdc(&prod.x, &prod.x, &prod.x) mulRdc(&prod.z, &prod.z, &prod.z) mulRdc(&prod.z, &prod.z, &prod.z) mulRdc(&prod.z, &prod.z, &prod.z) // Compute image curve params mulRdc(&coEd.c, &coEd.c, &prod.x) mulRdc(&coEd.a, &coEd.a, &prod.z) // Convert curve coefficients back to Montgomery addRdc(&co.a, &coEd.a, &coEd.c) subRdc(&co.c, &coEd.a, &coEd.c) addRdc(&co.a, &co.a, &co.a) } // montEval evaluates x^3 + Ax^2 + x. func montEval(res, A, x *fp) { var t fp *res = *x mulRdc(res, res, res) mulRdc(&t, A, x) addRdc(res, res, &t) addRdc(res, res, &one) mulRdc(res, res, x) } golang-github-cloudflare-circl-1.3.7/dh/csidh/curve_test.go000066400000000000000000000416721454601126700237000ustar00rootroot00000000000000package csidh import ( "math/big" "testing" ) // Actual test implementation. func TestXAdd(t *testing.T) { var P, Q, PdQ point var PaQ point var expPaQ big.Int // points from a Elliptic Curve defined in sage as follows: // A = 0x6055947AAFEBF773CE912680A6A32656073233D2FD6FDF4A143BE82D25B44ECC0431DE564C0F0D6591ACC62D6876E86F5D06B68C9EAF20D0DB0A6B99ED558512 // E = EllipticCurve(GF(p), [0, A, 0, 1, 0]) // where p is CSIDH's 511-bit prime checkXAdd := func() { xAdd(&PaQ, &P, &Q, &PdQ) ret := toNormX(&PaQ) if ret.Cmp(&expPaQ) != 0 { t.Errorf("\nExp: %s\nGot: %s", expPaQ.Text(16), ret.Text(16)) } } expPaQ.SetString("0x41C98C5D7FF118B1A3987733581FD69C0CC27D7B63BCCA525106B9945869C6DAEDAA3D5D9D2679237EF0D013BE68EF12731DBFB26E12576BAD1E824C67ABD125", 0) P.x = toFp("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD") P.z = toFp("1") Q.x = toFp("0x3C1A003C71436698B4A181CEB12BA4B4D1FF7BB14AAAF6FBDA6957C4EBA20AD8E3893DF6F64E67E81163E024C19C7E975F3EC61862F75502C3ED802370E75A3F") Q.z = toFp("1") PdQ.x = toFp("0x519B1928F752B0B2143C1C23EB247B370DBB5B9C29B9A3A064D7FBC1B67FAC34B6D3DDA0F3CB87C387B425B36F31B93A8E73252BA701927B767A9DE89D5A92AE") PdQ.z = toFp("1") checkXAdd() expPaQ.SetString("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD", 0) P.x = toFp("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD") P.z = toFp("1") Q.x = toFp("1") Q.z = toFp("0x0") PdQ.x = toFp(expPaQ.Text(10)) PdQ.z = toFp("1") checkXAdd() } func TestXDbl(t *testing.T) { var P, A point var PaP point var expPaP big.Int // points from a Elliptic Curve defined in sage as follows: // A = 0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138 // E = EllipticCurve(GF(p), [0, A, 0, 1, 0]) // where p is CSIDH's 511-bit prime expPaP.SetString("0x6115B5D8BB613D11BDFEA70D436D87C1515553F6A15061727B4001E0AF745AAA9F39EB9464982829D931F77DAB9D71B24FF0D1D34C347F2A51FD45821F2EA06F", 0) P.x = toFp("0x6C5B4D4AB0765AAB23C10F8455BE522D3A5363324D7AD641CC67C0A52FC1FFE9F3F8EDFE641478CA93D4D0016D83F21487FD4AF4E02F8A2C237CF27C5604BCC") P.z = toFp("1") A.x = toFp("0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138") A.z = toFp("1") xDbl(&PaP, &P, &A) ret := toNormX(&PaP) if ret.Cmp(&expPaP) != 0 { t.Errorf("\nExp: %s\nGot: %s", expPaP.Text(16), ret.Text(16)) } } func TestXDblAddNominal(t *testing.T) { var P, Q, PdQ point var PaP, PaQ point var expPaP, expPaQ big.Int var A coeff checkXDblAdd := func() { var A24 coeff // A24.a = 2*A.z + A.a addRdc(&A24.a, &A.c, &A.c) addRdc(&A24.a, &A24.a, &A.a) // A24.z = 4*A.z mulRdc(&A24.c, &A.c, &four) // Additionally will check if input can be same as output PaP = P PaQ = Q xDblAdd(&PaP, &PaQ, &PaP, &PaQ, &PdQ, &A24) retPaP := toNormX(&PaP) retPaQ := toNormX(&PaQ) if retPaP.Cmp(&expPaP) != 0 { t.Errorf("\nExp: %s\nGot: %s", expPaP.Text(16), retPaP.Text(16)) } if retPaQ.Cmp(&expPaQ) != 0 { t.Errorf("\nExp: %s\nGot: %s", expPaQ.Text(16), retPaQ.Text(16)) } } // 2*P expPaP.SetString("0x38F5B37271A3D8FA50107F88045D6F6B08355DD026C02E0306CE5875F47422736AD841B4122B2BD7DE6166BB6498F6A283378FF8250948E834F15CEA2D59A57B", 0) // P+Q expPaQ.SetString("0x53D9B44C5F61651612243CF7987F619FE6ACB5CF29538F96A63E7278E131F41A17D64388E31B028A5183EF9096AE82724BC34D8DDFD67AD68BD552A33C345B8C", 0) P.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") P.z = toFp("1") Q.x = toFp("0x465047949CD6574FDBE00EA365CAF7A95DC9DEBE96A188823CA8C9DD9F527CF81290D49864F61DF0C08C1D6052139230735CA6CFDBDC1A8820610CCD71861176") Q.z = toFp("1") PdQ.x = toFp("0x49D3B999A0A020B34473568A8F75B5405F2D3BE5A006595015FC6DDC6BED8AB2A51A887B6DC62C64354466865FFD69E50AD37F6F4FBD74119EB65EBC9367B556") PdQ.z = toFp("1") A.a = toFp("0x118F955D498D902FD42E5B2926F297CC814CD7649EC5B070295622F97C4A0D9BD34058A7E0E00CB73ED32FCC237F9F6B7D2A15F5CC7C4EC61ECEF80ACBB0EFA4") A.c = toFp("1") checkXDblAdd() // Case P=value, Q=(x=1, z=0). In this case PaQ==P; PaP=2*P expPaP.SetString("0x38F5B37271A3D8FA50107F88045D6F6B08355DD026C02E0306CE5875F47422736AD841B4122B2BD7DE6166BB6498F6A283378FF8250948E834F15CEA2D59A57B", 0) expPaQ.SetString("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9", 0) P.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") P.z = toFp("1") Q.x = toFp("1") Q.z = toFp("0") PdQ.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") PdQ.z = toFp("1") A.a = toFp("0x118F955D498D902FD42E5B2926F297CC814CD7649EC5B070295622F97C4A0D9BD34058A7E0E00CB73ED32FCC237F9F6B7D2A15F5CC7C4EC61ECEF80ACBB0EFA4") A.c = toFp("1") checkXDblAdd() } func TestXDblAddVSxDblxAdd(t *testing.T) { var P, Q, PdQ point var PaP1, PaQ1 point var PaP2, PaQ2 point var A point var A24 coeff P.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") P.z = toFp("1") Q.x = toFp("0x465047949CD6574FDBE00EA365CAF7A95DC9DEBE96A188823CA8C9DD9F527CF81290D49864F61DF0C08C1D6052139230735CA6CFDBDC1A8820610CCD71861176") Q.z = toFp("1") PdQ.x = toFp("0x49D3B999A0A020B34473568A8F75B5405F2D3BE5A006595015FC6DDC6BED8AB2A51A887B6DC62C64354466865FFD69E50AD37F6F4FBD74119EB65EBC9367B556") PdQ.z = toFp("1") A.x = toFp("0x118F955D498D902FD42E5B2926F297CC814CD7649EC5B070295622F97C4A0D9BD34058A7E0E00CB73ED32FCC237F9F6B7D2A15F5CC7C4EC61ECEF80ACBB0EFA4") A.z = toFp("1") // Precompute A24 for xDblAdd // (A+2C:4C) => (A24.x = A.x+2A.z; A24.z = 4*A.z) addRdc(&A24.a, &A.z, &A.z) addRdc(&A24.a, &A24.a, &A.x) mulRdc(&A24.c, &A.z, &four) for i := 0; i < numIter; i++ { xAdd(&PaQ2, &P, &Q, &PdQ) xDbl(&PaP2, &P, &A) xDblAdd(&PaP1, &PaQ1, &P, &Q, &PdQ, &A24) if !ceqpoint(&PaQ1, &PaQ2) { exp := toNormX(&PaQ1) got := toNormX(&PaQ2) t.Errorf("\nExp: \n\t%s\nGot from xAdd: \n\t%s", exp.Text(16), got.Text(16)) } if !ceqpoint(&PaP1, &PaP2) { exp := toNormX(&PaP1) got := toNormX(&PaP2) t.Errorf("\nExp: \n\t%s\nGot from xDbl: \n\t%s", exp.Text(16), got.Text(16)) } // Swap values for next operation PdQ = Q Q = P P = PaP1 } } func TestXMul(t *testing.T) { var P point var co coeff var expKP big.Int var k fp checkXMul := func() { var kP point xMul(&kP, &P, &co, &k) retKP := toNormX(&kP) if expKP.Cmp(&retKP) != 0 { t.Errorf("\nExp: %s\nGot: %s", expKP.Text(16), retKP.Text(16)) } // Check if first and second argument can overlap xMul(&P, &P, &co, &k) retKP = toNormX(&P) if expKP.Cmp(&retKP) != 0 { t.Errorf("\nExp: %s\nGot: %s", expKP.Text(16), retKP.Text(16)) } } // Case C=1 expKP.SetString("0x582B866603E6FBEBD21FE660FB34EF9466FDEC55FFBCE1073134CC557071147821BBAD225E30F7B2B6790B00ED9C39A29AA043F58AF995E440AFB13DA8E6D788", 0) P.x = toFp("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE") P.z = toFp("1") co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") co.c = toFp("1") k = fp{0x7A36C930A83EFBD5, 0xD0E80041ED0DDF9F, 0x5AA17134F1B8F877, 0x975711EC94168E51, 0xB3CAD962BED4BAC5, 0x3026DFDD7E4F5687, 0xE67F91AB8EC9C3AF, 0x34671D3FD8C317E7} checkXMul() // Check if algorithms works correctly with k=1 expKP.SetString("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE", 0) P.x = toFp("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE") P.z = toFp("1") co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") co.c = toFp("1") k = fp{1, 0, 0, 0, 0, 0, 0, 0} checkXMul() // Check if algorithms works correctly with value of k for which few small and high // order bits are 0 (test for odd number of cswaps in xMul) expKP.SetString("0x1925EDA0928C10F427B4E642E7E1481A670D1249956DED6A2292B9BAB841F6AA86A9F41459400845ED4A5E2531A14165F64FE4E43DBD85321B429C6DAE2E8987", 0) P.x = toFp("0x4CE8603817B9BB06515E921AA201D26B31F3CE181D1E18CD5CD704708CCAD47546CEEAB42B98EE67925A5259E0684A0489F574A999DE127F708B849ACAA12A63") P.z = toFp("1") co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") co.c = toFp("1") k = fp{0, 7, 0, 0, 0, 0, 0, 0} checkXMul() // Check if algorithms works correctly with value of k for which few small and high // order bits are 0 (test for even number of cswaps in xMul) expKP.SetString("0x30C02915C5967C3B6EB2196A934ADF38A183E9C7E814B54121F93048A8FC12D5036992FABF8D807581017A4C1F93D07352413F38F6A902FC76A8894FE8D94805", 0) P.x = toFp("0x2DDD15ED7C169BE6D9EC02CFE3DC507EC4A7A4D96DE3FAAB9BFCEA1B047807EA301E89830F2FDD0E7E642A85E7ACDE16BAD76DF140F719C4A7AB85153E7D69DC") P.z = toFp("1") co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") co.c = toFp("1") k = fp{0, 15, 0, 0, 0, 0, 0, 0} checkXMul() // xMul512 does NOT work correctly for k==0. In such case function will return 2*P. But // thanks to that fact we don't need to handle k==0 case, we get some speedup. expKP.SetString("0x6115B5D8BB613D11BDFEA70D436D87C1515553F6A15061727B4001E0AF745AAA9F39EB9464982829D931F77DAB9D71B24FF0D1D34C347F2A51FD45821F2EA06F", 0) P.x = toFp("0x6C5B4D4AB0765AAB23C10F8455BE522D3A5363324D7AD641CC67C0A52FC1FFE9F3F8EDFE641478CA93D4D0016D83F21487FD4AF4E02F8A2C237CF27C5604BCC") P.z = toFp("1") co.a = toFp("0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138") co.c = toFp("1") k = fp{0, 0, 0, 0, 0, 0, 0, 0} checkXMul() } func TestMappointHardcoded3(t *testing.T) { P := point{ x: fp{0xca1a2fdec38c669b, 0xf2fe3678ebeb978b, 0xfda3e9a6f0c719d, 0x6f7bffa41772570b, 0x3d90cdd6283dc150, 0x21b55b738eb1ded9, 0x209515d0a9f41dd6, 0x5275cf397d154a12}, z: fp{0x1fff8309761576e, 0xef239cbeda7c2ba1, 0x6136ae2d76e95873, 0x1f8f6ac909570cec, 0x780fdf0cc7d676d8, 0x548098fe92ed04e1, 0xb39da564701ef35d, 0x5fec19626df41306}, } A := coeff{ a: fp{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}, c: fp{0xc8fc8df598726f0a, 0x7b1bc81750a6af95, 0x5d319e67c1e961b4, 0xb0aa7275301955f1, 0x4a080672d9ba6c64, 0x97a5ef8a246ee77b, 0x6ea9e5d4383676a, 0x3496e2e117e0ec80}, } K := point{ x: fp{0x597616608e291c6f, 0xd14230b008736798, 0xa63099b1ace67e6e, 0xe37c13afd768bcfa, 0xc6ef718894f08135, 0x53a4fd09091f3522, 0xc9a1f9f670645fe1, 0x628c4a8efd83e5f0}, z: fp{0x8f18a654312ac1ad, 0xbc20a9b2472785c9, 0xdaf97c29bbf9e492, 0xf91a8c799e2f6119, 0xc8dc675cc8e528e6, 0x9a7b2c2f0df95171, 0x85629cd38cdd9fdb, 0x656d5253d3fd1a6e}, } var k uint64 = 3 expA := coeff{ a: fp{0x6fa92a66e77cfc1, 0x9efbfb7118f1832c, 0x441894cc5d1d24ae, 0x5a2f0fafa26761de, 0x8095c36d3a20a78a, 0xb22be0023612a135, 0x5eb844d06ef0f430, 0x52e53309d1c90cf8}, c: fp{0x98173d5664a23e5c, 0xd8fe1c6306bbc11a, 0xa774fbc502648059, 0x766a0d839aa62c83, 0x4b074f9b93d1633d, 0xf306019dbf87f505, 0x77c720ca059234b0, 0x3d47ab65269c5908}, } expP := point{ x: fp{0x91aba9b39f280495, 0xfbd8ea69d2990aeb, 0xb03e1b8ed7fe3dba, 0x3d30a41499f08998, 0xb15a42630de9c606, 0xa7dd487fef16f5c8, 0x8673948afed8e968, 0x57ecc8710004cd4d}, z: fp{0xce8819869a942526, 0xb98ca2ff79ef8969, 0xd49c9703743a1812, 0x21dbb090f9152e03, 0xbabdcac831b1adea, 0x8cee90762baa2ddd, 0xa0dd2ddcef809d96, 0x1de2a8887a32f19b}, } xIso(&P, &A, &K, k) if !eqFp(&P.x, &expP.x) || !eqFp(&P.z, &expP.z) { normP := toNormX(&P) normPExp := toNormX(&expP) t.Errorf("P != expP [\n %s != %s\n]", normP.Text(16), normPExp.Text(16)) } if !eqFp(&A.a, &expA.a) || !eqFp(&A.c, &expA.c) { t.Errorf("A != expA %X %X", A.a[0], expA.a[0]) } } func TestMappointHardcoded5(t *testing.T) { P := point{ x: fp{0xca1a2fdec38c669b, 0xf2fe3678ebeb978b, 0xfda3e9a6f0c719d, 0x6f7bffa41772570b, 0x3d90cdd6283dc150, 0x21b55b738eb1ded9, 0x209515d0a9f41dd6, 0x5275cf397d154a12}, z: fp{0x1fff8309761576e, 0xef239cbeda7c2ba1, 0x6136ae2d76e95873, 0x1f8f6ac909570cec, 0x780fdf0cc7d676d8, 0x548098fe92ed04e1, 0xb39da564701ef35d, 0x5fec19626df41306}, } A := coeff{ a: fp{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}, c: fp{0xc8fc8df598726f0a, 0x7b1bc81750a6af95, 0x5d319e67c1e961b4, 0xb0aa7275301955f1, 0x4a080672d9ba6c64, 0x97a5ef8a246ee77b, 0x6ea9e5d4383676a, 0x3496e2e117e0ec80}, } K := point{ x: fp{0x597616608e291c6f, 0xd14230b008736798, 0xa63099b1ace67e6e, 0xe37c13afd768bcfa, 0xc6ef718894f08135, 0x53a4fd09091f3522, 0xc9a1f9f670645fe1, 0x628c4a8efd83e5f0}, z: fp{0x8f18a654312ac1ad, 0xbc20a9b2472785c9, 0xdaf97c29bbf9e492, 0xf91a8c799e2f6119, 0xc8dc675cc8e528e6, 0x9a7b2c2f0df95171, 0x85629cd38cdd9fdb, 0x656d5253d3fd1a6e}, } var k uint64 = 5 expA := coeff{ a: fp{0x32076f58298ed474, 0x5094a1fc8696d307, 0x82e510594157944a, 0xb60ce760f88c83a9, 0xae8a28c325186983, 0xe31d2446a4ad2f18, 0xb266c612b5f141c1, 0x64283e618db5a705}, c: fp{0x4472b49b65272190, 0x2bd5919309778f56, 0x6132753691fe016c, 0x8f654849c09e6d34, 0xfa208dd9aea1ef12, 0xf7df0dd10071411a, 0x75afb7860500922c, 0x52fb7d34b129fb65}, } expP := point{ x: fp{0x3b75fc94b2a6df2d, 0x96d53dc9b0e867a0, 0x22e87202421d274e, 0x30a361440697ee1a, 0x8b52ee078bdbddcd, 0x64425d500e6b934d, 0xf47d1f568f6df391, 0x5d9d3607431395ab}, z: fp{0x746e02dafa040976, 0xcd408f2cddbf3a8e, 0xf643354e0e13a93f, 0x7c39ed96ce9a5e29, 0xfcdf26f1a1a550ca, 0x2fc8aafc4ca0a559, 0x5d204a2b14cf19ba, 0xbd2c3406762f05d}, } xIso(&P, &A, &K, k) if !eqFp(&P.x, &expP.x) || !eqFp(&P.z, &expP.z) { normP := toNormX(&P) normPExp := toNormX(&expP) t.Errorf("P != expP [\n %s != %s\n]", normP.Text(16), normPExp.Text(16)) } if !eqFp(&A.a, &expA.a) || !eqFp(&A.c, &expA.c) { t.Errorf("A != expA %X %X", A.a[0], expA.a[0]) } } func BenchmarkXMul(b *testing.B) { var kP, P point var co coeff var expKP big.Int var k fp // Case C=1 expKP.SetString("0x582B866603E6FBEBD21FE660FB34EF9466FDEC55FFBCE1073134CC557071147821BBAD225E30F7B2B6790B00ED9C39A29AA043F58AF995E440AFB13DA8E6D788", 0) P.x = toFp("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE") P.z = toFp("1") co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") co.c = toFp("1") k = fp{0x7A36C930A83EFBD5, 0xD0E80041ED0DDF9F, 0x5AA17134F1B8F877, 0x975711EC94168E51, 0xB3CAD962BED4BAC5, 0x3026DFDD7E4F5687, 0xE67F91AB8EC9C3AF, 0x34671D3FD8C317E7} for n := 0; n < b.N; n++ { xMul(&kP, &P, &co, &k) } } func BenchmarkXAdd(b *testing.B) { var P, Q, PdQ point var PaQ point P.x = toFp("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD") P.z = toFp("1") Q.x = toFp("0x3C1A003C71436698B4A181CEB12BA4B4D1FF7BB14AAAF6FBDA6957C4EBA20AD8E3893DF6F64E67E81163E024C19C7E975F3EC61862F75502C3ED802370E75A3F") Q.z = toFp("1") PdQ.x = toFp("0x519B1928F752B0B2143C1C23EB247B370DBB5B9C29B9A3A064D7FBC1B67FAC34B6D3DDA0F3CB87C387B425B36F31B93A8E73252BA701927B767A9DE89D5A92AE") PdQ.z = toFp("1") for n := 0; n < b.N; n++ { xAdd(&PaQ, &P, &Q, &PdQ) } } func BenchmarkXDbl(b *testing.B) { var P, A point var PaP point P.x = toFp("0x6C5B4D4AB0765AAB23C10F8455BE522D3A5363324D7AD641CC67C0A52FC1FFE9F3F8EDFE641478CA93D4D0016D83F21487FD4AF4E02F8A2C237CF27C5604BCC") P.z = toFp("1") A.x = toFp("0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138") A.z = toFp("1") for n := 0; n < b.N; n++ { xDbl(&PaP, &P, &A) } } func BenchmarkIsom(b *testing.B) { var P, kern point var expPhiP big.Int var co coeff k := uint64(2) expPhiP.SetString("0x5FEBD68F795F9AEB732ECF0D1507904922F2B0736704E0751EF242B4E191E6F630D83778B5E5681161FD071CDEF7DF4C3A41D0ECEB30E90B119C5BF86C5AB51A", 0) P.x = toFp("0x5FD8D226C228FD6AA3CCDCAB931C5D3AA000A46B47041F59D9724E517594F696D38F2CB45C987ACF68BB1057D8D518F926D8F55171F337D05354E0022BC66B23") P.z = toFp("1") co.a = toFp("0x9E8DBC4914E3C4F080592642DD0B08B9564AB3ADF75EE9B58A685443BA6E39A1ACD1201B7F034077AF344123880AF9D8C77575E6E782E00186881ECE8B87CA3") co.c = toFp("1") kern.x = toFp("0x594F77A49EABBF2A12025BC00E1DBC119CDA674B9FE8A00791724B42FEB7D225C4C9940B01B09B8F00B30B0E961212FB63E42614814E38EC9E5E5B0FEBF98C58") kern.z = toFp("1") for n := 0; n < b.N; n++ { xIso(&P, &co, &kern, k) } } golang-github-cloudflare-circl-1.3.7/dh/csidh/doc.go000066400000000000000000000006421454601126700222520ustar00rootroot00000000000000// Package csidh implements commutative supersingular isogeny-based Diffie-Hellman // key exchange algorithm (CSIDH) resulting from the group action. Implementation // uses prime field of a size 512-bits. // This implementation is highly experimental work and currently it is not suitable // for securing systems. // // References: // - cSIDH: ia.cr/2018/383 // - Faster cSIDH: ia.cr/2018/782 package csidh golang-github-cloudflare-circl-1.3.7/dh/csidh/fp511.go000066400000000000000000000134271454601126700223460ustar00rootroot00000000000000package csidh import ( "math/bits" ) // Constant time select. // if pick == 0xFF..FF (out = in1) // if pick == 0 (out = in2) // else out is undefined. func ctPick64(which uint64, in1, in2 uint64) uint64 { return (in1 & which) | (in2 & ^which) } // ctIsNonZero64 returns 0 in case i == 0, otherwise it returns 1. // Constant-time. func ctIsNonZero64(i uint64) int { // In case i==0 then i-1 will set MSB. Only in such case (i OR ~(i-1)) // will result in MSB being not set (logical implication: (i-1)=>i is // false iff (i-1)==0 and i==non-zero). In every other case MSB is // set and hence function returns 1. return int((i | (^(i - 1))) >> 63) } // Returns result of x= 0; i-- { v, c := bits.Sub64(y[i], x[i], 0) if c != 0 { return false } if v != 0 { return true } } // x == y return false } // r = x + y mod p. func addRdc(r, x, y *fp) { var c uint64 var t fp r[0], c = bits.Add64(x[0], y[0], 0) r[1], c = bits.Add64(x[1], y[1], c) r[2], c = bits.Add64(x[2], y[2], c) r[3], c = bits.Add64(x[3], y[3], c) r[4], c = bits.Add64(x[4], y[4], c) r[5], c = bits.Add64(x[5], y[5], c) r[6], c = bits.Add64(x[6], y[6], c) r[7], _ = bits.Add64(x[7], y[7], c) t[0], c = bits.Sub64(r[0], p[0], 0) t[1], c = bits.Sub64(r[1], p[1], c) t[2], c = bits.Sub64(r[2], p[2], c) t[3], c = bits.Sub64(r[3], p[3], c) t[4], c = bits.Sub64(r[4], p[4], c) t[5], c = bits.Sub64(r[5], p[5], c) t[6], c = bits.Sub64(r[6], p[6], c) t[7], c = bits.Sub64(r[7], p[7], c) w := 0 - c r[0] = ctPick64(w, r[0], t[0]) r[1] = ctPick64(w, r[1], t[1]) r[2] = ctPick64(w, r[2], t[2]) r[3] = ctPick64(w, r[3], t[3]) r[4] = ctPick64(w, r[4], t[4]) r[5] = ctPick64(w, r[5], t[5]) r[6] = ctPick64(w, r[6], t[6]) r[7] = ctPick64(w, r[7], t[7]) } // r = x - y. func sub512(r, x, y *fp) uint64 { var c uint64 r[0], c = bits.Sub64(x[0], y[0], 0) r[1], c = bits.Sub64(x[1], y[1], c) r[2], c = bits.Sub64(x[2], y[2], c) r[3], c = bits.Sub64(x[3], y[3], c) r[4], c = bits.Sub64(x[4], y[4], c) r[5], c = bits.Sub64(x[5], y[5], c) r[6], c = bits.Sub64(x[6], y[6], c) r[7], c = bits.Sub64(x[7], y[7], c) return c } // r = x - y mod p. func subRdc(r, x, y *fp) { var c uint64 // Same as sub512(r,x,y). Unfortunately // compiler is not able to inline it. r[0], c = bits.Sub64(x[0], y[0], 0) r[1], c = bits.Sub64(x[1], y[1], c) r[2], c = bits.Sub64(x[2], y[2], c) r[3], c = bits.Sub64(x[3], y[3], c) r[4], c = bits.Sub64(x[4], y[4], c) r[5], c = bits.Sub64(x[5], y[5], c) r[6], c = bits.Sub64(x[6], y[6], c) r[7], c = bits.Sub64(x[7], y[7], c) // if x r=x-y+p w := 0 - c r[0], c = bits.Add64(r[0], ctPick64(w, p[0], 0), 0) r[1], c = bits.Add64(r[1], ctPick64(w, p[1], 0), c) r[2], c = bits.Add64(r[2], ctPick64(w, p[2], 0), c) r[3], c = bits.Add64(r[3], ctPick64(w, p[3], 0), c) r[4], c = bits.Add64(r[4], ctPick64(w, p[4], 0), c) r[5], c = bits.Add64(r[5], ctPick64(w, p[5], 0), c) r[6], c = bits.Add64(r[6], ctPick64(w, p[6], 0), c) r[7], _ = bits.Add64(r[7], ctPick64(w, p[7], 0), c) } // Fixed-window mod exp for fpBitLen bit value with 4 bit window. Returned // result is a number in montgomery domain. // r = b ^ e (mod p). // Constant time. func modExpRdcCommon(r, b, e *fp, fpBitLen int) { var precomp [16]fp var t fp var c uint64 // Precompute step, computes an array of small powers of 'b'. As this // algorithm implements 4-bit window, we need 2^4=16 of such values. // b^0 = 1, which is equal to R from REDC. precomp[0] = one // b ^ 0 precomp[1] = *b // b ^ 1 for i := 2; i < 16; i = i + 2 { // OPTIMIZE: implement fast squaring. Then interleaving fast squaring // with multiplication should improve performance. mulRdc(&precomp[i], &precomp[i/2], &precomp[i/2]) // sqr mulRdc(&precomp[i+1], &precomp[i], b) } *r = one for i := fpBitLen/4 - 1; i >= 0; i-- { for j := 0; j < 4; j++ { mulRdc(r, r, r) } // note: non resistant to cache SCA idx := (e[i/16] >> uint((i%16)*4)) & 15 mulRdc(r, r, &precomp[idx]) } // if p <= r < 2p then r = r-p t[0], c = bits.Sub64(r[0], p[0], 0) t[1], c = bits.Sub64(r[1], p[1], c) t[2], c = bits.Sub64(r[2], p[2], c) t[3], c = bits.Sub64(r[3], p[3], c) t[4], c = bits.Sub64(r[4], p[4], c) t[5], c = bits.Sub64(r[5], p[5], c) t[6], c = bits.Sub64(r[6], p[6], c) t[7], c = bits.Sub64(r[7], p[7], c) w := 0 - c r[0] = ctPick64(w, r[0], t[0]) r[1] = ctPick64(w, r[1], t[1]) r[2] = ctPick64(w, r[2], t[2]) r[3] = ctPick64(w, r[3], t[3]) r[4] = ctPick64(w, r[4], t[4]) r[5] = ctPick64(w, r[5], t[5]) r[6] = ctPick64(w, r[6], t[6]) r[7] = ctPick64(w, r[7], t[7]) } // modExpRdc does modular exponentiation of 512-bit number. // Constant-time. func modExpRdc512(r, b, e *fp) { modExpRdcCommon(r, b, e, 512) } // modExpRdc does modular exponentiation of 64-bit number. // Constant-time. func modExpRdc64(r, b *fp, e uint64) { modExpRdcCommon(r, b, &fp{e}, 64) } // isNonQuadRes checks whether value v is quadratic residue. // Implementation uses Fermat's little theorem (or // Euler's criterion) // // a^(p-1) == 1, hence // (a^2) ((p-1)/2) == 1 // // Which means v is a quadratic residue iff v^((p-1)/2) == 1. // Caller provided v must be in montgomery domain. // Returns 0 in case v is quadratic residue or 1 in case // v is quadratic non-residue. func (v *fp) isNonQuadRes() int { var res fp var b uint64 modExpRdc512(&res, v, &pMin1By2) for i := range res { b |= res[i] ^ one[i] } return ctIsNonZero64(b) } // isZero returns false in case v is equal to 0, otherwise // true. Constant time. func (v *fp) isZero() bool { var r uint64 for i := 0; i < numWords; i++ { r |= v[i] } return ctIsNonZero64(r) == 0 } // equal checks if v is equal to in. Constant time. func (v *fp) equal(in *fp) bool { var r uint64 for i := range v { r |= v[i] ^ in[i] } return ctIsNonZero64(r) == 0 } golang-github-cloudflare-circl-1.3.7/dh/csidh/fp511_amd64.go000066400000000000000000000027441454601126700233410ustar00rootroot00000000000000//go:build amd64 && !noasm // +build amd64,!noasm package csidh import ( "math/bits" "golang.org/x/sys/cpu" ) var ( // Signals support for BMI2 (MULX) hasBMI2 = cpu.X86.HasBMI2 // Signals support for ADX and BMI2 hasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX ) var _ = hasBMI2 func mul512(r, m1 *fp, m2 uint64) { mul512Amd64(r, m1, m2) } func cswap512(x, y *fp, choice uint8) { cswap512Amd64(x, y, choice) } func mulRdc(r, x, y *fp) { mulRdcAmd64(r, x, y) } //go:noescape func mul512Amd64(a, b *fp, c uint64) //go:noescape func cswap512Amd64(x, y *fp, choice uint8) //go:noescape func mulBmiAsm(res, x, y *fp) // mulRdc performs montgomery multiplication r = x * y mod P. // Returned result r is already reduced and in Montgomery domain. func mulRdcAmd64(r, x, y *fp) { var t fp var c uint64 if hasADXandBMI2 { mulBmiAsm(r, x, y) } else { mulGeneric(r, x, y) } // if p <= r < 2p then r = r-p t[0], c = bits.Sub64(r[0], p[0], 0) t[1], c = bits.Sub64(r[1], p[1], c) t[2], c = bits.Sub64(r[2], p[2], c) t[3], c = bits.Sub64(r[3], p[3], c) t[4], c = bits.Sub64(r[4], p[4], c) t[5], c = bits.Sub64(r[5], p[5], c) t[6], c = bits.Sub64(r[6], p[6], c) t[7], c = bits.Sub64(r[7], p[7], c) w := 0 - c r[0] = ctPick64(w, r[0], t[0]) r[1] = ctPick64(w, r[1], t[1]) r[2] = ctPick64(w, r[2], t[2]) r[3] = ctPick64(w, r[3], t[3]) r[4] = ctPick64(w, r[4], t[4]) r[5] = ctPick64(w, r[5], t[5]) r[6] = ctPick64(w, r[6], t[6]) r[7] = ctPick64(w, r[7], t[7]) } golang-github-cloudflare-circl-1.3.7/dh/csidh/fp511_amd64.s000066400000000000000000000135031454601126700231710ustar00rootroot00000000000000// +build amd64 #include "textflag.h" // Multiplies 512-bit value by 64-bit value. Uses MULQ instruction to // multiply 2 64-bit values. // // Result: x = (y * z) mod 2^512 // // Registers used: AX, CX, DX, SI, DI, R8 // // func mul512Amd64(a, b *Fp, c uint64) TEXT ·mul512Amd64(SB), NOSPLIT, $0-24 MOVQ a+0(FP), DI // result MOVQ b+8(FP), SI // multiplicand // Check whether to use optimized implementation CMPB ·hasBMI2(SB), $1 JE mul512_mulx MOVQ c+16(FP), R10 // 64 bit multiplier, used by MULQ MOVQ R10, AX; MULQ 0(SI); MOVQ DX, R11; MOVQ AX, 0(DI) //x[0] MOVQ R10, AX; MULQ 8(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 8(DI) //x[1] MOVQ R10, AX; MULQ 16(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 16(DI) //x[2] MOVQ R10, AX; MULQ 24(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 24(DI) //x[3] MOVQ R10, AX; MULQ 32(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 32(DI) //x[4] MOVQ R10, AX; MULQ 40(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 40(DI) //x[5] MOVQ R10, AX; MULQ 48(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 48(DI) //x[6] MOVQ R10, AX; MULQ 56(SI); ADDQ R11, AX; MOVQ AX, 56(DI) //x[7] RET // Optimized for CPUs with BMI2 mul512_mulx: MOVQ c+16(FP), DX // 64 bit multiplier, used by MULX MULXQ 0(SI), AX, R10; MOVQ AX, 0(DI) // x[0] MULXQ 8(SI), AX, R11; ADDQ R10, AX; MOVQ AX, 8(DI) // x[1] MULXQ 16(SI), AX, R10; ADCQ R11, AX; MOVQ AX, 16(DI) // x[2] MULXQ 24(SI), AX, R11; ADCQ R10, AX; MOVQ AX, 24(DI) // x[3] MULXQ 32(SI), AX, R10; ADCQ R11, AX; MOVQ AX, 32(DI) // x[4] MULXQ 40(SI), AX, R11; ADCQ R10, AX; MOVQ AX, 40(DI) // x[5] MULXQ 48(SI), AX, R10; ADCQ R11, AX; MOVQ AX, 48(DI) // x[6] MULXQ 56(SI), AX, R11; ADCQ R10, AX; MOVQ AX, 56(DI) // x[7] RET TEXT ·cswap512Amd64(SB),NOSPLIT,$0-17 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVBLZX choice+16(FP), AX // AL = 0 or 1 // Make AX, so that either all bits are set or non // AX = 0 or 1 NEGQ AX // Fill xmm15. After this step first half of XMM15 is // just zeros and second half is whatever in AX MOVQ AX, X15 // Copy lower double word everywhere else. So that // XMM15=AL|AL|AL|AL. As AX has either all bits set // or non result will be that XMM15 has also either // all bits set or non of them. PSHUFD $0, X15, X15 #ifndef CSWAP_BLOCK #define CSWAP_BLOCK(idx) \ MOVOU (idx*16)(DI), X0 \ MOVOU (idx*16)(SI), X1 \ \ // X2 = mask & (X0 ^ X1) MOVO X1, X2 \ PXOR X0, X2 \ PAND X15, X2 \ \ PXOR X2, X0 \ PXOR X2, X1 \ \ MOVOU X0, (idx*16)(DI) \ MOVOU X1, (idx*16)(SI) #endif CSWAP_BLOCK(0) CSWAP_BLOCK(1) CSWAP_BLOCK(2) CSWAP_BLOCK(3) RET // mulAsm implements montgomery multiplication interleaved with // montgomery reduction. It uses MULX and ADCX/ADOX instructions. // Implementation specific to 511-bit prime 'p' // // func mulBmiAsm(res, x, y *fp) TEXT ·mulBmiAsm(SB),NOSPLIT,$8-24 MOVQ x+8(FP), DI // multiplicand MOVQ y+16(FP), SI // multiplier XORQ R8, R8 XORQ R9, R9 XORQ R10, R10 XORQ R11, R11 XORQ R12, R12 XORQ R13, R13 XORQ R14, R14 XORQ CX, CX MOVQ BP, 0(SP) // push: BP is Callee-save. XORQ BP, BP // Uses BMI2 (MULX) #ifdef MULS_MULX_512 #undef MULS_MULX_512 #endif #define MULS_MULX_512(idx, r0, r1, r2, r3, r4, r5, r6, r7, r8) \ \ // Reduction step MOVQ ( 0)(SI), DX \ MULXQ ( 8*idx)(DI), DX, AX \ ADDQ r0, DX \ MOVQ ·pNegInv(SB), AX \ MULXQ AX, DX, AX \ \ XORQ AX, AX; \ MOVQ ·p+ 0(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r0; ADCXQ BX, r1 \ MOVQ ·p+ 8(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r1; ADCXQ BX, r2 \ MOVQ ·p+16(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r2; ADCXQ BX, r3 \ MOVQ ·p+24(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r3; ADCXQ BX, r4 \ MOVQ ·p+32(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r4; ADCXQ BX, r5 \ MOVQ ·p+40(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r5; ADCXQ BX, r6 \ MOVQ ·p+48(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r6; ADCXQ BX, r7 \ MOVQ ·p+56(SB), AX; MULXQ AX, AX, BX; ADOXQ AX, r7; ADCXQ BX, r8 \ MOVQ $0, AX; ;;;;;;;;;;;;;;;;;;;;;;; ADOXQ AX, r8; \ \ // Multiplication step MOVQ (8*idx)(DI), DX \ \ XORQ AX, AX \ MULXQ ( 0)(SI), AX, BX; ADOXQ AX, r0; ADCXQ BX, r1 \ MULXQ ( 8)(SI), AX, BX; ADOXQ AX, r1; ADCXQ BX, r2 \ MULXQ (16)(SI), AX, BX; ADOXQ AX, r2; ADCXQ BX, r3 \ MULXQ (24)(SI), AX, BX; ADOXQ AX, r3; ADCXQ BX, r4 \ MULXQ (32)(SI), AX, BX; ADOXQ AX, r4; ADCXQ BX, r5 \ MULXQ (40)(SI), AX, BX; ADOXQ AX, r5; ADCXQ BX, r6 \ MULXQ (48)(SI), AX, BX; ADOXQ AX, r6; ADCXQ BX, r7 \ MULXQ (56)(SI), AX, BX; ADOXQ AX, r7; ADCXQ BX, r8 \ MOVQ $0, AX ; ADOXQ AX, r8; MULS_MULX_512(0, R8, R9, R10, R11, R12, R13, R14, CX, BP) MULS_MULX_512(1, R9, R10, R11, R12, R13, R14, CX, BP, R8) MULS_MULX_512(2, R10, R11, R12, R13, R14, CX, BP, R8, R9) MULS_MULX_512(3, R11, R12, R13, R14, CX, BP, R8, R9, R10) MULS_MULX_512(4, R12, R13, R14, CX, BP, R8, R9, R10, R11) MULS_MULX_512(5, R13, R14, CX, BP, R8, R9, R10, R11, R12) MULS_MULX_512(6, R14, CX, BP, R8, R9, R10, R11, R12, R13) MULS_MULX_512(7, CX, BP, R8, R9, R10, R11, R12, R13, R14) #undef MULS_MULX_512 MOVQ res+0(FP), DI MOVQ BP, ( 0)(DI) MOVQ R8, ( 8)(DI) MOVQ R9, (16)(DI) MOVQ R10, (24)(DI) MOVQ R11, (32)(DI) MOVQ R12, (40)(DI) MOVQ R13, (48)(DI) MOVQ R14, (56)(DI) MOVQ 0(SP), BP // pop: BP is Callee-save. // NOW DI needs to be reduced if > p RET golang-github-cloudflare-circl-1.3.7/dh/csidh/fp511_generic.go000066400000000000000000000107771454601126700240470ustar00rootroot00000000000000package csidh import "math/bits" // mul576 implements schoolbook multiplication of // 64x512-bit integer. Returns result modulo 2^512. // r = m1*m2. func mul512Generic(r, m1 *fp, m2 uint64) { var c, h, l uint64 c, r[0] = bits.Mul64(m2, m1[0]) h, l = bits.Mul64(m2, m1[1]) r[1], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[2]) r[2], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[3]) r[3], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[4]) r[4], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[5]) r[5], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[6]) r[6], c = bits.Add64(l, c, 0) c = h + c _, l = bits.Mul64(m2, m1[7]) r[7], _ = bits.Add64(l, c, 0) } // mul576 implements schoolbook multiplication of // 64x512-bit integer. Returns 576-bit result of // multiplication. // r = m1*m2. func mul576Generic(r *[9]uint64, m1 *fp, m2 uint64) { var c, h, l uint64 c, r[0] = bits.Mul64(m2, m1[0]) h, l = bits.Mul64(m2, m1[1]) r[1], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[2]) r[2], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[3]) r[3], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[4]) r[4], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[5]) r[5], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[6]) r[6], c = bits.Add64(l, c, 0) c = h + c h, l = bits.Mul64(m2, m1[7]) r[7], c = bits.Add64(l, c, 0) r[8], c = bits.Add64(h, c, 0) r[8] += c } // cswap512 implements constant time swap operation. // If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. // If choice is neither 0 nor 1 then behaviour is undefined. func cswap512Generic(x, y *fp, choice uint8) { var tmp uint64 mask64 := 0 - uint64(choice) for i := 0; i < numWords; i++ { tmp = mask64 & (x[i] ^ y[i]) x[i] = tmp ^ x[i] y[i] = tmp ^ y[i] } } // mulRdc performs montgomery multiplication r = x * y mod P. // Returned result r is already reduced and in Montgomery domain. func mulRdcGeneric(r, x, y *fp) { var t fp var c uint64 mulGeneric(r, x, y) // if p <= r < 2p then r = r-p t[0], c = bits.Sub64(r[0], p[0], 0) t[1], c = bits.Sub64(r[1], p[1], c) t[2], c = bits.Sub64(r[2], p[2], c) t[3], c = bits.Sub64(r[3], p[3], c) t[4], c = bits.Sub64(r[4], p[4], c) t[5], c = bits.Sub64(r[5], p[5], c) t[6], c = bits.Sub64(r[6], p[6], c) t[7], c = bits.Sub64(r[7], p[7], c) w := 0 - c r[0] = ctPick64(w, r[0], t[0]) r[1] = ctPick64(w, r[1], t[1]) r[2] = ctPick64(w, r[2], t[2]) r[3] = ctPick64(w, r[3], t[3]) r[4] = ctPick64(w, r[4], t[4]) r[5] = ctPick64(w, r[5], t[5]) r[6] = ctPick64(w, r[6], t[6]) r[7] = ctPick64(w, r[7], t[7]) } func mulGeneric(r, x, y *fp) { var s fp // keeps intermediate results var t1, t2 [9]uint64 var c, q uint64 for i := 0; i < numWords-1; i++ { q = ((x[i] * y[0]) + s[0]) * pNegInv[0] mul576Generic(&t1, &p, q) mul576Generic(&t2, y, x[i]) // x[i]*y + q_i*p t1[0], c = bits.Add64(t1[0], t2[0], 0) t1[1], c = bits.Add64(t1[1], t2[1], c) t1[2], c = bits.Add64(t1[2], t2[2], c) t1[3], c = bits.Add64(t1[3], t2[3], c) t1[4], c = bits.Add64(t1[4], t2[4], c) t1[5], c = bits.Add64(t1[5], t2[5], c) t1[6], c = bits.Add64(t1[6], t2[6], c) t1[7], c = bits.Add64(t1[7], t2[7], c) t1[8], _ = bits.Add64(t1[8], t2[8], c) // s = (s + x[i]*y + q_i * p) / R _, c = bits.Add64(t1[0], s[0], 0) s[0], c = bits.Add64(t1[1], s[1], c) s[1], c = bits.Add64(t1[2], s[2], c) s[2], c = bits.Add64(t1[3], s[3], c) s[3], c = bits.Add64(t1[4], s[4], c) s[4], c = bits.Add64(t1[5], s[5], c) s[5], c = bits.Add64(t1[6], s[6], c) s[6], c = bits.Add64(t1[7], s[7], c) s[7], _ = bits.Add64(t1[8], 0, c) } // last iteration stores result in r q = ((x[numWords-1] * y[0]) + s[0]) * pNegInv[0] mul576Generic(&t1, &p, q) mul576Generic(&t2, y, x[numWords-1]) t1[0], c = bits.Add64(t1[0], t2[0], c) t1[1], c = bits.Add64(t1[1], t2[1], c) t1[2], c = bits.Add64(t1[2], t2[2], c) t1[3], c = bits.Add64(t1[3], t2[3], c) t1[4], c = bits.Add64(t1[4], t2[4], c) t1[5], c = bits.Add64(t1[5], t2[5], c) t1[6], c = bits.Add64(t1[6], t2[6], c) t1[7], c = bits.Add64(t1[7], t2[7], c) t1[8], _ = bits.Add64(t1[8], t2[8], c) _, c = bits.Add64(t1[0], s[0], 0) r[0], c = bits.Add64(t1[1], s[1], c) r[1], c = bits.Add64(t1[2], s[2], c) r[2], c = bits.Add64(t1[3], s[3], c) r[3], c = bits.Add64(t1[4], s[4], c) r[4], c = bits.Add64(t1[5], s[5], c) r[5], c = bits.Add64(t1[6], s[6], c) r[6], c = bits.Add64(t1[7], s[7], c) r[7], _ = bits.Add64(t1[8], 0, c) } golang-github-cloudflare-circl-1.3.7/dh/csidh/fp511_noasm.go000066400000000000000000000005571454601126700235430ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package csidh func mul512(r, m1 *fp, m2 uint64) { mul512Generic(r, m1, m2) } func mul576(r *[9]uint64, m1 *fp, m2 uint64) { mul576Generic(r, m1, m2) } func cswap512(x, y *fp, choice uint8) { cswap512Generic(x, y, choice) } func mulRdc(r, x, y *fp) { mulRdcGeneric(r, x, y) } golang-github-cloudflare-circl-1.3.7/dh/csidh/fp511_test.go000066400000000000000000000177201454601126700234050ustar00rootroot00000000000000package csidh import ( "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) func testFp512Mul3Nominal(t *testing.T, f func(*fp, *fp, uint64)) { var mod, two64 big.Int // modulus: 2^512 mod.SetUint64(1).Lsh(&mod, 512) two64.SetUint64(1).Lsh(&two64, 64) for i := 0; i < numIter; i++ { multiplier64, _ := rand.Int(rand.Reader, &two64) mul64 := multiplier64.Uint64() fV := randomFp() exp, _ := new(big.Int).SetString(fp2S(fV), 16) exp.Mul(exp, multiplier64) // Truncate to 512 bits exp.Mod(exp, &mod) f(&fV, &fV, mul64) res, _ := new(big.Int).SetString(fp2S(fV), 16) if exp.Cmp(res) != 0 { test.ReportError(t, exp, res, fV) } } } // Check if mul512 produces result // z = x*y mod 2^512. func TestFp512Mul3_Nominal(t *testing.T) { testFp512Mul3Nominal(t, mul512) testFp512Mul3Nominal(t, mul512Generic) } func TestAddRdcRandom(t *testing.T) { for i := 0; i < numIter; i++ { a := randomFp() bigA, _ := new(big.Int).SetString(fp2S(a), 16) bigA.Mod(bigA, modulus) copy(a[:], intGetU64(bigA)) b := randomFp() bigB, _ := new(big.Int).SetString(fp2S(b), 16) bigB.Mod(bigB, modulus) copy(b[:], intGetU64(bigB)) addRdc(&a, &a, &b) bigRet, _ := new(big.Int).SetString(fp2S(a), 16) bigA.Add(bigA, bigB) bigA.Mod(bigA, modulus) if bigRet.Cmp(bigA) != 0 { test.ReportError(t, bigRet, bigA, a, b) } } } func TestAddRdcNominal(t *testing.T) { var res fp tmp := oneFp512 addRdc(&res, &tmp, &p) if !eqFp(&res, &tmp) { t.Errorf("Wrong value\n%X", res) } tmp = zeroFp512 addRdc(&res, &p, &p) if !eqFp(&res, &p) { t.Errorf("Wrong value\n%X", res) } tmp = fp{1, 1, 1, 1, 1, 1, 1, 1} addRdc(&res, &p, &tmp) if !eqFp(&res, &tmp) { t.Errorf("Wrong value\n%X", res) } tmp = fp{1, 1, 1, 1, 1, 1, 1, 1} exp := fp{2, 2, 2, 2, 2, 2, 2, 2} addRdc(&res, &tmp, &tmp) if !eqFp(&res, &exp) { t.Errorf("Wrong value\n%X", res) } } func TestFp512Sub3_Nominal(t *testing.T) { var ret fp var mod big.Int // modulus: 2^512 mod.SetUint64(1).Lsh(&mod, 512) for i := 0; i < numIter; i++ { a := randomFp() bigA, _ := new(big.Int).SetString(fp2S(a), 16) b := randomFp() bigB, _ := new(big.Int).SetString(fp2S(b), 16) sub512(&ret, &a, &b) bigRet, _ := new(big.Int).SetString(fp2S(ret), 16) bigA.Sub(bigA, bigB) // Truncate to 512 bits bigA.Mod(bigA, &mod) if bigRet.Cmp(bigA) != 0 { test.ReportError(t, bigRet, bigA, a, b) } } } func TestFp512Sub3_DoesntReturnCarry(t *testing.T) { a := fp{} b := fp{ 0xFFFFFFFFFFFFFFFF, 1, 0, 0, 0, 0, 0, 0, } c := fp{ 0xFFFFFFFFFFFFFFFF, 2, 0, 0, 0, 0, 0, 0, } if sub512(&a, &b, &c) != 1 { t.Error("Carry not returned") } } func TestFp512Sub3_ReturnsCarry(t *testing.T) { a := fp{} b := fp{ 0xFFFFFFFFFFFFFFFF, 2, 0, 0, 0, 0, 0, 0, } c := fp{ 0xFFFFFFFFFFFFFFFF, 1, 0, 0, 0, 0, 0, 0, } if sub512(&a, &b, &c) != 0 { t.Error("Carry not returned") } } func testCswap(t *testing.T, f func(*fp, *fp, uint8)) { arg1 := randomFp() arg2 := randomFp() arg1cpy := arg1 f(&arg1, &arg2, 0) if !eqFp(&arg1, &arg1cpy) { t.Error("cswap swapped") } arg1cpy = arg1 f(&arg1, &arg2, 1) if eqFp(&arg1, &arg1cpy) { t.Error("cswap didn't swapped") } arg1cpy = arg1 f(&arg1, &arg2, 0xF2) if eqFp(&arg1, &arg1cpy) { t.Error("cswap didn't swapped") } } func TestCswap(t *testing.T) { testCswap(t, cswap512Generic) testCswap(t, cswap512) } func TestSubRdc(t *testing.T) { var res fp // 1 - 1 mod P tmp := oneFp512 subRdc(&res, &tmp, &tmp) if !eqFp(&res, &zeroFp512) { t.Errorf("Wrong value\n%X", res) } zero(&res) // 0 - 1 mod P exp := p exp[0]-- subRdc(&res, &zeroFp512, &oneFp512) if !eqFp(&res, &exp) { t.Errorf("Wrong value\n%X\n%X", res, exp) } zero(&res) // P - (P-1) pMinusOne := p pMinusOne[0]-- subRdc(&res, &p, &pMinusOne) if !eqFp(&res, &oneFp512) { t.Errorf("Wrong value\n[%X != %X]", res, oneFp512) } zero(&res) subRdc(&res, &p, &oneFp512) if !eqFp(&res, &pMinusOne) { t.Errorf("Wrong value\n[%X != %X]", res, pMinusOne) } } func testMulRdc(t *testing.T, f func(*fp, *fp, *fp)) { var res fp m1 := fp{ 0x85E2579C786882D0, 0x4E3433657E18DA95, 0x850AE5507965A0B3, 0xA15BC4E676475964, } m2 := fp{ 0x85E2579C786882CF, 0x4E3433657E18DA95, 0x850AE5507965A0B3, 0xA15BC4E676475964, } // Expected m1m1 := fp{ 0xAEBF46E92C88A4B4, 0xCFE857977B946347, 0xD3B264FF08493901, 0x6EEB3D23746B6C7C, 0xC0CA874A349D64B4, 0x7AD4A38B406F8504, 0x38B6B6CEB82472FB, 0x1587015FD7DDFC7D, } m1m2 := fp{ 0x51534771258C4624, 0x2BFEDE86504E2160, 0xE8127D5E9329670B, 0x0C84DBD584491D75, 0x656C73C68B16E38C, 0x01C0DA470B30B8DE, 0x2532E3903EAA950B, 0x3F2C28EA97FE6FEC, } // 0*0 tmp := zeroFp512 f(&res, &tmp, &tmp) if !eqFp(&res, &tmp) { t.Errorf("Wrong value\n%X", res) } // 1*m1 == m1 zero(&res) f(&res, &m1, &one) if !eqFp(&res, &m1) { t.Errorf("Wrong value\n%X", res) } // m1*m2 < p zero(&res) f(&res, &m1, &m2) if !eqFp(&res, &m1m2) { t.Errorf("Wrong value\n%X", res) } // m1*m1 > p zero(&res) f(&res, &m1, &m1) if !eqFp(&res, &m1m1) { t.Errorf("Wrong value\n%X", res) } } func TestMulRdc(t *testing.T) { testMulRdc(t, mulRdcGeneric) testMulRdc(t, mulRdc) } func TestModExp(t *testing.T) { var resExp, base, exp big.Int var baseFp, expFp, resFp, resFpExp fp for i := 0; i < numIter; i++ { // Perform modexp with reference implementation // in Montgomery domain base.SetString(fp2S(randomFp()), 16) exp.SetString(fp2S(randomFp()), 16) resExp.Exp(&base, &exp, modulus) toMont(&base, true) toMont(&resExp, true) // Convert to fp copy(baseFp[:], intGetU64(&base)) copy(expFp[:], intGetU64(&exp)) copy(resFpExp[:], intGetU64(&resExp)) // Perform modexp with our implementation modExpRdc512(&resFp, &baseFp, &expFp) if !eqFp(&resFp, &resFpExp) { test.ReportError(t, resFp, intGetU64(&resExp), base, exp) } } } // Test uses Euler's Criterion. func TestIsNonQuadRes(t *testing.T) { var n, nMont big.Int var pm1o2, rawP big.Int var nMontFp fp // (p-1)/2 pm1o2.SetString("0x32da4747ba07c4dffe455868af1f26255a16841d76e446212d7dfe63499164e6d3d56362b3f9aa83a8b398660f85a792e1390dfa2bd6541a8dc0dc8299e3643d", 0) // modulus value (not in montgomery) rawP.SetString("0x65b48e8f740f89bffc8ab0d15e3e4c4ab42d083aedc88c425afbfcc69322c9cda7aac6c567f35507516730cc1f0b4f25c2721bf457aca8351b81b90533c6c87b", 0) // There is 641 quadratic residues in this range for i := uint64(1); i < uint64(numIter); i++ { n.SetUint64(i) n.Exp(&n, &pm1o2, &rawP) // exp == 1 iff n is quadratic non-residue exp := n.Cmp(big.NewInt(1)) if exp < 0 { panic("Should never happen") } nMont.SetUint64(i) toMont(&nMont, true) copy(nMontFp[:], intGetU64(&nMont)) ret := nMontFp.isNonQuadRes() if ret != exp { toMont(&nMont, false) t.Errorf("Test failed for value %s", nMont.Text(10)) } } } func TestCheckSmaller(t *testing.T) { // p-1 pMin1 := p pMin1[0]-- // p-1 < p => 1 if !isLess(&pMin1, &p) { t.Error("pMin1>p") } // p < p-1 => 0 if isLess(&p, &pMin1) { t.Error("p>pMin1") } // p == p => 0 if isLess(&p, &p) { t.Error("p==p") } } func BenchmarkFp(b *testing.B) { var res, arg1 fp var two64 big.Int two64.SetUint64(1).Lsh(&two64, 64) n, _ := rand.Int(rand.Reader, &two64) u64 := n.Uint64() arg2, arg3 := randomFp(), randomFp() b.Run("sub512", func(b *testing.B) { for n := 0; n < b.N; n++ { sub512(&arg1, &arg2, &arg3) } }) b.Run("mul", func(b *testing.B) { for n := 0; n < b.N; n++ { mul512(&arg2, &arg3, u64) } }) b.Run("cswap", func(b *testing.B) { for n := 0; n < b.N; n++ { cswap512(&arg1, &arg2, uint8(n%2)) } }) b.Run("add", func(b *testing.B) { for n := 0; n < b.N; n++ { addRdc(&res, &arg1, &arg2) } }) b.Run("sub", func(b *testing.B) { for n := 0; n < b.N; n++ { subRdc(&res, &arg1, &arg2) } }) b.Run("mul", func(b *testing.B) { for n := 0; n < b.N; n++ { mulRdc(&res, &arg1, &arg2) } }) b.Run("exp", func(b *testing.B) { for n := 0; n < b.N; n++ { modExpRdc512(&res, &arg1, &arg2) } }) } golang-github-cloudflare-circl-1.3.7/dh/csidh/testdata/000077500000000000000000000000001454601126700227655ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/csidh/testdata/csidh_testvectors.json000066400000000000000000005245371454601126700274370ustar00rootroot00000000000000{ "Vectors": [ { "Id": 0, "Pk1": "2fd62ea1798c0839387d17587a22dcbb89c5797531bb38eff0cd505575c91c440a70e88aa4e67ad267460e40235076dec6ea6f7b60b59aed2a199cc1eb12123c", "Pr1": "c4d4dccbfedd1b103c123ff2ed11345dfced1514decbc40cdee12e450fdb35fdb5b33ffb2d", "Pk2": "895ee9f9e96aebf244c20171133aa0c2601b89f98b9c1f2eff7a44bbfc646a4ff5468775dde42d75803d5298eb5b6d27212d49bf59238c0ddea0eeae8bded937", "Ss": "870ad67d9875cd535a8b4b5776c2eb59acaa872a5775231f75cef212449e40752ac557d12d556edcac68b1ee94a2a5ba6dce4f6bcb6e91c311d5759c83568e29", "status": "valid", "comment": "" }, { "Id": 1, "Pk1": "c017b2703feb1f429d7e101d34b52652a4dea6499c4731d494e1841c1d4333e8c3c6f986ea8e5a62b7943b61025fc273bce2e1c0430a69b78ec35141065de84e", "Pr1": "0c323ecd4fbbbbd12ccd5eb41d5c1f420ebf330e1521fc21c104cf0db0f0cb0dd5d10225fe", "Pk2": "9f189b6f09ec6ef686de1abc438e9708ceaac64cf01e9695c55e1997c5c13992f4e1c35e5c809af2d9be6ffad36e8966a94190f84962fd6e7f5fe9bbd7aee41f", "Ss": "755e8a3e344b0ef2accd8855ac292cdf1dd3d0f9e7403464f85a0784351f0317caae5455d4f8c2a1666adb364e9dc4aff578f02a4bb3da031a5e5e1e30f5dd30", "status": "valid", "comment": "" }, { "Id": 2, "Pk1": "758baaa1d991fce063ff29b4192dba6c8d9b6620ef858fefe2e5218c1902dc0d84c81877f0eba7ba3346dc6a67c292e2f3ee0567b5ad4a285fab92bd43441305", "Pr1": "3db1b323d054ec052201d02ff20103b250ceeeb243f40e5e24bf122ebfe30551e55ed0b1eb", "Pk2": "41d8d0a352cbdeb2ea16733e83b6a6e222abfc2afafd76451ee4231c47d527a58956b69abcccdc582706d4aababbedf26c242c7c1192f43f5d465feb77d72f63", "Ss": "b95b8b83f4fb3de618306608c5da7e774822f6e4e2f1e93eee0906f5a714c5d58d467cb9e5af617d0b9894dd5008f34fde855ac418b5460bc0109941b7f8151a", "status": "valid", "comment": "" }, { "Id": 3, "Pk1": "0cd103b51492be43c35c80523607142ae88f6896dc64e90bd710d6778688e2b3c2c6cd49d376d859d0ed84804d4584a1ac942cab87483c53bee22369aa0a0d65", "Pr1": "bfffb01ceb01e2544e1de44e30c21effee3212f5ee534b4b30fffebefbe3e400ebf13e0b2d", "Pk2": "5ec767260e61594ecf768cc0c3a381042184d58e4092c6c13eca657b2bceb1eb44275babf98741a64618b5c8998d18454c63e92ea0b7fdacdded1bedc44d4549", "Ss": "c962080c5170ecd996c904b363c9034c49472e177523247029a7d85fd3aa01eb589e17bbec73196fa3835f7460a0bdd75bebb3cd53467cd2d1eec5906d21761a", "status": "valid", "comment": "" }, { "Id": 4, "Pk1": "111fd8d9e336cad4578179638cf3d1e64a5ddc51c1f8a5fcc8bf321563c410e7e0ee7531ac7595b2eb13eddcb70df6919848edbafb941142ae9cce03e47e2d4c", "Pr1": "f00f025ec4feb142b2cd2e5d04ffc3b10ee4c1ec350ff41d553e1f0323efe305e24fc0f150", "Pk2": "87d6effecd8ee94b6f84521637187dd9fc4d29100e0ee4b07516c9889acf5fdebe9881dfeb902efd354b367a3ddba3773991cb1cd52ca4f25a7d18f739272462", "Ss": "20bfe627e1d0a6ff0ead98ab55049d190fb2a563f78b85b574d494c4760d8c567315f3ce7eec8852ae359f74d7b7f0c55ef24d72a285ab6b838f9b16d7cf8749", "status": "valid", "comment": "" }, { "Id": 5, "Pk1": "db8aa23c21ed69dd507048dd032050288f6330c97599d0b78f4091991d39f8b9ecc101d966d4049b38de7f21cb7dae42c02fb5f3d6323c74639f52cbcbf6553b", "Pr1": "4c23dc513b1ddcbdd5f2fc25bf540b1215ece4f244e1222f44c01515ec0bed1d4b2fcdf234", "Pk2": "d8d3bb64e2e354e0a4d209d05f39e7150f6dcd074cf5ac558706bc4428555e2c44dea6b036e5492cd5fe2e59e5bed9bde65aeccf8a47d6a28f8525283ec23a09", "Ss": "af726b0535a37777c3790db3ddf8118c7f795366d51c77d2decab720c799248e34c4417d825a1b3bf3de814bf27c8917ba16e8a83b7117709cb455f34fd37328", "status": "valid", "comment": "" }, { "Id": 6, "Pk1": "c170985f761b9742950f27256f6e5fe63564ace2bb1c1240c87f915b0fe3761295d3c0f8344d78872706124ba6c01b9f460d683801563c7f333404017b8c874d", "Pr1": "052dde3fcdfc0cd2efe2bd3512d1df32b304cbbbf4402e1cc55f00e3ec2cfdf4fc2c03cb0f", "Pk2": "096a2838cb794731790b102549905ceda31a94b6951038e6a73483e035045b75917fc8acf982b161418a9a667a8c2afc184feb48462520cc0e85f64a114f0438", "Ss": "80690d9623baf4e4881aa63f47f751ec88c9c099516a384f3c5d97179c8d33700679e28087f0318e51ed7839917c76dd0db74fc03e10fb1c539c92075368f85a", "status": "valid", "comment": "" }, { "Id": 7, "Pk1": "60270f86533c7394ba891009668d0c5f31dbdf22d6c74b8c1ffddc280d7a16a49797e14c9ae0b16cdaf337f718206d5dab380e345c2bcf9567e25c3eb757bd3f", "Pr1": "5b224f4dd4501cb0f15b045dd154cd50b25bf52234fbd1cb4db3e50f3b404eb3e4fc1ee530", "Pk2": "26dc974e40298a7a550d1d28f1eb9273bf16852327d2f2cfef768bda463b43346ec711bb3454bb5dd0a7778744bc6dab6de330f3024baaf249095ae916d87e43", "Ss": "46eaa33870b4be48fc84b4aafd3cb995852a5ab875cd75d46c40d8516988344a07ec30a4f4b1ff3b63f50a380ae409dabf805ad1af0d9cd4c66871c49aa2b613", "status": "valid", "comment": "" }, { "Id": 8, "Pk1": "007c8c48845b314d3d1cfc1376080e38ce3eb7ff8e876e91ecaa24ecd8778e7a5967930894afde516e585abb2252051e81281988a1f4f4b9fd3beeaaab76d42a", "Pr1": "b24131234103d5cf1c01543212bcc35bc334cd2ff202dccd04fc3ef5ff35352edce12cd431", "Pk2": "d4d8de755a9cf5e2c9df44770e1cd2561617cda5a469fa90ca0f3f3b78af682965e78ab05ddcc9618352c890e72f7cff35c218ca7185eaa2377e3ffc14774c51", "Ss": "14061ac3ea3ddd28a56387eacf9958cd7cbbdfc107b34b1c9c3de3b37db9417acfac5c53357d650e1bef3e5dec24891c6d8968851d6352aaea57aa2ed9a0f00a", "status": "valid", "comment": "" }, { "Id": 9, "Pk1": "43659c08a6d627d9cf4735c891aab0bf3ec481614910372fb5fc26e3742bdbe0ac352e5f9f210f8cdc7b005f353425cee6f5c962770447266bcc53267abd9e23", "Pr1": "1c5dfd3c25d5d42b1200b0f3ec443d0bebdff012eecd3cb2c1f4c4e32ef3bd0fe35bfe400e", "Pk2": "bd0c0009df67b0349efbebe675843ee0e730ca02c74305a49e4bc594cba5ea23ebbf422e88e4cbd233929c8f0cfd450f142323832025b3fe8ae9a963ef7f7105", "Ss": "0848e8785c4adc94057a07b0f4ba1c91eea3fff5f24f4af3ae39a92a4b724e85138c9622d484d350acd5191ac71ca6de6acef4715097e801fa57524de01edb01", "status": "valid", "comment": "" }, { "Id": 10, "Pk1": "8718af0c2f8d1934d36dabf98fd6dfc59b492c712966435da2a5b87ce7d8932d68b8133a8b67baa00ff2c153853e3f6455cb129e64ebcb8bb27da63cf03b9a32", "Pr1": "25dbdc2c5d133ee52d33f2cb5efdc14fd4d5334452bf3dff02451bc5e2c0c4031b5f432005", "Pk2": "2f51d9f132fd4dcd455b2824cb34bc3e40a1230fcb5806ac73b790f45ab424e3e1198fde46bfa3616d9ea774aec86b2bad6bc25fe1f69336b1165a6501df912c", "Ss": "3a01783110eb87f056dd74309eb930d88d04ed743957c49e3fc76cf0e8be519002b1df3f7a0fa25781341dff3903d455435e41d1470b60ba7480883e87185a44", "status": "valid", "comment": "" }, { "Id": 11, "Pk1": "c18552ebbc4c5eeae52527aaf836c85e118768183db8e806e1b8b62f4a41e20820f71e8e9e54fbdc6a23b8d1498a893683b6cad52f6c6e39e2e7a907bec9df2d", "Pr1": "d30105dd234510d550c5cd4fd5504b34b3dcdf1cb3f255fe104e2d4dd545b40d42ce2c15e1", "Pk2": "b1665e32f9d5109a6391ef6dc37805d417435c3bcd951c709723c793c5ead0f1b8ff6db0f832c3852017a86d44a1b99bd90a72ece5a16096cdec9ddf76294912", "Ss": "a510b28404fd18e5e09b86356c79a29f24bd510d6753bd76dd3559a4b6512282e9057fcb5d09a7c7ac7aae303254d979fe32963bae76daa38e440047f8a77a39", "status": "valid", "comment": "" }, { "Id": 12, "Pk1": "7350f4abf09ac07c06060eed93550f3a7e98d33aa8f27eb15b0d95be0464ac5bc076432ed72351b37aadb396b8cf508393b6ec69b21838e2cee8f0b78cbfa134", "Pr1": "be10bf10bb5b3ebbcceb11c4352b113400cbb411342b1cb21d443352b21203bee1e12fbebe", "Pk2": "b6e041a164df9c371ce0269edfc39d7a35b4912cdcee025f4cf94ed27d28e293c6aabdd12efbfe242cc3af779780dcf7989602d2040181053cb15e91af8cd218", "Ss": "f1839d3ee717d4e771ba98cb7d8f0876ef609d121cdb5242c08f024102880c54b70d8b736cd0619749b669c04a81e25f60a43d8de6ab0c99dd965fd04a55f61e", "status": "valid", "comment": "" }, { "Id": 13, "Pk1": "c75d4c97b1279fb71527e197cdb10187496847bec5f92d87aff488f94ed6e4af9106d90e138e9f76080fa3c2dc02bc53605729d61b44a713b73e55c0374aa419", "Pr1": "d1c4e5204ffc2efbc5fcbe4fc214e25f03d4c1bc52035d43c1ed34fec54535b2ceef40ff14", "Pk2": "555b2ee62bebf290ea165bc236b52dac676f2fc76035c7a932e5a7af124e765b01c2817f56ecc583becd812844b6900e65215d1f6d1fbf7702daac9b97ed7e55", "Ss": "907c30d6734023d0834d27a1217d2db171a18847fc23ac841950789e41e1b128e9530ff4adb6ee2a7696822a51860cdac102c88e6174bc36044942f843c40547", "status": "valid", "comment": "" }, { "Id": 14, "Pk1": "464384f617fae27179514b7b4231d24310c0125fa00889b3a301c7fbb2279d01f3d26693c0560d1da464d4d94f86a65c29b8a4a4621a75a51755c16f398bf533", "Pr1": "5dd0125dfd5c123d33be21e4fbbf13b0e13b00f5253cb151f3b22c02513042cc1c22f3e2bb", "Pk2": "c26c07be3dfacc0dd675a308be3eaad29c73af2e1fce1d2653e6c3773a9f49c2532206ba96c59c043f48f16ef133c5cb8f324633021171943a15c6bbb6629a61", "Ss": "54c51f9a31299a0985fae6d50cd7c74489533ddf8ec178f5e9af02e393b14e37fed7282ebeefa296e1279ba8f9f2ef0f2a62e45833d40ef54d49c80c4c758941", "status": "valid", "comment": "" }, { "Id": 15, "Pk1": "930dd66040ef7e32480a68ddbc9bfbf7b4469018652d9600121f25dc88ffb9ac9b15fb0f92a35cec66a258bfd0b7c3108c36ae2004bb88c9444a506a11d8cd36", "Pr1": "e4530435b302d0cc41c11fbf4bceb4c5cc11cc40bd55b1eb334f533edd1f554eb430f5efd1", "Pk2": "43d7531ecdedc868ee6f16172c22ee32d566b4c1a6951372ee10c43b6c6c08713308ea5b42b0c8217e1e9bee8971da9fa896012e06e29135850a2c138dbf043a", "Ss": "1e31b8f444a96180c65eaedb5392b75f177b5273f3c62393a415d0cf56f30d0f39542a661b4171716ccffcb6d6eefddeb19f8fffd682d8f7df5b4132e7c6e22c", "status": "valid", "comment": "" }, { "Id": 16, "Pk1": "abd38fd9948ca9a5de0d50e094e504fcf848c611f9ca0cc071b26bb5c39062892984c46a3d377f60cbfd7f1cbc9288dc4f2c072e31458a27ff97cc65f7e4252e", "Pr1": "ede0cfd2bb4c1333112ebd50ee01fe404b4cffe242e042ee5bc15fe3df2dfeb3cf255d23e4", "Pk2": "05fc229d372a5b7b00b8cb54c9cb4bad87b8a3627c06c00e10e4605281d4ba09b8bfde349c83eb45bb014d4f32e15be96c2520f55c6fd97f6a1b7e5582f64c3d", "Ss": "fb6af7aae48fb5778eaee3017454877b7ffd10609f17a3f85b58c7da6376812316631887c869a9eab534d8ed1be66dd2cf91243cb5b2b4022f225a93e9740616", "status": "valid", "comment": "" }, { "Id": 17, "Pk1": "4c0fd41c5d685da159648670760185bcc570e40719fd1a5418a03a70a44c9338ccce2e95657d9f63aa69d608736165a99858ccd070441848bf8e436271d41f34", "Pr1": "bec51245f5b2d411cdfd2bff4c504db225be510d523cf30dc1b233bbb5cc0eb120fbceeec4", "Pk2": 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"49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef42457659c460", "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", "status": "invalid_public_key2", "comment": "" }, { "Id": 326, "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef4245769da460", "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", "status": "invalid_public_key2", "comment": "" }, { "Id": 327, "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef4245769dc4d6", "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", "status": "invalid_public_key2", "comment": "" } ] }golang-github-cloudflare-circl-1.3.7/dh/csidh/utils_test.go000066400000000000000000000047741454601126700237160ustar00rootroot00000000000000package csidh import ( "crypto/rand" "encoding/binary" "fmt" "math/big" ) var ( // Number of iterations numIter = 10 // Modulus modulus, _ = new(big.Int).SetString(fp2S(p), 16) // Zero in fp zeroFp512 = fp{} // One in fp oneFp512 = fp{1, 0, 0, 0, 0, 0, 0, 0} // file with KAT vectors katFile = "testdata/csidh_testvectors.json" ) // Converts dst to Montgomery if "toMont==true" or from Montgomery domain otherwise. func toMont(dst *big.Int, toMont bool) { var bigP, bigR big.Int intSetU64(&bigP, p[:]) bigR.SetUint64(1) bigR.Lsh(&bigR, 512) if !toMont { bigR.ModInverse(&bigR, &bigP) } dst.Mul(dst, &bigR) dst.Mod(dst, &bigP) } func fp2S(v fp) string { var str string for i := 0; i < 8; i++ { str = fmt.Sprintf("%016x", v[i]) + str } return str } // zeroize fp. func zero(v *fp) { for i := range *v { v[i] = 0 } } // returns random value in a range (0,p). func randomFp() (u fp) { _ = binary.Read(rand.Reader, binary.LittleEndian, &u) return } // return x==y for fp. func eqFp(l, r *fp) bool { for idx := range l { if l[idx] != r[idx] { return false } } return true } // return x==y for point. func ceqpoint(l, r *point) bool { return eqFp(&l.x, &r.x) && eqFp(&l.z, &r.z) } // Converts src to big.Int. Function assumes that src is a slice of uint64 // values encoded in little-endian byte order. func intSetU64(dst *big.Int, src []uint64) { var tmp big.Int dst.SetUint64(0) for i := range src { tmp.SetUint64(src[i]) tmp.Lsh(&tmp, uint(i*64)) dst.Add(dst, &tmp) } } // Converts src to an array of uint64 values encoded in little-endian // byte order. func intGetU64(src *big.Int) []uint64 { var tmp, mod big.Int dst := make([]uint64, (src.BitLen()/64)+1) u64 := uint64(0) u64-- mod.SetUint64(u64) for i := 0; i < (src.BitLen()/64)+1; i++ { tmp.Set(src) tmp.Rsh(&tmp, uint(i)*64) tmp.And(&tmp, &mod) dst[i] = tmp.Uint64() } return dst } // Returns projective coordinate X of normalized EC 'point' (point.x / point.z). func toNormX(point *point) big.Int { var bigP, bigDnt, bigDor big.Int intSetU64(&bigP, p[:]) intSetU64(&bigDnt, point.x[:]) intSetU64(&bigDor, point.z[:]) bigDor.ModInverse(&bigDor, &bigP) bigDnt.Mul(&bigDnt, &bigDor) bigDnt.Mod(&bigDnt, &bigP) return bigDnt } // Converts string to fp element in Montgomery domain of cSIDH-512. func toFp(num string) fp { var tmp big.Int var ok bool var ret fp _, ok = tmp.SetString(num, 0) if !ok { panic("Can't parse a number") } toMont(&tmp, true) copy(ret[:], intGetU64(&tmp)) return ret } golang-github-cloudflare-circl-1.3.7/dh/curve4q/000077500000000000000000000000001454601126700214535ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/curve4q/curve4Q.go000066400000000000000000000013101454601126700233260ustar00rootroot00000000000000package curve4q import "github.com/cloudflare/circl/ecc/fourq" // Size is the size in bytes of keys. const Size = 32 // Key represents a public or private key of FourQ. type Key [Size]byte // KeyGen calculates a public key k from a secret key. func KeyGen(public, secret *Key) { var P fourq.Point P.ScalarBaseMult((*[Size]byte)(secret)) P.Marshal((*[Size]byte)(public)) } // Shared calculates a shared key k from Alice's secret and Bob's public key. // Returns true on success. func Shared(shared, secret, public *Key) bool { var P, Q fourq.Point ok := P.Unmarshal((*[Size]byte)(public)) Q.ScalarMult((*[Size]byte)(secret), &P) Q.Marshal((*[Size]byte)(shared)) ok = ok && Q.IsOnCurve() return ok } golang-github-cloudflare-circl-1.3.7/dh/curve4q/curve4Q_test.go000066400000000000000000000033301454601126700243710ustar00rootroot00000000000000package curve4q import ( "bytes" "crypto/rand" "fmt" "io" "testing" "github.com/cloudflare/circl/internal/test" ) func TestDH(t *testing.T) { var secretAlice, publicAlice, sharedAlice Key var secretBob, publicBob, sharedBob Key testTimes := 1 << 10 for i := 0; i < testTimes; i++ { _, _ = rand.Read(secretAlice[:]) _, _ = rand.Read(secretBob[:]) KeyGen(&publicAlice, &secretAlice) KeyGen(&publicBob, &secretBob) if ok := Shared(&sharedAlice, &secretAlice, &publicBob); !ok { test.ReportError(t, ok, true, secretAlice, publicBob) } if ok := Shared(&sharedBob, &secretBob, &publicAlice); !ok { test.ReportError(t, ok, true, secretBob, publicAlice) } got := sharedAlice want := sharedBob if !bytes.Equal(got[:], want[:]) { test.ReportError(t, got, want, secretAlice, secretBob) } } } func BenchmarkDH(b *testing.B) { var secret, public, shared Key _, _ = rand.Read(secret[:]) _, _ = rand.Read(public[:]) b.Run("keygen", func(b *testing.B) { for i := 0; i < b.N; i++ { KeyGen(&public, &secret) } }) b.Run("shared", func(b *testing.B) { for i := 0; i < b.N; i++ { Shared(&shared, &secret, &public) } }) } func ExampleKey() { var AliceSecret, BobSecret, AlicePublic, BobPublic, AliceShared, BobShared Key // Generating Alice's secret and public keys _, _ = io.ReadFull(rand.Reader, AliceSecret[:]) KeyGen(&AlicePublic, &AliceSecret) // Generating Bob's secret and public keys _, _ = io.ReadFull(rand.Reader, BobSecret[:]) KeyGen(&BobPublic, &BobSecret) // Deriving Alice's shared key Shared(&AliceShared, &AliceSecret, &BobPublic) // Deriving Bob's shared key Shared(&BobShared, &BobSecret, &AlicePublic) fmt.Println(AliceShared == BobShared) // Output: true } golang-github-cloudflare-circl-1.3.7/dh/curve4q/doc.go000066400000000000000000000003631454601126700225510ustar00rootroot00000000000000// Package curve4q implements Diffie-Hellman operations using the FourQ curve // at the 128-bit security level. // // References: // - https://eprint.iacr.org/2015/565 // - https://tools.ietf.org/html/draft-ladd-cfrg-4q-01 package curve4q golang-github-cloudflare-circl-1.3.7/dh/doc.go000066400000000000000000000001221454601126700211510ustar00rootroot00000000000000// Package dh provides variety of Diffie-Hellman key exchange methods. package dh golang-github-cloudflare-circl-1.3.7/dh/sidh/000077500000000000000000000000001454601126700210115ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/doc.go000066400000000000000000000035511454601126700221110ustar00rootroot00000000000000// Package sidh is deprecated, it provides SIDH and SIKE key encapsulation // mechanisms. // // # DEPRECATION NOTICE // // SIDH and SIKE are deprecated as were shown vulnerable to a key recovery // attack by Castryck-Decru's paper (https://eprint.iacr.org/2022/975). New // systems should not rely on this package. This package is frozen. // // # SIDH and SIKE // // This package provides implementation of experimental post-quantum // Supersingular Isogeny Diffie-Hellman (SIDH) as well as Supersingular // Isogeny Key Encapsulation (SIKE). // // It comes with implementations of three different field arithmetic // implementations sidh.Fp434, sidh.Fp503, and sidh.Fp751. // // | Algorithm | Public Key Size | Shared Secret Size | Ciphertext Size | // |-----------|-----------------|--------------------|-----------------| // | SIDH/p434 | 330 | 110 | N/A | // | SIDH/p503 | 378 | 126 | N/A | // | SIDH/p751 | 564 | 188 | N/A | // | SIKE/p434 | 330 | 16 | 346 | // | SIKE/p503 | 378 | 24 | 402 | // | SIKE/p751 | 564 | 32 | 596 | // // In order to instantiate SIKE/p751 KEM one needs to create a KEM object // and allocate internal structures. This can be done with NewSike751 helper. // After that, the kem variable can be used multiple times. // // var kem = sike.NewSike751(rand.Reader) // kem.Encapsulate(ciphertext, sharedSecret, publicBob) // kem.Decapsulate(sharedSecret, privateBob, publicBob, ciphertext) // // Code is optimized for AMD64 and aarch64. Generic implementation // is provided for other architectures. // // References: // // - [SIDH] https://eprint.iacr.org/2011/506 // - [SIKE] http://www.sike.org/files/SIDH-spec.pdf package sidh golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/000077500000000000000000000000001454601126700226255ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/common/000077500000000000000000000000001454601126700241155ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/common/doc.go000066400000000000000000000001631454601126700252110ustar00rootroot00000000000000// Package common provides types, variables, constants and functions commonly used in SIDH or SIKE. package common golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/common/params.go000066400000000000000000000012451454601126700257310ustar00rootroot00000000000000package common import "fmt" // Keeps mapping: SIDH prime field ID to domain parameters var sidhParams = make(map[uint8]SidhParams) // Params returns domain parameters corresponding to finite field and identified by // `id` provided by the caller. Function panics in case `id` wasn't registered earlier. func Params(id uint8) *SidhParams { if val, ok := sidhParams[id]; ok { return &val } panic("sidh: SIDH Params ID unregistered") } // Registers SIDH parameters for particular field. func Register(id uint8, p *SidhParams) { if _, ok := sidhParams[id]; ok { msg := fmt.Sprintf("sidh: Field with id %d already registered", id) panic(msg) } sidhParams[id] = *p } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/common/types.go000066400000000000000000000061501454601126700256120ustar00rootroot00000000000000package common const ( // corresponds to words in P751 FpMaxWords = 12 // corresponds to byte size of P751 SIDH private key for B MaxSidhPrivateKeyBsz = 48 // corresponds to byte size of P751 SIKE private key for B MaxSikePrivateKeyBsz = MaxSidhPrivateKeyBsz + MaxMsgBsz // corresponds to SIKE max length of 'n' (see 1.4 of SIKE spec in NIST PQC round 1) MaxMsgBsz = 40 // corresponds to byte size of shared secret generated by SIKEp751 MaxSharedSecretBsz = 188 // corresponds to by size of the P751 public key MaxPublicKeySz = 3 * FpMaxWords * 64 // corresponds to by size of the ciphertext produced by SIKE/P751 MaxCiphertextBsz = MaxMsgBsz + MaxPublicKeySz ) // Id's correspond to bitlength of the prime field characteristic // Currently Fp751 is the only one supported by this implementation const ( Fp503 uint8 = iota Fp751 Fp434 ) // Representation of an element of the base field F_p. // // No particular meaning is assigned to the representation -- it could represent // an element in Montgomery form, or not. Tracking the meaning of the field // element is left to higher types. type Fp [FpMaxWords]uint64 // Represents an intermediate product of two elements of the base field F_p. type FpX2 [2 * FpMaxWords]uint64 // Represents an element of the extended field Fp^2 = Fp(x+i) type Fp2 struct { A Fp B Fp } type DomainParams struct { // P, Q and R=P-Q base points AffineP, AffineQ, AffineR Fp2 // Size of a computation strategy for x-torsion group IsogenyStrategy []uint32 // Max size of secret key for x-torsion group SecretBitLen uint // Max size of secret key for x-torsion group SecretByteLen uint } type SidhParams struct { ID uint8 // Bytelen of P Bytelen int // The public key size, in bytes. PublicKeySize int // The shared secret size, in bytes. SharedSecretSize int // 2- and 3-torsion group parameter definitions A, B DomainParams // Precomputed identity element in the Fp2 in Montgomery domain OneFp2 Fp2 // Precomputed 1/2 in the Fp2 in Montgomery domain HalfFp2 Fp2 // Length of SIKE secret message. Must be one of {24,32,40}, // depending on size of prime field used (see [SIKE], 1.4 and 5.1) MsgLen int // Length of SIKE ephemeral KEM key (see [SIKE], 1.4 and 5.1) KemSize int // Byte size of ciphertext that KEM produces CiphertextSize int // Defines A,C constant for starting curve Cy^2 = x^3 + Ax^2 + x InitCurve ProjectiveCurveParameters } // Stores curve projective parameters equivalent to A/C. Meaning of the // values depends on the context. When working with isogenies over // subgroup that are powers of: // * three then (A:C) ~ (A+2C:A-2C) // * four then (A:C) ~ (A+2C: 4C) // See Appendix A of SIKE for more details type CurveCoefficientsEquiv struct { A Fp2 C Fp2 } // A point on the projective line P^1(F_{p^2}). // // This represents a point on the Kummer line of a Montgomery curve. The // curve is specified by a ProjectiveCurveParameters struct. type ProjectivePoint struct { X Fp2 Z Fp2 } // A point on the projective line P^1(F_{p^2}). // // This is used to work projectively with the curve coefficients. type ProjectiveCurveParameters struct { A Fp2 C Fp2 } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/common/utils.go000066400000000000000000000027001454601126700256030ustar00rootroot00000000000000package common import "encoding/binary" // Constant time select. // if pick == 1 (out = in1) // if pick == 0 (out = in2) // else out is undefined. func Cpick(pick int, out, in1, in2 []byte) { which := byte((int8(pick << 7)) >> 7) for i := range out { out[i] = (in1[i] & which) | (in2[i] & ^which) } } // Read 2*bytelen(p) bytes into the given ExtensionFieldElement. // // It is an error to call this function if the input byte slice is less than 2*bytelen(p) bytes long. func BytesToFp2(fp2 *Fp2, input []byte, bytelen int) { if len(input) < 2*bytelen { panic("input byte slice too short") } numW64 := (bytelen*8 + 63) / 64 a := make([]byte, 8*numW64) b := make([]byte, 8*numW64) copy(a[:bytelen], input[:bytelen]) copy(b[:bytelen], input[bytelen:]) for i := 0; i < numW64; i++ { fp2.A[i] = binary.LittleEndian.Uint64(a[i*8 : (i+1)*8]) fp2.B[i] = binary.LittleEndian.Uint64(b[i*8 : (i+1)*8]) } } // Convert the input to wire format. // // The output byte slice must be at least 2*bytelen(p) bytes long. func Fp2ToBytes(output []byte, fp2 *Fp2, bytelen int) { if len(output) < 2*bytelen { panic("output byte slice too short") } numW64 := (bytelen*8 + 63) / 64 a := make([]byte, 8*numW64) b := make([]byte, 8*numW64) for i := 0; i < numW64; i++ { binary.LittleEndian.PutUint64(a[i*8:(i+1)*8], fp2.A[i]) binary.LittleEndian.PutUint64(b[i*8:(i+1)*8], fp2.B[i]) } copy(output[:bytelen], a[:bytelen]) copy(output[bytelen:], b[:bytelen]) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/000077500000000000000000000000001454601126700233175ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/arith_amd64.s000066400000000000000000001050041454601126700256050ustar00rootroot00000000000000// +build amd64,!noasm #include "textflag.h" // p434 #define P434_0 $0xFFFFFFFFFFFFFFFF #define P434_3 $0xFDC1767AE2FFFFFF #define P434_4 $0x7BC65C783158AEA3 #define P434_5 $0x6CFC5FD681C52056 #define P434_6 $0x0002341F27177344 // p434 x 2 #define P434X2_0 $0xFFFFFFFFFFFFFFFE #define P434X2_1 $0xFFFFFFFFFFFFFFFF #define P434X2_3 $0xFB82ECF5C5FFFFFF #define P434X2_4 $0xF78CB8F062B15D47 #define P434X2_5 $0xD9F8BFAD038A40AC #define P434X2_6 $0x0004683E4E2EE688 // Redefine P434p1Zeros #define P434_P1_ZEROS 3 // Performs schoolbook multiplication of 128-bit with 256-bit // number. Uses MULX, ADOX, ADCX instruction. // // Uses registers: DX,AX // Calculates: // (I0,I1) x [M1][0,1,2,3] = (T0,T1,T2,T3,T4,T5) // |-128-| x |--- 256 ---| = |------ 384 ------| // Assuming the first digit multiplication was already performed. #define MULX128x256(I1, M1, T1, T2, T3, T4, T5) \ MOVQ M1+ 8(SB), AX \ MULXQ AX, T4, T2 \ XORQ AX, AX \ MOVQ M1+16(SB), AX \ MULXQ AX, T5, T3 \ ADOXQ T4, T1 \ // T1: interm1 ADOXQ T5, T2 \ // T2: interm2 MOVQ M1+24(SB), AX \ MULXQ AX, T5, T4 \ ADOXQ T5, T3 \ // T3: interm3 MOVL $0, AX \ ADOXQ AX, T4 \ // T4: interm4 \ XORQ AX, AX \ MOVQ I1, DX \ MOVQ M1+ 0(SB), AX \ MULXQ AX, T5, I1 \ // T0 <- C0 ADCXQ T5, T1 \ ADCXQ I1, T2 \ // T1 <- C1 MOVQ M1+ 8(SB), AX \ MULXQ AX, I1, T5 \ ADCXQ T5, T3 \ ADOXQ I1, T2 \ // T2 <- C2 MOVQ M1+16(SB), AX \ MULXQ AX, I1, T5 \ ADCXQ T5, T4 \ ADOXQ I1, T3 \ // T3 <- C3 MOVQ M1+24(SB), AX \ MULXQ AX, I1, T5 \ MOVL $0, AX \ ADCXQ AX, T5 \ ADOXQ I1, T4 \ // T4 <- C4 ADOXQ AX, T5 // T5 <- C5 // Performs schoolbook multiplication of 64-bit with 256-bit // number. Uses MULX and ADOX instructions. // // Uses registers: DX,AX // Calculates: // (I0) x [M1][0,1,2,3] = (T0,T1,T2,T3,T4) // |64| x |--- 256 ---| = |----- 320 ----| // Assuming the first digit multiplication was already performed. #define MULX64x256(M1, T1, T2, T3, T4, T5) \ MOVQ M1+ 8(SB), AX \ MULXQ AX, T4, T2 \ XORQ AX, AX \ MOVQ M1+16(SB), AX \ MULXQ AX, T5, T3 \ ADOXQ T4, T1 \ // T1 <- C1 ADOXQ T5, T2 \ // T2 <- C2 MOVQ M1+24(SB), AX \ MULXQ AX, T5, T4 \ ADOXQ T5, T3 \ // T3 <- C3 MOVL $0, AX \ ADOXQ AX, T4 // T4 <- C4 // Performs schoolbook multiplication of two 192-bit numbers // number. Uses MULX and ADOX instructions. // // Uses registers: DX,AX #define MULX192(IM0,M0,IM1,M1,ID,MDST,T0,T1,T2,T3,T4,T5,T6) \ MOVQ (0+IM0)(M0), DX \ MULXQ (0+IM1)(M1), T1, T0 \ // T0:T1 = A0*B0 MOVQ T1,(ID+0)(MDST) \ // MDST0 MULXQ (IM1+ 8)(M1), T2, T1 \ // T1:T2 = A0*B1 XORQ AX, AX \ ADOXQ T2, T0 \ MULXQ (IM1+16)(M1),T3, T2 \ // T2:T3 = A0*B2 ADOXQ T3, T1 \ \ MOVQ (IM0+8)(M0), DX \ MULXQ (IM1+0)(M1), T4, T3 \ // T3:T4 = A1*B0 ADOXQ AX, T2 \ XORQ AX, AX \ \ MULXQ (IM1+8)(M1), T6, T5 \ // T6:T7 = A1*B1 ADOXQ T0, T4 \ MOVQ T4,(ID+8)(MDST) \ // MDST1 ADCXQ T6, T3 \ \ MULXQ (IM1+16)(M1),T0, T6 \ // T6:T0 = A1*B2 ADOXQ T1, T3 \ ADCXQ T0, T5 \ ADCXQ AX, T6 \ ADOXQ T2, T5 \ \ MOVQ (IM0+16)(M0),DX \ MULXQ (IM1+ 0)(M1), T0, T1 \ // T1:T0 = A2*B0 ADOXQ AX, T6 \ XORQ AX, AX \ \ MULXQ (IM1+ 8)(M1), T2, T4 \ // T4:T2 = A2*B1 ADOXQ T3, T0 \ MOVQ T0, (ID+16)(MDST) \ // MDST2 ADCXQ T5, T1 \ \ MULXQ (IM1+16)(M1),T3, T0 \ // T0:T3 = A2*B2 ADCXQ T6, T4 \ ADCXQ AX, T0 \ ADOXQ T2, T1 \ ADOXQ T4, T3 \ ADOXQ T0, AX // Performs schoolbook multiplication of 2 256-bit numbers. Uses // MULX instruction. Result is stored in 256 bits pointed by $DST. // // Uses registers: DX,AX #define MULX256(IM0,M0,IM1,M1,ID,MDST,T0,T1,T2,T3,T4,T5,T6,T7,T8,T9) \ MOVQ (IM0+0)(M0), DX \ MULXQ (IM1+0)(M1), T1, T0 \ // A0*B[0-3] MOVQ T1, (ID+0)(MDST) \ MULXQ (IM1+8)(M1), T2, T1 \ XORQ AX, AX \ ADOXQ T2, T0 \ MULXQ (IM1+16)(M1),T3, T2 \ ADOXQ T3, T1 \ MULXQ (IM1+24)(M1),T4, T3 \ ADOXQ T4, T2 \ \ MOVQ (IM0+8)(M0), DX \ MULXQ (IM1+0)(M1), T4, T5 \ // A1*B[0-3] ADOXQ AX, T3 \ XORQ AX, AX \ MULXQ (IM1+8)(M1), T7, T6 \ ADOXQ T0, T4 \ MOVQ T4, (ID+8)(MDST) \ ADCXQ T7, T5 \ MULXQ (IM1+16)(M1),T8, T7 \ ADCXQ T8, T6 \ ADOXQ T1, T5 \ MULXQ (IM1+24)(M1),T9, T8 \ ADCXQ T9, T7 \ ADCXQ AX, T8 \ ADOXQ T2, T6 \ \ MOVQ (IM0+16)(M0),DX \ // A2*B[0-3] MULXQ (IM1+ 0)(M1), T0, T1 \ ADOXQ T3, T7 \ ADOXQ AX, T8 \ XORQ AX, AX \ MULXQ (IM1+8)(M1), T3, T2 \ ADOXQ T5, T0 \ MOVQ T0, (ID+16)(MDST) \ ADCXQ T3, T1 \ MULXQ (IM1+16)(M1),T4, T3 \ ADCXQ T4, T2 \ ADOXQ T6, T1 \ MULXQ (IM1+24)(M1),T9, T4 \ ADCXQ T9, T3 \ MOVQ (IM0+24)(M0),DX \ ADCXQ AX, T4 \ \ ADOXQ T7, T2 \ ADOXQ T8, T3 \ ADOXQ AX, T4 \ \ MULXQ (IM1+ 0)(M1), T0, T5\ // A3*B[0-3] XORQ AX, AX \ MULXQ (IM1+ 8)(M1), T7, T6\ ADCXQ T7, T5 \ ADOXQ T0, T1 \ MULXQ (IM1+16)(M1), T8, T7 \ ADCXQ T8, T6 \ ADOXQ T5, T2 \ MULXQ (IM1+24)(M1), T9, T8 \ ADCXQ T9, T7 \ ADCXQ AX, T8 \ ADOXQ T6, T3 \ ADOXQ T7, T4 \ ADOXQ AX, T8 \ MOVQ T1, (ID+24)(MDST) \ MOVQ T2, (ID+32)(MDST) \ MOVQ T3, (ID+40)(MDST) \ MOVQ T4, (ID+48)(MDST) \ MOVQ T8, (ID+56)(MDST) // Performs schoolbook multiplication of 64-bit with 256-bit // number. // // Uses registers: DX, AX #define MUL64x256(IDX,M0,M1,C0,C1,C2,C3,C4,T0) \ MOVQ (IDX)(M0), T0 \ \ XORQ C2, C2 \ MOVQ M1+0(SB), AX \ MULQ T0 \ MOVQ AX, C0 \ MOVQ DX, C1 \ \ XORQ C3, C3 \ MOVQ M1+8(SB), AX \ MULQ T0 \ ADDQ AX, C1 \ ADCQ DX, C2 \ \ XORQ C4, C4 \ MOVQ M1+16(SB), AX \ MULQ T0 \ ADDQ AX, C2 \ ADCQ DX, C3 \ \ MOVQ M1+24(SB), AX \ MULQ T0 \ ADDQ AX, C3 \ ADCQ DX, C4 // Performs schoolbook multiplication of 128-bit with 256-bit // number. Destroys RAX and RDX // // Uses registers: DX, AX #define MUL128x256(IDX,M0,M1,C0,C1,C2,C3,C4,C5,T0,T1) \ \ // A0 x B0 MOVQ (IDX+0)(M0), T0 \ MOVQ M1+0(SB), AX \ MULQ T0 \ XORQ C2, C2 \ MOVQ AX, C0 \ MOVQ DX, C1 \ \ // A0 x B1 MOVQ M1+8(SB), AX \ MULQ T0 \ XORQ C3, C3 \ ADDQ AX, C1 \ ADCQ DX, C2 \ \ // A1 x B0 MOVQ (IDX+8)(M0), T1 \ MOVQ M1+0(SB), AX \ MULQ T1 \ ADDQ AX, C1 \ ADCQ DX, C2 \ ADCQ $0, C3 \ \ // A0 x B2 XORQ C4, C4 \ MOVQ M1+16(SB), AX \ MULQ T0 \ ADDQ AX, C2 \ ADCQ DX, C3 \ ADCQ $0, C4 \ \ // A1 x B1 MOVQ M1+8(SB), AX \ MULQ T1 \ ADDQ AX, C2 \ ADCQ DX, C3 \ ADCQ $0, C4 \ \ // A0 x B3 MOVQ M1+24(SB), AX \ MULQ T0 \ XORQ C5, C5 \ ADDQ AX, C3 \ ADCQ DX, C4 \ ADCQ $0, C5 \ \ // A1 x B2 MOVQ M1+16(SB), AX \ MULQ T1 \ ADDQ AX, C3 \ ADCQ DX, C4 \ ADCQ $0, C5 \ \ // A1 x B3 MOVQ M1+24(SB), AX \ MULQ T1 \ ADDQ AX, C4 \ ADCQ DX, C5 // Montgomery reduction // Based on method described in Faz-Hernandez et al. https://eprint.iacr.org/2017/1015 #define REDC_MULX(P1, MUL01, MUL23, MUL45, MUL67) \ MOVQ 0x0(DI), DX \ MOVQ 0x8(DI), R14 \ MOVQ P1, AX \ MULXQ AX, R8, R9 \ MUL01 \ MOVQ 0x10(DI), DX \ MOVQ 0x48(DI), CX \ ADDQ 0x18(DI), R8 \ ADCQ 0x20(DI), R9 \ ADCQ 0x28(DI), R10 \ ADCQ 0x30(DI), R11 \ ADCQ 0x38(DI), R12 \ ADCQ 0x40(DI), R13 \ ADCQ $0, CX \ MOVQ P1, AX \ MULXQ AX, BX, BP \ MOVQ R9, 0x0(SI) \ MOVQ R10, 0x8(SI) \ MOVQ R11, 0x10(SI) \ MOVQ R12, 0x18(SI) \ MOVQ R13, 0x20(SI) \ MOVQ CX, 0x28(SI) \ MOVQ 0x50(DI), R9 \ MOVQ 0x58(DI), R10 \ MOVQ 0x60(DI), R11 \ MOVQ 0x68(DI), DI \ ADCQ $0, R9 \ ADCQ $0, R10 \ ADCQ $0, R11 \ ADCQ $0, DI \ MUL23 \ MOVQ 0x0(SI), DX \ ADDQ 0x08(SI), BX \ ADCQ 0x10(SI), BP \ ADCQ 0x18(SI), R12 \ ADCQ 0x20(SI), R13 \ ADCQ 0x28(SI), R14 \ MOVQ R14, 0x18(SI) \ MOVQ CX, R14 \ MOVQ $0, CX \ ADCQ R9, R14 \ ADCQ R10, CX \ MOVQ P1, AX \ MULXQ AX, R8, R9 \ MOVQ BP, 0x0(SI) \ MOVQ R12, 0x8(SI) \ MOVQ R13, 0x10(SI) \ ADCQ $0, R11 \ ADCQ $0, DI \ MUL45 \ MOVQ 0x0(SI), DX \ ADDQ 0x8(SI), R8 \ ADCQ 0x10(SI), R9 \ ADCQ 0x18(SI), R10 \ ADCQ R14, BP \ ADCQ CX, R12 \ ADCQ R11, R13 \ ADCQ $0, DI \ MOVQ P1, AX \ MULXQ AX, R14, BX \ MOVQ R8, 0x0(SI) \ MOVQ R9, 0x8(SI) \ MUL67 \ ADDQ R10, R14 \ ADCQ BP, BX \ ADCQ R12, R8 \ ADCQ R13, R9 \ ADCQ DI, R11 \ MOVQ R14, 0x10(SI) \ MOVQ BX, 0x18(SI) \ MOVQ R8, 0x20(SI) \ MOVQ R9, 0x28(SI) \ MOVQ R11, 0x30(SI) #define REDC_MULQ(MUL01, MUL23, MUL45, MUL67) \ MUL01 \ XORQ CX, CX \ ADDQ 0x18(DI), R8 \ ADCQ 0x20(DI), R9 \ ADCQ 0x28(DI), R10 \ ADCQ 0x30(DI), R11 \ ADCQ 0x38(DI), R12 \ ADCQ 0x40(DI), R13 \ ADCQ 0x48(DI), CX \ MOVQ R8, 0x18(DI) \ MOVQ R9, 0x20(DI) \ MOVQ R10, 0x28(DI) \ MOVQ R11, 0x30(DI) \ MOVQ R12, 0x38(DI) \ MOVQ R13, 0x40(DI) \ MOVQ CX, 0x48(DI) \ MOVQ 0x50(DI), R8 \ MOVQ 0x58(DI), R9 \ MOVQ 0x60(DI), R10 \ MOVQ 0x68(DI), R11 \ ADCQ $0, R8 \ ADCQ $0, R9 \ ADCQ $0, R10 \ ADCQ $0, R11 \ MOVQ R8, 0x50(DI) \ MOVQ R9, 0x58(DI) \ MOVQ R10, 0x60(DI) \ MOVQ R11, 0x68(DI) \ \ MUL23 \ XORQ CX, CX \ ADDQ 0x28(DI), R8 \ ADCQ 0x30(DI), R9 \ ADCQ 0x38(DI), R10 \ ADCQ 0x40(DI), R11 \ ADCQ 0x48(DI), R12 \ ADCQ 0x50(DI), R13 \ ADCQ 0x58(DI), CX \ MOVQ R8, 0x28(DI) \ MOVQ R9, 0x30(DI) \ MOVQ R10, 0x38(DI) \ MOVQ R11, 0x40(DI) \ MOVQ R12, 0x48(DI) \ MOVQ R13, 0x50(DI) \ MOVQ CX, 0x58(DI) \ MOVQ 0x60(DI), R8 \ MOVQ 0x68(DI), R9 \ ADCQ $0, R8 \ ADCQ $0, R9 \ MOVQ R8, 0x60(DI) \ MOVQ R9, 0x68(DI) \ \ MUL45 \ XORQ CX, CX \ ADDQ 0x38(DI), R8 \ ADCQ 0x40(DI), R9 \ ADCQ 0x48(DI), R10 \ ADCQ 0x50(DI), R11 \ ADCQ 0x58(DI), R12 \ ADCQ 0x60(DI), R13 \ ADCQ 0x68(DI), CX \ MOVQ R8, 0x0(SI) \ // OUT0 MOVQ R9, 0x8(SI) \ // OUT1 MOVQ R10, 0x48(DI) \ MOVQ R11, 0x50(DI) \ MOVQ R12, 0x58(DI) \ MOVQ R13, 0x60(DI) \ MOVQ CX, 0x68(DI) \ \ MUL67 \ ADDQ 0x48(DI), R8 \ ADCQ 0x50(DI), R9 \ ADCQ 0x58(DI), R10 \ ADCQ 0x60(DI), R11 \ ADCQ 0x68(DI), R12 \ MOVQ R8, 0x10(SI) \ // OUT2 MOVQ R9, 0x18(SI) \ // OUT3 MOVQ R10, 0x20(SI) \ // OUT4 MOVQ R11, 0x28(SI) \ // OUT5 MOVQ R12, 0x30(SI) // OUT6 TEXT ·cswapP434(SB),NOSPLIT,$0-17 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVB choice+16(FP), AL // AL = 0 or 1 MOVBLZX AL, AX // AX = 0 or 1 NEGQ AX // AX = 0x00..00 or 0xff..ff #ifndef CSWAP_BLOCK #define CSWAP_BLOCK(idx) \ MOVQ (idx*8)(DI), BX \ // BX = x[idx] MOVQ (idx*8)(SI), CX \ // CX = y[idx] MOVQ CX, DX \ // DX = y[idx] XORQ BX, DX \ // DX = y[idx] ^ x[idx] ANDQ AX, DX \ // DX = (y[idx] ^ x[idx]) & mask XORQ DX, BX \ // BX = (y[idx] ^ x[idx]) & mask) ^ x[idx] = x[idx] or y[idx] XORQ DX, CX \ // CX = (y[idx] ^ x[idx]) & mask) ^ y[idx] = y[idx] or x[idx] MOVQ BX, (idx*8)(DI) \ MOVQ CX, (idx*8)(SI) #endif CSWAP_BLOCK(0) CSWAP_BLOCK(1) CSWAP_BLOCK(2) CSWAP_BLOCK(3) CSWAP_BLOCK(4) CSWAP_BLOCK(5) CSWAP_BLOCK(6) #ifdef CSWAP_BLOCK #undef CSWAP_BLOCK #endif RET TEXT ·cmovP434(SB),NOSPLIT,$0-17 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVB choice+16(FP), AL // AL = 0 or 1 MOVBLZX AL, AX // AX = 0 or 1 NEGQ AX // AX = 0x00..00 or 0xff..ff #ifndef CMOV_BLOCK #define CMOV_BLOCK(idx) \ MOVQ (idx*8)(DI), BX \ // BX = x[idx] MOVQ (idx*8)(SI), DX \ // DX = y[idx] XORQ BX, DX \ // DX = y[idx] ^ x[idx] ANDQ AX, DX \ // DX = (y[idx] ^ x[idx]) & mask XORQ DX, BX \ // BX = (y[idx] ^ x[idx]) & mask) ^ x[idx] = x[idx] or y[idx] MOVQ BX, (idx*8)(DI) #endif CMOV_BLOCK(0) CMOV_BLOCK(1) CMOV_BLOCK(2) CMOV_BLOCK(3) CMOV_BLOCK(4) CMOV_BLOCK(5) CMOV_BLOCK(6) #ifdef CMOV_BLOCK #undef CMOV_BLOCK #endif RET TEXT ·addP434(SB),NOSPLIT,$0-24 MOVQ z+0(FP), DX MOVQ x+8(FP), DI MOVQ y+16(FP), SI // Used later to calculate a mask XORQ CX, CX // [R8-R14]: z = x + y MOVQ ( 0)(DI), R8; ADDQ ( 0)(SI), R8 MOVQ ( 8)(DI), R9; ADCQ ( 8)(SI), R9 MOVQ (16)(DI), R10; ADCQ (16)(SI), R10 MOVQ (24)(DI), R11; ADCQ (24)(SI), R11 MOVQ (32)(DI), R12; ADCQ (32)(SI), R12 MOVQ (40)(DI), R13; ADCQ (40)(SI), R13 MOVQ (48)(DI), R14; ADCQ (48)(SI), R14 XORQ DI, DI MOVQ P434X2_0, AX; SUBQ AX, R8 MOVQ P434X2_1, AX; SBBQ AX, R9 SBBQ AX, R10 MOVQ P434X2_3, AX; SBBQ AX, R11 MOVQ P434X2_4, AX; SBBQ AX, R12 MOVQ P434X2_5, AX; SBBQ AX, R13 MOVQ P434X2_6, AX; SBBQ AX, R14 // mask SBBQ $0, CX // if z<0 add P434x2 back MOVQ P434X2_0, R15; ANDQ CX, R15; MOVQ P434X2_1, AX; ANDQ CX, AX; ADDQ R8, R15; MOVQ R15, ( 0)(DX) ADCQ AX, R9; MOVQ R9, ( 8)(DX) ADCQ AX, R10; MOVQ R10, (16)(DX) ADCQ $0, DI MOVQ P434X2_3, R15; ANDQ CX, R15; MOVQ P434X2_4, R8; ANDQ CX, R8; MOVQ P434X2_5, R9; ANDQ CX, R9; MOVQ P434X2_6, R10; ANDQ CX, R10; BTQ $0, DI ADCQ R11, R15; MOVQ R15, (24)(DX) ADCQ R12, R8; MOVQ R8, (32)(DX) ADCQ R13, R9; MOVQ R9, (40)(DX) ADCQ R14, R10; MOVQ R10, (48)(DX) RET TEXT ·adlP434(SB),NOSPLIT,$0-24 MOVQ z+0(FP), DX MOVQ x+8(FP), DI MOVQ y+16(FP),SI MOVQ ( 0)(DI), R8 ADDQ ( 0)(SI), R8 MOVQ ( 8)(DI), R9 ADCQ ( 8)(SI), R9 MOVQ (16)(DI), R10 ADCQ (16)(SI), R10 MOVQ (24)(DI), R11 ADCQ (24)(SI), R11 MOVQ (32)(DI), R12 ADCQ (32)(SI), R12 MOVQ (40)(DI), R13 ADCQ (40)(SI), R13 MOVQ (48)(DI), R14 ADCQ (48)(SI), R14 MOVQ (56)(DI), R15 ADCQ (56)(SI), R15 MOVQ (64)(DI), AX ADCQ (64)(SI), AX MOVQ (72)(DI), BX ADCQ (72)(SI), BX MOVQ (80)(DI), CX ADCQ (80)(SI), CX MOVQ R8, ( 0)(DX) MOVQ R9, ( 8)(DX) MOVQ R10,(16)(DX) MOVQ R11,(24)(DX) MOVQ R12,(32)(DX) MOVQ R13,(40)(DX) MOVQ R14,(48)(DX) MOVQ R15,(56)(DX) MOVQ AX, (64)(DX) MOVQ BX, (72)(DX) MOVQ CX, (80)(DX) MOVQ (88)(DI), R8 ADCQ (88)(SI), R8 MOVQ (96)(DI), R9 ADCQ (96)(SI), R9 MOVQ (104)(DI), R10 ADCQ (104)(SI), R10 MOVQ R8, (88)(DX) MOVQ R9, (96)(DX) MOVQ R10,(104)(DX) RET TEXT ·subP434(SB),NOSPLIT,$0-24 MOVQ z+0(FP), DX MOVQ x+8(FP), DI MOVQ y+16(FP), SI // Used later to calculate a mask XORQ CX, CX MOVQ ( 0)(DI), R8; SUBQ ( 0)(SI), R8 MOVQ ( 8)(DI), R9; SBBQ ( 8)(SI), R9 MOVQ (16)(DI), R10; SBBQ (16)(SI), R10 MOVQ (24)(DI), R11; SBBQ (24)(SI), R11 MOVQ (32)(DI), R12; SBBQ (32)(SI), R12 MOVQ (40)(DI), R13; SBBQ (40)(SI), R13 MOVQ (48)(DI), R14; SBBQ (48)(SI), R14 // mask SBBQ $0, CX XORQ R15, R15 // if z<0 add p434x2 back MOVQ P434X2_0, DI; ANDQ CX, DI MOVQ P434X2_1, SI; ANDQ CX, SI MOVQ P434X2_3, AX; ANDQ CX, AX ADDQ DI, R8; MOVQ R8, ( 0)(DX) ADCQ SI, R9; MOVQ R9, ( 8)(DX) ADCQ SI, R10; MOVQ R10, (16)(DX) ADCQ AX, R11; MOVQ R11, (24)(DX) ADCQ $0, R15 MOVQ P434X2_4, R8; ANDQ CX, R8; MOVQ P434X2_5, R9; ANDQ CX, R9; MOVQ P434X2_6, R10; ANDQ CX, R10 BTQ $0, R15 ADCQ R8, R12; MOVQ R12, (32)(DX) ADCQ R9, R13; MOVQ R13, (40)(DX) ADCQ R10, R14; MOVQ R14, (48)(DX) RET TEXT ·sulP434(SB),NOSPLIT,$0-24 MOVQ z+0(FP), DX MOVQ x+8(FP), DI MOVQ y+16(FP), SI // Used later to store result of 0-borrow XORQ CX, CX // SUBC for first 10 limbs MOVQ ( 0)(DI), R8; SUBQ ( 0)(SI), R8 MOVQ ( 8)(DI), R9; SBBQ ( 8)(SI), R9 MOVQ (16)(DI), R10; SBBQ (16)(SI), R10 MOVQ (24)(DI), R11; SBBQ (24)(SI), R11 MOVQ (32)(DI), R12; SBBQ (32)(SI), R12 MOVQ (40)(DI), R13; SBBQ (40)(SI), R13 MOVQ (48)(DI), R14; SBBQ (48)(SI), R14 MOVQ (56)(DI), R15; SBBQ (56)(SI), R15 MOVQ (64)(DI), AX; SBBQ (64)(SI), AX MOVQ (72)(DI), BX; SBBQ (72)(SI), BX MOVQ R8, ( 0)(DX) MOVQ R9, ( 8)(DX) MOVQ R10, (16)(DX) MOVQ R11, (24)(DX) MOVQ R12, (32)(DX) MOVQ R13, (40)(DX) MOVQ R14, (48)(DX) MOVQ R15, (56)(DX) MOVQ AX, (64)(DX) MOVQ BX, (72)(DX) // SUBC for last 4 limbs MOVQ ( 80)(DI), R8; SBBQ ( 80)(SI), R8 MOVQ ( 88)(DI), R9; SBBQ ( 88)(SI), R9 MOVQ ( 96)(DI), R10; SBBQ ( 96)(SI), R10 MOVQ (104)(DI), R11; SBBQ (104)(SI), R11 // Store carry flag SBBQ $0, CX MOVQ R8, ( 80)(DX) MOVQ R9, ( 88)(DX) MOVQ R10, ( 96)(DX) MOVQ R11, (104)(DX) // Load p into registers: MOVQ P434_0, R8; ANDQ CX, R8 // P434_{1,2} = P434_0, so reuse R8 MOVQ P434_3, R9; ANDQ CX, R9 MOVQ P434_4, R10; ANDQ CX, R10 MOVQ P434_5, R11; ANDQ CX, R11 MOVQ P434_6, R12; ANDQ CX, R12 MOVQ (56 )(DX), AX; ADDQ R8, AX; MOVQ AX, (56 )(DX) MOVQ (56+ 8)(DX), AX; ADCQ R8, AX; MOVQ AX, (56+ 8)(DX) MOVQ (56+16)(DX), AX; ADCQ R8, AX; MOVQ AX, (56+16)(DX) MOVQ (56+24)(DX), AX; ADCQ R9, AX; MOVQ AX, (56+24)(DX) MOVQ (56+32)(DX), AX; ADCQ R10, AX; MOVQ AX, (56+32)(DX) MOVQ (56+40)(DX), AX; ADCQ R11, AX; MOVQ AX, (56+40)(DX) MOVQ (56+48)(DX), AX; ADCQ R12, AX; MOVQ AX, (56+48)(DX) RET TEXT ·modP434(SB),NOSPLIT,$0-8 MOVQ x+0(FP), DI // Zero AX for later use: XORQ AX, AX // Set x <- x - p MOVQ P434_0, R8 SUBQ R8, ( 0)(DI) // P434_{1,2} = P434_0, so reuse R8 MOVQ P434_3, R9 SBBQ R8, ( 8)(DI) SBBQ R8, (16)(DI) MOVQ P434_4, R10 SBBQ R9, (24)(DI) MOVQ P434_5, R11 SBBQ R10, (32)(DI) MOVQ P434_6, R12 SBBQ R11, (40)(DI) SBBQ R12, (48)(DI) // save carry SBBQ $0, AX // Conditionally add p to x if x-p < 0 ANDQ AX, R8 ANDQ AX, R9 ANDQ AX, R10 ANDQ AX, R11 ANDQ AX, R12 ADDQ R8, ( 0)(DI) ADCQ R8, ( 8)(DI) ADCQ R8, (16)(DI) ADCQ R9, (24)(DI) ADCQ R10,(32)(DI) ADCQ R11,(40)(DI) ADCQ R12,(48)(DI) RET // 434-bit multiplication using Karatsuba (one level), // schoolbook (one level). TEXT ·mulP434(SB),NOSPLIT,$112-24 MOVQ z+0(FP), CX MOVQ x+8(FP), DI MOVQ y+16(FP), SI // Check whether to use optimized implementation CMPB ·HasADXandBMI2(SB), $1 JE mul_with_mulx_adcx_adox // rcx[0-3] <- AH+AL XORQ AX, AX MOVQ 0x20(DI), R8 MOVQ 0x28(DI), R9 MOVQ 0x30(DI), R10 XORQ R11, R11 ADDQ 0x0(DI), R8 ADCQ 0x8(DI), R9 ADCQ 0x10(DI), R10 ADCQ 0x18(DI), R11 // store AH+AL mask SBBQ $0, AX MOVQ AX, 0x40(SP) // store AH+AL in 0-0x18(rcx) MOVQ R8, 0x0(CX) MOVQ R9, 0x8(CX) MOVQ R10, 0x10(CX) MOVQ R11, 0x18(CX) // r12-r15 <- BH+BL XORQ DX, DX MOVQ 0x20(SI), R12 MOVQ 0x28(SI), R13 MOVQ 0x30(SI), R14 XORQ R15, R15 ADDQ 0x0(SI), R12 ADCQ 0x8(SI), R13 ADCQ 0x10(SI), R14 ADCQ 0x18(SI), R15 SBBQ $0, DX // store BH+BL mask MOVQ DX, 0x48(SP) // (rsp[0-0x38]) <- (AH+AL)*(BH+BL) MOVQ (CX), AX MULQ R12 MOVQ AX, (SP) MOVQ DX, R8 XORQ R9, R9 MOVQ (CX), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 XORQ R10, R10 MOVQ 0x8(CX), AX MULQ R12 ADDQ AX, R8 MOVQ R8, 0x8(SP) ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (CX), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x10(CX), AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x8(CX), AX MULQ R13 ADDQ AX, R9 MOVQ R9, 0x10(SP) ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (CX),AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ 0x18(CX), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ 0x8(CX), AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ 0x10(CX), AX MULQ R13 ADDQ AX, R10 MOVQ R10, 0x18(SP) ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ 0x8(CX), AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ 0x18(CX), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ 0x10(CX), AX MULQ R14 ADDQ AX, R8 MOVQ R8, 0x20(SP) ADCQ DX, R9 ADCQ $0, R10 XORQ R11, R11 MOVQ 0x10(CX), AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R11 MOVQ 0x18(CX), AX MULQ R14 ADDQ AX, R9 MOVQ R9, 0x28(SP) ADCQ DX, R10 ADCQ $0, R11 MOVQ 0x18(CX), AX MULQ R15 ADDQ AX, R10 MOVQ R10, 0x30(SP) ADCQ DX, R11 MOVQ R11,0x38(SP) // r12-r15 <- masked (BH + BL) MOVQ 0x40(SP), AX ANDQ AX, R12 ANDQ AX, R13 ANDQ AX, R14 ANDQ AX, R15 // r8-r11 <- masked (AH + AL) MOVQ 0x48(SP), AX MOVQ 0x00(CX), R8 ANDQ AX, R8 MOVQ 0x08(CX), R9 ANDQ AX, R9 MOVQ 0x10(CX), R10 ANDQ AX, R10 MOVQ 0x18(CX), R11 ANDQ AX, R11 // r12-r15 <- masked (AH + AL) + masked (BH + BL) ADDQ R8, R12 ADCQ R9, R13 ADCQ R10, R14 ADCQ R11, R15 // rsp[0x20-0x38] <- (AH+AL) x (BH+BL) high MOVQ 0x20(SP), AX ADDQ AX, R12 MOVQ 0x28(SP), AX ADCQ AX, R13 MOVQ 0x30(SP), AX ADCQ AX, R14 MOVQ 0x38(SP), AX ADCQ AX, R15 MOVQ R12, 0x50(SP) MOVQ R13, 0x58(SP) MOVQ R14, 0x60(SP) MOVQ R15, 0x68(SP) // [rcx] <- CL = AL x BL MOVQ (DI), R11 MOVQ (SI), AX MULQ R11 XORQ R9, R9 MOVQ AX, (CX) MOVQ DX, R8 MOVQ 0x10(DI), R14 MOVQ 0x8(SI), AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 ADCQ DX, R9 MOVQ 0x8(DI), R12 MOVQ (SI), AX MULQ R12 ADDQ AX, R8 MOVQ R8, 0x8(CX) ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ 0x10(SI), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (SI), R13 MOVQ R14, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x8(SI), AX MULQ R12 ADDQ AX, R9 MOVQ R9, 0x10(CX) ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ 0x18(SI), AX MULQ R11 MOVQ 0x18(DI), R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ R15, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ 0x10(SI), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ 0x8(SI), AX MULQ R14 ADDQ AX, R10 MOVQ R10, 0x18(CX) ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ 0x18(SI), AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ 0x8(SI), AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ 0x10(SI), AX MULQ R14 ADDQ AX, R8 MOVQ R8, 0x20(CX) ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ 0x18(SI), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x10(SI), AX MULQ R15 ADDQ AX, R9 MOVQ R9, 0x28(CX) ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x18(SI), AX MULQ R15 ADDQ AX, R10 MOVQ R10, 0x30(CX) ADCQ DX, R8 MOVQ R8, 0x38(CX) // rcx[0x40-0x68] <- AH*BH // multiplies 2 192-bit numbers A,B MOVQ 0x20(DI), R11 MOVQ 0x20(SI), AX MULQ R11 XORQ R9, R9 MOVQ AX, 0x40(CX) MOVQ DX, R8 MOVQ 0x30(DI), R14 MOVQ 0x28(SI), AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 ADCQ DX, R9 MOVQ 0x28(DI), R12 MOVQ 0x20(SI), AX MULQ R12 ADDQ AX, R8 MOVQ R8, 0x48(CX) ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ 0x30(SI), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x20(SI), R13 MOVQ R14, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x28(SI), AX MULQ R12 ADDQ AX, R9 MOVQ R9, 0x50(CX) ADCQ DX, R10 ADCQ $0, R8 MOVQ 0x30(SI), AX MULQ R12 XORQ R12, R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R12 MOVQ 0x28(SI), AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R12 MOVQ R10, 0x58(CX) MOVQ 0x30(SI), AX MULQ R14 ADDQ AX, R8 ADCQ $0, R12 MOVQ R8, 0x60(CX) ADDQ R12, DX // [r8-r15] <- (AH+AL)x(BH+BL) - ALxBL MOVQ 0x0(SP), R8 SUBQ 0x0(CX), R8 MOVQ 0x8(SP), R9 SBBQ 0x8(CX), R9 MOVQ 0x10(SP), R10 SBBQ 0x10(CX), R10 MOVQ 0x18(SP), R11 SBBQ 0x18(CX), R11 MOVQ 0x50(SP), R12 SBBQ 0x20(CX), R12 MOVQ 0x58(SP), R13 SBBQ 0x28(CX), R13 MOVQ 0x60(SP), R14 SBBQ 0x30(CX), R14 MOVQ 0x68(SP), R15 SBBQ 0x38(CX), R15 // [r8-r15] <- (AH+AL) x (BH+BL) - ALxBL - AHxBH MOVQ 0x40(CX), AX SUBQ AX, R8 MOVQ 0x48(CX), AX SBBQ AX, R9 MOVQ 0x50(CX), AX SBBQ AX, R10 MOVQ 0x58(CX), AX SBBQ AX, R11 MOVQ 0x60(CX), AX SBBQ AX, R12 SBBQ DX, R13 SBBQ $0, R14 SBBQ $0, R15 // Final result ADDQ 0x20(CX), R8 MOVQ R8, 0x20(CX) // OUT4 ADCQ 0x28(CX), R9 MOVQ R9, 0x28(CX) // OUT5 ADCQ 0x30(CX), R10 MOVQ R10, 0x30(CX) // OUT6 ADCQ 0x38(CX), R11 MOVQ R11, 0x38(CX) // OUT7 ADCQ 0x40(CX), R12 MOVQ R12, 0x40(CX) // OUT8 ADCQ 0x48(CX), R13 MOVQ R13, 0x48(CX) // OUT9 ADCQ 0x50(CX), R14 MOVQ R14, 0x50(CX) // OUT10 ADCQ 0x58(CX), R15 MOVQ R15, 0x58(CX) // OUT11 MOVQ 0x60(CX), R12 ADCQ $0, R12 MOVQ R12, 0x60(CX) // OUT12 ADCQ $0, DX MOVQ DX, 0x68(CX) // OUT13 RET mul_with_mulx_adcx_adox: // Mul implementation for CPUs supporting two independent carry chain // (ADOX/ADCX) instructions and carry-less MULX multiplier XORQ AX, AX MOVQ 0x0(DI), R8 MOVQ 0x8(DI), R9 MOVQ 0x10(DI), R10 MOVQ 0x18(DI), R11 MOVQ BP, 0x70(SP) // push: BP is Callee-save. ADDQ 0x20(DI), R8 ADCQ 0x28(DI), R9 ADCQ 0x30(DI), R10 ADCQ $0, R11 SBBQ $0, AX MOVQ R8, 0x0(SP) MOVQ R9, 0x8(SP) MOVQ R10, 0x10(SP) MOVQ R11, 0x18(SP) // r12-r15 <- BH + BL, rbx <- mask XORQ BX, BX MOVQ 0x0(SI), R12 MOVQ 0x8(SI), R13 MOVQ 0x10(SI), R14 MOVQ 0x18(SI), R15 ADDQ 0x20(SI), R12 ADCQ 0x28(SI), R13 ADCQ 0x30(SI), R14 ADCQ $0, R15 SBBQ $0, BX MOVQ R12, 0x20(SP) MOVQ R13, 0x28(SP) MOVQ R14, 0x30(SP) MOVQ R15, 0x38(SP) // r12-r15 <- masked (BH + BL) ANDQ AX, R12 ANDQ AX, R13 ANDQ AX, R14 ANDQ AX, R15 // r8-r11 <- masked (AH + AL) ANDQ BX, R8 ANDQ BX, R9 ANDQ BX, R10 ANDQ BX, R11 // r8-r11 <- masked (AH + AL) + masked (BH + BL) ADDQ R12, R8 ADCQ R13, R9 ADCQ R14, R10 ADCQ R15, R11 MOVQ R8, 0x40(SP) MOVQ R9, 0x48(SP) MOVQ R10, 0x50(SP) MOVQ R11, 0x58(SP) // [rsp] <- CM = (AH+AL) x (BH+BL) MULX256(0,SP,32,SP,0,SP,R8,R9,R10,R11,R12,R13,R14,R15,BX,BP) // [rcx] <- CL = AL x BL (Result c0-c3) MULX256(0,DI,0,SI,0,CX,R8,R9,R10,R11,R12,R13,R14,R15,BX,BP) // [rcx+64], rbx, rbp, rax <- CH = AH x BH MULX192(32,DI,32,SI,64,CX,R8,BX,R10,BP,R12,R13,R14) // r8-r11 <- (AH+AL) x (BH+BL), final step MOVQ 0x40(SP), R8 MOVQ 0x48(SP), R9 MOVQ 0x50(SP), R10 MOVQ 0x58(SP), R11 MOVQ 0x20(SP), DX ADDQ DX, R8 MOVQ 0x28(SP), DX ADCQ DX, R9 MOVQ 0x30(SP), DX ADCQ DX, R10 MOVQ 0x38(SP), DX ADCQ DX, R11 // [rsp], x3-x5 <- (AH+AL) x (BH+BL) - ALxBL MOVQ 0x0(SP), R12 MOVQ 0x8(SP), R13 MOVQ 0x10(SP), R14 MOVQ 0x18(SP), R15 SUBQ 0x0(CX), R12 SBBQ 0x8(CX), R13 SBBQ 0x10(CX), R14 SBBQ 0x18(CX), R15 SBBQ 0x20(CX), R8 SBBQ 0x28(CX), R9 SBBQ 0x30(CX), R10 SBBQ 0x38(CX), R11 // r8-r15 <- (AH+AL) x (BH+BL) - ALxBL - AHxBH SUBQ 0x40(CX), R12 SBBQ 0x48(CX), R13 SBBQ 0x50(CX), R14 SBBQ BX, R15 SBBQ BP, R8 SBBQ AX, R9 SBBQ $0, R10 SBBQ $0, R11 ADDQ 0x20(CX), R12 MOVQ R12, 0x20(CX) // OUT4 ADCQ 0x28(CX), R13 MOVQ R13, 0x28(CX) // OUT5 ADCQ 0x30(CX), R14 MOVQ R14, 0x30(CX) // OUT6 ADCQ 0x38(CX), R15 MOVQ R15, 0x38(CX) // OUT7 ADCQ 0x40(CX), R8 MOVQ R8, 0x40(CX) // OUT8 ADCQ 0x48(CX), R9 MOVQ R9, 0x48(CX) // OUT9 ADCQ 0x50(CX), R10 MOVQ R10, 0x50(CX) // OUT10 ADCQ BX, R11 MOVQ R11, 0x58(CX) // OUT11 ADCQ $0, BP MOVQ BP, 0x60(CX) // OUT12 ADCQ $0, AX MOVQ AX, 0x68(CX) // OUT13 MOVQ 0x70(SP), BP // pop: BP is Callee-save. RET TEXT ·rdcP434(SB),$0-16 MOVQ z+0(FP), SI MOVQ x+8(FP), DI CMPB ·HasADXandBMI2(SB), $1 JE redc_bdw #define MUL01 MUL128x256( 0,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,R14,CX) #define MUL23 MUL128x256(16,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,R14,CX) #define MUL45 MUL128x256(32,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,R14,CX) #define MUL67 MUL64x256(48,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13) REDC_MULQ(MUL01, MUL23, MUL45, MUL67) #undef MUL01 #undef MUL23 #undef MUL45 #undef MUL67 RET // 434-bit montgomery reduction Uses MULX/ADOX/ADCX instructions // available on Broadwell micro-architectures and newer. redc_bdw: #define MULX01 MULX128x256(R14,·P434p1+(8*P434_P1_ZEROS),R9 ,R10,R11,R12,R13) #define MULX23 MULX128x256(R8 ,·P434p1+(8*P434_P1_ZEROS),BP ,R12,R13,R14,CX ) #define MULX45 MULX128x256(BX ,·P434p1+(8*P434_P1_ZEROS),R9 ,R10,BP ,R12,R13) #define MULX67 MULX64x256 ( ·P434p1+(8*P434_P1_ZEROS),BX ,R8 ,R9 ,R11,CX ) REDC_MULX(·P434p1+(8*P434_P1_ZEROS)+0(SB), MULX01, MULX23, MULX45, MULX67) #undef MULX01 #undef MULX23 #undef MULX45 #undef MULX67 RET golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/arith_amd64_test.go000066400000000000000000000052261454601126700270140ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build amd64 && !noasm // +build amd64,!noasm package p434 import ( "reflect" "testing" "testing/quick" "github.com/cloudflare/circl/dh/sidh/internal/common" "golang.org/x/sys/cpu" ) type OptimFlag uint const ( // Indicates that optimisation which uses MUL instruction should be used kUse_MUL OptimFlag = 1 << 0 // Indicates that optimisation which uses MULX, ADOX and ADCX instructions should be used kUse_MULXandADxX = 1 << 1 ) func resetCpuFeatures() { HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX } // Utility function used for testing Mul implementations. Tests caller provided // mulFunc against mul() func testMul(t *testing.T, f1, f2 OptimFlag) { doMulTest := func(multiplier, multiplicant common.Fp) bool { defer resetCpuFeatures() var resMulRef, resMulOptim common.FpX2 // Compute multiplier*multiplicant with first implementation HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX mulP434(&resMulOptim, &multiplier, &multiplicant) // Compute multiplier*multiplicant with second implementation HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX mulP434(&resMulRef, &multiplier, &multiplicant) // Compare results return reflect.DeepEqual(resMulRef, resMulOptim) } if err := quick.Check(doMulTest, quickCheckConfig); err != nil { t.Error(err) } } // Utility function used for testing REDC implementations. Tests caller provided // redcFunc against redc() func testRedc(t *testing.T, f1, f2 OptimFlag) { doRedcTest := func(aRR common.FpX2) bool { defer resetCpuFeatures() var resRedcF1, resRedcF2 common.Fp aRRcpy := aRR // Compute redc with first implementation HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX rdcP434(&resRedcF1, &aRR) // Compute redc with second implementation HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX rdcP434(&resRedcF2, &aRRcpy) // Compare results return reflect.DeepEqual(resRedcF2, resRedcF1) } if err := quick.Check(doRedcTest, quickCheckConfig); err != nil { t.Error(err) } } // Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX func TestMulWithMULXADxX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testMul(t, kUse_MULXandADxX, kUse_MUL) } // Ensures correctness of Montgomery reduction implementation which uses MULX // and ADCX/ADOX. func TestRedcWithMULXADxX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testRedc(t, kUse_MULXandADxX, kUse_MUL) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/arith_decl.go000066400000000000000000000024731454601126700257520ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build amd64 && !noasm // +build amd64,!noasm package p434 import ( . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cmovP434(x, y *Fp, choice uint8) // If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cswapP434(x, y *Fp, choice uint8) // Compute z = x + y (mod p). // //go:noescape func addP434(z, x, y *Fp) // Compute z = x - y (mod p). // //go:noescape func subP434(z, x, y *Fp) // Compute z = x + y, without reducing mod p. // //go:noescape func adlP434(z, x, y *FpX2) // Compute z = x - y, without reducing mod p. // //go:noescape func sulP434(z, x, y *FpX2) // Reduce a field element in [0, 2*p) to one in [0,p). // //go:noescape func modP434(x *Fp) // Computes z = x * y. // //go:noescape func mulP434(z *FpX2, x, y *Fp) // Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value // of x may be changed. z=x not allowed. // //go:noescape func rdcP434(z *Fp, x *FpX2) golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/arith_generic.go000066400000000000000000000104421454601126700264520ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build noasm || !amd64 // +build noasm !amd64 package p434 import ( "math/bits" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Compute z = x + y (mod p). func addP434(z, x, y *common.Fp) { var carry uint64 // z=x+y % P434 for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } // z = z - P434x2 carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Sub64(z[i], P434x2[i], carry) } // if z<0 add P434x2 back mask := uint64(0 - carry) carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(z[i], P434x2[i]&mask, carry) } } // Compute z = x - y (mod p). func subP434(z, x, y *common.Fp) { var borrow uint64 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } mask := uint64(0 - borrow) borrow = 0 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Add64(z[i], P434x2[i]&mask, borrow) } } // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. func cmovP434(x, y *common.Fp, choice uint8) { mask := 0 - uint64(choice) for i := 0; i < FpWords; i++ { x[i] ^= mask & (x[i] ^ y[i]) } } // Conditionally swaps bits in x and y in constant time. // mask indicates bits to be swapped (set bits are swapped) // For details see "Hackers Delight, 2.20" // // Implementation doesn't actually depend on a prime field. func cswapP434(x, y *common.Fp, mask uint8) { var tmp, mask64 uint64 mask64 = 0 - uint64(mask) for i := 0; i < FpWords; i++ { tmp = mask64 & (x[i] ^ y[i]) x[i] = tmp ^ x[i] y[i] = tmp ^ y[i] } } // Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) // with R=2^(FpWords*64). Destroys the input value. func rdcP434(z *common.Fp, x *common.FpX2) { var carry, t, u, v uint64 var hi, lo uint64 var count int count = P434p1Zeros for i := 0; i < FpWords; i++ { for j := 0; j < i; j++ { if j < (i - count + 1) { hi, lo = bits.Mul64(z[j], P434p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i] = v v = u u = t t = 0 } for i := FpWords; i < 2*FpWords-1; i++ { if count > 0 { count-- } for j := i - FpWords + 1; j < FpWords; j++ { if j < (FpWords - count) { hi, lo = bits.Mul64(z[j], P434p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i-FpWords] = v v = u u = t t = 0 } v, _ = bits.Add64(v, x[2*FpWords-1], 0) z[FpWords-1] = v } // Compute z = x * y. func mulP434(z *common.FpX2, x, y *common.Fp) { var u, v, t uint64 var hi, lo uint64 var carry uint64 for i := uint64(0); i < FpWords; i++ { for j := uint64(0); j <= i; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } for i := FpWords; i < (2*FpWords)-1; i++ { for j := i - FpWords + 1; j < FpWords; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } z[2*FpWords-1] = v } // Compute z = x + y, without reducing mod p. func adlP434(z, x, y *common.FpX2) { var carry uint64 for i := 0; i < 2*FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } } // Reduce a field element in [0, 2*p) to one in [0,p). func modP434(x *common.Fp) { var borrow, mask uint64 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Sub64(x[i], P434[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Add64(x[i], P434[i]&mask, borrow) } } // Compute z = x - y, without reducing mod p. func sulP434(z, x, y *common.FpX2) { var borrow, mask uint64 for i := 0; i < 2*FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := FpWords; i < 2*FpWords; i++ { z[i], borrow = bits.Add64(z[i], P434[i-FpWords]&mask, borrow) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/arith_test.go000066400000000000000000000070001454601126700260110ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p434 import ( "testing" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Package-level storage for this field element is intended to deter // compiler optimizations. var ( benchmarkFp common.Fp benchmarkFpX2 common.FpX2 bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} ) func TestFpCswap(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cswapP434(&x, &y, 0) for i := 0; i < FpWords; i++ { if (x[i] != one[i]) || (y[i] != two[i]) { t.Error("Found", x, "expected", one) } } cswapP434(&x, &y, 1) for i := 0; i < FpWords; i++ { if (x[i] != two[i]) || (y[i] != one[i]) { t.Error("Found", x, "expected", two) } } } func TestFpCmov(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cmovP434(&x, &y, 0) for i := 0; i < FpWords; i++ { if x[i] != one[i] { t.Error("Found", x, "expected", one) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } cmovP434(&x, &y, 1) for i := 0; i < FpWords; i++ { if x[i] != two[i] { t.Error("Found", x, "expected", two) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } } // Benchmarking for field arithmetic func BenchmarkMul(b *testing.B) { for n := 0; n < b.N; n++ { mulP434(&benchmarkFpX2, &bench_x, &bench_y) } } func BenchmarkRdc(b *testing.B) { z := bench_z // This benchmark actually computes garbage, because // rdcP434 mangles its input, but since it's // constant-time that shouldn't matter for the benchmarks. for n := 0; n < b.N; n++ { rdcP434(&benchmarkFp, &z) } } func BenchmarkAdd(b *testing.B) { for n := 0; n < b.N; n++ { addP434(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkSub(b *testing.B) { for n := 0; n < b.N; n++ { subP434(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkCswap(b *testing.B) { x, y := bench_x, bench_y for n := 0; n < b.N; n++ { cswapP434(&x, &y, 1) cswapP434(&x, &y, 0) } } func BenchmarkMod(b *testing.B) { x := bench_x for n := 0; n < b.N; n++ { modP434(&x) } } func BenchmarkX2AddLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { adlP434(&x, &y, &z) } } func BenchmarkX2SubLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { sulP434(&x, &y, &z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/core.go000066400000000000000000000205411454601126700246000ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p434 import ( crand "crypto/rand" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // ----------------------------------------------------------------------------- // Functions for traversing isogeny trees according to strategy. Key type 'A' is // // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR needed // for public key generation. func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { var xPA, xQA, xRA ProjectivePoint var xPB, xQB, xRB, xR ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny4 // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) // Secret isogeny phi.GenerateCurve(&xR) xPA = xPB xQA = xQB xRA = xRB phi.EvaluatePoint(&xPA) phi.EvaluatePoint(&xQA) phi.EvaluatePoint(&xRA) Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPA.X, &invZP) mul(&pub3Pt[1], &xQA.X, &invZQ) mul(&pub3Pt[2], &xRA.X, &invZR) } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { var xPB, xQB, xRB, xR ProjectivePoint var xPA, xQA, xRA ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny3 // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) phi.GenerateCurve(&xR) xPB = xPA xQB = xQA xRB = xRA phi.EvaluatePoint(&xPB) phi.EvaluatePoint(&xQB) phi.EvaluatePoint(&xRB) Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPB.X, &invZP) mul(&pub3Pt[1], &xQB.X, &invZQ) mul(&pub3Pt[2], &xRB.X, &invZR) } // ----------------------------------------------------------------------------- // Key agreement functions // // Establishing shared keys in in 2-torsion group func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny4 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyA(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients4(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } // Establishing shared keys in in 3-torsion group func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny3 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} //PUBLIC KEY VALIDATION if err := PublicKeyValidation(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen); err != nil { _, err_read := crand.Read(ss) if err_read != nil { panic("core: failed to generate random ss when public key verification fails") } return } xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyB(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients3(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/curve.go000066400000000000000000000341221454601126700247740ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p434 import ( "errors" . "github.com/cloudflare/circl/dh/sidh/internal/common" "math" ) // Stores isogeny 3 curve constants type isogeny3 struct { K1 Fp2 K2 Fp2 } // Stores isogeny 4 curve constants type isogeny4 struct { isogeny3 K3 Fp2 } // Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result // is returned in jBytes buffer, encoded in little-endian format. Caller // provided jBytes buffer has to be big enough to j-invariant value. In case // of SIDH, buffer size must be at least size of shared secret. // Implementation corresponds to Algorithm 9 from SIKE. func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { var t0, t1 Fp2 sqr(j, &cparams.A) // j = A^2 sqr(&t1, &cparams.C) // t1 = C^2 add(&t0, &t1, &t1) // t0 = t1 + t1 sub(&t0, j, &t0) // t0 = j - t0 sub(&t0, &t0, &t1) // t0 = t0 - t1 sub(j, &t0, &t1) // t0 = t0 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(j, j, &t1) // j = j * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&t1, &t0) // t1 = t0^2 mul(&t0, &t0, &t1) // t0 = t0 * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 inv(j, j) // j = 1/j mul(j, &t0, j) // j = t0 * j } // Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function // recovers projective coordinate A of a curve. This is Algorithm 10 from SIKE. func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { var t0, t1 Fp2 add(&t1, xp, xq) // t1 = Xp + Xq mul(&t0, xp, xq) // t0 = Xp * Xq mul(&curve.A, xr, &t1) // A = X(q-p) * t1 add(&curve.A, &curve.A, &t0) // A = A + t0 mul(&t0, &t0, xr) // t0 = t0 * X(q-p) sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t1, &t1, xr) // t1 = t1 + X(q-p) add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&curve.A, &curve.A) // A = A^2 inv(&t0, &t0) // t0 = 1/t0 mul(&curve.A, &curve.A, &t0) // A = A * t0 sub(&curve.A, &curve.A, &t1) // A = A - t1 } // Computes equivalence (A:C) ~ (A+2C : A-2C) func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coef CurveCoefficientsEquiv var c2 Fp2 add(&c2, &cparams.C, &cparams.C) // A24p = A+2*C add(&coef.A, &cparams.A, &c2) // A24m = A-2*C sub(&coef.C, &cparams.A, &c2) return coef } // Computes equivalence (A:C) ~ (A+2C : 4C) func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv add(&coefEq.C, &cparams.C, &cparams.C) // A24p = A+2C add(&coefEq.A, &cparams.A, &coefEq.C) // C24 = 4*C add(&coefEq.C, &coefEq.C, &coefEq.C) return coefEq } // Helper function for RightToLeftLadder(). Returns A+2C / 4. func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { var tmp Fp2 // 2C add(&tmp, &cparams.C, &cparams.C) // A+2C add(&ret, &cparams.A, &tmp) // 1/4C add(&tmp, &tmp, &tmp) inv(&tmp, &tmp) // A+2C/4C mul(&ret, &ret, &tmp) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { add(&cparams.A, &coefEq.A, &coefEq.C) // cparams.A = 2*(A+2C+A-2C) = 4A add(&cparams.A, &cparams.A, &cparams.A) // cparams.C = (A+2C-A+2C) = 4C sub(&cparams.C, &coefEq.A, &coefEq.C) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { // cparams.C = (4C)*1/2=2C mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) // cparams.A = A+2C - 2C = A sub(&cparams.A, &coefEq.A, &cparams.C) // cparams.C = 2C * 1/2 = C mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) } // Combined coordinate doubling and differential addition. Takes projective points // P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. // Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { var t0, t1, t2 Fp2 xQmP, zQmP := &QmP.X, &QmP.Z xPaQ, zPaQ := &PaQ.X, &PaQ.Z x2P, z2P := &dblP.X, &dblP.Z xP, zP := &P.X, &P.Z xQ, zQ := &Q.X, &Q.Z add(&t0, xP, zP) // t0 = Xp+Zp sub(&t1, xP, zP) // t1 = Xp-Zp sqr(x2P, &t0) // 2P.X = t0^2 sub(&t2, xQ, zQ) // t2 = Xq-Zq add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq mul(&t0, &t0, &t2) // t0 = t0 * t2 mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q return } // Given the curve parameters, xP = x(P), computes xP = x([2^k]P) // Safe to overlap xP, x2P. func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp add(&t1, x, z) // t1 = Xp + Zp sqr(&t0, &t0) // t0 = t0 ^ 2 sqr(&t1, &t1) // t1 = t1 ^ 2 mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 mul(x, z, &t1) // X2p = Z2p * t1 sub(&t1, &t1, &t0) // t1 = t1 - t0 mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 add(z, z, &t0) // Z2p = Z2p + t0 mul(z, z, &t1) // Zp = Z2p * t1 } } // Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). // // Safe to overlap xP, xR. func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1, t2, t3, t4, t5, t6 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp sqr(&t2, &t0) // t2 = t0^2 add(&t1, x, z) // t1 = Xp + Zp sqr(&t3, &t1) // t3 = t1^2 add(&t4, &t1, &t0) // t4 = t1 + t0 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t1, &t4) // t1 = t4^2 sub(&t1, &t1, &t3) // t1 = t1 - t3 sub(&t1, &t1, &t2) // t1 = t1 - t2 mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ mul(&t3, &t3, &t5) // t3 = t5 * t3 mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- mul(&t2, &t2, &t6) // t2 = t2 * t6 sub(&t3, &t2, &t3) // t3 = t2 - t3 sub(&t2, &t5, &t6) // t2 = t5 - t6 mul(&t1, &t2, &t1) // t1 = t2 * t1 add(&t2, &t3, &t1) // t2 = t3 + t1 sqr(&t2, &t2) // t2 = t2^2 mul(x, &t2, &t4) // X3p = t2 * t4 sub(&t1, &t3, &t1) // t1 = t3 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(z, &t1, &t0) // Z3p = t1 * t0 } } // Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). // // All xi, yi must be distinct. func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { var x1x2, t Fp2 mul(&x1x2, x1, x2) // x1*x2 mul(&t, &x1x2, x3) // 1/(x1*x2*x3) inv(&t, &t) mul(y1, &t, x2) // 1/x1 mul(y1, y1, x3) mul(y2, &t, x1) // 1/x2 mul(y2, y2, x3) mul(y3, &t, &x1x2) // 1/x3 } // Scalarmul3Pt is a right-to-left point multiplication that given the // x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. // nbits must be smaller or equal to len(scalar). func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { var R0, R2, R1 ProjectivePoint aPlus2Over4 := CalcAplus2Over4(cparams) R1 = *P R2 = *PmQ R0 = *Q // Iterate over the bits of the scalar, bottom to top prevBit := uint8(0) for i := uint(0); i < nbits; i++ { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) } cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) return R1 } // Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the // three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C // Output: // - Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var t0, t1, t2, t3, t4 Fp2 var coefEq CurveCoefficientsEquiv K1, K2 := &phi.K1, &phi.K2 sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 sqr(&t0, K1) // t0 = K1^2 add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 sqr(&t1, K2) // t1 = K2^2 add(&t2, &t0, &t1) // t2 = t0 + t1 add(&t3, K1, K2) // t3 = K1 + K2 sqr(&t3, &t3) // t3 = t3^2 sub(&t3, &t3, &t2) // t3 = t3 - t2 add(&t2, &t1, &t3) // t2 = t1 + t3 add(&t3, &t3, &t0) // t3 = t3 + t0 add(&t4, &t3, &t0) // t4 = t3 + t0 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t1, &t4) // t4 = t1 + t4 mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 add(&t4, &t1, &t2) // t4 = t1 + t2 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t0, &t4) // t4 = t0 + t4 mul(&t4, &t3, &t4) // t4 = t3 * t4 sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 return coefEq } // Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate // of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). // // The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve // parameters are returned by the GenerateCurve function used to construct phi. func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) { var t0, t1, t2 Fp2 K1, K2 := &phi.K1, &phi.K2 px, pz := &p.X, &p.Z add(&t0, px, pz) // t0 = XQ + ZQ sub(&t1, px, pz) // t1 = XQ - ZQ mul(&t0, K1, &t0) // t2 = K1 * t0 mul(&t1, K2, &t1) // t1 = K2 * t1 add(&t2, &t0, &t1) // t2 = t0 + t1 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t2, &t2) // t2 = t2 ^ 2 sqr(&t0, &t0) // t0 = t0 ^ 2 mul(px, px, &t2) // XQ'= XQ * t2 mul(pz, pz, &t0) // ZQ'= ZQ * t0 } // Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the // four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C // Output: // - Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv xp4, zp4 := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 sub(K2, xp4, zp4) add(K3, xp4, zp4) sqr(K1, zp4) add(K1, K1, K1) sqr(&coefEq.C, K1) add(K1, K1, K1) sqr(&coefEq.A, xp4) add(&coefEq.A, &coefEq.A, &coefEq.A) sqr(&coefEq.A, &coefEq.A) return coefEq } // Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate // of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). // // Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C // Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) { var t0, t1 Fp2 xq, zq := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 add(&t0, xq, zq) sub(&t1, xq, zq) mul(xq, &t0, K2) mul(zq, &t1, K3) mul(&t0, &t0, &t1) mul(&t0, &t0, K1) add(&t1, xq, zq) sub(zq, xq, zq) sqr(&t1, &t1) sqr(zq, zq) add(xq, &t0, &t1) sub(&t0, zq, &t0) mul(xq, xq, &t1) mul(zq, zq, &t0) } // PublicKeyValidation preforms public key/ciphertext validation using the CLN test. // CLN test: Check that P and Q are both of order 3^e3 and they generate the torsion E_A[3^e3] // A countermeasure for remote timing attacks on SIKE; suggested by https://eprint.iacr.org/2022/054.pdf // Any curve E_A (SIKE 434, 503, 751) that passes CLN test is supersingular. // Input: The public key / ciphertext P, Q, PmQ. The projective coordinate A of the curve defined by (P, Q, PmQ) // Outputs: Whether (P,Q,PmQ) follows the CLN test func PublicKeyValidation(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint) error { var PmQX, PmQZ Fp2 FromMontgomery(&PmQX, &PmQ.X) FromMontgomery(&PmQZ, &PmQ.Z) // PmQ is not point T or O if (isZero(&PmQX) == 1) || (isZero(&PmQZ) == 1) { return errors.New("curve: PmQ is invalid") } cparam := CalcCurveParamsEquiv3(cparams) // Compute e_3 = log3(2^(nbits+1)) var e3 uint32 e3_float := float64(int(nbits)+1) / math.Log2(3) e3 = uint32(e3_float) // Verify that P and Q generate E_A[3^e_3] by checking: [3^(e_3-1)]P != [+-3^(e_3-1)]Q var test_P, test_Q ProjectivePoint test_P = *P test_Q = *Q Pow3k(&test_P, &cparam, e3-1) Pow3k(&test_Q, &cparam, e3-1) var PZ, QZ Fp2 FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of full order 3^e_3 if (isZero(&PZ) == 1) || (isZero(&QZ) == 1) { return errors.New("curve: ciphertext/public key are not of full order 3^e3") } // PX/PZ = affine(PX) // QX/QZ = affine(QX) // If PX/PZ = QX/QZ, we have P=+-Q var PXQZ_PZQX_fromMont, PXQZ_PZQX, PXQZ, PZQX Fp2 mul(&PXQZ, &test_P.X, &test_Q.Z) mul(&PZQX, &test_P.Z, &test_Q.X) sub(&PXQZ_PZQX, &PXQZ, &PZQX) FromMontgomery(&PXQZ_PZQX_fromMont, &PXQZ_PZQX) // [3^(e_3-1)]P == [+-3^(e_3-1)]Q if isZero(&PXQZ_PZQX_fromMont) == 1 { return errors.New("curve: ciphertext/public key are not linearly independent") } // Check that Ord(P) = Ord(Q) = 3^(e_3) Pow3k(&test_P, &cparam, 1) Pow3k(&test_Q, &cparam, 1) FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of correct order 3^e_3 if (isZero(&PZ) == 0) || (isZero(&QZ) == 0) { return errors.New("curve: ciphertext/public key are not of correct order 3^e3") } return nil } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/curve_test.go000066400000000000000000000304631454601126700260370ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p434 import ( "bytes" crand "crypto/rand" . "github.com/cloudflare/circl/dh/sidh/internal/common" "io" "math" "math/rand" "testing" "time" ) func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { var t0, t1 Fp2 mul(&t0, &lhs.X, &rhs.Z) mul(&t1, &lhs.Z, &rhs.X) return vartimeEqFp2(&t0, &t1) } func toAffine(point *ProjectivePoint) *Fp2 { var affineX Fp2 inv(&affineX, &point.Z) mul(&affineX, &affineX, &point.X) return &affineX } func Test_jInvariant(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} jbufRes := make([]byte, params.SharedSecretSize) jbufExp := make([]byte, params.SharedSecretSize) var jInv Fp2 Jinvariant(&curve, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufRes, &jInv, params.Bytelen) jInv = expectedJ FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufExp, &jInv, params.Bytelen) if !bytes.Equal(jbufRes[:], jbufExp[:]) { t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) } } func TestProjectivePointVartimeEq(t *testing.T) { var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} xQ := xP // Scale xQ, which results in the same projective point mul(&xQ.X, &xQ.X, &curveA) mul(&xQ.Z, &xQ.Z, &curveA) if !vartimeEqProjFp2(&xP, &xQ) { t.Error("Expected the scaled point to be equal to the original") } } func TestPointMulVersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv4(&curve) var xP ProjectivePoint // x 2 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 1) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP2) { t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) } // x 4 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 2) afxQ = toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP4) { t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) } } func TestPointMul9VersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv3(&curve) var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow3k(&xP, &cparams, 2) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP9) { t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) } } func BenchmarkThreePointLadder(b *testing.B) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} for n := 0; n < b.N; n++ { ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) } } /* ------------------------------------------------------------------------- Generate invalid public key points / ciphertext for test TestKEMInvalidPK -------------------------------------------------------------------------*/ // Left-to-right Montgomery ladder, Algorithm 4 in Costello-Smith // Input: ProjectivePoint P (xP, zP) // Output: x([scalar]P), z([scalar]P) func montgomeryLadder(cparams *ProjectiveCurveParameters, P *ProjectivePoint, scalar []uint8, random uint) ProjectivePoint { var R0, R2, R1 ProjectivePoint coefEq := CalcCurveParamsEquiv4(cparams) // for xDbl aPlus2Over4 := CalcAplus2Over4(cparams) // for xDblAdd R0 = *P // RO <- P R1 = *P Pow2k(&R1, &coefEq, 1) // R1 <- [2]P R2 = *P // R2 = R1-R0 = P prevBit := uint8(0) for i := int(random); i >= 0; i-- { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, swap) R0, R1 = xDbladd(&R0, &R1, &R2, &aPlus2Over4) } cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, prevBit) return R0 } // P = P + T // From paper https://eprint.iacr.org/2017/212.pdf // The map tau_T: P->P+T is (X : Z) -> (Z : X) on Montgomery curves func tauT(P *ProjectivePoint) { P.X, P.Z = P.Z, P.X // magic! } // Construct Invalid public key tuple (P,Q) such that P and Q are linearly dependent // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKNoneLinear(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1) * 8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Make sure Q is of full order 3^e_3, var test_Q ProjectivePoint test_Q = Q var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1) / math.Log2(3) e3 = uint32(e3_float) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&test_Q, &cparam_q, e3-1) var test_QZ Fp2 FromMontgomery(&test_QZ, &test_Q.Z) // Q are not of full order 3^e_3 for isZero(&test_QZ) == 1 { rand.Seed(time.Now().UnixNano()) random_index = rand.Intn(int(params.B.SecretByteLen-1) * 8) Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) test_Q = Q Pow3k(&test_Q, &cparam_q, e3-1) FromMontgomery(&test_QZ, &test_Q.Z) } // invQz = 1/Q.Z var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect linearly dependent ciphertext to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that Q = [k]P + T, where k is random and T is the point of order 2. // Simulate HB and section 3.1.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKT(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1) * 8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Q = [k]P + T tauT(&Q) var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext involve point T to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[2^e2] // Simulate section 3.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKOrder2(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint P = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(params.A.SecretByteLen-1) * 8) random_index_q := rand.Intn(int(params.A.SecretByteLen-1) * 8) P = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index_p)) Q = montgomeryLadder(¶ms.InitCurve, &Q, secret, uint(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext in torsion E[2^e2] to fail, index_p: %v index_q: %v scalar: %v ", random_index_p, random_index_q, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[3^e3] but not of full order 3^e3 // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKFullOrder(t *testing.T) { var P, Q ProjectivePoint P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1) / math.Log2(3) e3 = uint32(e3_float) rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(e3)) random_index_q := rand.Intn(int(e3)) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&P, &cparam_q, uint32(random_index_p)) Pow3k(&Q, &cparam_q, uint32(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext not of full order to fail, index_p: %v index_q: %v ", random_index_p, random_index_q) } } // A trivial test case not covered by paper https://eprint.iacr.org/2022/054.pdf and HB // Countermeasure in https://eprint.iacr.org/2022/054.pdf only cares about P and Q // But if PmQ is point T or O, that can also lead to recovery of the first bit func testInvalidPmQ(t *testing.T) { var zero Fp2 var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: zero, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect PmQ as T to fail\n") } } // Test valid ciphertext // Where P, Q are linearly independent points of correct order 3^e3 in E[3^e3] func testValidPQ(t *testing.T) { var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify != nil { t.Errorf("\nExpect correct ciphertext to not fail\n") } } /* ------------------------------------------------------------------------- Public key / Ciphertext validation against attacks proposed in paper https://eprint.iacr.org/2022/054.pdf and HB -------------------------------------------------------------------------*/ func TestInvalidPK(t *testing.T) { t.Run("InvalidPmQ", testInvalidPmQ) t.Run("InvalidPKNoneLinear", testInvalidPKNoneLinear) t.Run("InvalidPKT", testInvalidPKT) t.Run("InvalidPKOrder2", testInvalidPKOrder2) t.Run("InvalidPKFullOrder", testInvalidPKFullOrder) t.Run("ValidPQ", testValidPQ) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/fp2.go000066400000000000000000000145231454601126700243420ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p434 import ( "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Montgomery multiplication. Input values must be already // in Montgomery domain. func mulP(dest, lhs, rhs *common.Fp) { var ab common.FpX2 mulP434(&ab, lhs, rhs) // = a*b*R*R rdcP434(dest, &ab) // = a*b*R mod p } // Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). // Uses variation of sliding-window algorithm from with window size // of 5 and least to most significant bit sliding (left-to-right) // See HAC 14.85 for general description. // // Allowed to overlap x with dest. // All values in Montgomery domains // Set dest = x^(2^k), for k >= 1, by repeated squarings. func p34(dest, x *common.Fp) { var lookup [16]common.Fp // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) // multiplications. powStrategy := []uint8{3, 10, 7, 5, 6, 5, 3, 8, 4, 7, 5, 6, 4, 5, 9, 6, 3, 11, 5, 5, 2, 8, 4, 7, 7, 8, 5, 6, 4, 8, 5, 2, 10, 6, 5, 4, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1} mulStrategy := []uint8{2, 15, 9, 8, 14, 12, 2, 8, 5, 15, 8, 15, 6, 6, 3, 2, 0, 10, 9, 13, 1, 12, 3, 7, 1, 10, 8, 11, 2, 15, 14, 1, 11, 12, 14, 3, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0} initialMul := uint8(8) // Precompute lookup table of odd multiples of x for window // size k=5. var xx common.Fp mulP(&xx, x, x) lookup[0] = *x for i := 1; i < 16; i++ { mulP(&lookup[i], &lookup[i-1], &xx) } // Now lookup = {x, x^3, x^5, ... } // so that lookup[i] = x^{2*i + 1} // so that lookup[k/2] = x^k, for odd k *dest = lookup[initialMul] for i := uint8(0); i < uint8(len(powStrategy)); i++ { mulP(dest, dest, dest) for j := uint8(1); j < powStrategy[i]; j++ { mulP(dest, dest, dest) } mulP(dest, dest, &lookup[mulStrategy[i]]) } } func add(dest, lhs, rhs *common.Fp2) { addP434(&dest.A, &lhs.A, &rhs.A) addP434(&dest.B, &lhs.B, &rhs.B) } func sub(dest, lhs, rhs *common.Fp2) { subP434(&dest.A, &lhs.A, &rhs.A) subP434(&dest.B, &lhs.B, &rhs.B) } func mul(dest, lhs, rhs *common.Fp2) { var bMinA, cMinD common.Fp var ac, bd common.FpX2 var adPlusBc common.FpX2 var acMinBd common.FpX2 // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). // // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i // // Use Karatsuba's trick: note that // // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d // // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. subP434(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R subP434(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R mulP434(&ac, &lhs.A, &rhs.A) // = a*c*R*R mulP434(&bd, &lhs.B, &rhs.B) // = b*d*R*R mulP434(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R adlP434(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R adlP434(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R rdcP434(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p sulP434(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R rdcP434(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p } // Set dest = 1/x // // Allowed to overlap dest with x. // // Returns dest to allow chaining operations. func inv(dest, x *common.Fp2) { var e1, e2 common.FpX2 var f1, f2 common.Fp // We want to compute // // 1 1 (a - bi) (a - bi) // -------- = -------- -------- = ----------- // (a + bi) (a + bi) (a - bi) (a^2 + b^2) // // Letting c = 1/(a^2 + b^2), this is // // 1/(a+bi) = a*c - b*ci. mulP434(&e1, &x.A, &x.A) // = a*a*R*R mulP434(&e2, &x.B, &x.B) // = b*b*R*R adlP434(&e1, &e1, &e2) // = (a^2 + b^2)*R*R rdcP434(&f1, &e1) // = (a^2 + b^2)*R mod p // Now f1 = a^2 + b^2 mulP(&f2, &f1, &f1) p34(&f2, &f2) mulP(&f2, &f2, &f2) mulP(&f2, &f2, &f1) mulP434(&e1, &x.A, &f2) rdcP434(&dest.A, &e1) subP434(&f1, &common.Fp{}, &x.B) mulP434(&e1, &f1, &f2) rdcP434(&dest.B, &e1) } func sqr(dest, x *common.Fp2) { var a2, aPlusB, aMinusB common.Fp var a2MinB2, ab2 common.FpX2 a := &x.A b := &x.B // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. addP434(&a2, a, a) // = a*R + a*R = 2*a*R addP434(&aPlusB, a, b) // = a*R + b*R = (a+b)*R subP434(&aMinusB, a, b) // = a*R - b*R = (a-b)*R mulP434(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R mulP434(&ab2, &a2, b) // = 2*a*b*R*R rdcP434(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p rdcP434(&dest.B, &ab2) // = 2*a*b*R mod p } // In case choice == 1, performs following swap in constant time: // // xPx <-> xQx // xPz <-> xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cswapP434(&xPx.A, &xQx.A, choice) cswapP434(&xPx.B, &xQx.B, choice) cswapP434(&xPz.A, &xQz.A, choice) cswapP434(&xPz.B, &xQz.B, choice) } // In case choice == 1, performs following moves in constant time: // // xPx <- xQx // xPz <- xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cmov(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cmovP434(&xPx.A, &xQx.A, choice) cmovP434(&xPx.B, &xQx.B, choice) cmovP434(&xPz.A, &xQz.A, choice) cmovP434(&xPz.B, &xQz.B, choice) } func isZero(x *common.Fp2) uint8 { r64 := uint64(0) for i := 0; i < FpWords; i++ { r64 |= x.A[i] | x.B[i] } r := uint8(0) for i := uint64(0); i < 64; i++ { r |= uint8((r64 >> i) & 0x1) } return 1 - r } // Converts in.A and in.B to Montgomery domain and stores // in 'out' // out.A = in.A * R mod p // out.B = in.B * R mod p // Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B func ToMontgomery(out, in *common.Fp2) { var aRR common.FpX2 // a*R*R mulP434(&aRR, &in.A, &P434R2) // a*R mod p rdcP434(&out.A, &aRR) mulP434(&aRR, &in.B, &P434R2) rdcP434(&out.B, &aRR) } // Converts in.A and in.B from Montgomery domain and stores // in 'out' // out.A = in.A mod p // out.B = in.B mod p // // After returning from the call 'in' is not modified. func FromMontgomery(out, in *common.Fp2) { var aR common.FpX2 // convert from montgomery domain copy(aR[:], in.A[:]) rdcP434(&out.A, &aR) // = a mod p in [0, 2p) modP434(&out.A) // = a mod p in [0, p) for i := range aR { aR[i] = 0 } copy(aR[:], in.B[:]) rdcP434(&out.B, &aR) modP434(&out.B) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/fp2_test.go000066400000000000000000000125601454601126700254000ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p434 import ( "math/rand" "reflect" "testing" "testing/quick" "github.com/cloudflare/circl/dh/sidh/internal/common" ) type testParams struct { Point common.ProjectivePoint Cparam common.ProjectiveCurveParameters ExtElem common.Fp2 } // Returns true if lhs = rhs. Takes variable time. func vartimeEqFp2(lhs, rhs *common.Fp2) bool { a := *lhs b := *rhs modP434(&a.A) modP434(&a.B) modP434(&b.A) modP434(&b.B) eq := true for i := 0; i < FpWords && eq; i++ { eq = eq && (a.A[i] == b.A[i]) eq = eq && (a.B[i] == b.B[i]) } return eq } func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { // Generation strategy: low limbs taken from [0,2^64); high limb // taken from smaller range // // Size hint is ignored since all elements are fixed size. // // Field elements taken in range [0,2p). Emulate this by capping // the high limb by the top digit of 2*p-1: // // sage: (2*p-1).digits(2^64)[-1] // // This still allows generating values >= 2p, but hopefully that // excess is OK (and if it's not, we'll find out, because it's for // testing...) highLimb := rand.Uint64() % P434x2[FpWords-1] fpElementGen := func() (fp common.Fp) { for i := 0; i < (FpWords - 1); i++ { fp[i] = rand.Uint64() } fp[FpWords-1] = highLimb return fp } return common.Fp2{A: fpElementGen(), B: fpElementGen()} } func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { return reflect.ValueOf( testParams{ common.ProjectivePoint{ X: c.generateFp2(rand), Z: c.generateFp2(rand), }, common.ProjectiveCurveParameters{ A: c.generateFp2(rand), C: c.generateFp2(rand), }, c.generateFp2(rand), }) } func TestOne(t *testing.T) { var tmp common.Fp2 mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { t.Error("Not equal 1") } } func TestFp2ToBytesRoundTrip(t *testing.T) { roundTrips := func(x testParams) bool { xBytes := make([]byte, 2*params.Bytelen) var xPrime common.Fp2 common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) return vartimeEqFp2(&xPrime, &x.ExtElem) } if err := quick.Check(roundTrips, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulDistributesOverAdd(t *testing.T) { mulDistributesOverAdd := func(x, y, z testParams) bool { // Compute t1 = (x+y)*z t1 := new(common.Fp2) add(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = x*z + y*z t2 := new(common.Fp2) t3 := new(common.Fp2) mul(t2, &x.ExtElem, &z.ExtElem) mul(t3, &y.ExtElem, &z.ExtElem) add(t2, t2, t3) return vartimeEqFp2(t1, t2) } if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulIsAssociative(t *testing.T) { isAssociative := func(x, y, z testParams) bool { // Compute t1 = (x*y)*z t1 := new(common.Fp2) mul(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = (y*z)*x t2 := new(common.Fp2) mul(t2, &y.ExtElem, &z.ExtElem) mul(t2, t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(isAssociative, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2SquareMatchesMul(t *testing.T) { sqrMatchesMul := func(x testParams) bool { // Compute t1 = (x*x) t1 := new(common.Fp2) mul(t1, &x.ExtElem, &x.ExtElem) // Compute t2 = x^2 t2 := new(common.Fp2) sqr(t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2Inv(t *testing.T) { inverseIsCorrect := func(x testParams) bool { z := new(common.Fp2) inv(z, &x.ExtElem) // Now z = (1/x), so (z * x) * x == x mul(z, z, &x.ExtElem) mul(z, z, &x.ExtElem) return vartimeEqFp2(z, &x.ExtElem) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 11)} if err := quick.Check(inverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func TestFp2Batch3Inv(t *testing.T) { batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { var x1Inv, x2Inv, x3Inv common.Fp2 inv(&x1Inv, &x1.ExtElem) inv(&x2Inv, &x2.ExtElem) inv(&x3Inv, &x3.ExtElem) var y1, y2, y3 common.Fp2 Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 8)} if err := quick.Check(batchInverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func BenchmarkFp2Mul(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { mul(w, z, z) } } func BenchmarkFp2Inv(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { inv(w, z) } } func BenchmarkFp2Square(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sqr(w, z) } } func BenchmarkFp2Add(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { add(w, z, z) } } func BenchmarkFp2Sub(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sub(w, z, z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/params.go000066400000000000000000000152251454601126700251360ustar00rootroot00000000000000package p434 //go:generate go run ../templates/gen.go P434 import ( "github.com/cloudflare/circl/dh/sidh/internal/common" "golang.org/x/sys/cpu" ) const ( // Number of uint64 limbs used to store field element FpWords = 7 ) var ( // HasADXandBMI2 signals support for ADX and BMI2 HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX // P434 is a prime used by field Fp434 P434 = common.Fp{ 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFDC1767AE2FFFFFF, 0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x2341F27177344, } // P434x2 = 2*p434 - 1 P434x2 = common.Fp{ 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFB82ECF5C5FFFFFF, 0xF78CB8F062B15D47, 0xD9F8BFAD038A40AC, 0x4683E4E2EE688, } // P434p1 = p434 + 1 P434p1 = common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xFDC1767AE3000000, 0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344, } // P434R2 = (2^448)^2 mod p P434R2 = common.Fp{ 0x28E55B65DCD69B30, 0xACEC7367768798C2, 0xAB27973F8311688D, 0x175CC6AF8D6C7C0B, 0xABCD92BF2DDE347E, 0x69E16A61C7686D9A, 0x000025A89BCDD12A, } // 1/2 * R mod p half = common.Fp2{ A: common.Fp{ 0x0000000000003A16, 0x0000000000000000, 0x0000000000000000, 0x5C87FA027E000000, 0x6C00D27DAACFD66A, 0x74992A2A2FBBA086, 0x0000767753DE976D, }, } // 1*R mod p one = common.Fp2{ A: common.Fp{ 0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000, 0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0000ECEEA7BD2EDA, }, } // 6*R mod p six = common.Fp2{ A: common.Fp{ 0x000000000002B90A, 0x0000000000000000, 0x0000000000000000, 0x5ADCCB2822000000, 0x187D24F39F0CAFB4, 0x9D353A4D394145A0, 0x00012559A0403298, }, } P434p1Zeros = 3 params = common.SidhParams{ ID: common.Fp434, // SIDH public key byte size. PublicKeySize: 330, // SIDH shared secret byte size. SharedSecretSize: 110, InitCurve: common.ProjectiveCurveParameters{ A: six, C: one, }, A: common.DomainParams{ // The x-coordinate of PA AffineP: common.Fp2{ A: common.Fp{ 0x05ADF455C5C345BF, 0x91935C5CC767AC2B, 0xAFE4E879951F0257, 0x70E792DC89FA27B1, 0xF797F526BB48C8CD, 0x2181DB6131AF621F, 0x00000A1C08B1ECC4, }, B: common.Fp{ 0x74840EB87CDA7788, 0x2971AA0ECF9F9D0B, 0xCB5732BDF41715D5, 0x8CD8E51F7AACFFAA, 0xA7F424730D7E419F, 0xD671EB919A179E8C, 0x0000FFA26C5A924A, }, }, // The x-coordinate of QA AffineQ: common.Fp2{ A: common.Fp{ 0xFEC6E64588B7273B, 0xD2A626D74CBBF1C6, 0xF8F58F07A78098C7, 0xE23941F470841B03, 0x1B63EDA2045538DD, 0x735CFEB0FFD49215, 0x0001C4CB77542876, }, B: common.Fp{ 0xADB0F733C17FFDD6, 0x6AFFBD037DA0A050, 0x680EC43DB144E02F, 0x1E2E5D5FF524E374, 0xE2DDA115260E2995, 0xA6E4B552E2EDE508, 0x00018ECCDDF4B53E, }, }, // The x-coordinate of RA = PA-QA AffineR: common.Fp2{ A: common.Fp{ 0x01BA4DB518CD6C7D, 0x2CB0251FE3CC0611, 0x259B0C6949A9121B, 0x60E17AC16D2F82AD, 0x3AA41F1CE175D92D, 0x413FBE6A9B9BC4F3, 0x00022A81D8D55643, }, B: common.Fp{ 0xB8ADBC70FC82E54A, 0xEF9CDDB0D5FADDED, 0x5820C734C80096A0, 0x7799994BAA96E0E4, 0x044961599E379AF8, 0xDB2B94FBF09F27E2, 0x0000B87FC716C0C6, }, }, // Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1 SecretBitLen: 216, // SecretBitLen in bytes. SecretByteLen: 28, // 2-torsion group computation strategy IsogenyStrategy: []uint32{ 0x30, 0x1C, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0D, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x15, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, }, }, B: common.DomainParams{ // The x-coordinate of PB AffineP: common.Fp2{ A: common.Fp{ 0x6E5497556EDD48A3, 0x2A61B501546F1C05, 0xEB919446D049887D, 0x5864A4A69D450C4F, 0xB883F276A6490D2B, 0x22CC287022D5F5B9, 0x0001BED4772E551F, }, B: common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, }, }, // The x-coordinate of QB AffineQ: common.Fp2{ A: common.Fp{ 0xFAE2A3F93D8B6B8E, 0x494871F51700FE1C, 0xEF1A94228413C27C, 0x498FF4A4AF60BD62, 0xB00AD2A708267E8A, 0xF4328294E017837F, 0x000034080181D8AE, }, B: common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, }, }, // The x-coordinate of RB = PB - QB AffineR: common.Fp2{ A: common.Fp{ 0x283B34FAFEFDC8E4, 0x9208F44977C3E647, 0x7DEAE962816F4E9A, 0x68A2BA8AA262EC9D, 0x8176F112EA43F45B, 0x02106D022634F504, 0x00007E8A50F02E37, }, B: common.Fp{ 0xB378B7C1DA22CCB1, 0x6D089C99AD1D9230, 0xEBE15711813E2369, 0x2B35A68239D48A53, 0x445F6FD138407C93, 0xBEF93B29A3F6B54B, 0x000173FA910377D3, }, }, // Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1. SecretBitLen: 217, // SecretBitLen in bytes. SecretByteLen: 28, // 3-torsion group computation strategy IsogenyStrategy: []uint32{ 0x42, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x20, 0x10, 0x08, 0x04, 0x03, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, }, }, OneFp2: one, HalfFp2: half, MsgLen: 16, // SIKEp434 provides 192 bit of classical security ([SIKE], 5.1) KemSize: 16, // ceil(434+7/8) Bytelen: 55, CiphertextSize: 16 + 330, } ) func init() { common.Register(common.Fp434, ¶ms) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p434/params_test.go000066400000000000000000000074231454601126700261760ustar00rootroot00000000000000package p434 // Contains values used by tests import ( "testing/quick" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Values computed using Sage var ( expectedJ = Fp2{ A: Fp{0x38ECC0A0F53BACB4, 0xF987759E90A6C0DD, 0xC3007B353AE699F6, 0xB2B7E62A4F182414, 0xA65A854B34034F1B, 0xC71EAD20BE427422, 0xFC94F0D8DD51}, B: Fp{0xFC3B47615764A089, 0x9D32DF1BA8CF22E5, 0x7B895EF92F44C690, 0xE83667F85BBFA475, 0xD44627DCF539CA71, 0x9619A0E7D6657401, 0x4BC5BF1D9B01}, } curveA = Fp2{ A: Fp{0x13A5A42C36E5E170, 0xC801DC4104E2C1DC, 0xB102AE39A7E24F31, 0x2FB616EA2E824C97, 0xB97073B55448AA67, 0x607266F7204D90DA, 0x1E98FE9739F27}, B: Fp{0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000, 0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0ECEEA7BD2EDA}, } curveC = Fp2{ A: Fp{0x8CBBA3505E5EDAB2, 0xB1DE7B91FBB77718, 0x6957392BFDC9BEB0, 0xC258E527E05FDDDE, 0x8C5FC7ADF5E50AE9, 0x1B2149FBEC2F4D18, 0x19FC2A5C79942}, B: Fp{0x000000000000E858, 0x0000000000000000, 0x0000000000000000, 0x721FE809F8000000, 0xB00349F6AB3F59A9, 0xD264A8A8BEEE8219, 0x1D9DD4F7A5DB5}, } affineXP = Fp2{ A: Fp{0x775C29CA29E5FC3F, 0xCAB15BD1A1AB2754, 0x2C7F5B5DC58096EB, 0x2EE7B0B5A789355A, 0xBBD7BC749FF4D74E, 0x1373A265C9A9D58B, 0x5C183CE99B13}, B: Fp{0x38CDA704EB4D517C, 0x2F8BA33C91C147D4, 0x4D17E97F04A8D431, 0x5DB8F238AE1B099F, 0x44DC758CE879824C, 0x7E95F1151F6DFA3C, 0xB59F64352B87}, } affineXP2 = Fp2{ A: Fp{0x2A5C658FD540804D, 0xA27CDB81FA7C6A5C, 0x6C36B6EB38B1B562, 0xC08642D636AF9A51, 0x36B2323A1279F346, 0x530BF3E8726D8B71, 0x61E38F638919}, B: Fp{0x5D835C52A68FC93D, 0x9E8FAF973A68306C, 0xB3C28FE9D155F61C, 0xCCE6FA22BC1A1FBF, 0xEAB44D8952802BA5, 0xEAAC0F259AAC3A8F, 0x959B242CE01A}, } affineXP4 = Fp2{ A: Fp{0xF824931762C6DC4A, 0xA9B0FD30136F4B50, 0xAF041BBAB14DC6B1, 0x0AD52F55527A9BA2, 0x282B236D61F08C59, 0x5D3D7EC0C5EB9DCB, 0x10BBDDEA44BF7}, B: Fp{0x77D92493AF97245B, 0xD717FEC838D464C6, 0xCAACD67DB3BF965D, 0x82D59FB89CDC0711, 0xF13CAE433F39CDE1, 0x9B55DFB11A585FFA, 0x0DC8BA1C054D3}, } affineXP9 = Fp2{ A: Fp{0x1F6F0785353A02C0, 0xCCB1B8524A63E37F, 0xB283C636B1FDD74C, 0xB76DBFF592DE6FF5, 0x15750EE706F18226, 0x50791362F26E459C, 0x1EA2A9074423}, B: Fp{0x945C6909DA5039A3, 0x349CFD24FD84FDAF, 0x2FD2F391F2E26E75, 0xEF73E8A634EBDC76, 0x59DDA2622AC22A6C, 0xE0370B80E15F61F4, 0xB302956A0276}, } // Inputs for testing 3-point-ladder threePointLadderInputs = []ProjectivePoint{ // x(P) { X: Fp2{ A: Fp{0x43941FA9244C059E, 0xD1F337D076941189, 0x6B6A8B3A8763C96A, 0x6DF569708D6C9482, 0x487EE5707A52F4AA, 0xDE396F6E2559689E, 0xE5EE3895A8991469, 0x2B0946695790A8}, B: Fp{0xAB552C0FDAED092E, 0x7DF895E43E7DCB1C, 0x35C700E761920C4B, 0xCC5807DD70DC117A, 0x0884039A5A8DB18A, 0xD04620B3D0738052, 0xA200835605138F10, 0x3FF2E59B2FDC6A}, }, Z: params.OneFp2, }, // x(Q) { X: Fp2{ A: Fp{0x77015826982BA1FD, 0x44024489673471E4, 0x1CAA2A5F4D5DA63B, 0xA183C07E50738C01, 0x8B97782D4E1A0DE6, 0x9B819522FBC38280, 0x0BDA46A937FB7B8A, 0x3B3614305914DF}, B: Fp{0xBF0366E97B3168D9, 0xAA522AC3879CEF0F, 0x0AF5EC975BD035C8, 0x1F26FEE7BBAC165C, 0xA0EE6A637724A6AB, 0xFB52101E36BA3A38, 0xD29CF5E376E17376, 0x1374A50DF57071}, }, Z: params.OneFp2, }, // x(P-Q) { X: Fp2{ A: Fp{0xD99279BBD41EA559, 0x35CF18E72F578214, 0x90473B1DC77F73E8, 0xBFFEA930B25D7F66, 0xFD558EA177B900B2, 0x7CFAD273A782A23E, 0x6B1F610822E0F611, 0x26D2D2EF9619B5}, B: Fp{0x534F83651CBCC75D, 0x591FB4757AED5D08, 0x0B04353D40BED542, 0x829A94703AAC9139, 0x0F9C2E6D7663EB5B, 0x5D2D0F90C283F746, 0x34C872AA12A7676E, 0x0ECDB605FBFA16}, }, Z: params.OneFp2, }, } scalar3Pt = [...]uint8{0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f, 0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f} ) var quickCheckConfig = &quick.Config{ MaxCount: (1 << 15), } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/000077500000000000000000000000001454601126700233145ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/arith_amd64.s000066400000000000000000001173551454601126700256160ustar00rootroot00000000000000// +build amd64,!noasm #include "textflag.h" // p503 #define P503_0 $0xFFFFFFFFFFFFFFFF #define P503_1 $0xFFFFFFFFFFFFFFFF #define P503_2 $0xFFFFFFFFFFFFFFFF #define P503_3 $0xABFFFFFFFFFFFFFF #define P503_4 $0x13085BDA2211E7A0 #define P503_5 $0x1B9BF6C87B7E7DAF #define P503_6 $0x6045C6BDDA77A4D0 #define P503_7 $0x004066F541811E1E // p503+1 #define P503P1_3 $0xAC00000000000000 #define P503P1_4 $0x13085BDA2211E7A0 #define P503P1_5 $0x1B9BF6C87B7E7DAF #define P503P1_6 $0x6045C6BDDA77A4D0 #define P503P1_7 $0x004066F541811E1E // p503x2 #define P503X2_0 $0xFFFFFFFFFFFFFFFE #define P503X2_1 $0xFFFFFFFFFFFFFFFF #define P503X2_2 $0xFFFFFFFFFFFFFFFF #define P503X2_3 $0x57FFFFFFFFFFFFFF #define P503X2_4 $0x2610B7B44423CF41 #define P503X2_5 $0x3737ED90F6FCFB5E #define P503X2_6 $0xC08B8D7BB4EF49A0 #define P503X2_7 $0x0080CDEA83023C3C #define REG_P1 DI #define REG_P2 SI #define REG_P3 DX // Performs schoolbook multiplication of 2 256-bit numbers. This optimized version // uses MULX instruction. Macro smashes value in DX. // Input: I0 and I1. // Output: O // All the other arguments are registers, used for storing temporary values #define MULS256_MULX(O, I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ MOVQ I0, DX \ MULXQ I1, T1, T0 \ // T0:T1 = A0*B0 MOVQ T1, O \ // O[0] MULXQ 8+I1, T2, T1 \ // T1:T2 = U0*V1 ADDQ T2, T0 \ MULXQ 16+I1, T3, T2 \ // T2:T3 = U0*V2 ADCQ T3, T1 \ MULXQ 24+I1, T4, T3 \ // T3:T4 = U0*V3 ADCQ T4, T2 \ \ // Column U1 MOVQ 8+I0, DX \ ADCQ $0, T3 \ MULXQ 0+I1, T4, T5 \ // T5:T4 = U1*V0 MULXQ 8+I1, T7, T6 \ // T6:T7 = U1*V1 ADDQ T7, T5 \ MULXQ 16+I1, T8, T7 \ // T7:T8 = U1*V2 ADCQ T8, T6 \ MULXQ 24+I1, T9, T8 \ // T8:T9 = U1*V3 ADCQ T9, T7 \ ADCQ $0, T8 \ ADDQ T0, T4 \ MOVQ T4, 8+O \ // O[1] ADCQ T1, T5 \ ADCQ T2, T6 \ ADCQ T3, T7 \ \ // Column U2 MOVQ 16+I0, DX \ ADCQ $0, T8 \ MULXQ 0+I1, T0, T1 \ // T1:T0 = U2*V0 MULXQ 8+I1, T3, T2 \ // T2:T3 = U2*V1 ADDQ T3, T1 \ MULXQ 16+I1, T4, T3 \ // T3:T4 = U2*V2 ADCQ T4, T2 \ MULXQ 24+I1, T9, T4 \ // T4:T9 = U2*V3 ADCQ T9, T3 \ \ // Column U3 MOVQ 24+I0, DX \ ADCQ $0, T4 \ ADDQ T5, T0 \ MOVQ T0, 16+O \ // O[2] ADCQ T6, T1 \ ADCQ T7, T2 \ ADCQ T8, T3 \ ADCQ $0, T4 \ MULXQ 0+I1, T0, T5 \ // T5:T0 = U3*V0 MULXQ 8+I1, T7, T6 \ // T6:T7 = U3*V1 ADDQ T7, T5 \ MULXQ 16+I1, T8, T7 \ // T7:T8 = U3*V2 ADCQ T8, T6 \ MULXQ 24+I1, T9, T8 \ // T8:T9 = U3*V3 ADCQ T9, T7 \ ADCQ $0, T8 \ \ // Add values in remaining columns ADDQ T0, T1 \ MOVQ T1, 24+O \ // O[3] ADCQ T5, T2 \ MOVQ T2, 32+O \ // O[4] ADCQ T6, T3 \ MOVQ T3, 40+O \ // O[5] ADCQ T7, T4 \ MOVQ T4, 48+O \ // O[6] ADCQ $0, T8 \ // O[7] MOVQ T8, 56+O // Performs schoolbook multiplication of 2 256-bit numbers. This optimized version // uses ADOX, ADCX and MULX instructions. Macro smashes values in AX and DX. // Input: I0 and I1. // Output: O // All the other arguments registers are used for storing temporary values #define MULS256_MULX_ADCX_ADOX(O, I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ \ // U0[0] MOVQ 0+I0, DX \ // MULX requires multiplayer in DX \ // T0:T1 = I1*DX MULXQ I1, T1, T0 \ // T0:T1 = U0*V0 (low:high) MOVQ T1, O \ // O0[0] MULXQ 8+I1, T2, T1 \ // T2:T1 = U0*V1 XORQ AX, AX \ ADOXQ T2, T0 \ MULXQ 16+I1, T3, T2 \ // T2:T3 = U0*V2 ADOXQ T3, T1 \ MULXQ 24+I1, T4, T3 \ // T3:T4 = U0*V3 ADOXQ T4, T2 \ \ // Column U1 MOVQ 8+I0, DX \ MULXQ I1, T4, T5 \ // T5:T4 = U1*V0 ADOXQ AX, T3 \ XORQ AX, AX \ MULXQ 8+I1, T7, T6 \ // T6:T7 = U1*V1 ADOXQ T0, T4 \ MOVQ T4, 8+O \ // O[1] ADCXQ T7, T5 \ MULXQ 16+I1, T8, T7 \ // T7:T8 = U1*V2 ADCXQ T8, T6 \ ADOXQ T1, T5 \ MULXQ 24+I1, T9, T8 \ // T8:T9 = U1*V3 ADCXQ T9, T7 \ ADCXQ AX, T8 \ ADOXQ T2, T6 \ \ // Column U2 MOVQ 16+I0, DX \ MULXQ I1, T0, T1 \ // T1:T0 = U2*V0 ADOXQ T3, T7 \ ADOXQ AX, T8 \ XORQ AX, AX \ MULXQ 8+I1, T3, T2 \ // T2:T3 = U2*V1 ADOXQ T5, T0 \ MOVQ T0, 16+O \ // O[2] ADCXQ T3, T1 \ MULXQ 16+I1, T4, T3 \ // T3:T4 = U2*V2 ADCXQ T4, T2 \ ADOXQ T6, T1 \ MULXQ 24+I1, T9, T4 \ // T9:T4 = U2*V3 ADCXQ T9, T3 \ MOVQ 24+I0, DX \ ADCXQ AX, T4 \ \ ADOXQ T7, T2 \ ADOXQ T8, T3 \ ADOXQ AX, T4 \ \ // Column U3 MULXQ I1, T0, T5 \ // T5:T0 = U3*B0 XORQ AX, AX \ MULXQ 8+I1, T7, T6 \ // T6:T7 = U3*B1 ADCXQ T7, T5 \ ADOXQ T0, T1 \ MULXQ 16+I1, T8, T7 \ // T7:T8 = U3*V2 ADCXQ T8, T6 \ ADOXQ T5, T2 \ MULXQ 24+I1, T9, T8 \ // T8:T9 = U3*V3 ADCXQ T9, T7 \ ADCXQ AX, T8 \ \ ADOXQ T6, T3 \ ADOXQ T7, T4 \ ADOXQ AX, T8 \ MOVQ T1, 24+O \ // O[3] MOVQ T2, 32+O \ // O[4] MOVQ T3, 40+O \ // O[5] MOVQ T4, 48+O \ // O[6] and O[7] below MOVQ T8, 56+O // Template of a macro that performs schoolbook multiplication of 128-bit with 320-bit // number. It uses MULX instruction This template must be customized with functions // performing ADD (add1, add2) and ADD-with-carry (adc1, adc2). addX/adcX may or may // not be instructions that use two independent carry chains. // Input: // * I0 128-bit number // * I1 320-bit number // * add1, add2: instruction performing integer addition and starting carry chain // * adc1, adc2: instruction performing integer addition with carry // Output: T[0-6] registers #define MULS_128x320(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, add1, add2, adc1, adc2) \ \ // Column 0 MOVQ I0, DX \ MOVQ I1+24(SB), AX \ MULXQ AX, T0, T1 \ MOVQ I1+32(SB), AX \ MULXQ AX, T4, T2 \ MOVQ I1+40(SB), AX \ MULXQ AX, T5, T3 \ XORQ AX, AX \ add1 T4, T1 \ adc1 T5, T2 \ MOVQ I1+48(SB), AX \ MULXQ AX, T7, T4 \ adc1 T7, T3 \ MOVQ I1+56(SB), AX \ MULXQ AX, T6, T5 \ adc1 T6, T4 \ MOVL $0, AX \ adc1 AX, T5 \ \ // Column 1 MOVQ 8+I0, DX \ MOVQ I1+24(SB), AX \ MULXQ AX, T6, T7 \ add2 T6, T1 \ adc2 T7, T2 \ MOVQ I1+32(SB), AX \ MULXQ AX, T8, T6 \ adc2 T6, T3 \ MOVQ I1+40(SB), AX \ MULXQ AX, T7, T9 \ adc2 T9, T4 \ MOVQ I1+48(SB), AX \ MULXQ AX, T9, T6 \ adc2 T6, T5 \ MOVQ I1+56(SB), AX \ MULXQ AX, DX, T6 \ MOVL $0, AX \ adc2 AX, T6 \ \ // Output XORQ AX, AX \ add1 T8, T2 \ adc1 T7, T3 \ adc1 T9, T4 \ adc1 DX, T5 \ adc1 AX, T6 // Multiplies 128-bit with 320-bit integer. Optimized with MULX instruction. #define MULS_128x320_MULX(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ MULS_128x320(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, ADDQ, ADDQ, ADCQ, ADCQ) // Multiplies 128-bit with 320-bit integer. Optimized with MULX, ADOX and ADCX instructions #define MULS_128x320_MULX_ADCX_ADOX(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ MULS_128x320(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, ADOXQ, ADCXQ, ADOXQ, ADCXQ) // Template of a macro performing multiplication of two 512-bit numbers. It uses one // level of Karatsuba and one level of schoolbook multiplication. Template must be // customized with macro performing schoolbook multiplication. // Input: // * I0, I1 - two 512-bit numbers // * MULS - either MULS256_MULX or MULS256_MULX_ADCX_ADOX // Output: OUT - 1024-bit long #define MUL(OUT, I0, I1, MULS) \ \ // R[8-11]: U1+U0 XORQ AX, AX \ MOVQ ( 0)(I0), R8 \ MOVQ ( 8)(I0), R9 \ MOVQ (16)(I0), R10 \ MOVQ (24)(I0), R11 \ ADDQ (32)(I0), R8 \ ADCQ (40)(I0), R9 \ ADCQ (48)(I0), R10 \ ADCQ (56)(I0), R11 \ SBBQ $0, AX \ // store mask MOVQ R8, ( 0)(SP) \ MOVQ R9, ( 8)(SP) \ MOVQ R10, (16)(SP) \ MOVQ R11, (24)(SP) \ \ \ // R[12-15]: V1+V0 XORQ BX, BX \ MOVQ ( 0)(I1), R12 \ MOVQ ( 8)(I1), R13 \ MOVQ (16)(I1), R14 \ MOVQ (24)(I1), R15 \ ADDQ (32)(I1), R12 \ ADCQ (40)(I1), R13 \ ADCQ (48)(I1), R14 \ ADCQ (56)(I1), R15 \ SBBQ $0, BX \ // store mask MOVQ R12, (32)(SP) \ MOVQ R13, (40)(SP) \ MOVQ R14, (48)(SP) \ MOVQ R15, (56)(SP) \ \ // Prepare mask for U0+U1 (U1+U0 mod 256^4 if U1+U0 sets carry flag, otherwise 0) ANDQ AX, R12 \ ANDQ AX, R13 \ ANDQ AX, R14 \ ANDQ AX, R15 \ \ // Prepare mask for V0+V1 (V1+V0 mod 256^4 if U1+U0 sets carry flag, otherwise 0) ANDQ BX, R8 \ ANDQ BX, R9 \ ANDQ BX, R10 \ ANDQ BX, R11 \ \ // res = masked(U0+U1) + masked(V0 + V1) ADDQ R12, R8 \ ADCQ R13, R9 \ ADCQ R14, R10 \ ADCQ R15, R11 \ \ // SP[64-96] <- res MOVQ R8, (64)(SP) \ MOVQ R9, (72)(SP) \ MOVQ R10, (80)(SP) \ MOVQ R11, (88)(SP) \ \ // BP will be used for schoolbook multiplication below MOVQ BP, 96(SP) \ // push: BP is Callee-save. \ // (U1+U0)*(V1+V0) MULS((64)(OUT), 0(SP), 32(SP), R8, R9, R10, R11, R12, R13, R14, R15, BX, BP) \ \ // U0 x V0 MULS(0(OUT), 0(I0), 0(I1), R8, R9, R10, R11, R12, R13, R14, R15, BX, BP) \ \ // U1 x V1 MULS(0(SP), 32(I0), 32(I1), R8, R9, R10, R11, R12, R13, R14, R15, BX, BP) \ \ // Recover BP MOVQ 96(SP), BP \ // pop: BP is Callee-save. \ // Final part of schoolbook multiplication; R[8-11] = (U0+U1) x (V0+V1) MOVQ (64)(SP), R8 \ MOVQ (72)(SP), R9 \ MOVQ (80)(SP), R10 \ MOVQ (88)(SP), R11 \ MOVQ (96)(OUT), AX \ ADDQ AX, R8 \ MOVQ (104)(OUT), AX \ ADCQ AX, R9 \ MOVQ (112)(OUT), AX \ ADCQ AX, R10 \ MOVQ (120)(OUT), AX \ ADCQ AX, R11 \ \ // R[12-15, 8-11] = (U0+U1) x (V0+V1) - U0xV0 MOVQ (64)(OUT), R12 \ MOVQ (72)(OUT), R13 \ MOVQ (80)(OUT), R14 \ MOVQ (88)(OUT), R15 \ SUBQ ( 0)(OUT), R12 \ SBBQ ( 8)(OUT), R13 \ SBBQ (16)(OUT), R14 \ SBBQ (24)(OUT), R15 \ SBBQ (32)(OUT), R8 \ SBBQ (40)(OUT), R9 \ SBBQ (48)(OUT), R10 \ SBBQ (56)(OUT), R11 \ \ // r8-r15 <- (U0+U1) x (V0+V1) - U0xV0 - U1xV1 SUBQ ( 0)(SP), R12 \ SBBQ ( 8)(SP), R13 \ SBBQ (16)(SP), R14 \ SBBQ (24)(SP), R15 \ SBBQ (32)(SP), R8 \ SBBQ (40)(SP), R9 \ SBBQ (48)(SP), R10 \ SBBQ (56)(SP), R11 \ \ ; ADDQ (32)(OUT), R12; MOVQ R12, ( 32)(OUT) \ ; ADCQ (40)(OUT), R13; MOVQ R13, ( 40)(OUT) \ ; ADCQ (48)(OUT), R14; MOVQ R14, ( 48)(OUT) \ ; ADCQ (56)(OUT), R15; MOVQ R15, ( 56)(OUT) \ MOVQ ( 0)(SP), AX; ADCQ AX, R8; MOVQ R8, ( 64)(OUT) \ MOVQ ( 8)(SP), AX; ADCQ AX, R9; MOVQ R9, ( 72)(OUT) \ MOVQ (16)(SP), AX; ADCQ AX, R10; MOVQ R10, ( 80)(OUT) \ MOVQ (24)(SP), AX; ADCQ AX, R11; MOVQ R11, ( 88)(OUT) \ MOVQ (32)(SP), R12; ADCQ $0, R12; MOVQ R12, ( 96)(OUT) \ MOVQ (40)(SP), R13; ADCQ $0, R13; MOVQ R13, (104)(OUT) \ MOVQ (48)(SP), R14; ADCQ $0, R14; MOVQ R14, (112)(OUT) \ MOVQ (56)(SP), R15; ADCQ $0, R15; MOVQ R15, (120)(OUT) // Template for calculating the Montgomery reduction algorithm described in // section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. Template must be // customized with schoolbook multiplication for 128 x 320-bit number. // This macro reuses memory of IN value and *changes* it. Smashes registers // R[8-15], BX, CX // Input: // * IN: 1024-bit number to be reduced // * MULS: either MULS_128x320_MULX or MULS_128x320_MULX_ADCX_ADOX // Output: OUT 512-bit #define REDC(OUT, IN, MULS) \ MULS(0(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, BP) \ XORQ R15, R15 \ ADDQ (24)(IN), R8 \ ADCQ (32)(IN), R9 \ ADCQ (40)(IN), R10 \ ADCQ (48)(IN), R11 \ ADCQ (56)(IN), R12 \ ADCQ (64)(IN), R13 \ ADCQ (72)(IN), R14 \ ADCQ (80)(IN), R15 \ MOVQ R8, (24)(IN) \ MOVQ R9, (32)(IN) \ MOVQ R10, (40)(IN) \ MOVQ R11, (48)(IN) \ MOVQ R12, (56)(IN) \ MOVQ R13, (64)(IN) \ MOVQ R14, (72)(IN) \ MOVQ R15, (80)(IN) \ MOVQ (88)(IN), R8 \ MOVQ (96)(IN), R9 \ MOVQ (104)(IN), R10 \ MOVQ (112)(IN), R11 \ MOVQ (120)(IN), R12 \ ADCQ $0, R8 \ ADCQ $0, R9 \ ADCQ $0, R10 \ ADCQ $0, R11 \ ADCQ $0, R12 \ MOVQ R8, (88)(IN) \ MOVQ R9, (96)(IN) \ MOVQ R10, (104)(IN) \ MOVQ R11, (112)(IN) \ MOVQ R12, (120)(IN) \ \ MULS(16(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, BP) \ XORQ R15, R15 \ ADDQ (40)(IN), R8 \ ADCQ (48)(IN), R9 \ ADCQ (56)(IN), R10 \ ADCQ (64)(IN), R11 \ ADCQ (72)(IN), R12 \ ADCQ (80)(IN), R13 \ ADCQ (88)(IN), R14 \ ADCQ (96)(IN), R15 \ MOVQ R8, (40)(IN) \ MOVQ R9, (48)(IN) \ MOVQ R10, (56)(IN) \ MOVQ R11, (64)(IN) \ MOVQ R12, (72)(IN) \ MOVQ R13, (80)(IN) \ MOVQ R14, (88)(IN) \ MOVQ R15, (96)(IN) \ MOVQ (104)(IN), R8 \ MOVQ (112)(IN), R9 \ MOVQ (120)(IN), R10 \ ADCQ $0, R8 \ ADCQ $0, R9 \ ADCQ $0, R10 \ MOVQ R8, (104)(IN) \ MOVQ R9, (112)(IN) \ MOVQ R10, (120)(IN) \ \ MULS(32(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, BP) \ XORQ R15, R15 \ XORQ BX, BX \ ADDQ ( 56)(IN), R8 \ ADCQ ( 64)(IN), R9 \ ADCQ ( 72)(IN), R10 \ ADCQ ( 80)(IN), R11 \ ADCQ ( 88)(IN), R12 \ ADCQ ( 96)(IN), R13 \ ADCQ (104)(IN), R14 \ ADCQ (112)(IN), R15 \ ADCQ (120)(IN), BX \ MOVQ R8, ( 56)(IN) \ MOVQ R10, ( 72)(IN) \ MOVQ R11, ( 80)(IN) \ MOVQ R12, ( 88)(IN) \ MOVQ R13, ( 96)(IN) \ MOVQ R14, (104)(IN) \ MOVQ R15, (112)(IN) \ MOVQ BX, (120)(IN) \ MOVQ R9, ( 0)(OUT) \ // Result: OUT[0] \ MULS(48(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, BP) \ ADDQ ( 72)(IN), R8 \ ADCQ ( 80)(IN), R9 \ ADCQ ( 88)(IN), R10 \ ADCQ ( 96)(IN), R11 \ ADCQ (104)(IN), R12 \ ADCQ (112)(IN), R13 \ ADCQ (120)(IN), R14 \ MOVQ R8, ( 8)(OUT) \ // Result: OUT[1] MOVQ R9, (16)(OUT) \ // Result: OUT[2] MOVQ R10, (24)(OUT) \ // Result: OUT[3] MOVQ R11, (32)(OUT) \ // Result: OUT[4] MOVQ R12, (40)(OUT) \ // Result: OUT[5] MOVQ R13, (48)(OUT) \ // Result: OUT[6] and OUT[7] MOVQ R14, (56)(OUT) TEXT ·modP503(SB), NOSPLIT, $0-8 MOVQ x+0(FP), REG_P1 // Zero AX for later use: XORQ AX, AX // Load p into registers: MOVQ P503_0, R8 // P503_{1,2} = P503_0, so reuse R8 MOVQ P503_3, R9 MOVQ P503_4, R10 MOVQ P503_5, R11 MOVQ P503_6, R12 MOVQ P503_7, R13 // Set x <- x - p SUBQ R8, ( 0)(REG_P1) SBBQ R8, ( 8)(REG_P1) SBBQ R8, (16)(REG_P1) SBBQ R9, (24)(REG_P1) SBBQ R10, (32)(REG_P1) SBBQ R11, (40)(REG_P1) SBBQ R12, (48)(REG_P1) SBBQ R13, (56)(REG_P1) // Save carry flag indicating x-p < 0 as a mask SBBQ $0, AX // Conditionally add p to x if x-p < 0 ANDQ AX, R8 ANDQ AX, R9 ANDQ AX, R10 ANDQ AX, R11 ANDQ AX, R12 ANDQ AX, R13 ADDQ R8, ( 0)(REG_P1) ADCQ R8, ( 8)(REG_P1) ADCQ R8, (16)(REG_P1) ADCQ R9, (24)(REG_P1) ADCQ R10,(32)(REG_P1) ADCQ R11,(40)(REG_P1) ADCQ R12,(48)(REG_P1) ADCQ R13,(56)(REG_P1) RET TEXT ·cswapP503(SB),NOSPLIT,$0-17 MOVQ x+0(FP), REG_P1 MOVQ y+8(FP), REG_P2 MOVB choice+16(FP), AL // AL = 0 or 1 MOVBLZX AL, AX // AX = 0 or 1 NEGQ AX // AX = 0x00..00 or 0xff..ff #ifndef CSWAP_BLOCK #define CSWAP_BLOCK(idx) \ MOVQ (idx*8)(REG_P1), BX \ // BX = x[idx] MOVQ (idx*8)(REG_P2), CX \ // CX = y[idx] MOVQ CX, DX \ // DX = y[idx] XORQ BX, DX \ // DX = y[idx] ^ x[idx] ANDQ AX, DX \ // DX = (y[idx] ^ x[idx]) & mask XORQ DX, BX \ // BX = (y[idx] ^ x[idx]) & mask) ^ x[idx] = x[idx] or y[idx] XORQ DX, CX \ // CX = (y[idx] ^ x[idx]) & mask) ^ y[idx] = y[idx] or x[idx] MOVQ BX, (idx*8)(REG_P1) \ MOVQ CX, (idx*8)(REG_P2) #endif CSWAP_BLOCK(0) CSWAP_BLOCK(1) CSWAP_BLOCK(2) CSWAP_BLOCK(3) CSWAP_BLOCK(4) CSWAP_BLOCK(5) CSWAP_BLOCK(6) CSWAP_BLOCK(7) #ifdef CSWAP_BLOCK #undef CSWAP_BLOCK #endif RET TEXT ·cmovP503(SB),NOSPLIT,$0-17 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVB choice+16(FP), AL // AL = 0 or 1 MOVBLZX AL, AX // AX = 0 or 1 NEGQ AX // AX = 0x00..00 or 0xff..ff #ifndef CMOV_BLOCK #define CMOV_BLOCK(idx) \ MOVQ (idx*8)(DI), BX \ // BX = x[idx] MOVQ (idx*8)(SI), DX \ // DX = y[idx] XORQ BX, DX \ // DX = y[idx] ^ x[idx] ANDQ AX, DX \ // DX = (y[idx] ^ x[idx]) & mask XORQ DX, BX \ // BX = (y[idx] ^ x[idx]) & mask) ^ x[idx] = x[idx] or y[idx] MOVQ BX, (idx*8)(DI) #endif CMOV_BLOCK(0) CMOV_BLOCK(1) CMOV_BLOCK(2) CMOV_BLOCK(3) CMOV_BLOCK(4) CMOV_BLOCK(5) CMOV_BLOCK(6) CMOV_BLOCK(7) #ifdef CMOV_BLOCK #undef CMOV_BLOCK #endif RET TEXT ·addP503(SB),NOSPLIT,$0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 // Used later to calculate a mask XORQ CX, CX // [R8-R15]: z = x + y MOVQ ( 0)(REG_P1), R8 MOVQ ( 8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 ADDQ ( 0)(REG_P2), R8 ADCQ ( 8)(REG_P2), R9 ADCQ (16)(REG_P2), R10 ADCQ (24)(REG_P2), R11 ADCQ (32)(REG_P2), R12 ADCQ (40)(REG_P2), R13 ADCQ (48)(REG_P2), R14 ADCQ (56)(REG_P2), R15 MOVQ P503X2_0, AX SUBQ AX, R8 MOVQ P503X2_1, AX SBBQ AX, R9 SBBQ AX, R10 MOVQ P503X2_3, AX SBBQ AX, R11 MOVQ P503X2_4, AX SBBQ AX, R12 MOVQ P503X2_5, AX SBBQ AX, R13 MOVQ P503X2_6, AX SBBQ AX, R14 MOVQ P503X2_7, AX SBBQ AX, R15 // mask SBBQ $0, CX // move z to REG_P3 MOVQ R8, ( 0)(REG_P3) MOVQ R9, ( 8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) // if z<0 add p503x2 back MOVQ P503X2_0, R8 MOVQ P503X2_1, R9 MOVQ P503X2_3, R10 MOVQ P503X2_4, R11 MOVQ P503X2_5, R12 MOVQ P503X2_6, R13 MOVQ P503X2_7, R14 ANDQ CX, R8 ANDQ CX, R9 ANDQ CX, R10 ANDQ CX, R11 ANDQ CX, R12 ANDQ CX, R13 ANDQ CX, R14 MOVQ ( 0)(REG_P3), AX; ADDQ R8, AX; MOVQ AX, ( 0)(REG_P3) MOVQ ( 8)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, ( 8)(REG_P3) MOVQ (16)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, (16)(REG_P3) MOVQ (24)(REG_P3), AX; ADCQ R10, AX; MOVQ AX, (24)(REG_P3) MOVQ (32)(REG_P3), AX; ADCQ R11, AX; MOVQ AX, (32)(REG_P3) MOVQ (40)(REG_P3), AX; ADCQ R12, AX; MOVQ AX, (40)(REG_P3) MOVQ (48)(REG_P3), AX; ADCQ R13, AX; MOVQ AX, (48)(REG_P3) MOVQ (56)(REG_P3), AX; ADCQ R14, AX; MOVQ AX, (56)(REG_P3) RET TEXT ·subP503(SB), NOSPLIT, $0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 // Used later to calculate a mask XORQ CX, CX MOVQ ( 0)(REG_P1), R8 MOVQ ( 8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 SUBQ ( 0)(REG_P2), R8 SBBQ ( 8)(REG_P2), R9 SBBQ (16)(REG_P2), R10 SBBQ (24)(REG_P2), R11 SBBQ (32)(REG_P2), R12 SBBQ (40)(REG_P2), R13 SBBQ (48)(REG_P2), R14 SBBQ (56)(REG_P2), R15 // mask SBBQ $0, CX // store x-y in REG_P3 MOVQ R8, ( 0)(REG_P3) MOVQ R9, ( 8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) // if z<0 add p503x2 back MOVQ P503X2_0, R8 MOVQ P503X2_1, R9 MOVQ P503X2_3, R10 MOVQ P503X2_4, R11 MOVQ P503X2_5, R12 MOVQ P503X2_6, R13 MOVQ P503X2_7, R14 ANDQ CX, R8 ANDQ CX, R9 ANDQ CX, R10 ANDQ CX, R11 ANDQ CX, R12 ANDQ CX, R13 ANDQ CX, R14 MOVQ ( 0)(REG_P3), AX; ADDQ R8, AX; MOVQ AX, ( 0)(REG_P3) MOVQ ( 8)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, ( 8)(REG_P3) MOVQ (16)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, (16)(REG_P3) MOVQ (24)(REG_P3), AX; ADCQ R10, AX; MOVQ AX, (24)(REG_P3) MOVQ (32)(REG_P3), AX; ADCQ R11, AX; MOVQ AX, (32)(REG_P3) MOVQ (40)(REG_P3), AX; ADCQ R12, AX; MOVQ AX, (40)(REG_P3) MOVQ (48)(REG_P3), AX; ADCQ R13, AX; MOVQ AX, (48)(REG_P3) MOVQ (56)(REG_P3), AX; ADCQ R14, AX; MOVQ AX, (56)(REG_P3) RET TEXT ·mulP503(SB), NOSPLIT, $104-24 MOVQ z+0(FP), CX MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 // Check whether to use optimized implementation CMPB ·HasADXandBMI2(SB), $1 JE mul_with_mulx_adcx_adox CMPB ·HasBMI2(SB), $1 JE mul_with_mulx // Generic x86 implementation (below) uses variant of Karatsuba method. // // Here we store the destination in CX instead of in REG_P3 because the // multiplication instructions use DX as an implicit destination // operand: MULQ $REG sets DX:AX <-- AX * $REG. // RAX and RDX will be used for a mask (0-borrow) XORQ AX, AX // RCX[0-3]: U1+U0 MOVQ (32)(REG_P1), R8 MOVQ (40)(REG_P1), R9 MOVQ (48)(REG_P1), R10 MOVQ (56)(REG_P1), R11 ADDQ ( 0)(REG_P1), R8 ADCQ ( 8)(REG_P1), R9 ADCQ (16)(REG_P1), R10 ADCQ (24)(REG_P1), R11 MOVQ R8, ( 0)(CX) MOVQ R9, ( 8)(CX) MOVQ R10, (16)(CX) MOVQ R11, (24)(CX) SBBQ $0, AX // R12-R15: V1+V0 XORQ DX, DX MOVQ (32)(REG_P2), R12 MOVQ (40)(REG_P2), R13 MOVQ (48)(REG_P2), R14 MOVQ (56)(REG_P2), R15 ADDQ ( 0)(REG_P2), R12 ADCQ ( 8)(REG_P2), R13 ADCQ (16)(REG_P2), R14 ADCQ (24)(REG_P2), R15 SBBQ $0, DX // Store carries on stack MOVQ AX, (64)(SP) MOVQ DX, (72)(SP) // (SP[0-3],R8,R9,R10,R11) <- (U0+U1)*(V0+V1). // MUL using comba; In comments below U=U0+U1 V=V0+V1 // U0*V0 MOVQ (CX), AX MULQ R12 MOVQ AX, (SP) // C0 MOVQ DX, R8 // U0*V1 XORQ R9, R9 MOVQ (CX), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 // U1*V0 XORQ R10, R10 MOVQ (8)(CX), AX MULQ R12 ADDQ AX, R8 MOVQ R8, (8)(SP) // C1 ADCQ DX, R9 ADCQ $0, R10 // U0*V2 XORQ R8, R8 MOVQ (CX), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 // U2*V0 MOVQ (16)(CX), AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 // U1*V1 MOVQ (8)(CX), AX MULQ R13 ADDQ AX, R9 MOVQ R9, (16)(SP) // C2 ADCQ DX, R10 ADCQ $0, R8 // U0*V3 XORQ R9, R9 MOVQ (CX), AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 // U3*V0 MOVQ (24)(CX), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 // U1*V2 MOVQ (8)(CX), AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 // U2*V1 MOVQ (16)(CX), AX MULQ R13 ADDQ AX, R10 MOVQ R10, (24)(SP) // C3 ADCQ DX, R8 ADCQ $0, R9 // U1*V3 XORQ R10, R10 MOVQ (8)(CX), AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 // U3*V1 MOVQ (24)(CX), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 // U2*V2 MOVQ (16)(CX), AX MULQ R14 ADDQ AX, R8 MOVQ R8, (32)(SP) // C4 ADCQ DX, R9 ADCQ $0, R10 // U2*V3 XORQ R11, R11 MOVQ (16)(CX), AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R11 // U3*V2 MOVQ (24)(CX), AX MULQ R14 ADDQ AX, R9 // C5 ADCQ DX, R10 ADCQ $0, R11 // U3*V3 MOVQ (24)(CX), AX MULQ R15 ADDQ AX, R10 // C6 ADCQ DX, R11 // C7 MOVQ (64)(SP), AX ANDQ AX, R12 ANDQ AX, R13 ANDQ AX, R14 ANDQ AX, R15 ADDQ R8, R12 ADCQ R9, R13 ADCQ R10, R14 ADCQ R11, R15 MOVQ (72)(SP), AX MOVQ (CX), R8 MOVQ (8)(CX), R9 MOVQ (16)(CX), R10 MOVQ (24)(CX), R11 ANDQ AX, R8 ANDQ AX, R9 ANDQ AX, R10 ANDQ AX, R11 ADDQ R12, R8 ADCQ R13, R9 ADCQ R14, R10 ADCQ R15, R11 MOVQ R8, (32)(SP) MOVQ R9, (40)(SP) MOVQ R10, (48)(SP) MOVQ R11, (56)(SP) // CX[0-7] <- AL*BL // U0*V0 MOVQ (REG_P1), R11 MOVQ (REG_P2), AX MULQ R11 XORQ R9, R9 MOVQ AX, (CX) // C0 MOVQ DX, R8 // U0*V1 MOVQ (16)(REG_P1), R14 MOVQ (8)(REG_P2), AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 ADCQ DX, R9 // U1*V0 MOVQ (8)(REG_P1), R12 MOVQ (REG_P2), AX MULQ R12 ADDQ AX, R8 MOVQ R8, (8)(CX) // C1 ADCQ DX, R9 ADCQ $0, R10 // U0*V2 XORQ R8, R8 MOVQ (16)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 // U2*V0 MOVQ (REG_P2), R13 MOVQ R14, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 // U1*V1 MOVQ (8)(REG_P2), AX MULQ R12 ADDQ AX, R9 MOVQ R9, (16)(CX) // C2 ADCQ DX, R10 ADCQ $0, R8 // U0*V3 XORQ R9, R9 MOVQ (24)(REG_P2), AX MULQ R11 MOVQ (24)(REG_P1), R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 // U3*V1 MOVQ R15, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 // U2*V2 MOVQ (16)(REG_P2), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 // U2*V3 MOVQ (8)(REG_P2), AX MULQ R14 ADDQ AX, R10 MOVQ R10, (24)(CX) // C3 ADCQ DX, R8 ADCQ $0, R9 // U3*V2 XORQ R10, R10 MOVQ (24)(REG_P2), AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 // U3*V1 MOVQ (8)(REG_P2), AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 // U2*V2 MOVQ (16)(REG_P2), AX MULQ R14 ADDQ AX, R8 MOVQ R8, (32)(CX) // C4 ADCQ DX, R9 ADCQ $0, R10 // U2*V3 XORQ R8, R8 MOVQ (24)(REG_P2), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 // U3*V2 MOVQ (16)(REG_P2), AX MULQ R15 ADDQ AX, R9 MOVQ R9, (40)(CX) // C5 ADCQ DX, R10 ADCQ $0, R8 // U3*V3 MOVQ (24)(REG_P2), AX MULQ R15 ADDQ AX, R10 MOVQ R10, (48)(CX) // C6 ADCQ DX, R8 MOVQ R8, (56)(CX) // C7 // CX[8-15] <- U1*V1 MOVQ (32)(REG_P1), R11 MOVQ (32)(REG_P2), AX MULQ R11 XORQ R9, R9 MOVQ AX, (64)(CX) // C0 MOVQ DX, R8 MOVQ (48)(REG_P1), R14 MOVQ (40)(REG_P2), AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 ADCQ DX, R9 MOVQ (40)(REG_P1), R12 MOVQ (32)(REG_P2), AX MULQ R12 ADDQ AX, R8 MOVQ R8, (72)(CX) // C1 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (48)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (32)(REG_P2), R13 MOVQ R14, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (40)(REG_P2), AX MULQ R12 ADDQ AX, R9 MOVQ R9, (80)(CX) // C2 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (56)(REG_P2), AX MULQ R11 MOVQ (56)(REG_P1), R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ R15, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (48)(REG_P2), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (40)(REG_P2), AX MULQ R14 ADDQ AX, R10 MOVQ R10, (88)(CX) // C3 ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ (56)(REG_P2), AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (40)(REG_P2), AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (48)(REG_P2), AX MULQ R14 ADDQ AX, R8 MOVQ R8, (96)(CX) // C4 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (56)(REG_P2), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (48)(REG_P2), AX MULQ R15 ADDQ AX, R9 MOVQ R9, (104)(CX) // C5 ADCQ DX, R10 ADCQ $0, R8 MOVQ (56)(REG_P2), AX MULQ R15 ADDQ AX, R10 MOVQ R10, (112)(CX) // C6 ADCQ DX, R8 MOVQ R8, (120)(CX) // C7 // [R8-R15] <- (U0+U1)*(V0+V1) - U1*V1 MOVQ (SP), R8 SUBQ (CX), R8 MOVQ (8)(SP), R9 SBBQ (8)(CX), R9 MOVQ (16)(SP), R10 SBBQ (16)(CX), R10 MOVQ (24)(SP), R11 SBBQ (24)(CX), R11 MOVQ (32)(SP), R12 SBBQ (32)(CX), R12 MOVQ (40)(SP), R13 SBBQ (40)(CX), R13 MOVQ (48)(SP), R14 SBBQ (48)(CX), R14 MOVQ (56)(SP), R15 SBBQ (56)(CX), R15 // [R8-R15] <- (U0+U1)*(V0+V1) - U1*V0 - U0*U1 MOVQ ( 64)(CX), AX; SUBQ AX, R8 MOVQ ( 72)(CX), AX; SBBQ AX, R9 MOVQ ( 80)(CX), AX; SBBQ AX, R10 MOVQ ( 88)(CX), AX; SBBQ AX, R11 MOVQ ( 96)(CX), AX; SBBQ AX, R12 MOVQ (104)(CX), DX; SBBQ DX, R13 MOVQ (112)(CX), DI; SBBQ DI, R14 MOVQ (120)(CX), SI; SBBQ SI, R15 // Final result ADDQ (32)(CX), R8; MOVQ R8, (32)(CX) ADCQ (40)(CX), R9; MOVQ R9, (40)(CX) ADCQ (48)(CX), R10; MOVQ R10, (48)(CX) ADCQ (56)(CX), R11; MOVQ R11, (56)(CX) ADCQ (64)(CX), R12; MOVQ R12, (64)(CX) ADCQ (72)(CX), R13; MOVQ R13, (72)(CX) ADCQ (80)(CX), R14; MOVQ R14, (80)(CX) ADCQ (88)(CX), R15; MOVQ R15, (88)(CX) ADCQ $0, AX; MOVQ AX, (96)(CX) ADCQ $0, DX; MOVQ DX, (104)(CX) ADCQ $0, DI; MOVQ DI, (112)(CX) ADCQ $0, SI; MOVQ SI, (120)(CX) RET mul_with_mulx_adcx_adox: // Mul implementation for CPUs supporting two independent carry chain // (ADOX/ADCX) instructions and carry-less MULX multiplier MUL(CX, REG_P1, REG_P2, MULS256_MULX_ADCX_ADOX) RET mul_with_mulx: // Mul implementation for CPUs supporting carry-less MULX multiplier. MUL(CX, REG_P1, REG_P2, MULS256_MULX) RET TEXT ·rdcP503(SB), $8-16 MOVQ z+0(FP), REG_P2 MOVQ x+8(FP), REG_P1 // Check whether to use optimized implementation CMPB ·HasADXandBMI2(SB), $1 JE redc_with_mulx_adcx_adox CMPB ·HasBMI2(SB), $1 JE redc_with_mulx MOVQ (REG_P1), R11 MOVQ P503P1_3, AX MULQ R11 XORQ R8, R8 ADDQ (24)(REG_P1), AX MOVQ AX, (24)(REG_P2) ADCQ DX, R8 XORQ R9, R9 MOVQ P503P1_4, AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 ADCQ DX, R9 MOVQ (8)(REG_P1), R12 MOVQ P503P1_3, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (32)(REG_P1), R8 MOVQ R8, (32)(REG_P2) // Z4 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P503P1_5, AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P503P1_4, AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (16)(REG_P1), R13 MOVQ P503P1_3, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (40)(REG_P1), R9 MOVQ R9, (40)(REG_P2) // Z5 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P503P1_6, AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P503P1_5, AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P503P1_4, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (24)(REG_P2), R14 MOVQ P503P1_3, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (48)(REG_P1), R10 MOVQ R10, (48)(REG_P2) // Z6 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P503P1_7, AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P503P1_6, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P503P1_5, AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P503P1_4, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (32)(REG_P2), R15 MOVQ P503P1_3, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (56)(REG_P1), R8 MOVQ R8, (56)(REG_P2) // Z7 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P503P1_7, AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P503P1_6, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P503P1_5, AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P503P1_4, AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (40)(REG_P2), CX MOVQ P503P1_3, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (64)(REG_P1), R9 MOVQ R9, (REG_P2) // Z0 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P503P1_7, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P503P1_6, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P503P1_5, AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P503P1_4, AX MULQ CX ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (48)(REG_P2), R13 MOVQ P503P1_3, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (72)(REG_P1), R10 MOVQ R10, (8)(REG_P2) // Z1 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P503P1_7, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P503P1_6, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P503P1_5, AX MULQ CX ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P503P1_4, AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (56)(REG_P2), R14 MOVQ P503P1_3, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (80)(REG_P1), R8 MOVQ R8, (16)(REG_P2) // Z2 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P503P1_7, AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P503P1_6, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P503P1_5, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P503P1_4, AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (88)(REG_P1), R9 MOVQ R9, (24)(REG_P2) // Z3 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P503P1_7, AX MULQ CX ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P503P1_6, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P503P1_5, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (96)(REG_P1), R10 MOVQ R10, (32)(REG_P2) // Z4 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P503P1_7, AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P503P1_6, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (104)(REG_P1), R8 // Z5 MOVQ R8, (40)(REG_P2) // Z5 ADCQ $0, R9 ADCQ $0, R10 MOVQ P503P1_7, AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADDQ (112)(REG_P1), R9 // Z6 MOVQ R9, (48)(REG_P2) // Z6 ADCQ $0, R10 ADDQ (120)(REG_P1), R10 // Z7 MOVQ R10, (56)(REG_P2) // Z7 RET redc_with_mulx_adcx_adox: // Implementation of the Montgomery reduction for CPUs // supporting two independent carry chain (ADOX/ADCX) // instructions and carry-less MULX multiplier MOVQ BP, 0(SP) // push: BP is Callee-save. REDC(REG_P2, REG_P1, MULS_128x320_MULX_ADCX_ADOX) MOVQ 0(SP), BP // pop: BP is Callee-save. RET redc_with_mulx: // Implementation of the Montgomery reduction for CPUs // supporting carry-less MULX multiplier. MOVQ BP, 0(SP) // push: BP is Callee-save. REDC(REG_P2, REG_P1, MULS_128x320_MULX) MOVQ 0(SP), BP // pop: BP is Callee-save. RET TEXT ·adlP503(SB), NOSPLIT, $0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 MOVQ (REG_P1), R8 MOVQ (8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 MOVQ (64)(REG_P1), AX MOVQ (72)(REG_P1), BX MOVQ (80)(REG_P1), CX ADDQ (REG_P2), R8 ADCQ (8)(REG_P2), R9 ADCQ (16)(REG_P2), R10 ADCQ (24)(REG_P2), R11 ADCQ (32)(REG_P2), R12 ADCQ (40)(REG_P2), R13 ADCQ (48)(REG_P2), R14 ADCQ (56)(REG_P2), R15 ADCQ (64)(REG_P2), AX ADCQ (72)(REG_P2), BX ADCQ (80)(REG_P2), CX MOVQ R8, (REG_P3) MOVQ R9, (8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) MOVQ AX, (64)(REG_P3) MOVQ BX, (72)(REG_P3) MOVQ CX, (80)(REG_P3) MOVQ (88)(REG_P1), R8 MOVQ (96)(REG_P1), R9 MOVQ (104)(REG_P1), R10 MOVQ (112)(REG_P1), R11 MOVQ (120)(REG_P1), R12 ADCQ (88)(REG_P2), R8 ADCQ (96)(REG_P2), R9 ADCQ (104)(REG_P2), R10 ADCQ (112)(REG_P2), R11 ADCQ (120)(REG_P2), R12 MOVQ R8, (88)(REG_P3) MOVQ R9, (96)(REG_P3) MOVQ R10, (104)(REG_P3) MOVQ R11, (112)(REG_P3) MOVQ R12, (120)(REG_P3) RET TEXT ·sulP503(SB), NOSPLIT, $0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 // Used later to store result of 0-borrow XORQ CX, CX // SUBC for first 11 limbs MOVQ (REG_P1), R8 MOVQ (8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 MOVQ (64)(REG_P1), AX MOVQ (72)(REG_P1), BX SUBQ (REG_P2), R8 SBBQ (8)(REG_P2), R9 SBBQ (16)(REG_P2), R10 SBBQ (24)(REG_P2), R11 SBBQ (32)(REG_P2), R12 SBBQ (40)(REG_P2), R13 SBBQ (48)(REG_P2), R14 SBBQ (56)(REG_P2), R15 SBBQ (64)(REG_P2), AX SBBQ (72)(REG_P2), BX MOVQ R8, (REG_P3) MOVQ R9, (8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) MOVQ AX, (64)(REG_P3) MOVQ BX, (72)(REG_P3) // SUBC for last 5 limbs MOVQ (80)(REG_P1), R8 MOVQ (88)(REG_P1), R9 MOVQ (96)(REG_P1), R10 MOVQ (104)(REG_P1), R11 MOVQ (112)(REG_P1), R12 MOVQ (120)(REG_P1), R13 SBBQ (80)(REG_P2), R8 SBBQ (88)(REG_P2), R9 SBBQ (96)(REG_P2), R10 SBBQ (104)(REG_P2), R11 SBBQ (112)(REG_P2), R12 SBBQ (120)(REG_P2), R13 MOVQ R8, (80)(REG_P3) MOVQ R9, (88)(REG_P3) MOVQ R10, (96)(REG_P3) MOVQ R11, (104)(REG_P3) MOVQ R12, (112)(REG_P3) MOVQ R13, (120)(REG_P3) // Now the carry flag is 1 if x-y < 0. If so, add p*2^512. SBBQ $0, CX // Load p into registers: MOVQ P503_0, R8 // P503_{1,2} = P503_0, so reuse R8 MOVQ P503_3, R9 MOVQ P503_4, R10 MOVQ P503_5, R11 MOVQ P503_6, R12 MOVQ P503_7, R13 ANDQ CX, R8 ANDQ CX, R9 ANDQ CX, R10 ANDQ CX, R11 ANDQ CX, R12 ANDQ CX, R13 MOVQ (64 )(REG_P3), AX; ADDQ R8, AX; MOVQ AX, (64 )(REG_P3) MOVQ (64+ 8)(REG_P3), AX; ADCQ R8, AX; MOVQ AX, (64+ 8)(REG_P3) MOVQ (64+16)(REG_P3), AX; ADCQ R8, AX; MOVQ AX, (64+16)(REG_P3) MOVQ (64+24)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, (64+24)(REG_P3) MOVQ (64+32)(REG_P3), AX; ADCQ R10, AX; MOVQ AX, (64+32)(REG_P3) MOVQ (64+40)(REG_P3), AX; ADCQ R11, AX; MOVQ AX, (64+40)(REG_P3) MOVQ (64+48)(REG_P3), AX; ADCQ R12, AX; MOVQ AX, (64+48)(REG_P3) MOVQ (64+56)(REG_P3), AX; ADCQ R13, AX; MOVQ AX, (64+56)(REG_P3) RET golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/arith_amd64_test.go000066400000000000000000000077641454601126700270220ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build amd64 && !noasm // +build amd64,!noasm package p503 import ( "reflect" "testing" "testing/quick" "github.com/cloudflare/circl/dh/sidh/internal/common" "golang.org/x/sys/cpu" ) type OptimFlag uint const ( // Indicates that optimisation which uses MUL instruction should be used kUse_MUL OptimFlag = 1 << 0 // Indicates that optimisation which uses MULX instruction should be used kUse_MULX = 1 << 1 // Indicates that optimisation which uses MULX, ADOX and ADCX instructions should be used kUse_MULXandADxX = 1 << 2 ) func resetCpuFeatures() { HasBMI2 = cpu.X86.HasBMI2 HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX } // Utility function used for testing Mul implementations. Tests caller provided // mulFunc against mul() func testMul(t *testing.T, f1, f2 OptimFlag) { doMulTest := func(multiplier, multiplicant common.Fp) bool { defer resetCpuFeatures() var resMulRef, resMulOptim common.FpX2 // Compute multiplier*multiplicant with first implementation HasBMI2 = (kUse_MULX & f1) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX mulP503(&resMulOptim, &multiplier, &multiplicant) // Compute multiplier*multiplicant with second implementation HasBMI2 = (kUse_MULX & f2) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX mulP503(&resMulRef, &multiplier, &multiplicant) // Compare results return reflect.DeepEqual(resMulRef, resMulOptim) } if err := quick.Check(doMulTest, quickCheckConfig); err != nil { t.Error(err) } } // Utility function used for testing REDC implementations. Tests caller provided // redcFunc against redc() func testRedc(t *testing.T, f1, f2 OptimFlag) { doRedcTest := func(aRR common.FpX2) bool { defer resetCpuFeatures() var resRedcF1, resRedcF2 common.Fp aRRcpy := aRR // Compute redc with first implementation HasBMI2 = (kUse_MULX & f1) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX rdcP503(&resRedcF1, &aRR) // Compute redc with second implementation HasBMI2 = (kUse_MULX & f2) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX rdcP503(&resRedcF2, &aRRcpy) // Compare results return reflect.DeepEqual(resRedcF2, resRedcF1) } if err := quick.Check(doRedcTest, quickCheckConfig); err != nil { t.Error(err) } } // Ensures correctness of implementation of mul operation which uses MULX func TestMulWithMULX(t *testing.T) { defer resetCpuFeatures() if !HasBMI2 { t.Skip("MULX not supported by the platform") } testMul(t, kUse_MULX, kUse_MUL) } // Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX func TestMulWithMULXADxX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testMul(t, kUse_MULXandADxX, kUse_MUL) } // Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX func TestMulWithMULXADxXAgainstMULX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testMul(t, kUse_MULX, kUse_MULXandADxX) } // Ensures correctness of Montgomery reduction implementation which uses MULX func TestRedcWithMULX(t *testing.T) { defer resetCpuFeatures() if !HasBMI2 { t.Skip("MULX not supported by the platform") } testRedc(t, kUse_MULX, kUse_MUL) } // Ensures correctness of Montgomery reduction implementation which uses MULX // and ADCX/ADOX. func TestRedcWithMULXADxX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testRedc(t, kUse_MULXandADxX, kUse_MUL) } // Ensures correctness of Montgomery reduction implementation which uses MULX // and ADCX/ADOX. func TestRedcWithMULXADxXAgainstMULX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testRedc(t, kUse_MULXandADxX, kUse_MULX) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/arith_arm64.s000066400000000000000000000356651454601126700256370ustar00rootroot00000000000000// +build arm64,!noasm #include "textflag.h" TEXT ·cmovP503(SB), NOSPLIT, $0-17 MOVD x+0(FP), R0 MOVD y+8(FP), R1 MOVB choice+16(FP), R2 // Set flags // If choice is not 0 or 1, this implementation will swap completely CMP $0, R2 LDP 0(R0), (R3, R4) LDP 0(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 0(R0) LDP 16(R0), (R3, R4) LDP 16(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 16(R0) LDP 32(R0), (R3, R4) LDP 32(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 32(R0) LDP 48(R0), (R3, R4) LDP 48(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 48(R0) RET TEXT ·cswapP503(SB), NOSPLIT, $0-17 MOVD x+0(FP), R0 MOVD y+8(FP), R1 MOVB choice+16(FP), R2 // Set flags // If choice is not 0 or 1, this implementation will swap completely CMP $0, R2 LDP 0(R0), (R3, R4) LDP 0(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 0(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 0(R1) LDP 16(R0), (R3, R4) LDP 16(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 16(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 16(R1) LDP 32(R0), (R3, R4) LDP 32(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 32(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 32(R1) LDP 48(R0), (R3, R4) LDP 48(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 48(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 48(R1) RET TEXT ·addP503(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 // Load first summand into R3-R10 // Add first summand and second summand and store result in R3-R10 LDP 0(R0), (R3, R4) LDP 0(R1), (R11, R12) LDP 16(R0), (R5, R6) LDP 16(R1), (R13, R14) ADDS R11, R3 ADCS R12, R4 ADCS R13, R5 ADCS R14, R6 LDP 32(R0), (R7, R8) LDP 32(R1), (R11, R12) LDP 48(R0), (R9, R10) LDP 48(R1), (R13, R14) ADCS R11, R7 ADCS R12, R8 ADCS R13, R9 ADC R14, R10 // Subtract 2 * p503 in R11-R17 from the result in R3-R10 LDP ·P503x2+0(SB), (R11, R12) LDP ·P503x2+24(SB), (R13, R14) SUBS R11, R3 SBCS R12, R4 LDP ·P503x2+40(SB), (R15, R16) SBCS R12, R5 SBCS R13, R6 MOVD ·P503x2+56(SB), R17 SBCS R14, R7 SBCS R15, R8 SBCS R16, R9 SBCS R17, R10 SBC ZR, ZR, R19 // If x + y - 2 * p503 < 0, R19 is 1 and 2 * p503 should be added AND R19, R11 AND R19, R12 AND R19, R13 AND R19, R14 AND R19, R15 AND R19, R16 AND R19, R17 ADDS R11, R3 ADCS R12, R4 STP (R3, R4), 0(R2) ADCS R12, R5 ADCS R13, R6 STP (R5, R6), 16(R2) ADCS R14, R7 ADCS R15, R8 STP (R7, R8), 32(R2) ADCS R16, R9 ADC R17, R10 STP (R9, R10), 48(R2) RET TEXT ·subP503(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 // Load x into R3-R10 // Subtract y from x and store result in R3-R10 LDP 0(R0), (R3, R4) LDP 0(R1), (R11, R12) LDP 16(R0), (R5, R6) LDP 16(R1), (R13, R14) SUBS R11, R3 SBCS R12, R4 SBCS R13, R5 SBCS R14, R6 LDP 32(R0), (R7, R8) LDP 32(R1), (R11, R12) LDP 48(R0), (R9, R10) LDP 48(R1), (R13, R14) SBCS R11, R7 SBCS R12, R8 SBCS R13, R9 SBCS R14, R10 SBC ZR, ZR, R19 // If x - y < 0, R19 is 1 and 2 * p503 should be added LDP ·P503x2+0(SB), (R11, R12) LDP ·P503x2+24(SB), (R13, R14) AND R19, R11 AND R19, R12 LDP ·P503x2+40(SB), (R15, R16) AND R19, R13 AND R19, R14 MOVD ·P503x2+56(SB), R17 AND R19, R15 AND R19, R16 AND R19, R17 ADDS R11, R3 ADCS R12, R4 STP (R3, R4), 0(R2) ADCS R12, R5 ADCS R13, R6 STP (R5, R6), 16(R2) ADCS R14, R7 ADCS R15, R8 STP (R7, R8), 32(R2) ADCS R16, R9 ADC R17, R10 STP (R9, R10), 48(R2) RET TEXT ·adlP503(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 LDP 0(R0), (R3, R4) LDP 0(R1), (R11, R12) LDP 16(R0), (R5, R6) LDP 16(R1), (R13, R14) ADDS R11, R3 ADCS R12, R4 STP (R3, R4), 0(R2) ADCS R13, R5 ADCS R14, R6 STP (R5, R6), 16(R2) LDP 32(R0), (R7, R8) LDP 32(R1), (R11, R12) LDP 48(R0), (R9, R10) LDP 48(R1), (R13, R14) ADCS R11, R7 ADCS R12, R8 STP (R7, R8), 32(R2) ADCS R13, R9 ADCS R14, R10 STP (R9, R10), 48(R2) LDP 64(R0), (R3, R4) LDP 64(R1), (R11, R12) LDP 80(R0), (R5, R6) LDP 80(R1), (R13, R14) ADCS R11, R3 ADCS R12, R4 STP (R3, R4), 64(R2) ADCS R13, R5 ADCS R14, R6 STP (R5, R6), 80(R2) LDP 96(R0), (R7, R8) LDP 96(R1), (R11, R12) LDP 112(R0), (R9, R10) LDP 112(R1), (R13, R14) ADCS R11, R7 ADCS R12, R8 STP (R7, R8), 96(R2) ADCS R13, R9 ADC R14, R10 STP (R9, R10), 112(R2) RET TEXT ·sulP503(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 LDP 0(R0), (R3, R4) LDP 0(R1), (R11, R12) LDP 16(R0), (R5, R6) LDP 16(R1), (R13, R14) SUBS R11, R3 SBCS R12, R4 STP (R3, R4), 0(R2) SBCS R13, R5 SBCS R14, R6 STP (R5, R6), 16(R2) LDP 32(R0), (R7, R8) LDP 32(R1), (R11, R12) LDP 48(R0), (R9, R10) LDP 48(R1), (R13, R14) SBCS R11, R7 SBCS R12, R8 STP (R7, R8), 32(R2) SBCS R13, R9 SBCS R14, R10 STP (R9, R10), 48(R2) LDP 64(R0), (R3, R4) LDP 64(R1), (R11, R12) LDP 80(R0), (R5, R6) LDP 80(R1), (R13, R14) SBCS R11, R3 SBCS R12, R4 SBCS R13, R5 SBCS R14, R6 LDP 96(R0), (R7, R8) LDP 96(R1), (R11, R12) LDP 112(R0), (R9, R10) LDP 112(R1), (R13, R14) SBCS R11, R7 SBCS R12, R8 SBCS R13, R9 SBCS R14, R10 SBC ZR, ZR, R15 // If x - y < 0, R15 is 1 and p503 should be added LDP ·P503+16(SB), (R16, R17) LDP ·P503+32(SB), (R19, R20) AND R15, R16 AND R15, R17 LDP ·P503+48(SB), (R21, R22) AND R15, R19 AND R15, R20 AND R15, R21 AND R15, R22 ADDS R16, R3 ADCS R16, R4 STP (R3, R4), 64(R2) ADCS R16, R5 ADCS R17, R6 STP (R5, R6), 80(R2) ADCS R19, R7 ADCS R20, R8 STP (R7, R8), 96(R2) ADCS R21, R9 ADC R22, R10 STP (R9, R10), 112(R2) RET // Expects that X0*Y0 is already in Z0(low),Z3(high) and X0*Y1 in Z1(low),Z2(high) // Z0 is not actually touched // Result of (X0-X1) * (Y0-Y1) will be in Z0-Z3 // Inputs get overwritten, except for X1 #define mul128x128comba(X0, X1, Y0, Y1, Z0, Z1, Z2, Z3, T0) \ MUL X1, Y0, X0 \ UMULH X1, Y0, Y0 \ ADDS Z3, Z1 \ ADC ZR, Z2 \ \ MUL Y1, X1, T0 \ UMULH Y1, X1, Y1 \ ADDS X0, Z1 \ ADCS Y0, Z2 \ ADC ZR, ZR, Z3 \ \ ADDS T0, Z2 \ ADC Y1, Z3 // Expects that X points to (X0-X1) // Result of (X0-X3) * (Y0-Y3) will be in Z0-Z7 // Inputs get overwritten, except X2-X3 and Y2-Y3 #define mul256x256karatsuba(X, X0, X1, X2, X3, Y0, Y1, Y2, Y3, Z0, Z1, Z2, Z3, Z4, Z5, Z6, Z7, T0, T1)\ ADDS X2, X0 \ // xH + xL, destroys xL ADCS X3, X1 \ ADCS ZR, ZR, T0 \ \ ADDS Y2, Y0, Z6 \ // yH + yL ADCS Y3, Y1, T1 \ ADC ZR, ZR, Z7 \ \ SUB T0, ZR, Z2 \ SUB Z7, ZR, Z3 \ AND Z7, T0 \ // combined carry \ AND Z2, Z6, Z0 \ // masked(yH + yL) AND Z2, T1, Z1 \ \ AND Z3, X0, Z4 \ // masked(xH + xL) AND Z3, X1, Z5 \ \ MUL Z6, X0, Z2 \ MUL T1, X0, Z3 \ \ ADDS Z4, Z0 \ UMULH T1, X0, Z4 \ ADCS Z5, Z1 \ UMULH Z6, X0, Z5 \ ADC ZR, T0 \ \ // (xH + xL) * (yH + yL) mul128x128comba(X0, X1, Z6, T1, Z2, Z3, Z4, Z5, Z7)\ \ LDP 0+X, (X0, X1) \ \ ADDS Z0, Z4 \ UMULH Y0, X0, Z7 \ UMULH Y1, X0, T1 \ ADCS Z1, Z5 \ MUL Y0, X0, Z0 \ MUL Y1, X0, Z1 \ ADC ZR, T0 \ \ // xL * yL mul128x128comba(X0, X1, Y0, Y1, Z0, Z1, T1, Z7, Z6)\ \ MUL Y2, X2, X0 \ UMULH Y2, X2, Y0 \ SUBS Z0, Z2 \ // (xH + xL) * (yH + yL) - xL * yL SBCS Z1, Z3 \ SBCS T1, Z4 \ MUL Y3, X2, X1 \ UMULH Y3, X2, Z6 \ SBCS Z7, Z5 \ SBCS ZR, T0 \ \ // xH * yH mul128x128comba(X2, X3, Y2, Y3, X0, X1, Z6, Y0, Y1)\ \ SUBS X0, Z2 \ // (xH + xL) * (yH + yL) - xL * yL - xH * yH SBCS X1, Z3 \ SBCS Z6, Z4 \ SBCS Y0, Z5 \ SBCS ZR, T0 \ \ ADDS T1, Z2 \ // (xH * yH) * 2^256 + ((xH + xL) * (yH + yL) - xL * yL - xH * yH) * 2^128 + xL * yL ADCS Z7, Z3 \ ADCS X0, Z4 \ ADCS X1, Z5 \ ADCS T0, Z6 \ ADC Y0, ZR, Z7 // This implements two-level Karatsuba with a 128x128 Comba multiplier // at the bottom TEXT ·mulP503(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 // Load xL in R3-R6, xH in R7-R10 // (xH + xL) in R25-R29 LDP 0(R0), (R3, R4) LDP 32(R0), (R7, R8) ADDS R3, R7, R25 ADCS R4, R8, R26 LDP 16(R0), (R5, R6) LDP 48(R0), (R9, R10) ADCS R5, R9, R27 ADCS R6, R10, R29 ADC ZR, ZR, R7 // Load yL in R11-R14, yH in R15-19 // (yH + yL) in R11-R14, destroys yL LDP 0(R1), (R11, R12) LDP 32(R1), (R15, R16) ADDS R15, R11 ADCS R16, R12 LDP 16(R1), (R13, R14) LDP 48(R1), (R17, R19) ADCS R17, R13 ADCS R19, R14 ADC ZR, ZR, R8 // Compute masks and combined carry SUB R7, ZR, R9 SUB R8, ZR, R10 AND R8, R7 // masked(yH + yL) AND R9, R11, R15 AND R9, R12, R16 AND R9, R13, R17 AND R9, R14, R19 // masked(xH + xL) AND R10, R25, R20 AND R10, R26, R21 AND R10, R27, R22 AND R10, R29, R23 // masked(xH + xL) + masked(yH + yL) in R15-R19 ADDS R20, R15 ADCS R21, R16 ADCS R22, R17 ADCS R23, R19 ADC ZR, R7 // Use z as temporary storage STP (R25, R26), 0(R2) // (xH + xL) * (yH + yL) mul256x256karatsuba(0(R2), R25, R26, R27, R29, R11, R12, R13, R14, R8, R9, R10, R20, R21, R22, R23, R24, R0, R1) MOVD x+8(FP), R0 MOVD y+16(FP), R1 ADDS R21, R15 ADCS R22, R16 ADCS R23, R17 ADCS R24, R19 ADC ZR, R7 // Load yL in R11-R14 LDP 0(R1), (R11, R12) LDP 16(R1), (R13, R14) // xL * yL mul256x256karatsuba(0(R0), R3, R4, R5, R6, R11, R12, R13, R14, R21, R22, R23, R24, R25, R26, R27, R29, R1, R2) MOVD z+0(FP), R2 MOVD y+16(FP), R1 // (xH + xL) * (yH + yL) - xL * yL SUBS R21, R8 SBCS R22, R9 STP (R21, R22), 0(R2) SBCS R23, R10 SBCS R24, R20 STP (R23, R24), 16(R2) SBCS R25, R15 SBCS R26, R16 SBCS R27, R17 SBCS R29, R19 SBC ZR, R7 // Load xH in R3-R6, yH in R11-R14 LDP 32(R0), (R3, R4) LDP 48(R0), (R5, R6) LDP 32(R1), (R11, R12) LDP 48(R1), (R13, R14) ADDS R25, R8 ADCS R26, R9 ADCS R27, R10 ADCS R29, R20 ADC ZR, ZR, R1 MOVD R20, 32(R2) // xH * yH mul256x256karatsuba(32(R0), R3, R4, R5, R6, R11, R12, R13, R14, R21, R22, R23, R24, R25, R26, R27, R29, R2, R20) NEG R1, R1 MOVD z+0(FP), R2 MOVD 32(R2), R20 // (xH + xL) * (yH + yL) - xL * yL - xH * yH in R8-R10,R20,R15-R19 // Store lower half in z, that's done SUBS R21, R8 SBCS R22, R9 STP (R8, R9), 32(R2) SBCS R23, R10 SBCS R24, R20 STP (R10, R20), 48(R2) SBCS R25, R15 SBCS R26, R16 SBCS R27, R17 SBCS R29, R19 SBC ZR, R7 // (xH * yH) * 2^512 + ((xH + xL) * (yH + yL) - xL * yL - xH * yH) * 2^256 + xL * yL // Store remaining limbs in z ADDS $1, R1 ADCS R21, R15 ADCS R22, R16 STP (R15, R16), 64(R2) ADCS R23, R17 ADCS R24, R19 STP (R17, R19), 80(R2) ADCS R7, R25 ADCS ZR, R26 STP (R25, R26), 96(R2) ADCS ZR, R27 ADC ZR, R29 STP (R27, R29), 112(R2) RET // Expects that X0*Y0 is already in Z0(low),Z3(high) and X0*Y1 in Z1(low),Z2(high) // Z0 is not actually touched // Result of (X0-X1) * (Y0-Y3) will be in Z0-Z5 // Inputs remain intact #define mul128x256comba(X0, X1, Y0, Y1, Y2, Y3, Z0, Z1, Z2, Z3, Z4, Z5, T0, T1, T2, T3)\ MUL X1, Y0, T0 \ UMULH X1, Y0, T1 \ ADDS Z3, Z1 \ ADC ZR, Z2 \ \ MUL X0, Y2, T2 \ UMULH X0, Y2, T3 \ ADDS T0, Z1 \ ADCS T1, Z2 \ ADC ZR, ZR, Z3 \ \ MUL X1, Y1, T0 \ UMULH X1, Y1, T1 \ ADDS T2, Z2 \ ADCS T3, Z3 \ ADC ZR, ZR, Z4 \ \ MUL X0, Y3, T2 \ UMULH X0, Y3, T3 \ ADDS T0, Z2 \ ADCS T1, Z3 \ ADC ZR, Z4 \ \ MUL X1, Y2, T0 \ UMULH X1, Y2, T1 \ ADDS T2, Z3 \ ADCS T3, Z4 \ ADC ZR, ZR, Z5 \ \ MUL X1, Y3, T2 \ UMULH X1, Y3, T3 \ ADDS T0, Z3 \ ADCS T1, Z4 \ ADC ZR, Z5 \ ADDS T2, Z4 \ ADC T3, Z5 // This implements the shifted 2^(B*w) Montgomery reduction from // https://eprint.iacr.org/2016/986.pdf with B = 4, w = 64 TEXT ·rdcP503(SB), NOSPLIT, $0-16 MOVD x+8(FP), R0 // Load x0-x1 LDP 0(R0), (R2, R3) // Load the prime constant in R25-R29 LDP ·P503p1s8+32(SB), (R25, R26) LDP ·P503p1s8+48(SB), (R27, R29) // [x0,x1] * p503p1s8 to R4-R9 MUL R2, R25, R4 // x0 * p503p1s8[0] UMULH R2, R25, R7 MUL R2, R26, R5 // x0 * p503p1s8[1] UMULH R2, R26, R6 mul128x256comba(R2, R3, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13) LDP 16(R0), (R3, R11) // x2 LDP 32(R0), (R12, R13) LDP 48(R0), (R14, R15) // Left-shift result in R4-R9 by 56 to R4-R10 ORR R9>>8, ZR, R10 LSL $56, R9 ORR R8>>8, R9 LSL $56, R8 ORR R7>>8, R8 LSL $56, R7 ORR R6>>8, R7 LSL $56, R6 ORR R5>>8, R6 LSL $56, R5 ORR R4>>8, R5 LSL $56, R4 ADDS R4, R11 // x3 ADCS R5, R12 // x4 ADCS R6, R13 ADCS R7, R14 ADCS R8, R15 LDP 64(R0), (R16, R17) LDP 80(R0), (R19, R20) MUL R3, R25, R4 // x2 * p503p1s8[0] UMULH R3, R25, R7 ADCS R9, R16 ADCS R10, R17 ADCS ZR, R19 ADCS ZR, R20 LDP 96(R0), (R21, R22) LDP 112(R0), (R23, R24) MUL R3, R26, R5 // x2 * p503p1s8[1] UMULH R3, R26, R6 ADCS ZR, R21 ADCS ZR, R22 ADCS ZR, R23 ADC ZR, R24 // [x2,x3] * p503p1s8 to R4-R9 mul128x256comba(R3, R11, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R0, R1, R2) ORR R9>>8, ZR, R10 LSL $56, R9 ORR R8>>8, R9 LSL $56, R8 ORR R7>>8, R8 LSL $56, R7 ORR R6>>8, R7 LSL $56, R6 ORR R5>>8, R6 LSL $56, R5 ORR R4>>8, R5 LSL $56, R4 ADDS R4, R13 // x5 ADCS R5, R14 // x6 ADCS R6, R15 ADCS R7, R16 MUL R12, R25, R4 // x4 * p503p1s8[0] UMULH R12, R25, R7 ADCS R8, R17 ADCS R9, R19 ADCS R10, R20 ADCS ZR, R21 MUL R12, R26, R5 // x4 * p503p1s8[1] UMULH R12, R26, R6 ADCS ZR, R22 ADCS ZR, R23 ADC ZR, R24 // [x4,x5] * p503p1s8 to R4-R9 mul128x256comba(R12, R13, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R0, R1, R2) ORR R9>>8, ZR, R10 LSL $56, R9 ORR R8>>8, R9 LSL $56, R8 ORR R7>>8, R8 LSL $56, R7 ORR R6>>8, R7 LSL $56, R6 ORR R5>>8, R6 LSL $56, R5 ORR R4>>8, R5 LSL $56, R4 ADDS R4, R15 // x7 ADCS R5, R16 // x8 ADCS R6, R17 ADCS R7, R19 MUL R14, R25, R4 // x6 * p503p1s8[0] UMULH R14, R25, R7 ADCS R8, R20 ADCS R9, R21 ADCS R10, R22 MUL R14, R26, R5 // x6 * p503p1s8[1] UMULH R14, R26, R6 ADCS ZR, R23 ADC ZR, R24 // [x6,x7] * p503p1s8 to R4-R9 mul128x256comba(R14, R15, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R0, R1, R2) ORR R9>>8, ZR, R10 LSL $56, R9 ORR R8>>8, R9 LSL $56, R8 ORR R7>>8, R8 LSL $56, R7 ORR R6>>8, R7 LSL $56, R6 ORR R5>>8, R6 LSL $56, R5 ORR R4>>8, R5 LSL $56, R4 MOVD z+0(FP), R0 ADDS R4, R17 ADCS R5, R19 STP (R16, R17), 0(R0) // Store final result to z ADCS R6, R20 ADCS R7, R21 STP (R19, R20), 16(R0) ADCS R8, R22 ADCS R9, R23 STP (R21, R22), 32(R0) ADC R10, R24 STP (R23, R24), 48(R0) RET TEXT ·modP503(SB), NOSPLIT, $0-8 MOVD x+0(FP), R0 // Keep x in R1-R8, p503 in R9-R14, subtract to R1-R8 LDP ·P503+16(SB), (R9, R10) LDP 0(R0), (R1, R2) LDP 16(R0), (R3, R4) SUBS R9, R1 SBCS R9, R2 LDP 32(R0), (R5, R6) LDP ·P503+32(SB), (R11, R12) SBCS R9, R3 SBCS R10, R4 LDP 48(R0), (R7, R8) LDP ·P503+48(SB), (R13, R14) SBCS R11, R5 SBCS R12, R6 SBCS R13, R7 SBCS R14, R8 SBC ZR, ZR, R15 // Mask with the borrow and add p503 AND R15, R9 AND R15, R10 AND R15, R11 AND R15, R12 AND R15, R13 AND R15, R14 ADDS R9, R1 ADCS R9, R2 STP (R1, R2), 0(R0) ADCS R9, R3 ADCS R10, R4 STP (R3, R4), 16(R0) ADCS R11, R5 ADCS R12, R6 STP (R5, R6), 32(R0) ADCS R13, R7 ADCS R14, R8 STP (R7, R8), 48(R0) RET golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/arith_decl.go000066400000000000000000000025371454601126700257500ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build (amd64 && !noasm) || (arm64 && !noasm) // +build amd64,!noasm arm64,!noasm package p503 import ( . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cmovP503(x, y *Fp, choice uint8) // If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cswapP503(x, y *Fp, choice uint8) // Compute z = x + y (mod p). // //go:noescape func addP503(z, x, y *Fp) // Compute z = x - y (mod p). // //go:noescape func subP503(z, x, y *Fp) // Compute z = x + y, without reducing mod p. // //go:noescape func adlP503(z, x, y *FpX2) // Compute z = x - y, without reducing mod p. // //go:noescape func sulP503(z, x, y *FpX2) // Reduce a field element in [0, 2*p) to one in [0,p). // //go:noescape func modP503(x *Fp) // Computes z = x * y. // //go:noescape func mulP503(z *FpX2, x, y *Fp) // Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value // of x may be changed. z=x not allowed. // //go:noescape func rdcP503(z *Fp, x *FpX2) golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/arith_generic.go000066400000000000000000000104651454601126700264540ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build noasm || (!amd64 && !arm64) // +build noasm !amd64,!arm64 package p503 import ( "math/bits" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Compute z = x + y (mod p). func addP503(z, x, y *common.Fp) { var carry uint64 // z=x+y % P503 for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } // z = z - P503x2 carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Sub64(z[i], P503x2[i], carry) } // if z<0 add P503x2 back mask := uint64(0 - carry) carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(z[i], P503x2[i]&mask, carry) } } // Compute z = x - y (mod p). func subP503(z, x, y *common.Fp) { var borrow uint64 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } mask := uint64(0 - borrow) borrow = 0 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Add64(z[i], P503x2[i]&mask, borrow) } } // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. func cmovP503(x, y *common.Fp, choice uint8) { mask := 0 - uint64(choice) for i := 0; i < FpWords; i++ { x[i] ^= mask & (x[i] ^ y[i]) } } // Conditionally swaps bits in x and y in constant time. // mask indicates bits to be swapped (set bits are swapped) // For details see "Hackers Delight, 2.20" // // Implementation doesn't actually depend on a prime field. func cswapP503(x, y *common.Fp, mask uint8) { var tmp, mask64 uint64 mask64 = 0 - uint64(mask) for i := 0; i < FpWords; i++ { tmp = mask64 & (x[i] ^ y[i]) x[i] = tmp ^ x[i] y[i] = tmp ^ y[i] } } // Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) // with R=2^(FpWords*64). Destroys the input value. func rdcP503(z *common.Fp, x *common.FpX2) { var carry, t, u, v uint64 var hi, lo uint64 var count int count = P503p1Zeros for i := 0; i < FpWords; i++ { for j := 0; j < i; j++ { if j < (i - count + 1) { hi, lo = bits.Mul64(z[j], P503p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i] = v v = u u = t t = 0 } for i := FpWords; i < 2*FpWords-1; i++ { if count > 0 { count-- } for j := i - FpWords + 1; j < FpWords; j++ { if j < (FpWords - count) { hi, lo = bits.Mul64(z[j], P503p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i-FpWords] = v v = u u = t t = 0 } v, _ = bits.Add64(v, x[2*FpWords-1], 0) z[FpWords-1] = v } // Compute z = x * y. func mulP503(z *common.FpX2, x, y *common.Fp) { var u, v, t uint64 var hi, lo uint64 var carry uint64 for i := uint64(0); i < FpWords; i++ { for j := uint64(0); j <= i; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } for i := FpWords; i < (2*FpWords)-1; i++ { for j := i - FpWords + 1; j < FpWords; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } z[2*FpWords-1] = v } // Compute z = x + y, without reducing mod p. func adlP503(z, x, y *common.FpX2) { var carry uint64 for i := 0; i < 2*FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } } // Reduce a field element in [0, 2*p) to one in [0,p). func modP503(x *common.Fp) { var borrow, mask uint64 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Sub64(x[i], P503[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Add64(x[i], P503[i]&mask, borrow) } } // Compute z = x - y, without reducing mod p. func sulP503(z, x, y *common.FpX2) { var borrow, mask uint64 for i := 0; i < 2*FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := FpWords; i < 2*FpWords; i++ { z[i], borrow = bits.Add64(z[i], P503[i-FpWords]&mask, borrow) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/arith_test.go000066400000000000000000000070001454601126700260060ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p503 import ( "testing" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Package-level storage for this field element is intended to deter // compiler optimizations. var ( benchmarkFp common.Fp benchmarkFpX2 common.FpX2 bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} ) func TestFpCswap(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cswapP503(&x, &y, 0) for i := 0; i < FpWords; i++ { if (x[i] != one[i]) || (y[i] != two[i]) { t.Error("Found", x, "expected", one) } } cswapP503(&x, &y, 1) for i := 0; i < FpWords; i++ { if (x[i] != two[i]) || (y[i] != one[i]) { t.Error("Found", x, "expected", two) } } } func TestFpCmov(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cmovP503(&x, &y, 0) for i := 0; i < FpWords; i++ { if x[i] != one[i] { t.Error("Found", x, "expected", one) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } cmovP503(&x, &y, 1) for i := 0; i < FpWords; i++ { if x[i] != two[i] { t.Error("Found", x, "expected", two) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } } // Benchmarking for field arithmetic func BenchmarkMul(b *testing.B) { for n := 0; n < b.N; n++ { mulP503(&benchmarkFpX2, &bench_x, &bench_y) } } func BenchmarkRdc(b *testing.B) { z := bench_z // This benchmark actually computes garbage, because // rdcP503 mangles its input, but since it's // constant-time that shouldn't matter for the benchmarks. for n := 0; n < b.N; n++ { rdcP503(&benchmarkFp, &z) } } func BenchmarkAdd(b *testing.B) { for n := 0; n < b.N; n++ { addP503(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkSub(b *testing.B) { for n := 0; n < b.N; n++ { subP503(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkCswap(b *testing.B) { x, y := bench_x, bench_y for n := 0; n < b.N; n++ { cswapP503(&x, &y, 1) cswapP503(&x, &y, 0) } } func BenchmarkMod(b *testing.B) { x := bench_x for n := 0; n < b.N; n++ { modP503(&x) } } func BenchmarkX2AddLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { adlP503(&x, &y, &z) } } func BenchmarkX2SubLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { sulP503(&x, &y, &z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/core.go000066400000000000000000000205411454601126700245750ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p503 import ( crand "crypto/rand" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // ----------------------------------------------------------------------------- // Functions for traversing isogeny trees according to strategy. Key type 'A' is // // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR needed // for public key generation. func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { var xPA, xQA, xRA ProjectivePoint var xPB, xQB, xRB, xR ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny4 // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) // Secret isogeny phi.GenerateCurve(&xR) xPA = xPB xQA = xQB xRA = xRB phi.EvaluatePoint(&xPA) phi.EvaluatePoint(&xQA) phi.EvaluatePoint(&xRA) Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPA.X, &invZP) mul(&pub3Pt[1], &xQA.X, &invZQ) mul(&pub3Pt[2], &xRA.X, &invZR) } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { var xPB, xQB, xRB, xR ProjectivePoint var xPA, xQA, xRA ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny3 // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) phi.GenerateCurve(&xR) xPB = xPA xQB = xQA xRB = xRA phi.EvaluatePoint(&xPB) phi.EvaluatePoint(&xQB) phi.EvaluatePoint(&xRB) Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPB.X, &invZP) mul(&pub3Pt[1], &xQB.X, &invZQ) mul(&pub3Pt[2], &xRB.X, &invZR) } // ----------------------------------------------------------------------------- // Key agreement functions // // Establishing shared keys in in 2-torsion group func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny4 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyA(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients4(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } // Establishing shared keys in in 3-torsion group func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny3 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} //PUBLIC KEY VALIDATION if err := PublicKeyValidation(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen); err != nil { _, err_read := crand.Read(ss) if err_read != nil { panic("core: failed to generate random ss when public key verification fails") } return } xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyB(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients3(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/curve.go000066400000000000000000000341221454601126700247710ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p503 import ( "errors" . "github.com/cloudflare/circl/dh/sidh/internal/common" "math" ) // Stores isogeny 3 curve constants type isogeny3 struct { K1 Fp2 K2 Fp2 } // Stores isogeny 4 curve constants type isogeny4 struct { isogeny3 K3 Fp2 } // Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result // is returned in jBytes buffer, encoded in little-endian format. Caller // provided jBytes buffer has to be big enough to j-invariant value. In case // of SIDH, buffer size must be at least size of shared secret. // Implementation corresponds to Algorithm 9 from SIKE. func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { var t0, t1 Fp2 sqr(j, &cparams.A) // j = A^2 sqr(&t1, &cparams.C) // t1 = C^2 add(&t0, &t1, &t1) // t0 = t1 + t1 sub(&t0, j, &t0) // t0 = j - t0 sub(&t0, &t0, &t1) // t0 = t0 - t1 sub(j, &t0, &t1) // t0 = t0 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(j, j, &t1) // j = j * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&t1, &t0) // t1 = t0^2 mul(&t0, &t0, &t1) // t0 = t0 * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 inv(j, j) // j = 1/j mul(j, &t0, j) // j = t0 * j } // Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function // recovers projective coordinate A of a curve. This is Algorithm 10 from SIKE. func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { var t0, t1 Fp2 add(&t1, xp, xq) // t1 = Xp + Xq mul(&t0, xp, xq) // t0 = Xp * Xq mul(&curve.A, xr, &t1) // A = X(q-p) * t1 add(&curve.A, &curve.A, &t0) // A = A + t0 mul(&t0, &t0, xr) // t0 = t0 * X(q-p) sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t1, &t1, xr) // t1 = t1 + X(q-p) add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&curve.A, &curve.A) // A = A^2 inv(&t0, &t0) // t0 = 1/t0 mul(&curve.A, &curve.A, &t0) // A = A * t0 sub(&curve.A, &curve.A, &t1) // A = A - t1 } // Computes equivalence (A:C) ~ (A+2C : A-2C) func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coef CurveCoefficientsEquiv var c2 Fp2 add(&c2, &cparams.C, &cparams.C) // A24p = A+2*C add(&coef.A, &cparams.A, &c2) // A24m = A-2*C sub(&coef.C, &cparams.A, &c2) return coef } // Computes equivalence (A:C) ~ (A+2C : 4C) func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv add(&coefEq.C, &cparams.C, &cparams.C) // A24p = A+2C add(&coefEq.A, &cparams.A, &coefEq.C) // C24 = 4*C add(&coefEq.C, &coefEq.C, &coefEq.C) return coefEq } // Helper function for RightToLeftLadder(). Returns A+2C / 4. func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { var tmp Fp2 // 2C add(&tmp, &cparams.C, &cparams.C) // A+2C add(&ret, &cparams.A, &tmp) // 1/4C add(&tmp, &tmp, &tmp) inv(&tmp, &tmp) // A+2C/4C mul(&ret, &ret, &tmp) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { add(&cparams.A, &coefEq.A, &coefEq.C) // cparams.A = 2*(A+2C+A-2C) = 4A add(&cparams.A, &cparams.A, &cparams.A) // cparams.C = (A+2C-A+2C) = 4C sub(&cparams.C, &coefEq.A, &coefEq.C) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { // cparams.C = (4C)*1/2=2C mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) // cparams.A = A+2C - 2C = A sub(&cparams.A, &coefEq.A, &cparams.C) // cparams.C = 2C * 1/2 = C mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) } // Combined coordinate doubling and differential addition. Takes projective points // P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. // Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { var t0, t1, t2 Fp2 xQmP, zQmP := &QmP.X, &QmP.Z xPaQ, zPaQ := &PaQ.X, &PaQ.Z x2P, z2P := &dblP.X, &dblP.Z xP, zP := &P.X, &P.Z xQ, zQ := &Q.X, &Q.Z add(&t0, xP, zP) // t0 = Xp+Zp sub(&t1, xP, zP) // t1 = Xp-Zp sqr(x2P, &t0) // 2P.X = t0^2 sub(&t2, xQ, zQ) // t2 = Xq-Zq add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq mul(&t0, &t0, &t2) // t0 = t0 * t2 mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q return } // Given the curve parameters, xP = x(P), computes xP = x([2^k]P) // Safe to overlap xP, x2P. func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp add(&t1, x, z) // t1 = Xp + Zp sqr(&t0, &t0) // t0 = t0 ^ 2 sqr(&t1, &t1) // t1 = t1 ^ 2 mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 mul(x, z, &t1) // X2p = Z2p * t1 sub(&t1, &t1, &t0) // t1 = t1 - t0 mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 add(z, z, &t0) // Z2p = Z2p + t0 mul(z, z, &t1) // Zp = Z2p * t1 } } // Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). // // Safe to overlap xP, xR. func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1, t2, t3, t4, t5, t6 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp sqr(&t2, &t0) // t2 = t0^2 add(&t1, x, z) // t1 = Xp + Zp sqr(&t3, &t1) // t3 = t1^2 add(&t4, &t1, &t0) // t4 = t1 + t0 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t1, &t4) // t1 = t4^2 sub(&t1, &t1, &t3) // t1 = t1 - t3 sub(&t1, &t1, &t2) // t1 = t1 - t2 mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ mul(&t3, &t3, &t5) // t3 = t5 * t3 mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- mul(&t2, &t2, &t6) // t2 = t2 * t6 sub(&t3, &t2, &t3) // t3 = t2 - t3 sub(&t2, &t5, &t6) // t2 = t5 - t6 mul(&t1, &t2, &t1) // t1 = t2 * t1 add(&t2, &t3, &t1) // t2 = t3 + t1 sqr(&t2, &t2) // t2 = t2^2 mul(x, &t2, &t4) // X3p = t2 * t4 sub(&t1, &t3, &t1) // t1 = t3 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(z, &t1, &t0) // Z3p = t1 * t0 } } // Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). // // All xi, yi must be distinct. func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { var x1x2, t Fp2 mul(&x1x2, x1, x2) // x1*x2 mul(&t, &x1x2, x3) // 1/(x1*x2*x3) inv(&t, &t) mul(y1, &t, x2) // 1/x1 mul(y1, y1, x3) mul(y2, &t, x1) // 1/x2 mul(y2, y2, x3) mul(y3, &t, &x1x2) // 1/x3 } // Scalarmul3Pt is a right-to-left point multiplication that given the // x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. // nbits must be smaller or equal to len(scalar). func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { var R0, R2, R1 ProjectivePoint aPlus2Over4 := CalcAplus2Over4(cparams) R1 = *P R2 = *PmQ R0 = *Q // Iterate over the bits of the scalar, bottom to top prevBit := uint8(0) for i := uint(0); i < nbits; i++ { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) } cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) return R1 } // Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the // three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C // Output: // - Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var t0, t1, t2, t3, t4 Fp2 var coefEq CurveCoefficientsEquiv K1, K2 := &phi.K1, &phi.K2 sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 sqr(&t0, K1) // t0 = K1^2 add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 sqr(&t1, K2) // t1 = K2^2 add(&t2, &t0, &t1) // t2 = t0 + t1 add(&t3, K1, K2) // t3 = K1 + K2 sqr(&t3, &t3) // t3 = t3^2 sub(&t3, &t3, &t2) // t3 = t3 - t2 add(&t2, &t1, &t3) // t2 = t1 + t3 add(&t3, &t3, &t0) // t3 = t3 + t0 add(&t4, &t3, &t0) // t4 = t3 + t0 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t1, &t4) // t4 = t1 + t4 mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 add(&t4, &t1, &t2) // t4 = t1 + t2 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t0, &t4) // t4 = t0 + t4 mul(&t4, &t3, &t4) // t4 = t3 * t4 sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 return coefEq } // Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate // of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). // // The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve // parameters are returned by the GenerateCurve function used to construct phi. func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) { var t0, t1, t2 Fp2 K1, K2 := &phi.K1, &phi.K2 px, pz := &p.X, &p.Z add(&t0, px, pz) // t0 = XQ + ZQ sub(&t1, px, pz) // t1 = XQ - ZQ mul(&t0, K1, &t0) // t2 = K1 * t0 mul(&t1, K2, &t1) // t1 = K2 * t1 add(&t2, &t0, &t1) // t2 = t0 + t1 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t2, &t2) // t2 = t2 ^ 2 sqr(&t0, &t0) // t0 = t0 ^ 2 mul(px, px, &t2) // XQ'= XQ * t2 mul(pz, pz, &t0) // ZQ'= ZQ * t0 } // Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the // four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C // Output: // - Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv xp4, zp4 := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 sub(K2, xp4, zp4) add(K3, xp4, zp4) sqr(K1, zp4) add(K1, K1, K1) sqr(&coefEq.C, K1) add(K1, K1, K1) sqr(&coefEq.A, xp4) add(&coefEq.A, &coefEq.A, &coefEq.A) sqr(&coefEq.A, &coefEq.A) return coefEq } // Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate // of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). // // Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C // Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) { var t0, t1 Fp2 xq, zq := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 add(&t0, xq, zq) sub(&t1, xq, zq) mul(xq, &t0, K2) mul(zq, &t1, K3) mul(&t0, &t0, &t1) mul(&t0, &t0, K1) add(&t1, xq, zq) sub(zq, xq, zq) sqr(&t1, &t1) sqr(zq, zq) add(xq, &t0, &t1) sub(&t0, zq, &t0) mul(xq, xq, &t1) mul(zq, zq, &t0) } // PublicKeyValidation preforms public key/ciphertext validation using the CLN test. // CLN test: Check that P and Q are both of order 3^e3 and they generate the torsion E_A[3^e3] // A countermeasure for remote timing attacks on SIKE; suggested by https://eprint.iacr.org/2022/054.pdf // Any curve E_A (SIKE 434, 503, 751) that passes CLN test is supersingular. // Input: The public key / ciphertext P, Q, PmQ. The projective coordinate A of the curve defined by (P, Q, PmQ) // Outputs: Whether (P,Q,PmQ) follows the CLN test func PublicKeyValidation(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint) error { var PmQX, PmQZ Fp2 FromMontgomery(&PmQX, &PmQ.X) FromMontgomery(&PmQZ, &PmQ.Z) // PmQ is not point T or O if (isZero(&PmQX) == 1) || (isZero(&PmQZ) == 1) { return errors.New("curve: PmQ is invalid") } cparam := CalcCurveParamsEquiv3(cparams) // Compute e_3 = log3(2^(nbits+1)) var e3 uint32 e3_float := float64(int(nbits)+1) / math.Log2(3) e3 = uint32(e3_float) // Verify that P and Q generate E_A[3^e_3] by checking: [3^(e_3-1)]P != [+-3^(e_3-1)]Q var test_P, test_Q ProjectivePoint test_P = *P test_Q = *Q Pow3k(&test_P, &cparam, e3-1) Pow3k(&test_Q, &cparam, e3-1) var PZ, QZ Fp2 FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of full order 3^e_3 if (isZero(&PZ) == 1) || (isZero(&QZ) == 1) { return errors.New("curve: ciphertext/public key are not of full order 3^e3") } // PX/PZ = affine(PX) // QX/QZ = affine(QX) // If PX/PZ = QX/QZ, we have P=+-Q var PXQZ_PZQX_fromMont, PXQZ_PZQX, PXQZ, PZQX Fp2 mul(&PXQZ, &test_P.X, &test_Q.Z) mul(&PZQX, &test_P.Z, &test_Q.X) sub(&PXQZ_PZQX, &PXQZ, &PZQX) FromMontgomery(&PXQZ_PZQX_fromMont, &PXQZ_PZQX) // [3^(e_3-1)]P == [+-3^(e_3-1)]Q if isZero(&PXQZ_PZQX_fromMont) == 1 { return errors.New("curve: ciphertext/public key are not linearly independent") } // Check that Ord(P) = Ord(Q) = 3^(e_3) Pow3k(&test_P, &cparam, 1) Pow3k(&test_Q, &cparam, 1) FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of correct order 3^e_3 if (isZero(&PZ) == 0) || (isZero(&QZ) == 0) { return errors.New("curve: ciphertext/public key are not of correct order 3^e3") } return nil } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/curve_test.go000066400000000000000000000304631454601126700260340ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p503 import ( "bytes" crand "crypto/rand" . "github.com/cloudflare/circl/dh/sidh/internal/common" "io" "math" "math/rand" "testing" "time" ) func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { var t0, t1 Fp2 mul(&t0, &lhs.X, &rhs.Z) mul(&t1, &lhs.Z, &rhs.X) return vartimeEqFp2(&t0, &t1) } func toAffine(point *ProjectivePoint) *Fp2 { var affineX Fp2 inv(&affineX, &point.Z) mul(&affineX, &affineX, &point.X) return &affineX } func Test_jInvariant(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} jbufRes := make([]byte, params.SharedSecretSize) jbufExp := make([]byte, params.SharedSecretSize) var jInv Fp2 Jinvariant(&curve, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufRes, &jInv, params.Bytelen) jInv = expectedJ FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufExp, &jInv, params.Bytelen) if !bytes.Equal(jbufRes[:], jbufExp[:]) { t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) } } func TestProjectivePointVartimeEq(t *testing.T) { var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} xQ := xP // Scale xQ, which results in the same projective point mul(&xQ.X, &xQ.X, &curveA) mul(&xQ.Z, &xQ.Z, &curveA) if !vartimeEqProjFp2(&xP, &xQ) { t.Error("Expected the scaled point to be equal to the original") } } func TestPointMulVersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv4(&curve) var xP ProjectivePoint // x 2 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 1) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP2) { t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) } // x 4 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 2) afxQ = toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP4) { t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) } } func TestPointMul9VersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv3(&curve) var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow3k(&xP, &cparams, 2) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP9) { t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) } } func BenchmarkThreePointLadder(b *testing.B) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} for n := 0; n < b.N; n++ { ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) } } /* ------------------------------------------------------------------------- Generate invalid public key points / ciphertext for test TestKEMInvalidPK -------------------------------------------------------------------------*/ // Left-to-right Montgomery ladder, Algorithm 4 in Costello-Smith // Input: ProjectivePoint P (xP, zP) // Output: x([scalar]P), z([scalar]P) func montgomeryLadder(cparams *ProjectiveCurveParameters, P *ProjectivePoint, scalar []uint8, random uint) ProjectivePoint { var R0, R2, R1 ProjectivePoint coefEq := CalcCurveParamsEquiv4(cparams) // for xDbl aPlus2Over4 := CalcAplus2Over4(cparams) // for xDblAdd R0 = *P // RO <- P R1 = *P Pow2k(&R1, &coefEq, 1) // R1 <- [2]P R2 = *P // R2 = R1-R0 = P prevBit := uint8(0) for i := int(random); i >= 0; i-- { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, swap) R0, R1 = xDbladd(&R0, &R1, &R2, &aPlus2Over4) } cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, prevBit) return R0 } // P = P + T // From paper https://eprint.iacr.org/2017/212.pdf // The map tau_T: P->P+T is (X : Z) -> (Z : X) on Montgomery curves func tauT(P *ProjectivePoint) { P.X, P.Z = P.Z, P.X // magic! } // Construct Invalid public key tuple (P,Q) such that P and Q are linearly dependent // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKNoneLinear(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1) * 8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Make sure Q is of full order 3^e_3, var test_Q ProjectivePoint test_Q = Q var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1) / math.Log2(3) e3 = uint32(e3_float) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&test_Q, &cparam_q, e3-1) var test_QZ Fp2 FromMontgomery(&test_QZ, &test_Q.Z) // Q are not of full order 3^e_3 for isZero(&test_QZ) == 1 { rand.Seed(time.Now().UnixNano()) random_index = rand.Intn(int(params.B.SecretByteLen-1) * 8) Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) test_Q = Q Pow3k(&test_Q, &cparam_q, e3-1) FromMontgomery(&test_QZ, &test_Q.Z) } // invQz = 1/Q.Z var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect linearly dependent ciphertext to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that Q = [k]P + T, where k is random and T is the point of order 2. // Simulate HB and section 3.1.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKT(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1) * 8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Q = [k]P + T tauT(&Q) var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext involve point T to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[2^e2] // Simulate section 3.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKOrder2(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint P = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(params.A.SecretByteLen-1) * 8) random_index_q := rand.Intn(int(params.A.SecretByteLen-1) * 8) P = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index_p)) Q = montgomeryLadder(¶ms.InitCurve, &Q, secret, uint(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext in torsion E[2^e2] to fail, index_p: %v index_q: %v scalar: %v ", random_index_p, random_index_q, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[3^e3] but not of full order 3^e3 // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKFullOrder(t *testing.T) { var P, Q ProjectivePoint P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1) / math.Log2(3) e3 = uint32(e3_float) rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(e3)) random_index_q := rand.Intn(int(e3)) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&P, &cparam_q, uint32(random_index_p)) Pow3k(&Q, &cparam_q, uint32(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext not of full order to fail, index_p: %v index_q: %v ", random_index_p, random_index_q) } } // A trivial test case not covered by paper https://eprint.iacr.org/2022/054.pdf and HB // Countermeasure in https://eprint.iacr.org/2022/054.pdf only cares about P and Q // But if PmQ is point T or O, that can also lead to recovery of the first bit func testInvalidPmQ(t *testing.T) { var zero Fp2 var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: zero, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect PmQ as T to fail\n") } } // Test valid ciphertext // Where P, Q are linearly independent points of correct order 3^e3 in E[3^e3] func testValidPQ(t *testing.T) { var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify != nil { t.Errorf("\nExpect correct ciphertext to not fail\n") } } /* ------------------------------------------------------------------------- Public key / Ciphertext validation against attacks proposed in paper https://eprint.iacr.org/2022/054.pdf and HB -------------------------------------------------------------------------*/ func TestInvalidPK(t *testing.T) { t.Run("InvalidPmQ", testInvalidPmQ) t.Run("InvalidPKNoneLinear", testInvalidPKNoneLinear) t.Run("InvalidPKT", testInvalidPKT) t.Run("InvalidPKOrder2", testInvalidPKOrder2) t.Run("InvalidPKFullOrder", testInvalidPKFullOrder) t.Run("ValidPQ", testValidPQ) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/doc.go000066400000000000000000000001401454601126700244030ustar00rootroot00000000000000// Package p503 provides implementation of field arithmetic used in SIDH and SIKE. package p503 golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/fp2.go000066400000000000000000000146321454601126700243400ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p503 import ( "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Montgomery multiplication. Input values must be already // in Montgomery domain. func mulP(dest, lhs, rhs *common.Fp) { var ab common.FpX2 mulP503(&ab, lhs, rhs) // = a*b*R*R rdcP503(dest, &ab) // = a*b*R mod p } // Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). // Uses variation of sliding-window algorithm from with window size // of 5 and least to most significant bit sliding (left-to-right) // See HAC 14.85 for general description. // // Allowed to overlap x with dest. // All values in Montgomery domains // Set dest = x^(2^k), for k >= 1, by repeated squarings. func p34(dest, x *common.Fp) { var lookup [16]common.Fp // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) // multiplications. powStrategy := []uint8{12, 5, 5, 2, 7, 11, 3, 8, 4, 11, 4, 7, 5, 6, 3, 7, 5, 7, 2, 12, 5, 6, 4, 6, 8, 6, 4, 7, 5, 5, 8, 5, 8, 5, 5, 8, 9, 3, 6, 2, 10, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3} mulStrategy := []uint8{12, 11, 10, 0, 1, 8, 3, 7, 1, 8, 3, 6, 7, 14, 2, 14, 14, 9, 0, 13, 9, 15, 5, 12, 7, 13, 7, 15, 6, 7, 9, 0, 5, 7, 6, 8, 8, 3, 7, 0, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 3} initialMul := uint8(0) // Precompute lookup table of odd multiples of x for window // size k=5. var xx common.Fp mulP(&xx, x, x) lookup[0] = *x for i := 1; i < 16; i++ { mulP(&lookup[i], &lookup[i-1], &xx) } // Now lookup = {x, x^3, x^5, ... } // so that lookup[i] = x^{2*i + 1} // so that lookup[k/2] = x^k, for odd k *dest = lookup[initialMul] for i := uint8(0); i < uint8(len(powStrategy)); i++ { mulP(dest, dest, dest) for j := uint8(1); j < powStrategy[i]; j++ { mulP(dest, dest, dest) } mulP(dest, dest, &lookup[mulStrategy[i]]) } } func add(dest, lhs, rhs *common.Fp2) { addP503(&dest.A, &lhs.A, &rhs.A) addP503(&dest.B, &lhs.B, &rhs.B) } func sub(dest, lhs, rhs *common.Fp2) { subP503(&dest.A, &lhs.A, &rhs.A) subP503(&dest.B, &lhs.B, &rhs.B) } func mul(dest, lhs, rhs *common.Fp2) { var bMinA, cMinD common.Fp var ac, bd common.FpX2 var adPlusBc common.FpX2 var acMinBd common.FpX2 // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). // // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i // // Use Karatsuba's trick: note that // // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d // // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. subP503(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R subP503(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R mulP503(&ac, &lhs.A, &rhs.A) // = a*c*R*R mulP503(&bd, &lhs.B, &rhs.B) // = b*d*R*R mulP503(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R adlP503(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R adlP503(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R rdcP503(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p sulP503(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R rdcP503(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p } // Set dest = 1/x // // Allowed to overlap dest with x. // // Returns dest to allow chaining operations. func inv(dest, x *common.Fp2) { var e1, e2 common.FpX2 var f1, f2 common.Fp // We want to compute // // 1 1 (a - bi) (a - bi) // -------- = -------- -------- = ----------- // (a + bi) (a + bi) (a - bi) (a^2 + b^2) // // Letting c = 1/(a^2 + b^2), this is // // 1/(a+bi) = a*c - b*ci. mulP503(&e1, &x.A, &x.A) // = a*a*R*R mulP503(&e2, &x.B, &x.B) // = b*b*R*R adlP503(&e1, &e1, &e2) // = (a^2 + b^2)*R*R rdcP503(&f1, &e1) // = (a^2 + b^2)*R mod p // Now f1 = a^2 + b^2 mulP(&f2, &f1, &f1) p34(&f2, &f2) mulP(&f2, &f2, &f2) mulP(&f2, &f2, &f1) mulP503(&e1, &x.A, &f2) rdcP503(&dest.A, &e1) subP503(&f1, &common.Fp{}, &x.B) mulP503(&e1, &f1, &f2) rdcP503(&dest.B, &e1) } func sqr(dest, x *common.Fp2) { var a2, aPlusB, aMinusB common.Fp var a2MinB2, ab2 common.FpX2 a := &x.A b := &x.B // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. addP503(&a2, a, a) // = a*R + a*R = 2*a*R addP503(&aPlusB, a, b) // = a*R + b*R = (a+b)*R subP503(&aMinusB, a, b) // = a*R - b*R = (a-b)*R mulP503(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R mulP503(&ab2, &a2, b) // = 2*a*b*R*R rdcP503(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p rdcP503(&dest.B, &ab2) // = 2*a*b*R mod p } // In case choice == 1, performs following swap in constant time: // // xPx <-> xQx // xPz <-> xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cswapP503(&xPx.A, &xQx.A, choice) cswapP503(&xPx.B, &xQx.B, choice) cswapP503(&xPz.A, &xQz.A, choice) cswapP503(&xPz.B, &xQz.B, choice) } // In case choice == 1, performs following moves in constant time: // // xPx <- xQx // xPz <- xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cmov(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cmovP503(&xPx.A, &xQx.A, choice) cmovP503(&xPx.B, &xQx.B, choice) cmovP503(&xPz.A, &xQz.A, choice) cmovP503(&xPz.B, &xQz.B, choice) } func isZero(x *common.Fp2) uint8 { r64 := uint64(0) for i := 0; i < FpWords; i++ { r64 |= x.A[i] | x.B[i] } r := uint8(0) for i := uint64(0); i < 64; i++ { r |= uint8((r64 >> i) & 0x1) } return 1 - r } // Converts in.A and in.B to Montgomery domain and stores // in 'out' // out.A = in.A * R mod p // out.B = in.B * R mod p // Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B func ToMontgomery(out, in *common.Fp2) { var aRR common.FpX2 // a*R*R mulP503(&aRR, &in.A, &P503R2) // a*R mod p rdcP503(&out.A, &aRR) mulP503(&aRR, &in.B, &P503R2) rdcP503(&out.B, &aRR) } // Converts in.A and in.B from Montgomery domain and stores // in 'out' // out.A = in.A mod p // out.B = in.B mod p // // After returning from the call 'in' is not modified. func FromMontgomery(out, in *common.Fp2) { var aR common.FpX2 // convert from montgomery domain copy(aR[:], in.A[:]) rdcP503(&out.A, &aR) // = a mod p in [0, 2p) modP503(&out.A) // = a mod p in [0, p) for i := range aR { aR[i] = 0 } copy(aR[:], in.B[:]) rdcP503(&out.B, &aR) modP503(&out.B) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/fp2_test.go000066400000000000000000000125601454601126700253750ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p503 import ( "math/rand" "reflect" "testing" "testing/quick" "github.com/cloudflare/circl/dh/sidh/internal/common" ) type testParams struct { Point common.ProjectivePoint Cparam common.ProjectiveCurveParameters ExtElem common.Fp2 } // Returns true if lhs = rhs. Takes variable time. func vartimeEqFp2(lhs, rhs *common.Fp2) bool { a := *lhs b := *rhs modP503(&a.A) modP503(&a.B) modP503(&b.A) modP503(&b.B) eq := true for i := 0; i < FpWords && eq; i++ { eq = eq && (a.A[i] == b.A[i]) eq = eq && (a.B[i] == b.B[i]) } return eq } func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { // Generation strategy: low limbs taken from [0,2^64); high limb // taken from smaller range // // Size hint is ignored since all elements are fixed size. // // Field elements taken in range [0,2p). Emulate this by capping // the high limb by the top digit of 2*p-1: // // sage: (2*p-1).digits(2^64)[-1] // // This still allows generating values >= 2p, but hopefully that // excess is OK (and if it's not, we'll find out, because it's for // testing...) highLimb := rand.Uint64() % P503x2[FpWords-1] fpElementGen := func() (fp common.Fp) { for i := 0; i < (FpWords - 1); i++ { fp[i] = rand.Uint64() } fp[FpWords-1] = highLimb return fp } return common.Fp2{A: fpElementGen(), B: fpElementGen()} } func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { return reflect.ValueOf( testParams{ common.ProjectivePoint{ X: c.generateFp2(rand), Z: c.generateFp2(rand), }, common.ProjectiveCurveParameters{ A: c.generateFp2(rand), C: c.generateFp2(rand), }, c.generateFp2(rand), }) } func TestOne(t *testing.T) { var tmp common.Fp2 mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { t.Error("Not equal 1") } } func TestFp2ToBytesRoundTrip(t *testing.T) { roundTrips := func(x testParams) bool { xBytes := make([]byte, 2*params.Bytelen) var xPrime common.Fp2 common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) return vartimeEqFp2(&xPrime, &x.ExtElem) } if err := quick.Check(roundTrips, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulDistributesOverAdd(t *testing.T) { mulDistributesOverAdd := func(x, y, z testParams) bool { // Compute t1 = (x+y)*z t1 := new(common.Fp2) add(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = x*z + y*z t2 := new(common.Fp2) t3 := new(common.Fp2) mul(t2, &x.ExtElem, &z.ExtElem) mul(t3, &y.ExtElem, &z.ExtElem) add(t2, t2, t3) return vartimeEqFp2(t1, t2) } if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulIsAssociative(t *testing.T) { isAssociative := func(x, y, z testParams) bool { // Compute t1 = (x*y)*z t1 := new(common.Fp2) mul(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = (y*z)*x t2 := new(common.Fp2) mul(t2, &y.ExtElem, &z.ExtElem) mul(t2, t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(isAssociative, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2SquareMatchesMul(t *testing.T) { sqrMatchesMul := func(x testParams) bool { // Compute t1 = (x*x) t1 := new(common.Fp2) mul(t1, &x.ExtElem, &x.ExtElem) // Compute t2 = x^2 t2 := new(common.Fp2) sqr(t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2Inv(t *testing.T) { inverseIsCorrect := func(x testParams) bool { z := new(common.Fp2) inv(z, &x.ExtElem) // Now z = (1/x), so (z * x) * x == x mul(z, z, &x.ExtElem) mul(z, z, &x.ExtElem) return vartimeEqFp2(z, &x.ExtElem) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 11)} if err := quick.Check(inverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func TestFp2Batch3Inv(t *testing.T) { batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { var x1Inv, x2Inv, x3Inv common.Fp2 inv(&x1Inv, &x1.ExtElem) inv(&x2Inv, &x2.ExtElem) inv(&x3Inv, &x3.ExtElem) var y1, y2, y3 common.Fp2 Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 8)} if err := quick.Check(batchInverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func BenchmarkFp2Mul(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { mul(w, z, z) } } func BenchmarkFp2Inv(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { inv(w, z) } } func BenchmarkFp2Square(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sqr(w, z) } } func BenchmarkFp2Add(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { add(w, z, z) } } func BenchmarkFp2Sub(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sub(w, z, z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/params.go000066400000000000000000000174711454601126700251400ustar00rootroot00000000000000package p503 //go:generate go run ../templates/gen.go P503 import ( "github.com/cloudflare/circl/dh/sidh/internal/common" "golang.org/x/sys/cpu" ) const ( // Number of uint64 limbs used to store field element FpWords = 8 ) // P503 is a prime used by field Fp503 var ( // According to https://github.com/golang/go/issues/28230, // variables referred from the assembly must be in the same package. // HasBMI2 signals support for MULX which is in BMI2 HasBMI2 = cpu.X86.HasBMI2 // HasADXandBMI2 signals support for ADX and BMI2 HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX // P503 is a prime used by field Fp503 P503 = common.Fp{ 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF, 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E, } // P503x2 = 2*p503 - 1 P503x2 = common.Fp{ 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF, 0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C, } // P503p1 = p503 + 1 P503p1 = common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000, 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E, } // P503R2 = (2^512)^2 mod p P503R2 = common.Fp{ 0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC, 0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771, } // P503p1s8 = p503 + 1 left-shifted by 8, assuming little endianness P503p1s8 = common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x085BDA2211E7A0AC, 0x9BF6C87B7E7DAF13, 0x45C6BDDA77A4D01B, 0x4066F541811E1E60, } // P503p1Zeros number of 0 digits in the least significant part of P503+1 P503p1Zeros = 3 // 1*R mod p one = common.Fp2{ A: common.Fp{ 0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000, 0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953, }, } // 1/2 * R mod p half = common.Fp2{ A: common.Fp{ 0x00000000000001FC, 0x0000000000000000, 0x0000000000000000, 0xB000000000000000, 0x3B69BB2464785D2A, 0x36824A2AF0FE9896, 0xF5899F427A94F309, 0x0033B15203C83BB8, }, } // 6*R mod p six = common.Fp2{ A: common.Fp{ 0x00000000000017D8, 0x0000000000000000, 0x0000000000000000, 0xE000000000000000, 0x30B1E6E3A51520FA, 0xB13BC3BF6FFB3992, 0x8045412EEB3E3DED, 0x0069182E2159DBB8, }, } params = common.SidhParams{ ID: common.Fp503, // SIDH public key byte size. PublicKeySize: 378, // SIDH shared secret byte size. SharedSecretSize: 126, A: common.DomainParams{ // The x-coordinate of PA AffineP: common.Fp2{ A: common.Fp{ 0x5D083011589AD893, 0xADFD8D2CB67D0637, 0x330C9AC34FFB6361, 0xF0D47489A2E805A2, 0x27E2789259C6B8DC, 0x63866A2C121931B9, 0x8D4C65A7137DCF44, 0x003A183AE5967B3F, }, B: common.Fp{ 0x7E3541B8C96D1519, 0xD3ADAEEC0D61A26C, 0xC0A2219CE7703DD9, 0xFF3E46658FCDBC52, 0xD5B38DEAE6E196FF, 0x1AAC826364956D58, 0xEC9F4875B9A5F27A, 0x001B0B475AB99843, }, }, // The x-coordinate of QA AffineQ: common.Fp2{ A: common.Fp{ 0x4D83695107D03BAD, 0x221F3299005E2FCF, 0x78E6AE22F30DECF2, 0x6D982DB5111253E4, 0x504C80A8AB4526A8, 0xEFD0C3AA210BB024, 0xCB77483501DC6FCF, 0x001052544A96BDF3, }, B: common.Fp{ 0x0D74FE3402BCAE47, 0xDF5B8CDA832D8AED, 0xB86BCF06E4BD837E, 0x892A2933A0FA1F63, 0x9F88FC67B6CCB461, 0x822926EA9DDA3AC8, 0xEAC8DDE5855425ED, 0x000618FE6DA37A80, }, }, // The x-coordinate of RA = PA-QA AffineR: common.Fp2{ A: common.Fp{ 0x1D9D32D2DC877C17, 0x5517CD8F71D5B02B, 0x395AFB8F6B60C117, 0x3AE31AC85F9098C8, 0x5F5341C198450848, 0xF8C609DBEA435C6A, 0xD832BC7EDC7BA5E4, 0x002AD98AA6968BF5, }, B: common.Fp{ 0xC466CAB0F73C2E5B, 0x7B1817148FB2CF9C, 0x873E87C099E470A0, 0xBB17AC6D17A7BAC1, 0xA146FDCD0F2E2A58, 0x88B311E9CEAB6201, 0x37604CF5C7951757, 0x0006804071C74BF9, }, }, // Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1 SecretBitLen: 250, // SecretBitLen in bytes. SecretByteLen: 32, // 2-torsion group computation strategy IsogenyStrategy: []uint32{ 0x3D, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x1D, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0D, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, }, }, B: common.DomainParams{ // The x-coordinate of PB AffineP: common.Fp2{ A: common.Fp{ 0xDF630FC5FB2468DB, 0xC30C5541C102040E, 0x3CDC9987B76511FC, 0xF54B5A09353D0CDD, 0x3ADBA8E00703C42F, 0x8253F9303DDC95D0, 0x62D30778763ABFD7, 0x001CD00FB581CD55, }, B: common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, }, }, // The x-coordinate of QB AffineQ: common.Fp2{ A: common.Fp{ 0x2E3457A12B429261, 0x311F94E89627DCF8, 0x5B71C98FD1DB73F6, 0x3671DB7DCFC21541, 0xB6D1484C9FE0CF4F, 0x19CD110717356E35, 0xF4F9FB00AC9919DF, 0x0035BC124D38A70B, }, B: common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, }, }, // The x-coordinate of RB = PB - QB AffineR: common.Fp2{ A: common.Fp{ 0x2E08BB99413D2952, 0xD3021467CD088D72, 0x21017AF859752245, 0x26314ED8FFD9DE5C, 0x4AF43C73344B6686, 0xCFA1F91149DF0993, 0xF327A95365587A89, 0x000DBF54E03D3906, }, B: common.Fp{ 0x03E03FF342F5F304, 0x993D604D7B4B6E56, 0x80412F4D9280E71F, 0x0FFDC9EF990B3982, 0xE584E64C51604931, 0x1374F42AC8B0BBD7, 0x07D5BC37DFA41A5F, 0x00396CCFD61FD34C, }, }, // Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1. SecretBitLen: 252, // SecretBitLen in bytes. SecretByteLen: 32, // 3-torsion group computation strategy IsogenyStrategy: []uint32{ 0x47, 0x26, 0x15, 0x0D, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, }, }, OneFp2: one, HalfFp2: half, MsgLen: 24, // SIKEp503 provides 192 bit of classical security ([SIKE], 5.1) KemSize: 24, // ceil(503+7/8) Bytelen: 63, CiphertextSize: 24 + 378, InitCurve: common.ProjectiveCurveParameters{ A: six, C: one, }, } ) func init() { common.Register(common.Fp503, ¶ms) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p503/params_test.go000066400000000000000000000126771454601126700262020ustar00rootroot00000000000000package p503 // Contains values used by tests import ( "testing/quick" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Values computed using Sage var ( // j = 3674553797500778604587777859668542828244523188705960771798425843588160903687122861541242595678107095655647237100722594066610650373491179241544334443939077738732728884873568393760629500307797547379838602108296735640313894560419*i + 3127495302417548295242630557836520229396092255080675419212556702820583041296798857582303163183558315662015469648040494128968509467224910895884358424271180055990446576645240058960358037224785786494172548090318531038910933793845 expectedJ = Fp2{ A: Fp{0x2c441d03b72e27c, 0xf2c6748151dbf84, 0x3a774f6191070e, 0xa7c6212c9c800ba6, 0x23921b5cf09abc27, 0x9e1baefbb3cd4265, 0x8cd6a289f12e10dc, 0x3fa364128cf87e}, B: Fp{0xe7497ac2bf6b0596, 0x629ee01ad23bd039, 0x95ee11587a119fa7, 0x572fb28a24772269, 0x3c00410b6c71567e, 0xe681e83a345f8a34, 0x65d21b1d96bd2d52, 0x7889a47e58901}, } // A = 8752234765512331234913716743014562460822083005386252003333602919474238975785850965349950219277942402920758585086620525443539725921333735154674119646075*i + 6339624979889725406021454983012408976766782818694212228554611573314701271183857175866122275755278397694585249002282183018114967373119429936587424396917 curveA = Fp2{ A: Fp{0xd9816986a543095f, 0xa78cb1d7217bec21, 0x9595dc97b74ea70, 0x9120a1da6b42797d, 0x59ef9d903f74e47c, 0x4c58a4cdc45b6d0b, 0x816d5213aaf7ee6d, 0x3892fee6bb7343}, B: Fp{0x28c5288acbedf11b, 0x2143a438c86f6c68, 0x7cb5c4ae9c4c8e34, 0xb478aea445eed48b, 0x24d5c175776db478, 0x234582f8676c0ebe, 0x56234267b625fb08, 0x2c6e58d84b1192}, } // C = 10458464853790890798085664692909194316288127038910691163573355876336993883402795907795767791362493831987298578966325154262747805705783782806176495638177*i + 7770984753616185271325854825309278833018655051139367603077592443785629339985729818288672809062782315510526648882226172896710704020683893684611137718845 curveC = Fp2{ A: Fp{0xe05948236f2f913b, 0xc45da9ad1219a255, 0x7a568972a32fc1d0, 0x30f00bdd7071c3b1, 0x3b761b8dac2c98bc, 0x760f21b2179737b6, 0x13217e6656a13476, 0x2606b798e685aa}, B: Fp{0x1c0171f78820052e, 0x440b7f7087e57140, 0xe0510c07b31b0e96, 0xd0cf489b2ac4aea9, 0x4fb328f1c1fdf783, 0xb3b4912342951cb7, 0x70a4b64e81961c42, 0x33eed63cf07181}, } // x(P) = 9720237205826983370867050298878715935679372786589878620121159082290288918688002583435964840822877971257659901481591644347943354235932355923042390796255*i + 634577413124118560098123299804750904956499531431297942628887930019161512075536652691244843248133437326050395005054997679717801535474938466995392156605 affineXP = Fp2{ A: Fp{0xb606d954d407faf2, 0x58a1ef6cd213a203, 0x9823b55033e62f7b, 0x59cafc060d5e25a1, 0x529685f1753526fc, 0xc2eac3d219989c7d, 0xc5e30c75dfd343a0, 0x378285adc968a0}, B: Fp{0x6670f36db977b9da, 0xa07e2fdda5e1a7f0, 0xf367a7a722aed87d, 0x6c269e06d595cd10, 0x8379aa6092d87700, 0x57276ce3557ee7ae, 0xac8107bfbcd28993, 0x3d6f98869617a7}, } affineXP2 = Fp2{ A: Fp{0x4e1133c2b3855902, 0x875a775c67597fbb, 0xd17eb74254141abb, 0x1d5a464a4f3391f5, 0x24405c332811d007, 0x7e47e3eb489a7372, 0x65b130dfd9efe605, 0xfa69fac179803}, B: Fp{0x329f5322e1be51ee, 0x9004dca8132ebd6f, 0x7cd87e447ca8a7b6, 0x10a6ec02c38ce69e, 0x8cef2ed7d112ac46, 0x5f385a9fc4b57cd7, 0x68a366354fe7a32e, 0x2223c1455486ac}, } affineXP4 = Fp2{ A: Fp{0x4eb695d34b46be8f, 0xfb5e76c58585f2d2, 0xa41f8aafa6dbb531, 0x4db82f5db5cfd144, 0x14dab0e3200cbba0, 0x430381706a279f81, 0xdf6707a57161f81, 0x44740f17197c3}, B: Fp{0xa2473705cdb6d4e9, 0xfa3cd67b9c15502c, 0xf0928166d0c5cee1, 0x6150aba0c874faaa, 0x6c0b18d6d92f9034, 0xcff71d340fc1e72e, 0x19a47027af917587, 0x25ed4bad443b8f}, } affineXP9 = Fp2{ A: Fp{0x112da30e288217e0, 0x5b336d527320a5f7, 0xbbf4d9403b68e3c6, 0x55eccb31c40b359c, 0x8907129ab69b3203, 0x69cc8c750125a915, 0xa41a38e6f530c0e1, 0xbe68e23af1b8d}, B: Fp{0x472c603765964213, 0xe4e64995b0769754, 0x4515583c74a6dd24, 0xff7c57f5818363a2, 0xbeaeb24662a92177, 0x8a54fa61fbf24c68, 0xa85542049eb45e12, 0x2b54caf655e285}, } // Inputs for testing 3-point-ladder threePointLadderInputs = []ProjectivePoint{ // x(P) { X: Fp2{ A: Fp{0x43941FA9244C059E, 0xD1F337D076941189, 0x6B6A8B3A8763C96A, 0x6DF569708D6C9482, 0x487EE5707A52F4AA, 0xDE396F6E2559689E, 0xE5EE3895A8991469, 0x2B0946695790A8}, B: Fp{0xAB552C0FDAED092E, 0x7DF895E43E7DCB1C, 0x35C700E761920C4B, 0xCC5807DD70DC117A, 0x0884039A5A8DB18A, 0xD04620B3D0738052, 0xA200835605138F10, 0x3FF2E59B2FDC6A}, }, Z: params.OneFp2, }, // x(Q) { X: Fp2{ A: Fp{0x77015826982BA1FD, 0x44024489673471E4, 0x1CAA2A5F4D5DA63B, 0xA183C07E50738C01, 0x8B97782D4E1A0DE6, 0x9B819522FBC38280, 0x0BDA46A937FB7B8A, 0x3B3614305914DF}, B: Fp{0xBF0366E97B3168D9, 0xAA522AC3879CEF0F, 0x0AF5EC975BD035C8, 0x1F26FEE7BBAC165C, 0xA0EE6A637724A6AB, 0xFB52101E36BA3A38, 0xD29CF5E376E17376, 0x1374A50DF57071}, }, Z: params.OneFp2, }, // x(P-Q) { X: Fp2{ A: Fp{0xD99279BBD41EA559, 0x35CF18E72F578214, 0x90473B1DC77F73E8, 0xBFFEA930B25D7F66, 0xFD558EA177B900B2, 0x7CFAD273A782A23E, 0x6B1F610822E0F611, 0x26D2D2EF9619B5}, B: Fp{0x534F83651CBCC75D, 0x591FB4757AED5D08, 0x0B04353D40BED542, 0x829A94703AAC9139, 0x0F9C2E6D7663EB5B, 0x5D2D0F90C283F746, 0x34C872AA12A7676E, 0x0ECDB605FBFA16}, }, Z: params.OneFp2, }, } scalar3Pt = [...]uint8{0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f, 0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f} ) var quickCheckConfig = &quick.Config{ MaxCount: (1 << 15), } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/000077500000000000000000000000001454601126700233215ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/arith_amd64.s000066400000000000000000001341601454601126700256140ustar00rootroot00000000000000// +build amd64,!noasm #include "textflag.h" // p751 + 1 #define P751P1_5 $0xEEB0000000000000 #define P751P1_6 $0xE3EC968549F878A8 #define P751P1_7 $0xDA959B1A13F7CC76 #define P751P1_8 $0x084E9867D6EBE876 #define P751P1_9 $0x8562B5045CB25748 #define P751P1_10 $0x0E12909F97BADC66 #define P751P1_11 $0x00006FE5D541F71C #define P751_0 $0xFFFFFFFFFFFFFFFF #define P751_5 $0xEEAFFFFFFFFFFFFF #define P751_6 $0xE3EC968549F878A8 #define P751_7 $0xDA959B1A13F7CC76 #define P751_8 $0x084E9867D6EBE876 #define P751_9 $0x8562B5045CB25748 #define P751_10 $0x0E12909F97BADC66 #define P751_11 $0x00006FE5D541F71C #define P751X2_0 $0xFFFFFFFFFFFFFFFE #define P751X2_1 $0xFFFFFFFFFFFFFFFF #define P751X2_5 $0xDD5FFFFFFFFFFFFF #define P751X2_6 $0xC7D92D0A93F0F151 #define P751X2_7 $0xB52B363427EF98ED #define P751X2_8 $0x109D30CFADD7D0ED #define P751X2_9 $0x0AC56A08B964AE90 #define P751X2_10 $0x1C25213F2F75B8CD #define P751X2_11 $0x0000DFCBAA83EE38 // The MSR code uses these registers for parameter passing. Keep using // them to avoid significant code changes. This means that when the Go // assembler does something strange, we can diff the machine code // against a different assembler to find out what Go did. #define REG_P1 DI #define REG_P2 SI #define REG_P3 DX TEXT ·modP751(SB), NOSPLIT, $0-8 MOVQ x+0(FP), REG_P1 // Zero AX for later use: XORQ AX, AX // Load p into registers: MOVQ P751_0, R8 // P751_{1,2,3,4} = P751_0, so reuse R8 MOVQ P751_5, R9 MOVQ P751_6, R10 MOVQ P751_7, R11 MOVQ P751_8, R12 MOVQ P751_9, R13 MOVQ P751_10, R14 MOVQ P751_11, R15 // Set x <- x - p SUBQ R8, (REG_P1) SBBQ R8, (8)(REG_P1) SBBQ R8, (16)(REG_P1) SBBQ R8, (24)(REG_P1) SBBQ R8, (32)(REG_P1) SBBQ R9, (40)(REG_P1) SBBQ R10, (48)(REG_P1) SBBQ R11, (56)(REG_P1) SBBQ R12, (64)(REG_P1) SBBQ R13, (72)(REG_P1) SBBQ R14, (80)(REG_P1) SBBQ R15, (88)(REG_P1) // Save carry flag indicating x-p < 0 as a mask in AX SBBQ $0, AX // Conditionally add p to x if x-p < 0 ANDQ AX, R8 ANDQ AX, R9 ANDQ AX, R10 ANDQ AX, R11 ANDQ AX, R12 ANDQ AX, R13 ANDQ AX, R14 ANDQ AX, R15 ADDQ R8, (REG_P1) ADCQ R8, (8)(REG_P1) ADCQ R8, (16)(REG_P1) ADCQ R8, (24)(REG_P1) ADCQ R8, (32)(REG_P1) ADCQ R9, (40)(REG_P1) ADCQ R10, (48)(REG_P1) ADCQ R11, (56)(REG_P1) ADCQ R12, (64)(REG_P1) ADCQ R13, (72)(REG_P1) ADCQ R14, (80)(REG_P1) ADCQ R15, (88)(REG_P1) RET TEXT ·cswapP751(SB), NOSPLIT, $0-17 MOVQ x+0(FP), REG_P1 MOVQ y+8(FP), REG_P2 MOVB choice+16(FP), AL // AL = 0 or 1 MOVBLZX AL, AX // AX = 0 or 1 NEGQ AX // RAX = 0x00..00 or 0xff..ff MOVQ (0*8)(REG_P1), BX // BX = x[0] MOVQ (0*8)(REG_P2), CX // CX = y[0] MOVQ CX, DX // DX = y[0] XORQ BX, DX // DX = y[0] ^ x[0] ANDQ AX, DX // DX = (y[0] ^ x[0]) & mask XORQ DX, BX // BX = (y[0] ^ x[0]) & mask) ^ x[0] = x[0] or y[0] XORQ DX, CX // CX = (y[0] ^ x[0]) & mask) ^ y[0] = y[0] or x[0] MOVQ BX, (0*8)(REG_P1) MOVQ CX, (0*8)(REG_P2) MOVQ (1*8)(REG_P1), BX MOVQ (1*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (1*8)(REG_P1) MOVQ CX, (1*8)(REG_P2) MOVQ (2*8)(REG_P1), BX MOVQ (2*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (2*8)(REG_P1) MOVQ CX, (2*8)(REG_P2) MOVQ (3*8)(REG_P1), BX MOVQ (3*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (3*8)(REG_P1) MOVQ CX, (3*8)(REG_P2) MOVQ (4*8)(REG_P1), BX MOVQ (4*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (4*8)(REG_P1) MOVQ CX, (4*8)(REG_P2) MOVQ (5*8)(REG_P1), BX MOVQ (5*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (5*8)(REG_P1) MOVQ CX, (5*8)(REG_P2) MOVQ (6*8)(REG_P1), BX MOVQ (6*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (6*8)(REG_P1) MOVQ CX, (6*8)(REG_P2) MOVQ (7*8)(REG_P1), BX MOVQ (7*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (7*8)(REG_P1) MOVQ CX, (7*8)(REG_P2) MOVQ (8*8)(REG_P1), BX MOVQ (8*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (8*8)(REG_P1) MOVQ CX, (8*8)(REG_P2) MOVQ (9*8)(REG_P1), BX MOVQ (9*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (9*8)(REG_P1) MOVQ CX, (9*8)(REG_P2) MOVQ (10*8)(REG_P1), BX MOVQ (10*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (10*8)(REG_P1) MOVQ CX, (10*8)(REG_P2) MOVQ (11*8)(REG_P1), BX MOVQ (11*8)(REG_P2), CX MOVQ CX, DX XORQ BX, DX ANDQ AX, DX XORQ DX, BX XORQ DX, CX MOVQ BX, (11*8)(REG_P1) MOVQ CX, (11*8)(REG_P2) RET TEXT ·cmovP751(SB),NOSPLIT,$0-17 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVB choice+16(FP), AL // AL = 0 or 1 MOVBLZX AL, AX // AX = 0 or 1 NEGQ AX // AX = 0x00..00 or 0xff..ff #ifndef CMOV_BLOCK #define CMOV_BLOCK(idx) \ MOVQ (idx*8)(DI), BX \ // BX = x[idx] MOVQ (idx*8)(SI), DX \ // DX = y[idx] XORQ BX, DX \ // DX = y[idx] ^ x[idx] ANDQ AX, DX \ // DX = (y[idx] ^ x[idx]) & mask XORQ DX, BX \ // BX = (y[idx] ^ x[idx]) & mask) ^ x[idx] = x[idx] or y[idx] MOVQ BX, (idx*8)(DI) #endif CMOV_BLOCK(0) CMOV_BLOCK(1) CMOV_BLOCK(2) CMOV_BLOCK(3) CMOV_BLOCK(4) CMOV_BLOCK(5) CMOV_BLOCK(6) CMOV_BLOCK(7) CMOV_BLOCK(8) CMOV_BLOCK(9) CMOV_BLOCK(10) CMOV_BLOCK(11) #ifdef CMOV_BLOCK #undef CMOV_BLOCK #endif RET TEXT ·addP751(SB), NOSPLIT, $0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 MOVQ (REG_P1), R8 MOVQ (8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 MOVQ (64)(REG_P1), CX ADDQ (REG_P2), R8 ADCQ (8)(REG_P2), R9 ADCQ (16)(REG_P2), R10 ADCQ (24)(REG_P2), R11 ADCQ (32)(REG_P2), R12 ADCQ (40)(REG_P2), R13 ADCQ (48)(REG_P2), R14 ADCQ (56)(REG_P2), R15 ADCQ (64)(REG_P2), CX MOVQ (72)(REG_P1), AX ADCQ (72)(REG_P2), AX MOVQ AX, (72)(REG_P3) MOVQ (80)(REG_P1), AX ADCQ (80)(REG_P2), AX MOVQ AX, (80)(REG_P3) MOVQ (88)(REG_P1), AX ADCQ (88)(REG_P2), AX MOVQ AX, (88)(REG_P3) MOVQ P751X2_0, AX SUBQ AX, R8 MOVQ P751X2_1, AX SBBQ AX, R9 SBBQ AX, R10 SBBQ AX, R11 SBBQ AX, R12 MOVQ P751X2_5, AX SBBQ AX, R13 MOVQ P751X2_6, AX SBBQ AX, R14 MOVQ P751X2_7, AX SBBQ AX, R15 MOVQ P751X2_8, AX SBBQ AX, CX MOVQ R8, (REG_P3) MOVQ R9, (8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) MOVQ CX, (64)(REG_P3) MOVQ (72)(REG_P3), R8 MOVQ (80)(REG_P3), R9 MOVQ (88)(REG_P3), R10 MOVQ P751X2_9, AX SBBQ AX, R8 MOVQ P751X2_10, AX SBBQ AX, R9 MOVQ P751X2_11, AX SBBQ AX, R10 MOVQ R8, (72)(REG_P3) MOVQ R9, (80)(REG_P3) MOVQ R10, (88)(REG_P3) MOVQ $0, AX SBBQ $0, AX MOVQ P751X2_0, SI ANDQ AX, SI MOVQ P751X2_1, R8 ANDQ AX, R8 MOVQ P751X2_5, R9 ANDQ AX, R9 MOVQ P751X2_6, R10 ANDQ AX, R10 MOVQ P751X2_7, R11 ANDQ AX, R11 MOVQ P751X2_8, R12 ANDQ AX, R12 MOVQ P751X2_9, R13 ANDQ AX, R13 MOVQ P751X2_10, R14 ANDQ AX, R14 MOVQ P751X2_11, R15 ANDQ AX, R15 MOVQ (REG_P3), AX ADDQ SI, AX MOVQ AX, (REG_P3) MOVQ (8)(REG_P3), AX ADCQ R8, AX MOVQ AX, (8)(REG_P3) MOVQ (16)(REG_P3), AX ADCQ R8, AX MOVQ AX, (16)(REG_P3) MOVQ (24)(REG_P3), AX ADCQ R8, AX MOVQ AX, (24)(REG_P3) MOVQ (32)(REG_P3), AX ADCQ R8, AX MOVQ AX, (32)(REG_P3) MOVQ (40)(REG_P3), AX ADCQ R9, AX MOVQ AX, (40)(REG_P3) MOVQ (48)(REG_P3), AX ADCQ R10, AX MOVQ AX, (48)(REG_P3) MOVQ (56)(REG_P3), AX ADCQ R11, AX MOVQ AX, (56)(REG_P3) MOVQ (64)(REG_P3), AX ADCQ R12, AX MOVQ AX, (64)(REG_P3) MOVQ (72)(REG_P3), AX ADCQ R13, AX MOVQ AX, (72)(REG_P3) MOVQ (80)(REG_P3), AX ADCQ R14, AX MOVQ AX, (80)(REG_P3) MOVQ (88)(REG_P3), AX ADCQ R15, AX MOVQ AX, (88)(REG_P3) RET TEXT ·subP751(SB), NOSPLIT, $0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 MOVQ (REG_P1), R8 MOVQ (8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 MOVQ (64)(REG_P1), CX SUBQ (REG_P2), R8 SBBQ (8)(REG_P2), R9 SBBQ (16)(REG_P2), R10 SBBQ (24)(REG_P2), R11 SBBQ (32)(REG_P2), R12 SBBQ (40)(REG_P2), R13 SBBQ (48)(REG_P2), R14 SBBQ (56)(REG_P2), R15 SBBQ (64)(REG_P2), CX MOVQ R8, (REG_P3) MOVQ R9, (8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) MOVQ CX, (64)(REG_P3) MOVQ (72)(REG_P1), AX SBBQ (72)(REG_P2), AX MOVQ AX, (72)(REG_P3) MOVQ (80)(REG_P1), AX SBBQ (80)(REG_P2), AX MOVQ AX, (80)(REG_P3) MOVQ (88)(REG_P1), AX SBBQ (88)(REG_P2), AX MOVQ AX, (88)(REG_P3) MOVQ $0, AX SBBQ $0, AX MOVQ P751X2_0, SI ANDQ AX, SI MOVQ P751X2_1, R8 ANDQ AX, R8 MOVQ P751X2_5, R9 ANDQ AX, R9 MOVQ P751X2_6, R10 ANDQ AX, R10 MOVQ P751X2_7, R11 ANDQ AX, R11 MOVQ P751X2_8, R12 ANDQ AX, R12 MOVQ P751X2_9, R13 ANDQ AX, R13 MOVQ P751X2_10, R14 ANDQ AX, R14 MOVQ P751X2_11, R15 ANDQ AX, R15 MOVQ (REG_P3), AX ADDQ SI, AX MOVQ AX, (REG_P3) MOVQ (8)(REG_P3), AX ADCQ R8, AX MOVQ AX, (8)(REG_P3) MOVQ (16)(REG_P3), AX ADCQ R8, AX MOVQ AX, (16)(REG_P3) MOVQ (24)(REG_P3), AX ADCQ R8, AX MOVQ AX, (24)(REG_P3) MOVQ (32)(REG_P3), AX ADCQ R8, AX MOVQ AX, (32)(REG_P3) MOVQ (40)(REG_P3), AX ADCQ R9, AX MOVQ AX, (40)(REG_P3) MOVQ (48)(REG_P3), AX ADCQ R10, AX MOVQ AX, (48)(REG_P3) MOVQ (56)(REG_P3), AX ADCQ R11, AX MOVQ AX, (56)(REG_P3) MOVQ (64)(REG_P3), AX ADCQ R12, AX MOVQ AX, (64)(REG_P3) MOVQ (72)(REG_P3), AX ADCQ R13, AX MOVQ AX, (72)(REG_P3) MOVQ (80)(REG_P3), AX ADCQ R14, AX MOVQ AX, (80)(REG_P3) MOVQ (88)(REG_P3), AX ADCQ R15, AX MOVQ AX, (88)(REG_P3) RET TEXT ·mulP751(SB), $96-24 // Here we store the destination in CX instead of in REG_P3 because the // multiplication instructions use DX as an implicit destination // operand: MULQ $REG sets DX:AX <-- AX * $REG. MOVQ z+0(FP), CX MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 XORQ AX, AX MOVQ (48)(REG_P1), R8 MOVQ (56)(REG_P1), R9 MOVQ (64)(REG_P1), R10 MOVQ (72)(REG_P1), R11 MOVQ (80)(REG_P1), R12 MOVQ (88)(REG_P1), R13 ADDQ (REG_P1), R8 ADCQ (8)(REG_P1), R9 ADCQ (16)(REG_P1), R10 ADCQ (24)(REG_P1), R11 ADCQ (32)(REG_P1), R12 ADCQ (40)(REG_P1), R13 MOVQ R8, (CX) MOVQ R9, (8)(CX) MOVQ R10, (16)(CX) MOVQ R11, (24)(CX) MOVQ R12, (32)(CX) MOVQ R13, (40)(CX) SBBQ $0, AX XORQ DX, DX MOVQ (48)(REG_P2), R8 MOVQ (56)(REG_P2), R9 MOVQ (64)(REG_P2), R10 MOVQ (72)(REG_P2), R11 MOVQ (80)(REG_P2), R12 MOVQ (88)(REG_P2), R13 ADDQ (REG_P2), R8 ADCQ (8)(REG_P2), R9 ADCQ (16)(REG_P2), R10 ADCQ (24)(REG_P2), R11 ADCQ (32)(REG_P2), R12 ADCQ (40)(REG_P2), R13 MOVQ R8, (48)(CX) MOVQ R9, (56)(CX) MOVQ R10, (64)(CX) MOVQ R11, (72)(CX) MOVQ R12, (80)(CX) MOVQ R13, (88)(CX) SBBQ $0, DX MOVQ AX, (80)(SP) MOVQ DX, (88)(SP) // (SP[0-8],R10,R8,R9) <- (AH+AL)*(BH+BL) MOVQ (CX), R11 MOVQ R8, AX MULQ R11 MOVQ AX, (SP) // c0 MOVQ DX, R14 XORQ R15, R15 MOVQ R9, AX MULQ R11 XORQ R9, R9 ADDQ AX, R14 ADCQ DX, R9 MOVQ (8)(CX), R12 MOVQ R8, AX MULQ R12 ADDQ AX, R14 MOVQ R14, (8)(SP) // c1 ADCQ DX, R9 ADCQ $0, R15 XORQ R8, R8 MOVQ R10, AX MULQ R11 ADDQ AX, R9 MOVQ (48)(CX), R13 ADCQ DX, R15 ADCQ $0, R8 MOVQ (16)(CX), AX MULQ R13 ADDQ AX, R9 ADCQ DX, R15 MOVQ (56)(CX), AX ADCQ $0, R8 MULQ R12 ADDQ AX, R9 MOVQ R9, (16)(SP) // c2 ADCQ DX, R15 ADCQ $0, R8 XORQ R9, R9 MOVQ (72)(CX), AX MULQ R11 ADDQ AX, R15 ADCQ DX, R8 ADCQ $0, R9 MOVQ (24)(CX), AX MULQ R13 ADDQ AX, R15 ADCQ DX, R8 ADCQ $0, R9 MOVQ R10, AX MULQ R12 ADDQ AX, R15 ADCQ DX, R8 ADCQ $0, R9 MOVQ (16)(CX), R14 MOVQ (56)(CX), AX MULQ R14 ADDQ AX, R15 MOVQ R15, (24)(SP) // c3 ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ (80)(CX), AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (64)(CX), AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (48)(CX), R15 MOVQ (32)(CX), AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (72)(CX), AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (24)(CX), R13 MOVQ (56)(CX), AX MULQ R13 ADDQ AX, R8 MOVQ R8, (32)(SP) // c4 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (88)(CX), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (64)(CX), AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (72)(CX), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (40)(CX), AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (80)(CX), AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (32)(CX), R15 MOVQ (56)(CX), AX MULQ R15 ADDQ AX, R9 MOVQ R9, (40)(SP) // c5 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (64)(CX), AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (88)(CX), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (80)(CX), AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (40)(CX), R11 MOVQ (56)(CX), AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (72)(CX), AX MULQ R13 ADDQ AX, R10 MOVQ R10, (48)(SP) // c6 ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ (88)(CX), AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (64)(CX), AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (80)(CX), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (72)(CX), AX MULQ R15 ADDQ AX, R8 MOVQ R8, (56)(SP) // c7 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (72)(CX), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (80)(CX), AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (88)(CX), AX MULQ R13 ADDQ AX, R9 MOVQ R9, (64)(SP) // c8 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (88)(CX), AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (80)(CX), AX MULQ R11 ADDQ AX, R10 // c9 ADCQ DX, R8 ADCQ $0, R9 MOVQ (88)(CX), AX MULQ R11 ADDQ AX, R8 // c10 ADCQ DX, R9 // c11 MOVQ (88)(SP), AX MOVQ (CX), DX ANDQ AX, R12 ANDQ AX, R14 ANDQ AX, DX ANDQ AX, R13 ANDQ AX, R15 ANDQ AX, R11 MOVQ (48)(SP), AX ADDQ AX, DX MOVQ (56)(SP), AX ADCQ AX, R12 MOVQ (64)(SP), AX ADCQ AX, R14 ADCQ R10, R13 ADCQ R8, R15 ADCQ R9, R11 MOVQ (80)(SP), AX MOVQ DX, (48)(SP) MOVQ R12, (56)(SP) MOVQ R14, (64)(SP) MOVQ R13, (72)(SP) MOVQ R15, (80)(SP) MOVQ R11, (88)(SP) MOVQ (48)(CX), R8 MOVQ (56)(CX), R9 MOVQ (64)(CX), R10 MOVQ (72)(CX), R11 MOVQ (80)(CX), R12 MOVQ (88)(CX), R13 ANDQ AX, R8 ANDQ AX, R9 ANDQ AX, R10 ANDQ AX, R11 ANDQ AX, R12 ANDQ AX, R13 MOVQ (48)(SP), AX ADDQ AX, R8 MOVQ (56)(SP), AX ADCQ AX, R9 MOVQ (64)(SP), AX ADCQ AX, R10 MOVQ (72)(SP), AX ADCQ AX, R11 MOVQ (80)(SP), AX ADCQ AX, R12 MOVQ (88)(SP), AX ADCQ AX, R13 MOVQ R8, (48)(SP) MOVQ R9, (56)(SP) MOVQ R11, (72)(SP) // CX[0-11] <- AL*BL MOVQ (REG_P1), R11 MOVQ (REG_P2), AX MULQ R11 XORQ R9, R9 MOVQ AX, (CX) // c0 MOVQ R10, (64)(SP) MOVQ DX, R8 MOVQ (8)(REG_P2), AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 MOVQ R12, (80)(SP) ADCQ DX, R9 MOVQ (8)(REG_P1), R12 MOVQ (REG_P2), AX MULQ R12 ADDQ AX, R8 MOVQ R8, (8)(CX) // c1 ADCQ DX, R9 MOVQ R13, (88)(SP) ADCQ $0, R10 XORQ R8, R8 MOVQ (16)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (REG_P2), R13 MOVQ (16)(REG_P1), AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (8)(REG_P2), AX MULQ R12 ADDQ AX, R9 MOVQ R9, (16)(CX) // c2 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (24)(REG_P2), AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (24)(REG_P1), AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (16)(REG_P2), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (16)(REG_P1), R14 MOVQ (8)(REG_P2), AX MULQ R14 ADDQ AX, R10 MOVQ R10, (24)(CX) // c3 ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ (32)(REG_P2), AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (16)(REG_P2), AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (32)(REG_P1), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (24)(REG_P2), AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (24)(REG_P1), R13 MOVQ (8)(REG_P2), AX MULQ R13 ADDQ AX, R8 MOVQ R8, (32)(CX) // c4 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (40)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (16)(REG_P2), AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (24)(REG_P2), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (40)(REG_P1), R11 MOVQ (REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (32)(REG_P2), AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (32)(REG_P1), R15 MOVQ (8)(REG_P2), AX MULQ R15 ADDQ AX, R9 MOVQ R9, (40)(CX) //c5 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (16)(REG_P2), AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (40)(REG_P2), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (32)(REG_P2), AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (8)(REG_P2), AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (24)(REG_P2), AX MULQ R13 ADDQ AX, R10 MOVQ R10, (48)(CX) // c6 ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ (40)(REG_P2), AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (16)(REG_P2), AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (32)(REG_P2), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (24)(REG_P2), AX MULQ R15 ADDQ AX, R8 MOVQ R8, (56)(CX) // c7 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (24)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (32)(REG_P2), AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (40)(REG_P2), AX MULQ R13 ADDQ AX, R9 MOVQ R9, (64)(CX) // c8 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (40)(REG_P2), AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (32)(REG_P2), AX MULQ R11 ADDQ AX, R10 MOVQ R10, (72)(CX) // c9 ADCQ DX, R8 ADCQ $0, R9 MOVQ (40)(REG_P2), AX MULQ R11 ADDQ AX, R8 MOVQ R8, (80)(CX) // c10 ADCQ DX, R9 MOVQ R9, (88)(CX) // c11 // CX[12-23] <- AH*BH MOVQ (48)(REG_P1), R11 MOVQ (48)(REG_P2), AX MULQ R11 XORQ R9, R9 MOVQ AX, (96)(CX) // c0 MOVQ DX, R8 MOVQ (56)(REG_P2), AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 ADCQ DX, R9 MOVQ (56)(REG_P1), R12 MOVQ (48)(REG_P2), AX MULQ R12 ADDQ AX, R8 MOVQ R8, (104)(CX) // c1 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (64)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (48)(REG_P2), R13 MOVQ (64)(REG_P1), AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (56)(REG_P2), AX MULQ R12 ADDQ AX, R9 MOVQ R9, (112)(CX) // c2 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (72)(REG_P2), AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (72)(REG_P1), AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (64)(REG_P2), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (64)(REG_P1), R14 MOVQ (56)(REG_P2), AX MULQ R14 ADDQ AX, R10 MOVQ R10, (120)(CX) // c3 ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ (80)(REG_P2), AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (64)(REG_P2), AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (80)(REG_P1), R15 MOVQ R13, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (72)(REG_P2), AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (72)(REG_P1), R13 MOVQ (56)(REG_P2), AX MULQ R13 ADDQ AX, R8 MOVQ R8, (128)(CX) // c4 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (88)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (64)(REG_P2), AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (72)(REG_P2), AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (88)(REG_P1), R11 MOVQ (48)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (80)(REG_P2), AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (56)(REG_P2), AX MULQ R15 ADDQ AX, R9 MOVQ R9, (136)(CX) // c5 ADCQ DX, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ (64)(REG_P2), AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (88)(REG_P2), AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (80)(REG_P2), AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (56)(REG_P2), AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (72)(REG_P2), AX MULQ R13 ADDQ AX, R10 MOVQ R10, (144)(CX) // c6 ADCQ DX, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ (88)(REG_P2), AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (64)(REG_P2), AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (80)(REG_P2), AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (72)(REG_P2), AX MULQ R15 ADDQ AX, R8 MOVQ R8, (152)(CX) // c7 ADCQ DX, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ (72)(REG_P2), AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (80)(REG_P2), AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (88)(REG_P2), AX MULQ R13 ADDQ AX, R9 MOVQ R9, (160)(CX) // c8 ADCQ DX, R10 ADCQ $0, R8 MOVQ (88)(REG_P2), AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 MOVQ (80)(REG_P2), AX MULQ R11 ADDQ AX, R10 MOVQ R10, (168)(CX) // c9 ADCQ DX, R8 MOVQ (88)(REG_P2), AX MULQ R11 ADDQ AX, R8 MOVQ R8, (176)(CX) // c10 ADCQ $0, DX MOVQ DX, (184)(CX) // c11 // [R8-R15,AX,DX,DI,(SP)] <- (AH+AL)*(BH+BL)-AL*BL MOVQ (SP), R8 SUBQ (CX), R8 MOVQ (8)(SP), R9 SBBQ (8)(CX), R9 MOVQ (16)(SP), R10 SBBQ (16)(CX), R10 MOVQ (24)(SP), R11 SBBQ (24)(CX), R11 MOVQ (32)(SP), R12 SBBQ (32)(CX), R12 MOVQ (40)(SP), R13 SBBQ (40)(CX), R13 MOVQ (48)(SP), R14 SBBQ (48)(CX), R14 MOVQ (56)(SP), R15 SBBQ (56)(CX), R15 MOVQ (64)(SP), AX SBBQ (64)(CX), AX MOVQ (72)(SP), DX SBBQ (72)(CX), DX MOVQ (80)(SP), DI SBBQ (80)(CX), DI MOVQ (88)(SP), SI SBBQ (88)(CX), SI MOVQ SI, (SP) // [R8-R15,AX,DX,DI,(SP)] <- (AH+AL)*(BH+BL) - AL*BL - AH*BH MOVQ (96)(CX), SI SUBQ SI, R8 MOVQ (104)(CX), SI SBBQ SI, R9 MOVQ (112)(CX), SI SBBQ SI, R10 MOVQ (120)(CX), SI SBBQ SI, R11 MOVQ (128)(CX), SI SBBQ SI, R12 MOVQ (136)(CX), SI SBBQ SI, R13 MOVQ (144)(CX), SI SBBQ SI, R14 MOVQ (152)(CX), SI SBBQ SI, R15 MOVQ (160)(CX), SI SBBQ SI, AX MOVQ (168)(CX), SI SBBQ SI, DX MOVQ (176)(CX), SI SBBQ SI, DI MOVQ (SP), SI SBBQ (184)(CX), SI // FINAL RESULT ADDQ (48)(CX), R8 MOVQ R8, (48)(CX) ADCQ (56)(CX), R9 MOVQ R9, (56)(CX) ADCQ (64)(CX), R10 MOVQ R10, (64)(CX) ADCQ (72)(CX), R11 MOVQ R11, (72)(CX) ADCQ (80)(CX), R12 MOVQ R12, (80)(CX) ADCQ (88)(CX), R13 MOVQ R13, (88)(CX) ADCQ (96)(CX), R14 MOVQ R14, (96)(CX) ADCQ (104)(CX), R15 MOVQ R15, (104)(CX) ADCQ (112)(CX), AX MOVQ AX, (112)(CX) ADCQ (120)(CX), DX MOVQ DX, (120)(CX) ADCQ (128)(CX), DI MOVQ DI, (128)(CX) ADCQ (136)(CX), SI MOVQ SI, (136)(CX) MOVQ (144)(CX), AX ADCQ $0, AX MOVQ AX, (144)(CX) MOVQ (152)(CX), AX ADCQ $0, AX MOVQ AX, (152)(CX) MOVQ (160)(CX), AX ADCQ $0, AX MOVQ AX, (160)(CX) MOVQ (168)(CX), AX ADCQ $0, AX MOVQ AX, (168)(CX) MOVQ (176)(CX), AX ADCQ $0, AX MOVQ AX, (176)(CX) MOVQ (184)(CX), AX ADCQ $0, AX MOVQ AX, (184)(CX) RET // This multiplies a 256-bit number pointed to by M0 with p751+1. // It is assumed that M1 points to p751+1 stored as a 768-bit Fp751Element. // C points to the place to store the result and should be at least 192 bits. // This should only be used when the BMI2 and ADX instruction set extensions // are available. #define mul256x448bmi2adx(M0, M1, C, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ MOVQ 0+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T1, T0 \ MOVQ M1+48(SB), AX \ MULXQ AX, T3, T2 \ MOVQ T1, 0+C \ // C0_final MOVQ M1+56(SB), AX \ MULXQ AX, T5, T4 \ ADOXQ T3, T0 \ ADOXQ T5, T2 \ MOVQ M1+64(SB), AX \ MULXQ AX, T3, T1 \ ADOXQ T3, T4 \ MOVQ M1+72(SB), AX \ MULXQ AX, T6, T5 \ ADOXQ T6, T1 \ MOVQ M1+80(SB), AX \ MULXQ AX, T7, T3 \ ADOXQ T7, T5 \ MOVQ M1+88(SB), AX \ MULXQ AX, T8, T6 \ ADOXQ T8, T3 \ MOVL $0, AX \ ADOXQ AX, T6 \ \ MOVQ 8+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T7, T8 \ ADCXQ T7, T0 \ MOVQ T0, 8+C \ // C1_final ADCXQ T8, T2 \ MOVQ M1+48(SB), AX \ MULXQ AX, T8, T7 \ ADOXQ T8, T2 \ ADCXQ T7, T4 \ MOVQ M1+56(SB), AX \ MULXQ AX, T8, T0 \ ADOXQ T8, T4 \ ADCXQ T1, T0 \ MOVQ M1+64(SB), AX \ MULXQ AX, T7, T1 \ ADCXQ T5, T1 \ MOVQ M1+72(SB), AX \ MULXQ AX, T8, T5 \ ADCXQ T5, T3 \ MOVQ M1+80(SB), AX \ MULXQ AX, T9, T5 \ ADCXQ T5, T6 \ MOVQ M1+88(SB), AX \ MULXQ AX, DX, T5 \ MOVL $0, AX \ ADCXQ AX, T5 \ \ ADOXQ T7, T0 \ ADOXQ T8, T1 \ ADOXQ T9, T3 \ ADOXQ DX, T6 \ ADOXQ AX, T5 \ \ MOVQ 16+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T7, T8 \ ADCXQ T7, T2 \ MOVQ T2, 16+C \ // C2_final ADCXQ T8, T4 \ MOVQ M1+48(SB), AX \ MULXQ AX, T7, T8 \ ADOXQ T7, T4 \ ADCXQ T8, T0 \ MOVQ M1+56(SB), AX \ MULXQ AX, T8, T2 \ ADOXQ T8, T0 \ ADCXQ T2, T1 \ MOVQ M1+64(SB), AX \ MULXQ AX, T7, T2 \ ADCXQ T2, T3 \ MOVQ M1+72(SB), AX \ MULXQ AX, T8, T2 \ ADCXQ T2, T6 \ MOVQ M1+80(SB), AX \ MULXQ AX, T9, T2 \ ADCXQ T2, T5 \ MOVQ M1+88(SB), AX \ MULXQ AX, DX, T2 \ MOVL $0, AX \ ADCXQ AX, T2 \ \ ADOXQ T7, T1 \ ADOXQ T8, T3 \ ADOXQ T9, T6 \ ADOXQ DX, T5 \ ADOXQ AX, T2 \ \ MOVQ 24+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T7, T8 \ ADCXQ T4, T7 \ ADCXQ T8, T0 \ MOVQ M1+48(SB), AX \ MULXQ AX, T9, T8 \ ADOXQ T9, T0 \ ADCXQ T8, T1 \ MOVQ M1+56(SB), AX \ MULXQ AX, T8, T4 \ ADOXQ T8, T1 \ ADCXQ T4, T3 \ MOVQ M1+64(SB), AX \ MULXQ AX, AX, T4 \ ADCXQ T4, T6 \ ADOXQ AX, T3 \ MOVQ M1+72(SB), AX \ MULXQ AX, T8, T4 \ ADCXQ T4, T5 \ MOVQ M1+80(SB), AX \ MULXQ AX, T9, T4 \ ADCXQ T4, T2 \ MOVQ M1+88(SB), AX \ MULXQ AX, DX, T4 \ MOVL $0, AX \ ADCXQ AX, T4 \ \ ADOXQ T8, T6 \ ADOXQ T9, T5 \ ADOXQ DX, T2 \ ADOXQ AX, T4 // This multiplies a 256-bit number pointed to by M0 with p751+1. // It is assumed that M1 points to p751+1 stored as a 768-bit Fp751Element. // C points to the place to store the result and should be at least 192 bits. // This should only be used when the BMI2 instruction set extension is // available. #define mul256x448bmi2(M0, M1, C, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ MOVQ 0+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T1, T0 \ MOVQ M1+48(SB), AX \ MULXQ AX, T3, T2 \ MOVQ T1, 0+C \ // C0_final MOVQ M1+56(SB), AX \ MULXQ AX, T5, T4 \ ADDQ T3, T0 \ ADCQ T5, T2 \ MOVQ M1+64(SB), AX \ MULXQ AX, T3, T1 \ ADCQ T3, T4 \ MOVQ M1+72(SB), AX \ MULXQ AX, T6, T5 \ ADCQ T6, T1 \ MOVQ M1+80(SB), AX \ MULXQ AX, T7, T3 \ ADCQ T7, T5 \ MOVQ M1+88(SB), AX \ MULXQ AX, T8, T6 \ ADCQ T8, T3 \ ADCQ $0, T6 \ \ MOVQ 8+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T7, T8 \ ADDQ T7, T0 \ MOVQ T0, 8+C \ // C1_final ADCQ T8, T2 \ MOVQ M1+48(SB), AX \ MULXQ AX, T8, T7 \ MOVQ T8, 32+C \ ADCQ T7, T4 \ MOVQ M1+56(SB), AX \ MULXQ AX, T8, T0 \ MOVQ T8, 40+C \ ADCQ T1, T0 \ MOVQ M1+64(SB), AX \ MULXQ AX, T7, T1 \ ADCQ T5, T1 \ MOVQ M1+72(SB), AX \ MULXQ AX, T8, T5 \ ADCQ T5, T3 \ MOVQ M1+80(SB), AX \ MULXQ AX, T9, T5 \ ADCQ T5, T6 \ MOVQ M1+88(SB), AX \ MULXQ AX, DX, T5 \ ADCQ $0, T5 \ \ XORQ AX, AX \ ADDQ 32+C, T2 \ ADCQ 40+C, T4 \ ADCQ T7, T0 \ ADCQ T8, T1 \ ADCQ T9, T3 \ ADCQ DX, T6 \ ADCQ AX, T5 \ \ MOVQ 16+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T7, T8 \ ADDQ T7, T2 \ MOVQ T2, 16+C \ // C2_final ADCQ T8, T4 \ MOVQ M1+48(SB), AX \ MULXQ AX, T7, T8 \ MOVQ T7, 32+C \ ADCQ T8, T0 \ MOVQ M1+56(SB), AX \ MULXQ AX, T8, T2 \ MOVQ T8, 40+C \ ADCQ T2, T1 \ MOVQ M1+64(SB), AX \ MULXQ AX, T7, T2 \ ADCQ T2, T3 \ MOVQ M1+72(SB), AX \ MULXQ AX, T8, T2 \ ADCQ T2, T6 \ MOVQ M1+80(SB), AX \ MULXQ AX, T9, T2 \ ADCQ T2, T5 \ MOVQ M1+88(SB), AX \ MULXQ AX, DX, T2 \ ADCQ $0, T2 \ \ XORQ AX, AX \ ADDQ 32+C, T4 \ ADCQ 40+C, T0 \ ADCQ T7, T1 \ ADCQ T8, T3 \ ADCQ T9, T6 \ ADCQ DX, T5 \ ADCQ AX, T2 \ \ MOVQ 24+M0, DX \ MOVQ M1+40(SB), AX \ MULXQ AX, T7, T8 \ ADDQ T4, T7 \ MOVQ T7, 8(SP) /* push T7 */ \ ADCQ T8, T0 \ MOVQ M1+48(SB), AX \ MULXQ AX, T9, T8 \ MOVQ T9, 32+C \ ADCQ T8, T1 \ MOVQ M1+56(SB), AX \ MULXQ AX, T8, T4 \ MOVQ T8, 40+C \ ADCQ T4, T3 \ MOVQ M1+64(SB), AX \ MULXQ AX, T7, T4 \ ADCQ T4, T6 \ MOVQ M1+72(SB), AX \ MULXQ AX, T8, T4 \ ADCQ T4, T5 \ MOVQ M1+80(SB), AX \ MULXQ AX, T9, T4 \ ADCQ T4, T2 \ MOVQ M1+88(SB), AX \ MULXQ AX, DX, T4 \ ADCQ $0, T4 \ \ XORQ AX, AX \ ADDQ 32+C, T0 \ ADCQ 40+C, T1 \ ADCQ T7, T3 \ ADCQ T8, T6 \ ADCQ T9, T5 \ ADCQ DX, T2 \ ADCQ AX, T4 \ MOVQ 8(SP), T7 /* pop T7 */ // Template for calculating the Montgomery reduction algorithm described in // section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. Template must be // customized with schoolbook multiplication for 256 x 448-bit number. // This macro reuses memory of IN value and *changes* it. Smashes registers // R[8-15], AX, BX, CX, DX, BP. // Input: // * M0: 1536-bit number to be reduced // * C : either mul256x448bmi2 or mul256x448bmi2adx // Output: OUT 768-bit #define REDC(C, M0, MULS) \ \ // a[0-3] x p751p1_nz --> result: [reg_p2+48], [reg_p2+56], [reg_p2+64], and rbp, r8:r14 MULS(M0, ·P751p1, 48+C, R8, R9, R13, R10, R14, R12, R11, BP, BX, CX) \ XORQ R15, R15 \ MOVQ 48+C, AX \ MOVQ 56+C, DX \ MOVQ 64+C, BX \ ADDQ 40+M0, AX \ ADCQ 48+M0, DX \ ADCQ 56+M0, BX \ MOVQ AX, 40+M0 \ MOVQ DX, 48+M0 \ MOVQ BX, 56+M0 \ ADCQ 64+M0, BP \ ADCQ 72+M0, R8 \ ADCQ 80+M0, R9 \ ADCQ 88+M0, R10 \ ADCQ 96+M0, R11 \ ADCQ 104+M0, R12 \ ADCQ 112+M0, R13 \ ADCQ 120+M0, R14 \ ADCQ 128+M0, R15 \ MOVQ BP, 64+M0 \ MOVQ R8, 72+M0 \ MOVQ R9, 80+M0 \ MOVQ R10, 88+M0 \ MOVQ R11, 96+M0 \ MOVQ R12, 104+M0 \ MOVQ R13, 112+M0 \ MOVQ R14, 120+M0 \ MOVQ R15, 128+M0 \ MOVQ 136+M0, R8 \ MOVQ 144+M0, R9 \ MOVQ 152+M0, R10 \ MOVQ 160+M0, R11 \ MOVQ 168+M0, R12 \ MOVQ 176+M0, R13 \ MOVQ 184+M0, R14 \ ADCQ $0, R8 \ ADCQ $0, R9 \ ADCQ $0, R10 \ ADCQ $0, R11 \ ADCQ $0, R12 \ ADCQ $0, R13 \ ADCQ $0, R14 \ MOVQ R8, 136+M0 \ MOVQ R9, 144+M0 \ MOVQ R10, 152+M0 \ MOVQ R11, 160+M0 \ MOVQ R12, 168+M0 \ MOVQ R13, 176+M0 \ MOVQ R14, 184+M0 \ \ // a[4-7] x p751p1_nz --> result: [reg_p2+48], [reg_p2+56], [reg_p2+64], and rbp, r8:r14 MULS(32+M0, ·P751p1, 48+C, R8, R9, R13, R10, R14, R12, R11, BP, BX, CX) \ XORQ R15, R15 \ MOVQ 48+C, AX \ MOVQ 56+C, DX \ MOVQ 64+C, BX \ ADDQ 72+M0, AX \ ADCQ 80+M0, DX \ ADCQ 88+M0, BX \ MOVQ AX, 72+M0 \ MOVQ DX, 80+M0 \ MOVQ BX, 88+M0 \ ADCQ 96+M0, BP \ ADCQ 104+M0, R8 \ ADCQ 112+M0, R9 \ ADCQ 120+M0, R10 \ ADCQ 128+M0, R11 \ ADCQ 136+M0, R12 \ ADCQ 144+M0, R13 \ ADCQ 152+M0, R14 \ ADCQ 160+M0, R15 \ MOVQ BP, 0+C \ // Final result c0 MOVQ R8, 104+M0 \ MOVQ R9, 112+M0 \ MOVQ R10, 120+M0 \ MOVQ R11, 128+M0 \ MOVQ R12, 136+M0 \ MOVQ R13, 144+M0 \ MOVQ R14, 152+M0 \ MOVQ R15, 160+M0 \ MOVQ 168+M0, R12 \ MOVQ 176+M0, R13 \ MOVQ 184+M0, R14 \ ADCQ $0, R12 \ ADCQ $0, R13 \ ADCQ $0, R14 \ MOVQ R12, 168+M0 \ MOVQ R13, 176+M0 \ MOVQ R14, 184+M0 \ \ // a[8-11] x p751p1_nz --> result: [reg_p2+48], [reg_p2+56], [reg_p2+64], and rbp, r8:r14 MULS(64+M0, ·P751p1, 48+C, R8, R9, R13, R10, R14, R12, R11, BP, BX, CX) \ MOVQ 48+C, AX \ // Final result c1:c11 MOVQ 56+C, DX \ MOVQ 64+C, BX \ ADDQ 104+M0, AX \ ADCQ 112+M0, DX \ ADCQ 120+M0, BX \ MOVQ AX, 8+C \ MOVQ DX, 16+C \ MOVQ BX, 24+C \ ADCQ 128+M0, BP \ ADCQ 136+M0, R8 \ ADCQ 144+M0, R9 \ ADCQ 152+M0, R10 \ ADCQ 160+M0, R11 \ ADCQ 168+M0, R12 \ ADCQ 176+M0, R13 \ ADCQ 184+M0, R14 \ MOVQ BP, 32+C \ MOVQ R8, 40+C \ MOVQ R9, 48+C \ MOVQ R10, 56+C \ MOVQ R11, 64+C \ MOVQ R12, 72+C \ MOVQ R13, 80+C \ MOVQ R14, 88+C TEXT ·rdcP751(SB), $16-16 MOVQ z+0(FP), REG_P2 MOVQ x+8(FP), REG_P1 // Check whether to use optimized implementation CMPB ·HasADXandBMI2(SB), $1 JE redc_with_mulx_adcx_adox CMPB ·HasBMI2(SB), $1 JE redc_with_mulx MOVQ (REG_P1), R11 MOVQ P751P1_5, AX MULQ R11 XORQ R8, R8 ADDQ (40)(REG_P1), AX MOVQ AX, (40)(REG_P2) // Z5 ADCQ DX, R8 XORQ R9, R9 MOVQ P751P1_6, AX MULQ R11 XORQ R10, R10 ADDQ AX, R8 ADCQ DX, R9 MOVQ (8)(REG_P1), R12 MOVQ P751P1_5, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (48)(REG_P1), R8 MOVQ R8, (48)(REG_P2) // Z6 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P751P1_7, AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_6, AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (16)(REG_P1), R13 MOVQ P751P1_5, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (56)(REG_P1), R9 MOVQ R9, (56)(REG_P2) // Z7 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P751P1_8, AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_7, AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_6, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (24)(REG_P1), R14 MOVQ P751P1_5, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (64)(REG_P1), R10 MOVQ R10, (64)(REG_P2) // Z8 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P751P1_9, AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_8, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_7, AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_6, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (32)(REG_P1), R15 MOVQ P751P1_5, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (72)(REG_P1), R8 MOVQ R8, (72)(REG_P2) // Z9 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P751P1_10, AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_9, AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_8, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_7, AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_6, AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (40)(REG_P2), CX MOVQ P751P1_5, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (80)(REG_P1), R9 MOVQ R9, (80)(REG_P2) // Z10 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P751P1_11, AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_10, AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_9, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_8, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_7, AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_6, AX MULQ CX ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (48)(REG_P2), R11 MOVQ P751P1_5, AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (88)(REG_P1), R10 MOVQ R10, (88)(REG_P2) // Z11 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P751P1_11, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_10, AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_9, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_8, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_7, AX MULQ CX ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_6, AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (56)(REG_P2), R12 MOVQ P751P1_5, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (96)(REG_P1), R8 MOVQ R8, (REG_P2) // Z0 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P751P1_11, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_10, AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_9, AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_8, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_7, AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_6, AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (64)(REG_P2), R13 MOVQ P751P1_5, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (104)(REG_P1), R9 MOVQ R9, (8)(REG_P2) // Z1 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P751P1_11, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_10, AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_9, AX MULQ CX ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_8, AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_7, AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_6, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ (72)(REG_P2), R14 MOVQ P751P1_5, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (112)(REG_P1), R10 MOVQ R10, (16)(REG_P2) // Z2 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P751P1_11, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_10, AX MULQ CX ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_9, AX MULQ R11 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_8, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_7, AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_6, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ (80)(REG_P2), R15 MOVQ P751P1_5, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (120)(REG_P1), R8 MOVQ R8, (24)(REG_P2) // Z3 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P751P1_11, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_10, AX MULQ R11 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_9, AX MULQ R12 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_8, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_7, AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_6, AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ (88)(REG_P2), CX MOVQ P751P1_5, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (128)(REG_P1), R9 MOVQ R9, (32)(REG_P2) // Z4 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P751P1_11, AX MULQ R11 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_10, AX MULQ R12 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_9, AX MULQ R13 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_8, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_7, AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_6, AX MULQ CX ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (136)(REG_P1), R10 MOVQ R10, (40)(REG_P2) // Z5 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P751P1_11, AX MULQ R12 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_10, AX MULQ R13 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_9, AX MULQ R14 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_8, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_7, AX MULQ CX ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (144)(REG_P1), R8 MOVQ R8, (48)(REG_P2) // Z6 ADCQ $0, R9 ADCQ $0, R10 XORQ R8, R8 MOVQ P751P1_11, AX MULQ R13 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_10, AX MULQ R14 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_9, AX MULQ R15 ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 MOVQ P751P1_8, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADCQ $0, R8 ADDQ (152)(REG_P1), R9 MOVQ R9, (56)(REG_P2) // Z7 ADCQ $0, R10 ADCQ $0, R8 XORQ R9, R9 MOVQ P751P1_11, AX MULQ R14 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_10, AX MULQ R15 ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 MOVQ P751P1_9, AX MULQ CX ADDQ AX, R10 ADCQ DX, R8 ADCQ $0, R9 ADDQ (160)(REG_P1), R10 MOVQ R10, (64)(REG_P2) // Z8 ADCQ $0, R8 ADCQ $0, R9 XORQ R10, R10 MOVQ P751P1_11, AX MULQ R15 ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 MOVQ P751P1_10, AX MULQ CX ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, R10 ADDQ (168)(REG_P1), R8 // Z9 MOVQ R8, (72)(REG_P2) // Z9 ADCQ $0, R9 ADCQ $0, R10 MOVQ P751P1_11, AX MULQ CX ADDQ AX, R9 ADCQ DX, R10 ADDQ (176)(REG_P1), R9 // Z10 MOVQ R9, (80)(REG_P2) // Z10 ADCQ $0, R10 ADDQ (184)(REG_P1), R10 // Z11 MOVQ R10, (88)(REG_P2) // Z11 RET redc_with_mulx_adcx_adox: // This implements the Montgomery reduction algorithm described in // section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. // This assumes that the BMI2 and ADX instruction set extensions are available. MOVQ BP, 0(SP) // push: BP is Callee-save. REDC(0(REG_P2), 0(REG_P1), mul256x448bmi2adx) MOVQ 0(SP), BP // pop: BP is Callee-save. RET redc_with_mulx: // This implements the Montgomery reduction algorithm described in // section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. // This assumes that the BMI2 instruction set extension is available. MOVQ BP, 0(SP) // push: BP is Callee-save. REDC(0(REG_P2), 0(REG_P1), mul256x448bmi2) MOVQ 0(SP), BP // pop: BP is Callee-save. RET TEXT ·adlP751(SB), NOSPLIT, $0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 MOVQ (REG_P1), R8 MOVQ (8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 MOVQ (64)(REG_P1), AX MOVQ (72)(REG_P1), BX MOVQ (80)(REG_P1), CX ADDQ (REG_P2), R8 ADCQ (8)(REG_P2), R9 ADCQ (16)(REG_P2), R10 ADCQ (24)(REG_P2), R11 ADCQ (32)(REG_P2), R12 ADCQ (40)(REG_P2), R13 ADCQ (48)(REG_P2), R14 ADCQ (56)(REG_P2), R15 ADCQ (64)(REG_P2), AX ADCQ (72)(REG_P2), BX ADCQ (80)(REG_P2), CX MOVQ R8, (REG_P3) MOVQ R9, (8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) MOVQ AX, (64)(REG_P3) MOVQ BX, (72)(REG_P3) MOVQ CX, (80)(REG_P3) MOVQ (88)(REG_P1), AX ADCQ (88)(REG_P2), AX MOVQ AX, (88)(REG_P3) MOVQ (96)(REG_P1), R8 MOVQ (104)(REG_P1), R9 MOVQ (112)(REG_P1), R10 MOVQ (120)(REG_P1), R11 MOVQ (128)(REG_P1), R12 MOVQ (136)(REG_P1), R13 MOVQ (144)(REG_P1), R14 MOVQ (152)(REG_P1), R15 MOVQ (160)(REG_P1), AX MOVQ (168)(REG_P1), BX MOVQ (176)(REG_P1), CX MOVQ (184)(REG_P1), DI ADCQ (96)(REG_P2), R8 ADCQ (104)(REG_P2), R9 ADCQ (112)(REG_P2), R10 ADCQ (120)(REG_P2), R11 ADCQ (128)(REG_P2), R12 ADCQ (136)(REG_P2), R13 ADCQ (144)(REG_P2), R14 ADCQ (152)(REG_P2), R15 ADCQ (160)(REG_P2), AX ADCQ (168)(REG_P2), BX ADCQ (176)(REG_P2), CX ADCQ (184)(REG_P2), DI MOVQ R8, (96)(REG_P3) MOVQ R9, (104)(REG_P3) MOVQ R10, (112)(REG_P3) MOVQ R11, (120)(REG_P3) MOVQ R12, (128)(REG_P3) MOVQ R13, (136)(REG_P3) MOVQ R14, (144)(REG_P3) MOVQ R15, (152)(REG_P3) MOVQ AX, (160)(REG_P3) MOVQ BX, (168)(REG_P3) MOVQ CX, (176)(REG_P3) MOVQ DI, (184)(REG_P3) RET TEXT ·sulP751(SB), NOSPLIT, $0-24 MOVQ z+0(FP), REG_P3 MOVQ x+8(FP), REG_P1 MOVQ y+16(FP), REG_P2 MOVQ (REG_P1), R8 MOVQ (8)(REG_P1), R9 MOVQ (16)(REG_P1), R10 MOVQ (24)(REG_P1), R11 MOVQ (32)(REG_P1), R12 MOVQ (40)(REG_P1), R13 MOVQ (48)(REG_P1), R14 MOVQ (56)(REG_P1), R15 MOVQ (64)(REG_P1), AX MOVQ (72)(REG_P1), BX MOVQ (80)(REG_P1), CX SUBQ (REG_P2), R8 SBBQ (8)(REG_P2), R9 SBBQ (16)(REG_P2), R10 SBBQ (24)(REG_P2), R11 SBBQ (32)(REG_P2), R12 SBBQ (40)(REG_P2), R13 SBBQ (48)(REG_P2), R14 SBBQ (56)(REG_P2), R15 SBBQ (64)(REG_P2), AX SBBQ (72)(REG_P2), BX SBBQ (80)(REG_P2), CX MOVQ R8, (REG_P3) MOVQ R9, (8)(REG_P3) MOVQ R10, (16)(REG_P3) MOVQ R11, (24)(REG_P3) MOVQ R12, (32)(REG_P3) MOVQ R13, (40)(REG_P3) MOVQ R14, (48)(REG_P3) MOVQ R15, (56)(REG_P3) MOVQ AX, (64)(REG_P3) MOVQ BX, (72)(REG_P3) MOVQ CX, (80)(REG_P3) MOVQ (88)(REG_P1), AX SBBQ (88)(REG_P2), AX MOVQ AX, (88)(REG_P3) MOVQ (96)(REG_P1), R8 MOVQ (104)(REG_P1), R9 MOVQ (112)(REG_P1), R10 MOVQ (120)(REG_P1), R11 MOVQ (128)(REG_P1), R12 MOVQ (136)(REG_P1), R13 MOVQ (144)(REG_P1), R14 MOVQ (152)(REG_P1), R15 MOVQ (160)(REG_P1), AX MOVQ (168)(REG_P1), BX MOVQ (176)(REG_P1), CX MOVQ (184)(REG_P1), DI SBBQ (96)(REG_P2), R8 SBBQ (104)(REG_P2), R9 SBBQ (112)(REG_P2), R10 SBBQ (120)(REG_P2), R11 SBBQ (128)(REG_P2), R12 SBBQ (136)(REG_P2), R13 SBBQ (144)(REG_P2), R14 SBBQ (152)(REG_P2), R15 SBBQ (160)(REG_P2), AX SBBQ (168)(REG_P2), BX SBBQ (176)(REG_P2), CX SBBQ (184)(REG_P2), DI MOVQ R8, (96)(REG_P3) MOVQ R9, (104)(REG_P3) MOVQ R10, (112)(REG_P3) MOVQ R11, (120)(REG_P3) MOVQ R12, (128)(REG_P3) MOVQ R13, (136)(REG_P3) MOVQ R14, (144)(REG_P3) MOVQ R15, (152)(REG_P3) MOVQ AX, (160)(REG_P3) MOVQ BX, (168)(REG_P3) MOVQ CX, (176)(REG_P3) MOVQ DI, (184)(REG_P3) // Now the carry flag is 1 if x-y < 0. If so, add p*2^768. MOVQ $0, AX SBBQ $0, AX // Load p into registers: MOVQ P751_0, R8 // P751_{1,2,3,4} = P751_0, so reuse R8 MOVQ P751_5, R9 MOVQ P751_6, R10 MOVQ P751_7, R11 MOVQ P751_8, R12 MOVQ P751_9, R13 MOVQ P751_10, R14 MOVQ P751_11, R15 ANDQ AX, R8 ANDQ AX, R9 ANDQ AX, R10 ANDQ AX, R11 ANDQ AX, R12 ANDQ AX, R13 ANDQ AX, R14 ANDQ AX, R15 ADDQ R8, (96 )(REG_P3) ADCQ R8, (96+ 8)(REG_P3) ADCQ R8, (96+16)(REG_P3) ADCQ R8, (96+24)(REG_P3) ADCQ R8, (96+32)(REG_P3) ADCQ R9, (96+40)(REG_P3) ADCQ R10, (96+48)(REG_P3) ADCQ R11, (96+56)(REG_P3) ADCQ R12, (96+64)(REG_P3) ADCQ R13, (96+72)(REG_P3) ADCQ R14, (96+80)(REG_P3) ADCQ R15, (96+88)(REG_P3) RET golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/arith_amd64_test.go000066400000000000000000000077641454601126700270270ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build amd64 && !noasm // +build amd64,!noasm package p751 import ( "reflect" "testing" "testing/quick" "github.com/cloudflare/circl/dh/sidh/internal/common" "golang.org/x/sys/cpu" ) type OptimFlag uint const ( // Indicates that optimisation which uses MUL instruction should be used kUse_MUL OptimFlag = 1 << 0 // Indicates that optimisation which uses MULX instruction should be used kUse_MULX = 1 << 1 // Indicates that optimisation which uses MULX, ADOX and ADCX instructions should be used kUse_MULXandADxX = 1 << 2 ) func resetCpuFeatures() { HasBMI2 = cpu.X86.HasBMI2 HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX } // Utility function used for testing Mul implementations. Tests caller provided // mulFunc against mul() func testMul(t *testing.T, f1, f2 OptimFlag) { doMulTest := func(multiplier, multiplicant common.Fp) bool { defer resetCpuFeatures() var resMulRef, resMulOptim common.FpX2 // Compute multiplier*multiplicant with first implementation HasBMI2 = (kUse_MULX & f1) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX mulP751(&resMulOptim, &multiplier, &multiplicant) // Compute multiplier*multiplicant with second implementation HasBMI2 = (kUse_MULX & f2) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX mulP751(&resMulRef, &multiplier, &multiplicant) // Compare results return reflect.DeepEqual(resMulRef, resMulOptim) } if err := quick.Check(doMulTest, quickCheckConfig); err != nil { t.Error(err) } } // Utility function used for testing REDC implementations. Tests caller provided // redcFunc against redc() func testRedc(t *testing.T, f1, f2 OptimFlag) { doRedcTest := func(aRR common.FpX2) bool { defer resetCpuFeatures() var resRedcF1, resRedcF2 common.Fp aRRcpy := aRR // Compute redc with first implementation HasBMI2 = (kUse_MULX & f1) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX rdcP751(&resRedcF1, &aRR) // Compute redc with second implementation HasBMI2 = (kUse_MULX & f2) == kUse_MULX HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX rdcP751(&resRedcF2, &aRRcpy) // Compare results return reflect.DeepEqual(resRedcF2, resRedcF1) } if err := quick.Check(doRedcTest, quickCheckConfig); err != nil { t.Error(err) } } // Ensures correctness of implementation of mul operation which uses MULX func TestMulWithMULX(t *testing.T) { defer resetCpuFeatures() if !HasBMI2 { t.Skip("MULX not supported by the platform") } testMul(t, kUse_MULX, kUse_MUL) } // Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX func TestMulWithMULXADxX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testMul(t, kUse_MULXandADxX, kUse_MUL) } // Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX func TestMulWithMULXADxXAgainstMULX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testMul(t, kUse_MULX, kUse_MULXandADxX) } // Ensures correctness of Montgomery reduction implementation which uses MULX func TestRedcWithMULX(t *testing.T) { defer resetCpuFeatures() if !HasBMI2 { t.Skip("MULX not supported by the platform") } testRedc(t, kUse_MULX, kUse_MUL) } // Ensures correctness of Montgomery reduction implementation which uses MULX // and ADCX/ADOX. func TestRedcWithMULXADxX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testRedc(t, kUse_MULXandADxX, kUse_MUL) } // Ensures correctness of Montgomery reduction implementation which uses MULX // and ADCX/ADOX. func TestRedcWithMULXADxXAgainstMULX(t *testing.T) { defer resetCpuFeatures() if !HasADXandBMI2 { t.Skip("MULX, ADCX and ADOX not supported by the platform") } testRedc(t, kUse_MULXandADxX, kUse_MULX) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/arith_arm64.s000066400000000000000000000631171454601126700256350ustar00rootroot00000000000000// +build arm64,!noasm #include "textflag.h" TEXT ·cmovP751(SB), NOSPLIT, $0-17 MOVD x+0(FP), R0 MOVD y+8(FP), R1 MOVB choice+16(FP), R2 // Set flags // If choice is not 0 or 1, this implementation will swap completely CMP $0, R2 LDP 0(R0), (R3, R4) LDP 0(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 0(R0) LDP 16(R0), (R3, R4) LDP 16(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 16(R0) LDP 32(R0), (R3, R4) LDP 32(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 32(R0) LDP 48(R0), (R3, R4) LDP 48(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 48(R0) LDP 64(R0), (R3, R4) LDP 64(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 64(R0) LDP 80(R0), (R3, R4) LDP 80(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 80(R0) RET TEXT ·cswapP751(SB), NOSPLIT, $0-17 MOVD x+0(FP), R0 MOVD y+8(FP), R1 MOVB choice+16(FP), R2 // Set flags // If choice is not 0 or 1, this implementation will swap completely CMP $0, R2 LDP 0(R0), (R3, R4) LDP 0(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 0(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 0(R1) LDP 16(R0), (R3, R4) LDP 16(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 16(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 16(R1) LDP 32(R0), (R3, R4) LDP 32(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 32(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 32(R1) LDP 48(R0), (R3, R4) LDP 48(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 48(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 48(R1) LDP 64(R0), (R3, R4) LDP 64(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 64(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 64(R1) LDP 80(R0), (R3, R4) LDP 80(R1), (R5, R6) CSEL EQ, R3, R5, R7 CSEL EQ, R4, R6, R8 STP (R7, R8), 80(R0) CSEL NE, R3, R5, R9 CSEL NE, R4, R6, R10 STP (R9, R10), 80(R1) RET TEXT ·addP751(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 // Load first summand into R3-R14 // Add first summand and second summand and store result in R3-R14 LDP 0(R0), (R3, R4) LDP 0(R1), (R15, R16) LDP 16(R0), (R5, R6) LDP 16(R1), (R17, R19) ADDS R15, R3 ADCS R16, R4 ADCS R17, R5 ADCS R19, R6 LDP 32(R0), (R7, R8) LDP 32(R1), (R15, R16) LDP 48(R0), (R9, R10) LDP 48(R1), (R17, R19) ADCS R15, R7 ADCS R16, R8 ADCS R17, R9 ADCS R19, R10 LDP 64(R0), (R11, R12) LDP 64(R1), (R15, R16) LDP 80(R0), (R13, R14) LDP 80(R1), (R17, R19) ADCS R15, R11 ADCS R16, R12 ADCS R17, R13 ADC R19, R14 // Subtract 2 * p751 in R15-R24 from the result in R3-R14 LDP ·P751x2+0(SB), (R15, R16) SUBS R15, R3 SBCS R16, R4 LDP ·P751x2+40(SB), (R17, R19) SBCS R16, R5 SBCS R16, R6 SBCS R16, R7 LDP ·P751x2+56(SB), (R20, R21) SBCS R17, R8 SBCS R19, R9 LDP ·P751x2+72(SB), (R22, R23) SBCS R20, R10 SBCS R21, R11 MOVD ·P751x2+88(SB), R24 SBCS R22, R12 SBCS R23, R13 SBCS R24, R14 SBC ZR, ZR, R25 // If x + y - 2 * p751 < 0, R25 is 1 and 2 * p751 should be added AND R25, R15 AND R25, R16 AND R25, R17 AND R25, R19 AND R25, R20 AND R25, R21 AND R25, R22 AND R25, R23 AND R25, R24 ADDS R15, R3 ADCS R16, R4 STP (R3, R4), 0(R2) ADCS R16, R5 ADCS R16, R6 STP (R5, R6), 16(R2) ADCS R16, R7 ADCS R17, R8 STP (R7, R8), 32(R2) ADCS R19, R9 ADCS R20, R10 STP (R9, R10), 48(R2) ADCS R21, R11 ADCS R22, R12 STP (R11, R12), 64(R2) ADCS R23, R13 ADC R24, R14 STP (R13, R14), 80(R2) RET TEXT ·subP751(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 // Load x into R3-R14 // Subtract y from x and store result in R3-R14 LDP 0(R0), (R3, R4) LDP 0(R1), (R15, R16) LDP 16(R0), (R5, R6) LDP 16(R1), (R17, R19) SUBS R15, R3 SBCS R16, R4 SBCS R17, R5 SBCS R19, R6 LDP 32(R0), (R7, R8) LDP 32(R1), (R15, R16) LDP 48(R0), (R9, R10) LDP 48(R1), (R17, R19) SBCS R15, R7 SBCS R16, R8 SBCS R17, R9 SBCS R19, R10 LDP 64(R0), (R11, R12) LDP 64(R1), (R15, R16) LDP 80(R0), (R13, R14) LDP 80(R1), (R17, R19) SBCS R15, R11 SBCS R16, R12 SBCS R17, R13 SBCS R19, R14 SBC ZR, ZR, R15 // If x - y < 0, R15 is 1 and 2 * p751 should be added LDP ·P751x2+0(SB), (R16, R17) AND R15, R16 AND R15, R17 LDP ·P751x2+40(SB), (R19, R20) AND R15, R19 AND R15, R20 ADDS R16, R3 ADCS R17, R4 STP (R3, R4), 0(R2) ADCS R17, R5 ADCS R17, R6 STP (R5, R6), 16(R2) ADCS R17, R7 ADCS R19, R8 STP (R7, R8), 32(R2) ADCS R20, R9 LDP ·P751x2+56(SB), (R16, R17) AND R15, R16 AND R15, R17 LDP ·P751x2+72(SB), (R19, R20) AND R15, R19 AND R15, R20 ADCS R16, R10 STP (R9, R10), 48(R2) ADCS R17, R11 ADCS R19, R12 STP (R11, R12), 64(R2) ADCS R20, R13 MOVD ·P751x2+88(SB), R16 AND R15, R16 ADC R16, R14 STP (R13, R14), 80(R2) RET TEXT ·adlP751(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 LDP 0(R0), (R3, R4) LDP 0(R1), (R15, R16) LDP 16(R0), (R5, R6) LDP 16(R1), (R17, R19) ADDS R15, R3 ADCS R16, R4 STP (R3, R4), 0(R2) ADCS R17, R5 ADCS R19, R6 STP (R5, R6), 16(R2) LDP 32(R0), (R7, R8) LDP 32(R1), (R15, R16) LDP 48(R0), (R9, R10) LDP 48(R1), (R17, R19) ADCS R15, R7 ADCS R16, R8 STP (R7, R8), 32(R2) ADCS R17, R9 ADCS R19, R10 STP (R9, R10), 48(R2) LDP 64(R0), (R11, R12) LDP 64(R1), (R15, R16) LDP 80(R0), (R13, R14) LDP 80(R1), (R17, R19) ADCS R15, R11 ADCS R16, R12 STP (R11, R12), 64(R2) ADCS R17, R13 ADCS R19, R14 STP (R13, R14), 80(R2) LDP 96(R0), (R3, R4) LDP 96(R1), (R15, R16) LDP 112(R0), (R5, R6) LDP 112(R1), (R17, R19) ADCS R15, R3 ADCS R16, R4 STP (R3, R4), 96(R2) ADCS R17, R5 ADCS R19, R6 STP (R5, R6), 112(R2) LDP 128(R0), (R7, R8) LDP 128(R1), (R15, R16) LDP 144(R0), (R9, R10) LDP 144(R1), (R17, R19) ADCS R15, R7 ADCS R16, R8 STP (R7, R8), 128(R2) ADCS R17, R9 ADCS R19, R10 STP (R9, R10), 144(R2) LDP 160(R0), (R11, R12) LDP 160(R1), (R15, R16) LDP 176(R0), (R13, R14) LDP 176(R1), (R17, R19) ADCS R15, R11 ADCS R16, R12 STP (R11, R12), 160(R2) ADCS R17, R13 ADC R19, R14 STP (R13, R14), 176(R2) RET TEXT ·sulP751(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 LDP 0(R0), (R3, R4) LDP 0(R1), (R15, R16) LDP 16(R0), (R5, R6) LDP 16(R1), (R17, R19) SUBS R15, R3 SBCS R16, R4 STP (R3, R4), 0(R2) SBCS R17, R5 SBCS R19, R6 STP (R5, R6), 16(R2) LDP 32(R0), (R7, R8) LDP 32(R1), (R15, R16) LDP 48(R0), (R9, R10) LDP 48(R1), (R17, R19) SBCS R15, R7 SBCS R16, R8 STP (R7, R8), 32(R2) SBCS R17, R9 SBCS R19, R10 STP (R9, R10), 48(R2) LDP 64(R0), (R11, R12) LDP 64(R1), (R15, R16) LDP 80(R0), (R13, R14) LDP 80(R1), (R17, R19) SBCS R15, R11 SBCS R16, R12 STP (R11, R12), 64(R2) SBCS R17, R13 SBCS R19, R14 STP (R13, R14), 80(R2) LDP 96(R0), (R3, R4) LDP 96(R1), (R15, R16) LDP 112(R0), (R5, R6) LDP 112(R1), (R17, R19) SBCS R15, R3 SBCS R16, R4 SBCS R17, R5 SBCS R19, R6 LDP 128(R0), (R7, R8) LDP 128(R1), (R15, R16) LDP 144(R0), (R9, R10) LDP 144(R1), (R17, R19) SBCS R15, R7 SBCS R16, R8 SBCS R17, R9 SBCS R19, R10 LDP 160(R0), (R11, R12) LDP 160(R1), (R15, R16) LDP 176(R0), (R13, R14) LDP 176(R1), (R17, R19) SBCS R15, R11 SBCS R16, R12 SBCS R17, R13 SBCS R19, R14 SBC ZR, ZR, R15 // If x - y < 0, R15 is 1 and p751 should be added MOVD ·P751+0(SB), R20 AND R15, R20 LDP ·P751+40(SB), (R16, R17) ADDS R20, R3 ADCS R20, R4 STP (R3, R4), 96(R2) ADCS R20, R5 ADCS R20, R6 STP (R5, R6), 112(R2) ADCS R20, R7 LDP ·P751+56(SB), (R19, R20) AND R15, R16 AND R15, R17 ADCS R16, R8 STP (R7, R8), 128(R2) ADCS R17, R9 LDP ·P751+72(SB), (R16, R17) AND R15, R19 AND R15, R20 ADCS R19, R10 STP (R9, R10), 144(R2) ADCS R20, R11 MOVD ·P751+88(SB), R19 AND R15, R16 AND R15, R17 ADCS R16, R12 STP (R11, R12), 160(R2) ADCS R17, R13 AND R15, R19 ADC R19, R14 STP (R13, R14), 176(R2) RET // Expects that X0*Y0 is already in Z0(low),Z3(high) and X0*Y1 in Z1(low),Z2(high) // Z0 is not actually touched // Result of (X0-X2) * (Y0-Y2) will be in Z0-Z5 // Inputs remain intact #define mul192x192comba(X0, X1, X2, Y0, Y1, Y2, Z0, Z1, Z2, Z3, Z4, Z5, T0, T1, T2, T3) \ MUL X1, Y0, T2 \ UMULH X1, Y0, T3 \ \ ADDS Z3, Z1 \ ADCS ZR, Z2 \ ADC ZR, ZR, Z3 \ \ MUL X0, Y2, T0 \ UMULH X0, Y2, T1 \ \ ADDS T2, Z1 \ ADCS T3, Z2 \ ADC ZR, Z3 \ \ MUL X1, Y1, T2 \ UMULH X1, Y1, T3 \ \ ADDS T0, Z2 \ ADCS T1, Z3 \ ADC ZR, ZR, Z4 \ \ MUL X2, Y0, T0 \ UMULH X2, Y0, T1 \ \ ADDS T2, Z2 \ ADCS T3, Z3 \ ADC ZR, Z4 \ \ MUL X1, Y2, T2 \ UMULH X1, Y2, T3 \ \ ADDS T0, Z2 \ ADCS T1, Z3 \ ADC ZR, Z4 \ \ MUL X2, Y1, T0 \ UMULH X2, Y1, T1 \ \ ADDS T2, Z3 \ ADCS T3, Z4 \ ADC ZR, ZR, Z5 \ \ MUL X2, Y2, T2 \ UMULH X2, Y2, T3 \ \ ADDS T0, Z3 \ ADCS T1, Z4 \ ADC ZR, Z5 \ \ ADDS T2, Z4 \ ADC T3, Z5 // Expects that X points to (X4-X6), Y to (Y4-Y6) // Result of (X0-X5) * (Y0-Y5) will be in (0(Z), 8(Z), 16(Z), T0-T8) // Inputs get overwritten #define mul384x384karatsuba(X, Y, Z, X0, X1, X2, X3, X4, X5, Y0, Y1, Y2, Y3, Y4, Y5, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10)\ ADDS X0, X3 \ // xH + xL, destroys xH ADCS X1, X4 \ ADCS X2, X5 \ ADC ZR, ZR, T10 \ \ ADDS Y0, Y3 \ // yH + yL, destroys yH ADCS Y1, Y4 \ ADCS Y2, Y5 \ ADC ZR, ZR, T6 \ \ SUB T10, ZR, T7 \ SUB T6, ZR, T8 \ AND T6, T10 \ // combined carry \ AND T7, Y3, T0 \ // masked(yH + yL) AND T7, Y4, T1 \ AND T7, Y5, T2 \ \ AND T8, X3, T3 \ // masked(xH + xL) AND T8, X4, T4 \ AND T8, X5, T5 \ \ ADDS T3, T0 \ ADCS T4, T1 \ STP (T0, T1), 0+Z \ \ MUL X3, Y3, T0 \ MUL X3, Y4, T1 \ \ ADCS T5, T2 \ MOVD T2, 16+Z \ \ UMULH X3, Y4, T2 \ UMULH X3, Y3, T3 \ \ ADC ZR, T10 \ \ // (xH + xL) * (yH + yL) mul192x192comba(X3, X4, X5, Y3, Y4, Y5, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9)\ \ MUL X0, Y0, X3 \ LDP 0+Z, (T6, T7) \ MOVD 16+Z, T8 \ \ UMULH X0, Y0, Y3 \ ADDS T6, T3 \ ADCS T7, T4 \ MUL X0, Y1, X4 \ ADCS T8, T5 \ ADC ZR, T10 \ UMULH X0, Y1, X5 \ \ // xL * yL mul192x192comba(X0, X1, X2, Y0, Y1, Y2, X3, X4, X5, Y3, Y4, Y5, T6, T7, T8, T9)\ \ STP (X3, X4), 0+Z \ MOVD X5, 16+Z \ \ SUBS X3, T0 \ // (xH + xL) * (yH + yL) - xL * yL SBCS X4, T1 \ LDP 0+X, (X3, X4) \ SBCS X5, T2 \ MOVD 16+X, X5 \ SBCS Y3, T3 \ SBCS Y4, T4 \ SBCS Y5, T5 \ SBC ZR, T10 \ \ ADDS Y3, T0 \ // ((xH + xL) * (yH + yL) - xL * yL) * 2^192 + xL * yL ADCS Y4, T1 \ LDP 0+Y, (Y3, Y4) \ MUL X3, Y3, X0 \ ADCS Y5, T2 \ UMULH X3, Y3, Y0 \ MOVD 16+Y, Y5 \ MUL X3, Y4, X1 \ ADCS ZR, T3 \ UMULH X3, Y4, X2 \ ADCS ZR, T4 \ ADCS ZR, T5 \ ADC ZR, T10 \ \ // xH * yH, overwrite xLow, yLow mul192x192comba(X3, X4, X5, Y3, Y4, Y5, X0, X1, X2, Y0, Y1, Y2, T6, T7, T8, T9)\ \ SUBS X0, T0 \ // ((xH + xL) * (yH + yL) - xL * yL - xH * yH) SBCS X1, T1 \ SBCS X2, T2 \ SBCS Y0, T3 \ SBCS Y1, T4 \ SBCS Y2, T5 \ SBC ZR, T10 \ \ ADDS X0, T3 \ ADCS X1, T4 \ ADCS X2, T5 \ ADCS T10, Y0, T6 \ ADCS ZR, Y1, T7 \ ADC ZR, Y2, T8 TEXT ·mulP751(SB), NOSPLIT, $0-24 MOVD z+0(FP), R2 MOVD x+8(FP), R0 MOVD y+16(FP), R1 // Load xL in R3-R8, xH in R9-R14 // (xH + xL) in R3-R8, destroys xH LDP 0(R0), (R3, R4) LDP 48(R0), (R9, R10) ADDS R9, R3 ADCS R10, R4 LDP 16(R0), (R5, R6) LDP 64(R0), (R11, R12) ADCS R11, R5 ADCS R12, R6 LDP 32(R0), (R7, R8) LDP 80(R0), (R13, R14) ADCS R13, R7 ADCS R14, R8 ADC ZR, ZR, R22 // Load yL in R9-R14, yH in R15-21 // (yH + yL) in R9-R14, destroys yH LDP 0(R1), (R9, R10) LDP 48(R1), (R15, R16) ADDS R15, R9 ADCS R16, R10 LDP 16(R1), (R11, R12) LDP 64(R1), (R17, R19) ADCS R17, R11 ADCS R19, R12 LDP 32(R1), (R13, R14) LDP 80(R1), (R20, R21) ADCS R20, R13 ADCS R21, R14 ADC ZR, ZR, R23 // Compute masks and combined carry SUB R22, ZR, R24 SUB R23, ZR, R25 AND R23, R22 // Store xH, yH in z so mul384x384karatsuba can retrieve them from memory // It doesn't have enough registers // Meanwhile computed masked(xH + xL) in R15-R21 STP (R6, R7), 0(R2) AND R25, R3, R15 AND R25, R4, R16 STP (R8, R12), 16(R2) AND R25, R5, R17 AND R25, R6, R19 STP (R13, R14), 32(R2) AND R25, R7, R20 AND R25, R8, R21 // Masked(xH + xL) + masked(yH + yL) in R15-R21 // Store intermediate values in z AND R24, R9, R25 AND R24, R10, R26 ADDS R25, R15 ADCS R26, R16 STP (R15, R16), 96(R2) AND R24, R11, R25 AND R24, R12, R26 ADCS R25, R17 ADCS R26, R19 STP (R17, R19), 112(R2) AND R24, R13, R25 AND R24, R14, R26 ADCS R25, R20 ADCS R26, R21 STP (R20, R21), 128(R2) // Store carry in R29 so it can remain there ADC ZR, R22, R29 // (xH + xL) * (yH + yL) mul384x384karatsuba(0(R2), 24(R2), 48(R2), R3, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13, R14, R15, R16, R17, R19, R20, R21, R22, R23, R24, R25, R26) // Load masked(xH + xL) + masked(yH + yL) and add that to its top half // Store the result back in z STP (R15, R16), 72(R2) LDP 96(R2), (R3, R4) ADDS R3, R19 STP (R17, R19), 88(R2) ADCS R4, R20 LDP 112(R2), (R5, R6) ADCS R5, R21 STP (R20, R21), 104(R2) ADCS R6, R22 LDP 128(R2), (R7, R8) ADCS R7, R23 STP (R22, R23), 120(R2) ADCS R8, R24 MOVD R24, 136(R2) ADC ZR, R29 // Load xL, yL LDP 0(R0), (R3, R4) LDP 16(R0), (R5, R6) LDP 32(R0), (R7, R8) LDP 0(R1), (R9, R10) LDP 16(R1), (R11, R12) LDP 32(R1), (R13, R14) // xL * yL mul384x384karatsuba(24(R0), 24(R1), 0(R2), R3, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13, R14, R15, R16, R17, R19, R20, R21, R22, R23, R24, R25, R26) // (xH + xL) * (yH + yL) - xL * yL in R3-R14 LDP 0(R2), (R12, R13) LDP 48(R2), (R3, R4) SUBS R12, R3 LDP 64(R2), (R5, R6) MOVD 16(R2), R14 SBCS R13, R4 SBCS R14, R5 LDP 80(R2), (R7, R8) SBCS R15, R6 SBCS R16, R7 LDP 96(R2), (R9, R10) SBCS R17, R8 SBCS R19, R9 LDP 112(R2), (R11, R12) SBCS R20, R10 SBCS R21, R11 LDP 128(R2), (R13, R14) SBCS R22, R12 SBCS R23, R13 SBCS R24, R14 SBC ZR, R29 STP (R15, R16), 24(R2) MOVD R17, 40(R2) // ((xH + xL) * (yH + yL) - xL * yL) * 2^384 + xL * yL and store back in z ADDS R19, R3 ADCS R20, R4 STP (R3, R4), 48(R2) ADCS R21, R5 ADCS R22, R6 STP (R5, R6), 64(R2) ADCS R23, R7 ADCS R24, R8 STP (R7, R8), 80(R2) ADCS ZR, R9 ADCS ZR, R10 STP (R9, R10), 96(R2) ADCS ZR, R11 ADCS ZR, R12 STP (R11, R12), 112(R2) ADCS ZR, R13 ADCS ZR, R14 STP (R13, R14), 128(R2) ADC ZR, R29 // Load xH, yH LDP 48(R0), (R3, R4) LDP 64(R0), (R5, R6) LDP 80(R0), (R7, R8) LDP 48(R1), (R9, R10) LDP 64(R1), (R11, R12) LDP 80(R1), (R13, R14) // xH * yH mul384x384karatsuba(72(R0), 72(R1), 144(R2), R3, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13, R14, R15, R16, R17, R19, R20, R21, R22, R23, R24, R25, R26) LDP 144(R2), (R12, R13) MOVD 160(R2), R14 // (xH + xL) * (yH + yL) - xL * yL - xH * yH in R3-R14 // Store lower half in z, that's done LDP 48(R2), (R3, R4) SUBS R12, R3 LDP 64(R2), (R5, R6) SBCS R13, R4 SBCS R14, R5 LDP 80(R2), (R7, R8) SBCS R15, R6 SBCS R16, R7 LDP 96(R2), (R9, R10) SBCS R17, R8 SBCS R19, R9 LDP 112(R2), (R11, R12) SBCS R20, R10 SBCS R21, R11 LDP 128(R2), (R13, R14) SBCS R22, R12 SBCS R23, R13 STP (R3, R4), 48(R2) SBCS R24, R14 STP (R5, R6), 64(R2) SBC ZR, R29 STP (R7, R8), 80(R2) // (xH * yH) * 2^768 + ((xH + xL) * (yH + yL) - xL * yL - xH * yH) * 2^384 + xL * yL // Store remaining limbs in z LDP 144(R2), (R3, R4) MOVD 160(R2), R5 ADDS R3, R9 ADCS R4, R10 STP (R9, R10), 96(R2) ADCS R5, R11 ADCS R15, R12 STP (R11, R12), 112(R2) ADCS R16, R13 ADCS R17, R14 STP (R13, R14), 128(R2) ADCS R29, R19 ADCS ZR, R20 STP (R19, R20), 144(R2) ADCS ZR, R21 ADCS ZR, R22 STP (R21, R22), 160(R2) ADCS ZR, R23 ADC ZR, R24 STP (R23, R24), 176(R2) RET TEXT ·rdcP751(SB), NOSPLIT, $0-16 MOVD z+0(FP), R0 MOVD x+8(FP), R1 // Load p751+1 in R14-R17, R29, R19-R20, spread over arithmetic LDP ·P751p1+40(SB), (R14, R15) // z0-z11 will be R2-R13 // Load x0-x4 to z0-z4 and x5, spread over arithmetic LDP 0(R1), (R2, R3) // x5 iteration MUL R2, R14, R22 LDP 32(R1), (R6, R21) UMULH R2, R14, R23 ADDS R21, R22, R7 // Set z5 ADC ZR, R23, R25 // x6 iteration MUL R2, R15, R22 MOVD 48(R1), R21 UMULH R2, R15, R23 ADDS R22, R25 ADC R23, ZR, R26 MUL R3, R14, R22 LDP ·P751p1+56(SB), (R16, R17) UMULH R3, R14, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, ZR, R24 ADDS R21, R25, R8 // Set z6 ADCS ZR, R26 ADC ZR, R24 // x7 iteration MUL R2, R16, R22 MOVD 56(R1), R21 UMULH R2, R16, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, ZR, R25 MUL R3, R15, R22 LDP 16(R1), (R4, R5) UMULH R3, R15, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R4, R14, R22 LDP ·P751p1+72(SB), (R29, R19) UMULH R4, R14, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 ADDS R21, R26, R9 // Set z7 ADCS ZR, R24 ADC ZR, R25 // x8 iteration MUL R2, R17, R22 MOVD 64(R1), R21 UMULH R2, R17, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, ZR, R26 MUL R3, R16, R22 MOVD ·P751p1+88(SB), R20 UMULH R3, R16, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R4, R15, R22 UMULH R4, R15, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R5, R14, R22 UMULH R5, R14, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 ADDS R24, R21, R10 // Set z8 ADCS ZR, R25 ADC ZR, R26 // x9 iteration MUL R2, R29, R22 MOVD 72(R1), R21 UMULH R2, R29, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, ZR, R24 MUL R3, R17, R22 UMULH R3, R17, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R4, R16, R22 UMULH R4, R16, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R5, R15, R22 UMULH R5, R15, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R6, R14, R22 UMULH R6, R14, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 ADDS R21, R25, R11 // Set z9 ADCS ZR, R26 ADC ZR, R24 // x10 iteration MUL R2, R19, R22 MOVD 80(R1), R21 UMULH R2, R19, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, ZR, R25 MUL R3, R29, R22 UMULH R3, R29, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R4, R17, R22 UMULH R4, R17, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R5, R16, R22 UMULH R5, R16, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R6, R15, R22 UMULH R6, R15, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R7, R14, R22 UMULH R7, R14, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 ADDS R21, R26, R12 // Set z10 ADCS ZR, R24 ADC ZR, R25 // x11 iteration MUL R2, R20, R22 MOVD 88(R1), R21 UMULH R2, R20, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, ZR, R26 MUL R3, R19, R22 UMULH R3, R19, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R4, R29, R22 UMULH R4, R29, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R5, R17, R22 UMULH R5, R17, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R6, R16, R22 UMULH R6, R16, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R7, R15, R22 UMULH R7, R15, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R8, R14, R22 UMULH R8, R14, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 ADDS R21, R24, R13 // Set z11 ADCS ZR, R25 ADC ZR, R26 // x12 iteration MUL R3, R20, R22 MOVD 96(R1), R21 UMULH R3, R20, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, ZR, R24 MUL R4, R19, R22 UMULH R4, R19, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R5, R29, R22 UMULH R5, R29, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R6, R17, R22 UMULH R6, R17, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R7, R16, R22 UMULH R7, R16, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R8, R15, R22 UMULH R8, R15, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R9, R14, R22 UMULH R9, R14, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 ADDS R21, R25, R2 // Set z0 ADCS ZR, R26 ADC ZR, R24 // x13 iteration MUL R4, R20, R22 MOVD 104(R1), R21 UMULH R4, R20, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, ZR, R25 MUL R5, R19, R22 UMULH R5, R19, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R6, R29, R22 UMULH R6, R29, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R7, R17, R22 UMULH R7, R17, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R8, R16, R22 UMULH R8, R16, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R9, R15, R22 UMULH R9, R15, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R10, R14, R22 UMULH R10, R14, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 ADDS R21, R26, R3 // Set z1 STP (R2, R3), 0(R0) ADCS ZR, R24 ADC ZR, R25 // x14 iteration MUL R5, R20, R22 MOVD 112(R1), R21 UMULH R5, R20, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, ZR, R26 MUL R6, R19, R22 UMULH R6, R19, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R7, R29, R22 UMULH R7, R29, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R8, R17, R22 UMULH R8, R17, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R9, R16, R22 UMULH R9, R16, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R10, R15, R22 UMULH R10, R15, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R11, R14, R22 UMULH R11, R14, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 ADDS R21, R24, R4 // Set z2 ADCS ZR, R25 ADC ZR, R26 // x15 iteration MUL R6, R20, R22 MOVD 120(R1), R21 UMULH R6, R20, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, ZR, R24 MUL R7, R19, R22 UMULH R7, R19, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R8, R29, R22 UMULH R8, R29, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R9, R17, R22 UMULH R9, R17, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R10, R16, R22 UMULH R10, R16, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R11, R15, R22 UMULH R11, R15, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R12, R14, R22 UMULH R12, R14, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 ADDS R21, R25, R5 // Set z3 STP (R4, R5), 16(R0) ADCS ZR, R26 ADC ZR, R24 // x16 iteration MUL R7, R20, R22 MOVD 128(R1), R21 UMULH R7, R20, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, ZR, R25 MUL R8, R19, R22 UMULH R8, R19, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R9, R29, R22 UMULH R9, R29, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R10, R17, R22 UMULH R10, R17, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R11, R16, R22 UMULH R11, R16, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R12, R15, R22 UMULH R12, R15, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R13, R14, R22 UMULH R13, R14, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 ADDS R21, R26, R6 // Set z4 ADCS ZR, R24 ADC ZR, R25 // x17 iteration MUL R8, R20, R22 MOVD 136(R1), R21 UMULH R8, R20, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, ZR, R26 MUL R9, R19, R22 UMULH R9, R19, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R10, R29, R22 UMULH R10, R29, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R11, R17, R22 UMULH R11, R17, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R12, R16, R22 UMULH R12, R16, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R13, R15, R22 UMULH R13, R15, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 ADDS R21, R24, R7 // Set z5 STP (R6, R7), 32(R0) ADCS ZR, R25 ADC ZR, R26 // x18 iteration MUL R9, R20, R22 MOVD 144(R1), R21 UMULH R9, R20, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, ZR, R24 MUL R10, R19, R22 UMULH R10, R19, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R11, R29, R22 UMULH R11, R29, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R12, R17, R22 UMULH R12, R17, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 MUL R13, R16, R22 UMULH R13, R16, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 ADDS R21, R25, R8 // Set z6 ADCS ZR, R26 ADC ZR, R24 // x19 iteration MUL R10, R20, R22 MOVD 152(R1), R21 UMULH R10, R20, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, ZR, R25 MUL R11, R19, R22 UMULH R11, R19, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R12, R29, R22 UMULH R12, R29, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 MUL R13, R17, R22 UMULH R13, R17, R23 ADDS R22, R26 ADCS R23, R24 ADC ZR, R25 ADDS R21, R26, R9 // Set z7 STP (R8, R9), 48(R0) ADCS ZR, R24 ADC ZR, R25 // x20 iteration MUL R11, R20, R22 MOVD 160(R1), R21 UMULH R11, R20, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, ZR, R26 MUL R12, R19, R22 UMULH R12, R19, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 MUL R13, R29, R22 UMULH R13, R29, R23 ADDS R22, R24 ADCS R23, R25 ADC ZR, R26 ADDS R21, R24, R10 // Set z8 ADCS ZR, R25 ADC ZR, R26 // x21 iteration MUL R12, R20, R22 MOVD 168(R1), R21 UMULH R12, R20, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, ZR, R24 MUL R13, R19, R22 UMULH R13, R19, R23 ADDS R22, R25 ADCS R23, R26 ADC ZR, R24 ADDS R21, R25, R11 // Set z9 STP (R10, R11), 64(R0) ADCS ZR, R26 ADC ZR, R24 // x22 iteration MUL R13, R20, R22 MOVD 176(R1), R21 UMULH R13, R20, R23 ADDS R22, R26 ADC R23, R24 ADDS R21, R26, R12 // Set z10 MOVD 184(R1), R21 ADC R21, R24, R13 // Set z11 STP (R12, R13), 80(R0) RET TEXT ·modP751(SB), NOSPLIT, $0-8 MOVD x+0(FP), R0 // Keep x in R1-R12, p751 in R13-R21, subtract to R1-R12 MOVD ·P751+0(SB), R13 LDP 0(R0), (R1, R2) LDP 16(R0), (R3, R4) SUBS R13, R1 SBCS R13, R2 LDP 32(R0), (R5, R6) LDP ·P751+40(SB), (R14, R15) SBCS R13, R3 SBCS R13, R4 LDP 48(R0), (R7, R8) LDP ·P751+56(SB), (R16, R17) SBCS R13, R5 SBCS R14, R6 LDP 64(R0), (R9, R10) LDP ·P751+72(SB), (R19, R20) SBCS R15, R7 SBCS R16, R8 LDP 80(R0), (R11, R12) MOVD ·P751+88(SB), R21 SBCS R17, R9 SBCS R19, R10 SBCS R20, R11 SBCS R21, R12 SBC ZR, ZR, R22 // Mask with the borrow and add p751 AND R22, R13 AND R22, R14 AND R22, R15 AND R22, R16 AND R22, R17 AND R22, R19 AND R22, R20 AND R22, R21 ADDS R13, R1 ADCS R13, R2 STP (R1, R2), 0(R0) ADCS R13, R3 ADCS R13, R4 STP (R3, R4), 16(R0) ADCS R13, R5 ADCS R14, R6 STP (R5, R6), 32(R0) ADCS R15, R7 ADCS R16, R8 STP (R7, R8), 48(R0) ADCS R17, R9 ADCS R19, R10 STP (R9, R10), 64(R0) ADCS R20, R11 ADC R21, R12 STP (R11, R12), 80(R0) RET golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/arith_decl.go000066400000000000000000000025371454601126700257550ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build (amd64 && !noasm) || (arm64 && !noasm) // +build amd64,!noasm arm64,!noasm package p751 import ( . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cmovP751(x, y *Fp, choice uint8) // If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cswapP751(x, y *Fp, choice uint8) // Compute z = x + y (mod p). // //go:noescape func addP751(z, x, y *Fp) // Compute z = x - y (mod p). // //go:noescape func subP751(z, x, y *Fp) // Compute z = x + y, without reducing mod p. // //go:noescape func adlP751(z, x, y *FpX2) // Compute z = x - y, without reducing mod p. // //go:noescape func sulP751(z, x, y *FpX2) // Reduce a field element in [0, 2*p) to one in [0,p). // //go:noescape func modP751(x *Fp) // Computes z = x * y. // //go:noescape func mulP751(z *FpX2, x, y *Fp) // Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value // of x may be changed. z=x not allowed. // //go:noescape func rdcP751(z *Fp, x *FpX2) golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/arith_generic.go000066400000000000000000000104651454601126700264610ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build noasm || (!amd64 && !arm64) // +build noasm !amd64,!arm64 package p751 import ( "math/bits" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Compute z = x + y (mod p). func addP751(z, x, y *common.Fp) { var carry uint64 // z=x+y % P751 for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } // z = z - P751x2 carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Sub64(z[i], P751x2[i], carry) } // if z<0 add P751x2 back mask := uint64(0 - carry) carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(z[i], P751x2[i]&mask, carry) } } // Compute z = x - y (mod p). func subP751(z, x, y *common.Fp) { var borrow uint64 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } mask := uint64(0 - borrow) borrow = 0 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Add64(z[i], P751x2[i]&mask, borrow) } } // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. func cmovP751(x, y *common.Fp, choice uint8) { mask := 0 - uint64(choice) for i := 0; i < FpWords; i++ { x[i] ^= mask & (x[i] ^ y[i]) } } // Conditionally swaps bits in x and y in constant time. // mask indicates bits to be swapped (set bits are swapped) // For details see "Hackers Delight, 2.20" // // Implementation doesn't actually depend on a prime field. func cswapP751(x, y *common.Fp, mask uint8) { var tmp, mask64 uint64 mask64 = 0 - uint64(mask) for i := 0; i < FpWords; i++ { tmp = mask64 & (x[i] ^ y[i]) x[i] = tmp ^ x[i] y[i] = tmp ^ y[i] } } // Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) // with R=2^(FpWords*64). Destroys the input value. func rdcP751(z *common.Fp, x *common.FpX2) { var carry, t, u, v uint64 var hi, lo uint64 var count int count = P751p1Zeros for i := 0; i < FpWords; i++ { for j := 0; j < i; j++ { if j < (i - count + 1) { hi, lo = bits.Mul64(z[j], P751p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i] = v v = u u = t t = 0 } for i := FpWords; i < 2*FpWords-1; i++ { if count > 0 { count-- } for j := i - FpWords + 1; j < FpWords; j++ { if j < (FpWords - count) { hi, lo = bits.Mul64(z[j], P751p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i-FpWords] = v v = u u = t t = 0 } v, _ = bits.Add64(v, x[2*FpWords-1], 0) z[FpWords-1] = v } // Compute z = x * y. func mulP751(z *common.FpX2, x, y *common.Fp) { var u, v, t uint64 var hi, lo uint64 var carry uint64 for i := uint64(0); i < FpWords; i++ { for j := uint64(0); j <= i; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } for i := FpWords; i < (2*FpWords)-1; i++ { for j := i - FpWords + 1; j < FpWords; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } z[2*FpWords-1] = v } // Compute z = x + y, without reducing mod p. func adlP751(z, x, y *common.FpX2) { var carry uint64 for i := 0; i < 2*FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } } // Reduce a field element in [0, 2*p) to one in [0,p). func modP751(x *common.Fp) { var borrow, mask uint64 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Sub64(x[i], P751[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Add64(x[i], P751[i]&mask, borrow) } } // Compute z = x - y, without reducing mod p. func sulP751(z, x, y *common.FpX2) { var borrow, mask uint64 for i := 0; i < 2*FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := FpWords; i < 2*FpWords; i++ { z[i], borrow = bits.Add64(z[i], P751[i-FpWords]&mask, borrow) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/arith_test.go000066400000000000000000000070001454601126700260130ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p751 import ( "testing" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Package-level storage for this field element is intended to deter // compiler optimizations. var ( benchmarkFp common.Fp benchmarkFpX2 common.FpX2 bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} ) func TestFpCswap(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cswapP751(&x, &y, 0) for i := 0; i < FpWords; i++ { if (x[i] != one[i]) || (y[i] != two[i]) { t.Error("Found", x, "expected", one) } } cswapP751(&x, &y, 1) for i := 0; i < FpWords; i++ { if (x[i] != two[i]) || (y[i] != one[i]) { t.Error("Found", x, "expected", two) } } } func TestFpCmov(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cmovP751(&x, &y, 0) for i := 0; i < FpWords; i++ { if x[i] != one[i] { t.Error("Found", x, "expected", one) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } cmovP751(&x, &y, 1) for i := 0; i < FpWords; i++ { if x[i] != two[i] { t.Error("Found", x, "expected", two) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } } // Benchmarking for field arithmetic func BenchmarkMul(b *testing.B) { for n := 0; n < b.N; n++ { mulP751(&benchmarkFpX2, &bench_x, &bench_y) } } func BenchmarkRdc(b *testing.B) { z := bench_z // This benchmark actually computes garbage, because // rdcP751 mangles its input, but since it's // constant-time that shouldn't matter for the benchmarks. for n := 0; n < b.N; n++ { rdcP751(&benchmarkFp, &z) } } func BenchmarkAdd(b *testing.B) { for n := 0; n < b.N; n++ { addP751(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkSub(b *testing.B) { for n := 0; n < b.N; n++ { subP751(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkCswap(b *testing.B) { x, y := bench_x, bench_y for n := 0; n < b.N; n++ { cswapP751(&x, &y, 1) cswapP751(&x, &y, 0) } } func BenchmarkMod(b *testing.B) { x := bench_x for n := 0; n < b.N; n++ { modP751(&x) } } func BenchmarkX2AddLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { adlP751(&x, &y, &z) } } func BenchmarkX2SubLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { sulP751(&x, &y, &z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/core.go000066400000000000000000000205411454601126700246020ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p751 import ( crand "crypto/rand" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // ----------------------------------------------------------------------------- // Functions for traversing isogeny trees according to strategy. Key type 'A' is // // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR needed // for public key generation. func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { var xPA, xQA, xRA ProjectivePoint var xPB, xQB, xRB, xR ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny4 // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) // Secret isogeny phi.GenerateCurve(&xR) xPA = xPB xQA = xQB xRA = xRB phi.EvaluatePoint(&xPA) phi.EvaluatePoint(&xQA) phi.EvaluatePoint(&xRA) Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPA.X, &invZP) mul(&pub3Pt[1], &xQA.X, &invZQ) mul(&pub3Pt[2], &xRA.X, &invZR) } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { var xPB, xQB, xRB, xR ProjectivePoint var xPA, xQA, xRA ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny3 // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) phi.GenerateCurve(&xR) xPB = xPA xQB = xQA xRB = xRA phi.EvaluatePoint(&xPB) phi.EvaluatePoint(&xQB) phi.EvaluatePoint(&xRB) Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPB.X, &invZP) mul(&pub3Pt[1], &xQB.X, &invZQ) mul(&pub3Pt[2], &xRB.X, &invZR) } // ----------------------------------------------------------------------------- // Key agreement functions // // Establishing shared keys in in 2-torsion group func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny4 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyA(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients4(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } // Establishing shared keys in in 3-torsion group func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny3 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} //PUBLIC KEY VALIDATION if err := PublicKeyValidation(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen); err != nil { _, err_read := crand.Read(ss) if err_read != nil { panic("core: failed to generate random ss when public key verification fails") } return } xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyB(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients3(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/curve.go000066400000000000000000000341221454601126700247760ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p751 import ( "errors" . "github.com/cloudflare/circl/dh/sidh/internal/common" "math" ) // Stores isogeny 3 curve constants type isogeny3 struct { K1 Fp2 K2 Fp2 } // Stores isogeny 4 curve constants type isogeny4 struct { isogeny3 K3 Fp2 } // Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result // is returned in jBytes buffer, encoded in little-endian format. Caller // provided jBytes buffer has to be big enough to j-invariant value. In case // of SIDH, buffer size must be at least size of shared secret. // Implementation corresponds to Algorithm 9 from SIKE. func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { var t0, t1 Fp2 sqr(j, &cparams.A) // j = A^2 sqr(&t1, &cparams.C) // t1 = C^2 add(&t0, &t1, &t1) // t0 = t1 + t1 sub(&t0, j, &t0) // t0 = j - t0 sub(&t0, &t0, &t1) // t0 = t0 - t1 sub(j, &t0, &t1) // t0 = t0 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(j, j, &t1) // j = j * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&t1, &t0) // t1 = t0^2 mul(&t0, &t0, &t1) // t0 = t0 * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 inv(j, j) // j = 1/j mul(j, &t0, j) // j = t0 * j } // Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function // recovers projective coordinate A of a curve. This is Algorithm 10 from SIKE. func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { var t0, t1 Fp2 add(&t1, xp, xq) // t1 = Xp + Xq mul(&t0, xp, xq) // t0 = Xp * Xq mul(&curve.A, xr, &t1) // A = X(q-p) * t1 add(&curve.A, &curve.A, &t0) // A = A + t0 mul(&t0, &t0, xr) // t0 = t0 * X(q-p) sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t1, &t1, xr) // t1 = t1 + X(q-p) add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&curve.A, &curve.A) // A = A^2 inv(&t0, &t0) // t0 = 1/t0 mul(&curve.A, &curve.A, &t0) // A = A * t0 sub(&curve.A, &curve.A, &t1) // A = A - t1 } // Computes equivalence (A:C) ~ (A+2C : A-2C) func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coef CurveCoefficientsEquiv var c2 Fp2 add(&c2, &cparams.C, &cparams.C) // A24p = A+2*C add(&coef.A, &cparams.A, &c2) // A24m = A-2*C sub(&coef.C, &cparams.A, &c2) return coef } // Computes equivalence (A:C) ~ (A+2C : 4C) func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv add(&coefEq.C, &cparams.C, &cparams.C) // A24p = A+2C add(&coefEq.A, &cparams.A, &coefEq.C) // C24 = 4*C add(&coefEq.C, &coefEq.C, &coefEq.C) return coefEq } // Helper function for RightToLeftLadder(). Returns A+2C / 4. func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { var tmp Fp2 // 2C add(&tmp, &cparams.C, &cparams.C) // A+2C add(&ret, &cparams.A, &tmp) // 1/4C add(&tmp, &tmp, &tmp) inv(&tmp, &tmp) // A+2C/4C mul(&ret, &ret, &tmp) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { add(&cparams.A, &coefEq.A, &coefEq.C) // cparams.A = 2*(A+2C+A-2C) = 4A add(&cparams.A, &cparams.A, &cparams.A) // cparams.C = (A+2C-A+2C) = 4C sub(&cparams.C, &coefEq.A, &coefEq.C) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { // cparams.C = (4C)*1/2=2C mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) // cparams.A = A+2C - 2C = A sub(&cparams.A, &coefEq.A, &cparams.C) // cparams.C = 2C * 1/2 = C mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) } // Combined coordinate doubling and differential addition. Takes projective points // P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. // Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { var t0, t1, t2 Fp2 xQmP, zQmP := &QmP.X, &QmP.Z xPaQ, zPaQ := &PaQ.X, &PaQ.Z x2P, z2P := &dblP.X, &dblP.Z xP, zP := &P.X, &P.Z xQ, zQ := &Q.X, &Q.Z add(&t0, xP, zP) // t0 = Xp+Zp sub(&t1, xP, zP) // t1 = Xp-Zp sqr(x2P, &t0) // 2P.X = t0^2 sub(&t2, xQ, zQ) // t2 = Xq-Zq add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq mul(&t0, &t0, &t2) // t0 = t0 * t2 mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q return } // Given the curve parameters, xP = x(P), computes xP = x([2^k]P) // Safe to overlap xP, x2P. func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp add(&t1, x, z) // t1 = Xp + Zp sqr(&t0, &t0) // t0 = t0 ^ 2 sqr(&t1, &t1) // t1 = t1 ^ 2 mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 mul(x, z, &t1) // X2p = Z2p * t1 sub(&t1, &t1, &t0) // t1 = t1 - t0 mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 add(z, z, &t0) // Z2p = Z2p + t0 mul(z, z, &t1) // Zp = Z2p * t1 } } // Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). // // Safe to overlap xP, xR. func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1, t2, t3, t4, t5, t6 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp sqr(&t2, &t0) // t2 = t0^2 add(&t1, x, z) // t1 = Xp + Zp sqr(&t3, &t1) // t3 = t1^2 add(&t4, &t1, &t0) // t4 = t1 + t0 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t1, &t4) // t1 = t4^2 sub(&t1, &t1, &t3) // t1 = t1 - t3 sub(&t1, &t1, &t2) // t1 = t1 - t2 mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ mul(&t3, &t3, &t5) // t3 = t5 * t3 mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- mul(&t2, &t2, &t6) // t2 = t2 * t6 sub(&t3, &t2, &t3) // t3 = t2 - t3 sub(&t2, &t5, &t6) // t2 = t5 - t6 mul(&t1, &t2, &t1) // t1 = t2 * t1 add(&t2, &t3, &t1) // t2 = t3 + t1 sqr(&t2, &t2) // t2 = t2^2 mul(x, &t2, &t4) // X3p = t2 * t4 sub(&t1, &t3, &t1) // t1 = t3 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(z, &t1, &t0) // Z3p = t1 * t0 } } // Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). // // All xi, yi must be distinct. func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { var x1x2, t Fp2 mul(&x1x2, x1, x2) // x1*x2 mul(&t, &x1x2, x3) // 1/(x1*x2*x3) inv(&t, &t) mul(y1, &t, x2) // 1/x1 mul(y1, y1, x3) mul(y2, &t, x1) // 1/x2 mul(y2, y2, x3) mul(y3, &t, &x1x2) // 1/x3 } // Scalarmul3Pt is a right-to-left point multiplication that given the // x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. // nbits must be smaller or equal to len(scalar). func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { var R0, R2, R1 ProjectivePoint aPlus2Over4 := CalcAplus2Over4(cparams) R1 = *P R2 = *PmQ R0 = *Q // Iterate over the bits of the scalar, bottom to top prevBit := uint8(0) for i := uint(0); i < nbits; i++ { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) } cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) return R1 } // Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the // three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C // Output: // - Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var t0, t1, t2, t3, t4 Fp2 var coefEq CurveCoefficientsEquiv K1, K2 := &phi.K1, &phi.K2 sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 sqr(&t0, K1) // t0 = K1^2 add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 sqr(&t1, K2) // t1 = K2^2 add(&t2, &t0, &t1) // t2 = t0 + t1 add(&t3, K1, K2) // t3 = K1 + K2 sqr(&t3, &t3) // t3 = t3^2 sub(&t3, &t3, &t2) // t3 = t3 - t2 add(&t2, &t1, &t3) // t2 = t1 + t3 add(&t3, &t3, &t0) // t3 = t3 + t0 add(&t4, &t3, &t0) // t4 = t3 + t0 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t1, &t4) // t4 = t1 + t4 mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 add(&t4, &t1, &t2) // t4 = t1 + t2 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t0, &t4) // t4 = t0 + t4 mul(&t4, &t3, &t4) // t4 = t3 * t4 sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 return coefEq } // Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate // of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). // // The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve // parameters are returned by the GenerateCurve function used to construct phi. func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) { var t0, t1, t2 Fp2 K1, K2 := &phi.K1, &phi.K2 px, pz := &p.X, &p.Z add(&t0, px, pz) // t0 = XQ + ZQ sub(&t1, px, pz) // t1 = XQ - ZQ mul(&t0, K1, &t0) // t2 = K1 * t0 mul(&t1, K2, &t1) // t1 = K2 * t1 add(&t2, &t0, &t1) // t2 = t0 + t1 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t2, &t2) // t2 = t2 ^ 2 sqr(&t0, &t0) // t0 = t0 ^ 2 mul(px, px, &t2) // XQ'= XQ * t2 mul(pz, pz, &t0) // ZQ'= ZQ * t0 } // Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the // four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C // Output: // - Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv xp4, zp4 := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 sub(K2, xp4, zp4) add(K3, xp4, zp4) sqr(K1, zp4) add(K1, K1, K1) sqr(&coefEq.C, K1) add(K1, K1, K1) sqr(&coefEq.A, xp4) add(&coefEq.A, &coefEq.A, &coefEq.A) sqr(&coefEq.A, &coefEq.A) return coefEq } // Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate // of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). // // Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C // Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) { var t0, t1 Fp2 xq, zq := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 add(&t0, xq, zq) sub(&t1, xq, zq) mul(xq, &t0, K2) mul(zq, &t1, K3) mul(&t0, &t0, &t1) mul(&t0, &t0, K1) add(&t1, xq, zq) sub(zq, xq, zq) sqr(&t1, &t1) sqr(zq, zq) add(xq, &t0, &t1) sub(&t0, zq, &t0) mul(xq, xq, &t1) mul(zq, zq, &t0) } // PublicKeyValidation preforms public key/ciphertext validation using the CLN test. // CLN test: Check that P and Q are both of order 3^e3 and they generate the torsion E_A[3^e3] // A countermeasure for remote timing attacks on SIKE; suggested by https://eprint.iacr.org/2022/054.pdf // Any curve E_A (SIKE 434, 503, 751) that passes CLN test is supersingular. // Input: The public key / ciphertext P, Q, PmQ. The projective coordinate A of the curve defined by (P, Q, PmQ) // Outputs: Whether (P,Q,PmQ) follows the CLN test func PublicKeyValidation(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint) error { var PmQX, PmQZ Fp2 FromMontgomery(&PmQX, &PmQ.X) FromMontgomery(&PmQZ, &PmQ.Z) // PmQ is not point T or O if (isZero(&PmQX) == 1) || (isZero(&PmQZ) == 1) { return errors.New("curve: PmQ is invalid") } cparam := CalcCurveParamsEquiv3(cparams) // Compute e_3 = log3(2^(nbits+1)) var e3 uint32 e3_float := float64(int(nbits)+1) / math.Log2(3) e3 = uint32(e3_float) // Verify that P and Q generate E_A[3^e_3] by checking: [3^(e_3-1)]P != [+-3^(e_3-1)]Q var test_P, test_Q ProjectivePoint test_P = *P test_Q = *Q Pow3k(&test_P, &cparam, e3-1) Pow3k(&test_Q, &cparam, e3-1) var PZ, QZ Fp2 FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of full order 3^e_3 if (isZero(&PZ) == 1) || (isZero(&QZ) == 1) { return errors.New("curve: ciphertext/public key are not of full order 3^e3") } // PX/PZ = affine(PX) // QX/QZ = affine(QX) // If PX/PZ = QX/QZ, we have P=+-Q var PXQZ_PZQX_fromMont, PXQZ_PZQX, PXQZ, PZQX Fp2 mul(&PXQZ, &test_P.X, &test_Q.Z) mul(&PZQX, &test_P.Z, &test_Q.X) sub(&PXQZ_PZQX, &PXQZ, &PZQX) FromMontgomery(&PXQZ_PZQX_fromMont, &PXQZ_PZQX) // [3^(e_3-1)]P == [+-3^(e_3-1)]Q if isZero(&PXQZ_PZQX_fromMont) == 1 { return errors.New("curve: ciphertext/public key are not linearly independent") } // Check that Ord(P) = Ord(Q) = 3^(e_3) Pow3k(&test_P, &cparam, 1) Pow3k(&test_Q, &cparam, 1) FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of correct order 3^e_3 if (isZero(&PZ) == 0) || (isZero(&QZ) == 0) { return errors.New("curve: ciphertext/public key are not of correct order 3^e3") } return nil } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/curve_test.go000066400000000000000000000304631454601126700260410ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p751 import ( "bytes" crand "crypto/rand" . "github.com/cloudflare/circl/dh/sidh/internal/common" "io" "math" "math/rand" "testing" "time" ) func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { var t0, t1 Fp2 mul(&t0, &lhs.X, &rhs.Z) mul(&t1, &lhs.Z, &rhs.X) return vartimeEqFp2(&t0, &t1) } func toAffine(point *ProjectivePoint) *Fp2 { var affineX Fp2 inv(&affineX, &point.Z) mul(&affineX, &affineX, &point.X) return &affineX } func Test_jInvariant(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} jbufRes := make([]byte, params.SharedSecretSize) jbufExp := make([]byte, params.SharedSecretSize) var jInv Fp2 Jinvariant(&curve, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufRes, &jInv, params.Bytelen) jInv = expectedJ FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufExp, &jInv, params.Bytelen) if !bytes.Equal(jbufRes[:], jbufExp[:]) { t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) } } func TestProjectivePointVartimeEq(t *testing.T) { var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} xQ := xP // Scale xQ, which results in the same projective point mul(&xQ.X, &xQ.X, &curveA) mul(&xQ.Z, &xQ.Z, &curveA) if !vartimeEqProjFp2(&xP, &xQ) { t.Error("Expected the scaled point to be equal to the original") } } func TestPointMulVersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv4(&curve) var xP ProjectivePoint // x 2 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 1) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP2) { t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) } // x 4 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 2) afxQ = toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP4) { t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) } } func TestPointMul9VersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv3(&curve) var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow3k(&xP, &cparams, 2) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP9) { t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) } } func BenchmarkThreePointLadder(b *testing.B) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} for n := 0; n < b.N; n++ { ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) } } /* ------------------------------------------------------------------------- Generate invalid public key points / ciphertext for test TestKEMInvalidPK -------------------------------------------------------------------------*/ // Left-to-right Montgomery ladder, Algorithm 4 in Costello-Smith // Input: ProjectivePoint P (xP, zP) // Output: x([scalar]P), z([scalar]P) func montgomeryLadder(cparams *ProjectiveCurveParameters, P *ProjectivePoint, scalar []uint8, random uint) ProjectivePoint { var R0, R2, R1 ProjectivePoint coefEq := CalcCurveParamsEquiv4(cparams) // for xDbl aPlus2Over4 := CalcAplus2Over4(cparams) // for xDblAdd R0 = *P // RO <- P R1 = *P Pow2k(&R1, &coefEq, 1) // R1 <- [2]P R2 = *P // R2 = R1-R0 = P prevBit := uint8(0) for i := int(random); i >= 0; i-- { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, swap) R0, R1 = xDbladd(&R0, &R1, &R2, &aPlus2Over4) } cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, prevBit) return R0 } // P = P + T // From paper https://eprint.iacr.org/2017/212.pdf // The map tau_T: P->P+T is (X : Z) -> (Z : X) on Montgomery curves func tauT(P *ProjectivePoint) { P.X, P.Z = P.Z, P.X // magic! } // Construct Invalid public key tuple (P,Q) such that P and Q are linearly dependent // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKNoneLinear(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1) * 8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Make sure Q is of full order 3^e_3, var test_Q ProjectivePoint test_Q = Q var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1) / math.Log2(3) e3 = uint32(e3_float) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&test_Q, &cparam_q, e3-1) var test_QZ Fp2 FromMontgomery(&test_QZ, &test_Q.Z) // Q are not of full order 3^e_3 for isZero(&test_QZ) == 1 { rand.Seed(time.Now().UnixNano()) random_index = rand.Intn(int(params.B.SecretByteLen-1) * 8) Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) test_Q = Q Pow3k(&test_Q, &cparam_q, e3-1) FromMontgomery(&test_QZ, &test_Q.Z) } // invQz = 1/Q.Z var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect linearly dependent ciphertext to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that Q = [k]P + T, where k is random and T is the point of order 2. // Simulate HB and section 3.1.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKT(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1) * 8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Q = [k]P + T tauT(&Q) var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext involve point T to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[2^e2] // Simulate section 3.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKOrder2(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil { t.Error("Fail read random bytes") } var P, Q ProjectivePoint P = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(params.A.SecretByteLen-1) * 8) random_index_q := rand.Intn(int(params.A.SecretByteLen-1) * 8) P = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index_p)) Q = montgomeryLadder(¶ms.InitCurve, &Q, secret, uint(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext in torsion E[2^e2] to fail, index_p: %v index_q: %v scalar: %v ", random_index_p, random_index_q, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[3^e3] but not of full order 3^e3 // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKFullOrder(t *testing.T) { var P, Q ProjectivePoint P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1) / math.Log2(3) e3 = uint32(e3_float) rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(e3)) random_index_q := rand.Intn(int(e3)) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&P, &cparam_q, uint32(random_index_p)) Pow3k(&Q, &cparam_q, uint32(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect ciphertext not of full order to fail, index_p: %v index_q: %v ", random_index_p, random_index_q) } } // A trivial test case not covered by paper https://eprint.iacr.org/2022/054.pdf and HB // Countermeasure in https://eprint.iacr.org/2022/054.pdf only cares about P and Q // But if PmQ is point T or O, that can also lead to recovery of the first bit func testInvalidPmQ(t *testing.T) { var zero Fp2 var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: zero, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify == nil { t.Errorf("\nExpect PmQ as T to fail\n") } } // Test valid ciphertext // Where P, Q are linearly independent points of correct order 3^e3 in E[3^e3] func testValidPQ(t *testing.T) { var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify != nil { t.Errorf("\nExpect correct ciphertext to not fail\n") } } /* ------------------------------------------------------------------------- Public key / Ciphertext validation against attacks proposed in paper https://eprint.iacr.org/2022/054.pdf and HB -------------------------------------------------------------------------*/ func TestInvalidPK(t *testing.T) { t.Run("InvalidPmQ", testInvalidPmQ) t.Run("InvalidPKNoneLinear", testInvalidPKNoneLinear) t.Run("InvalidPKT", testInvalidPKT) t.Run("InvalidPKOrder2", testInvalidPKOrder2) t.Run("InvalidPKFullOrder", testInvalidPKFullOrder) t.Run("ValidPQ", testValidPQ) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/doc.go000066400000000000000000000001401454601126700244100ustar00rootroot00000000000000// Package p751 provides implementation of field arithmetic used in SIDH and SIKE. package p751 golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/fp2.go000066400000000000000000000153171454601126700243460ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p751 import ( "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Montgomery multiplication. Input values must be already // in Montgomery domain. func mulP(dest, lhs, rhs *common.Fp) { var ab common.FpX2 mulP751(&ab, lhs, rhs) // = a*b*R*R rdcP751(dest, &ab) // = a*b*R mod p } // Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). // Uses variation of sliding-window algorithm from with window size // of 5 and least to most significant bit sliding (left-to-right) // See HAC 14.85 for general description. // // Allowed to overlap x with dest. // All values in Montgomery domains // Set dest = x^(2^k), for k >= 1, by repeated squarings. func p34(dest, x *common.Fp) { var lookup [16]common.Fp // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) // multiplications. powStrategy := []uint8{5, 7, 6, 2, 10, 4, 6, 9, 8, 5, 9, 4, 7, 5, 5, 4, 8, 3, 9, 5, 5, 4, 10, 4, 6, 6, 6, 5, 8, 9, 3, 4, 9, 4, 5, 6, 6, 2, 9, 4, 5, 5, 5, 7, 7, 9, 4, 6, 4, 8, 5, 8, 6, 6, 2, 9, 7, 4, 8, 8, 8, 4, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2} mulStrategy := []uint8{15, 11, 10, 0, 15, 3, 3, 3, 4, 4, 9, 7, 11, 11, 5, 3, 12, 2, 10, 8, 5, 2, 8, 3, 5, 4, 11, 4, 0, 9, 2, 1, 12, 7, 5, 14, 15, 0, 14, 5, 6, 4, 5, 13, 6, 9, 7, 15, 1, 14, 11, 15, 12, 5, 0, 10, 9, 7, 7, 10, 14, 6, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1} initialMul := uint8(13) // Precompute lookup table of odd multiples of x for window // size k=5. var xx common.Fp mulP(&xx, x, x) lookup[0] = *x for i := 1; i < 16; i++ { mulP(&lookup[i], &lookup[i-1], &xx) } // Now lookup = {x, x^3, x^5, ... } // so that lookup[i] = x^{2*i + 1} // so that lookup[k/2] = x^k, for odd k *dest = lookup[initialMul] for i := uint8(0); i < uint8(len(powStrategy)); i++ { mulP(dest, dest, dest) for j := uint8(1); j < powStrategy[i]; j++ { mulP(dest, dest, dest) } mulP(dest, dest, &lookup[mulStrategy[i]]) } } func add(dest, lhs, rhs *common.Fp2) { addP751(&dest.A, &lhs.A, &rhs.A) addP751(&dest.B, &lhs.B, &rhs.B) } func sub(dest, lhs, rhs *common.Fp2) { subP751(&dest.A, &lhs.A, &rhs.A) subP751(&dest.B, &lhs.B, &rhs.B) } func mul(dest, lhs, rhs *common.Fp2) { var bMinA, cMinD common.Fp var ac, bd common.FpX2 var adPlusBc common.FpX2 var acMinBd common.FpX2 // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). // // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i // // Use Karatsuba's trick: note that // // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d // // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. subP751(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R subP751(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R mulP751(&ac, &lhs.A, &rhs.A) // = a*c*R*R mulP751(&bd, &lhs.B, &rhs.B) // = b*d*R*R mulP751(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R adlP751(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R adlP751(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R rdcP751(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p sulP751(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R rdcP751(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p } // Set dest = 1/x // // Allowed to overlap dest with x. // // Returns dest to allow chaining operations. func inv(dest, x *common.Fp2) { var e1, e2 common.FpX2 var f1, f2 common.Fp // We want to compute // // 1 1 (a - bi) (a - bi) // -------- = -------- -------- = ----------- // (a + bi) (a + bi) (a - bi) (a^2 + b^2) // // Letting c = 1/(a^2 + b^2), this is // // 1/(a+bi) = a*c - b*ci. mulP751(&e1, &x.A, &x.A) // = a*a*R*R mulP751(&e2, &x.B, &x.B) // = b*b*R*R adlP751(&e1, &e1, &e2) // = (a^2 + b^2)*R*R rdcP751(&f1, &e1) // = (a^2 + b^2)*R mod p // Now f1 = a^2 + b^2 mulP(&f2, &f1, &f1) p34(&f2, &f2) mulP(&f2, &f2, &f2) mulP(&f2, &f2, &f1) mulP751(&e1, &x.A, &f2) rdcP751(&dest.A, &e1) subP751(&f1, &common.Fp{}, &x.B) mulP751(&e1, &f1, &f2) rdcP751(&dest.B, &e1) } func sqr(dest, x *common.Fp2) { var a2, aPlusB, aMinusB common.Fp var a2MinB2, ab2 common.FpX2 a := &x.A b := &x.B // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. addP751(&a2, a, a) // = a*R + a*R = 2*a*R addP751(&aPlusB, a, b) // = a*R + b*R = (a+b)*R subP751(&aMinusB, a, b) // = a*R - b*R = (a-b)*R mulP751(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R mulP751(&ab2, &a2, b) // = 2*a*b*R*R rdcP751(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p rdcP751(&dest.B, &ab2) // = 2*a*b*R mod p } // In case choice == 1, performs following swap in constant time: // // xPx <-> xQx // xPz <-> xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cswapP751(&xPx.A, &xQx.A, choice) cswapP751(&xPx.B, &xQx.B, choice) cswapP751(&xPz.A, &xQz.A, choice) cswapP751(&xPz.B, &xQz.B, choice) } // In case choice == 1, performs following moves in constant time: // // xPx <- xQx // xPz <- xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cmov(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cmovP751(&xPx.A, &xQx.A, choice) cmovP751(&xPx.B, &xQx.B, choice) cmovP751(&xPz.A, &xQz.A, choice) cmovP751(&xPz.B, &xQz.B, choice) } func isZero(x *common.Fp2) uint8 { r64 := uint64(0) for i := 0; i < FpWords; i++ { r64 |= x.A[i] | x.B[i] } r := uint8(0) for i := uint64(0); i < 64; i++ { r |= uint8((r64 >> i) & 0x1) } return 1 - r } // Converts in.A and in.B to Montgomery domain and stores // in 'out' // out.A = in.A * R mod p // out.B = in.B * R mod p // Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B func ToMontgomery(out, in *common.Fp2) { var aRR common.FpX2 // a*R*R mulP751(&aRR, &in.A, &P751R2) // a*R mod p rdcP751(&out.A, &aRR) mulP751(&aRR, &in.B, &P751R2) rdcP751(&out.B, &aRR) } // Converts in.A and in.B from Montgomery domain and stores // in 'out' // out.A = in.A mod p // out.B = in.B mod p // // After returning from the call 'in' is not modified. func FromMontgomery(out, in *common.Fp2) { var aR common.FpX2 // convert from montgomery domain copy(aR[:], in.A[:]) rdcP751(&out.A, &aR) // = a mod p in [0, 2p) modP751(&out.A) // = a mod p in [0, p) for i := range aR { aR[i] = 0 } copy(aR[:], in.B[:]) rdcP751(&out.B, &aR) modP751(&out.B) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/fp2_test.go000066400000000000000000000125601454601126700254020ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p751 import ( "math/rand" "reflect" "testing" "testing/quick" "github.com/cloudflare/circl/dh/sidh/internal/common" ) type testParams struct { Point common.ProjectivePoint Cparam common.ProjectiveCurveParameters ExtElem common.Fp2 } // Returns true if lhs = rhs. Takes variable time. func vartimeEqFp2(lhs, rhs *common.Fp2) bool { a := *lhs b := *rhs modP751(&a.A) modP751(&a.B) modP751(&b.A) modP751(&b.B) eq := true for i := 0; i < FpWords && eq; i++ { eq = eq && (a.A[i] == b.A[i]) eq = eq && (a.B[i] == b.B[i]) } return eq } func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { // Generation strategy: low limbs taken from [0,2^64); high limb // taken from smaller range // // Size hint is ignored since all elements are fixed size. // // Field elements taken in range [0,2p). Emulate this by capping // the high limb by the top digit of 2*p-1: // // sage: (2*p-1).digits(2^64)[-1] // // This still allows generating values >= 2p, but hopefully that // excess is OK (and if it's not, we'll find out, because it's for // testing...) highLimb := rand.Uint64() % P751x2[FpWords-1] fpElementGen := func() (fp common.Fp) { for i := 0; i < (FpWords - 1); i++ { fp[i] = rand.Uint64() } fp[FpWords-1] = highLimb return fp } return common.Fp2{A: fpElementGen(), B: fpElementGen()} } func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { return reflect.ValueOf( testParams{ common.ProjectivePoint{ X: c.generateFp2(rand), Z: c.generateFp2(rand), }, common.ProjectiveCurveParameters{ A: c.generateFp2(rand), C: c.generateFp2(rand), }, c.generateFp2(rand), }) } func TestOne(t *testing.T) { var tmp common.Fp2 mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { t.Error("Not equal 1") } } func TestFp2ToBytesRoundTrip(t *testing.T) { roundTrips := func(x testParams) bool { xBytes := make([]byte, 2*params.Bytelen) var xPrime common.Fp2 common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) return vartimeEqFp2(&xPrime, &x.ExtElem) } if err := quick.Check(roundTrips, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulDistributesOverAdd(t *testing.T) { mulDistributesOverAdd := func(x, y, z testParams) bool { // Compute t1 = (x+y)*z t1 := new(common.Fp2) add(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = x*z + y*z t2 := new(common.Fp2) t3 := new(common.Fp2) mul(t2, &x.ExtElem, &z.ExtElem) mul(t3, &y.ExtElem, &z.ExtElem) add(t2, t2, t3) return vartimeEqFp2(t1, t2) } if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulIsAssociative(t *testing.T) { isAssociative := func(x, y, z testParams) bool { // Compute t1 = (x*y)*z t1 := new(common.Fp2) mul(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = (y*z)*x t2 := new(common.Fp2) mul(t2, &y.ExtElem, &z.ExtElem) mul(t2, t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(isAssociative, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2SquareMatchesMul(t *testing.T) { sqrMatchesMul := func(x testParams) bool { // Compute t1 = (x*x) t1 := new(common.Fp2) mul(t1, &x.ExtElem, &x.ExtElem) // Compute t2 = x^2 t2 := new(common.Fp2) sqr(t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2Inv(t *testing.T) { inverseIsCorrect := func(x testParams) bool { z := new(common.Fp2) inv(z, &x.ExtElem) // Now z = (1/x), so (z * x) * x == x mul(z, z, &x.ExtElem) mul(z, z, &x.ExtElem) return vartimeEqFp2(z, &x.ExtElem) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 11)} if err := quick.Check(inverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func TestFp2Batch3Inv(t *testing.T) { batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { var x1Inv, x2Inv, x3Inv common.Fp2 inv(&x1Inv, &x1.ExtElem) inv(&x2Inv, &x2.ExtElem) inv(&x3Inv, &x3.ExtElem) var y1, y2, y3 common.Fp2 Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 8)} if err := quick.Check(batchInverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func BenchmarkFp2Mul(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { mul(w, z, z) } } func BenchmarkFp2Inv(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { inv(w, z) } } func BenchmarkFp2Square(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sqr(w, z) } } func BenchmarkFp2Add(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { add(w, z, z) } } func BenchmarkFp2Sub(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sub(w, z, z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/params.go000066400000000000000000000236721454601126700251450ustar00rootroot00000000000000package p751 //go:generate go run ../templates/gen.go P751 import ( "github.com/cloudflare/circl/dh/sidh/internal/common" "golang.org/x/sys/cpu" ) const ( // Number of uint64 limbs used to store field element FpWords = 12 ) var ( // HasBMI2 signals support for MULX which is in BMI2 HasBMI2 = cpu.X86.HasBMI2 // HasADXandBMI2 signals support for ADX and BMI2 HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX // P751 is a prime used by field Fp751 P751 = common.Fp{ 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xeeafffffffffffff, 0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876, 0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c, } // P751x2 = 2*p751 - 1 P751x2 = common.Fp{ 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF, 0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED, 0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38, } // P751p1 = p751 + 1 P751p1 = common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xeeb0000000000000, 0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876, 0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c, } // P751R2 = (2^768)^2 mod p P751R2 = common.Fp{ 0x233046449DAD4058, 0xDB010161A696452A, 0x5E36941472E3FD8E, 0xF40BFE2082A2E706, 0x4932CCA8904F8751, 0x1F735F1F1EE7FC81, 0xA24F4D80C1048E18, 0xB56C383CCDB607C5, 0x441DD47B735F9C90, 0x5673ED2C6A6AC82A, 0x06C905261132294B, 0x000041AD830F1F35, } // P751p1Zeros number of 0 digits in the least significant part of P751+1 P751p1Zeros = 5 // 1*R mod p one = common.Fp2{ A: common.Fp{ 0x00000000000249ad, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8310000000000000, 0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2, }, } // 1/2 * R mod p half = common.Fp2{ A: common.Fp{ 0x00000000000124D6, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xB8E0000000000000, 0x9C8A2434C0AA7287, 0xA206996CA9A378A3, 0x6876280D41A41B52, 0xE903B49F175CE04F, 0x0F8511860666D227, 0x00004EA07CFF6E7F, }, } // 6*R mod p six = common.Fp2{ A: common.Fp{ 0x00000000000DBA10, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x3500000000000000, 0x3714FE4EB8399915, 0xC3A2584753EB43F4, 0xA3151D605C520428, 0xC116CF5232C7C978, 0x49A84D4B8EFAF6AA, 0x0000305731E97514, }, } params = common.SidhParams{ ID: common.Fp751, // SIDH public key byte size. PublicKeySize: 564, // SIDH shared secret byte size. SharedSecretSize: 188, A: common.DomainParams{ // The x-coordinate of PA AffineP: common.Fp2{ A: common.Fp{ 0x884F46B74000BAA8, 0xBA52630F939DEC20, 0xC16FB97BA714A04D, 0x082536745B1AB3DB, 0x1117157F446F9E82, 0xD2F27D621A018490, 0x6B24AB523D544BCD, 0x9307D6AA2EA85C94, 0xE1A096729528F20F, 0x896446F868F3255C, 0x2401D996B1BFF8A5, 0x00000EF8786A5C0A, }, B: common.Fp{ 0xAEB78B3B96F59394, 0xAB26681E29C90B74, 0xE520AC30FDC4ACF1, 0x870AAAE3A4B8111B, 0xF875BDB738D64EFF, 0x50109A7ECD7ED6BC, 0x4CC64848FF0C56FB, 0xE617CB6C519102C9, 0x9C74B3835921E609, 0xC91DDAE4A35A7146, 0x7FC82A155C1B9129, 0x0000214FA6B980B3, }, }, // The x-coordinate of QA AffineQ: common.Fp2{ A: common.Fp{ 0x0F93CC38680A8CA9, 0x762E733822E7FED7, 0xE549F005AC0ADB67, 0x94A71FDD2C43A4ED, 0xD48645C2B04721C5, 0x432DA1FE4D4CA4DC, 0xBC99655FAA7A80E8, 0xB2C6D502BCFD4823, 0xEE92F40CA2EC8BDB, 0x7B074132EFB6D16C, 0x3340B46FA38A7633, 0x0000215749657F6C, }, B: common.Fp{ 0xECFF375BF3079F4C, 0xFBFE74B043E80EF3, 0x17376CBE3C5C7AD1, 0xC06327A7E29CDBF2, 0x2111649C438BF3D4, 0xC1F9298261BA2E97, 0x1F9FECE869CFD1C2, 0x01A39B4FC9346D62, 0x147CD1D3E82A3C9F, 0xDE84E9D249E533EE, 0x1C48A5ADFB7C578D, 0x000061ACA0B82E1D, }, }, // The x-coordinate of RA = PA-QA AffineR: common.Fp2{ A: common.Fp{ 0x1600C525D41059F1, 0xA596899A0A1D83F7, 0x6BFDEED6D2B23F35, 0x5C7E707270C23910, 0x276CA1A4E8369411, 0xB193651A602925A0, 0x243D239F1CA1F04A, 0x543DC6DA457860AD, 0xCDA590F325181DE9, 0xD3AB7ACFDA80B395, 0x6C97468580FDDF7B, 0x0000352A3E5C4C77, }, B: common.Fp{ 0x9B794F9FD1CC3EE8, 0xDB32E40A9B2FD23E, 0x26192A2542E42B67, 0xA18E94FCA045BCE7, 0x96DC1BC38E7CDA2D, 0x9A1D91B752487DE2, 0xCC63763987436DA3, 0x1316717AACCC551D, 0xC4C368A4632AFE72, 0x4B6EA85C9CCD5710, 0x7A12CAD582C7BC9A, 0x00001C7E240149BF, }, }, // Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1 SecretBitLen: 372, // SecretBitLen in bytes. SecretByteLen: 47, // 2-torsion group computation strategy IsogenyStrategy: []uint32{ 0x50, 0x30, 0x1B, 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x15, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x21, 0x14, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x08, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, }, }, B: common.DomainParams{ // The x-coordinate of PB AffineP: common.Fp2{ A: common.Fp{ 0x85691AAF4015F88C, 0x7478C5B8C36E9631, 0x7EF2A185DE4DD6E2, 0x943BBEE46BEB9DC7, 0x1A3EC62798792D22, 0x791BC4B084B31D69, 0x03DBE6522CEA17C4, 0x04749AA65D665D83, 0x3D52B5C45EF450F3, 0x0B4219848E36947D, 0xA4CF7070466BDE27, 0x0000334B1FA6D193, }, B: common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, }, }, // The x-coordinate of QB AffineQ: common.Fp2{ A: common.Fp{ 0x8E7CB3FA53211340, 0xD67CE54F7A05EEE0, 0xFDDC2C8BCE46FC38, 0x08587FAE3110DF1E, 0xD6B8246FA22B058B, 0x4DAC3ACC905A5DBD, 0x51D0BF2FADCED3E8, 0xE5A2406DF6484425, 0x907F177584F671B8, 0x4738A2FFCCED051C, 0x2B0067B4177E4853, 0x00002806AC948D3D, }, B: common.Fp{ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, }, }, // The x-coordinate of RB = PB - QB AffineR: common.Fp2{ A: common.Fp{ 0xB56457016D1D6D1C, 0x03DECCB38F39C491, 0xDFB910AC8A559452, 0xA9D0F17D1FF24883, 0x8562BBAF515C248C, 0x249B2A6DDB1CB67D, 0x3131AF96FB46835C, 0xE10258398480C3E1, 0xEAB5E2B872D4FAB1, 0xB71E63875FAEB1DF, 0xF8384D4F13757CF6, 0x0000361EC9B09912, }, B: common.Fp{ 0x58C967899ED16EF4, 0x81998376DC622A4B, 0x3D1C1DCFE0B12681, 0x9347DEBB953E1730, 0x9ABB344D3A82C2D7, 0xE4881BD2820552B2, 0x0037247923D90266, 0x2E3156EDB157E5A5, 0xF86A46A7506823F7, 0x8FE5523A7B7F1CFC, 0xFA3CFFA38372F67B, 0x0000692DCE85FFBD, }, }, // Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1. SecretBitLen: 378, // SecretBitLen in bytes. SecretByteLen: 48, // 3-torsion group computation strategy IsogenyStrategy: []uint32{ 0x70, 0x3F, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x1F, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x31, 0x1F, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x15, 0x0C, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, }, }, OneFp2: one, HalfFp2: half, MsgLen: 32, // SIKEp751 provides 128 bit of classical security ([SIKE], 5.1) KemSize: 32, // ceil(751+7/8) Bytelen: 94, CiphertextSize: 32 + 564, InitCurve: common.ProjectiveCurveParameters{ A: six, C: one, }, } ) func init() { common.Register(common.Fp751, ¶ms) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/p751/params_test.go000066400000000000000000000205571454601126700262030ustar00rootroot00000000000000package p751 // Contains values used by tests import ( "testing/quick" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) var ( expectedJ = Fp2{ A: Fp{0xc7a8921c1fb23993, 0xa20aea321327620b, 0xf1caa17ed9676fa8, 0x61b780e6b1a04037, 0x47784af4c24acc7a, 0x83926e2e300b9adf, 0xcd891d56fae5b66, 0x49b66985beb733bc, 0xd4bcd2a473d518f, 0xe242239991abe224, 0xa8af5b20f98672f8, 0x139e4d4e4d98}, B: Fp{0xb5b52a21f81f359, 0x715e3a865db6d920, 0x9bac2f9d8911978b, 0xef14acd8ac4c1e3d, 0xe81aacd90cfb09c8, 0xaf898288de4a09d9, 0xb85a7fb88c5c4601, 0x2c37c3f1dd303387, 0x7ad3277fe332367c, 0xd4cbee7f25a8e6f8, 0x36eacbe979eaeffa, 0x59eb5a13ac33}, } // A = 4385300808024233870220415655826946795549183378139271271040522089756750951667981765872679172832050962894122367066234419550072004266298327417513857609747116903999863022476533671840646615759860564818837299058134292387429068536219*i + 1408083354499944307008104531475821995920666351413327060806684084512082259107262519686546161682384352696826343970108773343853651664489352092568012759783386151707999371397181344707721407830640876552312524779901115054295865393760 curveA = Fp2{ A: Fp{0x8319eb18ca2c435e, 0x3a93beae72cd0267, 0x5e465e1f72fd5a84, 0x8617fa4150aa7272, 0x887da24799d62a13, 0xb079b31b3c7667fe, 0xc4661b150fa14f2e, 0xd4d2b2967bc6efd6, 0x854215a8b7239003, 0x61c5302ccba656c2, 0xf93194a27d6f97a2, 0x1ed9532bca75}, B: Fp{0xb6f541040e8c7db6, 0x99403e7365342e15, 0x457e9cee7c29cced, 0x8ece72dc073b1d67, 0x6e73cef17ad28d28, 0x7aed836ca317472, 0x89e1de9454263b54, 0x745329277aa0071b, 0xf623dfc73bc86b9b, 0xb8e3c1d8a9245882, 0x6ad0b3d317770bec, 0x5b406e8d502b}, } // C = 933177602672972392833143808100058748100491911694554386487433154761658932801917030685312352302083870852688835968069519091048283111836766101703759957146191882367397129269726925521881467635358356591977198680477382414690421049768*i + 9088894745865170214288643088620446862479558967886622582768682946704447519087179261631044546285104919696820250567182021319063155067584445633834024992188567423889559216759336548208016316396859149888322907914724065641454773776307 curveC = Fp2{ A: Fp{0x4fb2358bbf723107, 0x3a791521ac79e240, 0x283e24ef7c4c922f, 0xc89baa1205e33cc, 0x3031be81cff6fee1, 0xaf7a494a2f6a95c4, 0x248d251eaac83a1d, 0xc122fca1e2550c88, 0xbc0451b11b6cfd3d, 0x9c0a114ab046222c, 0x43b957b32f21f6ea, 0x5b9c87fa61de}, B: Fp{0xacf142afaac15ec6, 0xfd1322a504a071d5, 0x56bb205e10f6c5c6, 0xe204d2849a97b9bd, 0x40b0122202fe7f2e, 0xecf72c6fafacf2cb, 0x45dfc681f869f60a, 0x11814c9aff4af66c, 0x9278b0c4eea54fe7, 0x9a633d5baf7f2e2e, 0x69a329e6f1a05112, 0x1d874ace23e4}, } // x(P) = 8172151271761071554796221948801462094972242987811852753144865524899433583596839357223411088919388342364651632180452081960511516040935428737829624206426287774255114241789158000915683252363913079335550843837650671094705509470594*i + 9326574858039944121604015439381720195556183422719505497448541073272720545047742235526963773359004021838961919129020087515274115525812121436661025030481584576474033630899768377131534320053412545346268645085054880212827284581557 affineXP = Fp2{ A: Fp{0xe8d05f30aac47247, 0x576ec00c55441de7, 0xbf1a8ec5fe558518, 0xd77cb17f77515881, 0x8e9852837ee73ec4, 0x8159634ad4f44a6b, 0x2e4eb5533a798c5, 0x9be8c4354d5bc849, 0xf47dc61806496b84, 0x25d0e130295120e0, 0xdbef54095f8139e3, 0x5a724f20862c}, B: Fp{0x3ca30d7623602e30, 0xfb281eddf45f07b7, 0xd2bf62d5901a45bc, 0xc67c9baf86306dd2, 0x4e2bd93093f538ca, 0xcfd92075c25b9cbe, 0xceafe9a3095bcbab, 0x7d928ad380c85414, 0x37c5f38b2afdc095, 0x75325899a7b779f4, 0xf130568249f20fdd, 0x178f264767d1}, } // x([2]P) = 1476586462090705633631615225226507185986710728845281579274759750260315746890216330325246185232948298241128541272709769576682305216876843626191069809810990267291824247158062860010264352034514805065784938198193493333201179504845*i + 3623708673253635214546781153561465284135688791018117615357700171724097420944592557655719832228709144190233454198555848137097153934561706150196041331832421059972652530564323645509890008896574678228045006354394485640545367112224 affineXP2 = Fp2{ A: Fp{0x2a77afa8576ce979, 0xab1360e69b0aeba0, 0xd79e3e3cbffad660, 0x5fd0175aa10f106b, 0x1800ebafce9fbdbc, 0x228fc9142bdd6166, 0x867cf907314e34c3, 0xa58d18c94c13c31c, 0x699a5bc78b11499f, 0xa29fc29a01f7ccf1, 0x6c69c0c5347eebce, 0x38ecee0cc57}, B: Fp{0x43607fd5f4837da0, 0x560bad4ce27f8f4a, 0x2164927f8495b4dd, 0x621103fdb831a997, 0xad740c4eea7db2db, 0x2cde0442205096cd, 0x2af51a70ede8324e, 0x41a4e680b9f3466, 0x5481f74660b8f476, 0xfcb2f3e656ff4d18, 0x42e3ce0837171acc, 0x44238c30530c}, } // x([2^2]P) = 441719501189485559222919502512761433931671682884872259563221427434901842337947564993718830905758163254463901652874331063768876314142359813382575876106725244985607032091781306919778265250690045578695338669105227100119314831452*i + 6961734028200975729170216310486458180126343885294922940439352055937945948015840788921225114530454649744697857047401608073256634790353321931728699534700109268264491160589480994022419317695690866764726967221310990488404411684053 affineXP4 = Fp2{ A: Fp{0x6f9dbe4c39175153, 0xf2fec757eb99e88, 0x43d7361a93733d91, 0x3abd10ed19c85a3d, 0xc4de9ab9c5ef7181, 0x53e375901684c900, 0x68ffc3e7d71c41ff, 0x47adab62c8d942fe, 0x226a33fd6fbb381d, 0x87ef4c8fdd83309a, 0xaca1cf44c5fa8799, 0x6cbae86c755f}, B: Fp{0x4c80c37fe68282a7, 0xbd8b9d7248bf553a, 0x1fb0e8e74d5e1762, 0xb63fa0e4e5f91482, 0xc675ab8a45a1439, 0xdfa6772deace7820, 0xf0d813d71d9a9255, 0x53a1a58c634534bd, 0x4ebfc6485fdfd888, 0x6991fe4358bcf169, 0xc0547bdaca85b6fd, 0xf461548d632}, } // x([3^2]P) = 3957171963425208493644602380039721164492341594850197356580248639045894821895524981729970650520936632013218950972842867220898274664982599375786979902471523505057611521217523103474682939638645404445093536997296151472632038973463*i + 1357869545269286021642168835877253886774707209614159162748874474269328421720121175566245719916322684751967981171882659798149072149161259103020057556362998810229937432814792024248155991141511691087135859252304684633946087474060 affineXP9 = Fp2{ A: Fp{0x7c0daa0f04ded4e0, 0x52dc4f883d85e065, 0x91afbdc2c1714d0b, 0xb7b3db8e658cfeba, 0x43d4e72a692882f3, 0x535c56d83753da30, 0xc8a58724433cbf5d, 0x351153c0a5e74219, 0x2c81827d19f93dd5, 0x26ef8aca3370ea1a, 0x1cf939a6dd225dec, 0x3403cb28ad41}, B: Fp{0x93e7bc373a9ff7b, 0x57b8cc47635ebc0f, 0x92eab55689106cf3, 0x93643111d421f24c, 0x1c58b519506f6b7a, 0xebd409fb998faa13, 0x5c86ed799d09d80e, 0xd9a1d764d6363562, 0xf95e87f92fb0c4cc, 0x6b2bbaf5632a5609, 0x2d9b6a809dfaff7f, 0x29c0460348b}, } // Inputs for testing 3-point-ladder threePointLadderInputs = []ProjectivePoint{ // x(P) { X: Fp2{ A: Fp{0xe8d05f30aac47247, 0x576ec00c55441de7, 0xbf1a8ec5fe558518, 0xd77cb17f77515881, 0x8e9852837ee73ec4, 0x8159634ad4f44a6b, 0x2e4eb5533a798c5, 0x9be8c4354d5bc849, 0xf47dc61806496b84, 0x25d0e130295120e0, 0xdbef54095f8139e3, 0x5a724f20862c}, B: Fp{0x3ca30d7623602e30, 0xfb281eddf45f07b7, 0xd2bf62d5901a45bc, 0xc67c9baf86306dd2, 0x4e2bd93093f538ca, 0xcfd92075c25b9cbe, 0xceafe9a3095bcbab, 0x7d928ad380c85414, 0x37c5f38b2afdc095, 0x75325899a7b779f4, 0xf130568249f20fdd, 0x178f264767d1}, }, Z: params.OneFp2, }, // x(Q) { X: Fp2{ A: Fp{0x2b71a2a93ad1e10e, 0xf0b9842a92cfb333, 0xae17373615a27f5c, 0x3039239f428330c4, 0xa0c4b735ed7dcf98, 0x6e359771ddf6af6a, 0xe986e4cac4584651, 0x8233a2b622d5518, 0xbfd67bf5f06b818b, 0xdffe38d0f5b966a6, 0xa86b36a3272ee00a, 0x193e2ea4f68f}, B: Fp{0x5a0f396459d9d998, 0x479f42250b1b7dda, 0x4016b57e2a15bf75, 0xc59f915203fa3749, 0xd5f90257399cf8da, 0x1fb2dadfd86dcef4, 0x600f20e6429021dc, 0x17e347d380c57581, 0xc1b0d5fa8fe3e440, 0xbcf035330ac20e8, 0x50c2eb5f6a4f03e6, 0x86b7c4571}, }, Z: params.OneFp2, }, // x(P-Q) { X: Fp2{ A: Fp{0x4aafa9f378f7b5ff, 0x1172a683aa8eee0, 0xea518d8cbec2c1de, 0xe191bcbb63674557, 0x97bc19637b259011, 0xdbeae5c9f4a2e454, 0x78f64d1b72a42f95, 0xe71cb4ea7e181e54, 0xe4169d4c48543994, 0x6198c2286a98730f, 0xd21d675bbab1afa5, 0x2e7269fce391}, B: Fp{0x23355783ce1d0450, 0x683164cf4ce3d93f, 0xae6d1c4d25970fd8, 0x7807007fb80b48cf, 0xa005a62ec2bbb8a2, 0x6b5649bd016004cb, 0xbb1a13fa1330176b, 0xbf38e51087660461, 0xe577fddc5dd7b930, 0x5f38116f56947cd3, 0x3124f30b98c36fde, 0x4ca9b6e6db37}, }, Z: params.OneFp2, }, } scalar3Pt = [...]uint8{84, 222, 146, 63, 85, 18, 173, 162, 167, 38, 10, 8, 143, 176, 93, 228, 247, 128, 50, 128, 205, 42, 15, 137, 119, 67, 43, 3, 61, 91, 237, 24, 235, 12, 53, 96, 186, 164, 232, 223, 197, 224, 64, 109, 137, 63, 246, 4} ) var quickCheckConfig = &quick.Config{ MaxCount: (1 << 15), } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/000077500000000000000000000000001454601126700246235ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/arith_decl.gotemp000066400000000000000000000027371454601126700301470ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build {{if .OPT_ARM}}({{end}}amd64 && !noasm{{if .OPT_ARM}}) || (arm64 && !noasm){{end}} // +build amd64,!noasm{{if .OPT_ARM}} arm64,!noasm{{end}} package {{.PACKAGE}} import ( . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cmov{{.FIELD}}(x, y *Fp, choice uint8) // If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. // //go:noescape func cswap{{.FIELD}}(x, y *Fp, choice uint8) // Compute z = x + y (mod p). // //go:noescape func add{{.FIELD}}(z, x, y *Fp) // Compute z = x - y (mod p). // //go:noescape func sub{{.FIELD}}(z, x, y *Fp) // Compute z = x + y, without reducing mod p. // //go:noescape func adl{{.FIELD}}(z, x, y *FpX2) // Compute z = x - y, without reducing mod p. // //go:noescape func sul{{.FIELD}}(z, x, y *FpX2) // Reduce a field element in [0, 2*p) to one in [0,p). // //go:noescape func mod{{.FIELD}}(x *Fp) // Computes z = x * y. // //go:noescape func mul{{.FIELD}}(z *FpX2, x, y *Fp) // Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value // of x may be changed. z=x not allowed. // //go:noescape func rdc{{.FIELD}}(z *Fp, x *FpX2) golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/arith_generic.gotemp000066400000000000000000000110221454601126700306370ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. //go:build {{if .OPT_ARM}}noasm || (!amd64 && !arm64){{else}}noasm || !amd64{{end}} // +build {{if .OPT_ARM}}noasm !amd64,!arm64{{else}}noasm !amd64{{end}} package {{.PACKAGE}} import ( "math/bits" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Compute z = x + y (mod p). func add{{.FIELD}}(z, x, y *common.Fp) { var carry uint64 // z=x+y % {{.FIELD}} for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } // z = z - {{.FIELD}}x2 carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Sub64(z[i], {{.FIELD}}x2[i], carry) } // if z<0 add {{.FIELD}}x2 back mask := uint64(0 - carry) carry = 0 for i := 0; i < FpWords; i++ { z[i], carry = bits.Add64(z[i], {{.FIELD}}x2[i]&mask, carry) } } // Compute z = x - y (mod p). func sub{{.FIELD}}(z, x, y *common.Fp) { var borrow uint64 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } mask := uint64(0 - borrow) borrow = 0 for i := 0; i < FpWords; i++ { z[i], borrow = bits.Add64(z[i], {{.FIELD}}x2[i]&mask, borrow) } } // If choice = 0, leave x unchanged. If choice = 1, sets x to y. // If choice is neither 0 nor 1 then behaviour is undefined. // This function executes in constant time. func cmov{{.FIELD}}(x, y *common.Fp, choice uint8) { mask := 0 - uint64(choice) for i := 0; i < FpWords; i++ { x[i] ^= mask & (x[i] ^ y[i]) } } // Conditionally swaps bits in x and y in constant time. // mask indicates bits to be swapped (set bits are swapped) // For details see "Hackers Delight, 2.20" // // Implementation doesn't actually depend on a prime field. func cswap{{.FIELD}}(x, y *common.Fp, mask uint8) { var tmp, mask64 uint64 mask64 = 0 - uint64(mask) for i := 0; i < FpWords; i++ { tmp = mask64 & (x[i] ^ y[i]) x[i] = tmp ^ x[i] y[i] = tmp ^ y[i] } } // Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) // with R=2^(FpWords*64). Destroys the input value. func rdc{{.FIELD}}(z *common.Fp, x *common.FpX2) { var carry, t, u, v uint64 var hi, lo uint64 var count int count = {{.FIELD}}p1Zeros for i := 0; i < FpWords; i++ { for j := 0; j < i; j++ { if j < (i - count + 1) { hi, lo = bits.Mul64(z[j], {{.FIELD}}p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i] = v v = u u = t t = 0 } for i := FpWords; i < 2*FpWords-1; i++ { if count > 0 { count-- } for j := i - FpWords + 1; j < FpWords; j++ { if j < (FpWords - count) { hi, lo = bits.Mul64(z[j], {{.FIELD}}p1[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } } v, carry = bits.Add64(v, x[i], 0) u, carry = bits.Add64(u, 0, carry) t += carry z[i-FpWords] = v v = u u = t t = 0 } v, _ = bits.Add64(v, x[2*FpWords-1], 0) z[FpWords-1] = v } // Compute z = x * y. func mul{{.FIELD}}(z *common.FpX2, x, y *common.Fp) { var u, v, t uint64 var hi, lo uint64 var carry uint64 for i := uint64(0); i < FpWords; i++ { for j := uint64(0); j <= i; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } for i := FpWords; i < (2*FpWords)-1; i++ { for j := i - FpWords + 1; j < FpWords; j++ { hi, lo = bits.Mul64(x[j], y[i-j]) v, carry = bits.Add64(lo, v, 0) u, carry = bits.Add64(hi, u, carry) t += carry } z[i] = v v = u u = t t = 0 } z[2*FpWords-1] = v } // Compute z = x + y, without reducing mod p. func adl{{.FIELD}}(z, x, y *common.FpX2) { var carry uint64 for i := 0; i < 2*FpWords; i++ { z[i], carry = bits.Add64(x[i], y[i], carry) } } // Reduce a field element in [0, 2*p) to one in [0,p). func mod{{.FIELD}}(x *common.Fp) { var borrow, mask uint64 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Sub64(x[i], {{.FIELD}}[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := 0; i < FpWords; i++ { x[i], borrow = bits.Add64(x[i], {{.FIELD}}[i]&mask, borrow) } } // Compute z = x - y, without reducing mod p. func sul{{.FIELD}}(z, x, y *common.FpX2) { var borrow, mask uint64 for i := 0; i < 2*FpWords; i++ { z[i], borrow = bits.Sub64(x[i], y[i], borrow) } // Sets all bits if borrow = 1 mask = 0 - borrow borrow = 0 for i := FpWords; i < 2*FpWords; i++ { z[i], borrow = bits.Add64(z[i], {{.FIELD}}[i-FpWords]&mask, borrow) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/arith_test.gotemp000066400000000000000000000071341454601126700302130ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package {{.PACKAGE}} import ( "testing" "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Package-level storage for this field element is intended to deter // compiler optimizations. var ( benchmarkFp common.Fp benchmarkFpX2 common.FpX2 bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} ) func TestFpCswap(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cswap{{.FIELD}}(&x, &y, 0) for i := 0; i < FpWords; i++ { if (x[i] != one[i]) || (y[i] != two[i]) { t.Error("Found", x, "expected", one) } } cswap{{.FIELD}}(&x, &y, 1) for i := 0; i < FpWords; i++ { if (x[i] != two[i]) || (y[i] != one[i]) { t.Error("Found", x, "expected", two) } } } func TestFpCmov(t *testing.T) { one := common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} two := common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} x := one y := two cmov{{.FIELD}}(&x, &y, 0) for i := 0; i < FpWords; i++ { if x[i] != one[i] { t.Error("Found", x, "expected", one) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } cmov{{.FIELD}}(&x, &y, 1) for i := 0; i < FpWords; i++ { if x[i] != two[i] { t.Error("Found", x, "expected", two) } if y[i] != two[i] { t.Error("Found", y, "expected", two) } } } // Benchmarking for field arithmetic func BenchmarkMul(b *testing.B) { for n := 0; n < b.N; n++ { mul{{.FIELD}}(&benchmarkFpX2, &bench_x, &bench_y) } } func BenchmarkRdc(b *testing.B) { z := bench_z // This benchmark actually computes garbage, because // rdc{{.FIELD}} mangles its input, but since it's // constant-time that shouldn't matter for the benchmarks. for n := 0; n < b.N; n++ { rdc{{.FIELD}}(&benchmarkFp, &z) } } func BenchmarkAdd(b *testing.B) { for n := 0; n < b.N; n++ { add{{.FIELD}}(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkSub(b *testing.B) { for n := 0; n < b.N; n++ { sub{{.FIELD}}(&benchmarkFp, &bench_x, &bench_y) } } func BenchmarkCswap(b *testing.B) { x, y := bench_x, bench_y for n := 0; n < b.N; n++ { cswap{{.FIELD}}(&x, &y, 1) cswap{{.FIELD}}(&x, &y, 0) } } func BenchmarkMod(b *testing.B) { x := bench_x for n := 0; n < b.N; n++ { mod{{.FIELD}}(&x) } } func BenchmarkX2AddLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { adl{{.FIELD}}(&x, &y, &z) } } func BenchmarkX2SubLazy(b *testing.B) { x, y, z := bench_z, bench_z, bench_z for n := 0; n < b.N; n++ { sul{{.FIELD}}(&x, &y, &z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/core.gotemp000066400000000000000000000205561454601126700270000ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package {{.PACKAGE}} import ( crand "crypto/rand" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // ----------------------------------------------------------------------------- // Functions for traversing isogeny trees according to strategy. Key type 'A' is // // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR needed // for public key generation. func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny4 cparam := CalcCurveParamsEquiv4(curve) strat := params.A.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow2k(xR, &cparam, 2*k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } phi.EvaluatePoint(phiP) phi.EvaluatePoint(phiQ) phi.EvaluatePoint(phiR) // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed // for public key generation. func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { points := make([]ProjectivePoint, 0, 8) indices := make([]int, 0, 8) var i, sIdx int var phi isogeny3 cparam := CalcCurveParamsEquiv3(curve) strat := params.B.IsogenyStrategy stratSz := len(strat) for j := 1; j <= stratSz; j++ { for i <= stratSz-j { points = append(points, *xR) indices = append(indices, i) k := strat[sIdx] sIdx++ Pow3k(xR, &cparam, k) i += int(k) } cparam = phi.GenerateCurve(xR) for k := 0; k < len(points); k++ { phi.EvaluatePoint(&points[k]) } // pop xR from points *xR, points = points[len(points)-1], points[:len(points)-1] i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] } } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { var xPA, xQA, xRA ProjectivePoint var xPB, xQB, xRB, xR ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny4 // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) // Secret isogeny phi.GenerateCurve(&xR) xPA = xPB xQA = xQB xRA = xRB phi.EvaluatePoint(&xPA) phi.EvaluatePoint(&xQA) phi.EvaluatePoint(&xRA) Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPA.X, &invZP) mul(&pub3Pt[1], &xQA.X, &invZQ) mul(&pub3Pt[2], &xRA.X, &invZR) } // Generate a public key in the 2-torsion group. Public key is a set // of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { var xPB, xQB, xRB, xR ProjectivePoint var xPA, xQA, xRA ProjectivePoint var invZP, invZQ, invZR Fp2 var phi isogeny3 // Load points for B xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Load points for A xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} // Find isogeny kernel xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) phi.GenerateCurve(&xR) xPB = xPA xQB = xQA xRB = xRA phi.EvaluatePoint(&xPB) phi.EvaluatePoint(&xQB) phi.EvaluatePoint(&xRB) Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) mul(&pub3Pt[0], &xPB.X, &invZP) mul(&pub3Pt[1], &xQB.X, &invZQ) mul(&pub3Pt[2], &xRB.X, &invZR) } // ----------------------------------------------------------------------------- // Key agreement functions // // Establishing shared keys in in 2-torsion group func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny4 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyA(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients4(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } // Establishing shared keys in in 3-torsion group func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { var xP, xQ, xQmP ProjectivePoint var xR ProjectivePoint var phi isogeny3 var jInv Fp2 // Recover curve coefficients cparam := params.InitCurve RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) // Find kernel of the morphism xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} //PUBLIC KEY VALIDATION if err := PublicKeyValidation(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen); err != nil { _, err_read := crand.Read(ss) if err_read != nil { panic("core: failed to generate random ss when public key verification fails") } return } xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) // Traverse isogeny tree traverseTreeSharedKeyB(&cparam, &xR) // Calculate j-invariant on isogenous curve c := phi.GenerateCurve(&xR) RecoverCurveCoefficients3(&cparam, &c) Jinvariant(&cparam, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(ss, &jInv, params.Bytelen) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/curve.gotemp000066400000000000000000000341121454601126700271650ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package {{.PACKAGE}} import ( "math" "errors" . "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Stores isogeny 3 curve constants type isogeny3 struct { K1 Fp2 K2 Fp2 } // Stores isogeny 4 curve constants type isogeny4 struct { isogeny3 K3 Fp2 } // Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result // is returned in jBytes buffer, encoded in little-endian format. Caller // provided jBytes buffer has to be big enough to j-invariant value. In case // of SIDH, buffer size must be at least size of shared secret. // Implementation corresponds to Algorithm 9 from SIKE. func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { var t0, t1 Fp2 sqr(j, &cparams.A) // j = A^2 sqr(&t1, &cparams.C) // t1 = C^2 add(&t0, &t1, &t1) // t0 = t1 + t1 sub(&t0, j, &t0) // t0 = j - t0 sub(&t0, &t0, &t1) // t0 = t0 - t1 sub(j, &t0, &t1) // t0 = t0 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(j, j, &t1) // j = j * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&t1, &t0) // t1 = t0^2 mul(&t0, &t0, &t1) // t0 = t0 * t1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t0, &t0, &t0) // t0 = t0 + t0 inv(j, j) // j = 1/j mul(j, &t0, j) // j = t0 * j } // Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function // recovers projective coordinate A of a curve. This is Algorithm 10 from SIKE. func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { var t0, t1 Fp2 add(&t1, xp, xq) // t1 = Xp + Xq mul(&t0, xp, xq) // t0 = Xp * Xq mul(&curve.A, xr, &t1) // A = X(q-p) * t1 add(&curve.A, &curve.A, &t0) // A = A + t0 mul(&t0, &t0, xr) // t0 = t0 * X(q-p) sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 add(&t0, &t0, &t0) // t0 = t0 + t0 add(&t1, &t1, xr) // t1 = t1 + X(q-p) add(&t0, &t0, &t0) // t0 = t0 + t0 sqr(&curve.A, &curve.A) // A = A^2 inv(&t0, &t0) // t0 = 1/t0 mul(&curve.A, &curve.A, &t0) // A = A * t0 sub(&curve.A, &curve.A, &t1) // A = A - t1 } // Computes equivalence (A:C) ~ (A+2C : A-2C) func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coef CurveCoefficientsEquiv var c2 Fp2 add(&c2, &cparams.C, &cparams.C) // A24p = A+2*C add(&coef.A, &cparams.A, &c2) // A24m = A-2*C sub(&coef.C, &cparams.A, &c2) return coef } // Computes equivalence (A:C) ~ (A+2C : 4C) func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv add(&coefEq.C, &cparams.C, &cparams.C) // A24p = A+2C add(&coefEq.A, &cparams.A, &coefEq.C) // C24 = 4*C add(&coefEq.C, &coefEq.C, &coefEq.C) return coefEq } // Helper function for RightToLeftLadder(). Returns A+2C / 4. func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { var tmp Fp2 // 2C add(&tmp, &cparams.C, &cparams.C) // A+2C add(&ret, &cparams.A, &tmp) // 1/4C add(&tmp, &tmp, &tmp) inv(&tmp, &tmp) // A+2C/4C mul(&ret, &ret, &tmp) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { add(&cparams.A, &coefEq.A, &coefEq.C) // cparams.A = 2*(A+2C+A-2C) = 4A add(&cparams.A, &cparams.A, &cparams.A) // cparams.C = (A+2C-A+2C) = 4C sub(&cparams.C, &coefEq.A, &coefEq.C) return } // Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { // cparams.C = (4C)*1/2=2C mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) // cparams.A = A+2C - 2C = A sub(&cparams.A, &coefEq.A, &cparams.C) // cparams.C = 2C * 1/2 = C mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) } // Combined coordinate doubling and differential addition. Takes projective points // P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. // Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { var t0, t1, t2 Fp2 xQmP, zQmP := &QmP.X, &QmP.Z xPaQ, zPaQ := &PaQ.X, &PaQ.Z x2P, z2P := &dblP.X, &dblP.Z xP, zP := &P.X, &P.Z xQ, zQ := &Q.X, &Q.Z add(&t0, xP, zP) // t0 = Xp+Zp sub(&t1, xP, zP) // t1 = Xp-Zp sqr(x2P, &t0) // 2P.X = t0^2 sub(&t2, xQ, zQ) // t2 = Xq-Zq add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq mul(&t0, &t0, &t2) // t0 = t0 * t2 mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q return } // Given the curve parameters, xP = x(P), computes xP = x([2^k]P) // Safe to overlap xP, x2P. func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp add(&t1, x, z) // t1 = Xp + Zp sqr(&t0, &t0) // t0 = t0 ^ 2 sqr(&t1, &t1) // t1 = t1 ^ 2 mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 mul(x, z, &t1) // X2p = Z2p * t1 sub(&t1, &t1, &t0) // t1 = t1 - t0 mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 add(z, z, &t0) // Z2p = Z2p + t0 mul(z, z, &t1) // Zp = Z2p * t1 } } // Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). // // Safe to overlap xP, xR. func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { var t0, t1, t2, t3, t4, t5, t6 Fp2 x, z := &xP.X, &xP.Z for i := uint32(0); i < k; i++ { sub(&t0, x, z) // t0 = Xp - Zp sqr(&t2, &t0) // t2 = t0^2 add(&t1, x, z) // t1 = Xp + Zp sqr(&t3, &t1) // t3 = t1^2 add(&t4, &t1, &t0) // t4 = t1 + t0 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t1, &t4) // t1 = t4^2 sub(&t1, &t1, &t3) // t1 = t1 - t3 sub(&t1, &t1, &t2) // t1 = t1 - t2 mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ mul(&t3, &t3, &t5) // t3 = t5 * t3 mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- mul(&t2, &t2, &t6) // t2 = t2 * t6 sub(&t3, &t2, &t3) // t3 = t2 - t3 sub(&t2, &t5, &t6) // t2 = t5 - t6 mul(&t1, &t2, &t1) // t1 = t2 * t1 add(&t2, &t3, &t1) // t2 = t3 + t1 sqr(&t2, &t2) // t2 = t2^2 mul(x, &t2, &t4) // X3p = t2 * t4 sub(&t1, &t3, &t1) // t1 = t3 - t1 sqr(&t1, &t1) // t1 = t1^2 mul(z, &t1, &t0) // Z3p = t1 * t0 } } // Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). // // All xi, yi must be distinct. func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { var x1x2, t Fp2 mul(&x1x2, x1, x2) // x1*x2 mul(&t, &x1x2, x3) // 1/(x1*x2*x3) inv(&t, &t) mul(y1, &t, x2) // 1/x1 mul(y1, y1, x3) mul(y2, &t, x1) // 1/x2 mul(y2, y2, x3) mul(y3, &t, &x1x2) // 1/x3 } // Scalarmul3Pt is a right-to-left point multiplication that given the // x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. // nbits must be smaller or equal to len(scalar). func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { var R0, R2, R1 ProjectivePoint aPlus2Over4 := CalcAplus2Over4(cparams) R1 = *P R2 = *PmQ R0 = *Q // Iterate over the bits of the scalar, bottom to top prevBit := uint8(0) for i := uint(0); i < nbits; i++ { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) } cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) return R1 } // Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the // three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C // Output: // - Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var t0, t1, t2, t3, t4 Fp2 var coefEq CurveCoefficientsEquiv K1, K2 := &phi.K1, &phi.K2 sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 sqr(&t0, K1) // t0 = K1^2 add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 sqr(&t1, K2) // t1 = K2^2 add(&t2, &t0, &t1) // t2 = t0 + t1 add(&t3, K1, K2) // t3 = K1 + K2 sqr(&t3, &t3) // t3 = t3^2 sub(&t3, &t3, &t2) // t3 = t3 - t2 add(&t2, &t1, &t3) // t2 = t1 + t3 add(&t3, &t3, &t0) // t3 = t3 + t0 add(&t4, &t3, &t0) // t4 = t3 + t0 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t1, &t4) // t4 = t1 + t4 mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 add(&t4, &t1, &t2) // t4 = t1 + t2 add(&t4, &t4, &t4) // t4 = t4 + t4 add(&t4, &t0, &t4) // t4 = t0 + t4 mul(&t4, &t3, &t4) // t4 = t3 * t4 sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 return coefEq } // Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate // of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). // // The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve // parameters are returned by the GenerateCurve function used to construct phi. func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) { var t0, t1, t2 Fp2 K1, K2 := &phi.K1, &phi.K2 px, pz := &p.X, &p.Z add(&t0, px, pz) // t0 = XQ + ZQ sub(&t1, px, pz) // t1 = XQ - ZQ mul(&t0, K1, &t0) // t2 = K1 * t0 mul(&t1, K2, &t1) // t1 = K2 * t1 add(&t2, &t0, &t1) // t2 = t0 + t1 sub(&t0, &t1, &t0) // t0 = t1 - t0 sqr(&t2, &t2) // t2 = t2 ^ 2 sqr(&t0, &t0) // t0 = t0 ^ 2 mul(px, px, &t2) // XQ'= XQ * t2 mul(pz, pz, &t0) // ZQ'= ZQ * t0 } // Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the // four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). // // Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C // Output: // - Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ // - Isogeny phi with constants in F_p^2 func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { var coefEq CurveCoefficientsEquiv xp4, zp4 := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 sub(K2, xp4, zp4) add(K3, xp4, zp4) sqr(K1, zp4) add(K1, K1, K1) sqr(&coefEq.C, K1) add(K1, K1, K1) sqr(&coefEq.A, xp4) add(&coefEq.A, &coefEq.A, &coefEq.A) sqr(&coefEq.A, &coefEq.A) return coefEq } // Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate // of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). // // Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C // Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) { var t0, t1 Fp2 xq, zq := &p.X, &p.Z K1, K2, K3 := &phi.K1, &phi.K2, &phi.K3 add(&t0, xq, zq) sub(&t1, xq, zq) mul(xq, &t0, K2) mul(zq, &t1, K3) mul(&t0, &t0, &t1) mul(&t0, &t0, K1) add(&t1, xq, zq) sub(zq, xq, zq) sqr(&t1, &t1) sqr(zq, zq) add(xq, &t0, &t1) sub(&t0, zq, &t0) mul(xq, xq, &t1) mul(zq, zq, &t0) } // PublicKeyValidation preforms public key/ciphertext validation using the CLN test. // CLN test: Check that P and Q are both of order 3^e3 and they generate the torsion E_A[3^e3] // A countermeasure for remote timing attacks on SIKE; suggested by https://eprint.iacr.org/2022/054.pdf // Any curve E_A (SIKE 434, 503, 751) that passes CLN test is supersingular. // Input: The public key / ciphertext P, Q, PmQ. The projective coordinate A of the curve defined by (P, Q, PmQ) // Outputs: Whether (P,Q,PmQ) follows the CLN test func PublicKeyValidation(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint) error { var PmQX, PmQZ Fp2 FromMontgomery(&PmQX, &PmQ.X) FromMontgomery(&PmQZ, &PmQ.Z) // PmQ is not point T or O if((isZero(&PmQX)==1)||(isZero(&PmQZ)==1)){ return errors.New("curve: PmQ is invalid") } cparam := CalcCurveParamsEquiv3(cparams) // Compute e_3 = log3(2^(nbits+1)) var e3 uint32 e3_float := float64(int(nbits)+1)/math.Log2(3) e3 = uint32(e3_float) // Verify that P and Q generate E_A[3^e_3] by checking: [3^(e_3-1)]P != [+-3^(e_3-1)]Q var test_P, test_Q ProjectivePoint test_P = *P test_Q = *Q Pow3k(&test_P, &cparam, e3-1) Pow3k(&test_Q, &cparam, e3-1) var PZ, QZ Fp2 FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of full order 3^e_3 if((isZero(&PZ)==1)||(isZero(&QZ)==1)){ return errors.New("curve: ciphertext/public key are not of full order 3^e3") } // PX/PZ = affine(PX) // QX/QZ = affine(QX) // If PX/PZ = QX/QZ, we have P=+-Q var PXQZ_PZQX_fromMont, PXQZ_PZQX, PXQZ, PZQX Fp2 mul(&PXQZ, &test_P.X, &test_Q.Z) mul(&PZQX, &test_P.Z, &test_Q.X) sub(&PXQZ_PZQX, &PXQZ, &PZQX) FromMontgomery(&PXQZ_PZQX_fromMont, &PXQZ_PZQX) // [3^(e_3-1)]P == [+-3^(e_3-1)]Q if(isZero(&PXQZ_PZQX_fromMont)==1){ return errors.New("curve: ciphertext/public key are not linearly independent") } // Check that Ord(P) = Ord(Q) = 3^(e_3) Pow3k(&test_P, &cparam, 1) Pow3k(&test_Q, &cparam, 1) FromMontgomery(&PZ, &test_P.Z) FromMontgomery(&QZ, &test_Q.Z) // P, Q are not of correct order 3^e_3 if((isZero(&PZ)==0)||(isZero(&QZ)==0)){ return errors.New("curve: ciphertext/public key are not of correct order 3^e3") } return nil } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/curve_test.gotemp000066400000000000000000000304451454601126700302310ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package {{.PACKAGE}} import ( "bytes" "testing" "math" "math/rand" crand "crypto/rand" "io" . "github.com/cloudflare/circl/dh/sidh/internal/common" "time" ) func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { var t0, t1 Fp2 mul(&t0, &lhs.X, &rhs.Z) mul(&t1, &lhs.Z, &rhs.X) return vartimeEqFp2(&t0, &t1) } func toAffine(point *ProjectivePoint) *Fp2 { var affineX Fp2 inv(&affineX, &point.Z) mul(&affineX, &affineX, &point.X) return &affineX } func Test_jInvariant(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} jbufRes := make([]byte, params.SharedSecretSize) jbufExp := make([]byte, params.SharedSecretSize) var jInv Fp2 Jinvariant(&curve, &jInv) FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufRes, &jInv, params.Bytelen) jInv = expectedJ FromMontgomery(&jInv, &jInv) Fp2ToBytes(jbufExp, &jInv, params.Bytelen) if !bytes.Equal(jbufRes[:], jbufExp[:]) { t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) } } func TestProjectivePointVartimeEq(t *testing.T) { var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} xQ := xP // Scale xQ, which results in the same projective point mul(&xQ.X, &xQ.X, &curveA) mul(&xQ.Z, &xQ.Z, &curveA) if !vartimeEqProjFp2(&xP, &xQ) { t.Error("Expected the scaled point to be equal to the original") } } func TestPointMulVersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv4(&curve) var xP ProjectivePoint // x 2 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 1) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP2) { t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) } // x 4 xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow2k(&xP, &cparams, 2) afxQ = toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP4) { t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) } } func TestPointMul9VersusSage(t *testing.T) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} cparams := CalcCurveParamsEquiv3(&curve) var xP ProjectivePoint xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} Pow3k(&xP, &cparams, 2) afxQ := toAffine(&xP) if !vartimeEqFp2(afxQ, &affineXP9) { t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) } } func BenchmarkThreePointLadder(b *testing.B) { curve := ProjectiveCurveParameters{A: curveA, C: curveC} for n := 0; n < b.N; n++ { ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) } } /* ------------------------------------------------------------------------- Generate invalid public key points / ciphertext for test TestKEMInvalidPK -------------------------------------------------------------------------*/ // Left-to-right Montgomery ladder, Algorithm 4 in Costello-Smith // Input: ProjectivePoint P (xP, zP) // Output: x([scalar]P), z([scalar]P) func montgomeryLadder(cparams *ProjectiveCurveParameters, P *ProjectivePoint, scalar []uint8, random uint) ProjectivePoint { var R0, R2, R1 ProjectivePoint coefEq := CalcCurveParamsEquiv4(cparams) // for xDbl aPlus2Over4 := CalcAplus2Over4(cparams) // for xDblAdd R0 = *P // RO <- P R1 = *P Pow2k(&R1, &coefEq, 1) // R1 <- [2]P R2 = *P // R2 = R1-R0 = P prevBit := uint8(0) for i := int(random); i >= 0; i-- { bit := (scalar[i>>3] >> (i & 7) & 1) swap := prevBit ^ bit prevBit = bit cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, swap) R0, R1 = xDbladd(&R0, &R1, &R2, &aPlus2Over4) } cswap(&R0.X, &R0.Z, &R1.X, &R1.Z, prevBit) return R0 } // P = P + T // From paper https://eprint.iacr.org/2017/212.pdf // The map tau_T: P->P+T is (X : Z) -> (Z : X) on Montgomery curves func tauT(P *ProjectivePoint) { P.X, P.Z = P.Z, P.X // magic! } // Construct Invalid public key tuple (P,Q) such that P and Q are linearly dependent // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKNoneLinear(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil{ t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1)*8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Make sure Q is of full order 3^e_3, var test_Q ProjectivePoint test_Q = Q var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1)/math.Log2(3) e3 = uint32(e3_float) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&test_Q, &cparam_q, e3-1) var test_QZ Fp2 FromMontgomery(&test_QZ, &test_Q.Z) // Q are not of full order 3^e_3 for((isZero(&test_QZ)==1)){ rand.Seed(time.Now().UnixNano()) random_index = rand.Intn(int(params.B.SecretByteLen-1)*8) Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) test_Q = Q Pow3k(&test_Q, &cparam_q, e3-1) FromMontgomery(&test_QZ, &test_Q.Z) } // invQz = 1/Q.Z var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify==nil{ t.Errorf("\nExpect linearly dependent ciphertext to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that Q = [k]P + T, where k is random and T is the point of order 2. // Simulate HB and section 3.1.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKT(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil{ t.Error("Fail read random bytes") } var P, Q ProjectivePoint rand.Seed(time.Now().UnixNano()) random_index := rand.Intn(int(params.B.SecretByteLen-1)*8) // Set P as a point of order 3^e3 P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} // Set Q = [k]P, where k = secret[:random_index] Q = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index)) // Q = [k]P + T tauT(&Q) var invQz Fp2 invQz = Q.Z inv(&invQz, &invQz) mul(&P.X, &P.X, &P.Z) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify==nil{ t.Errorf("\nExpect ciphertext involve point T to fail, index: %v scalar: %v ", random_index, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[2^e2] // Simulate section 3.2 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKOrder2(t *testing.T) { // Generate random scalar as secret secret := make([]byte, params.B.SecretByteLen) _, err := io.ReadFull(crand.Reader, secret) if err != nil{ t.Error("Fail read random bytes") } var P, Q ProjectivePoint P = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(params.A.SecretByteLen-1)*8) random_index_q := rand.Intn(int(params.A.SecretByteLen-1)*8) P = montgomeryLadder(¶ms.InitCurve, &P, secret, uint(random_index_p)) Q = montgomeryLadder(¶ms.InitCurve, &Q, secret, uint(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify==nil{ t.Errorf("\nExpect ciphertext in torsion E[2^e2] to fail, index_p: %v index_q: %v scalar: %v ", random_index_p, random_index_q, secret) } } // Construct Invalid public key tuple (P,Q) such that P and Q are in E[3^e3] but not of full order 3^e3 // Simulate section 3.1.1 of paper https://eprint.iacr.org/2022/054.pdf // We only construct point P and Q because in the attacks the third point is P-Q by construction // and the countermeasure does not test it // Without loss of generality, we assume the curve is the starting curve func testInvalidPKFullOrder(t *testing.T) { var P, Q ProjectivePoint P = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} Q = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} var e3 uint32 e3_float := float64(int(params.B.SecretBitLen)+1)/math.Log2(3) e3 = uint32(e3_float) rand.Seed(time.Now().UnixNano()) random_index_p := rand.Intn(int(e3)) random_index_q := rand.Intn(int(e3)) cparam_q := CalcCurveParamsEquiv3(¶ms.InitCurve) Pow3k(&P, &cparam_q, uint32(random_index_p)) Pow3k(&Q, &cparam_q, uint32(random_index_q)) var invQz, invPz Fp2 invQz = Q.Z invPz = P.Z inv(&invQz, &invQz) inv(&invPz, &invPz) mul(&P.X, &P.X, &invPz) mul(&Q.X, &Q.X, &invQz) var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: P.X, Z: params.OneFp2} xQ = ProjectivePoint{X: Q.X, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify==nil{ t.Errorf("\nExpect ciphertext not of full order to fail, index_p: %v index_q: %v ", random_index_p, random_index_q) } } // A trivial test case not covered by paper https://eprint.iacr.org/2022/054.pdf and HB // Countermeasure in https://eprint.iacr.org/2022/054.pdf only cares about P and Q // But if PmQ is point T or O, that can also lead to recovery of the first bit func testInvalidPmQ(t *testing.T) { var zero Fp2 var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: zero, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify==nil{ t.Errorf("\nExpect PmQ as T to fail\n") } } // Test valid ciphertext // Where P, Q are linearly independent points of correct order 3^e3 in E[3^e3] func testValidPQ(t *testing.T) { var xP, xQ, xQmP ProjectivePoint xP = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} xQ = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} xQmP = ProjectivePoint{X: params.OneFp2, Z: params.OneFp2} error_verify := PublicKeyValidation(¶ms.InitCurve, &xP, &xQ, &xQmP, params.B.SecretBitLen) if error_verify!=nil{ t.Errorf("\nExpect correct ciphertext to not fail\n") } } /* ------------------------------------------------------------------------- Public key / Ciphertext validation against attacks proposed in paper https://eprint.iacr.org/2022/054.pdf and HB -------------------------------------------------------------------------*/ func TestInvalidPK(t *testing.T) { t.Run("InvalidPmQ", testInvalidPmQ) t.Run("InvalidPKNoneLinear", testInvalidPKNoneLinear) t.Run("InvalidPKT", testInvalidPKT) t.Run("InvalidPKOrder2", testInvalidPKOrder2) t.Run("InvalidPKFullOrder", testInvalidPKFullOrder) t.Run("ValidPQ", testValidPQ) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/fp2.gotemp000066400000000000000000000142311454601126700265300ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package {{.PACKAGE}} import ( "github.com/cloudflare/circl/dh/sidh/internal/common" ) // Montgomery multiplication. Input values must be already // in Montgomery domain. func mulP(dest, lhs, rhs *common.Fp) { var ab common.FpX2 mul{{.FIELD}}(&ab, lhs, rhs) // = a*b*R*R rdc{{.FIELD}}(dest, &ab) // = a*b*R mod p } // Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). // Uses variation of sliding-window algorithm from with window size // of 5 and least to most significant bit sliding (left-to-right) // See HAC 14.85 for general description. // // Allowed to overlap x with dest. // All values in Montgomery domains // Set dest = x^(2^k), for k >= 1, by repeated squarings. func p34(dest, x *common.Fp) { var lookup [16]common.Fp // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) // multiplications. powStrategy := {{.P34_POW_STRATEGY}} mulStrategy := {{.P34_MUL_STRATEGY}} initialMul := uint8({{.P34_INITIAL_MUL}}) // Precompute lookup table of odd multiples of x for window // size k=5. var xx common.Fp mulP(&xx, x, x) lookup[0] = *x for i := 1; i < 16; i++ { mulP(&lookup[i], &lookup[i-1], &xx) } // Now lookup = {x, x^3, x^5, ... } // so that lookup[i] = x^{2*i + 1} // so that lookup[k/2] = x^k, for odd k *dest = lookup[initialMul] for i := uint8(0); i < uint8(len(powStrategy)); i++ { mulP(dest, dest, dest) for j := uint8(1); j < powStrategy[i]; j++ { mulP(dest, dest, dest) } mulP(dest, dest, &lookup[mulStrategy[i]]) } } func add(dest, lhs, rhs *common.Fp2) { add{{.FIELD}}(&dest.A, &lhs.A, &rhs.A) add{{.FIELD}}(&dest.B, &lhs.B, &rhs.B) } func sub(dest, lhs, rhs *common.Fp2) { sub{{.FIELD}}(&dest.A, &lhs.A, &rhs.A) sub{{.FIELD}}(&dest.B, &lhs.B, &rhs.B) } func mul(dest, lhs, rhs *common.Fp2) { var bMinA, cMinD common.Fp var ac, bd common.FpX2 var adPlusBc common.FpX2 var acMinBd common.FpX2 // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). // // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i // // Use Karatsuba's trick: note that // // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d // // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. sub{{.FIELD}}(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R sub{{.FIELD}}(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R mul{{.FIELD}}(&ac, &lhs.A, &rhs.A) // = a*c*R*R mul{{.FIELD}}(&bd, &lhs.B, &rhs.B) // = b*d*R*R mul{{.FIELD}}(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R adl{{.FIELD}}(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R adl{{.FIELD}}(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R rdc{{.FIELD}}(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p sul{{.FIELD}}(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R rdc{{.FIELD}}(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p } // Set dest = 1/x // // Allowed to overlap dest with x. // // Returns dest to allow chaining operations. func inv(dest, x *common.Fp2) { var e1, e2 common.FpX2 var f1, f2 common.Fp // We want to compute // // 1 1 (a - bi) (a - bi) // -------- = -------- -------- = ----------- // (a + bi) (a + bi) (a - bi) (a^2 + b^2) // // Letting c = 1/(a^2 + b^2), this is // // 1/(a+bi) = a*c - b*ci. mul{{.FIELD}}(&e1, &x.A, &x.A) // = a*a*R*R mul{{.FIELD}}(&e2, &x.B, &x.B) // = b*b*R*R adl{{.FIELD}}(&e1, &e1, &e2) // = (a^2 + b^2)*R*R rdc{{.FIELD}}(&f1, &e1) // = (a^2 + b^2)*R mod p // Now f1 = a^2 + b^2 mulP(&f2, &f1, &f1) p34(&f2, &f2) mulP(&f2, &f2, &f2) mulP(&f2, &f2, &f1) mul{{.FIELD}}(&e1, &x.A, &f2) rdc{{.FIELD}}(&dest.A, &e1) sub{{.FIELD}}(&f1, &common.Fp{}, &x.B) mul{{.FIELD}}(&e1, &f1, &f2) rdc{{.FIELD}}(&dest.B, &e1) } func sqr(dest, x *common.Fp2) { var a2, aPlusB, aMinusB common.Fp var a2MinB2, ab2 common.FpX2 a := &x.A b := &x.B // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. add{{.FIELD}}(&a2, a, a) // = a*R + a*R = 2*a*R add{{.FIELD}}(&aPlusB, a, b) // = a*R + b*R = (a+b)*R sub{{.FIELD}}(&aMinusB, a, b) // = a*R - b*R = (a-b)*R mul{{.FIELD}}(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R mul{{.FIELD}}(&ab2, &a2, b) // = 2*a*b*R*R rdc{{.FIELD}}(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p rdc{{.FIELD}}(&dest.B, &ab2) // = 2*a*b*R mod p } // In case choice == 1, performs following swap in constant time: // // xPx <-> xQx // xPz <-> xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cswap{{.FIELD}}(&xPx.A, &xQx.A, choice) cswap{{.FIELD}}(&xPx.B, &xQx.B, choice) cswap{{.FIELD}}(&xPz.A, &xQz.A, choice) cswap{{.FIELD}}(&xPz.B, &xQz.B, choice) } // In case choice == 1, performs following moves in constant time: // // xPx <- xQx // xPz <- xQz // // Otherwise returns xPx, xPz, xQx, xQz unchanged func cmov(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cmov{{.FIELD}}(&xPx.A, &xQx.A, choice) cmov{{.FIELD}}(&xPx.B, &xQx.B, choice) cmov{{.FIELD}}(&xPz.A, &xQz.A, choice) cmov{{.FIELD}}(&xPz.B, &xQz.B, choice) } func isZero(x *common.Fp2) uint8 { r64 := uint64(0) for i := 0; i < FpWords; i++ { r64 |= x.A[i] | x.B[i] } r := uint8(0) for i := uint64(0); i < 64; i++ { r |= uint8((r64 >> i) & 0x1) } return 1 - r } // Converts in.A and in.B to Montgomery domain and stores // in 'out' // out.A = in.A * R mod p // out.B = in.B * R mod p // Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B func ToMontgomery(out, in *common.Fp2) { var aRR common.FpX2 // a*R*R mul{{.FIELD}}(&aRR, &in.A, &{{.FIELD}}R2) // a*R mod p rdc{{.FIELD}}(&out.A, &aRR) mul{{.FIELD}}(&aRR, &in.B, &{{.FIELD}}R2) rdc{{.FIELD}}(&out.B, &aRR) } // Converts in.A and in.B from Montgomery domain and stores // in 'out' // out.A = in.A mod p // out.B = in.B mod p // // After returning from the call 'in' is not modified. func FromMontgomery(out, in *common.Fp2) { var aR common.FpX2 // convert from montgomery domain copy(aR[:], in.A[:]) rdc{{.FIELD}}(&out.A, &aR) // = a mod p in [0, 2p) mod{{.FIELD}}(&out.A) // = a mod p in [0, p) for i := range aR { aR[i] = 0 } copy(aR[:], in.B[:]) rdc{{.FIELD}}(&out.B, &aR) mod{{.FIELD}}(&out.B) } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/fp2_test.gotemp000066400000000000000000000126261454601126700275750ustar00rootroot00000000000000// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package {{.PACKAGE}} import ( "math/rand" "reflect" "testing" "testing/quick" "github.com/cloudflare/circl/dh/sidh/internal/common" ) type testParams struct { Point common.ProjectivePoint Cparam common.ProjectiveCurveParameters ExtElem common.Fp2 } // Returns true if lhs = rhs. Takes variable time. func vartimeEqFp2(lhs, rhs *common.Fp2) bool { a := *lhs b := *rhs mod{{.FIELD}}(&a.A) mod{{.FIELD}}(&a.B) mod{{.FIELD}}(&b.A) mod{{.FIELD}}(&b.B) eq := true for i := 0; i < FpWords && eq; i++ { eq = eq && (a.A[i] == b.A[i]) eq = eq && (a.B[i] == b.B[i]) } return eq } func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { // Generation strategy: low limbs taken from [0,2^64); high limb // taken from smaller range // // Size hint is ignored since all elements are fixed size. // // Field elements taken in range [0,2p). Emulate this by capping // the high limb by the top digit of 2*p-1: // // sage: (2*p-1).digits(2^64)[-1] // // This still allows generating values >= 2p, but hopefully that // excess is OK (and if it's not, we'll find out, because it's for // testing...) highLimb := rand.Uint64() % {{.FIELD}}x2[FpWords-1] fpElementGen := func() (fp common.Fp) { for i := 0; i < (FpWords - 1); i++ { fp[i] = rand.Uint64() } fp[FpWords-1] = highLimb return fp } return common.Fp2{A: fpElementGen(), B: fpElementGen()} } func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { return reflect.ValueOf( testParams{ common.ProjectivePoint{ X: c.generateFp2(rand), Z: c.generateFp2(rand), }, common.ProjectiveCurveParameters{ A: c.generateFp2(rand), C: c.generateFp2(rand), }, c.generateFp2(rand), }) } func TestOne(t *testing.T) { var tmp common.Fp2 mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { t.Error("Not equal 1") } } func TestFp2ToBytesRoundTrip(t *testing.T) { roundTrips := func(x testParams) bool { xBytes := make([]byte, 2*params.Bytelen) var xPrime common.Fp2 common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) return vartimeEqFp2(&xPrime, &x.ExtElem) } if err := quick.Check(roundTrips, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulDistributesOverAdd(t *testing.T) { mulDistributesOverAdd := func(x, y, z testParams) bool { // Compute t1 = (x+y)*z t1 := new(common.Fp2) add(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = x*z + y*z t2 := new(common.Fp2) t3 := new(common.Fp2) mul(t2, &x.ExtElem, &z.ExtElem) mul(t3, &y.ExtElem, &z.ExtElem) add(t2, t2, t3) return vartimeEqFp2(t1, t2) } if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2MulIsAssociative(t *testing.T) { isAssociative := func(x, y, z testParams) bool { // Compute t1 = (x*y)*z t1 := new(common.Fp2) mul(t1, &x.ExtElem, &y.ExtElem) mul(t1, t1, &z.ExtElem) // Compute t2 = (y*z)*x t2 := new(common.Fp2) mul(t2, &y.ExtElem, &z.ExtElem) mul(t2, t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(isAssociative, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2SquareMatchesMul(t *testing.T) { sqrMatchesMul := func(x testParams) bool { // Compute t1 = (x*x) t1 := new(common.Fp2) mul(t1, &x.ExtElem, &x.ExtElem) // Compute t2 = x^2 t2 := new(common.Fp2) sqr(t2, &x.ExtElem) return vartimeEqFp2(t1, t2) } if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { t.Error(err) } } func TestFp2Inv(t *testing.T) { inverseIsCorrect := func(x testParams) bool { z := new(common.Fp2) inv(z, &x.ExtElem) // Now z = (1/x), so (z * x) * x == x mul(z, z, &x.ExtElem) mul(z, z, &x.ExtElem) return vartimeEqFp2(z, &x.ExtElem) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 11)} if err := quick.Check(inverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func TestFp2Batch3Inv(t *testing.T) { batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { var x1Inv, x2Inv, x3Inv common.Fp2 inv(&x1Inv, &x1.ExtElem) inv(&x2Inv, &x2.ExtElem) inv(&x3Inv, &x3.ExtElem) var y1, y2, y3 common.Fp2 Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) } // This is more expensive; run fewer tests fasterCheckConfig := &quick.Config{MaxCount: (1 << 8)} if err := quick.Check(batchInverseIsCorrect, fasterCheckConfig); err != nil { t.Error(err) } } func BenchmarkFp2Mul(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { mul(w, z, z) } } func BenchmarkFp2Inv(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { inv(w, z) } } func BenchmarkFp2Square(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sqr(w, z) } } func BenchmarkFp2Add(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { add(w, z, z) } } func BenchmarkFp2Sub(b *testing.B) { z := &common.Fp2{A: bench_x, B: bench_y} w := new(common.Fp2) for n := 0; n < b.N; n++ { sub(w, z, z) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/internal/templates/gen.go000066400000000000000000000107421454601126700257270ustar00rootroot00000000000000// The following directive is necessary to make the package coherent: //go:build ignore // +build ignore // This program generates contributors.go. It can be invoked by running // go generate package main import ( "bytes" "fmt" "go/format" "os" "strings" "text/template" ) var p34 = map[string]struct { pow_strategy string mul_strategy string mul_initial int }{ "P434": { pow_strategy: "[]uint8{3, 10, 7, 5, 6, 5, 3, 8, 4, 7, 5, 6, 4, 5, 9, 6, 3, 11, 5, 5, 2, 8, 4, 7, 7, 8, 5, 6, 4, 8, 5, 2, 10, 6, 5, 4, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1}", mul_strategy: "[]uint8{2, 15, 9, 8, 14, 12, 2, 8, 5, 15, 8, 15, 6, 6, 3, 2, 0, 10, 9, 13, 1, 12, 3, 7, 1, 10, 8, 11, 2, 15, 14, 1, 11, 12, 14, 3, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0}", mul_initial: 8, }, "P503": { pow_strategy: "[]uint8{12, 5, 5, 2, 7, 11, 3, 8, 4, 11, 4, 7, 5, 6, 3, 7, 5, 7, 2, 12, 5, 6, 4, 6, 8, 6, 4, 7, 5, 5, 8, 5, 8, 5, 5, 8, 9, 3, 6, 2, 10, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3}", mul_strategy: "[]uint8{12, 11, 10, 0, 1, 8, 3, 7, 1, 8, 3, 6, 7, 14, 2, 14, 14, 9, 0, 13, 9, 15, 5, 12, 7, 13, 7, 15, 6, 7, 9, 0, 5, 7, 6, 8, 8, 3, 7, 0, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 3}", mul_initial: 0, }, "P751": { pow_strategy: "[]uint8{5, 7, 6, 2, 10, 4, 6, 9, 8, 5, 9, 4, 7, 5, 5, 4, 8, 3, 9, 5, 5, 4, 10, 4, 6, 6, 6, 5, 8, 9, 3, 4, 9, 4, 5, 6, 6, 2, 9, 4, 5, 5, 5, 7, 7, 9, 4, 6, 4, 8, 5, 8, 6, 6, 2, 9, 7, 4, 8, 8, 8, 4, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2}", mul_strategy: "[]uint8{15, 11, 10, 0, 15, 3, 3, 3, 4, 4, 9, 7, 11, 11, 5, 3, 12, 2, 10, 8, 5, 2, 8, 3, 5, 4, 11, 4, 0, 9, 2, 1, 12, 7, 5, 14, 15, 0, 14, 5, 6, 4, 5, 13, 6, 9, 7, 15, 1, 14, 11, 15, 12, 5, 0, 10, 9, 7, 7, 10, 14, 6, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1}", mul_initial: 13, }, } // P434 optimized implementation for // ARM64 is not ported yet var opt_arm = map[string]bool{ "P434": false, "P503": true, "P751": true, } // Generates an 'fileNameBase.go' from 'fileNameBase.gotemp' file // for a given finite 'field'. Maps placeholders to 'values'. func gen(field, fileNameBase string, values interface{}) { // Template files are located in ../templates and have // extension .gotemp templateFile := "../templates/" + fileNameBase + ".gotemp" t, err := template.ParseFiles(templateFile) if err != nil { panic(fmt.Sprintf("Cannot open template file %s", templateFile)) } var buf bytes.Buffer err = t.Execute(&buf, values) if err != nil { panic("bad template execution") } // Formating output code code, err := format.Source(buf.Bytes()) if err != nil { panic("error formating code") } // name of the output .go file outFileName := fileNameBase + ".go" out, err := os.Create(outFileName) if err != nil { panic("Cannot open file") } _, err = out.Write(code) if err != nil { panic("error writing code") } err = out.Close() if err != nil { panic("Cant close generated file") } } func main() { field := os.Args[1] s := struct { FIELD string PACKAGE string P34_POW_STRATEGY string P34_MUL_STRATEGY string P34_INITIAL_MUL int OPT_ARM bool }{ FIELD: field, PACKAGE: strings.ToLower(field), P34_POW_STRATEGY: p34[field].pow_strategy, P34_MUL_STRATEGY: p34[field].mul_strategy, P34_INITIAL_MUL: p34[field].mul_initial, OPT_ARM: opt_arm[field], } targets := map[string]interface{}{ "arith_decl": s, "arith_generic": s, "curve": s, "fp2": s, "core": s, // tests "arith_test": s, "fp2_test": s, "curve_test": s, } for v, s := range targets { gen(field, v, s) } } golang-github-cloudflare-circl-1.3.7/dh/sidh/sidh.go000066400000000000000000000217431454601126700222760ustar00rootroot00000000000000package sidh import ( "errors" "io" "github.com/cloudflare/circl/dh/sidh/internal/common" "github.com/cloudflare/circl/dh/sidh/internal/p434" "github.com/cloudflare/circl/dh/sidh/internal/p503" "github.com/cloudflare/circl/dh/sidh/internal/p751" ) // I keep it bool in order to be able to apply logical NOT. // // Deprecated: not cryptographically secure. type KeyVariant uint // Base type for public and private key. Used mainly to carry domain // parameters. type key struct { // Domain parameters of the algorithm to be used with a key params *common.SidhParams // Flag indicates whether corresponds to 2-, 3-torsion group or SIKE keyVariant KeyVariant } // Defines operations on public key // // Deprecated: not cryptographically secure. type PublicKey struct { key // x-coordinates of P,Q,P-Q in this exact order affine3Pt [3]common.Fp2 } // Defines operations on private key // // Deprecated: not cryptographically secure. type PrivateKey struct { key // Secret key Scalar []byte // Used only by KEM S []byte } // Identifiers correspond to the bitlength of the prime field characteristic. const ( Fp434 = common.Fp434 Fp503 = common.Fp503 Fp751 = common.Fp751 ) const ( // First 2 bits identify SIDH variant third bit indicates // whether key is a SIKE variant (set) or SIDH (not set) // 001 - SIDH: corresponds to 2-torsion group KeyVariantSidhA KeyVariant = 1 << 0 // 010 - SIDH: corresponds to 3-torsion group KeyVariantSidhB = 1 << 1 // 110 - SIKE KeyVariantSike = 1<<2 | KeyVariantSidhB ) // Accessor to key variant. func (key *key) Variant() KeyVariant { return key.keyVariant } // NewPublicKey initializes public key. // Usage of this function guarantees that the object is correctly initialized. // // Deprecated: not cryptographically secure. func NewPublicKey(id uint8, v KeyVariant) *PublicKey { return &PublicKey{key: key{params: common.Params(id), keyVariant: v}} } // Import clears content of the public key currently stored in the structure // and imports key stored in the byte string. Returns error in case byte string // size is wrong. Doesn't perform any validation. func (pub *PublicKey) Import(input []byte) error { if len(input) != pub.Size() { return errors.New("sidh: input to short") } ssSz := pub.params.SharedSecretSize common.BytesToFp2(&pub.affine3Pt[0], input[0:ssSz], pub.params.Bytelen) common.BytesToFp2(&pub.affine3Pt[1], input[ssSz:2*ssSz], pub.params.Bytelen) common.BytesToFp2(&pub.affine3Pt[2], input[2*ssSz:3*ssSz], pub.params.Bytelen) switch pub.params.ID { case Fp434: p434.ToMontgomery(&pub.affine3Pt[0], &pub.affine3Pt[0]) p434.ToMontgomery(&pub.affine3Pt[1], &pub.affine3Pt[1]) p434.ToMontgomery(&pub.affine3Pt[2], &pub.affine3Pt[2]) case Fp503: p503.ToMontgomery(&pub.affine3Pt[0], &pub.affine3Pt[0]) p503.ToMontgomery(&pub.affine3Pt[1], &pub.affine3Pt[1]) p503.ToMontgomery(&pub.affine3Pt[2], &pub.affine3Pt[2]) case Fp751: p751.ToMontgomery(&pub.affine3Pt[0], &pub.affine3Pt[0]) p751.ToMontgomery(&pub.affine3Pt[1], &pub.affine3Pt[1]) p751.ToMontgomery(&pub.affine3Pt[2], &pub.affine3Pt[2]) default: panic("Unsupported key") } return nil } // Exports currently stored key. In case structure hasn't been filled with key data // returned byte string is filled with zeros. func (pub *PublicKey) Export(out []byte) { var feTmp [3]common.Fp2 ssSz := pub.params.SharedSecretSize switch pub.params.ID { case Fp434: p434.FromMontgomery(&feTmp[0], &pub.affine3Pt[0]) p434.FromMontgomery(&feTmp[1], &pub.affine3Pt[1]) p434.FromMontgomery(&feTmp[2], &pub.affine3Pt[2]) case Fp503: p503.FromMontgomery(&feTmp[0], &pub.affine3Pt[0]) p503.FromMontgomery(&feTmp[1], &pub.affine3Pt[1]) p503.FromMontgomery(&feTmp[2], &pub.affine3Pt[2]) case Fp751: p751.FromMontgomery(&feTmp[0], &pub.affine3Pt[0]) p751.FromMontgomery(&feTmp[1], &pub.affine3Pt[1]) p751.FromMontgomery(&feTmp[2], &pub.affine3Pt[2]) default: panic("Unsupported key") } common.Fp2ToBytes(out[0:ssSz], &feTmp[0], pub.params.Bytelen) common.Fp2ToBytes(out[ssSz:2*ssSz], &feTmp[1], pub.params.Bytelen) common.Fp2ToBytes(out[2*ssSz:3*ssSz], &feTmp[2], pub.params.Bytelen) } // Size returns size of the public key in bytes. func (pub *PublicKey) Size() int { return pub.params.PublicKeySize } // NewPrivateKey initializes private key. // Usage of this function guarantees that the object is correctly initialized. // // Deprecated: not cryptographically secure. func NewPrivateKey(id uint8, v KeyVariant) *PrivateKey { prv := &PrivateKey{key: key{params: common.Params(id), keyVariant: v}} if (v & KeyVariantSidhA) == KeyVariantSidhA { prv.Scalar = make([]byte, prv.params.A.SecretByteLen) } else { prv.Scalar = make([]byte, prv.params.B.SecretByteLen) } if v == KeyVariantSike { prv.S = make([]byte, prv.params.MsgLen) } return prv } // Exports currently stored key. In case structure hasn't been filled with key data // returned byte string is filled with zeros. func (prv *PrivateKey) Export(out []byte) { copy(out, prv.S) copy(out[len(prv.S):], prv.Scalar) } // Size returns size of the private key in bytes. func (prv *PrivateKey) Size() int { tmp := len(prv.Scalar) if prv.Variant() == KeyVariantSike { tmp += prv.params.MsgLen } return tmp } // Size returns size of the shared secret. func (prv *PrivateKey) SharedSecretSize() int { return prv.params.SharedSecretSize } // Import clears content of the private key currently stored in the structure // and imports key from octet string. In case of SIKE, the random value 'S' // must be prepended to the value of actual private key (see SIKE spec for details). // Function doesn't import public key value to PrivateKey object. func (prv *PrivateKey) Import(input []byte) error { if len(input) != prv.Size() { return errors.New("sidh: input to short") } copy(prv.S, input[:len(prv.S)]) copy(prv.Scalar, input[len(prv.S):]) return nil } // Generates random private key for SIDH or SIKE. Generated value is // formed as little-endian integer from key-space <2^(e2-1)..2^e2 - 1> // for KeyVariant_A or <2^(s-1)..2^s - 1>, where s = floor(log_2(3^e3)), // for KeyVariant_B. // // Returns error in case user provided RNG fails. func (prv *PrivateKey) Generate(rand io.Reader) error { var dp *common.DomainParams if (prv.keyVariant & KeyVariantSidhA) == KeyVariantSidhA { dp = &prv.params.A } else { dp = &prv.params.B } if prv.keyVariant == KeyVariantSike { if _, err := io.ReadFull(rand, prv.S); err != nil { return err } } // Private key generation takes advantage of the fact that keyspace for secret // key is (0, 2^x - 1), for some positive value of 'x' (see SIKE, 1.3.8). // It means that all bytes in the secret key, but the last one, can take any // value between <0x00,0xFF>. Similarly for the last byte, but generation // needs to chop off some bits, to make sure generated value is an element of // a key-space. if _, err := io.ReadFull(rand, prv.Scalar); err != nil { return err } prv.Scalar[len(prv.Scalar)-1] &= (1 << (dp.SecretBitLen % 8)) - 1 // Make sure scalar is SecretBitLen long. SIKE spec says that key // space starts from 0, but I'm not comfortable with having low // value scalars used for private keys. It is still secure as per // table 5.1 in [SIKE]. prv.Scalar[len(prv.Scalar)-1] |= 1 << ((dp.SecretBitLen % 8) - 1) return nil } // Generates public key. func (prv *PrivateKey) GeneratePublicKey(pub *PublicKey) { isA := (prv.keyVariant & KeyVariantSidhA) == KeyVariantSidhA if (pub.keyVariant != prv.keyVariant) || (pub.params.ID != prv.params.ID) { panic("sidh: incompatible public key") } switch prv.params.ID { case Fp434: if isA { p434.PublicKeyGenA(&pub.affine3Pt, prv.Scalar) } else { p434.PublicKeyGenB(&pub.affine3Pt, prv.Scalar) } case Fp503: if isA { p503.PublicKeyGenA(&pub.affine3Pt, prv.Scalar) } else { p503.PublicKeyGenB(&pub.affine3Pt, prv.Scalar) } case Fp751: if isA { p751.PublicKeyGenA(&pub.affine3Pt, prv.Scalar) } else { p751.PublicKeyGenB(&pub.affine3Pt, prv.Scalar) } default: panic("Field not supported") } } // Computes a SIDH shared secret. Function requires that pub has different // KeyVariant than prv. Length of returned output is 2*ceil(log_2 P)/8), // where P is a prime defining finite field. // // Caller must make sure key SIDH key pair is not used more than once. func (prv *PrivateKey) DeriveSecret(ss []byte, pub *PublicKey) { isA := (prv.keyVariant & KeyVariantSidhA) == KeyVariantSidhA if (pub.keyVariant == prv.keyVariant) || (pub.params.ID != prv.params.ID) { panic("sidh: public and private are incompatible") } switch prv.params.ID { case Fp434: if isA { p434.DeriveSecretA(ss, prv.Scalar, &pub.affine3Pt) } else { p434.DeriveSecretB(ss, prv.Scalar, &pub.affine3Pt) } case Fp503: if isA { p503.DeriveSecretA(ss, prv.Scalar, &pub.affine3Pt) } else { p503.DeriveSecretB(ss, prv.Scalar, &pub.affine3Pt) } case Fp751: if isA { p751.DeriveSecretA(ss, prv.Scalar, &pub.affine3Pt) } else { p751.DeriveSecretB(ss, prv.Scalar, &pub.affine3Pt) } default: panic("Field not supported") } } golang-github-cloudflare-circl-1.3.7/dh/sidh/sidh_test.go000066400000000000000000000530341454601126700233330ustar00rootroot00000000000000package sidh import ( "bytes" "crypto/rand" "encoding/hex" "fmt" "math/big" "testing" "github.com/cloudflare/circl/dh/sidh/internal/common" . "github.com/cloudflare/circl/internal/test" ) /* ------------------------------------------------------------------------- Test data -------------------------------------------------------------------------*/ type sidhVec struct { id uint8 name string PkA string PrA string PkB string PrB string } var tdataSidh = map[uint8]sidhVec{ Fp434: { id: Fp434, name: "P-434", PrA: "3A727E04EA9B7E2A766A6F846489E7E7B915263BCEED308BB10FC900", PrB: "E37BFE55B43B32448F375903D8D226EC94ADBFEA1D2B3536EB987001", PkA: "9E668D1E6750ED4B91EE052C32839CA9DD2E56D52BC24DECC950AAAD" + "24CEED3F9049C77FE80F0B9B01E7F8DAD7833EEC2286544D6380009C" + "379CDD3E7517CEF5E20EB01F8231D52FC30DC61D2F63FB357F85DC63" + "96E8A95DB9740BD3A972C8DB7901B31F074CD3E45345CA78F9008171" + "30E688A29A7CF0073B5C00FF2C65FBE776918EF9BD8E75B29EF7FAB7" + "91969B60B0C5B37A8992EDEF95FA7BAC40A95DAFE02E237301FEE9A7" + "A43FD0B73477E8035DD12B73FAFEF18D39904DDE3653A754F36BE188" + "8F6607C6A7951349A414352CF31A29F2C40302DB406C48018C905EB9" + "DC46AFBF42A9187A9BB9E51B587622A2862DC7D5CC598BF38ED6320F" + "B51D8697AD3D7A72ABCC32A393F0133DA8DF5E253D9E00B760B2DF34" + "2FCE974DCFE946CFE4727783531882800F9E5DD594D6D5A6275EEFEF" + "9713ED838F4A06BB34D7B8D46E0B385AAEA1C7963601", PkB: "C9F73E4497AAA3FDF9EB688135866A8A83934BA10E273B8CC3808CF0" + "C1F5FAB3E9BB295885881B73DEBC875670C0F51C4BB40DF5FEDE01B8" + "AF32D1BF10508B8C17B2734EB93B2B7F5D84A4A0F2F816E9E2C32AC2" + "53C0B6025B124D05A87A9E2A8567930F44BAA14219B941B6B400B4AE" + "D1D796DA12A5A9F0B8F3F5EE9DD43F64CB24A3B1719DF278ADF56B5F" + "3395187829DA2319DEABF6BBD6EDA244DE2B62CC5AC250C1009DD1CD" + "4712B0B37406612AD002B5E51A62B51AC9C0374D143ABBBD58275FAF" + "C4A5E959C54838C2D6D9FB43B7B2609061267B6A2E6C6D01D295C422" + "3E0D3D7A4CDCFB28A7818A737935279751A6DD8290FD498D1F6AD5F4" + "FFF6BDFA536713F509DCE8047252F1E7D0DD9FCC414C0070B5DCCE36" + "65A21A032D7FBE749181032183AFAD240B7E671E87FBBEC3A8CA4C11" + "AA7A9A23AC69AE2ACF54B664DECD27753D63508F1B02", }, Fp503: { id: Fp503, name: "P-503", PrA: "D5B94224FA1AD1701EC277FDA83462D09E87181C2E583C5F09FD446A43F25103", PrB: "FF0EF91753D71D83D912656856086007AD2CF3B2A979B2BD63E5313BFD276506", PkA: "FFB9A589DBB3975A20373F1AD3B449880E1DA47916FCD7C751A019AAA8E95A03" + "4ADA1AE8BFCF6FBF70F323713318E25315DE865B29C9124982594BF78CD61C09" + "B98C22307DFD4FC0958C58EC0D144828006E510FA4072D721B48D1A3CFEA02F6" + "062324FE1B68F457CF29BD4EB1FB68D0684EE69F53A3FAC327404341BB39365B" + "5DE885034C9A6DD6798CB08126183C696D0302730D489584AC8D6BCADF3AB4DE" + "FFC227D3B1701462DA15BF68EF2B07C44712DB5429B74063202F43DC0EA7919D" + "B95025B2B03E5A3EBF57FF37E21838CE8F5531F491315E576A260DC2F515DDF2" + "4DEDE54CA69737CE6442B4219CD472D9CCCF8AF12B5C5B23ACB9C22929924ABA" + "52C820932C82435518B920AFC43F2041263AE98D29E58B73F33A5DD42AAC7533" + "404B4AC2B83DD2C7BEA7676930B6007CC185C264672B75F5332C18429BBC7B0F" + "2EA3F746995A298E7443FFB0C1B27DCA7D19635064AF3B87938960587F56B724" + "C1EF1FF012B056D7301F8713295B7734563542D4259B8BEA260C", PkB: "AA3303F79FCE4855DE125B239D10BEC3B7082E55B08C769A9765F1BF41A31210" + "66382D6BF2857D85138CC17D69593B8FC7703D22C553FB077DFB3AC577CF1E55" + "2AED6DC0368123E01DDD70059A47E31E06423D2F697A3DA5D621EB5FF2A52EE7" + "CA7D3BD01B427AC14CB6099E03C6639A3BAC9B939297CEB10F276F93CF16A1EE" + "1B8085DE3DA037C911491B145B034A47B42A996A61C2313FEF166FD3665B0AE8" + "C201A268DA01AB52E4759ACCC1DD09685A17CDA5D44AF847931ABB221D62E241" + "2329394445ADFD662C77472A9268F40AB540177C0E6F1D59026E595C46FBED2F" + "703838C5F3D7A811B500237596C5E960AA1F2989C5F17DD60D8A752569DBF250" + "E01C63C9790D014CE05A9D8683814A320E30185E478AF9ABD761DADDA8DE7E3E" + "A53C224AC8313C176D14BD0F04AB09A9D0D0302ACBF768EB4DB03681EAE3BC10" + "21CAA429A1490AE1D6E0CA9D6BC4BCD14B1CFE694226D03E8731E9E0B3760877" + "7D56630B31298CC05B6FF6C1A08935312D8E95B8056AD7831A22", }, Fp751: { id: Fp751, name: "P-751", // PrA - Alice's Private Key: 2*randint(0,2^371) PrA: "B1937F2B009FD9F785C5AD899F5ED2FD064218C07A76798D1433336E093DF184CA0CAF6E7C92B320E89632A7765F0B", // PrB - Bob's Private Key: 3*randint(0,3^238) PrB: "54DB4380D4134E187F5793FA82A4F18B39CA2F8F1C145FFB040FC917E2F41542037FF227F3A4AAFB17A6983AA88B4403", PkA: "2B53BB7C002A9D18B077D068C38353ADFD57A3CA0E431D92CCB8060D41A83A09" + "C1500BEE63FB07DA1DBEDB4AF145F22C2D8152B07B7E124F06643C7AB5B1C48D" + "581FC4C6FB7FC165F6E02F40B47D81400B84B6288DEAB38DE795B51486430974" + "788377770D46B0ABC1F3F7C3647A0E38ACED475EA8EE990F3C5A7668452478C1" + "975993E126B405E476AD6A10E9DD4E135ADA910BE41A8F93331268791F7B958A" + "0888052D1CF7B9128058A258002F22AC48E2C296E3935033139D336FDEB33E9B" + "8713663B1705B566AC4F4455FD0E710A5236C18011EA971DDD18633F9022C432" + "B225EC401FCD4C233B8BF91BE5944D1A657516CE4B844D0BC6049478046B60B6" + "BE163E41CCE743054806B13FAC0A1FA393C866D74A5A93A938209287324FAB46" + "295F5B271C9D8CFEE17868599202D7AEF1A67EBE2FA2A27AD9E0991CEDEE270D" + "1E7639425D94A0F0A2EFDE90B86D5D7F03F3CF97D30415CAA661F865ADB788E6" + "3F79EE2FE8637D9DCAF3BCD5C42AE499688048BBB49F216B4714675FD87F7CCC" + "37A0C2EA56BB53675584F7648BA052F963C35387ECC4DDED4F8076934FF32D5D" + "77B5D3C57553757A4CB9588C4575D4CC4CA8280370041A6FF03007C31D0712E8" + "327CC5BC9885F896904FAB4EE167745260D331C3E85E8A32FCCD23093F2C55A9" + "EA8D7BECEFC3564D3C3D4CE585B62785773B2228742185C97D6F51CD3E3CF885" + "5CF37F305734E97A86479580FDB9983DDCAE9D0F1B125523DB2FE58339240A58" + "131D0EFD14A560A6F7EDE774F6C3C54F46DD0830", PkB: "E93E4E2B0E7348C088FD91F8E3B17CC52B55C5E8933B6D00B3757E5347C5A0AE" + "5F1A6051C32FB20A41013A244484C8D0501B6A3516A634581E08C907F29D651C" + "BCC5B6CA6BAC4DCC980CD36155B60A2108134D3F78ED19ADA2B8B20184302FD7" + "47E096B01ABB33CB76B115D673B00F76913281CF7A0B44FF5CF1A256B8138FE6" + "77AB8D22FEBBCB10EB46E442D0AD96A126DD24E941280C7AB3F9FAC2832A149C" + "AD93D221EDCB406303F5A1B38F43F310244D766239A7F4D89EED4C6FD272BC4F" + "F7C4E34F3E5E77BFF59D6FE5C0D3937F574ABE81C2FC1FEDD98F43323F8F2D7C" + "154DCEBF410FCF698A4E6506D6FD6E4A861395F75698C810A527E00ADC118C90" + "9CDE7729B24C6E7DE9C92CFB592CB9A4BAC54DB468AA52724452CC7A7B40509B" + "B7894ACCF2C7933537FD52DB312D7FBC4FDE01AC2350CD25ABDD5E6F3AEF87BA" + "1BE23691544EB6A4F8FA9CF2BE70B9665EA479B44DC3C61D4651CDDB53656B6F" + "3A2D139EC6BE8550B8A623CCA30EB5374F70C67A932712002006F3D73190384F" + "6D3BEC9DB9F46E9B7AE2891E615752E74DC112579CF43283E8B6EBEF4C802BD6" + "700A97B9739E8694B48D8CB9C8ABBC915A834FF1DBF2C823B3E156D0A415C558" + "71B719BD9DD215F57C8D19A6B4F8CD93283D6EBD135347DAAF4F20C54D24017F" + "5E6AF400AB6DC98AD2D5810E59360DF64503599FAF6FBAB720CC557DEEF0F528" + "249DEB530C8F310465E0BE2B4041C24DAF783BC4EE71D27C760FA7CFD4A9A691" + "70BCBA465CA242961671DF0C53A8112CCD708D58", }, } /* ------------------------------------------------------------------------- Helpers -------------------------------------------------------------------------*/ // Converts string to private key. func convToPrv(s string, v KeyVariant, id uint8) *PrivateKey { key := NewPrivateKey(id, v) hex, e := hex.DecodeString(s) if e != nil { panic("non-hex number provided") } e = key.Import(hex) if e != nil { panic("Can't import private key") } return key } // Converts string to public key. func convToPub(s string, v KeyVariant, id uint8) *PublicKey { key := NewPublicKey(id, v) hex, e := hex.DecodeString(s) if e != nil { panic("non-hex number provided") } e = key.Import(hex) if e != nil { panic("Can't import public key") } return key } /* Unit tests */ func testKeygen(t *testing.T, v sidhVec) { pubA := NewPublicKey(v.id, KeyVariantSidhA) pubB := NewPublicKey(v.id, KeyVariantSidhB) alicePrivate := convToPrv(v.PrA, KeyVariantSidhA, v.id) bobPrivate := convToPrv(v.PrB, KeyVariantSidhB, v.id) expPubA := convToPub(v.PkA, KeyVariantSidhA, v.id) expPubB := convToPub(v.PkB, KeyVariantSidhB, v.id) alicePrivate.GeneratePublicKey(pubA) bobPrivate.GeneratePublicKey(pubB) got := make([]byte, expPubA.Size()) exp := make([]byte, expPubA.Size()) pubA.Export(got) expPubA.Export(exp) if !bytes.Equal(got, exp) { t.Fatalf("unexpected value of public key A\ngot [%X]\nexp [%X]", got, exp) } got = make([]byte, expPubB.Size()) exp = make([]byte, expPubB.Size()) pubB.Export(got) expPubB.Export(exp) if !bytes.Equal(got, exp) { t.Fatalf("unexpected value of public key B\ngot [%X]\nexp [%X]", got, exp) } } func testRoundtrip(t *testing.T, v sidhVec) { var err error pubA := NewPublicKey(v.id, KeyVariantSidhA) pubB := NewPublicKey(v.id, KeyVariantSidhB) prvA := NewPrivateKey(v.id, KeyVariantSidhA) prvB := NewPrivateKey(v.id, KeyVariantSidhB) s1 := make([]byte, common.Params(v.id).SharedSecretSize) s2 := make([]byte, common.Params(v.id).SharedSecretSize) // Generate private keys err = prvA.Generate(rand.Reader) CheckNoErr(t, err, "key generation failed") err = prvB.Generate(rand.Reader) CheckNoErr(t, err, "key generation failed") // Generate public keys prvA.GeneratePublicKey(pubA) prvB.GeneratePublicKey(pubB) // Derive shared secret prvB.DeriveSecret(s1, pubA) prvA.DeriveSecret(s2, pubB) if !bytes.Equal(s1[:], s2[:]) { t.Fatalf("Two shared keys do not match:\ns1 [%X]\ns2 [%X]", s1, s2) } } func testKeyAgreement(t *testing.T, v sidhVec) { var err error s1 := make([]byte, common.Params(v.id).SharedSecretSize) s2 := make([]byte, common.Params(v.id).SharedSecretSize) // KeyPairs alicePublic := convToPub(v.PkA, KeyVariantSidhA, v.id) bobPublic := convToPub(v.PkB, KeyVariantSidhB, v.id) alicePrivate := convToPrv(v.PrA, KeyVariantSidhA, v.id) bobPrivate := convToPrv(v.PrB, KeyVariantSidhB, v.id) // Do actual test bobPrivate.DeriveSecret(s1, alicePublic) alicePrivate.DeriveSecret(s2, bobPublic) if !bytes.Equal(s1[:], s2[:]) { t.Fatalf("two shared keys do not match\ngot [%X]\nexp [%X]", s1, s2) } // Negative case dec, err := hex.DecodeString(v.PkA) CheckNoErr(t, err, "decoding failed") dec[0] = ^dec[0] err = alicePublic.Import(dec) CheckNoErr(t, err, "import failed") bobPrivate.DeriveSecret(s1, alicePublic) alicePrivate.DeriveSecret(s2, bobPublic) if bytes.Equal(s1[:], s2[:]) { t.Fatalf("DeriveSecret produces wrong results. The two shared keys match, but they shouldn't") } } func testImportExport(t *testing.T, v sidhVec) { var err error a := NewPublicKey(v.id, KeyVariantSidhA) b := NewPublicKey(v.id, KeyVariantSidhB) // Import keys aHex, err := hex.DecodeString(v.PkA) CheckNoErr(t, err, "invalid hex-number provided") err = a.Import(aHex) CheckNoErr(t, err, "import failed") bHex, err := hex.DecodeString(v.PkB) CheckNoErr(t, err, "invalid hex-number provided") err = b.Import(bHex) CheckNoErr(t, err, "import failed") aBytes := make([]byte, a.Size()) bBytes := make([]byte, b.Size()) a.Export(aBytes) b.Export(bBytes) // Export and check if same if !bytes.Equal(bBytes, bHex) || !bytes.Equal(aBytes, aHex) { t.Fatalf("export/import failed") } if (len(bBytes) != b.Size()) || (len(aBytes) != a.Size()) { t.Fatalf("wrong size of exported keys") } // Ensure that public key is unchanged after it is exported aBytes2 := make([]byte, a.Size()) bBytes2 := make([]byte, b.Size()) a.Export(aBytes2) b.Export(bBytes2) if !bytes.Equal(aBytes, aBytes2) || !bytes.Equal(bBytes, bBytes2) { t.Fatalf("Second export doesn't match first export") } } func testPrivateKeyBelowMax(t *testing.T, vec sidhVec) { for variant, keySz := range map[KeyVariant]*common.DomainParams{ KeyVariantSidhA: &common.Params(vec.id).A, KeyVariantSidhB: &common.Params(vec.id).B, } { func(v KeyVariant, dp *common.DomainParams) { blen := int(dp.SecretByteLen) prv := NewPrivateKey(vec.id, v) secretBytes := make([]byte, prv.Size()) // Calculate either (2^e2 - 1) or (2^s - 1); where s=ceil(log_2(3^e3))) maxSecretVal := big.NewInt(int64(dp.SecretBitLen)) maxSecretVal.Exp(big.NewInt(int64(2)), maxSecretVal, nil) maxSecretVal.Sub(maxSecretVal, big.NewInt(1)) // Do same test 1000 times for i := 0; i < 1000; i++ { err := prv.Generate(rand.Reader) CheckNoErr(t, err, "Private key generation") // Convert to big-endian, as that's what expected by (*Int)SetBytes() prv.Export(secretBytes) for i := 0; i < blen/2; i++ { tmp := secretBytes[i] ^ secretBytes[blen-i-1] secretBytes[i] = tmp ^ secretBytes[i] secretBytes[blen-i-1] = tmp ^ secretBytes[blen-i-1] } prvBig := new(big.Int).SetBytes(secretBytes) // Check if generated key is bigger then acceptable if prvBig.Cmp(maxSecretVal) == 1 { t.Error("Generated private key is wrong") } } }(variant, keySz) } } func TestKeyAgreementP751_AliceEvenNumber(t *testing.T) { // even alice v := tdataSidh[Fp751] v.PkA = "FDED78E9F490CB518BD6357E18FEEB63FFEFEBE907338B3ABCA74A7E590DBF79" + "0C732AB9E3778244608CD563064BDF6AAEF511CEAF07C702309ADAA7EBEBC6B3" + "D7B00F5C02FB2FEDA763B2D695FD27F93F45D3AC58C2F0524A942D6DE407B651" + "1854A1D974F11A8686CF8AD675A081F4B668F3C6617029AA33FD597C8910AB37" + "F71DBE004A3FF8442C4B65DE51201DFAE6F9DC20FDE5B998D19C23589437229D" + "724B4378602321F247276E7B4E441383C9BE6D277A127362D9C9FB68A41C5F5B" + "9D2BA63FA790D62315DECF5049F0476A43D30BC1E8A36047C8EE0DA9E0A3937E" + "BDF52A91BC53266A82CBF2CEAB227CB6D5075B486679CA7701F6F35C53499B45" + "A451CE37C57B9BB1276142F495B83D987BD4B62E78E3084DCF3EB906D19DFA8F" + "819DFC7FDF104C1A01CCF8D933B91EBD72CDE83A502B1FB0A5DF782BC7085766" + "AE795123903A2D30F0F79073D27CF71BA4C9D3CA86512842AA8B5AEB729C78B1" + "E15392E20A6043C05F88F6F412C3C9FE14F8FAAE8B8482514822162F93E81615" + "BDD77363F872D0506FFDC1809C165A5C8A19F8EA0254D73E08202A6FF3AF43CF" + "A7EC9B137AE003A19440DCE2EF3CFC99080F75E683AF6D0E25DF55C60B2A8013" + "FA3D59828D31C2360DF83E202FB48AFAA65AF7279137E827B80E761FA49B842A" + "A70FD4E77B284A14B8E28C8B11B389E1160DD9877C8D5A5A1471E605F1848369" + "3F7578B3733DDEE117227E35B1765FEBB765B340A084E8D99176C0837099C864" + "C71C864842D3E9B58CB870AD45F3B6BE476FEB6D" v.PrA = "C09957CC83045FB4C3726384D784476ACB6FFD92E5B15B3C2D451BA063F1BD4CE" + "D8FBCF682A98DD0954D37BCAF730F" testKeyAgreement(t, v) } /* ------------------------------------------------------------------------- Wrappers for 'testing' SIDH -------------------------------------------------------------------------*/ func testSidhVec(t *testing.T, m *map[uint8]sidhVec, f func(t *testing.T, v sidhVec)) { for i := range *m { v := (*m)[i] t.Run(v.name, func(t *testing.T) { f(t, v) }) } } func TestKeygen(t *testing.T) { testSidhVec(t, &tdataSidh, testKeygen) } func TestRoundtrip(t *testing.T) { testSidhVec(t, &tdataSidh, testRoundtrip) } func TestImportExport(t *testing.T) { testSidhVec(t, &tdataSidh, testImportExport) } func TestKeyAgreement(t *testing.T) { testSidhVec(t, &tdataSidh, testKeyAgreement) } func TestPrivateKeyBelowMax(t *testing.T) { testSidhVec(t, &tdataSidh, testPrivateKeyBelowMax) } /* ------------------------------------------------------------------------- Benchmarking -------------------------------------------------------------------------*/ func BenchmarkSidhKeyAgreementP751(b *testing.B) { // KeyPairs alicePublic := convToPub(tdataSidh[Fp751].PkA, KeyVariantSidhA, Fp751) bobPublic := convToPub(tdataSidh[Fp751].PkB, KeyVariantSidhB, Fp751) alicePrivate := convToPrv(tdataSidh[Fp751].PrA, KeyVariantSidhA, Fp751) bobPrivate := convToPrv(tdataSidh[Fp751].PrB, KeyVariantSidhB, Fp751) var ss [2 * 94]byte for i := 0; i < b.N; i++ { // Derive shared secret bobPrivate.DeriveSecret(ss[:], alicePublic) alicePrivate.DeriveSecret(ss[:], bobPublic) } } func BenchmarkSidhKeyAgreementP503(b *testing.B) { // KeyPairs alicePublic := convToPub(tdataSidh[Fp503].PkA, KeyVariantSidhA, Fp503) bobPublic := convToPub(tdataSidh[Fp503].PkB, KeyVariantSidhB, Fp503) alicePrivate := convToPrv(tdataSidh[Fp503].PrA, KeyVariantSidhA, Fp503) bobPrivate := convToPrv(tdataSidh[Fp503].PrB, KeyVariantSidhB, Fp503) var ss [2 * 63]byte for i := 0; i < b.N; i++ { // Derive shared secret bobPrivate.DeriveSecret(ss[:], alicePublic) alicePrivate.DeriveSecret(ss[:], bobPublic) } } func BenchmarkSidhKeyAgreementP434(b *testing.B) { // KeyPairs alicePublic := convToPub(tdataSidh[Fp434].PkA, KeyVariantSidhA, Fp434) bobPublic := convToPub(tdataSidh[Fp434].PkB, KeyVariantSidhB, Fp434) alicePrivate := convToPrv(tdataSidh[Fp434].PrA, KeyVariantSidhA, Fp434) bobPrivate := convToPrv(tdataSidh[Fp434].PrB, KeyVariantSidhB, Fp434) var ss [2 * 63]byte for i := 0; i < b.N; i++ { // Derive shared secret bobPrivate.DeriveSecret(ss[:], alicePublic) alicePrivate.DeriveSecret(ss[:], bobPublic) } } func BenchmarkAliceKeyGenPrvP751(b *testing.B) { prv := NewPrivateKey(Fp751, KeyVariantSidhA) for n := 0; n < b.N; n++ { _ = prv.Generate(rand.Reader) } } func BenchmarkAliceKeyGenPrvP503(b *testing.B) { prv := NewPrivateKey(Fp503, KeyVariantSidhA) for n := 0; n < b.N; n++ { _ = prv.Generate(rand.Reader) } } func BenchmarkAliceKeyGenPrvP434(b *testing.B) { prv := NewPrivateKey(Fp434, KeyVariantSidhA) for n := 0; n < b.N; n++ { _ = prv.Generate(rand.Reader) } } func BenchmarkBobKeyGenPrvP751(b *testing.B) { prv := NewPrivateKey(Fp751, KeyVariantSidhB) for n := 0; n < b.N; n++ { _ = prv.Generate(rand.Reader) } } func BenchmarkBobKeyGenPrvP503(b *testing.B) { prv := NewPrivateKey(Fp503, KeyVariantSidhB) for n := 0; n < b.N; n++ { _ = prv.Generate(rand.Reader) } } func BenchmarkBobKeyGenPrvP434(b *testing.B) { prv := NewPrivateKey(Fp434, KeyVariantSidhB) for n := 0; n < b.N; n++ { _ = prv.Generate(rand.Reader) } } func BenchmarkAliceKeyGenPubP751(b *testing.B) { prv := NewPrivateKey(Fp751, KeyVariantSidhA) pub := NewPublicKey(Fp751, KeyVariantSidhA) _ = prv.Generate(rand.Reader) for n := 0; n < b.N; n++ { prv.GeneratePublicKey(pub) } } func BenchmarkAliceKeyGenPubP503(b *testing.B) { prv := NewPrivateKey(Fp503, KeyVariantSidhA) pub := NewPublicKey(Fp503, KeyVariantSidhA) _ = prv.Generate(rand.Reader) for n := 0; n < b.N; n++ { prv.GeneratePublicKey(pub) } } func BenchmarkAliceKeyGenPubP434(b *testing.B) { prv := NewPrivateKey(Fp434, KeyVariantSidhA) pub := NewPublicKey(Fp434, KeyVariantSidhA) _ = prv.Generate(rand.Reader) for n := 0; n < b.N; n++ { prv.GeneratePublicKey(pub) } } func BenchmarkBobKeyGenPubP751(b *testing.B) { prv := NewPrivateKey(Fp751, KeyVariantSidhB) pub := NewPublicKey(Fp751, KeyVariantSidhB) _ = prv.Generate(rand.Reader) for n := 0; n < b.N; n++ { prv.GeneratePublicKey(pub) } } func BenchmarkBobKeyGenPubP503(b *testing.B) { prv := NewPrivateKey(Fp503, KeyVariantSidhB) pub := NewPublicKey(Fp503, KeyVariantSidhB) _ = prv.Generate(rand.Reader) for n := 0; n < b.N; n++ { prv.GeneratePublicKey(pub) } } func BenchmarkBobKeyGenPubP434(b *testing.B) { prv := NewPrivateKey(Fp434, KeyVariantSidhB) pub := NewPublicKey(Fp434, KeyVariantSidhB) _ = prv.Generate(rand.Reader) for n := 0; n < b.N; n++ { prv.GeneratePublicKey(pub) } } func BenchmarkSharedSecretAliceP751(b *testing.B) { aPr := convToPrv(tdataSidh[Fp751].PrA, KeyVariantSidhA, Fp751) bPk := convToPub(tdataSidh[Fp751].PkB, KeyVariantSidhB, Fp751) var ss [2 * 94]byte for n := 0; n < b.N; n++ { aPr.DeriveSecret(ss[:], bPk) } } func BenchmarkSharedSecretAliceP503(b *testing.B) { aPr := convToPrv(tdataSidh[Fp503].PrA, KeyVariantSidhA, Fp503) bPk := convToPub(tdataSidh[Fp503].PkB, KeyVariantSidhB, Fp503) var ss [2 * 63]byte for n := 0; n < b.N; n++ { aPr.DeriveSecret(ss[:], bPk) } } func BenchmarkSharedSecretAliceP434(b *testing.B) { aPr := convToPrv(tdataSidh[Fp434].PrA, KeyVariantSidhA, Fp434) bPk := convToPub(tdataSidh[Fp434].PkB, KeyVariantSidhB, Fp434) var ss [2 * 63]byte for n := 0; n < b.N; n++ { aPr.DeriveSecret(ss[:], bPk) } } func BenchmarkSharedSecretBobP751(b *testing.B) { // m_B = 3*randint(0,3^238) aPk := convToPub(tdataSidh[Fp751].PkA, KeyVariantSidhA, Fp751) bPr := convToPrv(tdataSidh[Fp751].PrB, KeyVariantSidhB, Fp751) var ss [2 * 94]byte for n := 0; n < b.N; n++ { bPr.DeriveSecret(ss[:], aPk) } } func BenchmarkSharedSecretBobP503(b *testing.B) { // m_B = 3*randint(0,3^238) aPk := convToPub(tdataSidh[Fp503].PkA, KeyVariantSidhA, Fp503) bPr := convToPrv(tdataSidh[Fp503].PrB, KeyVariantSidhB, Fp503) var ss [2 * 63]byte for n := 0; n < b.N; n++ { bPr.DeriveSecret(ss[:], aPk) } } func BenchmarkSharedSecretBobP434(b *testing.B) { // m_B = 3*randint(0,3^238) aPk := convToPub(tdataSidh[Fp434].PkA, KeyVariantSidhA, Fp434) bPr := convToPrv(tdataSidh[Fp434].PrB, KeyVariantSidhB, Fp434) var ss [2 * 63]byte for n := 0; n < b.N; n++ { bPr.DeriveSecret(ss[:], aPk) } } // Examples func ExamplePrivateKey() { // import "github.com/cloudflare/circl/dh/sidh" // Alice's key pair prvA := NewPrivateKey(Fp503, KeyVariantSidhA) pubA := NewPublicKey(Fp503, KeyVariantSidhA) // Bob's key pair prvB := NewPrivateKey(Fp503, KeyVariantSidhB) pubB := NewPublicKey(Fp503, KeyVariantSidhB) // Generate keypair for Alice err := prvA.Generate(rand.Reader) if err != nil { fmt.Print(err) } prvA.GeneratePublicKey(pubA) // Generate keypair for Bob err = prvB.Generate(rand.Reader) if err != nil { fmt.Print(err) } prvB.GeneratePublicKey(pubB) // Buffers storing shared secret ssA := make([]byte, prvA.SharedSecretSize()) ssB := make([]byte, prvA.SharedSecretSize()) // Alice calculates shared secret with hers private // key and Bob's public key prvA.DeriveSecret(ssA[:], pubB) // Bob calculates shared secret with hers private // key and Alice's public key prvB.DeriveSecret(ssB[:], pubA) // Check if ssA == ssB fmt.Printf("%t\n", bytes.Equal(ssA, ssB)) // Output: // true } golang-github-cloudflare-circl-1.3.7/dh/sidh/sike.go000066400000000000000000000173711454601126700223040ustar00rootroot00000000000000package sidh import ( "crypto/subtle" "errors" "io" "github.com/cloudflare/circl/dh/sidh/internal/common" "github.com/cloudflare/circl/internal/sha3" ) // SIKE KEM interface. // // Deprecated: not cryptographically secure. type KEM struct { allocated bool rng io.Reader msg []byte secretBytes []byte params *common.SidhParams shake sha3.State } // NewSike434 instantiates SIKE/p434 KEM. // // Deprecated: not cryptographically secure. func NewSike434(rng io.Reader) *KEM { var c KEM c.Allocate(Fp434, rng) return &c } // NewSike503 instantiates SIKE/p503 KEM. // // Deprecated: not cryptographically secure. func NewSike503(rng io.Reader) *KEM { var c KEM c.Allocate(Fp503, rng) return &c } // NewSike751 instantiates SIKE/p751 KEM. // // Deprecated: not cryptographically secure. func NewSike751(rng io.Reader) *KEM { var c KEM c.Allocate(Fp751, rng) return &c } // Allocate allocates KEM object for multiple SIKE operations. The rng // must be cryptographically secure PRNG. func (c *KEM) Allocate(id uint8, rng io.Reader) { c.rng = rng c.params = common.Params(id) c.msg = make([]byte, c.params.MsgLen) c.secretBytes = make([]byte, c.params.A.SecretByteLen) c.shake = sha3.NewShake256() c.allocated = true } // Encapsulate receives the public key and generates SIKE ciphertext and shared secret. // The generated ciphertext is used for authentication. // Error is returned in case PRNG fails. Function panics in case wrongly formatted // input was provided. func (c *KEM) Encapsulate(ciphertext, secret []byte, pub *PublicKey) error { if !c.allocated { panic("KEM unallocated") } if KeyVariantSike != pub.keyVariant { panic("Wrong type of public key") } if len(secret) < c.SharedSecretSize() { panic("shared secret buffer to small") } if len(ciphertext) < c.CiphertextSize() { panic("ciphertext buffer to small") } // Generate ephemeral value _, err := io.ReadFull(c.rng, c.msg[:]) if err != nil { return err } var buf [3 * common.MaxSharedSecretBsz]byte skA := PrivateKey{ key: key{ params: c.params, keyVariant: KeyVariantSidhA, }, Scalar: c.secretBytes, } pkA := NewPublicKey(c.params.ID, KeyVariantSidhA) pub.Export(buf[:]) c.shake.Reset() _, _ = c.shake.Write(c.msg) _, _ = c.shake.Write(buf[:3*c.params.SharedSecretSize]) _, _ = c.shake.Read(skA.Scalar) // Ensure bitlength is not bigger then to 2^e2-1 skA.Scalar[len(skA.Scalar)-1] &= (1 << (c.params.A.SecretBitLen % 8)) - 1 skA.GeneratePublicKey(pkA) c.generateCiphertext(ciphertext, &skA, pkA, pub, c.msg[:]) // K = H(msg||(c0||c1)) c.shake.Reset() _, _ = c.shake.Write(c.msg) _, _ = c.shake.Write(ciphertext) _, _ = c.shake.Read(secret[:c.SharedSecretSize()]) return nil } // Decapsulate given the keypair and ciphertext as inputs, Decapsulate outputs a shared // secret if plaintext verifies correctly, otherwise function outputs random value. // Decapsulation may panic in case input is wrongly formatted, in particular, size of // the 'ciphertext' must be exactly equal to c.CiphertextSize(). func (c *KEM) Decapsulate(secret []byte, prv *PrivateKey, pub *PublicKey, ciphertext []byte) error { if !c.allocated { panic("KEM unallocated") } if KeyVariantSike != pub.keyVariant { panic("Wrong type of public key") } if pub.keyVariant != prv.keyVariant { panic("Public and private key are of different type") } if len(secret) < c.SharedSecretSize() { panic("shared secret buffer to small") } if len(ciphertext) != c.CiphertextSize() { panic("ciphertext buffer to small") } var m [common.MaxMsgBsz]byte var r [common.MaxSidhPrivateKeyBsz]byte var pkBytes [3 * common.MaxSharedSecretBsz]byte skA := PrivateKey{ key: key{ params: c.params, keyVariant: KeyVariantSidhA, }, Scalar: c.secretBytes, } pkA := NewPublicKey(c.params.ID, KeyVariantSidhA) c1Len, err := c.decrypt(m[:], prv, ciphertext) if err != nil { return err } // r' = G(m'||pub) pub.Export(pkBytes[:]) c.shake.Reset() _, _ = c.shake.Write(m[:c1Len]) _, _ = c.shake.Write(pkBytes[:3*c.params.SharedSecretSize]) _, _ = c.shake.Read(r[:c.params.A.SecretByteLen]) // Ensure bitlength is not bigger than 2^e2-1 r[c.params.A.SecretByteLen-1] &= (1 << (c.params.A.SecretBitLen % 8)) - 1 err = skA.Import(r[:c.params.A.SecretByteLen]) if err != nil { return err } skA.GeneratePublicKey(pkA) pkA.Export(pkBytes[:]) // S is chosen at random when generating a key and unknown to other party. It is // important that S is unpredictable to the other party. Without this check, would // be possible to recover a secret, by providing series of invalid ciphertexts. // // See more details in "On the security of supersingular isogeny cryptosystems" // (S. Galbraith, et al., 2016, ePrint #859). mask := subtle.ConstantTimeCompare(pkBytes[:c.params.PublicKeySize], ciphertext[:pub.params.PublicKeySize]) common.Cpick(mask, m[:c1Len], m[:c1Len], prv.S) c.shake.Reset() _, _ = c.shake.Write(m[:c1Len]) _, _ = c.shake.Write(ciphertext) _, _ = c.shake.Read(secret[:c.SharedSecretSize()]) return nil } // Resets internal state of KEM. Function should be used // after Allocate and between subsequent calls to Encapsulate // and/or Decapsulate. func (c *KEM) Reset() { for i := range c.msg { c.msg[i] = 0 } for i := range c.secretBytes { c.secretBytes[i] = 0 } } // Returns size of resulting ciphertext. func (c *KEM) CiphertextSize() int { return c.params.CiphertextSize } // Returns size of resulting shared secret. func (c *KEM) SharedSecretSize() int { return c.params.KemSize } // PublicKeySize returns size of the public key in bytes. func (c *KEM) PublicKeySize() int { return c.params.PublicKeySize } // Size returns size of the private key in bytes. func (c *KEM) PrivateKeySize() int { return int(c.params.B.SecretByteLen) + c.params.MsgLen } func (c *KEM) generateCiphertext(ctext []byte, skA *PrivateKey, pkA, pkB *PublicKey, ptext []byte) { var n [common.MaxMsgBsz]byte var j [common.MaxSharedSecretBsz]byte ptextLen := skA.params.MsgLen skA.DeriveSecret(j[:], pkB) c.shake.Reset() _, _ = c.shake.Write(j[:skA.params.SharedSecretSize]) _, _ = c.shake.Read(n[:ptextLen]) for i := range ptext { n[i] ^= ptext[i] } pkA.Export(ctext) copy(ctext[pkA.Size():], n[:ptextLen]) } // encrypt uses SIKE public key to encrypt plaintext. Requires cryptographically secure // PRNG. Returns ciphertext in case encryption succeeds. Returns error in case PRNG fails // or wrongly formated input was provided. func (c *KEM) encrypt(ctext []byte, rng io.Reader, pub *PublicKey, ptext []byte) error { ptextLen := len(ptext) // c1 must be security level + 64 bits (see [SIKE] 1.4 and 4.3.3) if ptextLen != pub.params.KemSize { return errors.New("unsupported message length") } skA := NewPrivateKey(pub.params.ID, KeyVariantSidhA) pkA := NewPublicKey(pub.params.ID, KeyVariantSidhA) err := skA.Generate(rng) if err != nil { return err } skA.GeneratePublicKey(pkA) c.generateCiphertext(ctext, skA, pkA, pub, ptext) return nil } // decrypt uses SIKE private key to decrypt ciphertext. Returns plaintext in case // decryption succeeds or error in case unexpected input was provided. // Constant time. func (c *KEM) decrypt(n []byte, prv *PrivateKey, ctext []byte) (int, error) { var c1Len int var j [common.MaxSharedSecretBsz]byte pkLen := prv.params.PublicKeySize // ctext is a concatenation of (ciphertext = pubkey_A || c1) // it must be security level + 64 bits (see [SIKE] 1.4 and 4.3.3) // Lengths has been already checked by Decapsulate() c1Len = len(ctext) - pkLen c0 := NewPublicKey(prv.params.ID, KeyVariantSidhA) err := c0.Import(ctext[:pkLen]) prv.DeriveSecret(j[:], c0) c.shake.Reset() _, _ = c.shake.Write(j[:prv.params.SharedSecretSize]) _, _ = c.shake.Read(n[:c1Len]) for i := range n[:c1Len] { n[i] ^= ctext[pkLen+i] } return c1Len, err } golang-github-cloudflare-circl-1.3.7/dh/sidh/sike_test.go000066400000000000000000000442171454601126700233420ustar00rootroot00000000000000package sidh import ( "bufio" "bytes" "crypto/rand" "encoding/hex" "fmt" "io" "os" "strings" "testing" "github.com/cloudflare/circl/dh/sidh/internal/common" . "github.com/cloudflare/circl/internal/test" ) type sikeVec struct { id uint8 name string kem *KEM KatFile string PkB string PrB string } var tdataSike = map[uint8]sikeVec{ Fp434: { Fp434, "P-434", NewSike434(rand.Reader), "testdata/PQCkemKAT_374.rsp", "1BD0A2E81307B6F96461317DDF535ACC0E59C742627BAE60D27605E10FAF722D" + "22A73E184CB572A12E79DCD58C6B54FB01442114CBE9010B6CAEC25D04C16C5E" + "42540C1524C545B8C67614ED4183C9FA5BD0BE45A7F89FBC770EE8E7E5E391C7" + "EE6F35F74C29E6D9E35B1663DA01E48E9DEB2347512D366FDE505161677055E3" + "EF23054D276E817E2C57025DA1C10D2461F68617F2D11256EEE4E2D7DBDF6C8E" + "34F3A0FD00C625428CB41857002159DAB94267ABE42D630C6AAA91AF837C7A67" + "40754EA6634C45454C51B0BB4D44C3CCCCE4B32C00901CF69C008D013348379B" + "2F9837F428A01B6173584691F2A6F3A3C4CF487D20D261B36C8CDB1BC158E2A5" + "162A9DA4F7A97AA0879B9897E2B6891B672201F9AEFBF799C27B2587120AC586" + "A511360926FB7DA8EBF5CB5272F396AE06608422BE9792E2CE9BEF21BF55B7EF" + "F8DC7EC8C99910D3F800", "4B622DE1350119C45A9F2E2EF3DC5DF56A27FCDFCDDAF58CD69B903752D68C20" + "0934E160B234E49EDE247601", }, Fp503: { Fp503, "P-503", NewSike503(rand.Reader), "testdata/PQCkemKAT_434.rsp", "4032A90B6C036B7D2A83878AD116641AD319E420235A505F3F5C3DEC27C87A6C" + "BA0792201D6E7B196C582D43CAF86CB2C7DEFA6598B543C946CDDF62EF9A328C" + "8719B66BA5052231DAE13AF7D9CDEBB4ED327773C7AE0818F41AF1D28CD78B16" + "C996232528235C8392B8FCFD925CB311B2A801B0402A90E527261EA32F2BEF67" + "7C544908D5509B8AB7D7BF20456727AD358AD585306A0B28F6B2AA583CE8A3E0" + "BB92D8CD55347D39D4E3C30D3D0F96EABB721A6968CDD143FE9227643CF697FB" + "2DF0B71322B5EA1505D0DDBF70A2FD1193011F3BC18AA1E127C614B76969DCDA" + "45A2072B519A1074FDA49F5C828450C6A007BF8D7CDDD5D2FC112119C679CA3A" + "B16C6960B25F6C681A7DCED0F0E3901740D3DBF3A33011EB7DA460E8ADA80EE3" + "45B2B71420950A9A803E4F11330EB91CCABB1EEE4D875A109D7724ABD201272C" + "0B4981BDCDFA70F3430A89D2A88EEED474CF0CFAC65CE883F44B4722FA280C6F" + "A9C4724D414B35AF69D6ECB21BFDA23BFF6B66C22C2451DC8E1C", "7BF6938C975658AEB8B4D37CFFBDE25D97E561F36C219A0E8FE645816DBBC7ED7B57" + "7700AE8DC3138E97A0C3F6F002065C92A0B1B8180208", }, Fp751: { Fp751, "P-751", NewSike751(rand.Reader), "testdata/PQCkemKAT_644.rsp", "E1A758EC0D418BFE86D8077B5BB169133C06C1F2A067D8B202D9D058FFC51F63" + "FD26155A6577C74BA7F1A27E7BA51982517B923615DEB00BE408920A07831DF5" + "978CFDDD0BF690A264353A4A16B666F90586D7F89A193CE09375D389C1379A7A" + "528581C3ACB002CD2DC4F0FD672568FF9050BA8365C7FEFC5E6ED089B921DE68" + "04091A0744DE3EB14D426A3F7DA215C50312617C1C2697243980D06056F2CCE8" + "8AE7AE73C7343C0B7104C9F2870A94FED744CF6E94630514B6CEAB0E64733BB6" + "FA67B931E5D8206010475CBE8BC587248D65D89D8CD9C8BBFA93E8B5F9EB9130" + "773DED665D52ABBD91C4C8C255F73C0FC82501AE33330E9F308DE7177CBF83E4" + "E26E334D7CB09019E638147FC58ED372AF660F14C194BC80E9666325C98E0F80" + "877271D4A6BF514F603703D8A697874CD50A34D92F5AAEA84633CCF96801BD51" + "7BF425DEE4A32AAF06684052473EA14643C3D535440FB2240A988D09F297C5A3" + "88CB3DE60ED943F124034B90EFF611221F80F78EC124956338A105F6636B063D" + "7E48BFBD5D614310FB97D86F122E4AE6F9DDF4977A93ED7D0CE2A94E346A1A03" + "D3219CF21907B85A5BCDC713F93A4406A22E03B1655A66E1F6741A2F953E6FE0" + "868B2614BABEF1943BBBCB1B66D3E7017E533EA84F291240B56AB33EF1DC3F3D" + "E99DBF9E8BE51A0076E462BCDD825EA96D7F63C99177C305C257B31461F4C23D" + "43115F0220409E8880BBB2468586D03461E807BE824B693874911B2B52AF06FD" + "BDC47F5A0159729641A7C950AB9E03F2DC045135", "0001020304050607080900010203040506070809000102030405060708090102" + "8626ED79D451140800E03B59B956F8210E556067407D13DC90FA9E8B872BFB8F" + "AB0A7289852106E40538D3575C500201", }, } // Encrypt, Decrypt, check if input/output plaintext is the same. func testPKERoundTrip(t *testing.T, v sikeVec) { // Message to be encrypted var pt [common.MaxMsgBsz]byte params := common.Params(v.id) ct := make([]byte, v.kem.CiphertextSize()) msg := make([]byte, params.MsgLen) for i := range msg { msg[i] = byte(i) } // Import keys pkB := NewPublicKey(params.ID, KeyVariantSike) skB := NewPrivateKey(params.ID, KeyVariantSike) pkHex, err := hex.DecodeString(v.PkB) CheckNoErr(t, err, "Test vector wrong") skHex, err := hex.DecodeString(v.PrB) CheckNoErr(t, err, "Test vector wrong") err = pkB.Import(pkHex) CheckNoErr(t, err, "Public key import failed") err = skB.Import(skHex) CheckNoErr(t, err, "Private key import failed") err = v.kem.encrypt(ct, rand.Reader, pkB, msg[:]) CheckNoErr(t, err, "PKE roundtrip - encryption failed") ptLen, err := v.kem.decrypt(pt[:], skB, ct) CheckNoErr(t, err, "PKE roundtrip - description failed") if !bytes.Equal(pt[:ptLen], msg[:]) { t.Errorf("Decryption failed \n got : %X\n exp : %X", pt[:ptLen], msg) } } // Generate key and check if can encrypt. func testPKEKeyGeneration(t *testing.T, v sikeVec) { var err error params := common.Params(v.id) var pt [common.MaxMsgBsz]byte msg := make([]byte, params.MsgLen) ct := make([]byte, v.kem.CiphertextSize()) // static buffer to ensure no overrides pk := NewPublicKey(v.id, KeyVariantSike) sk := NewPrivateKey(v.id, KeyVariantSike) for i := range msg { msg[i] = byte(i) } err = sk.Generate(rand.Reader) CheckNoErr(t, err, "PKE key generation") sk.GeneratePublicKey(pk) err = v.kem.encrypt(ct, rand.Reader, pk, msg[:]) CheckNoErr(t, err, "PKE encryption") ptLen, err := v.kem.decrypt(pt[:], sk, ct) CheckNoErr(t, err, "PKE key decryption") if !bytes.Equal(pt[:ptLen], msg[:]) { t.Fatalf("Decryption failed \n got : %X\n exp : %X", pt, msg) } } func testNegativePKE(t *testing.T, v sikeVec) { var err error var msg [common.MaxMsgBsz]byte ct := make([]byte, v.kem.CiphertextSize()) pk := NewPublicKey(v.id, KeyVariantSike) sk := NewPrivateKey(v.id, KeyVariantSike) // Generate key err = sk.Generate(rand.Reader) CheckNoErr(t, err, "key generation") sk.GeneratePublicKey(pk) // bytelen(msg) - 1 err = v.kem.encrypt(ct, rand.Reader, pk, msg[:v.kem.params.KemSize+8-1]) CheckIsErr(t, err, "PKE encryption doesn't fail") for _, v := range ct { if v != 0 { t.Fatal("Returned ciphertext must be not changed") } } } func testKEMRoundTrip(t *testing.T, pkB, skB []byte, v sikeVec) { // Import keys var err error var ssE [common.MaxSharedSecretBsz]byte var ssD [common.MaxSharedSecretBsz]byte pk := NewPublicKey(v.id, KeyVariantSike) sk := NewPrivateKey(v.id, KeyVariantSike) ct := make([]byte, v.kem.CiphertextSize()) ssBsz := v.kem.SharedSecretSize() err = pk.Import(pkB) CheckNoErr(t, err, "Public key import failed") err = sk.Import(skB) CheckNoErr(t, err, "Private key import failed") v.kem.Reset() err = v.kem.Encapsulate(ct, ssE[:], pk) CheckNoErr(t, err, "Encapsulation failed") v.kem.Reset() err = v.kem.Decapsulate(ssD[:ssBsz], sk, pk, ct) CheckNoErr(t, err, "Decapsulation failed") if !bytes.Equal(ssE[:v.kem.SharedSecretSize()], ssD[:v.kem.SharedSecretSize()]) { t.Errorf("Shared secrets from decapsulation and encapsulation differ [%s]", v.name) } } func testKEMKeyGeneration(t *testing.T, v sikeVec) { var ssE [common.MaxSharedSecretBsz]byte var ssD [common.MaxSharedSecretBsz]byte ct := make([]byte, v.kem.CiphertextSize()) sk := NewPrivateKey(v.id, KeyVariantSike) pk := NewPublicKey(v.id, KeyVariantSike) CheckNoErr(t, sk.Generate(rand.Reader), "error: key generation") sk.GeneratePublicKey(pk) // calculated shared secret v.kem.Reset() err := v.kem.Encapsulate(ct, ssE[:], pk) CheckNoErr(t, err, "encapsulation failed") v.kem.Reset() err = v.kem.Decapsulate(ssD[:v.kem.SharedSecretSize()], sk, pk, ct) CheckNoErr(t, err, "decapsulation failed") if !bytes.Equal(ssE[:], ssD[:]) { t.Fatalf("KEM failed \n encapsulated: %X\n decapsulated: %X", ssD[:], ssE[:]) } } func testNegativeKEM(t *testing.T, v sikeVec) { var ssE [common.MaxSharedSecretBsz]byte var ssD [common.MaxSharedSecretBsz]byte var ssTmp [common.MaxSharedSecretBsz]byte ct := make([]byte, v.kem.CiphertextSize()) ssBsz := v.kem.SharedSecretSize() sk := NewPrivateKey(v.id, KeyVariantSike) pk := NewPublicKey(v.id, KeyVariantSike) CheckNoErr(t, sk.Generate(rand.Reader), "error: key generation") sk.GeneratePublicKey(pk) v.kem.Reset() err := v.kem.Encapsulate(ct, ssE[:], pk) CheckNoErr(t, err, "pre-requisite for a test failed") // Try decapsulate too small ciphertext v.kem.Reset() CheckNoErr( t, CheckPanic(func() { _ = v.kem.Decapsulate(ssTmp[:ssBsz], sk, pk, ct[:len(ct)-2]) }), "Decapsulation must panic if ciphertext is too small") ctTmp := make([]byte, len(ct)+1) // Try decapsulate too big ciphertext v.kem.Reset() CheckNoErr( t, CheckPanic(func() { _ = v.kem.Decapsulate(ssTmp[:ssBsz], sk, pk, ctTmp) }), "Decapsulation must panic if ciphertext is too big") // Change ciphertext ct[0] = ct[0] - 1 v.kem.Reset() err = v.kem.Decapsulate(ssD[:ssBsz], sk, pk, ct) CheckNoErr(t, err, "decapsulation returns error when invalid ciphertext provided") if bytes.Equal(ssE[:], ssD[:]) { // no idea how this could ever happen, but it would be very bad t.Error("critical error") } // Try encapsulating with SIDH key pkSidh := NewPublicKey(v.id, KeyVariantSidhB) prSidh := NewPrivateKey(v.id, KeyVariantSidhB) v.kem.Reset() CheckNoErr( t, CheckPanic(func() { _ = v.kem.Encapsulate(ct, ssE[:], pkSidh) }), "encapsulation accepts SIDH public key") // Try decapsulating with SIDH key v.kem.Reset() CheckNoErr( t, CheckPanic(func() { _ = v.kem.Decapsulate(ssD[:ssBsz], prSidh, pk, ct) }), "encapsulation accepts SIDH public key") } // In case invalid ciphertext is provided, SIKE's decapsulation must // return same (but unpredictable) result for a given key. func testNegativeKEMSameWrongResult(t *testing.T, v sikeVec) { var ssE [common.MaxSharedSecretBsz]byte var ssD1 [common.MaxSharedSecretBsz]byte var ssD2 [common.MaxSharedSecretBsz]byte ct := make([]byte, v.kem.CiphertextSize()) ssBsz := v.kem.SharedSecretSize() sk := NewPrivateKey(v.id, KeyVariantSike) pk := NewPublicKey(v.id, KeyVariantSike) CheckNoErr(t, sk.Generate(rand.Reader), "error: key generation") sk.GeneratePublicKey(pk) v.kem.Reset() err := v.kem.Encapsulate(ct, ssE[:], pk) CheckNoErr(t, err, "pre-requisite for a test failed") // make ciphertext wrong ct[0] = ct[0] - 1 v.kem.Reset() err = v.kem.Decapsulate(ssD1[:ssBsz], sk, pk, ct) CheckNoErr(t, err, "pre-requisite for a test failed") // change secret keysecond decapsulation must be done with same, but imported private key var expSk [common.MaxSikePrivateKeyBsz]byte sk.Export(expSk[:]) // create new private key sk = NewPrivateKey(v.id, KeyVariantSike) CheckNoErr(t, sk.Import(expSk[:sk.Size()]), "import failed") // try decapsulating again. v.kem.Reset() err = v.kem.Decapsulate(ssD2[:ssBsz], sk, pk, ct) CheckNoErr(t, err, "pre-requisite for a test failed") // ssD1 must be same as ssD2 if !bytes.Equal(ssD1[:], ssD2[:]) { t.Error("decapsulation is insecure") } // ssD1 and ssD2 must be different than ssE if bytes.Equal(ssE[:], ssD1[:]) || bytes.Equal(ssE[:], ssD2[:]) { // this test requires that decapsulation returns wrong result t.Errorf("test implementation error") } } func testKAT(t *testing.T, v sikeVec) { ssGot := make([]byte, v.kem.SharedSecretSize()) testDecapsulation := func(pk, sk, ct, ssExpected []byte) { pubKey := NewPublicKey(v.id, KeyVariantSike) prvKey := NewPrivateKey(v.id, KeyVariantSike) if pubKey.Import(pk) != nil || prvKey.Import(sk) != nil { panic("sike test: can't load KAT") } err := v.kem.Decapsulate(ssGot, prvKey, pubKey, ct) CheckNoErr(t, err, "sike test: can't perform decapsulation KAT") if !bytes.Equal(ssGot, ssExpected) { t.Fatalf("KAT decapsulation failed\n") } } readAndCheckLine := func(r *bufio.Reader) []byte { // Read next line from buffer line, isPrefix, err := r.ReadLine() if err != nil || isPrefix { panic("Wrong format of input file") } // Function expects that line is in format "KEY = HEX_VALUE". Get // value, which should be a hex string hexst := strings.Split(string(line), "=")[1] hexst = strings.TrimSpace(hexst) // Convert value to byte string ret, err := hex.DecodeString(hexst) if err != nil { panic("Wrong format of input file") } return ret } testKeygen := func(pk, sk []byte) { // Import provided private key prvKey := NewPrivateKey(v.id, KeyVariantSike) pubKey := NewPublicKey(v.id, KeyVariantSike) pubKeyBytes := make([]byte, pubKey.Size()) CheckNoErr(t, prvKey.Import(sk), "Can't load KAT") // Generate public key prvKey.GeneratePublicKey(pubKey) pubKey.Export(pubKeyBytes) if !bytes.Equal(pubKeyBytes, pk) { t.Errorf("Public key differ [%s]", v.name) } } f, err := os.Open(v.KatFile) if err != nil { t.Fatal(err) } r := bufio.NewReader(f) for { line, isPrefix, err := r.ReadLine() if err != nil || isPrefix { if err == io.EOF { break } else { t.Fatal(err) } } if len(strings.TrimSpace(string(line))) == 0 || line[0] == '#' { continue } // count _ = strings.Split(string(line), "=")[1] // seed _ = readAndCheckLine(r) // pk pk := readAndCheckLine(r) // sk (secret key in test vector is concatenation of // MSG + SECRET_BOB_KEY + PUBLIC_BOB_KEY. We use only MSG+SECRET_BOB_KEY sk := readAndCheckLine(r) sk = sk[:v.kem.params.MsgLen+int(v.kem.params.B.SecretByteLen)] // ct ct := readAndCheckLine(r) // ss ss := readAndCheckLine(r) testKeygen(pk, sk) testDecapsulation(pk, sk, ct, ss) testKEMRoundTrip(t, pk, sk, v) } } // Interface to "testing" /* ------------------------------------------------------------------------- Wrappers for 'testing' SIDH -------------------------------------------------------------------------*/ func testSike(t *testing.T, m *map[uint8]sikeVec, f func(*testing.T, sikeVec)) { for i := range *m { v := (*m)[i] t.Run(v.name, func(t *testing.T) { f(t, v) }) } } func TestPKERoundTrip(t *testing.T) { testSike(t, &tdataSike, testPKERoundTrip) } func TestPKEKeyGeneration(t *testing.T) { testSike(t, &tdataSike, testPKEKeyGeneration) } func TestNegativePKE(t *testing.T) { testSike(t, &tdataSike, testNegativePKE) } func TestKEMKeyGeneration(t *testing.T) { testSike(t, &tdataSike, testKEMKeyGeneration) } func TestNegativeKEM(t *testing.T) { testSike(t, &tdataSike, testNegativeKEM) } func TestKAT(t *testing.T) { testSike(t, &tdataSike, testKAT) } func TestNegativeKEMSameWrongResult(t *testing.T) { testSike(t, &tdataSike, testNegativeKEMSameWrongResult) } func TestKEMRoundTrip(t *testing.T) { for _, val := range tdataSike { // fmt.Printf("\tTesting: %s\n", val.name) pk, err := hex.DecodeString(val.PkB) CheckNoErr(t, err, "public key B not a number") sk, err := hex.DecodeString(val.PrB) CheckNoErr(t, err, "private key B not a number") testKEMRoundTrip(t, pk, sk, val) } } /* ------------------------------------------------------------------------- Benchmarking -------------------------------------------------------------------------*/ func benchSike(t *testing.B, m *map[uint8]sikeVec, f func(*testing.B, sikeVec)) { for i := range *m { v := (*m)[i] t.Run(v.name, func(t *testing.B) { f(t, v) }) } } func benchKeygen(b *testing.B, v sikeVec) { pub := NewPublicKey(v.id, KeyVariantSike) prv := NewPrivateKey(v.id, KeyVariantSike) _ = prv.Generate(rand.Reader) b.ResetTimer() for n := 0; n < b.N; n++ { prv.GeneratePublicKey(pub) } } func benchmarkEncaps(b *testing.B, v sikeVec) { pub := NewPublicKey(v.id, KeyVariantSike) prv := NewPrivateKey(v.id, KeyVariantSike) if prv.Generate(rand.Reader) != nil { b.FailNow() } prv.GeneratePublicKey(pub) var ct [common.MaxCiphertextBsz]byte var ss [common.MaxSharedSecretBsz]byte b.ResetTimer() for n := 0; n < b.N; n++ { v.kem.Reset() _ = v.kem.Encapsulate(ct[:], ss[:], pub) } } func benchmarkDecaps(b *testing.B, v sikeVec) { var ct [common.MaxCiphertextBsz]byte var ss [common.MaxSharedSecretBsz]byte ssBsz := v.kem.SharedSecretSize() pkA := NewPublicKey(v.id, KeyVariantSike) prvA := NewPrivateKey(v.id, KeyVariantSike) pkB := NewPublicKey(v.id, KeyVariantSike) prvB := NewPrivateKey(v.id, KeyVariantSike) if prvA.Generate(rand.Reader) != nil || prvB.Generate(rand.Reader) != nil { b.FailNow() } prvA.GeneratePublicKey(pkA) prvB.GeneratePublicKey(pkB) v.kem.Reset() err := v.kem.Encapsulate(ct[:], ss[:], pkA) if err != nil { b.FailNow() } ctSlc := ct[:v.kem.CiphertextSize()] b.ResetTimer() for n := 0; n < b.N; n++ { v.kem.Reset() _ = v.kem.Decapsulate(ss[:ssBsz], prvA, pkB, ctSlc) } } func BenchmarkKeygen(b *testing.B) { benchSike(b, &tdataSike, benchKeygen) } func BenchmarkEncaps(b *testing.B) { benchSike(b, &tdataSike, benchmarkEncaps) } func BenchmarkDecaps(b *testing.B) { benchSike(b, &tdataSike, benchmarkDecaps) } func ExampleKEM() { // Alice's key pair prvA := NewPrivateKey(Fp503, KeyVariantSike) pubA := NewPublicKey(Fp503, KeyVariantSike) // Bob's key pair prvB := NewPrivateKey(Fp503, KeyVariantSike) pubB := NewPublicKey(Fp503, KeyVariantSike) // Generate keypair for Alice err := prvA.Generate(rand.Reader) if err != nil { panic(err) } prvA.GeneratePublicKey(pubA) // Generate keypair for Bob err = prvB.Generate(rand.Reader) if err != nil { panic(err) } prvB.GeneratePublicKey(pubB) // Initialize internal KEM structures kem := NewSike503(rand.Reader) // Create buffers for ciphertext, shared secret received // from encapsulation and shared secret from decapsulation ct := make([]byte, kem.CiphertextSize()) ssE := make([]byte, kem.SharedSecretSize()) ssD := make([]byte, kem.SharedSecretSize()) // Alice performs encapsulation with Bob's public key err = kem.Encapsulate(ct, ssE, pubB) if err != nil { panic(err) } // Bob performs decapsulation with his key pair err = kem.Decapsulate(ssD, prvB, pubB, ct) if err != nil { panic(err) } fmt.Printf("%t\n", bytes.Equal(ssE, ssD)) // Bob performs encapsulation with Alice's public key err = kem.Encapsulate(ct, ssE, pubA) if err != nil { panic(err) } // Alice performs decapsulation with hers key pair err = kem.Decapsulate(ssD, prvA, pubA, ct) if err != nil { panic(err) } fmt.Printf("%t\n", bytes.Equal(ssE, ssD)) // Output: // true // true } golang-github-cloudflare-circl-1.3.7/dh/sidh/testdata/000077500000000000000000000000001454601126700226225ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/sidh/testdata/PQCkemKAT_374.rsp000066400000000000000000006751001454601126700254360ustar00rootroot00000000000000# SIKEp434 count = 0 seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 pk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sk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ct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ss = 35F7F8FF388714DEDC41F139078CEDC9 count = 1 seed = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC81ADDE6AEEB4A5A875C3BFCADFA958F pk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sk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ct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ss = 9D7EDCCC78E60EFDDD75D585AD920730 count = 2 seed = 64335BF29E5DE62842C941766BA129B0643B5E7121CA26CFC190EC7DC3543830557FDD5C03CF123A456D48EFEA43C868 pk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sk = 4B622DE1350119C45A9F2E2EF3DC5DF56A27FCDFCDDAF58CD69B903752D68C200934E160B234E49EDE2476011BD0A2E81307B6F96461317DDF535ACC0E59C742627BAE60D27605E10FAF722D22A73E184CB572A12E79DCD58C6B54FB01442114CBE9010B6CAEC25D04C16C5E42540C1524C545B8C67614ED4183C9FA5BD0BE45A7F89FBC770EE8E7E5E391C7EE6F35F74C29E6D9E35B1663DA01E48E9DEB2347512D366FDE505161677055E3EF23054D276E817E2C57025DA1C10D2461F68617F2D11256EEE4E2D7DBDF6C8E34F3A0FD00C625428CB41857002159DAB94267ABE42D630C6AAA91AF837C7A6740754EA6634C45454C51B0BB4D44C3CCCCE4B32C00901CF69C008D013348379B2F9837F428A01B6173584691F2A6F3A3C4CF487D20D261B36C8CDB1BC158E2A5162A9DA4F7A97AA0879B9897E2B6891B672201F9AEFBF799C27B2587120AC586A511360926FB7DA8EBF5CB5272F396AE06608422BE9792E2CE9BEF21BF55B7EFF8DC7EC8C99910D3F800 ct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ss = 68C17AB42604D799578D835DC7256001 count = 3 seed = 225D5CE2CEAC61930A07503FB59F7C2F936A3E075481DA3CA299A80F8C5DF9223A073E7B90E02EBF98CA2227EBA38C1A pk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sk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ct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ss = E0BD6870B0308BACBDA1061628CE8F0D count = 4 seed = EDC76E7C1523E3862552133FEA4D2AB05C69FB54A9354F0846456A2A407E071DF4650EC0E0A5666A52CD09462DBC51F9 pk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sk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ct = CDD134EDDFA2B2E9C6DE157E1ED68E0FE13798D243A0630D1566A459680A7BF93D81664866F560D59DC18D43D6400734087D4F3831C6003E21D02091176298BA40154011081E972AA1AD5BA3CB8BB069A721E2C09946D1F45AB6B9B3CD7E867F910AA6CD409413BB6488EE88F6013C44D83C55B0748DDFE5312571F7A1745B5AE94EC18002A367ACC7C83D33AE2391641FB0F8D129F8CD249E718EA5828F76EAF5CE053100711E510D753215604C0AAA6B325DD6D81E564983EF3820BB4908F6BBDA16B3B6E1FE2D0D01C3C33A73E2BB6DEF6D83B8D0481E376C8501E0FD3617273D4BB9577D6AB6485530D08116C4D9EE8A76767FEE8BE93B04BD1101AD86B642F8D3D8C3F5349734C683AA20420AD3BF250235962505CC934D87E32020F717D0018457838079ACE67F7E6C5D81DB53C40A54D755911E042778471E610F8D8860E47505F63234161100CE2EE0B19ED2A830497D0D70A6E61BD3 ss = 18C6E6AE1527E5A612E98F2018FDD744 count = 5 seed = AA93649193C2C5985ACF8F9E6AC50C36AE16A2526D7C684F7A3BB4ABCD7B6FF790E82BADCE89BC7380D66251F97AAAAA pk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sk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ct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ss = 377A154FEDAC0A7DF1DFB1409D34F568 count = 6 seed = 2E014DC7C2696B9F6D4AF555CBA4B931B34863FF60E2341D4FDFE472FEF2FE2C33E0813FC5CAFDE4E30277FE522A9049 pk = 235B59C4931909215173C321D2BE02DDD8F4227D1AFAF566BBFCDD8E9280F63A7D1AA346C3B01F429AD66689D9912A5C4C36241A314200403282704705DBBBA6917E131FCF5541BDED9478B08649619D8F6FE9D4D5BB9B28F3F851C5AFF4B31A4D94858876BF3218D68FF88A8A018E55B5B9C7A664001BC7793C2052841329A80DAC59A919BB4C51ED106FF12646327E08E6CBA2F3FA92CBA3655640681E93EAF9F8A0BE0092576BD86705BA9FA4546F78659A8F4C162763F37F8376E480BB15F15AF187B02A1ACE9F9A994977A076FD8C9CEE72C2F58B6C06570602F37989AFC2A59068F95F510AC7565D90B8D101CCF66A3C3A758319F690D59843F1E5142A701B2622944DA1D8B48E0AD0FD888EA0D41D018C387AEA8B7A9DCD0F1536822A9E7C9056784637637D9FA3F242C84A20B29558A3C73DC38462527F6659572317DAD665727952769FAB00 sk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ct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ss = 20702B740B8447FEBB904FC9BF411637 count = 7 seed = AEFB28FDD34E0AB403A703B535296E3A545CA479C1D8148E2D501B3C8DD8B1034BD986F13F1A7B4671BE769359FD2AAB pk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sk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ct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ss = CBC8B73A7F31E6E4B909DF774D17E1A2 count = 8 seed = CBE5161E8DE02DDA7DE204AEB0FBB4CA81344BA8C30FE357A4664E5D2988A03B64184D7DC69F8D367550E5FEA0876D41 pk = AC97BE89E1D09C95148DCA3A189D52B8C39251DFDD534264C0CAC77ECD7E0A6A4625E95CD0FDAD68522C20AAE8D0FFABC262E95F3A1401A0626EC88F43FD1403B1EA5D052D89D65501E3DFB735BA92EAFA34AE5657322957EDC1DD52FF5620B85412355A1C2C866405269FCEDF0045092A0D136D64834DD7DE0BC7ED46DBC671C5C34AA76147E65670A569B349646412BA9D015155D85BC39075FEAB1DB50042B570DAC10028C016EB01199EB50C03DB532F675E1FBC00FDBF70D756C71DF66BC63831B42AC1F4EBD7B2F5042E00053F14EC10A803B69B5455E80D018263D184B8220300640C0442A82667258387F2A7FDD26425E07E4637F159951E16D460D7C89F131BE2FDBD6C0069C1F781FA789FE5BC00805BC7390C6300C6E075710C0394AC840DBBEC175620ECFB0AAE71902EA5141CFBC0B4473C954C67C62544412DBE142401013D9C984200 sk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ct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ss = 1246DD9FC2F3E56DE0C452A7D2B86573 count = 9 seed = B4663A7A9883386A2AE4CBD93787E247BF26087E3826D1B8DBEB679E49C0BB286E114F0E9F42F61F63DEC42B4F974846 pk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sk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ct = A8A6B1ABA6920A714B66734100197CDD934E56FE7E98ECB11B6B7A2975A939E5AAADA310E063A0C15A32136F02767A49361635704FF700D019D06583AD98FD283C5138BE0A591430DF5560C9F83C9B256DFF69859FD6D08E2FC811DC59D2D2F081510F9F48640CF261CBCDBA7101D19453344F2CF82E4307E4EC21C09C2A5DCEDF387CAD493A2E1E8D6F657043D207F441605D7EDB21730ADF82B04A364A730A2E728D1B0136EB3F1ED669E17125C6B7E6922B306C3CABC46B20071ADE1021767A8E4977F70868F6FF9F6F9D2AD6A9051374C7F94BBCF1F8B82E3C00F522B515134D8763CD6984BF86F28DF8B766556FDCA9E8697EB4D7F1604DF738AE1307EC008C6A6B2EB5184407F64991A94A49DC0CCE01879EF0A781B7F47A31F3579EF53AAF9B7818E4C818F8F262CB5BAB557D594833F7AA3016EFB757773F8DC9DCA55FFCFFC6D28E3BC1D701A52D911F82CD7F717B3215D5E5FAA555 ss = B09D92921E68FA2CD595FF094B9BAA6B count = 10 seed = 980D0BA7C8F8B23D0E948A6029FF2659810EA1360064663A8994D0333C8543EE5FF5D6D5C9ACF446E61DC464F792B9D3 pk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sk = 2F1D8A3BEBB34540324B9485FDF3D5BE1913E716E52EF135BBC36077D16C70CF656E07A895F704902629630141DBDA29EE49155B922C93C96B7F12D55194828187F3E11CD38DAD1AAFA7F6A6FA9E1C4C12658F4A7541B2238EE9A5AAB532520CB61E0071B7C7932DE780BFA88D10766CB04C1957C964A850C00D9F3C79DAB54320B5D83C11B831651D7E8981AFA8523C5FA587868EFF138A7D009322269125F89B2F2E1CD4C38F29385000A8EBA4C70D67890ED38317E2FC12BBA2B246CCF9ABED1B05A5D52B1D83BDE8FCC43C5F6BAD013E7C125B72A711CC32B000EE81A50BAB72EFD106E560A93FECEFD96777630F607CF75090C049FD7A9EF88A2BF6F423933909A66916F4003D6A6AB0AE9D192591742E59ED338675F6D21A7B58844CCC054C325E369E3C67B658CC8192EED3BE171888712942826D7A4D8CAB051002C4082A05C7DCC8B4C267A3861AAC5F415DFC6594BDE00BB3164008B7BED93597CF39B7484574704CAD537275B7BEC8C2FEFECFEC18EC00 ct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ss = B49ABAAE30A790FECE54A3F113FD575B count = 11 seed = 6C029462CA42ED520F10A579F52687101105E0B90C6E7BFA582A4C112B579D5AD0A0ABD38F72ABCFDCAAF5893A112BDC pk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sk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ct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ss = A663DA396F96655AED1602ACFB1C83B3 count = 12 seed = DB00120937570D62331F4C3F19A10465231EFF46465CDEE336A0D46AA1E7493DF80F18617F9FFD0476CF7784A403EF4F pk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sk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ct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ss = 040192B84326A814B18C80CA838F94C9 count = 13 seed = BD26C0B9A33E3B9B4C5D7EA32D5BD1FC371015BE163C86F584E49BFD5362C8D8341161CD1308115B2A03B7E5EADDD418 pk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sk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ct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ss = 897ECF117CAD056AA7607F485F5EDBBD count = 14 seed = E2819EF86853BCA1B9DEE7EE1C1619988964F9A913E635AACF0D96CA6E0300D084329DABD8F149E24176D22757404260 pk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sk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ct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ss = 694A4A8AAD90783D407AC750E7B787A1 count = 15 seed = 669C4EF8A051CE201DA65FC4BC34D398EC1F806276FC5D987AD71D93BC12DC8F107B58BE6E8422A0795C88CB9A0E7488 pk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sk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ct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ss = C13E65613329AF85AF74CEF46B8384CA count = 16 seed = 9DEBCCFE818F6B5204DB4EA09C03EC9A19DCF1629C1527685B8A29776BB1DAAEC45F8ABF8F0ADC9A8C8BD6E2DF6D8048 pk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sk = EF99224A03A85A46EF115474EC5B5D628BD0CF95F3E495FD375B444F9B9C1FC8A23857EEF27896A08FE7B80079D967425432D24A0C3977DAD8B1B74440AAB34950413665F6F0B5CB40C96B78550C950A5F7CD2AAD088AEEBA931F97D0277B11964E501A6A741C08C6445D013B8AAD9CB2DF9B88F9A08E481513016CD46DD0EE1EB56732369A8C8CBA34A2F38947E2290FE61593BBFB1D28DE300CD6F0A175773FA411BA7E6A4ECC136561F1F98DB691603FC53E71DDB911673AE43AE5C6ECED2D899CA95EEA8C26163C5671EAD30F6D800F03DFB43C7A46C7CE485993A489E785A396AC1719C30F751AA9E9A6BC7A0E28FFB7B60A4F4EFC95FD3D8B3694155CDE492DDD10D5A1902C1D096FFD81C8D771E3F00026A9EC646CCDC973A0D4F92C31A1A7EE05A8CC41ACA004BE01DF8A312804F1F905B6F7F099C99885A8213023B2863489779C86C1DF6D9AEA76A1586A4EFDE52A965516D457EF6A9537B7FFAE6B5D31EE6F1580C0DFFEAA7C9C00E3FE7D48720CEBE00 ct = 509F931C69B91B463F9184495F8036417E4A7D7E59085CE1C500F438B088FF86806487AEED6C644FC04D6C470796F39C18CB689BCC1F01DD65379668EFB5749EA8002F5411B131A6A8F733E7DAD73C553EB8A62428F854D8244BC5137B921ED3F5C5D3E85E981FCA403DA91106023C47ABFF15A8B8B12BCAFFB33E0657C4118C4F9B0B632C77D96807AE509281207E157577E51426897B1D3DA003A30AC4813D725CD8B50141968CCB11877104AB6BC2F30BAC781C228C0378BDF38C79ED5772E505F3B9EAB2F5F075FDACB1C0FBF54B2003EC1EA0436D18F2209100391321A03A5EA2100AAAB510267C97A4C51E99BA40F457B831B8DECD43C51357BB711392B9C60A78B65EC4EF46A9C7A20050D690961502F2E58D319EEF77CA1AAD1E6BEEB36EC89619B38DB2862AFDA4E4F48C359CBDF49BFF88C359BC53EE9416F2B368E410270CA28F498F7D0055AA195855AA118D011490262C8875D8 ss = 71CF8ED3966D7D1DC1E355644F91FAC3 count = 17 seed = 8098AE7A92C10F707D405F7DEA02C2EFBEF44EFA132BA8AEFE81BD45E543ECEC74F10920AE48A40B0653D63532517F2A pk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sk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ct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ss = FACCC640638E1613E321D6A9BF931BE9 count = 18 seed = D5F23808871544E9C1D6EACE2028362B48E225312F77663E9F78CAFEB512B908CD9E25875D61A16EC615F4B8FF826856 pk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sk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ct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ss = 019ACAE70F324EF52D715966BDE79FBA count = 19 seed = 822CB47BE2266E182F34546924D753A5E3369011047E6950B00BC392F8FEC19EA87C26D8021D377DF86DC76C24C5F827 pk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sk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ct = A6D8DC0B0DCFFEF0E34728FE4DE79A1D59FC9C9AA0FB6361EE18451550D69B313758E1DA7BE3C9E6783C16DEB7B00603109ACF879C56012635C2925DB4DF0D2FEAA89134C1FD33A487C852105DEFA6DF4BAD559B645C96049811445AD49F1ACCA668CFC12D0561747C4A251CC501A6751C36ADDC183AE86DBE1794DCD7AEB9CBEA6ADF4F18011AC2624D0B0E4AE3377AD2E4E7458693FB3D04C4020F3A008988F5DC8F0801232AD1725DB94C378425EBE6CCB3C6AEEBB9A774663AA8A72988A2C6380F56F2FCCDCE3497903B9E9AA3EB6C0809F21ECD5442E8AECB01FCD8CF9AAA3BE92A2FB0D5D43E5703F8939BF15AA6935997B9DE26A4D83FC4A9CA42D4E89591C698640FE3C5E5DFB925076A393B74CE014E8D257FA543FB29F915C5274F74EA862F6065E93FEE25845322ED62ADBB5A0709C7072F520C9B220FE8EFC67B3F5A9AC21CA2B12EE7001A8BCD24CD1F7776630D9F3025034D2D ss = 031C5FBEE7FD72BEA84A703A739FF9B8 count = 20 seed = 81401DB81138D6874E91B7C11D59596E4ACE543F5A3471B6FB00999221765FEC3CA057ABE20F03B2D59003375FD71FE8 pk = E5ADFE2A2841DDE0CBAB4F9A9E8D4EC1A07FA5456ECC04C76AC192B968BC030073D066B1D9129D6B6A74092500E3E812B18E7A77959701696C5C603FADD6E1415AF1F64FDFA173C967195A6A018F3946C3A446AE08013EB73ED4F83BFA103F1E7CE0DFC46D566021C306D197740041802A3CA75CDD8984AD4534D7988A338A31639AD33090488EB76B3120346CF64350EE772C8031A74C7B1362F96A6E969D11B61EDEFF014647540DAF3C9A78BC2975CCE93A2A02B9EF54B3F767D21A5FE9C2D885716079A207BED74B55C34D1D2E4FB8243FCD839916CF1B3F16009A2118E0F012AC828117209E74CCAD66C80D9D7B4BA06330DF23A9122D82A5043C31AF133A6D3A99169C17FC8AF5A42765FA3D96F26B011B9DD08673C53691B011DA58AE666570F8849EBB66855BFAC516720944B65A4B71D6D4F35EB4CBF85E61C02FA9347EA39D8042ED292302 sk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ct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ss = FBE3D8D78996D62A3652F8B86D15ED92 count = 21 seed = 30B5DE5B73681EC08AAA03F6F2D2169525D25F4042A5E3695A20A52CA54927B85F8BB948FC21DF7DEFC3910B28674994 pk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sk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ct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ss = 3D7E8D87B57B2B32DA794159078EA043 count = 22 seed = E335DF8FC0D890588C3E305AC92C7160FF199E07C85760A828933750E3FED8C83B0DBE802234481ECF890A32D7A2884F pk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sk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ct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ss = C24173C7DA58B449DD977568836FF856 count = 23 seed = FBEA1BC2C379F4F8FDCB0DE260D31CDB064C9EA9B1D6DFBE91B3692ADD1D34DEC9C9FFAE7BF5E72ED2743BA3F9F2E43D pk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sk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ct = 545FC97ED910F330B4BA794B368DA77BBD174EF9A654487FDCEA4406A438B04FFAA75336C67F4EFB6EA650645CE1B69D1C8E44FE798500BE8B169B7063B1ACC4A9E4AEBFA175783796190C638F47669B1EA271DF591F4730EA87BCE2BA2427BCC3A1F73FC94A6387CB4C3ED80401BFCBCDDECA82DDB51F4622B33104E5D4483E8D99317A7AC5CE38FFAFFA64C7BCF551D5E4DFF9723E998C5B8A6C5B73680610725EB29901E15EBC7B9979720ACF893E7A72945D4B7B9F8304E3F3D8DF2A7A80AA6FE71C341968166CFD9A218B78640E8CF268901506D8F391F4B801C6DE231CA5A43E1CE9F06CA5AA5AD7330A0906CB96DD0D914B33F75C98FFAAD43CE6850291ADE9241DFE69FF699FF7171D38E4FEDFEA0114316D23BAB6F9F214E3D49A1580085340ED30FF160EFF8ED54CFA3067DA31DC71D25C2D176B5157ACD7ECD42B55B8D839218B935EFC0141E6103357A6CD3F3DE4EC8BD20DB364 ss = A5D8459E0B0C063FF5696743360F4186 count = 24 seed = 7E87FB886BC3C7C9FC12569F465D2ECD12532E76CC27C65644C8D3DD603B0CB2D036C5974E675058F271D5C82AD7A813 pk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sk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ct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ss = D5D19932C9F4580ECB0EAAE0504526AC count = 25 seed = AD1424E804F306C7FF513DA4C1E8D445AFCA7BC942FAC5C0B335733AAF70693712ECBDE26EA726EE0F9FD9D52A83B1A4 pk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sk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ct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ss = F777EF5840DD876797535F8122B2DFBA count = 26 seed = 7C33CA0E987226C8524DD56C811FA4D1CCF9995B1E4E4DD5B1481974E88CFABFBF6787775C2611CEFB27ED4403EA9B46 pk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sk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ct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ss = B2F713B6EE25BD7E567BEBCC5997F6A4 count = 27 seed = 54770EA1252EA2857D6635151194F5F520ADEA8A41E409FF498D40C271359858FE2B084D5B96BEE087B8E8F4DD4E00C5 pk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sk = CCB073C4B90BE0AD746E26FB093B60C7E0B4194DB681E84934D511565454BE2532A70B22663D775EFCB50700579CAF24BCA30BA44F3214AC535775263C4530AEB8B471F7B92BCF218FCEE3C88F32B03C8202B4B16E88D0F3333A5C2B775FDC04ED6E001A164D01F369A1A8FE5874A86A02D4DEAD4D36B5F5EB86EDCC04606CB20966AF09D52687FFA85B0B45D0A4F2B5F0149805929B56DEC301CD45C9443F116E0A827E22F6676CD3DAE9B099BBE661D2118DD08234C5F936F2102EBBBB0743DACFAFBAE266A440D05715A750314AA1004FDEE91BB4A2B6D8B80E794E56C79A3BC328DA4D7FBDE3F9CD68E53DE212661D1F45D4559EE29ADC7950CE354FD6888EA56CFC7358E80131F9C32241DF762B6BE1349A342DD8E4483FF9CDBF557B5E8C65DB210BC35D33379DE7379F12423427262E261CC1138039779255345E003D8EAF0D3B3887AC221D1DE20A7E11D18EB50D9E5160CC6EDC1C2B0EBEC2AB22626C18396335C9F34BF68A3866ECC081C29A2D410D8D01 ct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ss = B5004ADF0D36CFB07BD259921AF706CC count = 28 seed = CD6CFE94E9C0A1CC4FFDCD2D7876504BE5F50F1D1CA5CF93482943465B268276056F2781F4DE805C138976CA72621387 pk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sk = 2E889F44E28901E9AC7CA6B2FFFCB124E0978A0CBACB4248BFD50609838543E787EA931800CADBE9F4A2D500C7A15174B16833D563B47A3A8658A929DCD5413F80249CD506F1F8E345FE18DAED3CB4291F5064FC44BF06A148B05403CE1A10DD2F41018CFD898325DCDDF46484624317AB7883985F9FC31366F786A36BE40B7C111BC1AB71B61F5D763B625DF9C1C27F498F4C8EDAD8B17D6B015644608EEDFD2130E71F3D03FE9B1269DF2FCCCE385FA13D2EBB0EF6BCEB676121AA14B7FFB7C6AACF1468866AD7EAF31E3D2732C970001243989EB52F71577B978342CF0154EB3A46264892F9FE1D6BED6C0DF4FD626FB633180D3FD351C2951F5F063C2496931DFCE025F80500BBB68C8D4F7BEC39D56556181157D0E8423400CDDA2234B8F34329E44CEE0E8CC6D768284ECB20E5F797FF686D3BEAC587A7F5D99A8D01E57CA3ABAB77733ABA512507E69738E0DF9138CCD0E70A14617FBFB7938107EB18F47F536383CBE96316BBAC8FD787981191DD59B9CE00 ct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ss = 4F8AE0D0BC2AA3FF8717C6C7A876924B count = 29 seed = 265EB2DE7099E4BD5614E5DE7F0C2A05C78EF3E8E2DD4AE4CB70F3E5E59C8D1D88248303F07DE0C5508652DA66B47222 pk = 6A534BF74C6D58027DC079040D66CB118F898B435017BD11F10F5C17209EE5622DE035BF0D9B7754571173F16764D64BBBB00C6D577C0174476727253EA41211FA32F2BEAEBD9BF9D7D1D24DBDEF9326ED807C726394E0D5F70A6E9C2FD3536BA45AD16A1E223262BD85DBD992007DC4F4AE07D9E8B460AE2D1D6C94EFC898FC4297E603901D15E2B17C0D73180E9BBCE6B0C373780744BF3744161926C53BA18EF2688601D5AD8E623856809A460AB077C813D28FE82A8D91DB0830991047EA507E64C7000A8A89C14119846A360CD4E3D8A9EEAC984710FC5C4001EA827D32416068CCA6E666E1CF610B6BB2CE58E9A85B99358C0F1F9B3CB1C10D53D2EE9BD68A6625D24857585B36AE1E53D7E49ABBAA0074A77FB1AB394A13D07EE9C42DA45935F4CF5A726EC71FC68A2A181F508FFD34E4AB07D786E9A3662176DCBD42FAD52EC598366B796100 sk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ct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ss = 0DA2A1D17AE0CDE68A74B4BF76ED8D71 count = 30 seed = 806BBD111F27C2668318387BD0830F65EC21A51AF01985EF48D03D64E1958FF7EE5133A4EBF6DBF36329BCAAF65F40EA pk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sk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ct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ss = 5B0C71C6C97FA1FFD3A31B6598B80749 count = 31 seed = AD540A9CE816D6FB1661E5483C44F6FDD00C9E7BD1A8CEDA4B4C4D3697D4F78ED0A56954996CCB7DA96ECB8F5CB15809 pk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sk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ct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ss = B566B8997380CE9ABBA5A871A09D934E count = 32 seed = 288A5F2684D862A86D2790AFDDDDBAC6FDA934EE7D2E6DA1508BB550838609E8107312B28E00A6C01706374CCD3AEFA7 pk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sk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ct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ss = 968C0162E93282100048613EF3C737D6 count = 33 seed = 4635DC5BB92EF98CDB6220DF0DD717C7F8158375EAA2B78FC3F0B58E9C9653E92684CAD3461D9158A481DA3D14694C44 pk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sk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ct = B456E8BB9C8D4CEF7EC7B5AE3D67F608C36227A26AA10CDFBD2E4CD949D586B0A60937D09329CE83EC8363FF1F8C171A2034FFF6E2AB00FD430A62678F4ED7E382CFB3A1D2E6DFBECB34B0862466D5D21CD281304CE0304606FA64EA45C98A8122CA453EF0C1DE69FCA2447E1D012AD5D1C153435568910F1580954143C5423DE782C493520A5653BD0009135A1665F46CDE58BC23841867D94A4969340F70727744212901F94C5A6B128C7DA96CE66B1D0BCA66AC33C3CE1995E544E99F0E410D5114BEFF28F055BE6EFD723F640CBFA035EF2C6538257D478B530040B8DEB4277217C80532D5F660BF3EC2FFBEC67FD6FFB78CF4684C637280BEB0FE6C0F2A2168474268AA46272A399F39EE282C89D91F014EA52E255432CEFC32FA7DC717F45A9820A5DC1D88B0F3763368E7F608159733BC18C8FC0CCE9A1621BD5E25B679DE75405EE853D11F02E2D0435B1B0494EF7CEE0546E49CEA0C ss = 4CF1CCA95A4F53EDEAEAF084D0D6A0FB count = 34 seed = 5DA2C51B4ACF488C8BDED5E985CC4702E4A7BCB248B5AC18AABA529F7F9CBF30EFA776E99F76D5C1686E94F50FB57DAE pk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sk = D76B3573F596EB286AB5231FEEC74996E8B7BE3C815A5D5D76C69722A85C212B66491CEF853A65710F3E6201755BECCBAEC71D99A39FAD1E7D64F741DDA159A12534D9E39DF3E4E5545314C41DDAB46F1045B275C02966242C3D077078F6668A9223014EAA908643BAF38B65BA06619F14DBB2F915FA998C31A36DF317BD75966B580E9DFEFDB8FB613664C95D00DBA0128B9AE2C2695FCD9401E0AF77F7539C14E0635893D3D0407BB82BEF1B14853EF1B79AD6A242B816761FBED743FC2F5758F53D21F583B2824E7BA760C84EDAB40067FDD800926EA6D5D0F434F905FB6980CCCAD6D1768D8F090779F8B5380A48B890DB4F81FFE52DDEB5EC1B9AA0D5E0960A9754496CD7018427DA38718AA3C54DA5CB81847ECC41BA4AA3FD4451EDB0759F2B4EDC24EEB22C3780B1A6CCB7C2EF5CD85BCE9A09B3B1331CF2FFFA00F790D58F7A3D0C77AB91E2BAD875648B34B7206D2B5DDF411569EA39713876F60D89D5FD724ACABBB8713303EA5AB89930B7DE87279F01 ct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ss = AE968D6A27804749820215D949802EF1 count = 35 seed = 4D2239E84B052109A78DBAB6D80C51A86D38248105970476B74A0B78B9CFAB6283E30D5A406FAE1C7F54F8BAE1110EE4 pk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sk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ct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ss = 106D77DECF74C78D230AE3A4C60E9209 count = 36 seed = EE762F5C9021C36446706A88EF16312F4A12C725CD7AFFF1484337C91EDA8E89F7007F3705747D29907B3FB7500E5074 pk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sk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ct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ss = 265DCCF5815CF483644326C4BD905550 count = 37 seed = D882BA69AC8BBC88715F1C6387531F53273A5DAB87E66FAA8221A7F628D2BDEEE1CBC59C0E08D0ADD84520A3A70C1389 pk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sk = A1B52D871612A1C611AE0944F9E718585D189DC4AC1BB9A9329D942E322E0175D03AE93B11DCE9CE0046DE0023E28D43F846DCCC539A3DE1864657579B9DEDB6CCB6B339E2F181C9F4FCCDCE9FC7F3B40F92C5098D78A68F11837C0A7BCF44D26E21014B0CBCEBB86BC92D8009A7CFF8544B4116EA1518679BEC46BF11B8C451FFAA032B1AE58B91D9C2E4D5489C77BC6E5853E4E6BB9FC7FE0199BFBA3177BCB574502E5D07E81867FD7FFF2F0C2B030996D5629F80FF4F97BEAE55BFF4A3E5593D07FCFDEF632D609F1ECEA9AD727C01B5B463C7089B6CE458002F488F16773DD2FB6C838D39154AE328D55D48558397C30F772B44C4449C5E6E6BECD46D6AF9F1C5ED86CA4700B666AD1153D4DF7E75CE07C0965383B2EA85A1206BF2CAB2A18D1BF9233212792DFD7C4FED46D9E7B11DBF9ACA42FF5A0696C26AEF6500BACD4695FC2D8189D58FA5D49C0ABA66E1255D15794D2168CF72B357CCD1923AEB384727A48EF43B3EF80DA1D994368603FBB370405301 ct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ss = E3A35F1CB2667A2FFDCE38CE2FE22205 count = 38 seed = 6C3AFF39F5D097096D882F24717718C8A702382DC4AAFFD7629763FDA73C163CF084807BBB0C9F600CD31A7135F48AEC pk = 2ACED76575102E9CA0AEF82D980EAD88889D4BDD5D5434D7EB162309EDC1E6619B90AD83AFFBDF90AC0DAE4DF4B00FF4B63A96ADA65D004AC8423058F244A1BF4FF112F396D82C15E6835414BF44D56DE3C5833D9267A737B48009A6EF15E8BCE9893195984CD94E2319BCB08500DE313971527E4B6AC7677B654C8BCE46AE14E0E4BF705876DED05B5EB478068663FED13EBB045FAB2ECDD92124352E70BD7F84B3C63701376F75BA7ABCDA55D586397BD459D8F6D2EB06F16425293E10E86CC9AFD61F41E04493338699FB43423F769DC2D2EB9C2F4D1D6D1B8B01530FA5577E4483BC912ECCA04170B76D25EC70646085C1C56778DCA20F4874A384710220FBD562F0409BA6E866FFCE374CA3431494B2010B561D3491A746C031DC7FB712746C0D4DF6D6738C4D78E84C7C9384C62BFA8CC9DC598993E2EB2E2BA0D10AC3862BAAA9B4725241CD00 sk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ct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ss = B58E59F4A05558B84AE4851836CC49B2 count = 39 seed = CF520B92A2E3677AFD003EC1EC6EF136A709D78F828C9C0DD4946EFBD451C5FAABFC83CA66F9D3D17EE4220553B7A69F pk = 0F0B839F996D4D1E8F08AFA3A1EFBBFB28BE9A35E187F27431D48D05220A98DF798C2432C2B28D966B8806E83F7C6DDDB9AF95FDF4C90088D311DC95BE43024AC244A1ED221F16153D6BA687EFD5A628918209F869DB38BFB2C44C95F5FA8753CD350E09C3D5DD1455EEEE4FE90006649D4839FDE8B88029AB779D48479080558FD4DAD1390C981CD7CB30FB82342344A52AF58F076983F257B1E1A1062B79D62C32737B0109FC20E92E9A264825E8B477A50B41157F1928A94596CD2D65F3386CCCE7907E9CFDFB78BD9718C1F6DE7F87150F3BC8E129BDCF093200D63A1F74F38C77C903E67C3913CE22E7B879DF5AEE80FC7D1C52E6380F9C715432A326DCF451446C90BE35D1DF2CA71E1E85814CDBD4014AD1F145E161AC634CD22A3276D8073377F40AFAC4166EC55A434F8BCD1A55F5FB7C29FE35A6460F245F08B67846FCCBE07559CF19D601 sk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ct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ss = 2F93D724C4655F62C3BC06277EFE84CB count = 40 seed = 197E5D562DE7E01BED4FC597DB28DC6EFDF0179F3A5BDA5F94CAA39D67BAE730540534D59A7A06C8448F628DA8B7859F pk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sk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ct = AFA49BE5FA86BD3317A0DCB7B86B38B8A585B3D0755C127C6AF2CC1CE190363B0F40C14DB8B7F426D800348B2C2D0BF39788166178C90199BA184F96662741A6592D1FF1E777EF7B9AC68402067CA677243CAE3A5116A270C4A6362228DEE70595C4FD39E7F906C906BC36575E018814CA8FA5D7D16E0B75E1AD4E946EEF64D551769E00B7A58B13436382E0AB82A5759349EAE99A69339193DBD0B51115A3727CE689050155A5FE08145441C60C9D36A81E47DA6D1872B914D64BA1C8DB53DA264453A5E74A8B14D6401710069A9CAB211CA4C27964C94A69EBEE014EF1CB1743F35093C33F3692F13859955B2911CB6FDFDBB7CBBBC164FCF8772DC09EE0756C822269FF58F1A2DDF6273893228658B0F001DA2C9E0243F750B0C4E231DED2B56139938B079B2D9FDCF9198806689D4B6CB2659A28197C2BF4A22CE9AD87DDC2D2B54593703C1E1A01C3F0DE7422029F4E69CA6F91730C37ED ss = B899E849D60739D059CF343F459E7230 count = 41 seed = F170583CB451D8A45D105457C02C01A33A40350616ED8515BD49067142F61EFB00F07857E4FFF3FE11E7164C648C76ED pk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sk = 47550E9EDACB6DDCE3D9AB81F6B61080A9565C4770C1E638BEBFDAB6C9724C0371A22DF2F3EED0FFDACFE8003E31D5B9C4FAA343548D389DA16BA6D1EF1E9124B45B7967EB704ECA8F92757AF6073766C60147D3E80197785B01222E937C6D5EF0180159E8EEFD36A81F83687BA289AD1D8F6B670FA6769FCAD4885D63B18B872DA9D237A7B3940D04167ABB9607A43C5857C50DA3CA41878C00158C037DF87BD887FE08B0D680CE17E3A155FEE2CA9C7C61E98C55DF845D7BFACEC8CA2C7D70A369F2F057CCD5E1C74FC3C968E49E260218E036B49BEE4E5B31A2B584695D24064EAEF02EB715E33DE8A47431AAAB5164D2962F7E019EB40CFCFFC34D4FE16EBF5B786A28EA67014C6B7B5DD887147DE93E26D968596B4D641BEF8510630F5270A06A1469DEBD3F97C2E2D7C41B57364E7A108B78EA7CF3C0F7D6B9FD93007B5799737117CAD561FA9715FB204C9048374CCE2149E09401CE7E9DCA4F083AEE4B0929EFC6844EA7151322154D30B974AE70FDF61701 ct = D650509DDE7464111B4EA141829D2AE11C99A6A6048D81F8E4B84FD3CF0C3A3CE1E517C383ED69872692629F221D2D7162CD48833E9501EC94E5FE08640D787EB57282DA5DA19A1AACF4E5F6404DB460B6CB6D080C1FAA0136FED6148677CB751CFBA76ACA6767283BF355D1EE00EF753300EACA94B208A403DB0A489E8FF98BB37245E70D51C1174DDC3CA05B1F8BF668E05BAF40C65AE7091E913DF829B59746559C60003709342F980D8CE03AB73468895480E419361B2703096ABBAE078BA806FD49961AF166D861E25A479C13BC91C94D2DF4C40CCD796B07018E876D89189D36FC852816D88ACD9818299AD1BF4B93214501951D759073173B99377241D2F026D90B71BDD749B429693CFF9AA4BD9A00F994B2155D0568C905C605DAD83B193BAC6E9845DF9ED18FE095329CAD5D874AB9BA3B0ADCD2C52F2E61D10F53D848E48CAC018766FD01C9EE56FFDF8B3A224FFFDB433440D874 ss = 8FA20B8DCB491DE5FADF49328709045D count = 42 seed = 44A6774B2CAC02DFF210FF861A090561A453DB311F47B6FEDB81811872D5D9489F5FC4103010139AE53FCAED209DC9BE pk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sk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ct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ss = C42E0777D7ABAC1417C39BF318CF4F5A count = 43 seed = 49E1855588B6235DF2A400C4A70AEDF8AB17B6E5E2891AA745F132FA2E7AB0C8117C1DF37C39F5D57624EB77C2B4A091 pk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sk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ct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ss = 801A1A7CA92866C67832D4E33D5C771B count = 44 seed = DF0E41D2F6F86C1F79D31FD5878E7AB434FC0AF3A0D5F47D2AB3FEF31A42BD949B0E3629DF9F575BEFBB62E829E51DAE pk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sk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ct = 2F76E5EB32E7476CBB33890AD997AA2A9DCAC8354E810D4E9BAC76EF28FF5E6B914DF4CFAF8E1A36FED7014FC3F7238FF1428B615A1D016EC2560EE809CA20204025E2E6F6ED7115A05545996D7B186FA2E83022075BD63FB800FA28A9762F02C17A8C89DE435236B742DC3D4701B5D654E2B09F9112D14E1922C8D579D68BDBC507C82422A770BF5AE64CDCB751A809A3804405E7984A68DF674847BE790985E3CF75A8002EF07B7732928F21FC87AB4E1FCED3BCF74B0982290511A60B5BE65E5FAC885426A8FB9550D6CAD225A8860DF034D8E3E088B63930650078854EEA7F6323F4C9F783F6F8D889769AF037AEAD6805BFC9DB1D408DBAD09680E99BD1E2B068968D0B934A2988453D1DB6AE1E124800246D8AB7C59A9F8C82D7567E316D2CD2D05D122042D9BFFF81E569A0AB5AA1EFACB0BE9851FB15511B9CAF745500E5A853F86940D40E01BF9B9F3E74418C343F2B9CA8E457C7D6 ss = F8E403222BF0E2ADAF1F08C95D008ADA count = 45 seed = D3C9EBBA6EB03CCB5C9B9D2C8D7F0CFBBF50841E24396CDDF0E56525B38918C2FBE6C34CC1B93F7BCD4F4D5777E1A488 pk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sk = E9ACBB774BE970206C3A738E243B420864E3C9BE202513B43165B8BE1F2DCE13088992F78B590D6DB2233A019BC769B4CD1637CC475A63DE751C41B30B71DE90A23301846EF3BE062DCA54C42EC189EFE6F5078E9EAEABBCFB3B182EA7108A82639D012EC1161215475CFEA257FC9F2625B40C34F4862E5077097D2D9263FE574C1236E07595A3BF8F40DB367D7C1753D39F98591AD363DA9501AE0EE69305F4E4076E6CABFD2EDBADBCD3D2D228C83C2A7BB0438DF57E9DF20A29FADF414F7803BFEB9E5566D797820B46A9E5FFB3AF00CABA26F15FC79C6E926D0309B95DA0DB28F0A00B6A9D25BBA050B24AE447896516543A215ABB6E056FBF0BF5AA9CF78B573AD94B90FD01671865145687EA8CAA6C695EAD2A250483F4F7375F22D253A54D02E07C2ECD84C3E2092D157512B00EBF797FE94A5ED0EEA0C55D8A000084BA5EFF506B09B6DFA30192F21A0D5332C52608B4F18BD7F89576D8E543AD55D316348E79FEA81734D1A00A9848A997207DD25055A000 ct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ss = 35E3D14C2920FC09FF5D0E159609FAE4 count = 46 seed = 6B3996E8BC6F52879F2B7BE012C44AD555707CB7E5FD8ABB3457A298336D6FDC9EB7853008FF13201D5969A315C7E493 pk = 3855AEE68558398E50CF49B80C47635620A9615408A1DAAA44F71DAEC5628B1AAA48A867F13B4176561BEAD2977FDD349D4D3179EAEE00D1422CF125602802F4AB08102F9DF7C424AC1D882C4EB39C29B147C560CE9FD6260037F9900CB052E4536B3532775A7F5B5BA99BA03901EE24DA256BFEA66EB5CAB03763B933A29156E72B0B82CE014403F4CB65ED06027256182ED0435E855F1EEF5A8B40348E47628041252A00750BC000779CEFD5B19E94D25C7ACCFF0C49D74362837A97719A8B31E11EEEDCC33FDEEC0760DE1862AA999485FF8AF8178CBA394922026E447E6AC2BAE3D31069764C8E0B80A2C749D94954010A324C49D737113AD179E8AAB6CF24B42967EBA28776671D563E852837501CC80094C3CD5041D31AE72717C1B747CF3351F878F356E351DA56DB8AD154FEA375AA878F6298C60F4FF501FEB44095E0F1D1A6AD6C91948401 sk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ct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ss = 63FE00582274725260514057BF36BFB3 count = 47 seed = 730B65ECE22DE27D573CE3AEA7CB021C415DF210D228808D91D4F380070FFCB0778B683C71D4853DEB569C822765F2A3 pk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sk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ct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ss = 9A176F2E3F1B00AC7385E9CE14BD60A6 count = 48 seed = 5522A5A891A9A9B5514F4556AFD8DF40B9CEC63A01492F0CB8A1DB073A285A963E4A9FF2376C88662F7D8D241F8ACF17 pk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sk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ct = 878A0E555EE2243BEE1CDA2BD6DDCEAA0CE5269DF7C2B71C78DE51194FFF8F613D7065D790C38F5A30744A597616718BD4509FF988390143B08C52B658E64E81D267128E56605607A3A6CC903B265FF6B8F4A141B5E2BACC453C5178D992CFA662DF049BFDC13425B08F624E7900A32599CDB0B7899AC104D7A6BFD9866407C2DC477497D381357A7A5B1E2CA3BEE48B6CE31764757BC91BA90F678D0FD4456985383628004F0B1C929384E1CFF8E2B838472C284AD23A631D8B189AA048A58D1F9327B5B139B60047E2C9FCD3F4AFC1ADA2EE88CBAE8F1F6A341C01D3FCA36C8FFEF006BAB338363745230AB09EF0C2EADA67DF23F08C67D082349D12864ABFEFD0677F8CD253B7C4B5985AE13D89FB762001F54B4A50021FA3C7AACA6DAD85D540EDC2127CA638ED8C2B52DD0F607895C347B27990A2EA5E2F565F2EE45B977C40E8266ADE4A4B250068964C321EE0E31973B6F9906D1C1236 ss = 7388DE674871722069D24664917D44B1 count = 49 seed = 1853E72329353B3F89AE6A1B1EF700DA8ED3C10D19F9E61EE9252E28EBB0E15802EE43083A12A0B7527088832605E3AB pk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sk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ct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ss = 82BE0F91FFED9DF2F66E264621DA7121 count = 50 seed = 027C3D5847ED4470931141104F25B19AE76117CBB64B224EE424FFB782E9A0E988839E0BDED0DF666FE8E5FCBB5DBC09 pk = 4F780D5C1047ECF584DD204B2CC68102DD0FE9D5FAED786302D8DD7DF41617F9BDFFB120EDE1BCB1E653BEAA873996AE53FC5EB07B2F01FF0C6E0F885525E214E8A6E9F92A8D69E10FF9660E5FA5DF6FE843BE5DA347B44ABA8B14535BF8380C1D1B692AA345F9E5E79AA1E3DA01410F49FBD5B13128156D84F801E5521C91903FA14740D393149BE1A94221EB95F10AF676CBEA84C6DA1E94B08547FACF44ED219200BA01E52161E21BD716AB760DF8C54A7A9838326C1811340ED2E1ADB1F33707CCFAF252E0211C6882C0F74C4DC275385430BA0845446E3533022972C815F0D257E308E7745F5A2FA40F3BBAD0850A6BD0AE2C7D2EE4174827E7796015EB8214ABE8CC102E381B599C4330D26BCAB0E2000E27A842342E7CAB920BCEBE5C69E5F1A0792B43A19006E20B45DB8D1B3133928CF2703680B7956EC2930D1CA626B7393C7EC9450E4600 sk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ct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ss = 6D343ABF2D3FE4ED15E5B57E54EFCD94 count = 51 seed = 450751D4401737459C6D93E6C5F2FBCC4A3AF7CD7250CCF404BBB817A67BAB7B4C9D0EF4570BFE25CF919DA331C31D88 pk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sk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ct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ss = A1C30FF86FDE868B5D09FBADC336D4DC count = 52 seed = 5DE720F2D152BF4E1F96A61E7AE5F1BED6B8548E32638C2CCEC9F43B87D1BB43DFCF334F0582984D27E440D519AB662F pk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sk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ct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ss = EEC1AEF4A49E035594CF00B7C02F9019 count = 53 seed = D71729DCBB27D7CB39E9E905025D3E55C8602EFBCC483C9B866EBF82326157833169243C14550AD728BD1470F39C642E pk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sk = CD6A99396EB3539CA663A51E42063A3A6E29681BA52735192A80FA5D709F1AF1417DEA2C3235668327427600737261D6870E16D9090AF3C4BFE788C0B31975F27AE90F44FBCBC8903CD79FD2327FDD89DFD4E1EA6DF35641563096FAECD0CD4ABE18014A0D070A5393BBE654585E5A932891DA67ABA32F8D80DF166E64F95072B751FABE434F38C62D7DAF8F7A50D03C6C09E9ACD9EDAAD7B9016072EA9BCD673D3E1B365CA17A2F17D6434D96EF04FACBB4D835B1974D4664DD5813621E895F3C01988D06B371932840C105E819D38E00C634BA9772B227A3B17D104744A4D3F2E0E4923A65FD97133BC854F4815021769E4122824CFECA04D20B1F122DDD175EBE095C3DA94E00B41D9B0B73D49FDB1DF811FD013C5DC69B66E291100794381D04EB4EC9588ED23C68DE7165EBA479E831C34EAB7EE12C4BE2FC9C07C200229C9B3479F3265BF2B45C86DD37A0F7107EB01BB034D2F65A8E996DA3A415D7FBC6E420D1B253FB25B827148D4D4A3278107BE77D3101 ct = 4D0CA2C37A3B14E09C0970DAA3CC5C13B486C4993AC910D2E72260D2382CC0D50603648B715D31CF7081CF709F76F456BF031FAFE27301CDEA5086C041DC07F5B582B71123A85C5C6D461C027C8772E6D4B0D9F2AACA2EAFD46702145AAD45895A160E11BA17B97538DC0668EC00CF5116041498764E937498EC2D2E0854C0DF508570FCCB74E9C659CCE5534383341EAFC0D0620A137D08519E38993660AFBB6C1E73620153DE56C904BE16E6753A552394A49EF9925667888DAEF0FA8BDB604382B03991C02BEC4861A37E711BE96E926A4AEFA5F5568AE2495501FD96148155C2377B16CACC5A26EE3836E6383C15A1C2D63BE77C4A99A36F62AEE32D10C22B7A569E654DD72E8F1444DF45A2B00AA346009153B38CB839CB211F8F3E5D5D348E0D43FCC66267F170432F5D3BF4879440C682DAA27E476F254795F06870EEB8C54A0ED96C7FAC34005D837019AB202BBE4609D72644445F88 ss = 0BF8ED57229D0B958D41DC39CA6C6F94 count = 54 seed = A7C2C8EDB3601396BEB2DF0657EC82FD5780A2723581A9E03DEE1CDB018440439BB1142CAB0487C5D136E9AF46338AB7 pk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sk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ct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ss = A3ABAE416B3EFD3FA907D5C21E9B8F51 count = 55 seed = 467F6158CB86B724039FF18C47950AE5C49170163C910FC9A9B30141F86E9C06EBCEC91497BCD156D95758C9F0C6EF91 pk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sk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ct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ss = 66A0B0B4DF621E5AA3B0D21CDD7D9164 count = 56 seed = 687C02DE1041ABAC7B2C1E6EC2A7C3375552ED5EDB10E3A8139C24CC76BDA44D719D8121A81D47A0B762B4E9EEB85235 pk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sk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ct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ss = A345B90C57E48D5257A155B917500E62 count = 57 seed = 4142237070C216BCBE245A39BD9220533C97651D84832B26727855AD994A0760C52B9319AD404693E4248B8C5FF324B3 pk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sk = 6A1AEE5E708C1B47F02BDACCE4F56C86CA9F6F64AE7EB3C493F0D576ADACCABC44FDE623EBCBD94785F31C003701DDF09F3DD9D871D4D663EFC9DADA11FFCEF725F363F544D68DC9453C0D1A39EF81251D101C50CF2D6C428FAC2597B11824D3350C00D8A42F20B9ACA29379375DF81BDA41FA4B3F17F3363DB150CC568E9436C29CC51C99D13C1E0A76CDE29BE2BDE30232D11542668809C001DA076B316F4B2511016001649C08EA73EF7F0701C16EB62798575DC713697A8B0550BF30A63E673C0E3E968E8788D784522D519EDEB60036415ED153629685CC8BA3DE6E23350933AB3E552102FA940884290E7296C8A948F38A907734C7493BA93392494A67DF881CF8D342E5015451FCCCE54ED98EB606A3ACB6240624856537935ACECD0546BD39353495B1A1B8231C2F970B752AEDA92D5E7891F52CBCE841803CF7001274ECD6397F1A8B27AABD9470BF1D18AB9AF401CB454E158BFA3960D4624F072A14EDBDCCDCE63410FCDC1D762B6AF0DAE11A1B4D7100 ct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ss = 48F4CAAAC964251E2A039063C206E99B count = 58 seed = BD334D7B7EB14E00E68863F2E5551A095F8AF10681C28353FD19B9A7E70B8BFE266840860609008A567ABC66316C77CE pk = AD5CA25928A95A69099DBD0E2AB67494CBE404741115FEC47EE8D44588EC55323D633791020CE18C4CBCF315A63109DF9EB41C9CF37A00D73EEA2F67DA46E38507567740E4FB0FFB31659995E1F24BA21A32A27DCA0963B03F880588CE54F5C08FFE81F8480C86D0AA83A7E8C700B8A4A8C2EA85DEDB049AAB634871C40DFEFE3E66A123203F3345223BBE04F35CE4F5053FBFF8D2087B3080F67679AC6A35E9681CEDD801A91A45B6324D09E48126551EB613085E708198E134742D771DCCBEC10BD249AF80D3EF8B3074B85395B866B1A9446A8390ABE7FB0CA70088CC702018182B6BA52B2F621C118F95D691265FDA98EE072B2F61E14C835EDEA8266A0864EEC302BA7A75A2E79D7ED8D74568FDA2BD01885197037A0C99E0BA2822F95046A3A3938977E0EB8930DB4D3B130B627CBC7F6B49FFBADC5ED1092B2800DD283215DB044728AC939201 sk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ct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ss = A5611782265E1932DF3B7E736F40BA3A count = 59 seed = A0264C58AB1F2CBCB212077FD378D340307ACCB31F1312137CF84E3D3135044D4EAE8BD38BC3E540A0C14D46458F6179 pk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sk = A453BCACDD2B0D4646009E5ED451C3C4E810FDFF3E1086663F6C7B489742305D34B1FDD7159072FA736B97018CA6ABBED1FC3E64B29FA9F87E149A906BB5FC7C69BB386ABCCCD2CD1755EEF206FD9F801139F62BBCDF136B9AE3F1076B29584D07AA0183A6A1F092976FFC146D2022D77A0F132DC1A8E32E510729B00CA76A172D41A553072177D2ABA1E087D7FF1EE4642CABAB83D9C9B1EA0144C76374657D4BFA797CBE29C0F2CA863A4AF30EFCA9DEEB76EE64E823A6D27E73DA326A65D49B4DDE6AF41594CBDADB27152F6CD71D023B719F7CF53C9DC2262C6C1910284264399B75AF086548FA8F955D2BC3467EA78E873B200997AD4CE2C6DFDCCD9DBA90B7B2D276837301AA1B4F88864096B0B4A4E0A4F8542EDA77DCB92AF456D930E29040D8ACB57C5813E6E051FC51A4D9537B51FD5182656D86E08EAF01EC01925A6B7BE77D58C998B3D21C5F64DDCFE561AEE1732B01C7315BAB1F4AFE0400789FA36939EC389F9964FC735C75B86B6E64D041443901 ct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ss = BBA5BD08A7BD6DB8620A1C1149B00D03 count = 60 seed = 99A9CDBFC674AB3FF2C64CDED7D697A6E27A767434A47AFF7C3FBF3C6A22D6043D27868955286A13EFE3DE36D22EC48E pk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sk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ct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ss = E72DEB6A7678A71CC4986737F98204E5 count = 61 seed = C799D57B41F28C5C446DFC58A5AC6499C4BCF3C162AFD2B09A16549826EC2A6F689E44BAFC4ACC82F5D6AEC23F4A3993 pk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sk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ct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ss = 14E0D35F4EEF91D784C700B5C9E99296 count = 62 seed = F7AE036A0176A9DE9A036A542DD2840033277C44AE936D10B768566216DE9D4395CD42B116873B69D9804BA6CCBC05D5 pk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sk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ct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ss = 3588D259EA898E25FE7883554B9B4A77 count = 63 seed = D995D38F934B6E1A7CA77C9522E3D037676CC939B0C8BD4B84394B3DC91A791F09D2D97199258C9943DA955E7F7B26FC pk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sk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ct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ss = 5CA9F51BE147CEAD8A910A5AACBE78CF count = 64 seed = 5929F02A271725CB40200DE32D9D03D8BEA53B53AC83186C42C7F565CCB1CA508305D470850CF86E9B2C61A5B8CA1C93 pk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sk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ct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ss = 5E0D47D983AD86F377EC2B28DF453778 count = 65 seed = 905074033D7B75DEB2D06A2F29144EB377B452534C5710632989F02D45312D156557E96D4486020826DB200153BC4A8B pk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sk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ct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ss = 3F4B8410B799D38F26202CAC1B52A37C count = 66 seed = A3E2E511AFA7BB560446BDADF67D2EE2E16FFC7BAEAE7EFB8C5455068BBD4E91BF9BE9D98B280072FABA7712C75B26D4 pk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sk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ct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ss = 19949A812632BA36C87F77EE12C9529B count = 67 seed = 074AB1A37BA5A0403D8F68D26FB787BC2C90F5EF88F2A6D286C3E6B168ABD85D393D8225618608B8EEB301D26AF53BC0 pk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sk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ct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ss = 5D20C1D82577713863D76ED5A40C184D count = 68 seed = CC0C86CC0ABF86FA21899BE1953913C00E7C46E6B5F730C4E88B3C034012763981D7F14459D3081638080378348856EA pk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sk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ct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ss = 3774A74D416427DF3F63B8AE681FDCB5 count = 69 seed = 6D5A7CC326ECF3983C4E7683F45263A37F692F3BCD2D920E1FD9584350119E74F9A3F905F70D3E20318C1413DE2A0DEA pk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sk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ct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ss = 202E3D6D3132D36F93EF6BD8BA489C3D count = 70 seed = F68FC0314DEA88F66AFAA76E6C9B6804B13D4876924410D1F526FAC59A62E26C560B125B1D0F8B461F1FC2E351EFFB4F pk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sk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ct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ss = 9B5515A30B0C0C147AE152BDFB20599D count = 71 seed = A229218B0D51F58D915DF549901548FB0722F352C7470900E7E4D8399205764A319BBDDBD06C00E8C5932722EE5A404D pk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sk = DBF1C465FFF3D9F783BD9EE61A573715CB9A1309AD27732313B1CE192CBC3D6F14BE491F71FDC193BB041200779C9EF12283079228CA485CB6BF4986186A8C31BF00F2D906DE37CEF7E03B6D322F518E5B5B7938440F9B3F1BBB56C148A5CC185BE50118CE92909B8CC652CD7AF99C838AB25B21A115669A536470E206B274F694598D421B808E076F7F9746CB86A02D09883C006BCB4C8FF4009E6265E73EB9520521090186A961CD9F9D8B116FE306EEC8F72CAC10A05D56E7D411FEA5F88208C96AA85351E0491AC36B7405537711011E33FAEB9AB94A63FA2D236664F837C4046936C3786875A00FF51E92AB77A7F81FAB18AA657BCCC8BB8BBD58388A3E4B23617F6E7875002D6B11CF6A3C0A64EFD1C1706D8FD4712F0D9A30F294AE8C406F4774FFFC752632830A514B1C2D83005DDBFB22738DA9C3DC22425606001BEB79B8AB56C78C1893FDB887F2E20C7C546628EF2D585166D1AC1335C701F54A21E85DF8FC48BD66D731AD157692FF3B2437E85F0D02 ct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ss = E8F99D5CFDF7D84DCFB663A77856D6B3 count = 72 seed = 6960F21C7350DCF41B4770C551DC8692D8BA2C0B6E162C589166FF22E7A1AC0F94C2F48504A5F7EB0DA094DF427BC98A pk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sk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ct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ss = 58FF3C071363D83AA6B6B330A6E48D5F count = 73 seed = 53DF46012CAD4A745B7A3C06E18CA95E0B839FD8161E3025749A0887549EB0ED6A44EEEA08BD6060D6509DBF7E9DC864 pk = 3BE5CA49D556D1110C266C6AA2630C76656730C67B0D221A25A53E68A61AF5E5E62F09E5A210FF63E6FC83AEE7067C0C5945A08EFC9D01C5BE185F968A156B1EB1F81550D7513415AF3B5CACA0E8550A3837C360E454BABEFD53079296302A86717BB495B464F70DF4F7BEC634002ADCFC680C347A16A65591944495BABBA684782C44DF252637DFC16B7C346E66BDEE8C53FFA952D25862865629209918ACEBE5FE846B0164BCF37149AFEAE222C7DC0B2DB657A365C936071055D52A19A1E20458AE94DAAA5B472423D9876D4598DEA7550F793F64E2F153F9CF018315A053742073D5E6E47BFC72155BD4DB566CBD60A6C3394B84EBE66A5552928C44CD34574D34F36B024807EC501BD8F115FF6B066101765AA098CBD6CB1627CB851573B153DA3E767E713C3960F1E034D4880F238E3D1F67D391863A8178FA51E41DB1DB73BEAACFD3E38DD701 sk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ct = 45B85520B276EEECB71AECADCB02674CD14D2D35108207C8053807291BE2443BC5BF59566F582007BFBC418987C6685C4587E7AB984F00905136A595DEC7B9A70BF8A34D84D924D1C14B5FC4706C0DE7A1B886A8A6F9E100F8BFD1924F581F0250CFF6CA33139F8DFA9ED2BAEF01BA369656EDBBDADF489860DD6AF421DC7C2DE8C94B5B35F2AAB071496EB4C30B091830B40FB599C9E6494C776299D2696DB123B21024023D518CF99CD614D4F44DD730263AA9D9245F1A7793C75E4B7FF3E71F96D85A02EE2CAD361A3873A2E0A40F1C1E9043A03DD9D475946301E88930E226CAAAFE8D84FE49DC70A6EC9839ACEC4CD315417F05C2807404F98A0E6B4ED1F6B707C0B9035ECB2E0965AA15C1CEC22C010213B5252C33586DBC66EEC7EBB83B849EC9A46D2C48E52F78C24B0E3F9D00D380D4C0AF1ACBCD7F7582AF5F76EBC58FDB75271840EE07017D0D7275AAB4062C0C8FA446ABA19191 ss = A4E753CE52D682D4BD468D9BD872A6D8 count = 74 seed = DEB963F8B1D8FBDF499D564BA8D2D47915BB402DA02F17031B37B4039A842AFB9B7E48F37200605992BD2429427A7A4E pk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sk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ct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ss = D229BBB3CA9080B96B26D87F2FBFCC26 count = 75 seed = 8E2995F1B3E43853B18916BB1212ACEB05898E2B177A87ABEB928AD7184E59695C56B2CCCF5DB80853C28A525E327D13 pk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sk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ct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ss = C96B986298CC6BFDA4253200192D1573 count = 76 seed = 9218943C51FD2DE47E509AAC67EFF176795102F37D7A2017E3AFD768FCDA7877AF38739B00FCDF227C2FD62EB635942C pk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sk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ct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ss = B1466D6C93EDFD9DDA1805592F90690D count = 77 seed = 542E20078ADD5296050AF150360F057F6B9AB3BA835589DD56987DE805F900B906505B5390A0D86CBA28038992DFC59A pk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sk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ct = F7B3FADEFE141BF309B476DFC9E621AAD059F8A0902C5217D8923E2F60655C87BCBCA4E49366F95A1C28A40D42C9238C2D0FCF30FCE301EEA357DE19D698CE5DDCF4152F9FE766FAFD0A4F6A8C1DE63F33A810F08C7FA39863EE8A35B1634ECA054C78AA961532E9C1D9C3D98E005EF456E603B246FE280DD5069A6CA40353F318A453E51E4BA3905096401E3AA9750228BBA806C98762D8AE5E4C98859D97A2FAAF97790174125CB37420224A8CB0E025D4BD55B93DE058769EA1CF436B1401660481DAC65049F25014671BDA6138C3F56EBA6235D75DB58C0A0D01EF2240227274D3ED866D0471C000C05F177587203F60CDCE413417EE7934A166D45C104469B031E292376253EC892230EF620E28A3F3005559C9D7D7735865ABF7041DA0180FD60493B6DF3E3463590B5FE02CB278D566144DF82838A5564C97948C8E66C245995B1EFBC7402A013F525D7D6262291C6CE4F1EED0904E8B ss = 437B7246BE78180BA44324C3B743A028 count = 78 seed = 6A85A61DD08C0733FCBC158ABB49FE0B0D96A50DCCA140A2E9F5A254F1901985844613B1C656C0CB0112620591B88AD0 pk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sk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ct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ss = A7CC77ABAC122AE68F6D5F9BC4A01AD1 count = 79 seed = 7F4A56EDA151E7B097CFB8EF980440FFF707AFFBA91867C89522CED6C5FF3BD7F5F00BB49DDD615D9361A7E4EFA42851 pk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sk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ct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ss = 1668F6FE2A022440D748D2225256D97D count = 80 seed = 09FC004519BCF85B20D25D314A0DFC79E00CB6262A7DDDF9C52473641AFB8CFA0F5DD5F53558184CAAE9EC34B459E98E pk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sk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ct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ss = 8C09C3984055F2706130AE9F5291B941 count = 81 seed = E3C41CCA6F04CFE7732FD54DE30CC5CAAC93E2F80E76AED7D24A962A3969C1B6A311459A3EC3E510E3E9B1E4291D4D7D pk = E763483C849CF162B8B7EFB8C0AAD1FD8430CB09B8B9358D2874819C50ED045A3E7A1F67096161F37A5559BC48BCAFDBBC1AFFE7480901AAB866BB717B4DEE853BAA07CE2F0E56EA510D09514E1102B2E05B3F7059803032EFD941BD494ED97D36053AA51D3BAC6731C6857A94003FAFBF92D70578D25071625F0B0111CA1A21E1236A671CDBABF023297796D8089E740C05608B3F5BE5C3C462FB52902D73735EA3872F023A22D7AB2324C2D12E3356ED61A21C02FB245BFE5E62BFAE46387448A7294FDB54ECF7922E21299C4C2F170718458428E0A2C21B772102D236FB733788DCDEE112CF533BF8528E5D5BD41167BFA8C79E4CCB26B4C9CACCD5534324CE7953DB4DC994D79856D9B46DF7AE2F61C90154997BF205796F86E9F52980E8D73BA371FB9B9C85C6E35A6E7706C1C11A6AE4FC1DABAF4B28E2BB2D0F50687AC8F85721619D5ABFDC00 sk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ct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ss = 657A6670077450DF16010E2B27552FF6 count = 82 seed = 373FDDE922CFC416ED96B444E445BDD0962E8989F6C50ADF9912A89937C57217D3600B06C95440448E3F601AE69CA5BE pk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sk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ct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ss = F83EC12EBE74AD7A567E22537E605B62 count = 83 seed = 16BEF67F7AC3A755C59C816478B75FCC16CE5844DB537791ACCD1EBD49D2824B105FD2E970F728C8F0CF16E439A9AE2F pk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sk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ct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ss = DA75F7C38E010985947EF930BA6B83E7 count = 84 seed = D0611F9AE5BE4DA5D7EADC9109944348E716CB3DAEE545721EEA8C892E7831CF2E54603146454CBFD92387739E9A78D8 pk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sk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ct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ss = 389E75A62D289C99CD55DEE471EFD8FE count = 85 seed = FBC38D7614D7718E931EDB850D2C6F0C5EEA9EE889B3E25BD69AC255D5B91E885D93E808E66BF9C88C655DC594DA5792 pk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sk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ct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ss = 57651B54AEAEEEA98B87A7D60BE38C90 count = 86 seed = 1722219CB5DB47374EB0AF0232C856A57F026F1CB09E5A5799F4C333DD422FF6A0A67C4DA502FAAE727FB2D45DAFCF35 pk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sk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ct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ss = F6082FA9C2DF2BBAB518B4DE9F489231 count = 87 seed = AC139B78FD16CA0F26D6D7F9E15345C888D857B1910CF38D883339B37EAD2DCAC30F7CF10176F23FF34B4488EB79437C pk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sk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ct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ss = 35C62EBA540CB14180433A41CADE8988 count = 88 seed = CC7152849C98D5FED2813275D32069E44824ECB14EAEF425CE017448CD9A401C91C06D0F7EED6D22B7BBE8BA6C429EC3 pk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sk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ct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ss = 8FBB1675631012AA69F22561CCAFE1FB count = 89 seed = 96D9A06F88FF2C2036FA8E914B89C765E4A510B468DEE40F914F78858C811857EFE9FD0E17C0048E7389E8D996B7E2B0 pk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sk = 470B4943F0FE7FD0D8EC5185ABA0D1DB7CC710FAF7C1C1F4A4A8419DEB87C915EF692895903BAE280771460125866D1F4A0D7F7252C128D035CA93460542C32E545077D57BEA62FFE92C37B83C040ED2D7E2341ED7B406D1D9A0BCD82BCE3C9BCE1200E625EEAB1A74EC3AF9E0B18949627E0890A949DFC367DB9C0915A3541422B9E0CC632B45ADBC0F18E749B0875869116CD6145DE3BC540067F8E8BAB51AF4005306FEFF6478F567CE0B0476836606E7B7FDBCD888A5C863ED338C0B2DB7FD99220D84EFEF722D78A262081404DF01EF4AD81A528EF02650A4B8F1F4EAAB96B467289DF861781F4EF505A09EB95FD54023597C23E0DE8AE2942778F967C1CDC688E4E1161001EDBBF26CA03005DAECBE4C672662778D42464190C6AA95B0906B3995CB99F02D16413F056635BADEC34DF3B43EBE29866FF6FBB64F2F01E87CE3EB63B52765172361823F6981E02CA2BF33AD5FFB2B062F58B44FCB8F40B309E80278A804D9F6A572B5FA936BC391FA95686DF501 ct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ss = B3076F1E54E9218D8A56359AD11267AA count = 90 seed = D26CE360D399BF7B89DC364AA7AC06BB513EAB8F527383E93E30727EDC3F22C262AA0EC70257B39EDFF0630DCDC1B79A pk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sk = 6DF4385DB978D27B27D2AA5E452E41529B8E8792F075F00ABD73FC790D3297EF894C5475CA4323B06E63EE017DCBA0D39939F14443FBFF5A5A7655117CF4ABDDDAA931E1F9F5F2F4DDD9F23D9BD14405C885A5FF48C19BCA55E85CB6C994329FDF410142E78EF67F6502759B0BC2ED49EA8E69B0F0662080803F6D3A08AC2FADE6515F238482328C0E97C96CBC6134BA569870A27754F32D970186491403DA9C984DA754BB8CD3F2A2C117EF7BA1FB1F9D24AC04F989E6DD1EE421EEA63BA820E435D0EAFBB535C2AEDE244CF1EB43C9016BE24B68B1393512CC8E6DC4A0B9B2C8B8D9BBC0354D592101CA78F7058B32DDBE732C7752D489D4774049A25FD8F58FAC2A95B7BDB60131B6C1C121EB81C4C86A79813538F7B4E4FA3FB72A82A33C8DFC5073AA7B9D5BC01E10AC03FBF84045C718CF108CC4A5584E205E2DB1014F901110951736A4CC27F72E0CE59D4BB32A8DDD9E1699D59ED3982689C0576E009784E07526F45EC75F6F0C3C6E5D358F0A848485E500 ct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ss = FA89E11860344D23EF3708B4E18E6228 count = 91 seed = C5856298C3CB6AC9787A0F30938537AB2635B96F6D19CC9522063360E7A5C88E644929D2879180E3E5BCAD2422B7CFC3 pk = D838126D3EA3E3B661E4533ED9718149448B1E506E14B8B04DA7F945DDCF4B5363733086D5FA5F4E250EE1E8447827103EDF71E80F2F009600AC670B23DF0C598BFC21C5F5D9A25A03053380D148DADE2CA60626E0339489A91CD6F81C38039BB09E93D94C79584C79AF201954011623DDDEB03231F99013AF1595CAE2438F4013273673527DB83F7F28D3A13887910891EF3AB644059E8DFEC05CB671683265BE53BD3901FBF356BD8794AD73F644F527D24497A25110C24808DF4F2B924E71D99A33440C33DC84B99071EF05317DFD2990B193A7C54143D59FF301EFFB7B94A46DA50C7915FBCFC823E36B39144CA8F21BCAD4070ECEB81F13F7588986C90555390F096EC1C3DC2BBE0F218BE4F3A06E0A00F65A67CD56D9A18CFC51867D0C38293FB226F8855FF20B95C5C9A9D23126CE42A08382F03BDB5E9CF5E01C164EAE3DBABB2690B54B6E01 sk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ct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ss = F835B064E9CFE827C979E4DFF55328F6 count = 92 seed = A28EAD0A08E7228AEFF602B16A1E752278B8ED1E91DAC67994F5ADC372E1D82F95CC390CD97AB9212275E0566C833FD8 pk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sk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ct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ss = 2A25258531402CB564E80DFDEB153127 count = 93 seed = 92877D706DAF88EF3412EB143DB8CD91BC047A9A43B7ACDAA42523560DEE4C172697BE4332042FCAB91135839BF74AB2 pk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sk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ct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ss = 878871AEECAEAE84525E0D7E98CF15DD count = 94 seed = BB4C0082CA4044B1FF60B036C9B0E0495D58667156786C530BC69D949A13BFAFF53798E456423D7A0E162A60039367D7 pk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sk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ct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ss = 6D17E0011D13654679310C7137BEFF80 count = 95 seed = 121D90E70AF6204445D0DEB28AC0C108262719E9FD3476ACA74BBFDE89FAF04D8D5F89A624E8A75DB80431F0D10AD28F pk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sk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ct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ss = 8C41BCA14516014306BE132DC6EFDDDA count = 96 seed = B3AC6503206ACCC2A92CBC210D020A2654726911D11CE676AA04FEAA08AF1D20C654E4105883AE470EC3AB299075D420 pk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sk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ct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ss = A6DB9C606E364AECDF4AC552B41757DE count = 97 seed = 59EFF60B1EF6185DB34EE1E3B1DD2F159106CECEAA79BEB74923B4F5623D5BC52DBF5D2594A1F7C6C64D12CF144E9ED4 pk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sk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ct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ss = F68927D6306B93CC1F822E2CBB5C43B3 count = 98 seed = DDDCA9DC31BEA737D3F474E7560B37FACB2F53C803E768FFAADE7669FF94B1D4FBD17068CFFD5DFDD24AADADA4EF6B12 pk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sk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ct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ss = ABB141C9189DD1D2F5BCD86C02037C36 count = 99 seed = 2A6F7386B815366F572AEB6C79E272CC21B7095FE09575F18072C9D677DA23BC9C8A4BC393B7524604D299BEDD260C8B pk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sk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ct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ss = DA40C7AB4E2ED76E4A3BDB509B806E5C golang-github-cloudflare-circl-1.3.7/dh/sidh/testdata/PQCkemKAT_434.rsp000066400000000000000000010002401454601126700254170ustar00rootroot00000000000000# SIKEp503 count = 0 seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 pk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sk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ct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ss = AF1280151C2C59B4D4150B18BA7F71590523CEA83C9BDDDA count = 1 seed = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC81ADDE6AEEB4A5A875C3BFCADFA958F pk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sk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ct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ss = 810D3549BEB3DD6E45EEADBB75386F6A63FF3330ECB04C22 count = 2 seed = 64335BF29E5DE62842C941766BA129B0643B5E7121CA26CFC190EC7DC3543830557FDD5C03CF123A456D48EFEA43C868 pk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sk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ct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ss = 68CFB6A6E01FB2FFD8707C8278D705E0DCB53A502BFAD6B4 count = 3 seed = 225D5CE2CEAC61930A07503FB59F7C2F936A3E075481DA3CA299A80F8C5DF9223A073E7B90E02EBF98CA2227EBA38C1A pk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sk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ct = 2310AA9B6DED40FAC980646C368ACDF8263AB65B5262CED6EFD708222FD5B133EF6EF22A56B940228CA115BF7A9021454467F35FDACA7FA185D3704A4AC630246FA53B2A57FCD146BA8761853110BF380C6B3EFF773B81C941C4258F32C5E392E1F2E4BBC36C0D483AB7CFEECC2679B35A06C50FFD0D9B6C3299C166002ED90EA16030A95CF1C3F1F07B6B7F79FE286FCD2E9C23B95878D48A841F588858EF235B05CB06564A8083ECACFF091A179092AFC512BB652F9128C2C32A462570BF8BD59EA43EAEDCB0E80EB4DA4FBE82379200DCA2ADE33E0168ECDB06EC57C4564946A4BE1D07EE1DB50A05445E1C1274949EE0E3E0444EBC56F7737A275F9B3CD1ACF5E24C96275D9BE24B3846AB7C9019AB51BEE384FF0F0B7EEDBA3FAA640425854478C4D03FC710415880FA6E05F7D39D6ADAF8D781BB71183D0DF40FE456ECA30D789E8A97D271D59FEA9152E2C31898EB6272AF8E9022476FA21193971DBCD7F92F0A2984E3DC16FAA1AAFE85B3A9B935ECD3D6E9D25506265D2F9B7AD4899B5BA812EDEA355CB03C8E220782405079AA ss = 6CB10B8CF5C9E4D96562A962E5C1B0553799BCE28197C48B count = 4 seed = EDC76E7C1523E3862552133FEA4D2AB05C69FB54A9354F0846456A2A407E071DF4650EC0E0A5666A52CD09462DBC51F9 pk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sk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ct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ss = 815FA89CD9C0C6DEBD6D4C3F4B38FDBA423C8AE4555C6939 count = 5 seed = AA93649193C2C5985ACF8F9E6AC50C36AE16A2526D7C684F7A3BB4ABCD7B6FF790E82BADCE89BC7380D66251F97AAAAA pk = B1EA55A82BD335EAD91F9242F35213F5B9F49400E2D7AA0CC3491DACB960172DE119BB65CC0A782FD3290590D3604F1DB38AB5DCA5FB8CC01621FD21EA192B133E3B442DE7B1DF9E3C403DFCE43C023EB5DEB435F9D1BF00C6F3A923CE8A5993C377BCE6A96EBAB9904EE4D27644CF3F3566C3447C555B693A921DE2D41BEC1A04218FA743844EC770B340CB25AFE1E68A9401829A858661745990452E2CD02489DB2D4948EE47EB77CC84CB45364BD877F9246BC1201C57D5A6D4771E004013FE0EBCDF9CEB597EDDD8AB968812386D2804ECD968DD91F7B764679E081082A7A4E855FECFB134EDFF1112A286C504170454FBE64B295682561DDD329A4BD9A386B07D7CA06F4A24FFD6A6B290A24377206928997CED46975B400D9B1F52DC3272A3638CF1A03B7837FBD07ECA3A03E9B87D9E48AB94B53DF7D13F78FF48DAFB3615345716623E3D34D06A143C7D6D8E6D1E0CC3C064DC2880A2B39B1AF72B2F89B4D66A65C2EE2E539C862F1F836F8E2C3E731ADA4A2807EF31 sk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ct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ss = 4668C26A46478B62B40E5BED0BF71492A7FDB443FC010AB2 count = 6 seed = 2E014DC7C2696B9F6D4AF555CBA4B931B34863FF60E2341D4FDFE472FEF2FE2C33E0813FC5CAFDE4E30277FE522A9049 pk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sk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ct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ss = F9CDF2C113564143F3CF1EF59E20785D99974121A6832AEC count = 7 seed = AEFB28FDD34E0AB403A703B535296E3A545CA479C1D8148E2D501B3C8DD8B1034BD986F13F1A7B4671BE769359FD2AAB pk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sk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ct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ss = 7D5AFA784F3C460498AAA1782428C25E4C3DC97B6F7D3125 count = 8 seed = CBE5161E8DE02DDA7DE204AEB0FBB4CA81344BA8C30FE357A4664E5D2988A03B64184D7DC69F8D367550E5FEA0876D41 pk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sk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ct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ss = AD7F7BACCD3229AD8F3B853754F8AFBEE4975C7865EB3980 count = 9 seed = B4663A7A9883386A2AE4CBD93787E247BF26087E3826D1B8DBEB679E49C0BB286E114F0E9F42F61F63DEC42B4F974846 pk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sk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ct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ss = BB5168A89FE38D502434B5793D857FDA3422DCCFBDD75558 count = 10 seed = 980D0BA7C8F8B23D0E948A6029FF2659810EA1360064663A8994D0333C8543EE5FF5D6D5C9ACF446E61DC464F792B9D3 pk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sk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ct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ss = E889EDBF6075EFCC85A5ACEADAAE48EF56528C64A974A837 count = 11 seed = 6C029462CA42ED520F10A579F52687101105E0B90C6E7BFA582A4C112B579D5AD0A0ABD38F72ABCFDCAAF5893A112BDC pk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sk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ct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ss = 0BFB00221273D530945D57C734E626B5D744F3FE2D959B9A count = 12 seed = DB00120937570D62331F4C3F19A10465231EFF46465CDEE336A0D46AA1E7493DF80F18617F9FFD0476CF7784A403EF4F pk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sk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ct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ss = 9701C45E2E2383F51C50E6947D7C77771C93D856199A7D80 count = 13 seed = BD26C0B9A33E3B9B4C5D7EA32D5BD1FC371015BE163C86F584E49BFD5362C8D8341161CD1308115B2A03B7E5EADDD418 pk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sk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ct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ss = 87821E5176B41FF8B7516EBBF94124E2EE89911B41553898 count = 14 seed = E2819EF86853BCA1B9DEE7EE1C1619988964F9A913E635AACF0D96CA6E0300D084329DABD8F149E24176D22757404260 pk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sk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ct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ss = 40052343FF691A8F901C248C9D19CAADCEBA83B499571B10 count = 15 seed = 669C4EF8A051CE201DA65FC4BC34D398EC1F806276FC5D987AD71D93BC12DC8F107B58BE6E8422A0795C88CB9A0E7488 pk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sk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ct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ss = 78720FFAE156234DD39387DE9A82199740E064F564E43329 count = 16 seed = 9DEBCCFE818F6B5204DB4EA09C03EC9A19DCF1629C1527685B8A29776BB1DAAEC45F8ABF8F0ADC9A8C8BD6E2DF6D8048 pk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sk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ct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ss = 4C6DF97FE533560C98ECC1A26A597C456B4DF521F77D2306 count = 17 seed = 8098AE7A92C10F707D405F7DEA02C2EFBEF44EFA132BA8AEFE81BD45E543ECEC74F10920AE48A40B0653D63532517F2A pk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sk = B12F6FD965EA9C5B947DB80FC60C83D5E232DCA82E7263020F6AA3E88F7FA8A96067F8CDAECEEAC90C2D0B5E277E56E9C405EC9420C302029E85F47B655AC8BFDC11498DDA7B702D011131F858BCA91527646B69B664880994741CF637E339F6FE3298059EFC0D75822A7A8BE0804D4E48DF22D674471E9192F369A48C3DBA2361B926244E90A860E8CAE80673D15F487C66F00BD04B600518B8D40FF93007E26DACDCE31459FD0EE63243F6237AC513AD3FF50E482577452839CD397307176DE32984D92F12E4802BB1A5620B2ED84A7E2E6FACA25698C20F1F2EB2799903241E4C99E1408A57D00141D45E6736D61A968EE9F114ABF191E8D3DECBF7D8EC8330DB9A1F4EEA470E8AC09B22E14841F7E2AFD6EF2D23D2B47C77FFF5525F373A5C8F06E3F769277A88B8EFCD345E6D97D987E5063716A274361CC49D04045C2E7A0ACF3EC7028E59DD8862E7B11598C1417385CE8BF841F6EF47A70D6194D82139F015428D1C2613D8B2A7FB565B3D0974F633A41C9DFBCE89AC6263E27F3FE6CA0E23C82853B1304F0AE71E66222151A489BFE383C608543243253C025EADAC039D62AAA49C1224FFDAD9805FD481054305 ct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ss = 28367E5CB625250393C5614DE4D4E7DDDDD84945C815B3A7 count = 18 seed = D5F23808871544E9C1D6EACE2028362B48E225312F77663E9F78CAFEB512B908CD9E25875D61A16EC615F4B8FF826856 pk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sk = 9F52AF92CA165FDC38788F2B59BA02E01C8281FF7C1E60504F3029E1BE4E1C0258C3A22FF5B50B2674CC094BA7018DA2A61569845C17D20F5A71A94E0A6A3BEA30C367C682AD51E820CF9B5C4790E5B703CF9DC8AF6004B6F68970770A2303EE49AD5ECF7F48E1DF4A1F8B214B8E8274EAD984424EA5287A257D23176FCC8E0109F6ED0310EDE51DD0D4162C56FB03976BCCA82ABC94AA85A3B7DA59989D00F4CC73D84C822E3F83C1A8BE86A244E97AD8B65BC1CB37ECCF547A1B2FFAF6369A15042B106AD8F85954FCA5868AEEFCE3BBE5F1425826BEFD3F342C14C5A3071C28936C536EADC428634EBDF2B16B0CB4FE4EBFCC1A906B4860A17B5F8E333EC4DBC4E432D788C10311B261359F2F2DF74D02350C96132140E90FB67499E6C837F49FC2A87C6E3784D19301D39F4B39B8EA19E813A60F8DB75C7BD50ECC0A5F3B2F9C1C60D46D86A9E327E3C102769720A3CDA910FD9F74CAD6885B95B50D32A26CE9D55BDF84E4C34EB4211B6751AB7E9FF31B73854537DC9F4E84781CB6FC9B11D90D1F083CB1A3DF08CFC4D24114B8C0524ED60EF93CC66CFBCA043E667AF1675CC6DB6139DB4B659021177AC63784F33C ct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ss = 37F56382B810B4107E0629B8F426D77EF9425CF8C532187A count = 19 seed = 822CB47BE2266E182F34546924D753A5E3369011047E6950B00BC392F8FEC19EA87C26D8021D377DF86DC76C24C5F827 pk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sk = 851EA90FD3854CBF28FE39FB81F68E4B14345CF0D6EEE7EC1C0EC046899A777655233E4E1B5CA44E9AFBDC67964BFD5D5E3DBB45E60D030FA3EFF37BF2DA86E5B41B10EB6321F9F5A46898E255939587358B1083102D5021407CA4B2F4F4EE2B837FA392F4DD1BF94BBA154F56968B57CC5C8FC5B6E73412A83747FD42AA5B537D7A6BA455FA56564229596424CB9F4831A42ECAA486888C7814B6DA3441792A703836767DA0DCA522C5B166468DEFA2D4485CC2FD2D5FD4990A9154F8F0C8F3D5AEDE6139DA6C9D97ABE2E8630750F127DF2AED7C76CC3AD37C9958B966C3678188CA32319340899C64A606BE8750196DA97DE6259DC556A15939ED56349695F944F756B8075A2B1AD65F6169DC33F8B8DDE8AB2C83792442378F5A5167CD69117398AD69B719E1943F3A096701FF912B585033AACFBAC194A7522D95A6EF792C0281EE8B813BD08A2D1EEB58B0FE156CDDD683CD8D582036D6779BD03F67BCC58A1EAD7CDE649DA4D9B84F864350B739583191339D5DD469F677B463E2274F36D8E270E2301541D10CF29BF10318357BE3F8C4B60697B9EA3B7896F5BB886938CF117B26CD7D1A5D69F3E2B843C68B392D ct = CAC32EA5CB119EB0C6901B31E5800BDC1C59471CCAFD4C6E5F08D5C282B9E0DF6D2411F8602F346B2BD20945D90317F4E6135921E3022D78D4267D41D9D007A1E0B6C1C9C5C2A8153DB0248F41DD31498BFC753375CF250C1062FC3DF6825B76E0F8B938C3A4C2EAA90A5AC01A03A89C6CA2F8D5C95EF848E9A8924C0240CD96DCAF7723AFEE617315918C152E2A2BC1448EB34E589932402AB2B841AD2E9B9E5A3B2994484F59960D0D020F66E69B9985388A6CB56977E41CF906701A83AE8D8AC0CEC6C3200597D0102A1B90A8A4EFB4CFF5AC3C492E568EC216E828959DE8F703178E669042E42761D765A2CB1577ADEDB7F6A020AD8DDE56B6152B98E1E3DB908A6F3BB9EC358079E510C9EE1FCF238D78B6AD8EA82F3C70BDF44A346E27732483E56C2F3EB271B55D56422260C43A54629019296D09848431E86664C4E1E498648E85139D30E54903BD5A8458F2A67DD6EE8456077FC9D6546BB941335FA0D4B4991352E46D2CCC00DB3F1143DD70402DF2CFFF4779661E737C2305F79589850F2C8ED42E799C6A5414E5BAF590D523 ss = 7669B8EDA6CBD1625F419F5C04D6933DDD9941441755C07D count = 20 seed = 81401DB81138D6874E91B7C11D59596E4ACE543F5A3471B6FB00999221765FEC3CA057ABE20F03B2D59003375FD71FE8 pk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sk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ct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ss = 11EB8F2019A872C000DE74CECF48C1F1260C72756933CADC count = 21 seed = 30B5DE5B73681EC08AAA03F6F2D2169525D25F4042A5E3695A20A52CA54927B85F8BB948FC21DF7DEFC3910B28674994 pk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sk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ct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ss = 2802B84BABFC1973FF4D9D2ED0CB2B190E017A010F21092D count = 22 seed = E335DF8FC0D890588C3E305AC92C7160FF199E07C85760A828933750E3FED8C83B0DBE802234481ECF890A32D7A2884F pk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sk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ct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ss = FF9EB3E0434A52E2883FC31009E1F6D10C7E505E324F9B78 count = 23 seed = FBEA1BC2C379F4F8FDCB0DE260D31CDB064C9EA9B1D6DFBE91B3692ADD1D34DEC9C9FFAE7BF5E72ED2743BA3F9F2E43D pk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sk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ct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ss = 25356B80E1208646C29DBA5EF1348D3265E8FF9E767C4465 count = 24 seed = 7E87FB886BC3C7C9FC12569F465D2ECD12532E76CC27C65644C8D3DD603B0CB2D036C5974E675058F271D5C82AD7A813 pk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sk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ct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ss = 8D38A9FB575D15AEF5725AE38E75203DB4AFAF6D43171914 count = 25 seed = AD1424E804F306C7FF513DA4C1E8D445AFCA7BC942FAC5C0B335733AAF70693712ECBDE26EA726EE0F9FD9D52A83B1A4 pk = DE96C16B07415B67553420B347DD8782E5FB834CE71744D68A423A4775F14D2D2A9373D049097352C9979E8F49D235D12EDD7608C4A2A7B52CC610698D653A8D573A111D9F42EA748C718E5DC82D5F429F12FCFACF6DDF3D95E38BB9429FD23285155492BEB51C18406A50EE0861940844A1C834CB6D579D23E7FF9546141EB6C8AC8BF6338976B1DEE0A89B1871D00060984639984E74DB5FD5D35BAD61B80192B0F1D044435E1470811B7BE30AC0D9A8BFC7C6E14B65AE67636443400AA5A0C764D65D3617E35556AE46D8D08BA8CCFB83A8905500C5259B9A665C5842435089EE8296B36E21FF50AC47A3F47F4D7BF16AEC0AEDF382F23D65F3362F3C06CB6880FF5BF953941EB076EABDC6F135619DBFCB3C705AC9C742BA67AB5E98C0ED21F8AAC3DFE8136AD67B82C27A07259288381C8AC39F31F998331F9E4226F102E5F4614A1C9CA78FB5B16F47F7EF3FABE5E50A01EDEDEF687B1263514FDA8A8BB6EA150150B1C8E7F6F0045F450454F5FA26A58ABF8757FD5C20 sk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ct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ss = 46A4994AFBC3A5F11BBB0B1764169F37C03C65C265331C70 count = 26 seed = 7C33CA0E987226C8524DD56C811FA4D1CCF9995B1E4E4DD5B1481974E88CFABFBF6787775C2611CEFB27ED4403EA9B46 pk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sk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ct = 12BBBDC2344D6F29BF4CEA447A5B28283573EF13BC0975AA96EDE6D9478CEB702D9C3346A205639ED29848EE51F50E858A54E2CDE6BC867BF4F807391E1415B465162FB1157FE2E828700084892B3D04EE7764B2575AB7D517FB7A319BEBCE90C672A1574E2808E918C9CC44D6DE05525A07D522918B65BF320218326409962B263AB2E2B479707FE73D079D59AC976227961BEA2AE293FC4FE01016495B2E1ECA1DF8E7C6FB4B15831EDDCFD6CB58CF16FEA6ABB172B1B622E0603F0506053881C4F12616D8386C2054460EFF4DB31A2B0FF1EBB4BEF106F80E7B3FDBEB95503C891107876381D01D3EF5B9A46D2F658986C59F94CDD73031D55115384E13562A03236A54DC6F8A73313AFBF37F222E0047BB44DA44C6F9FBFBC50DBB44C7251C4903CCE7F7DD8CB43FBF563A8EA19438DA37AD58BABCDFAA6023725374691A47F43D082EA53A20924D795122CC263E1AD5FA4AC08DD17F632D831B0B38231136C7CA1699A1A34D3C0C62DEABCBEF4ED6BD1D500ECCFAF9760FB68A756BC77426482D0D3BB435522E5BF7049603A936AB6C ss = 50070F02BE770A0C58C395E7B59ABDCD9C94DFF0CA296C83 count = 27 seed = 54770EA1252EA2857D6635151194F5F520ADEA8A41E409FF498D40C271359858FE2B084D5B96BEE087B8E8F4DD4E00C5 pk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sk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ct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ss = 63579BEB1B9E77A63D12C42ACCC45CB12113BBD158A98B62 count = 28 seed = CD6CFE94E9C0A1CC4FFDCD2D7876504BE5F50F1D1CA5CF93482943465B268276056F2781F4DE805C138976CA72621387 pk = 87D7F0EA9A83C8FF9E507D0E66268AB7E20A5BCC9630DDEEC511C0F321EF86CD5EC5C9EF8769CAE18DBC600A54873A1059378736DC9D6F55ED8C692DD1EC30F897C5E9F9C6E84BE8BEA02773A99395591E237372E8FF1D484B56DF2D54EA10ED20B32FE64D97857862E46CB3825D0DBDB031319E4871120D7202DF9F7B2B045ABA4907111D39F8DDDF1D35F078DF3970515C753C169F5B4F1AEB7CF154F307C68DBF095BA4D6DE4F5D932C14841DF41A8E4627612E6B2CCD7E7D8EFD1417D69B18422AC7420B316B143E6BBAF5B52AE02935DB5C77652F3380394307CC5DC60CC712B3690BBF6ADC5028ADF63194402C8DE5AF46DC27593723D7E622F8ED04804DFCE3A800EFC35C40066FCE4A66AE2A60CDAB5F11E340A2358666B5F6B2D09592E9D653D12562DAD1C661B23E96A5EE068C5687D8690CFF9A7235B46A5D4B60E112755E3F9FBB92A46EDCA6D7029F578C0053D7FE34A3E6663FD5437A500E47B3E0F6F854878E5AB499D63FA567D350EDC5314E7BE3BF86FC31 sk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ct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ss = 7AE5663B12E00FB60985F50DC46F2CC949E917EB3C313C8A count = 29 seed = 265EB2DE7099E4BD5614E5DE7F0C2A05C78EF3E8E2DD4AE4CB70F3E5E59C8D1D88248303F07DE0C5508652DA66B47222 pk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sk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ct = EA0A417DC1A13A15DB5FCA1AA40ADEE75F0EBC983F335707DB45B74E1A57BE06EEC132A7DBA217339408B004FF8899F1AAE064C49E8959D3CE6F054E426508413F62A78F38BBAED74F943805D38BBB57896741DFEC86E29D56C4E3E60F5FC5E293601B86E8FE2D5F54ECE703242B3EAECF627FDE6C03CAC65F7A3C03272637F510F8B4D92731F4149C5837072E7E1FD7169DA5DAFDDDAC4B2C248EED3F24FB004C763D655FE46DE11A7E6FBBD6D26B4956D06CBF4D72127C19A662D21413B46FC9AFF4A06FA5F6FC9C1A072DB9A98BEB805B82B7667A4AEB0D84B1FC4D6D8C42B4DE4AA60DAC7D19E66007BED6D9D444853A25CCDD11BF8222FD903E9B9B08E70BB3425A499313725148A70C8D3A959122F77077891384F152AE433ACCAC91D029F19C706EC0ED16148315466666C9776AA0B5651D566671575028A784A6FC5C38A8A1FCB7B986373A861493E6EA1D8F5C24CFE0399BC3695CFF1026CED8A1F2017F2DB363ABA2E08AF8402807656E49F92986660F8C615FBC3957B35C2EAF0E885D28BBF6FF52B97F460A649B2544A357C0 ss = 7BDFDADCAD41A5B6822F31918D6D7AE2E281C88856EFFFE2 count = 30 seed = 806BBD111F27C2668318387BD0830F65EC21A51AF01985EF48D03D64E1958FF7EE5133A4EBF6DBF36329BCAAF65F40EA pk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sk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ct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ss = 2070A68D724543C3916FC37A02561C82556DB7A8EE97BEBE count = 31 seed = AD540A9CE816D6FB1661E5483C44F6FDD00C9E7BD1A8CEDA4B4C4D3697D4F78ED0A56954996CCB7DA96ECB8F5CB15809 pk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sk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ct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ss = 0AF322CD0E4C18F9886C22C619E933858A45DBB3FF192835 count = 32 seed = 288A5F2684D862A86D2790AFDDDDBAC6FDA934EE7D2E6DA1508BB550838609E8107312B28E00A6C01706374CCD3AEFA7 pk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sk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ct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ss = 7DE608427494E125EEEFD9835047F49D8375C7A5CAE1BF2C count = 33 seed = 4635DC5BB92EF98CDB6220DF0DD717C7F8158375EAA2B78FC3F0B58E9C9653E92684CAD3461D9158A481DA3D14694C44 pk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sk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ct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ss = FA133C56508F068C3BA387BD3E0664A420D5F8F427901B6C count = 34 seed = 5DA2C51B4ACF488C8BDED5E985CC4702E4A7BCB248B5AC18AABA529F7F9CBF30EFA776E99F76D5C1686E94F50FB57DAE pk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sk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ct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ss = 03F6FF9E4AEE904E7060DBE69BFC53DF8A76F7FE8C07A482 count = 35 seed = 4D2239E84B052109A78DBAB6D80C51A86D38248105970476B74A0B78B9CFAB6283E30D5A406FAE1C7F54F8BAE1110EE4 pk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sk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ct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ss = 0E6998CA7260CDE93D7CE60CA8CBD1AB6076EC79DBC94377 count = 36 seed = EE762F5C9021C36446706A88EF16312F4A12C725CD7AFFF1484337C91EDA8E89F7007F3705747D29907B3FB7500E5074 pk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sk = 056661B38038DA4FDD7426F32A81576C73ED84843B30516879238A80DCFD7C992D84B2DFFA67493E669243D4FA38C46B090BDF86BC5484017D6DB450BB97FA0557B94795596DD6A65F956239F0A4924D2E869CBFD8E30FED394CF80B473FF51395F0ACE8CE4A50AF6335152413562B499DA9AB75E07203B8A6F178943400C8CA01FF7CCC00183FB917C44ADBF09335BF9011E824EC1C687A91608076DB1710DBC0C98AC8443C447A2ACA28367FD11A840E4891A4D834F911F58E44971768B77198A18629B66BF83B8187B81E429A07946CEBF46ECA19BCDC2841E65A8E09D7C66C2087F8BB9F49A9CF2BDC06ABB3960D188F1C4104C6F69DB354198827EA60A6BA11C366A1A83868F06892B306AF2C7A9BBFA3EDDA6277BA761E877258BA29EA013A0E90A404E1F8C17FB41C1B18F55F18BCD02CC523C3CC7DAAABB55545BF618434C3E09138388E3C583800C52C5A1261AD7E1140C5FD812E8BB9A7DAF4D75EB0A2E773C73BFB2C1C4DB4E95070BAFD37C23BC37AD988913D2744C195976B0B52B7DCAA1BB31ABF59565876BA98DACE8763375362CA10E42568D68212413AD4F78682D24E3925C13CE6EBF23D2BA8EFF335 ct = 33C8DC5381CC3CE7E50F82C66DA129B3C827A0657A577E0940D2AEDA06A2DE05DB3FE58842F6EF004DBF929A22AF309D0DCCBA66D6CAA8E1612D8533137E2730A94654A51E10B32513BD733A53915E827EE6FAC8A71F5D84CD5B64BBED011E749D96BFEC3999E2AB10281CE9136CF7C57DAC304EA259B3031883557FBF0AC9BF9F11B07A3903BF1CA77BE1FB4F716D5014F656B4615176ADF65CF1189B2B42D0482072A49197FCA56DD9460545D4ECFC9DB09C76ABA5DD156BEFA8243E0503BA20867B0E02A6363C8042C419A5EE8C8549C288DA90E1EB612B477E75BDC56BD50F858163F11D27E1BAE9E20B6160E1E42EC5CFB07E7908FDE9302527B53614ECE02451B61A9A26A9BED4D9C3EE29C60B0DB045BD9C4813154BEDEB77BBBBF43C908FA12516D027B95A67D43C0F811C809A318F14913C11E64DC81FA1541B1A4A72E93B6AE17687246D9DFB820481A3FD2E08E8F9CA4768F53E04B0328FAE2956B8E100A474023A2F893B5078E6C98F684168FA8397E74AAEFE32D23966FE358FE4AFB990D6FA7C9D2F7B74861367F0540818 ss = 9272A0390B05170693287EB6A6A93CB28F8F5A49731F5873 count = 37 seed = D882BA69AC8BBC88715F1C6387531F53273A5DAB87E66FAA8221A7F628D2BDEEE1CBC59C0E08D0ADD84520A3A70C1389 pk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sk = A1B52D871612A1C611AE0944F9E71858F35D3BD14F20E96A1F135CF64B6403E103AFAE34DA038613E2853BBFC36BAAFA3C6A95347193F30CF81EA80547B4FE29D3A7353D31307C97AA173E35B90C0116645184E60262A10FD6FE042184803EDAFB1D53BA7BB9F1B17E9B37C50A1271E41A34469DDC962B14D40C093E76F2AD9D39F474F4D30D749CC4385A34CCFD305B385628BF6C539F97E5854A432E251FF170F31319900CA5C75867E69DAE733A89D39FF6356012CC26259EE970A6DF942EE5CC0A3B2926707B32D19B4589670FAD59E11BBE7FFE74D36DF1257EE0277A1C7015E88E32123F023CFEB6D33047E4A7D2BEBCB806B4705022E7D426D8D3BD69419B532EB4848541E0E60EB644A13126A2210B5D40792A74049BC77BBD41D021E8F94E5DA1D00E8F716D8B60623E29AAC7689A2EE2AC3D6953C1A036DD19CF470068D2362B4D0E1A416279514696207C723AC2069657C4DAF2B3C749EDC4E4CAF5BFFBFF5ACD8715B0E5E8F00CB1D711104D233B1FF22CE183BB22011F27156EBC7DAFF060F4FF7CEBAADC59B6062589C26728A3A4F13DF2706727D3F3CADC7CE80F475C902661DBC75DD0C627F437D7943F ct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ss = 72F6DA9DA867652E3E80628EF1D9AC389D41020985D0655F count = 38 seed = 6C3AFF39F5D097096D882F24717718C8A702382DC4AAFFD7629763FDA73C163CF084807BBB0C9F600CD31A7135F48AEC pk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sk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ct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ss = 51114A60F9D0E1CBF25CA1A7E1CF78C0B38FCE11BEF7B004 count = 39 seed = CF520B92A2E3677AFD003EC1EC6EF136A709D78F828C9C0DD4946EFBD451C5FAABFC83CA66F9D3D17EE4220553B7A69F pk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sk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ct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ss = 7B624C0703A0A47F62C174681C0CCD4B6F031C40CC05E6DF count = 40 seed = 197E5D562DE7E01BED4FC597DB28DC6EFDF0179F3A5BDA5F94CAA39D67BAE730540534D59A7A06C8448F628DA8B7859F pk = 0F57DED59D6FF0F82D79EFF2DAE83CC9B75B29696B83687CA0925A06838A99A8157B17D384569CB11DB8DA003F921FFEB7D6FC59A44177A65A98417F7B64059CD40095B471ACEA5E06E972B9E714E97FDD6824E0756ED9439C720AE9BEF8CA6E47EB6CBAE61EC00F73E3035F9B10F14903296175334F9DE7FD452E71242ABFB77F74842F2480DCB3309E6536E6718A9E06CF68D477FDFC7405DEFA4AEC7644F1BE2104E53B4BA744759539B90CC7A30FE3A3357B7DF761F1DC657D191E5C9397F7190B7FAC16E3C22EAB251391426A71AA67467EB10715E8113C2B4608170029E20F390241E0432982CB30B6F0A7961B85D0BAED6239F12ED1983A2DF129DD86944004C22D6C1026CD83CD159D472CF91EB3A1ADAF36CD0EF720E539BDDA0E1A86E1B170AC4D29A026380BA057FC6EFFAAF49F4E599E4B207DE009A99B4CE6BB9233CA2F0FA912E50277AD683EE2509322A7C11AC0A7850BB5DB1101CCBD5EC894BCB7D8EA88AAF0EC52135D002CB930A7D90200EA219494B724 sk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ct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ss = E33DDC85305ABB33EC79D7B3FD5DAF44F4B620B6F2F044CF count = 41 seed = F170583CB451D8A45D105457C02C01A33A40350616ED8515BD49067142F61EFB00F07857E4FFF3FE11E7164C648C76ED pk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sk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ct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ss = B94904EC21529938A5A4651EA576E0372483E6ACD980767F count = 42 seed = 44A6774B2CAC02DFF210FF861A090561A453DB311F47B6FEDB81811872D5D9489F5FC4103010139AE53FCAED209DC9BE pk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sk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ct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ss = 4747804B324F5E1700861C0456762F30839CC5D9D7A3CBA7 count = 43 seed = 49E1855588B6235DF2A400C4A70AEDF8AB17B6E5E2891AA745F132FA2E7AB0C8117C1DF37C39F5D57624EB77C2B4A091 pk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sk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ct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ss = 841903B25A4F1A31C10CBD2357067D22EB25DFC04C58AE38 count = 44 seed = DF0E41D2F6F86C1F79D31FD5878E7AB434FC0AF3A0D5F47D2AB3FEF31A42BD949B0E3629DF9F575BEFBB62E829E51DAE pk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sk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ct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ss = 55501CE296D88A5A9C9C962B05C7562B8924ACF2128AB352 count = 45 seed = D3C9EBBA6EB03CCB5C9B9D2C8D7F0CFBBF50841E24396CDDF0E56525B38918C2FBE6C34CC1B93F7BCD4F4D5777E1A488 pk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sk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ct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ss = FE6EEBD0E2902D868889C1C39A0DC8D1E85B5DCA4DB880CF count = 46 seed = 6B3996E8BC6F52879F2B7BE012C44AD555707CB7E5FD8ABB3457A298336D6FDC9EB7853008FF13201D5969A315C7E493 pk = C2BCE85E112FAFCDC1327B624AC82D2572B73930F7E0F5F81247376356158F7387233F845674DDE0601988EB30720A83C3E58138194C9A05ED9A1C5E74392725B8907B2B90A5B5109A043A10E91C762DF9FA65EE7E0E370A55858D955DBE9BBBDED1160487B7A12D8E3872858AA4E938D07328E217B03A4264A8711FFB1EF9091C617910BC74219E5383F99BA96BA253E6F157E3CF5925C3456B10FD00EEAA03F21D7B97209F805A31B20DE89A30C68E504F51F9DDCEA61CDE895CD414CB291948A1D58D73F726C329121515563A60C48223246A209F782FB757F547E55610D454D76BE1CF88E35D9FBDBA99C4E7C0689CA659421C33D7575BA059368BD8EC79F67A76664A3D2D6293363262DD9E5E9222F9BBB1F3AD0AA9B48742333D532EC5C2F91A64D8E73AA17E04A0CBC37324E4F0984047012B6B81B6AD0B1521C855AA501005D4FD5BFC0C09AC4105E506C27FB54076EE270E3DCF93A9B2D4B2952E19EAA6206EB60237B9B2BA235E6D822E494F6C897A14A91EC13820 sk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ct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ss = 2B4F3F6BA7D91D8FCA27DBF1B57B8949F1C90D369C619AD4 count = 47 seed = 730B65ECE22DE27D573CE3AEA7CB021C415DF210D228808D91D4F380070FFCB0778B683C71D4853DEB569C822765F2A3 pk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sk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ct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ss = 4770EAE83744168254FF4CAC72D7A3E9624CFB7AEE0187ED count = 48 seed = 5522A5A891A9A9B5514F4556AFD8DF40B9CEC63A01492F0CB8A1DB073A285A963E4A9FF2376C88662F7D8D241F8ACF17 pk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sk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ct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ss = A2791C017E6396143C0DEF06601118E458FE5A975A6871DF count = 49 seed = 1853E72329353B3F89AE6A1B1EF700DA8ED3C10D19F9E61EE9252E28EBB0E15802EE43083A12A0B7527088832605E3AB pk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sk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ct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ss = 2C2738D9C4FE9120ACD0F19D46EFC45B4C53BEACF8B213F3 count = 50 seed = 027C3D5847ED4470931141104F25B19AE76117CBB64B224EE424FFB782E9A0E988839E0BDED0DF666FE8E5FCBB5DBC09 pk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sk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ct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ss = 38046EE145F00DA177F6C1EE6EB51FDFCE21F360B25C2FDF count = 51 seed = 450751D4401737459C6D93E6C5F2FBCC4A3AF7CD7250CCF404BBB817A67BAB7B4C9D0EF4570BFE25CF919DA331C31D88 pk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sk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ct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ss = 4A6C24DB6F372A28188D43BDFE07416177EA68E265CE3482 count = 52 seed = 5DE720F2D152BF4E1F96A61E7AE5F1BED6B8548E32638C2CCEC9F43B87D1BB43DFCF334F0582984D27E440D519AB662F pk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sk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ct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ss = 6611465188E82C488DAA81274C8E37E2B3C93A885D9009A7 count = 53 seed = D71729DCBB27D7CB39E9E905025D3E55C8602EFBCC483C9B866EBF82326157833169243C14550AD728BD1470F39C642E pk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sk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ct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ss = 3F068357967BF2EA7A4C4A1C3A7DCDEAB3690623416DDAA9 count = 54 seed = A7C2C8EDB3601396BEB2DF0657EC82FD5780A2723581A9E03DEE1CDB018440439BB1142CAB0487C5D136E9AF46338AB7 pk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sk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ct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ss = DE7DC467814DC94405A38C45B0E6FA2984DCC97598D75874 count = 55 seed = 467F6158CB86B724039FF18C47950AE5C49170163C910FC9A9B30141F86E9C06EBCEC91497BCD156D95758C9F0C6EF91 pk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sk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ct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ss = EABE408DD38AB61A83E0E1515ED453208B6C687EFD749C02 count = 56 seed = 687C02DE1041ABAC7B2C1E6EC2A7C3375552ED5EDB10E3A8139C24CC76BDA44D719D8121A81D47A0B762B4E9EEB85235 pk = 2D7EA08921DAA4C52AAD77E37C5C02F633DEEBBF793184C5DA9DF45CBE5F5DA56D8F4D7E61E517DFF0FF4C2849ED0B2D2B83570EC8935D2083760553A7A134EDBC01B44731B3032A700300DCD25CF8443B39EE22F0DC960C409886151D2C777082EC9E342D373912684AC5F98BE3CABD509CA7141DCB6F24D67A428C9C39AE86EE7BEECA86D70EC57DD67789B998E5239A6A1C624DDC6991B05BF9F70A0070913B9B0D64AE60AC20B598B18C1476CD22FD1474473E277EF6743DE4E6018C4E306D24CCA8895E1F2459305BDE9D466BF54F5234E1491166D58DD1BA56962BD6C0BD6632EB9799BD7FD6C7F01FD835C14ACD4532597FF500B4C14A7E1AAE3F0748E27AEF6789E93A42AD10E57DE310BE2F7D5DFA4FD8F0D9DA4A3ABABCBF674999A1126CEC08C22272AFD0C6A46BE8A0F738609B7633F37CC9F2A0166051CA343351FD244469E15C882A454D91BEF6ED3C88D26CBFD0AB003C97E7C9A9E53C259127FEB5336564135F14F519C90D4A5ED283B9F9D248A24254331E sk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ct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ss = 3CC2D29433CE0F0B2CED2B8EEC0000798EEE8C0B93D2D1A7 count = 57 seed = 4142237070C216BCBE245A39BD9220533C97651D84832B26727855AD994A0760C52B9319AD404693E4248B8C5FF324B3 pk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sk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ct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ss = 15ADDD6F14BF3F56D5EC1747A00A4BDEB6E01EB242D939FD count = 58 seed = BD334D7B7EB14E00E68863F2E5551A095F8AF10681C28353FD19B9A7E70B8BFE266840860609008A567ABC66316C77CE pk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sk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ct = 5ECE6B89BDC8CA7843493040B9E31E0C7DAC41A23EAF2B4317DE9A444F10DF86C877A29C6BD6AB3898634E37FA391CBFFC356D4C304589FAA564E2962351086C214E5FBCE1D809E961BC8D7138056F1F2A01F8C2EC246C2624A1997700E8CF65DBC3ABDF79B6ACFA6F8435564FBE3C04A06F9FBE1587726235610EE1A8153C816D40AFA0510F157267FC6003FF44C653F197C7D1EF8315564A82898AA3F6775AF68B2D352B1E28F79E4317B3E8E4EC83AAF9DEBAA1BA424EDB4DE2DF0178352E01567560DC54762C07F1E5DF732764EF6741A64DEE31D04FCF74E5DF9F23CAB1C7823D49588BBB77C9D70A61F0A0D771A778695DE565110C6BD7AF26DE441304FE78827284D3C635C17E9655E1E3B034C1B072BE0AAF78F3513772CC320684A80BF0D78EF8FC2887F4D42D28265EE611EF15E8F027F1C618393428102DC14DA76C6308BCFC087592181EB8256388FBBDEEEA6B91F69A991E3EE88DA515EC561F70F75FA5342A969C272724DFC376888AEBCED23AE910DD9E271F7805D8C9024CBD6E1014E0B9EEBCC1F8146AA8F21799C15E ss = 609CE20AA0876C387C66550A52B0EED700B56BE5D4E1B5AE count = 59 seed = A0264C58AB1F2CBCB212077FD378D340307ACCB31F1312137CF84E3D3135044D4EAE8BD38BC3E540A0C14D46458F6179 pk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sk = A453BCACDD2B0D4646009E5ED451C3C45F08FB827EF733DB7A3CC8AA3239D4C52CE4C95AFDEFF6EFBFACAC10D294EDC0E7CF4535059BFD0A0C84F64BD6A8A8981A7BB846BB66329B8323795CB2ECB58CA242FA6391A38AC78D5C2F2355207F4A37211976CE2C552D21DD5B2F35ADCD2ECB502AC85A4B3350E076F843DBFD5126238175AAF041FA98BE3F4E3D86656DE9348C4B0DD0352F2C49BC0EB71ED650B809DD428CCBDAF30F4E9D3D3627F5B30C124313F1B33B6764CBD00B8A90FBF9F5DC737768FE25A570602A02AADC057009C487B53ED07D8DCCDD4148BB9FA1619BB0C93777FCDA3CD25B9F0D8CC1D0C34F04D3E1FD032D1B6918686D0C3A647C348DADF60CFFA0DB45CC3F0F70C7FD810745189599ACFFF9BDA5A865E108556F11F4C34B9ADE1C716BBE2661B859D52F333EDE1D272857725BB22B35C0F95391818FB461E510979C6E72300F86B595415D940DA0E57C9873489F67F38FE7ABD9C8D4945CD71E96325F43F154F275CCF1A58CC22E758251018F64D2151C0C844C607E3230DC1A6345FFA2909C19E5A05E5747B89BA400E5D8750711AEEAA37B25C9C19706C96422AE32E3C2C42BBB4ED1ABB32B ct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ss = DC5408384C412EFE0E18E8BDCF488CF5D0534867A416A697 count = 60 seed = 99A9CDBFC674AB3FF2C64CDED7D697A6E27A767434A47AFF7C3FBF3C6A22D6043D27868955286A13EFE3DE36D22EC48E pk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sk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ct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ss = 6EDF4309E3AC18F07A764E64386AEEC8750E934997BF8684 count = 61 seed = C799D57B41F28C5C446DFC58A5AC6499C4BCF3C162AFD2B09A16549826EC2A6F689E44BAFC4ACC82F5D6AEC23F4A3993 pk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sk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ct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ss = 74900EF600281F369AA1B1D1472FBE03D608C826E33CACDB count = 62 seed = F7AE036A0176A9DE9A036A542DD2840033277C44AE936D10B768566216DE9D4395CD42B116873B69D9804BA6CCBC05D5 pk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sk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ct = 818C523C10EAE59B093DFEDC3083B4AEA2F86DD8F902CB935D5F984FBA9C2E453F971B90EC326CD02B3C6C5FA25CD3D5D3ED3CC2D463DD7D5550427E0A0A3E387609BEEE98F723C9124B16D7B59955488EE008C40A25F7F7F6E6621A826169F7E8F01382AF6C5F49136742C61899A97B38376E35DBA5E65E391A5951B91B86CFEB066E80D82B06A0C0F5ECF326A411A2E5C49F58CA6B1F95DC7E79AEF474BCB1E485836E2F220FCF29CC5CEEDDE1C2D374B27A116B84BAEA728C88F51399AC8FF101F384A9AEE0FEB03CEC12873B406F486E8D64DD15F65A475A91E5F98337CEFE2861AB2C63C291DB14242BC0D0892BFC929CE0ABDECDAA4C2B05118C4300D69334679C64662F0E34321941A0E5BA638259A2410EC56D18204A96837F5A0C186F9D0436FFBFEA8612DE6F665765A875E676056EDF700A0E0F102D0889E7D0A93238013D38D7C9BE7312D1C96C9960FD3C28A6C62D874155AB1672D4B09D4F1D051FBBD9863CCC80B20A50966E4659DD03265816080E6BB614222D63AECFFA58C2A94539700CEB3A825E4B5B0041CD1610E2 ss = 45EFF041C387924E111B34C419C409635FB2F40B78F975BA count = 63 seed = D995D38F934B6E1A7CA77C9522E3D037676CC939B0C8BD4B84394B3DC91A791F09D2D97199258C9943DA955E7F7B26FC pk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sk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ct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ss = 6709B260549C1BBAFB6A97C9034D8F67ED3F62BB1BC80C1F count = 64 seed = 5929F02A271725CB40200DE32D9D03D8BEA53B53AC83186C42C7F565CCB1CA508305D470850CF86E9B2C61A5B8CA1C93 pk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sk = F8EE95521060C03BB8DACC79F7EB7DB640F545F315613A353FC3D8392CB53F36ED647364A04E37278A0E0A45B720F4A75C580C9920EBA90D93D631D8B20BBCEEDF747C9C0F11E3FC1D4FF941918FF83BE03E82E940E900E6834E677253BDD5A9D31DCB51583E8B03BD5D77BEB07EE5C7EB5970C191FF30640A7AF99E215E2E7869DACB85FCE00EC81E63541FE5715CD32C42403D5A030ABE7DD6AA7C01EC3887091663ADAA63749FA9B4EA3CE9AC7162D3DC17E52F1CDC266A4515142C338B46EAEBF57EAD51843BC280014A4614051A34EC19AB00D8D959394CDBA9CBF3316338B45051B941BE8AAED12CF6E9E28A3DE508A8CF2CEE34817C1544E8EB5225A52589C0CB12BB6F4A9ACA0391FC113662F96D292C584E5484304C33B1D574EBE590C3C115AA4C53F8320A0D6D81028D007D0F7A103A97555844362583770698FE8CBC3E57A3559E11A70EC507BC4363D99620C4CB86029A94C72964445C0BC9827F55CF4CE36674D7B8F6F93C226261FF8BE517FA637486BE6B23D88F9CDB9C001BA4041E72257744480FD8B302F7E45C8417C976B8A12609CA55853A6C0E77BC58D26218FA3619678F0CC51D2770BE509605 ct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ss = DC80EF72E53CB172CB6E9290CD310350E8304DC71BA1C17A count = 65 seed = 905074033D7B75DEB2D06A2F29144EB377B452534C5710632989F02D45312D156557E96D4486020826DB200153BC4A8B pk = 630F5938E8EB2CF9870133861FD28529930BE4A3167509F385128932428D6E3E6C4CB75AD1BDDB878FC64B1A15D83938590C20889D9507149457732BC5383832B705FD4C1618A287455BCB1B320A05B81F991C2585D003DE13216C2DDCF73E967E89D3D372CD009BCD27735784A74396125228BD4EFDE8E04A50C259FB24D25341567DA6C21136AA40C89943057E33E2224B3DFC149A144BA126B6982A12D61839AECC276DE4C4E145FF5D2396A308A368AD852F05D2FAA51FA57D250E67DD5E3BFBBD76C68ABD9954A11415B42959C8F583FFF91A22D18C0787C8E6EED9C371AB2CCE10C633FB6381A03517B142314E022404E72266064D25B978133B3240262C99968004F954F1B6C21C565C373BA4795CE60345CA3D90AA951AB5E5AA4A6E005234D72887EF6CBBE4A4FF38DF2AEC1BE3CD4D051ED24FF1D31684EB14A8329CA28610DAE6D6684992F09B36D1F42BFBD6174DEC4CFCBBF345973AC1D2F550CA5C421F12D61CBD2ABF78C9D1D55E6C965D49E7FF31B2B04040 sk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ct = 4D5DD6632ED5B0D79DB34A8E0E6606313AE97DDB80CE5551667A7AC71C727073B6AC34C5F61B7DE541659675E2FB18747E4FBA71ADC9A83029B4104270A82203D8FCCFF49B8ABA725498544F36CC2FE40485171060A3F8E1CB6BDBEA4FAD74C71676A90130379BD1590D8CDE4CC5DCC818F2981866585A68BFDC6222A52BE23C190BBD612357574E4D69192D6AD0B148FCE9E809B4047CAA681432F6C978DCE1FB5A5DA4CF1CC684C2E975A51F6B8AB6B91DABCEB31C8A5F0B71040139526D60A2E0B59D7657E0F22357E984F38E2D6B28844130F3034C1829DC0018525FC9466BEE22FD9388657019C7EBF205A1D1E59B1391CA591CDBD2590D842419A2DA22A9A01E2D75964F61C5C4CEEF33CB3A43B0316E0389B0B3FC6079DF08FFCA1C2E0378D4839D53B342C9183C25415821FE891B43941B97A4EC517009086117629C8D085A668C984B9A786E47D290962C2D7AFA8C08E803E1E453EB20861F857B77A33BBF1EF3BEA013C410EA8C647B9BCF4B1E3DFF53FBF524863B20A344EA208AA711978D4C99D84327BE76BE21A8FE3DBCD7 ss = 59939CEE498FF3CD5B49C1203224641E4F3A0C55DD2A523A count = 66 seed = A3E2E511AFA7BB560446BDADF67D2EE2E16FFC7BAEAE7EFB8C5455068BBD4E91BF9BE9D98B280072FABA7712C75B26D4 pk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sk = C0407E41DDF48D333978B89BCF2DB01E4613425B456249E7B2DCA81E3F5F748D23C9D356A2209F6B2D60247B2E45C9808DE497F64F12460343105C18A44661C66BA5BD3E14E2BDD34A9D4297FA897CA3F517EA39F847078232E5DBB3B8F9100DA20D55FD66A02CF46074F02D0A1F1B6DEEA7A7B403B812D74C0E8FD263F9D7BB619192B61B86FC556DDA699A906E26D199E142DA42DFB7E9ED593D93C1C055C9974E1CC2E83DA334492AE1BD045FF04D1587DB70523DC9EF35736F6011C9FCA21A82C77A8DE8727C8CE3A1D638E40F9E8906D5F574607089F63C06DF9B6C9B8272EB6240EF7E81EC0EADE3899D9E3D1A19ECFCF837636C5D8932EE84724FBE078E9D719E9BD43908B41DE54CE8AEA63C6FA99B4E2680B51DAA7427668648AF391A7BA294859728F98385A42281611A6C9325FD1E94D0D056421C53CAC7EA1C0E22BA32217DA76B648EACC7BC445085EEEC4DBC0403140D6AAB44D36F182F3340A34E25D55BC5621C0BA31413A5AE5A2181580C8779BC8F693B488CCFCD8247BE87B2A1B9CE5DECCD98F57C7FA8A22338001DBDFA058D00F01C7737CB1E00682AA436547C84AFBAEE00866BBE28E3D9C57C30 ct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ss = A32F6F1DA77E156A2523D3E043F261E4D8E9483939B317C7 count = 67 seed = 074AB1A37BA5A0403D8F68D26FB787BC2C90F5EF88F2A6D286C3E6B168ABD85D393D8225618608B8EEB301D26AF53BC0 pk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sk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ct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ss = 792F6220241942B423BAE0232B51DE055043E707FE6D3CF8 count = 68 seed = CC0C86CC0ABF86FA21899BE1953913C00E7C46E6B5F730C4E88B3C034012763981D7F14459D3081638080378348856EA pk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sk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ct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ss = 9FB845B159F6BB1DB99708B4152E5023830D317A78ECC0C6 count = 69 seed = 6D5A7CC326ECF3983C4E7683F45263A37F692F3BCD2D920E1FD9584350119E74F9A3F905F70D3E20318C1413DE2A0DEA pk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sk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ct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ss = 2020D67892B0948A4C08FFA87F6DD300270783D2C0FC5169 count = 70 seed = F68FC0314DEA88F66AFAA76E6C9B6804B13D4876924410D1F526FAC59A62E26C560B125B1D0F8B461F1FC2E351EFFB4F pk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sk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ct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ss = 4850D52145D1B8A34A6E725E8531DAC658A18CFC94C44B4A count = 71 seed = A229218B0D51F58D915DF549901548FB0722F352C7470900E7E4D8399205764A319BBDDBD06C00E8C5932722EE5A404D pk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sk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ct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ss = FFA07CF6EDDE214FFF98EA251C4DEE8614E7CA2B0045E59F count = 72 seed = 6960F21C7350DCF41B4770C551DC8692D8BA2C0B6E162C589166FF22E7A1AC0F94C2F48504A5F7EB0DA094DF427BC98A pk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sk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ct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ss = BA828873D946191AE2D6823F33E0A97B19BD4FDFFE0528BE count = 73 seed = 53DF46012CAD4A745B7A3C06E18CA95E0B839FD8161E3025749A0887549EB0ED6A44EEEA08BD6060D6509DBF7E9DC864 pk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sk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ct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ss = 0F6EB990A39CE2345A3D3340ED763CD0C37CA2D21C13999C count = 74 seed = DEB963F8B1D8FBDF499D564BA8D2D47915BB402DA02F17031B37B4039A842AFB9B7E48F37200605992BD2429427A7A4E pk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sk = AE0F65E29F38804A6759F70F4D01E2AAFF7FE1C91EBC4F89E03FF73E02A217659F53D8C47556BF3D8C94040F630D63605E2D0F923579370CCC8CE6FF50B23579F7400E2D0889EB8455276FA195F9708F1F74ABBD978FB707D41D100FA241B29346D6D3D048F0348A8E0AC825CBBA139173920F4C70A803501DB25E43E9FB0AE625791B400FEF61338BB402DA2E3205B15F7A798DF5FB856C3C3F5A04F5F729494DB41884861D0036A8CF6E32269C646754B8113E501F4DC9FEAC0D284C805628E0462FF634CC1B291DE2D3C1B5D10100FDF8FFFE9240C1C5BB61CB927E0FDCA9460039A8F7E28D2F81D1304A55165F0FAEE0066A1897AF29469A2E376F6D520435D3068E5CB9BE4645194E22B83D94371DD2B4CB4D1B949CF8D699B4A0BF55C8631D79F41181CA0A88B2211AAC04BE1D96ABBE0DB10DC1E1A16D9DBF600C7E22999CD65AE6CCA052A1C6B3EE68E114BDEF3BF5D8622FA5162423C38493FE0E6E9F5A20F4B90DAAC2A63053C1466B26C7E415002B31880B2E65375402FE9F81E645DFF1CAF5CAF8DFB9077E6A69DB1798DFD730A44D924C4CDBBC0C52D3CF179A6B53148555F00609C6606F6B51B4665A1924 ct = 7C8AB30D6F3D0C6C3B932C50512DEFA808913A59C10F68740BD743A6BED7509CAE3D6440030B10B85DC762FB0EB432867202FCDD481F89DBEEF919B0C8B73F086F86A666CC8437529694A5C18E902BCCE8EDA0D30BEDB812E72425D5B098D10722BB492BB5474E9187764C963E4BFC6CEB578182BB84B94275B268D18B218B1DBF000E3C9BEA622BF763913E18BF87843DB707D0DCF1FEF46C8A8FABB218E3EC79A9FD99420696152C648EA50F59E3D4C4C607DDA503E20A5451535D2CF234CDB4D486DCFCFA31808AE1A516BCEE9B90D7E1F2A269DCE171547B3516BFF3FE1DA415DEB901FCE47A174FCAE8B155C00D41DF2CE4E833C2E0A684D3372A0CCF1EBD9EC00731A992A4132A397BB3D4B695518EA32C41FD17E19980B17484DEA217722EBD53CB0D05C3C33292EF96ED1AD09B3DB0FF26409B5B235F2E1D6A8BD9B0BA16FBDA285EEC04F08A90985913BA620B949CE42957A084505FBEC588D2A811EBB87FB038DF1D5CED67378AFF21876538FC7148620D3AA136080AFEA98E86A27AC772E63E16F48AE88D9714039B7EA26FDD ss = 9A0CE5F63E14A51EE73FC499B06CAD8C065CBD2CCF52E806 count = 75 seed = 8E2995F1B3E43853B18916BB1212ACEB05898E2B177A87ABEB928AD7184E59695C56B2CCCF5DB80853C28A525E327D13 pk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sk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ct = EDAD72D61F6AB163D9993D55082228DD46495C14B70FA41CFF4AB0D7142687E89FDC951FC0BEB9781ACECC15F8374BB86A75F4446A2A12FC60AD30C0C1B10446795EF1B3B95EA9010862F0A1027D7A0FECA5870F87D3C88AB1B813F9AF03F952882E2F152C7CD8B1959012415F885A2AD68BDF84258E16A0225DDC7DA438C7C39D2B56DC2A291BE156F6D66EBFD01CA940C18E827847A13164D098E9FDE43807A78EEB84AB81669F1647C8D6527601B7CEB1DDAFC9E4B2EC437895F9321EC845787E930FD891A1B5111A39915EF7274488137ECFE07EA9DF4D2A7A1185ED8037B2C6973623BD79F4F4F38A6DBA59B0961E38B47CE9C3CBFEE174E520B3918B323F50F003DB9A76C143B0FAEBA0EE395D8C53FF947876016E2906B4CAAECA44B44D35722D51CE63F2C76D83CEC671F4C6CCF0B22322952E2F86312D187F5C88B15A9426D1CC5E601A8942754AE4C0A981AFB72EFA9E9268A23AEE814FCC30C1639BBE6FF613F376834460B7976C10A10AFCA6A9B17F8F5DF803381CF5FDDF3FE54B21E7807B798181D80DA7D1C5D6EE80ED4F ss = 3B2476445718E7F3D3B24A14337C1DE26F9612AAAD6E522E count = 76 seed = 9218943C51FD2DE47E509AAC67EFF176795102F37D7A2017E3AFD768FCDA7877AF38739B00FCDF227C2FD62EB635942C pk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sk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ct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ss = A752CC792C587805D30F9FE4250155822492E10A93161E61 count = 77 seed = 542E20078ADD5296050AF150360F057F6B9AB3BA835589DD56987DE805F900B906505B5390A0D86CBA28038992DFC59A pk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sk = 241191401A63AFA750F05662E354DDDBC683C776CE3222BEA59B3BD23B49A95BC1FAD20070FEC930B6060BD827D742B077092E422268E10DF719DAC81F1F140FABD43474E31471E9F1732886FC66B4DA09B926E5727702E78CDA06384727EDBFA17D339336EF683ECC8DF3401350A81C0C038E60B56A3646DEDB4293AD1C824B09AC83F07EDCBF9E558A2993E1D59271415FFC56A6ED7A361454401AF0BB667B255BE7F9F855DFFCDF6A548AE06F326050D6D61B723F36493F0B6447D2C18465C8B62C53DC50C864CFB1728575CE6A6734CEA506169E0A3CB971432FEB96C961D829B8757D7C91D329E25FCB78EAF2DD723F070324E14F7072FFE03AF40B699B29F381066D8E5E7754AEFAE650ADC3A1A688B54B838DDAF34A3E9CB9E228DE2AC4ED45E279DB9097673F8B764424B5C617C5731CA3034E1F89D2E929BB46DA4B30F34668AC442FE71F4DCB8459408909BD5B6A6909710839DD4D4696EB73C87FA0DBD903C42D6ADA5E1FDCCCE49BCBF6AD48354DAF5268CF239BB5C854D90BD25B60AEBC57B330F42953DBBB402D957288E3259B69019B26976A60757F038DE317CB9B02478F48F3FB88A915B38201E3E839 ct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ss = 43C4B61F15FB7124ABA3F8E872901C308909310E67AB95D2 count = 78 seed = 6A85A61DD08C0733FCBC158ABB49FE0B0D96A50DCCA140A2E9F5A254F1901985844613B1C656C0CB0112620591B88AD0 pk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sk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ct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ss = 0B6B8EC0C8CFB0ED111785D7CBDE0162A44C96D58772E5C8 count = 79 seed = 7F4A56EDA151E7B097CFB8EF980440FFF707AFFBA91867C89522CED6C5FF3BD7F5F00BB49DDD615D9361A7E4EFA42851 pk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sk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ct = 2C6F1C997D00EE31E35DD4A45BE079AB61CB0EBB6DA09B31E3DCBF45833A29774711DFAD2EC8488E992236D22BE1BA98E983E9447EF45342D1E0D852BD65009273E2CDFDD8F82C78F6798AE8D194FA10701C53505375C16D8A15C51FB996BF3503090A83374A3EAF9C65323E8C146CAECBF71B1AE623F836540192141101189D71F9F5F5566B2DCC3C629481654F6C897F18ADE97C442715FEB67270434F483FBE43AC98DB0C95C741CD279ADE91F2B5C552E00231ECF9C24EE5CE442A3555259FF0CAB25496B3B43162C826CB4249102F808A568D6E3B804D21AD2222B25F034989DFC9C4D78487A6F2A513A12DA15FF46124577AC3DA408178F322BE51F89869135E21804BC6C3C5DA9FB14B1D6324234A5D666AC9418FD639D703F908D43826C54A8CDE4A79051066B4C0CEBBD3F0B22B1CAD29053D213EC92A918CCE8EC29C9F1478FAAEA2CB5B83B20BEF8DA51C101FD9AC66478A6F92E5D034E260521D750F3CBA3481232EF8625DFD18DA8992DA977F67B5D05E354D3B9853F5C23BA2BE3B93392865B5A440BADF3F456C78383B55 ss = C506F215F739D554DA46B2C9FA8F98DA69B52E1FE7BC5574 count = 80 seed = 09FC004519BCF85B20D25D314A0DFC79E00CB6262A7DDDF9C52473641AFB8CFA0F5DD5F53558184CAAE9EC34B459E98E pk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sk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ct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ss = 8E29194E92798F63A56372A284CBA20051D66FCE75098C33 count = 81 seed = E3C41CCA6F04CFE7732FD54DE30CC5CAAC93E2F80E76AED7D24A962A3969C1B6A311459A3EC3E510E3E9B1E4291D4D7D pk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sk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ct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ss = 78B38CCB78A36C6AC719A53A4A571DF65F7021AC114D0742 count = 82 seed = 373FDDE922CFC416ED96B444E445BDD0962E8989F6C50ADF9912A89937C57217D3600B06C95440448E3F601AE69CA5BE pk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sk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ct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ss = ED9343F159A608F60E3990C496282C01BBF5E6D1E5582C5D count = 83 seed = 16BEF67F7AC3A755C59C816478B75FCC16CE5844DB537791ACCD1EBD49D2824B105FD2E970F728C8F0CF16E439A9AE2F pk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sk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ct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ss = 37BBC45B6B83CDB5B8E1E01B05C8DCCA445E9362D853C869 count = 84 seed = D0611F9AE5BE4DA5D7EADC9109944348E716CB3DAEE545721EEA8C892E7831CF2E54603146454CBFD92387739E9A78D8 pk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sk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ct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ss = 93816F7FAE6511D47D153C04DD1AE13FF21FD701EC3B8839 count = 85 seed = FBC38D7614D7718E931EDB850D2C6F0C5EEA9EE889B3E25BD69AC255D5B91E885D93E808E66BF9C88C655DC594DA5792 pk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sk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ct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ss = 32F85E3ABC134C88F5994A0C9EE049FE07AF4D7EE67F12C6 count = 86 seed = 1722219CB5DB47374EB0AF0232C856A57F026F1CB09E5A5799F4C333DD422FF6A0A67C4DA502FAAE727FB2D45DAFCF35 pk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sk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ct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ss = 882D3F7190680B6DF68439A524D5EFDE787649DDD43D45FF count = 87 seed = AC139B78FD16CA0F26D6D7F9E15345C888D857B1910CF38D883339B37EAD2DCAC30F7CF10176F23FF34B4488EB79437C pk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sk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ct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ss = 44F2C67406C5E032106545CC7118D8F3FC0A0FF6C1EA93BC count = 88 seed = CC7152849C98D5FED2813275D32069E44824ECB14EAEF425CE017448CD9A401C91C06D0F7EED6D22B7BBE8BA6C429EC3 pk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sk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ct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ss = 4E77D3896C5494B0B06FEACB1DB71A345638B0D8BB0908DB count = 89 seed = 96D9A06F88FF2C2036FA8E914B89C765E4A510B468DEE40F914F78858C811857EFE9FD0E17C0048E7389E8D996B7E2B0 pk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sk = 470B4943F0FE7FD0D8EC5185ABA0D1DB09D112934E4FB4788B2809FD40008BE70A6B184981101724BC3D5EC5E1956B510B82FD5AD0668A0AA846439524CE37BA030BB465502028F419F2A64014D9D6C5D419E0BD99144FBC3B6ECE1DFC3CD59E0240376A7A1DD1AA0748D7A92F65559C13F91304C2AC3B9FC1B870118B33BE372BE80186815B935C5C92CD4F2310DFDEA02E6E8E73F94F7D85EEB4BF03745FC6E296084EB63DBEBB0A6C3A6DF96E7A7D5D17CA50C011159BBB247F59BB9F5F59EB3DBA11C933EBB2D6D2C7117FBA4A3156CFC420EA05E6F81B802EEB56F164731EBFC4066D93C4944BBC43679A7071EB010E4A222C0A04A8EF8A3A18ADA8BE668D2EAA9780198CD827D9E7A3CF1D4BFA76C5872F0A1DBABA91E041C77D3026E53FDA38C1D5A0ECAF41E5029F5D373A0FF2C661153D0522EC1553E1B72894EFC1C7BEABB7F6991FC1E9E599743610BCB98212DC9470209A4F9043C049DCB36FDD03AEFDE167964530E24538B9C10F294B9C4B0CB8B4B9E4977EBCC006A81BA71DDE6D12DEEC7D1C8C4A0714A93BEB58A7EE3112F356813C4142DDD01F933B7B5D7A008F708D9AA12799E25B8B62627AC09B1A ct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ss = B41F3712746A65094FDC479A3AC76C79E7516AC03C6EF8F4 count = 90 seed = D26CE360D399BF7B89DC364AA7AC06BB513EAB8F527383E93E30727EDC3F22C262AA0EC70257B39EDFF0630DCDC1B79A pk = B424191885F225F3908E03A9A0B1961D9276123707A18F3A3E21D1DC22D059190F5C98E37A8819B2431D9350307BF9091399BAEEA45972F53EB85D7F8DFA24576D4445B7956C28CD1FD421B2B66386FCDFFD12D05446BBE679F0F24E1E078C1D3B78F7C9CDDCB8148CBE848A9E8CCBF066F407456EFD64D8F569AA740A3CAEAC7EABD16D176EB0AB477767119A033BDAF7C843E59D8D67D270925ADEA34C2190972A01363B0F5E4EC1EEC3D66322B84A1F5EDBE1037962637950E4F828F1E234D22674B1A83D11BA4D07CCE892A93D5A9D24F5CAFAA9CA5E5F05EAD36705A78B17FC83875645D0F25854FB688E78F0C7E10E65C4F0770CD852ED8608F9516DD37B8EE57940AC17CA394F992AFEECCF6D25AC97CA5E3896792FD28B3153D454193407AC6607888E877B262CF6E43212B2C00DD0DF890C4937FEF515A1CBF9684895CCA19CFEB7A4A3FDF2B79F83580DD883593E835EC3F54DBBABCDBB8E6C0AF5430620A6DB87BA461C8E71A96DBC01D3B3E133C1D783461B021A sk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ct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ss = 9197966351C732D5EAA75C7CD6E38B416B2CC72F02B06C18 count = 91 seed = C5856298C3CB6AC9787A0F30938537AB2635B96F6D19CC9522063360E7A5C88E644929D2879180E3E5BCAD2422B7CFC3 pk = F361885521DDD8390666967A8AEC562395B51D40C56E6CE0C739AED0995605987F846E0ED295453974A1CA8CAAB4D4179EDBA830BE2897A2DC961B0ED1C7038A603A909D3A67ABB820474AA5B576D8C3FCEAD2B3E3E0082227586EEE253FF4F608CB4F41B426CE34C33C4746921B731218FAF5CDD26623F1A6F80EC13C041011F37322C4FE8B67987B4A8FBC5383CA4298B90E1A3E468325E0FED1F9101EB58BE72902971870DD74EBAC1C97CFD8E5A57CA9E8C8DF6DF6C6A2824BA43C9208C8CA360000EF7B775C3C08291687A671052151E6CB2821500A0C4A50D0EF258BB4971DB335CEBF58A2BF8CC9C533CFE0150C0546239FFD550E0BF9981A1CADAD08ADC22964FCA003BFEC5BD88B74D954F35AF61B8A142B0DC063A7AEC30C39173E4C2FC9E0C397A51742BFF17AB303BA0BC94CF38B8DEA92968A123CBB63F80206DE2F3A441BC35BAA56011368F77145A802341636EA94863FF843080612968E746568783AEDA5FDEDA2C50454E353D9742AE8A3892EF053AEEF21 sk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ct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ss = 010C547D684CBF7E3EF15DEF1EFF805B2648CE3D55141115 count = 92 seed = A28EAD0A08E7228AEFF602B16A1E752278B8ED1E91DAC67994F5ADC372E1D82F95CC390CD97AB9212275E0566C833FD8 pk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sk = 690EB71FD7052B906EAEC09937A8ED374E0B02AFA27C2F1481C38C2CB5CFAFAC81B96A810AB749B61806B6D54C9F8CF4BF1BE0192423280F26C6A6EB7C3975D91BFC6F1958CAFB8C323AC01FA62675E7D0F5ACCBC514F5A53851F8869B4747747CE288A7531EC97E1EC481BE52175CC91434493709C5261DE8819759F8B1E10D0F2E3A08A1CBAB97790CD57C3D1BFEBEB47832A584C955249A75EA121800111AC674186C6E75F15CDB10C09D81EBA51F1691D8B7CA33458415D787235BEE9A5AB1D8718F1224DD47FD079B8E59DF02C756A1E05AA1258242D0E4499D6D7016538DE26D3A11F7465797BF2CDD27EC837AA924E5B6010379032BC56052B5802E15B31C00399FA216A6040AD49F37E5EBC4E96B27AC141400ED9515F90F2EE500C405FA20F173FA84367C14609251643B2E04EB2701F906A2254634B6B6D85D203633CF014BAA3F51450A1D570D0EC878BEBC5768D8328A61E2AF98ADC74FC5BB925B19D487606ACAAA7A4FE31471709E296C6B39ABCB409090C06D455E31475A4F74EB271E96FDDD644F67D6FC1AA4D99CC3CDA1542CD5AA6200B8920A65D9A97217E20F940B23BBDFE0CDBEDDA51CCB8EE205 ct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ss = A14DB72B151FA84E5CB3EF9AC1EA2AD63B037B0C754CEE07 count = 93 seed = 92877D706DAF88EF3412EB143DB8CD91BC047A9A43B7ACDAA42523560DEE4C172697BE4332042FCAB91135839BF74AB2 pk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sk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ct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ss = E36C98F835D5A87FD733DB9B9B18A47C13B892489ACF18B8 count = 94 seed = BB4C0082CA4044B1FF60B036C9B0E0495D58667156786C530BC69D949A13BFAFF53798E456423D7A0E162A60039367D7 pk = 8645941AC39A55345AF9F2755FD29802C1AFA0ACF9A8ED5B977299D6A20B5495D47D929019A0652BD250552DD60A2920506C4D79322E5A264B0133AA2DCD2406E4AD1ADCAEC4B25F03BB977749C8EC2FCB2942163B438D7638F593AE576FDFB4DDECD2637A2525387F94DEF7DF3ED08D6171D305A32180B6EFCECEC3FC1510D4F0A5E2E620F299482E9A10581AC3214B43CF57ECCD54803A0DC9371F104A42CFE07BC53FBB460C3E936A00487B1007DD27F2CFB4F6ACDF90066C687E0ABFB26FB7D03F2BF42B634596A1DF16FC5C9F4DE9E724A9EC7B702AEC40AC936DCD4EC287B1D4AAD564115F2A00EA2E2A8754572931896230F119DDC86FD73215A6523CB550D8B23D64F1A1BF1F1BDAC23733A591C8DAFDE26543926BBBE7329A2E21B34706226718427DC24FC3BA2C217A57BB7324DDCE5C1DE642920D246077265A018C6DE1D0824445A0D9413A0461C60A89DD72D697D7208509AD360BB655F9E5D52FA3DE8937BD9AFA810F8116FDB7E8358649FD5F3C7078A26224 sk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ct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ss = ECD17431A46D090C552345203774607486E221ADA06125DC count = 95 seed = 121D90E70AF6204445D0DEB28AC0C108262719E9FD3476ACA74BBFDE89FAF04D8D5F89A624E8A75DB80431F0D10AD28F pk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sk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ct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ss = EB336F774D19B142F59AD745419C288CD4876C478F8D923F count = 96 seed = B3AC6503206ACCC2A92CBC210D020A2654726911D11CE676AA04FEAA08AF1D20C654E4105883AE470EC3AB299075D420 pk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sk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ct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ss = 9C09F9F457B9A961DDAD79027B92AB15257CDD6FEB7E91BB count = 97 seed = 59EFF60B1EF6185DB34EE1E3B1DD2F159106CECEAA79BEB74923B4F5623D5BC52DBF5D2594A1F7C6C64D12CF144E9ED4 pk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sk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ct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ss = 3C988FB8F65F3CCF385CEDC792AFE350C019C819A697FC47 count = 98 seed = DDDCA9DC31BEA737D3F474E7560B37FACB2F53C803E768FFAADE7669FF94B1D4FBD17068CFFD5DFDD24AADADA4EF6B12 pk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sk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ct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ss = 1CB460A2C31B62A729B4D0E781498CE4C4C8B6819CFD3F3A count = 99 seed = 2A6F7386B815366F572AEB6C79E272CC21B7095FE09575F18072C9D677DA23BC9C8A4BC393B7524604D299BEDD260C8B pk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sk = 195D6C86A3DF4C21E3007D7F2768B43C74CB3060E0ECA77FAE77E0F9F21EABD8C0C6EEA7767F4E10FDE5C2D79B8400BF96B19014B457EC01D10B725FA678E2B06C026AF41AB8728C777C643D959AFF59DD51698CF563D171F3187C6BFCCCF8764CCEBAA6508B0EE619912EEE8C5D3061FB67B383D5DF2B9A40B7023A5D1459757EFEB3638A6834DB338AB82D3B6BFDDD498770ACFBF9CEE3ED01D6990A80A2275D19095C08E456AF201E3EBE266AC5120E7A32CEC4323F43A9E29A442EE3E29E80658F20CDBB733E80940A88EC9C07843AC7E99EFC9DD27DB34E21A5F641AC94B2B95F7CC846CEE3B3ED74D041805381E65D9F1229F11A3EBCD2B3F04C5FC6E7FA87B933138EBE473E47C6B05B829596133F42ED4BF315164B31C524B82532EB0B84E547C5649DC542B017F43460C78F10834737054AA600E6419397DD0F0D594221BB64A429E82786667B17EFA10AFA58FF5DE963D825FFD6F93A5FC9E4741C91BA79FB5C4AF49E90431E0262BD6D334E4039C67F47496690906736D3ED3138DFA9A3817BF8886F64BFB686BDB1FFD20639525CA9BBC2DD5F57D494E20A88591BB7DBE887AB1E89BCA517BE5572DC9F3F40 ct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ss = A047B7E873C8EA4ECE4B143C3E0896E9E9C7863511508292 golang-github-cloudflare-circl-1.3.7/dh/sidh/testdata/PQCkemKAT_644.rsp000066400000000000000000013517201454601126700254360ustar00rootroot00000000000000# SIKEp751 count = 0 seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 pk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sk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ct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ss = FEE94595E8A05C50113C044D4D8558DA101035EBBF604AA41D0AAA75B8A7F786 count = 1 seed = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC81ADDE6AEEB4A5A875C3BFCADFA958F pk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sk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ct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ss = A8F68D31099FD86235B5A72D9DB689F25AE6FD1EDF0765744F83A6A6577EC0BC count = 2 seed = 64335BF29E5DE62842C941766BA129B0643B5E7121CA26CFC190EC7DC3543830557FDD5C03CF123A456D48EFEA43C868 pk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sk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ct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ss = 52FBD8CC39FC5F77D544B9613452B8361BFF5EA79268331B02FF7F0EE145F54F count = 3 seed = 225D5CE2CEAC61930A07503FB59F7C2F936A3E075481DA3CA299A80F8C5DF9223A073E7B90E02EBF98CA2227EBA38C1A pk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sk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ct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ss = 4067DF0B490370B1EBA7995594556B209958D1F6B187DAE48362DB8A89E51594 count = 4 seed = EDC76E7C1523E3862552133FEA4D2AB05C69FB54A9354F0846456A2A407E071DF4650EC0E0A5666A52CD09462DBC51F9 pk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sk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ct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ss = CE4798DE43EBFA6B34FB7F22DA2B4CF80864D7F8EDABCDF3FD0E7BF8B0EBD3E6 count = 5 seed = AA93649193C2C5985ACF8F9E6AC50C36AE16A2526D7C684F7A3BB4ABCD7B6FF790E82BADCE89BC7380D66251F97AAAAA pk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sk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ct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ss = D9EF3DBB942B9EEB02E9AD654C1F99A4FC7C2D779500C616FC7E9FB17BBACEA6 count = 6 seed = 2E014DC7C2696B9F6D4AF555CBA4B931B34863FF60E2341D4FDFE472FEF2FE2C33E0813FC5CAFDE4E30277FE522A9049 pk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sk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ct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ss = 83C18909FD73AD3732ED11B61AADFC25867E17CE0900C7F001293770325169E0 count = 7 seed = AEFB28FDD34E0AB403A703B535296E3A545CA479C1D8148E2D501B3C8DD8B1034BD986F13F1A7B4671BE769359FD2AAB pk = DEF8B8B4B7E05C8CF64A994558B0C7C608FBD949D2EF1B0E121FCDA0200F50C910CFDC3F842388A8F8F1C0FB80F6A3E2ABD66ED929CBA9BF207AE080204C52B65CE5A78F783D2573D6ED193A3305A6F2BB8A1D9F53E0152F4F390E94030B33F0D7074EDCDE4AFB5AEE2902D9B3E105999D2572ADFDEB37480F4D6C148ABE81DEB47BD42814BFD99E570DC4DD75C77D066BA1FBF691FB06DAF924541ADFAFC3ABB525151E8067B6EAC9BB738A3A548C3913060B0F697DDB6E78B8A029348D5E76452DC8D766F9CF31986CC93FE8B64DF46F08A43C7D80EF098B294D6409FC4685CAECA0F80D758C89DFE3906673DDB6B1F759F38BEB469F2CA2E96AAF17D5D34CC9D8D6B700056592CFB63BA00A0EF77EB05DF2CFDEAD26846E12ADC4F2E0BA6380BD7761C5C1A8FE090F3B9E4ECE454F22D72495926573F5032B06388634B6B4D0BA7B4C0AD721726A6F2746F98A1C9A68827110C621CDA6036AE46814F7839F65E91616EA6E2B5168CB5A05F8A8F42CC538BD684729D5071CDD7C980891D096DD527D0749B8D378DD2C172CBD2D3BCBCB78AB66778EDF3E16A614B42FD5738476F098EF638EBEEA67F0FD64012663C01392A6384E0FD37386BAEDDAB8F769A1135DA12911624FF7CE4AB4B7D231AA3998052EBA090FC1DEA22B83CA1ECF2B8FEC74824A1554E9B9BCBD5DB58020FCA5FDB4FC5FA75E332BB9C47FDF772CDEFD91A73A89953ADABE47F1CFD52C6E4F250C46A973D577A09FB840999FD2779D2A218796B8D511BA81D9DD435DB55D1ECE517FAC60 sk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ct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ss = 600D281AA7B4FD07967253C51C8628F082C0DC380246C5BEC4105483E2B6D62D count = 8 seed = CBE5161E8DE02DDA7DE204AEB0FBB4CA81344BA8C30FE357A4664E5D2988A03B64184D7DC69F8D367550E5FEA0876D41 pk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sk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ct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ss = 4CA2CE6B6EE911DC23E50973C0F4999B7463192A2DF4F4055C519665736BEBF2 count = 9 seed = B4663A7A9883386A2AE4CBD93787E247BF26087E3826D1B8DBEB679E49C0BB286E114F0E9F42F61F63DEC42B4F974846 pk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sk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ct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ss = 0AC4196CED9103213B8ADEA333A872DFB2B029B1B9095E32BC24D30441DC4E8C count = 10 seed = 980D0BA7C8F8B23D0E948A6029FF2659810EA1360064663A8994D0333C8543EE5FF5D6D5C9ACF446E61DC464F792B9D3 pk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sk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ct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ss = FE8CF769164A3ACB29D531BB06E430386CFA36FEDC4D2DFE4769D738BD0F776F count = 11 seed = 6C029462CA42ED520F10A579F52687101105E0B90C6E7BFA582A4C112B579D5AD0A0ABD38F72ABCFDCAAF5893A112BDC pk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sk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ct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ss = 5313944F9D23D149C82725924F10941F841755A508DBF62D937BA7B5AB6C2F19 count = 12 seed = DB00120937570D62331F4C3F19A10465231EFF46465CDEE336A0D46AA1E7493DF80F18617F9FFD0476CF7784A403EF4F pk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sk = CBDFF028766D558AF4466EF14043A1A9CF765F7748C63CC09DCEB59AB39A4E4D8E9A30597E4B52FFA87A54B83C91D12A5E9C2CD90FCAC2C11B3A348240411A4C555A3DEF09A64C09E9EB370293203E03E486F95A900785251E9701A98CE265F8DADF0CB4F278779F1A3EE5189F6725E22B63BBF50F83C4B028A49115C7B9C8AE21E06D4E4752318B7E9D3C951C0FF5B5378CD2FE2B1E3607233E0F78B4C6AE795B7B2EE27A940DA53513D006BE57403998E257880757419506778F7BD6C2E1657BC59408D15D70570E82F5F2ACB1652D64DAA68353803CAFA569297260C80D2709A6179C1220AF98D26F1A6498DA56784B112A8FF05B58881D8F17B9D50808E3F4B35DCC86F95B75D397C66A9C19A51083ACBA34FD6D21C5B871B89357015077E0DDA34DD6331235F162860EB4FCBD11ECC8AE23D50626EEEFB53BC220923F180ED3DC6271FADE8FABE5A057E1C6E01DFD421EB166C1D4571853C5CD40C39C753A08B9074D3F8A824C4B53BC48D661B03D34582389257B5F198680F73F5B7F8350F765990BB490E8FF800944388B187BDDB35DDE70493E873493085F446B0D87368A0F8BBAF9D9EBF42370927339068BBB7C0555C47C894DA5659EB7D6D3DB5E7F5F3AEE2BDD432D6969D8E8FC6720CBC5CD956DDAF4EB7E1C4A6E777F6CFFB4E4742C71B25B82A36A6F978DD8CE8A8EC2757ED17521E38215C71DB6159235F83BFEA2693F1A12F5A7D1E6516E8D4E18D275F7DA27626C2896D620E49F2767ABB56FA98C2C051130E42ACBCEE8860E05991E25CF865B55ACED4535EF74ACB6BE8BD104A5F8396B998885BF1738B042BB61F3D14433084944A21DF135013F00ED02B0699C03924FDB027F3B38B9269252E1044E09B529582DB86F4993589BB916447C063F ct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ss = 7961DE81F9C4303484CE85F5EC4128D8C211A7CEE8A3821D5CC391DCBAEBD42F count = 13 seed = BD26C0B9A33E3B9B4C5D7EA32D5BD1FC371015BE163C86F584E49BFD5362C8D8341161CD1308115B2A03B7E5EADDD418 pk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sk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ct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ss = BD7157664183C42F6DE8C8707071C4E731151E9327FAFD536C634207DE2BD4E5 count = 14 seed = E2819EF86853BCA1B9DEE7EE1C1619988964F9A913E635AACF0D96CA6E0300D084329DABD8F149E24176D22757404260 pk = 6DF986F5E8ADC7F0DE157900ACC1ED39337970897D0D2DE5D1B22D7658C7A4E0C7D6E7ADE1A90E18F4B16C5A536470D19BD9DDF2BFA5E597A34DC469FE4D9FB21306AD00B8FA1237B0F6F2CA2DDAF476EBF0F7F8A066D3A6A91321BA025ADBB417E310D49083D83ECFE1CEE408FDFF7AB94555143001ECF38337D95EF7C5708C66AF4BCB95CAE9E77AE0E8C38B3EB45A55B422CDD732C19B722F2FA19F7F33E5F42F959A1AA7C632AFE463C98774F9F1EF3F25749BE740C81F10865C36F119887ECCC263F2749AA88722ED244EA51B28E0A04B0FF67F519EF9EB90867EE2EDD35960D5DD0A23687CBA1C3B712D72D6D21E8AB4A2E6BD6C6403BD99E3138D298CBFE3ECE1C2281660EC828C6071A417E8AC14289A992505BF8D1A9DC80330B778CA7EACF08C3225A2672FF04673BAD08AFF71B763F9AC1DD852C82A520A942941E120D5CBD84C4F9A233CBBA23083CBC2987DB711586382C642206D3D0656986657EB331443DBD94AC04DA7BFF89B9D160EEE5EC1183BBA2B15276D778F756A1ED572702BAA5A35DB697AC7C5D6BF2D7FE619EED1A9140CF2640407E69F69D99D076F620E389FA7D198DA7CA35CD2B21FD98DCEB5C4DE7A0205DEDAF1AFCFACA456E6B4E1CDEC8539589D58FF2F11515D75E57C2E3A55EBA40EFA13EA948141A796D3B11ED4CD95479066A2C9E94187762C24DE36733CC289894A7B183D206B4F56A86AFE4CDCD93DFDF301E37D59C489663C2952A8A7190CAE7D4CFF853A5AE3FDDA6F3AC7C0284E6C50853AB56A450B19D20923 sk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ct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ss = E52C1D2BEDD3E134DC03578F9D427521121B98F7954E97EE50A752F30D1ED7C4 count = 15 seed = 669C4EF8A051CE201DA65FC4BC34D398EC1F806276FC5D987AD71D93BC12DC8F107B58BE6E8422A0795C88CB9A0E7488 pk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sk = 97B5665676E59E3538EBADAA8CD50DF1F9FDA1502D9894C616A946078E56B621DF05318B5F655EFE36F1B678CF4B875108A18DB2FA312261CAF839F84BD956C55EF849036D6447BEDB6010EE65403B029DEBCEFFD1BFE934A2D24AE3BF61EDC788E4617CAF342D5BE9E8995DB446F4ED577A5D873A92A9CCC71D67E149804EAE541CDCAC026F2908BAF0A02BA5117A72789F9BCE83CCCB22F694524E2135E76BFC0BDCA7E6DFCF22F1C51C778867ED35EC84FE21E5C1D387D5CE0EC6FDE303BFAAEB5FA39ED38A746B0F8BE64F12379417002046536E9EB419167042F15A60E5F9D20F64FF17285D650F56E6A9D5F849D05495E05CA20D899BD1277FB998561927C49FD1BB7F8E21A2ADF3632CA033B5DB127B2E50FEF7AC6C4C1B12D8918167D344DDB512ED68C1273F77BB321023A47DDF51EF28239FEA55BE4608476911FF80983FFC468A71211FD61A020D653F106B38B1FB35DBB724B4CC1F2833156A2FA3D1D66E017D9AF5C42C411B0D29782C9840CFF6B738FDE7C3F4E1FC016117351DF9989586E41CEC190D85576790FD4A357830A56AC0B96919298CF0C5F495CE6954BFAA9AF111F9719164ED459ED4F16CDC6F8960B5E9F6023D89B3B4E456F613154D0DE68EC22DDA4098625FF8A92742EFE8F9232125AC4A7A766C844FF3029B83EA9BBF51FC051FAD92C16B9333D0FFFD758E70A8C8C2A37FACC2BDF9A5805330CA762254737F6D7294D2C805DC0D92FE2330DF07C7E60692CF57AC9293A0CAC9ADB22B3E70CF5CB1F5E292CABE763BCE29A98257896539205743C49BFAF3F9C93812907AD1549747AAB10A96E25887E43DE4B3AF5D5175B2CE86AB17739922B965E0422EC0EE4FB3E0B53C38A14E873A2B8C986DA1A2D7F8B479285615D5E2E9A51A ct = A8CFBD5F62B4E10A83682BF369C76C262C6F514689D2FCD79D0D598C35BDED17E697A9A373BC4329293687AE43BA0C0C757AE0AF86DF9695EFB2ACD23ED1045F03DE4D95C94AF5D14A2675A5D073248CEE0A3C7758008F9D061BC4869A2058DD26F10CD443E4E90B8CBA66E6241EB065B481A07D94129682C794CB01A2FBD7992519DC1DAA5B161B257C1A7D40D0BB74108D418F14BABB625F416E8A2FF2CAA739D6AF60E08BD2D763D79C7D2C075E30A38BA4DBA581106DAE854447D3038767BD67E2E20A0917179A6003F3318F43CA7B60891E7BD6B462A023DCD09D4B8C3360D102141A0F79EFBDBE07AA6E4DA5C4A56D9580E32F1B634033BCDD861931EC5EEE747779B6113E73D310EBA3F5D69FDE05DD43E5F1E7D12F1EADC61CE8CB60CFE98CA836B3E7D66B63924CB2F96E084FA36C1041BAFDE398DBBE0408C45F01796C39566463DDA78EB6D980674224C1F8299AEE7250E32EEB975D53145875097EDAB942ACAFEA3554928E9C2D3F46569CEB3461128D55166FA2DD3F1CADCAF2977E966D0382661BEEEBA408A90AF33A716B28E3F814A8ABE41208A815360F01E2183A7134F321C8039083B2B3B1A2BD7DF11F7B58524D6D748B2A73ADC0B7F8211C975C3625F0F768F40F0936C38027717AAAC2481E36D989371CF68ABA3FD6E1E2FE4ADED7C920DED0163664DBD85CD73E8C97DA6CE7EA744D833857EB740A79693F63EDE69058428EB3B69DFE9EE00A01C58DCD529284E7C50B382320720A25335730D28C2BF164DAC56B5CB7C2330AD83C3548F163D4DF38E2F19117918FFD83962423B16C23EB536D7F59CA9C4A7AE81933 ss = ECA5B827963949B33CB9113F7C46F82FBF1B457B50CECF17D436328B9A37D9DB count = 16 seed = 9DEBCCFE818F6B5204DB4EA09C03EC9A19DCF1629C1527685B8A29776BB1DAAEC45F8ABF8F0ADC9A8C8BD6E2DF6D8048 pk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sk = EF99224A03A85A46EF115474EC5B5D620DA6795D6EFCCA4C9135D19958A9DE62DF7D92DDA83E6B2EF4CCE08C9134563063068A196D7B1A1A13623E48AE12528E90150F7F22A2EFB276D6C4FF6DDAFA02EAAD1B28CFBD736B988B8CE312D45BF9EAD403612012A232A28041533E49C698FC7727C90D5C7F33E772DD88C54086F492DA1231792A65D79EBA5CE5302976B1E451F19217A2D18C3C76E6A42DD30167B3D52C041539D6924DACDE682D2FE96329C785F54DF4F3821E75E424C8E27EC058F91FA27F0FEFB8A5F666B34A8B050C96833F2BE9C9E892F3C97990D04EA934F7DD04632F5B7C71ABD3720CD61DF1511A4D85C794C33B7BBA49E3FDA965AE4996B61C9CC93F23CF165E7C18E963B54344AF9BAED76FE8C1BD43053A335E453FD6FE2E037CB0C625C5F7D3D27A44D5438010C298586D9AB83C7EDCDA443D1956CC8B2F2E9767EE61D694AB1E6F9A391D363FF87192525341AF252EDD2F028800AA9DE163C30EEC12372EE7D9A9E31E409817F1865F6AAF13EC9EF9C43DA0DECB3186D2EE7A096E2F01FD8E7BE12C12A2D030604527739F0859E79D267CDEDF972F91950AF101408AB68072D76E180478BCD3BE60D4A63680BDB0AF151245F82011B0C922A82495553DDDEDBE3D112116CF9D4717F3C44381C1CAAF1DE147B3C15B6057A9E8824BD5468194B437A09CB04849B385BC0DA69F1AD093BD5312DC8D2EE7246188F62A4579DFB483CF9FD06328236F2B78380E2393602B7ADE11E42185C8175F8052536CD8C089E352C28B40C905B7643E84E464DA3B629B732D6C7B88B05A3669B13961AB60364239323C8140887071B1D780090749DE0E42190C7C4AC8984F97816408DE7BE20FC862E329AD28FDD5FB89AE7537451B2A20BD838E2C36C012 ct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ss = AFD8B8D5D0F1AFB1ADE6E9BA85615A1ACAEBCD56C3541E8B50ED409071528791 count = 17 seed = 8098AE7A92C10F707D405F7DEA02C2EFBEF44EFA132BA8AEFE81BD45E543ECEC74F10920AE48A40B0653D63532517F2A pk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sk = B12F6FD965EA9C5B947DB80FC60C83D5E232DCA82E7263027C19BD62E5A6FF550F6AA3E88F7FA8A96067F8CDAECEEAC90C2D0B5E277E56E9C405EC9420C302520E0A9CAA76F59A0A6B1638B301A87103433D0F9FBBC6418114F0E7A2672847294C915F175FAB00F2AF220BDAD477345C0BFA490E45E10E0B8BE6C7D494D32C68A934C81D1A6A880CD7BFBBCEF7265096C84C3E8EC25C4339DF659726C25DE4CA31D9799A34776EEB134EEF43A46CAE47AD332F28C60CE66C5A22852ED9FF2DEB5931FDC175FE84F4078E6DECE1CFF434BDE317398CB85EEA70BDFC69DEB0B60EB78697B16260595360068691C3320B3D6D5B191112646F211CEED149ADE146066ED904FDA739B1D28F1FDC384B8C6C0C390045893D82288F23FFB4E80DFBCA4807E461726B4DA0F026D577CC3CCE40296CF4E546E70A91B4D0124CF5AD6BC8FBE8B556F7955F16684B598A0A02C900E130C5E1E99C3366B93EB92A3D76372FF1393D941CBC63B9C97D5803032B141FE106FB3D1AD04EF6D8FE49CD059F1AE8FF1AACD32B0034E524D69089E57BE5F8BA9DA70AB7B1155440612865D789BAE822687EB7CAFB51B7C8D6159F95AA53485CD38B8E0F854F681DD1410B516AB159AC5124A070F25731370A71B4504D168B6F25C3F2D1E1526150D3CBE16EFCC41F19D4C4921EA305B388F474F9EB621571D1550F013BB50CD0E96280EA721002BD6543D0041F9EBB7DE4F943D667C238C04C6A853EB4BD925372F336DFF75ED18B89A6FF441FF86BA1817296AE263BC381C86621F2AE6FB8F43183531F26E25C3BAA69013856350514D097211E28E34CA27FD0B6C6D82E8AB824EA10FEE5E8B036728920466386DE8C9BDFF463E043834D8F2055C4B98692F8C1A101CA6962DED9D323FE105F ct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ss = EC2D4533BF7280BEC229663F6665053B5178A11DD78863CAD12FFC64ABD684B4 count = 18 seed = D5F23808871544E9C1D6EACE2028362B48E225312F77663E9F78CAFEB512B908CD9E25875D61A16EC615F4B8FF826856 pk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sk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ct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ss = 0D484236F0F718A7383605DD732B0CBD682C860F8899C84683ABAE97DF04BD2C count = 19 seed = 822CB47BE2266E182F34546924D753A5E3369011047E6950B00BC392F8FEC19EA87C26D8021D377DF86DC76C24C5F827 pk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sk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ct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ss = 1C22BEDBBC26C82AF8DCF84F69B8F6DB4877F12C4063098EAF9B3D8E574CDC86 count = 20 seed = 81401DB81138D6874E91B7C11D59596E4ACE543F5A3471B6FB00999221765FEC3CA057ABE20F03B2D59003375FD71FE8 pk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sk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ct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ss = 901E8EED2324D6571E0940041B4243A8771F0C72208EFAB0B7DA51E57387C5AE count = 21 seed = 30B5DE5B73681EC08AAA03F6F2D2169525D25F4042A5E3695A20A52CA54927B85F8BB948FC21DF7DEFC3910B28674994 pk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sk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ct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ss = 54173A3AF286B4F253B6DD8F013F0C025A03C2086E236594D98B0F4FDFF1F178 count = 22 seed = E335DF8FC0D890588C3E305AC92C7160FF199E07C85760A828933750E3FED8C83B0DBE802234481ECF890A32D7A2884F pk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sk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ct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ss = A9562321DF5970375856AAF0BC0416202AA3D570E4495ABD5061483519091D6D count = 23 seed = FBEA1BC2C379F4F8FDCB0DE260D31CDB064C9EA9B1D6DFBE91B3692ADD1D34DEC9C9FFAE7BF5E72ED2743BA3F9F2E43D pk = B44C351990310EE5ECEDBAC6D1A6A5DC01DF5A1C9C7ADF9EFF5E8515760414D33AF07925C86F9026B2E1332BCC3D4C4FB2B493ABED5AF35BB683FA97D6F86DE2AEAB800CF2F4DBBFBE029DB6BB56C1104A1F8BD1F06FEDECFFA05C749E5B01146EBD335A6C16B5E9420FA621233DF6F27AEC7FE2CE418F8882EEAAC70263A75EC579CE31C4579DEF56E03C94C0887DCF9429DB6B866C3058B47DEB34C62FFC28D32C189F31AA620AE82FFB1038D5B8E499DA89EFB97C233AB0721F5E04D4E6EB030FD8501C63C93F2AEB1DFBB9B7D06FAD8436564DB022BED3D9C1E1EDC62E0ED1AA3A84582B8219CC77217C592A3DF1C031CA0F64731F9B96B62DECE8FB659228A52D6375E2EDEEBD884E45410273A2DBBCE6B60F543B57D663EE65787EF04EFCF182DBD4AEED5F82A99D7DFF7B22C1D3C8D4BCD54B75107ADFEB6FF4DDB1E1C38907836E1F65A5F46D40F161B78BAB03BAE4B557C42BBF3B4462FEAE3DBFFE4122A4B44F98DA92EF9ECA2474343D0DD5F1E241EFFB3049E7C2C812335ECC83613BDC558380E1BA70C56167C2ACEAA7474716FF0507BBE50CF9B5093B146FFD0AE6F8EF2107AA2A1F5E575633C156ED90B543235CF739174E2695246EB6B1BC21E8345ECD621134188EA4830B020CD02900804D152619A64248490039EF34668E37ED14C4978B751BAD878AE073C038B290B8844CA5DAD395A4CC07218CCC6A8879BA96C55D5C42A77C4213B019294B5DF43E70E58F0AD41BFC4F1A34E3B53DED4905B98ADEE24B71C02FC06828B283D981A217 sk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ct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ss = F48295BD40FB0E919907CD0BA11405B9ACC83E48E5151754E8960B8E67B62350 count = 24 seed = 7E87FB886BC3C7C9FC12569F465D2ECD12532E76CC27C65644C8D3DD603B0CB2D036C5974E675058F271D5C82AD7A813 pk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sk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ct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ss = 28F8E24C2F07FF65E730AD254594D812BE3E5F2F1C70CF77542B084A8FBF9535 count = 25 seed = AD1424E804F306C7FF513DA4C1E8D445AFCA7BC942FAC5C0B335733AAF70693712ECBDE26EA726EE0F9FD9D52A83B1A4 pk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sk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ct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ss = 68575A048C1E588D59F7BFD9CDA877D3CA23B93D35A51E9D07920859334AA036 count = 26 seed = 7C33CA0E987226C8524DD56C811FA4D1CCF9995B1E4E4DD5B1481974E88CFABFBF6787775C2611CEFB27ED4403EA9B46 pk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sk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ct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ss = A7E213A4F0A8DDEDEFB8028BA3573D1BA53051317E6D8E8C84FB1329F639FBC7 count = 27 seed = 54770EA1252EA2857D6635151194F5F520ADEA8A41E409FF498D40C271359858FE2B084D5B96BEE087B8E8F4DD4E00C5 pk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sk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ct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ss = 51DB4F6AD943370717E83479F265C1A3456334002DFFF6F52CC07BE5462772F5 count = 28 seed = CD6CFE94E9C0A1CC4FFDCD2D7876504BE5F50F1D1CA5CF93482943465B268276056F2781F4DE805C138976CA72621387 pk = CA8676FA2967729E49DB43D3A7CFE53C515D00B756F7F99D7F4E4021BA35F7DB1802C439F477A747CC4E2CB0DFF94B514F6F13F1B756DF218088F79416357256C5B43E21B521B2E679E11A20D487892CC821C5823CE7A978D6A307B6C33D8C9C50198DFC7B7175EA9779134DEAF25CD4F91EF9C721B0B21D51731FD46985009075B54EA5E7614F296A7DA87B6D1D6EBF2E23E452F89918233D08D5D0C7CCAD927B1DD0578D24E8DB2F4C6145CEB5EBEC9ECD2D75F22A2C2C591CC55160270481AE622BF2AB193B30C07417A02AB7DEF719BC4A9388B19CEBDD622C9DAD90FCC9C9C5D73E9038E6A48BB76DE7CCCC061D7480CD17FD0A5C5AFA71BEDB5CB97EA4A0F8FAD6F371AD12169BBCBBD9ACF6F4CC8135F5A54BDA93C616C6B09D73F4914C669350D8885E58A9C766608B24A246DC9C7C3CEB39BFA70EF20D75AB446A37F0A71E9C53D4FC78D41E7823A94B775F4AD66A200744F9660C85821E1CDA6AB07386578477C531D90FA5148967E2EBF1B51844553EEFF1006BA2CD045A64DBE93A06810699BED01A07001934F62E66383DE7008714218A4C29AC56FC45B6C104B054468FAE594C570BBC076D93F98F463716FF5D7475B9E69EDF1540BCE1ED58D8AA2992D0695FE8B07A4053B9087B4A5A7E1ABA9D4B1DF426349952FB5381E083F4B24A8A4D9401F7CD233F3645CECCF43361938202241141E8CD5F3CFA72DA990D90EC7237EC2AD18A44E051A2E1F146AF5B238AD4867574523664EF60D90477E963D97C0EEAF8482E83C709048F572CD90031 sk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ct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ss = 9F8E75879E6A84A9A4B921A80FCD6D581EA2988939775C9FA8723516ACD7E164 count = 29 seed = 265EB2DE7099E4BD5614E5DE7F0C2A05C78EF3E8E2DD4AE4CB70F3E5E59C8D1D88248303F07DE0C5508652DA66B47222 pk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sk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ct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ss = 8531E180C5DF105DE8D5C100883A17B6FCE95F3CB7BB1C293C0EF16EA96E5FA1 count = 30 seed = 806BBD111F27C2668318387BD0830F65EC21A51AF01985EF48D03D64E1958FF7EE5133A4EBF6DBF36329BCAAF65F40EA pk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sk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ct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ss = 4D99061B6937AA37901AAED330B5ADB04694E8FCCE7D4347B75436827F2B250D count = 31 seed = AD540A9CE816D6FB1661E5483C44F6FDD00C9E7BD1A8CEDA4B4C4D3697D4F78ED0A56954996CCB7DA96ECB8F5CB15809 pk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sk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ct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ss = 3A328629E9EA491DD8FC925AE18FFF3E9C2CB62291FF4AFC4D4812D08A4CB508 count = 32 seed = 288A5F2684D862A86D2790AFDDDDBAC6FDA934EE7D2E6DA1508BB550838609E8107312B28E00A6C01706374CCD3AEFA7 pk = 6F9B51F984FA359492D49673FB6B0B4F3DBB40F9B7FAD4DCFF53CA0027A90C159A4D194196407A5888677ECDDD1EDE91987B88410807D1FF7778381D0093E146C97ADE11665753046DAA71D7B1E73ABD6BE162EDDDB38FD27942951B84612CDB4CB6C32A8B9F6171F882D253054DA25C1C4EAFCD2F32EEFB44ECB4A0355277A53D2B3A2F09EE39C1FA6E3D72C496CA6FEABE1612BA779687AD0BB931D3764C6151C96A423972DBDB95C9C115F5FAF805B9C30A7F5056DCA4DA368160D86DB81C7693B85DA7E468B659F8E59EC29817630F6B955F5640A1E96DD40C9FD24AE070A851BAFA6E5F54D036BDD2033C07758AC12800E95A7198206B60F82ECEF64DA178D120362CF1479A11B6C59A1DB7D09112506F6569882A4F4E3A70FF6F097DF51EF518220146D6D910649DD95721D109733468BC00DC4543932416A78842809E9B3EF5448CC6D6770C983051679F4CE6C4055ED25BE28F348F493DD0ECA587E804DA23AC8D36A4E28E7F66EE31FD4D4501D08F913C77BE3A903EAE62A374D53914E634B22739F90CB5C2CDA474E9C57C1141239C1BD81A113B80E76DFFFD302C3EA3D96DF9DEF164905CD7EC114660491BB9A71E61103DF96E4EEF8C7A40AA2A56B84455BC9B2F67CB40FAB8D9AC2FC89C1E76CAAA6A6D524902EF6443884AA88421C695166B293D98BB51260B84CC765AF1DB263297F644872B9D6A12883B1796E125E5E0B0FB555FDBC12DEF51C4120378AC743E04A1B15198092A573A21C600813875981B5FE991ADD615C13B79143FD49B1E sk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ct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ss = C8F7F0A56DB64B70D4EE4A22263722C76D1AB9178B707DFD931CB81D4906F258 count = 33 seed = 4635DC5BB92EF98CDB6220DF0DD717C7F8158375EAA2B78FC3F0B58E9C9653E92684CAD3461D9158A481DA3D14694C44 pk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sk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ct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ss = 78696DC7DCF46923FBEC1AED5FD2EF9DC4FFB8045BCCADEA8D7557BC301E756C count = 34 seed = 5DA2C51B4ACF488C8BDED5E985CC4702E4A7BCB248B5AC18AABA529F7F9CBF30EFA776E99F76D5C1686E94F50FB57DAE pk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sk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ct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ss = 41F998F447908AD3448A348F8E73441FBA26717A83C1306C22BD8BCD4F8A525D count = 35 seed = 4D2239E84B052109A78DBAB6D80C51A86D38248105970476B74A0B78B9CFAB6283E30D5A406FAE1C7F54F8BAE1110EE4 pk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sk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ct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ss = A03F8B99F2B60AE8EC6679DB247508197CD8AC61735605BACDBEB15A320BFFAC count = 36 seed = EE762F5C9021C36446706A88EF16312F4A12C725CD7AFFF1484337C91EDA8E89F7007F3705747D29907B3FB7500E5074 pk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sk = 056661B38038DA4FDD7426F32A81576C73ED84843B305168A374F934E27A4E1B79238A80DCFD7C992D84B2DFFA67493E669243D4FA38C46B090BDF86BC548411A77127B247925850220B0BE970AA3500720209A2E76F0312177438B8D22611EC2CE360C6206CADA64225D8AF09AD7C85939FBA1C2B59FEF265726496917AB7A803BED112FF1DD14FEDC9DAD6DAA78F986305FD777CB9CD98FBB628E60B080A526CB69AFA91D3FB94EF9728396331209AF0C0D7E65B9858CF932701DF8E8205C598C4B911457F2048486A52554BC55360CC21ACB1DDE3EDCC97703291EE2A5DB544B0BE185CD380ACF509BFF3892AFE7A38840984C444D5CC6E9A9DDD3C8886C0D4AEEAE2AA8AF34486CED02F3EF468FBC8B40FF56E2E255EFA6D31D989F73D85FCD74B6D0EB95A2B55309AED92D4A311F6980E9C91B015047EBB45413794298CCC3910055BC771FBAABFAD11BCE3CC524D0A5F3249398AA0FE139D398E43F519447BF42DF7A9CE34E24DB290159017149DE05556D662548C90131308BDE61B2E14F49C9A8F79100FB44B4C182C03EC9A4443BFDB3DED409B62963A711FED8191CE26D6F17B69889F10EC49632FAD9816AC75BB8C96895F6ADE175A7507D38C10CB37A72504B89C047F63706F6B4DA04CFA805D291F84DA600FB94D4950EEC077150788177CFC18874F528C8962A2BA12336ECFCBA5BFDDAE0D8CDDDBDC90542F5334FC9B5754BCE7F55DEE1249D8695E6C07DE58F2AFED87C50122F0C40BD5BC0A2C47FDD346A5E7E883A801CED84B9D8EF76DAA259785C8039FAC1B82F9E25432BFDB429026E93D814984C74568A029FF0128CF9E5ACBB293580F8DA8E9854022103E5084F51896A0A09F4FC1517CD2274DCCD9E2CE15AF82A4EB6557A684C3152F0716 ct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ss = 228AF7F8303C8994F39B92F62BF8EAAA5D34BE0459D946ACB21CFABFC0714BE5 count = 37 seed = D882BA69AC8BBC88715F1C6387531F53273A5DAB87E66FAA8221A7F628D2BDEEE1CBC59C0E08D0ADD84520A3A70C1389 pk = 31E409C9E8C5498B444F62C15A9DE8E7A82B0743AF9698E4A68B898FE78F583CAAFE652ACB7FF00B1D39F96580090C34D00544A10AF9EEDB5A3B22B6D3D9598162BFBFD42883B9189BA8AA699BBE41B1F7772C2C202C6C15429DC293D4626F50F4A98CF475BF03B34DCF2E2010F5AE7AB821B0D4BAF7D61A668FD4AFCF43AA445AA938179F451D974E131AF3A73AA1A24987292DC1629B2F69713BE18F10FED32EC8D133B254A65F0A6111A36ABA564B29908CE3AE285E111AFAAD5A819A458101199ACF475A87DCBA7A54AF10B7880468468678F9A8BC2BD73F128EB1C0BDB74872AF2F84A06CAF06660E1ED89A36026656C3A5AAD6D6D1E7ACD2AA6F78C9D32C5324A86AC18ED7236660D9A58BD67229507A74EACAF1C1F9148199804A39EFCB854073560ED9CFF3CCF02A1E53457FD3BD342FF27C8D7B446E222AC8C564684BBB471972A0FAD9A46F618B19E3D7638095E158349C1AFB5F032A0A1AF68003A644D39FA6B2215B0C0F6167E986495D3E8A6882F876BB0007229275118DCC78346A347B046F2EBAE7F84B3B6BCECED6457A1589B0644B5FB213B809542290A5C619264B9C4BEDAB132BEA56B6790274A2D57C0CA001CC99A4D590DD7DABD64179E8AA04471AE85086E964A35175F8E96991A171561E0E19F45187D7FD24DC443B4D40D6A11F918B3054D566971EFB038916E621771D2DA01CD8B76C2213D3ACC71E6AE89F8C7BDDBE3FA064660E12289EC9DAE88586147FA979F7A19D4461895D060A8F68CC8FD2F64C9F63EDD1BD505AF39441 sk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ct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ss = 1A8218B58D3BE190E1050D633BB557DCD7C0C697BADF63E85B1D9355818DC3E7 count = 38 seed = 6C3AFF39F5D097096D882F24717718C8A702382DC4AAFFD7629763FDA73C163CF084807BBB0C9F600CD31A7135F48AEC pk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sk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ct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ss = A100827B09A30655B6CA3B34578B3BAAEB6241D32F00C83FF0E72355C6B1D102 count = 39 seed = CF520B92A2E3677AFD003EC1EC6EF136A709D78F828C9C0DD4946EFBD451C5FAABFC83CA66F9D3D17EE4220553B7A69F pk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sk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ct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ss = B002FB1959388037C5C6BD4836F6ECD0C8F1E458150E55F71598508493AD891B count = 40 seed = 197E5D562DE7E01BED4FC597DB28DC6EFDF0179F3A5BDA5F94CAA39D67BAE730540534D59A7A06C8448F628DA8B7859F pk = 361A539EDC2374CC6DEFCA9A883A116A6222632F4F2014E49E870F9EBCDC72288BAE0CD499BBBE728683C90CCEDFB8F8E27033522224BFB652EDCBA2ECCC55E4267816366F35A105660C8995301470980CB8623F513BBAE758FE234B002A9D2034EE92ED0E8158D47F9E27047F4A81BB0A75BB1F60097167220F19C701469DC4E46F908AA1C0911775CE5DAA2F12674B999F829C6EEDD740D8AD931B52740F6AF2343257294653FE58C0AB188974FCB0AFC7808CAC993A7ED1568D4B6B1D4F2BB1427E398877AF974E858CB7955E4DB3FCF6F401AF6C99A042B6ACB6208B747F86ADB892708AF5E5E4131F72073AC8683DD1647BC4C0CB0A2B607E30C72A4898D318DF3ADA358B4D265C35B7F2E09B338D4AF388BEABE49FF325F7CBF0B2956B8F4F300D71C7D5287A84A84C432D5FED588F7069BDCB53215F5DCEE1F23DD86A00B8D194EE69F7F371FAEF7BEBDF9C1D30397F420019E803C7A2F08DD794EB454B898AC7E574F028DEF70979F59E7FB1B7D8F75FBC996855ECFD8EFDC0581463074760B789A2309738317D49B7000D6D7A1F651BA4FAB57AEE170FAE4145C76000E9CFCD96A99F1318AD91EF091A22265E797388620040D3EFAD0C3B671F43DAAC889E78CDF60E9D0AA539F5B5D4014C1BCB0AA56C07FA8C4C15769E023EC63460917073EC6FBAE1919CE449323CB2037EBE04CCA9BA1EC0C1FDC8E075D833D047884D24F41EA3A663332942D07A568A1D3CC32C35BA2AAF6465366BC3CC5D756F16B76C4A3105C5B3073D441A8222532D91F94D sk = 588760826DCFBD36D9ABE6AE44A669BB3EBBA6A218EAB69E30F18A3BD536576E0E860576285483BB5FD36E2F944D32C4317BEBC1E441470C1372046A790D79D4F817C85D204EE860346635D4A8393902361A539EDC2374CC6DEFCA9A883A116A6222632F4F2014E49E870F9EBCDC72288BAE0CD499BBBE728683C90CCEDFB8F8E27033522224BFB652EDCBA2ECCC55E4267816366F35A105660C8995301470980CB8623F513BBAE758FE234B002A9D2034EE92ED0E8158D47F9E27047F4A81BB0A75BB1F60097167220F19C701469DC4E46F908AA1C0911775CE5DAA2F12674B999F829C6EEDD740D8AD931B52740F6AF2343257294653FE58C0AB188974FCB0AFC7808CAC993A7ED1568D4B6B1D4F2BB1427E398877AF974E858CB7955E4DB3FCF6F401AF6C99A042B6ACB6208B747F86ADB892708AF5E5E4131F72073AC8683DD1647BC4C0CB0A2B607E30C72A4898D318DF3ADA358B4D265C35B7F2E09B338D4AF388BEABE49FF325F7CBF0B2956B8F4F300D71C7D5287A84A84C432D5FED588F7069BDCB53215F5DCEE1F23DD86A00B8D194EE69F7F371FAEF7BEBDF9C1D30397F420019E803C7A2F08DD794EB454B898AC7E574F028DEF70979F59E7FB1B7D8F75FBC996855ECFD8EFDC0581463074760B789A2309738317D49B7000D6D7A1F651BA4FAB57AEE170FAE4145C76000E9CFCD96A99F1318AD91EF091A22265E797388620040D3EFAD0C3B671F43DAAC889E78CDF60E9D0AA539F5B5D4014C1BCB0AA56C07FA8C4C15769E023EC63460917073EC6FBAE1919CE449323CB2037EBE04CCA9BA1EC0C1FDC8E075D833D047884D24F41EA3A663332942D07A568A1D3CC32C35BA2AAF6465366BC3CC5D756F16B76C4A3105C5B3073D441A8222532D91F94D ct = 50549477D288277D282C8F47709358B7D76122459B5ED4269BA853D53048B56B93707F5AFEEE4EE3EE4735BB1BF741BC985D0F665281FC470631BAC74049F2C3743550259865184A4767A87FDED82A76A7D8358A5893A2247CD0AB5256565ACB85E2504E8844B4EC6AE7B20B1838C7F46294783ACCA2E02B3022919A86E5996D82A0543CEC76344F7091E1B1B9C8B03E436589EC342031E2D3CFCDE63EBE5D41E6DDC6300C57CD65DF2048CC65AFE8491F68F04F427FD6673B206025B38166BFFBA84DD3DCB077BC8C0195B3A74EB7279280289FF960A547AD3015013151B27BA1233355EEF8E3CE9183D2452F0EC3FCA583865EBDC462C88383E9626FD5E24EEE1A9BBBD8C00A990F56F1EEDFFAFB0ABE8345D5302F9C4B323B6D7FEC16F8293A3CC8B3E01F432C10D8F6B1FDA3B309760A05D26C37658DB8BA2712BDFE8E328479CB4D47650F8C43A5473AA08AD85EDA6D72D8635F0374B515F7DE6856ABE4B9FF8147E8C8602ABA9AC578D8CB6ACA08E6BC62EE8A646A7D54643297835E51958EEFF6E9B570BBE575320FC78592D3023F34CCE5DE7DE4647032296F37051B576D01B24D53C58D7D202DAB3CAA5E928A64192779A34A5087966EEC1C67038DA0E09D700BAECB05188832EB9D5BA20FE65BC94AE0591AB7A24ACE7A7EC36D862DEDAE66F82B22EB39010EF67AD29BA871B889314550069C502CC868193BD823B7541987A6C15DFC053DFB59FD12FB32F92FCA748F5AF0361AC41ACBA221E2B938EBA80C57E711CE3954EEC54E915AD4C3AC443C0BCCBABB0E55B112A69044029E54BA8AE899E2ECA2924FC222ED62394CE51038 ss = E168D04F9EF20435AAEEB03FA2A556CD628F309F512994AC8D45C5BD9A4C7CEB count = 41 seed = F170583CB451D8A45D105457C02C01A33A40350616ED8515BD49067142F61EFB00F07857E4FFF3FE11E7164C648C76ED pk = A0CDFA83F19BD1932E2DC1341227BA516B6955E12980D01BDD34EA4AE2FD8EB38F79068BAE6129B677426996AFEB165AA5218501774F11B54A6072CED608FA2B6F8F1CDDB4AE3BE4992383F0847735093B16E6DD2945F68F26F6B957E545B0E46BB3B78FF9A044C2956A3F36A169F071EA208AA5B59049EDE86FAB2BF96B750AF08B68EAC5EAF95FAFED36A728DB68CA29E458F9DB4D41EB6862DF2AF4A86C47BB65521DE99CAEA6DA371E304C3D5608DB6DED47E6FAFAB2C04EA4400E213392A0A1A492480450093856F298291B6305495F9E0CA01503086ECEDCA6F6CE04101CDDF1DEEF31873D63AE6C6618335FF90DBAD5ED09A2412390CAA29EE1A4572D6398044FB33D6256C0A06A97C6A4C598E60A26CFDF7897BA163B1B82D0EBAB25DA84FC57447C3FB36D83B25C08A019615A01ACF3DBB5D1F99EDCDBDFFB6F077B5D704BF77089B3E6941C3F49C642413A34F4A6AEE0445C6CC9C47EFC71B30BC44E131F2BE95C0E17F80C1B27F999BB393302E4210C66966920B1C48A36CC48F70E1A3DA3B6CC69330750BCBC44A95F611262A1BD5E9991E175EF9164ED360451E565B02818DCA7BEBFA237E3370D602C2C9E5CB58EA9A21C2C7C94DB68F18C2AEEB7CE7E6E3A91B68BFFA3FF3C07F42E96BEF6BF7724BC626A3E86F67D85601BD402FB7AABA039A43ACA3725A9E9CDB41C5420B15699DFD438E1A36D0E60751DAAA54879109EE4AE7A67051E194BB8ED6D0620614FCB12B950E1D5AE8CD308FD5625359A418D971AA44CA303BEEDD4E6363C0345 sk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ct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ss = 42C434E1950DD73BC7D791973F82DB4BCD84EC988A8FA3C95737BA9B5DC5A597 count = 42 seed = 44A6774B2CAC02DFF210FF861A090561A453DB311F47B6FEDB81811872D5D9489F5FC4103010139AE53FCAED209DC9BE pk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sk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ct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ss = 5C9EF53393459AD3D3EE31C82CFF7AC2B7C48F1BB01F6874A461D2B94D6FD5AD count = 43 seed = 49E1855588B6235DF2A400C4A70AEDF8AB17B6E5E2891AA745F132FA2E7AB0C8117C1DF37C39F5D57624EB77C2B4A091 pk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sk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ct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ss = 7073D9867E71CF32C57CFF13577E31EE75EDC74D3B4CD56271266921D6074C23 count = 44 seed = DF0E41D2F6F86C1F79D31FD5878E7AB434FC0AF3A0D5F47D2AB3FEF31A42BD949B0E3629DF9F575BEFBB62E829E51DAE pk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sk = C719F9B2D16399B7326CE4ECA30DABEFE8FDAAB18E9F6DF888B0A134EF355570E40771856EB77E4633504899FCB86C6A3D433D0B8D60E26F07BD61F1D4ED69BD43ECB0987E039EEFB08896A033E7C703EA179E39A1BAA9063BA77CCCF9FFAF9139E419362F818C173AC1911DD9EEFE0594406C0C30D0910AF8E87CD77872C7B7F8459F7CD5FB50CF0CB14AD97682F7BC9F81DB01588996E86D816F3143F10C05581394A88A33B8B00277D9552E4BFF58C76D15DEBB07E05C8C7FF6B51E266F144D34945CD87BEE2D80D3B75F7B965B5022D1D2F957CA93A44472E93DD3F542B1D0FED3D3B64E8AD75B3146A0F09195EA782FA7F82A6EF309E007980A6F68A96CDC9DD78BD836AC2AE63063064A36146841E5041B813AEEA8145CBB30BA9252EE0A94C4EBF34E94DC9D0CC407AA1F041E775C632E8C075DC8390FB83A4E431CEE59887866DD87B2DF3CCA8F4EC0344C8A8F288765516AF374A03C8C65F968E24BEEB3D043EBD50E103050CFCC355106BAE026C5BDA09C9D8292449F6C5CE060EB678B92B0E45D28177F60F3CA98665CF5C504EC0AA7D99A8E54ADD5BE8653F8892A582017A1A996A6DC40B16D98695DA8BDBFFB722D7632758C931DA06F420411B3DFAB16AF73BB1CB3EE6DBE838626330D5C69EA2A300C3D113764AF733094964C8DB9A070E9F2815D6C524D0ACC924559580F9FB59254EAC0D9BC4C33D52CB1840E9DA29B7A47D42111E5E2F42E09DCB9CBBAC6368C8F23607234E19F09F06E0205D5CDEF4EE9229D0F2338D64D65905DF7DE09686E7C4B7397C68A89F1F9BB1A4BC6DFFC05B5A11FAF6BB9EE47F2DBDDD75B9E3AB731098F6B9E8B30787693EA03B6FC69CCBEFC966B4A2ADC00AB93D810D1DF11B448CABC64052866567EA480024D3A ct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ss = 91BE7DD57957734D1F99FBB3B8348466866D62661B3A5C635E6A0FE0B26CB238 count = 45 seed = D3C9EBBA6EB03CCB5C9B9D2C8D7F0CFBBF50841E24396CDDF0E56525B38918C2FBE6C34CC1B93F7BCD4F4D5777E1A488 pk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sk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ct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ss = 7D632857976B5828CA4134D42DDD775C4050823D501713B7AB62413136C5C13E count = 46 seed = 6B3996E8BC6F52879F2B7BE012C44AD555707CB7E5FD8ABB3457A298336D6FDC9EB7853008FF13201D5969A315C7E493 pk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sk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ct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ss = 9D5CC018D88D15BB1A5D3D7AEC6770B93F101F92403A890AE941A63A8734BBBF count = 47 seed = 730B65ECE22DE27D573CE3AEA7CB021C415DF210D228808D91D4F380070FFCB0778B683C71D4853DEB569C822765F2A3 pk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sk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ct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ss = 4C1117E3E10F8035448ADAB5EAA7F03B204B4D6319887D11AA75678EA6304FF3 count = 48 seed = 5522A5A891A9A9B5514F4556AFD8DF40B9CEC63A01492F0CB8A1DB073A285A963E4A9FF2376C88662F7D8D241F8ACF17 pk = DC74114035A37B5328891E908AB48E3D663B9E356835F50D821E9B67C199F43B5A1BB1F6B67390DEBF8E6BD88933FBDD1C88BE423228D3C753D4BBBE6CD5BB05A12FD0F07922C0427AB0FBE5101608A3BE583FF5BD318C85857D8D2567256665F2DF31195D21718008B1AF1270E8910E804E78D1B84370A6D2E51E6F10DB3F35030E9E96E6A8D7D034BD217CBD193A8D9EF1684D0AB0AF90FD8505BBC55D2EBA9D61025167DC674CADDFC70E9F36716BA8563B3344F2D9B5D0B69419D21D03BECBFDD64630EC9EC5CC0B9A98D54A3A8129BF40FA2D02DDA6D38AED591388074A134CD2FBA03DABEE6D819422C80C7224A10C0359BF8FC9442A9CA8B42B074BC327707BCFBD539FAABD2FD813E0F62EF0E0B66085ABE9E692934C86757FB83182362AE7D3AB32BB7034B12CCD4A25C3E46C0BFB8D4F14C41039A4638457BE60B4D8501E258B38BCF3ACFFD40C8DE77FD8FB0C5113278203712FE2CA365B7A67F216B0D0F5E2004DE1BFAA3EF8893E6D1F8BAAB9561AC6C23E0959CFD7F0B33B557BF95F9940C624BD6EF7EB5F25367C766C5DA650E68CBC200B7BFA056DCE8F8D2882560D0BB3C4970905F2437366A958570B7B8B997009BCB90A82D3FA7DAE4D2331D3EB55B7EACD330184803E0359328400499D2D3922360EF8CC47A0055E202BEDEF49ABD84A3F46C0E0DD5347778FBA5727561093B91B41A5B68187822D29F3B4CD0E0BF44D0BFE6E20E2A4DF8A0F4E02B102BD5C80882AABCFB6DBC0E3FA1FCEE6DB6B55B53F2F97D39075CF8A1681511562 sk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ct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ss = 4ACEF422DBB0D1F49DD4367046C29FC7CA96FBD872A025D000DEE4CCBA6B8951 count = 49 seed = 1853E72329353B3F89AE6A1B1EF700DA8ED3C10D19F9E61EE9252E28EBB0E15802EE43083A12A0B7527088832605E3AB pk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sk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ct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ss = C54E70E7194F597FCEE8B17013B77285223253A43FB6EA82D32C532ED4E4F41C count = 50 seed = 027C3D5847ED4470931141104F25B19AE76117CBB64B224EE424FFB782E9A0E988839E0BDED0DF666FE8E5FCBB5DBC09 pk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sk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ct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ss = 828E97638076B1AE2CE45C961FE4A34315EA7AC451F95731A2A1A569977AE047 count = 51 seed = 450751D4401737459C6D93E6C5F2FBCC4A3AF7CD7250CCF404BBB817A67BAB7B4C9D0EF4570BFE25CF919DA331C31D88 pk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sk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ct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ss = 2798DC47E7CE8E60B363CA03CFF8B45F2EA8A302D781EA9E441E7643D0446DAE count = 52 seed = 5DE720F2D152BF4E1F96A61E7AE5F1BED6B8548E32638C2CCEC9F43B87D1BB43DFCF334F0582984D27E440D519AB662F pk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sk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ct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ss = A9CC3793476808A1248911D3B0D7DCDB32CF92575AF827FF5E71DC9FDE6033AA count = 53 seed = D71729DCBB27D7CB39E9E905025D3E55C8602EFBCC483C9B866EBF82326157833169243C14550AD728BD1470F39C642E pk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sk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ct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ss = AAEE1E32F40266D77EED391768ABCDF3D4232B3752FB153A24FD2810E52397D2 count = 54 seed = A7C2C8EDB3601396BEB2DF0657EC82FD5780A2723581A9E03DEE1CDB018440439BB1142CAB0487C5D136E9AF46338AB7 pk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sk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ct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ss = 4853F43FC733C3F60B0A45F127AAA7A7ABD6E2685E492CBFB0D89CB616F3A3FC count = 55 seed = 467F6158CB86B724039FF18C47950AE5C49170163C910FC9A9B30141F86E9C06EBCEC91497BCD156D95758C9F0C6EF91 pk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sk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ct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ss = 8C5FA3CE335959851C3C06CAFD39CDB9E1848E8D4F72128FD9842AB5BF244F17 count = 56 seed = 687C02DE1041ABAC7B2C1E6EC2A7C3375552ED5EDB10E3A8139C24CC76BDA44D719D8121A81D47A0B762B4E9EEB85235 pk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sk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ct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ss = D41874A2E197464EEFE132987F3B7D48B102D828D9783F66FD0D38E84BD323A3 count = 57 seed = 4142237070C216BCBE245A39BD9220533C97651D84832B26727855AD994A0760C52B9319AD404693E4248B8C5FF324B3 pk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sk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ct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ss = 160593FEC401B6BE109A262AF3CD83B1DB8EBBDFBE7773EE40F8AE6E9399FDBB count = 58 seed = BD334D7B7EB14E00E68863F2E5551A095F8AF10681C28353FD19B9A7E70B8BFE266840860609008A567ABC66316C77CE pk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sk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ct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ss = DDAEBC31AA82FECEE4CF6364556A5D79986BD2BEFFFC519CF1AEDDDB26A04915 count = 59 seed = A0264C58AB1F2CBCB212077FD378D340307ACCB31F1312137CF84E3D3135044D4EAE8BD38BC3E540A0C14D46458F6179 pk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sk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ct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ss = E2EFF280E3820BAAF517F9B5C328FDD24447D83950CC4FB37FFE57DC20AD10BE count = 60 seed = 99A9CDBFC674AB3FF2C64CDED7D697A6E27A767434A47AFF7C3FBF3C6A22D6043D27868955286A13EFE3DE36D22EC48E pk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sk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ct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ss = BC6C4B7FB37F8074CED5D09537104E7D2F8A25020E28E13D63D86E9A5619C784 count = 61 seed = C799D57B41F28C5C446DFC58A5AC6499C4BCF3C162AFD2B09A16549826EC2A6F689E44BAFC4ACC82F5D6AEC23F4A3993 pk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sk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ct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ss = 54DF5956155EB8EC96F4BF24A1E85984B2376FB0CADC4A51DC5B15B78B91C7B9 count = 62 seed = F7AE036A0176A9DE9A036A542DD2840033277C44AE936D10B768566216DE9D4395CD42B116873B69D9804BA6CCBC05D5 pk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sk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ct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ss = 1BEA35EECCA0EB3A88C2E9366E1AFE6E263921F4973F8A69E37E2ED15621FA92 count = 63 seed = D995D38F934B6E1A7CA77C9522E3D037676CC939B0C8BD4B84394B3DC91A791F09D2D97199258C9943DA955E7F7B26FC pk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sk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ct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ss = 0C77A265D4D025CF8A1234D18336AA4E635A7D5F52C058AEED0A100656D701B3 count = 64 seed = 5929F02A271725CB40200DE32D9D03D8BEA53B53AC83186C42C7F565CCB1CA508305D470850CF86E9B2C61A5B8CA1C93 pk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sk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ct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ss = 643DF928F7681C94AFC18C6CC19F2FA446FAF7D7F38111D42C4BB3EB3F09292E count = 65 seed = 905074033D7B75DEB2D06A2F29144EB377B452534C5710632989F02D45312D156557E96D4486020826DB200153BC4A8B pk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sk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ct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ss = E39C1892E0D8EBCA1E85DB794E65C5F5954FD6929E64FDCAE0E5B47EF2B46A5B count = 66 seed = A3E2E511AFA7BB560446BDADF67D2EE2E16FFC7BAEAE7EFB8C5455068BBD4E91BF9BE9D98B280072FABA7712C75B26D4 pk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sk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ct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ss = D4835589F1FBD94049273F28D19D358ED11331E6F1167B42F48ED20633705506 count = 67 seed = 074AB1A37BA5A0403D8F68D26FB787BC2C90F5EF88F2A6D286C3E6B168ABD85D393D8225618608B8EEB301D26AF53BC0 pk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sk = 334382D39164D1989696A2FF77B25A28AF8BEAD9883B5365EB6FCCA7C1781CC9ABA5068AF837BE962F439F233593D193CE5E08F7D66EFB3389885927B89D252397F0169ADCCE240CCE953AC7B438B901BC147B3779F6624049B7DD2BA7E78A329033BA5665AAF1279F96695D7DB1991EF639CC3B045757AF4659F6003710EA441F33297863C97DDA7630F678C398F7A01A36BB62A05439C3BBEF0BBABDA9767C55D8D9A0C79C199D660903015D0E61FFB87094DA18EE616E261AE3E0828C033787880F429D1149FA263F62DA619F6AF7FF6087DE2D0207F363F333785775079CB6F1F9CDEB98A16DE28B633026C263B4DB845DC979EFF1C1326C1C80B7843C4F904DC0832E3EBB4EFF38A84E38CE267DB870EFF1430073A01212CA694A79662C8E5D00B0C28E067DFB3D3CC4CBBF7B0C17975DF306175110F383C431F09A9218F529F07A283DD70925B3AF21E13AEB5A622BEBD3C5CBF2E1D399089DFBA9371B0D9885B76DE8D88F73542F85DB7508122578E7D4B960C772842C452BC44104300F2B6C8902479D03B71B703DFAB5198AECE4DE304546B520BD68603AECB25BF473F7B81DA29E7624E610236C0DF25F202A32F172E6C55482C9A02399BBC4DDBA41D3544C7D5F5960FE519E08CFA56A853EF6D0086EF5D905C2DEBDBCBCCBB55C65BA89659F4A0B9CF5E5AB7B836BE2744D74BB3AC8E53F30C1481D1D1C8520D658A7016BE5A091B279FA4F28536656A3D4814096D87CDAF8314C52F71637202E7F15F8829921EA57CF070277704C18B0BF12A8F7362EA0C070C650A4D1AF4998859C4A641FE7D2072C41C33F1C6478AB9568D49DE213B5F0A43AE8D4E1527F051145227B44E109665802CCFD55378A051154130B0BD4CDB97E86A524C702114B224A5310 ct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ss = 4ECDE05F4C24C19F931695A8F6DED0DB21469A35A232792A2055E0FA129BF6E6 count = 68 seed = CC0C86CC0ABF86FA21899BE1953913C00E7C46E6B5F730C4E88B3C034012763981D7F14459D3081638080378348856EA pk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sk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ct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ss = 436AEEE24290F4A1117A9A52451BE197BFEAFF56944CE8C67F783C1482F5C6F6 count = 69 seed = 6D5A7CC326ECF3983C4E7683F45263A37F692F3BCD2D920E1FD9584350119E74F9A3F905F70D3E20318C1413DE2A0DEA pk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sk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ct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ss = 5DDE361F4EEA78A44F19ED387F5548126E26E35AE403F3A42A695817EA665D59 count = 70 seed = F68FC0314DEA88F66AFAA76E6C9B6804B13D4876924410D1F526FAC59A62E26C560B125B1D0F8B461F1FC2E351EFFB4F pk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sk = 3E809EC8DD0FEC0D911A4E3FAC20F70FBB128C5DE94DC7184CA7310AE9157A98D8128601C28B1DEF8D393A0DB283229F7C7383152A814E7CEFE8EF9D9768C473AD3022B265A1EA4CB233CAB79A52FB025EF6DC358AF8A72280930D1DA2BE63E18AA7E2806302ED77F7D5BB13941C82C8A1A26A899BAFE62E542A0F06DBDBCAC759AAD11285C4C7C4B05022B89B099090654802D40CA7185437A42A7EEAB66FABE44DD2ECDB3655D40F4347A6375FE67A35D1B04BED6EC2C05655B35FE576446E1B5F256AC7F1A1BD6124E8523D2E6162D25E931E3CD00559903410FF1E7ACA06D083E70767871DFFFFE1030F4CD2B8A008981059C776ACDF82668FEA1246F279C002E58B4709653B9A840E0554301F8C219CB994FA1E216044D4117254AA263C6B6F417E5A947D5B5C3C9FE6BC804E8D5D4897FF1FD5087E40CD72DB8057B536D48A6EFB7262A8E194C34E46FA82D2FB99206294EFBF2F6D3AFC3380A19F8A360A708911DFA2A66767324827B217A9BCDC3BD91701F74A1C7DBD100D94D5CFA0F7D7E2996368BFB51AD25CF989882DA4BFAA66666A6BF764CC38DE795BA33251DA7946C2ED64ECB3711AC78CD6BA7B1C8863B9B69F61A3DD4374936A6E9D285F2EAC953D0D2633349971FA1B8D554F07F12BF61BFDD7AD2A5728D830C6C617EE272A12A6B56820B208E90D14972E6903861612DB8B11E18806C42F1FBAAE2E3AEEA9662CBE3924B974FF4F16E115DB0D9B34B10404D88908B98180EC8A9348597D436B003526D609366C95026D19F5DA0CE6929A547479C07958215370F4893C7B7568E95C68ACE58BC8C95C8445FD0CC1BBAEDF1B2334924990F6CA97D5BDCA168C1F75094B1ADE20D4CD9627F408F7536314CAE52E63E13CE775E0B1B176B50A86DB61 ct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ss = BBBEE89DF51764C8983ED543DD446DB770B9B64ACDDA2F974A469846744DAC13 count = 71 seed = A229218B0D51F58D915DF549901548FB0722F352C7470900E7E4D8399205764A319BBDDBD06C00E8C5932722EE5A404D pk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sk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ct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ss = A16B54DCCACC968F4A80AD53A969A20C5850E04719C28A07C25ADC6F3EA77D91 count = 72 seed = 6960F21C7350DCF41B4770C551DC8692D8BA2C0B6E162C589166FF22E7A1AC0F94C2F48504A5F7EB0DA094DF427BC98A pk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sk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ct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ss = 8CB2314A3D7B8BCBD157E04D0907A2EA79512BBFDE626433B4977E3C79C26D79 count = 73 seed = 53DF46012CAD4A745B7A3C06E18CA95E0B839FD8161E3025749A0887549EB0ED6A44EEEA08BD6060D6509DBF7E9DC864 pk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sk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ct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ss = 3BC6E89EB86810163951340118ED66AD0B8B84EA6021DF32384D9EE2ED438716 count = 74 seed = DEB963F8B1D8FBDF499D564BA8D2D47915BB402DA02F17031B37B4039A842AFB9B7E48F37200605992BD2429427A7A4E pk = 05951FFF0481D50C64B950DEBEC328FA03BC56160E337249E40085CA62463297285326C04CA1329498D9E8C64C285892431C0885426AC0072D19F6E0536FB458C4A7C8E78783DE18B2B023F86B8A9B654393F367CF7BA6CCB70853C6A811522E9DE23FD1AB771DE47AEDBA45FC5254BBFC6E8C3996CF07DF51B6859C8728252D0A0E8BEFCB50E70812B7151A45C5FACEF1192D587C104530C47123C7E3C2AC835CD84CD0B55F520C2A94A32892CCEF5F899C8CBA869D23215F278D0AC256BAF2712733EAC7C5AF7C3DA8A1763ECC1280A7BB8D7B753945A6C8C7C943AF6BCB59AA65330E2985587159836623FEB4F77D85455E6AD247877A37004C8A7771E1AF652A661309176F36B32375059C62828DF7734C1ED6C1CB6BE8537B583DB05137545F44B41DB305B32CE983CC06B7D6B0B7AE65B1434CE87CCFC4A6C1CECAFA4A01537BDC7232E42F5AEB256D2356F026826B0B196C409881DBDB2F5EC9708F23EEEA7D6D3F3626E960F9D155AE8071C2C9C5AF40EFF3F746DEA5B6AB572C74AFC35A025C303858428EFCE81190FBBF490C3F9A5119B6965D2E407782E8F56A04E6D5E59F3C04AC3DE8D9342E5F96D5BB5F83298FE9571355EB70F3774BF9BA98D0D76F8D702855F293AEAC144038D92BDA7E9555B9378E48DC890044615C51A03AA81CF22106D50A695CDB2F65A2FC57D131AE93296A6F743CE44DA901DF2441502066D28316B5620518D58460FD80E5768BDB56DED3DEA43783CD26B18BB774DEA9A627AA105C842D7AA36151419877C657E731 sk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ct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ss = 9C96C97D3032D9A7283A9F4488D291CC7484F8F6DCA8B17419B04DDBFD9A12E1 count = 75 seed = 8E2995F1B3E43853B18916BB1212ACEB05898E2B177A87ABEB928AD7184E59695C56B2CCCF5DB80853C28A525E327D13 pk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sk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ct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ss = 2193074EA86C6435F13AAF99E488F9CD34049D64EDE5A0DE7A84F5DB6474CF2D count = 76 seed = 9218943C51FD2DE47E509AAC67EFF176795102F37D7A2017E3AFD768FCDA7877AF38739B00FCDF227C2FD62EB635942C pk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sk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ct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ss = B22BAE3C5A03DB642A25672388E7735BF8E23AD6814CFA72F7B9E5F62614F7B4 count = 77 seed = 542E20078ADD5296050AF150360F057F6B9AB3BA835589DD56987DE805F900B906505B5390A0D86CBA28038992DFC59A pk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sk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ct = 9F4F2652D29424A545B1423EC43166248F49588258F6CF2307D0335D26CF172CF2FE4AA2DC42DDE14E98245D3482C4427E26EB4361C5D2404D2386EF63593FBDC935AC2D4FAA05E23EB8AC0CDA617289F7E3B34AFF9934A3526EB03CA33DF92D02E1C22EFB3C93813EA2F4E9C37935BB2BE85F173EC9AF42CC2198DD94C9B793BFDC30FD13E45E527F66B708E043A08B0E5FFD6F51EC1BC5E151FC4364578FD77E950552C4A9EB93E7BEF5617D9B1AA4A0134BDD353DB14CC3D7032AE512B1EE75FAF0C04C5911F4218B69DF28A8F0051A6041B3A4D9C54B1E3C4052EF71E21F18A3329CBC021D7881D1A284BB8F085B0E2814649D8CA66C1BEE7EECD7A5D3F468D6F64EFB02DBABFB4220B9C8892512FC4772ED64E5732F4C43E481D138C548DDC74900916C2C00DC629ED0E3E096918CC933A4AED2A50793BF189B7F73D3EFC4B206544A10CECC4BA79051475C6285E7A8F6BD1D06756B7F5BA22376E81D3366634DB67D60BE3912024167F257448585D50A16D20CF5368E6CD197022091CD96ABCBA9CF4638D19D9C798C67B33AB0027AEEC25FA303D8B0A8D7AD9563A4A5A6BF7A37DE7307DC23B8777C4899F8713CC2D664761938EAAF6B305B6CD73BEA41502D8FC89017E7F5606DE25549BFC18553F8EDA9690B4AE282B028E4378BACEC6457A99ACA4808D799344A8D339B7A5AEF36227DCF5FF5B3BB95F1E83251AE1B369BDAF153B09FCC607EB98EF4AC4B500FB1A9949797AB80B6B7AEFECA72110A7BFF1F7E43AC7F0DAC9C1A39F40721655B4C699C723B0A21D555BBC92E7D71E51F1638F06C2CDA1206152E42635A7F35A3AEAC ss = F5ACBF38290E446BE322E745C3E123CE1EF475BD16D450B49F56251633AAD8BC count = 78 seed = 6A85A61DD08C0733FCBC158ABB49FE0B0D96A50DCCA140A2E9F5A254F1901985844613B1C656C0CB0112620591B88AD0 pk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sk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ct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ss = E91077A726D3A16BAF511702ECB961A3E5D2102DD9A1C2C21AE8E6C90F2F587C count = 79 seed = 7F4A56EDA151E7B097CFB8EF980440FFF707AFFBA91867C89522CED6C5FF3BD7F5F00BB49DDD615D9361A7E4EFA42851 pk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sk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ct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ss = EF215F75EC5E2F67DE8ABF225E3513EAFFEBE589280EFC35AE0B822DA239F24F count = 80 seed = 09FC004519BCF85B20D25D314A0DFC79E00CB6262A7DDDF9C52473641AFB8CFA0F5DD5F53558184CAAE9EC34B459E98E pk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sk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ct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ss = 4A14C1B95864A51D1211B0110C208BC620194747173C7AB5FA6FA9506A2B9540 count = 81 seed = E3C41CCA6F04CFE7732FD54DE30CC5CAAC93E2F80E76AED7D24A962A3969C1B6A311459A3EC3E510E3E9B1E4291D4D7D pk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sk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ct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ss = 8C46A9F4111F3A275FAFCE4FCF0BBCF828A0A9006D0A9C632F1B5B8E669D23C4 count = 82 seed = 373FDDE922CFC416ED96B444E445BDD0962E8989F6C50ADF9912A89937C57217D3600B06C95440448E3F601AE69CA5BE pk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sk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ct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ss = 60F62850F54096EF4D8AB44D5050086D48889FEF1D2523B2BAFF585D2E4BDACC count = 83 seed = 16BEF67F7AC3A755C59C816478B75FCC16CE5844DB537791ACCD1EBD49D2824B105FD2E970F728C8F0CF16E439A9AE2F pk = A4F1F0D3BCB4691FD6DF0AA806F5DBBC4AF3A47AFBB54322DD3AF167990C0021CB5048EBE843FB7F2F0E2286FB118A51131A72DDF244F29027BDACC0AA35B5201E8BF62A6FB9975EA343774742712697F04ED316C7718D8D232318D2C026AAACD25357315B80B2C07108463CF087B8543920832FD1BB3E086C23DD931BF8DC3E644D7D886521E49141ABA61616C0AD9A020C3DB87470A26CE2693FD9E686C856DE27714CDE70AA995E9D1F6BB272D80A375ACCE6B51FDB10B205D500ED999B1F7BD9E9F5A79542FDDEC48C34CED28D85412F7E12C607FFEE47E7596C98D986A8D960ED9694A6A6143CC2F5C32FFCC5ABF00DD9632AF44FEDCD811C9A78914E075A1961B1AA46E3F24F5173BC56847DB2B3EF6E11123E482A4605613E90A553DE7F876AA6074FC3858B0556157882CDF89FCD44088C598B63AB0268FA41BC4886917086905BE1346536B1AF177DCB8D22A5FC935E0214AB750AC844F4A2D0446BC313F2837396230E5EC23A084303D71CEAE7808F10D9F3590E8838DBE5F092E425B8ADB9296D4FD078A5B07A7DCD477DC170B772EBC8CD21A730024756BB11BB5211B6E5796E520C99FA75AE17550903BCAF567242ED49BECF7EDDA5DF6074EF88B1A8616EBA5571CA1C561046EA69DFC49F5457E146A3EB23B328BCCA188541EB92CBE5B7B23D9554F29B56087236F08CD81C446E174773ECBB28FE1D82D95B62F045BF118CA14F8CBDCCCDB740FE7EB8D2BFB1BB154E6B479B0D6520E87B9DDFBB30600AD55978BC8B57EF5DFAA9BAEDF2BF6F sk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ct = 565FF76C749334B07E05D036DB9948B1223D840382D16C4A1D22DA6E482D78D368CD0BB837125917C4A8E284467EB0231AD84B3A69F955FC3AD37866AAB529B705D56C440FA81E072248456CB687F21F92BF8926F54CC4D7EE776F24C24328C74707890867394D29C9B84BC52DBDE1174DBD94985E116F1D191BD158CC2A0BFEC5AEA2872CB10C6D1D2AC64A3C9A9B83329EB5A9C82FFD452AD5531DA5B87C1B309D52FC39AEB9A07BE6F2307A198267487D24E092E0C4516DA0E44D0366C2F12CD2CBAF9F0C013C4BE6BA698D9E195F53407C6E4887FB8958D75AD71F1B069C58703681235DDD163B934F56EA74714A58AFE1C9B4C6B15513CB594088C238621279A9EA36089B0C4CAAB949B151CA79788A66F2BF0DF1EE8E0740382D385FD8317EEBA3C6D89948638A598DEC4BDE58B86461185EC13D232DE3DB999F0B03F395F5FB96ABC90EA5B706438A2DFD7D79F100A0D65BD2089FC902B1F79762AD19F65816DA545FE3CE3181A0F8A9D1C9DE4ADF495BD92BE9014F7209591F4D3A056CC207D916E38566249A98F05CF2918DFCAAC68BBA833889987BF54F3E72E2DA4A0C4350015D4CE1F420B25BABA8B295017D62B4FD30FAE5512A139AB505EF42191029F941D960B9D7110A810EFB5DB54B53C87FB52B9F08CF6D88B967B2B80F8F855A78DC3C1B20B0A8771CB6934BBDE64B9B18A248B9948ED7A793FB7AE940167460BA5F1D032BC68FB1066466DCF70F4B1C9779C02D9D633A32B550ED588E3C738EEB58DDE8891D661818AB7417F0DE760D2FF3BAFADF7D31747EB031A6A192486C9C5B2692BD9C7B723A7E0939BBC19EC3FD ss = 4EEA80450240413B5947E8CC918E91C4F1662655FBBBB2EEDBA9D802B76835F9 count = 84 seed = D0611F9AE5BE4DA5D7EADC9109944348E716CB3DAEE545721EEA8C892E7831CF2E54603146454CBFD92387739E9A78D8 pk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sk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ct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ss = A6AA55F4F84ACE96FCCFD113B3B77E885748F05E84A0F8BB68B5B59AB3813116 count = 85 seed = FBC38D7614D7718E931EDB850D2C6F0C5EEA9EE889B3E25BD69AC255D5B91E885D93E808E66BF9C88C655DC594DA5792 pk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sk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ct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ss = B51F055A645FAE20F634F62243B398358544C00F2E93DBF55FA69EA82C00B43A count = 86 seed = 1722219CB5DB47374EB0AF0232C856A57F026F1CB09E5A5799F4C333DD422FF6A0A67C4DA502FAAE727FB2D45DAFCF35 pk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sk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ct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ss = B8FAEF117C9BAD91B8BD4D1A37FB64485D9C9A010468E9E4EA5311DB7C8857C6 count = 87 seed = AC139B78FD16CA0F26D6D7F9E15345C888D857B1910CF38D883339B37EAD2DCAC30F7CF10176F23FF34B4488EB79437C pk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sk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ct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ss = EAFACA5348B53B62BC5565C113BE92CD302B694CF1DC54FC30205B4D5DD815ED count = 88 seed = CC7152849C98D5FED2813275D32069E44824ECB14EAEF425CE017448CD9A401C91C06D0F7EED6D22B7BBE8BA6C429EC3 pk = 5B9752DC03E94B0E0DCAAD5B96CF86A7B29A5BEADAB46904AA02EBFFF4DA14F4DDE9116E95E3ECD38BE2626A397FD2EB9B40E2390D83EB0A338034D11D084B1C771CDFBC2D7D290638D549359CAD4A8CF6F71FFBEAE540578E725DBCBA5A822B76CCA381E91BFC44D7D5F837CE79489B9162B5D3427F17FF370014D75021FC7BF71B694A8752F1F15D4079AD079009CC1D5F0395EA522D232160225FF382A50D022F208C859AF110C40CE8DF1FEE25F372A49C304B9E936FC9FDC53A1D4F85DC962ABF3CAD68DD5F1C25ABC568B093AC64724660ECD14A2D9A91D19145BD2561B7F249933057E1693932B9D7345BD740E22B21E6B4D6C1175C385330F6C47E7BB79A3A2F2A5A079403E15099CF7C7F33D552634AB136E910F00E5218C88A52657FB5913F45893259C1F62B1210A3AE17D42494B1009683729E49005E64B8F927075E9AC7DF8254337413025F2E83DA25039F50C73B8B79CF757659F805F579ED5A9552DF284B0D6EB853BE60750DC0E1554BDAD04ED0292709AB8C18C0BF8953072AFE03BCD9384A4C395230128FD73E0BE5B6C26C2B3D9E64AF5F8433BB76FCE6B7F13DE6DB093CF5ACE0851BDA462D208D2E019010474B7431585D788F54C321D5A60D8CCF787A699EA2DAE9C093B93526286E1A4375CC330063361779D6A02800327713701C4E12833ECF1F588302B4A5C9E17058CAE0A59D2196024A6CDC79735853299A2E48405C990D3CCB56BDC4688C53A2124E023522B86A16EB51AD417832C9AEE6A7F78A588739482B88CE93C56B27 sk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ct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ss = 623C452049FBC352C8332F8BC3060C96A6BBC4EC0691EE5B4792236E0941D288 count = 89 seed = 96D9A06F88FF2C2036FA8E914B89C765E4A510B468DEE40F914F78858C811857EFE9FD0E17C0048E7389E8D996B7E2B0 pk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sk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ct = 80F2A678D9586068514C42DEEF6B7DAEA43ECF28CC5E9C7D4E17337D6106DCC8D8B34156F7AED23DC236577DCF2EC147C65FA35BA6431C2ECEE5E1656CA1E1B141B610305C7EA10F2CF4E0DCEDF6CC4A8851D9E0012E387147792AC26B00C98B6CA0CA51D51FB1B0CB55A643099F7B3CB4CD4C9E8017E1E624EDEFE5225322A709B592FF2E51981E108F1F93E342F09E1254128756F928668987BA203D647D59E3C9F81A946D10283845BFA5B6000C4072ECADF355313881DDC7E801B3205BECC8FCE83F4C18ADF6993EEE5C40472AD07A353C3A9EBD733899288328AA3AF314E43AFF4E9B7B6B667025434DEE131C37ACECDF09BDC456D65384021DE5F2024BD0960CEAE3D2A5E3E7AD9A82480F3D30529C8C654E263397E220EDCA10FBE0F3EFFF74ED4BBE546EA9F338273B8E012370048BA06A5976E2C19ABE29DE3A564EDEBB92E089DE0ADAF4A6D91FA6E24202B69ABE4EBA264BAA9A04AF40917E0FEC119F2E15FAA2B7390E2030A53CCB4958766E286572E2D156566955B244B0A9408761AB7581C8259665F06E361D6BB6CDEB6AA41B7F3D9F4C9FFAE9DC423007BF5E33360AEC933CF113F45E64B58CBC74111EC55D9FBEC66BE36D1FD0CF120B9EEA442F3DE2BCD516A1F347E0A5566D6266A6F6152E487DC1D3857FF203D518CD6290F5B47620ACDDDB6184C12C714B122CCC75277BB49180DA116CFCB2EF059865B6737B93D8F41D61ABB8C74D57DF7F5722FA68567979C8F539E75F4C9A6FB4E779F5D4C9A0EC16D207DB95613715FF68F0F035F0C27596A032347A2F748C577EBE07C1E6B70EED73289EE99204984656171B8F ss = 6914DE332BF69D644EF33F1838FEFB16A62069B48C8DEE9308169EF59C7D7E7C count = 90 seed = D26CE360D399BF7B89DC364AA7AC06BB513EAB8F527383E93E30727EDC3F22C262AA0EC70257B39EDFF0630DCDC1B79A pk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sk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ct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ss = F0072B8ABE7D3C6B1686702E58B9C9F15D91B3765954B237D851F441E976A94E count = 91 seed = C5856298C3CB6AC9787A0F30938537AB2635B96F6D19CC9522063360E7A5C88E644929D2879180E3E5BCAD2422B7CFC3 pk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sk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ct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ss = A70CA9CADC09966C85907688FA6AECC1C0AE83FF905770A34FC6E2B3F8287AB3 count = 92 seed = A28EAD0A08E7228AEFF602B16A1E752278B8ED1E91DAC67994F5ADC372E1D82F95CC390CD97AB9212275E0566C833FD8 pk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sk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ct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ss = FF6EBBCDD38D9A61610D7E3E450FC770AA2CE350F7DE4F6EC9838FA77FBD6B90 count = 93 seed = 92877D706DAF88EF3412EB143DB8CD91BC047A9A43B7ACDAA42523560DEE4C172697BE4332042FCAB91135839BF74AB2 pk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sk = 32E0EA9089FA928482C0770DA545AF1BB871A03CE38604138B0D08EA2A10CA2BC06C5BEF7B6508409DAF847A64C8D30D0974FD3BA7476DC76C46B458A036D8844F53696845942EAA424C6F6CCC89B7014844E31EBCFEBE37F7373AA3B43800EECF64139FD37837DC008A9294CEEDCAA0DB3D5685E0FAA0FBC00F831ADCDE17361246E9B43B024BF5248EC3642CA9877C023795463C3A18150F78B9DEDA588450A61A72B6DA4A0EBF0BD8B51DB56FCC37C5D146C563319B60AB06359EA30AF2E5EEB6458FCEA150197B948181E34E7A45BCB560EAC289A4E83793F9529CD7EFAB360C48B6C10AABC01D586DA4256FB46B68D85673A013076A133E5D7EB381C5EA342053834B4FD0CE3514B65A7B8D930D04AFA7885FC3B31AB19D7B9B5D7443E96A307CC27CD68272F66AFC3D9C75B9137CF037101F7206FABA897FB64F924A75EBD392B83D2EDE47D558A39FEB68553C486404308B4C5E23ECC597DB7C9720663CB1FAC5EBD07D0A110C27908357670D6B80A5B873E57FC0DACED4478A168EF1AFD60DD48F31337523DDD7BAAE0A86C0DD85F3E07E31523F61774CA6C6228BB0E2604194E94CF9C27FFE8EDB82346A73E188B7C0E9EDCBD7DAF899172D071C07381587FAC49E8F5131BC94DD5121BE438344B65433A3CC2491D3E16759F3F17DB2688CFD6499AFB6C0C314B942617BEBEA9E2A524E902D1DEE1330D51056AF1B9ED656F400A6C0756FD5DFF56187261636AEFB5A8DE703A38D7DBD810385EE6F37E0ADC4BE2AD7F47278848D406BE2888ABEE8B1FF10D4F30DB42EFF29DAB08AA51FA4146A9F654A4D8D28C59E96343EA595927C115C4329064E80984071F8856D9610886522245C0F4B2C64C89389E8F5179D2C3BD66F08F46ED77A0DB5200A7EAD3F1F ct = 51BD77ABD9D3DB71DE8E52323DF7252D4CEEC5DF926ACB40EA2092FAB125DF945685AC14BA5BD62994012E8EEA14A0C739DBC93E98D65D0B13A24CDA0D77474CEE19D281F532DA28F33808B001EC1076FE253CF8F009E6379217A471075EA1E44BA477724DAE6A4D2A60FB03D63B74ECF011FF827FFD2901B8DF86A6C45BCB28A0738C3BFAA8099D85B9CE4F8FBEC94F75C4C9D9969A75366787866C1A1970DBE379510203E72FDDC6F35C4BCC3AE4474964AEB0CCB4B870F79F6C25AB54064A413892BB7D32B8B162D97B1CE64E0EDCC1E0AAF06E4174E0C32242C8369D2DAFF7559E5795AD804E9EB8D83260073DE595039331B0DE0FA43B02BB9D45D3DF648622D9F645271C7F110E0754038C51D718491A230D77D8147208490CC655AFEDC9F6862A4A80F3B2134411EC3FC51210A09C605D330FDA76CC54C6DA9BA251E8BC13D4277063685F2A2BAC732AB1A890EB8A37AA29877356DCFD98297D8B208510C04C617BA0E57635996546508D06C5420560DAF0CFD06D5D137509FC0C127B5216B3388BD3E18893E660F33987BD7F692B1BB2D9ED78201511561D551BF39E368589D1810981686E33AC72953F9926B3D6F1950CE751F1DB2070E62CC3B441768651FD1C169D38612D5FE0AC267A7B7352BA42496DDD1B6FAA2DF33047C44E45769B81C83374CA139F727D64AE9D5A1F1D2F0136EC01E63D6CC73C340B83B8D08E3F05F2AF8FD7A5C755FDAE3455650AC0D5B35098B16B3516521BBCB9934ACB60267E430E34EB10D205877E09E3C1953ED13ADE9B6C7612E06BF5A161D2A26AC2678A9E3F1DDEC8E83B07A711127203175136 ss = F5526D8ABC4C7F0DC7170F16D117E21B3028BA78B29B0C6B271092133B69C121 count = 94 seed = BB4C0082CA4044B1FF60B036C9B0E0495D58667156786C530BC69D949A13BFAFF53798E456423D7A0E162A60039367D7 pk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sk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ct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ss = D7F0A7517BD8A4A25AECCAF23FEDE668DB53DB84A6CC09BC6FBB57F88C466A72 count = 95 seed = 121D90E70AF6204445D0DEB28AC0C108262719E9FD3476ACA74BBFDE89FAF04D8D5F89A624E8A75DB80431F0D10AD28F pk = 50FC5B70312F2FB129B1C13B76AC9791AA9631AE5EEDF9C98E38048ECB6168C67329ED29C2E340B87EB66D788B1ED1ED1E6F472510D712C7ED05852FB91AC3F47D3CE481F8840681E547021FB340DD4C54EB4ECE55920042433CD0E2414C47DE72C46FCFF8C7E000C45FBD515AEE02371F9467F6619761D2D5DDF32109EEA0CF5E8DF1112804FDB29A8369C316FC7C5934D005AC9CBB328FBF538C13110B71F5AB8B09789AFCEF40D81539BACC5062CB9AA3B2C262E21649ADF72351512C0F2E66098465322B7D82DBC89DEC68263939D72B09CB3366FF66111593630930F9049DE1DE0AD52CEF907EEE36B8DEA0F8DDBB9D9A7E642416A6970DBF62E8FB19B7D50EF8D61645A5374BCC796D6BB4D9710A762797BCA2404DD7304A3E396AAC9F6F281B5F136B68205E802A34DE7BC6F8AD637FCABE8E10550301F03C538D795627E4A73ADB77B244D038F71B38B21AE90F5F6877538A32005E3E894E51B0998A64E4C4A870C892100AF3CABC5898949B13B1C256572BDC35B7623F8204EF950BCAD9DFEFFCF0CF9FCEB38149DBB1C9772E7669279038DBACCE5EF5B642E6F2307D84E62E35805FCFEF2EB0A2C45E69306E63F73A9DCBEDDCCCFE95C2909611EA2535B98D39844D632B95A90DEC9EDBBF9A27886A1A4C8116C6A4D7C90E96B085DABCDB169950E0E5A275135F562E92B67C981F3ED0B3E7DA0E3B283D99EDFCB9A9B9AB9590BA3B253BDB4F8D80BAE986C4814641E6E6D5B08C1EC5DBA1D67F6753C8D74C8512D7344090937DE2E6114417AF9D36 sk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ct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ss = 1CE301DB31CAF217E8F86F2C4DE763B97AEB7A2D72064CB63A5569E5C713D54B count = 96 seed = B3AC6503206ACCC2A92CBC210D020A2654726911D11CE676AA04FEAA08AF1D20C654E4105883AE470EC3AB299075D420 pk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sk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ct = 121855DCA45A42006F934DE3E00D481373DEF60AC619166CC412777D7770CE1BF93B40C65B78C5470DCE4988DA3437839F5C550E7E04E90870C207BF1D2A4F681ABA1111CED2A3879B4E6B7CFC287625C585772DA5070DEC1192BFAD740D5B41E9C3379297D0BA852CBF06F93D8B664725900D5D1C29094D2750CAD10176B9316D5A979B60E6134EF31E9A8FA0AE1C0A71F0A8941D336ED3FD7422A26E981304FB71054663386AA8E71F1947C94087D6B8721F415198C03F8BAA0F6B65E7325CCE9CD6C8B95F8E5C2EA9521459D7448C6B9135BA06F62D06AF96189C0375DD03CAE6C71236A187573D8CAF453BF79C9718B3362F2BA5FE60EF9EA71F9940BF743E61041A1BEDC4A70C95B0F9A1C2E485D39C6E5C9D29F8B3892E32F2B7E2A23217645BCE131E8E5A38F5EF408CE3FE700AFDC99BF2823AD8B721CFB98BDC27096123EB2F1D82D75170B507FDCE783D1B03A153F83FFE0A6CBB6D542AD605E55E6764AF07EE249DD8CC760B4EE8D9EDCC6E9F0C9A701B5A207E1288597A78016F116F646564000B39291DE681DFE37C0CBD95628609AFCD3051F0114103E50341AA9AF9BBDC3171AB91966993D5B726AE81502D6FA0B101ECF2D4EA502325DFCEA3D80FCFA1AF2A39EF3D3C8946FB2ACE99C2731F252C9D07FCB75AB2381EFAF1AEA83A2C8AE3C70A55906C25C21F8A0E7D5128864721306F47F85BBE1DF83DB03BABF31B78DC50DA42FE60BD238D7815299198501FA6C67C865D4CC6D0164CAC1D245BAC2B165215777AF85832C8788252BDCE4A6B3FE2B7AD346F1149388CF9412174EE1700913C36DC7BB11DEF0112952D3D0C ss = 6D33FE9327795188EF4404E03A913F58918AE8A29C34B28C9124B4689E2E63A7 count = 97 seed = 59EFF60B1EF6185DB34EE1E3B1DD2F159106CECEAA79BEB74923B4F5623D5BC52DBF5D2594A1F7C6C64D12CF144E9ED4 pk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sk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ct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ss = 864742A6F00FCB874217B6159D2090F8C7F45092337EEB3D9185C72429CDD5F5 count = 98 seed = DDDCA9DC31BEA737D3F474E7560B37FACB2F53C803E768FFAADE7669FF94B1D4FBD17068CFFD5DFDD24AADADA4EF6B12 pk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sk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ct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ss = 5CA7F1A531AA82BBF918A7C07F7F155D83E94EFBF4ED58EE7C0E89ED6C80F2C0 count = 99 seed = 2A6F7386B815366F572AEB6C79E272CC21B7095FE09575F18072C9D677DA23BC9C8A4BC393B7524604D299BEDD260C8B pk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sk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ct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ss = 8ABCE489762C5BBC4C2326539BDA39B08CDE688D81EC4F75F11946550E603D57 golang-github-cloudflare-circl-1.3.7/dh/x25519/000077500000000000000000000000001454601126700207375ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/x25519/curve.go000066400000000000000000000057271454601126700224250ustar00rootroot00000000000000package x25519 import ( fp "github.com/cloudflare/circl/math/fp25519" ) // ladderJoye calculates a fixed-point multiplication with the generator point. // The algorithm is the right-to-left Joye's ladder as described // in "How to precompute a ladder" in SAC'2017. func ladderJoye(k *Key) { w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. fp.SetOne(&w[1]) // x1 = 1 fp.SetOne(&w[2]) // z1 = 1 w[3] = fp.Elt{ // x2 = G-S 0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e, 0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb, 0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad, 0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e, } fp.SetOne(&w[4]) // z2 = 1 const n = 255 const h = 3 swap := uint(1) for s := 0; s < n-h; s++ { i := (s + h) / 8 j := (s + h) % 8 bit := uint((k[i] >> uint(j)) & 1) copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) diffAdd(&w, swap^bit) swap = bit } for s := 0; s < h; s++ { double(&w[1], &w[2]) } toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) } // ladderMontgomery calculates a generic scalar point multiplication // The algorithm implemented is the left-to-right Montgomery's ladder. func ladderMontgomery(k, xP *Key) { w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. w[0] = *(*fp.Elt)(xP) // x1 = xP fp.SetOne(&w[1]) // x2 = 1 w[3] = *(*fp.Elt)(xP) // x3 = xP fp.SetOne(&w[4]) // z3 = 1 move := uint(0) for s := 255 - 1; s >= 0; s-- { i := s / 8 j := s % 8 bit := uint((k[i] >> uint(j)) & 1) ladderStep(&w, move^bit) move = bit } toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) } func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { fp.Inv(z, z) fp.Mul(x, x, z) _ = fp.ToBytes(k[:], x) } var lowOrderPoints = [5]fp.Elt{ { /* (0,_,1) point of order 2 on Curve25519 */ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, }, { /* (1,_,1) point of order 4 on Curve25519 */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, }, { /* (x,_,1) first point of order 8 on Curve25519 */ 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00, }, { /* (x,_,1) second point of order 8 on Curve25519 */ 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57, }, { /* (-1,_,1) a point of order 4 on the twist of Curve25519 */ 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, }, } golang-github-cloudflare-circl-1.3.7/dh/x25519/curve_amd64.go000066400000000000000000000012421454601126700234040ustar00rootroot00000000000000//go:build amd64 && !purego // +build amd64,!purego package x25519 import ( fp "github.com/cloudflare/circl/math/fp25519" "golang.org/x/sys/cpu" ) var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX var _ = hasBmi2Adx func double(x, z *fp.Elt) { doubleAmd64(x, z) } func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } //go:noescape func ladderStepAmd64(w *[5]fp.Elt, b uint) //go:noescape func diffAddAmd64(w *[5]fp.Elt, b uint) //go:noescape func doubleAmd64(x, z *fp.Elt) //go:noescape func mulA24Amd64(z, x *fp.Elt) golang-github-cloudflare-circl-1.3.7/dh/x25519/curve_amd64.h000066400000000000000000000066431454601126700232400ustar00rootroot00000000000000#define ladderStepLeg \ addSub(x2,z2) \ addSub(x3,z3) \ integerMulLeg(b0,x2,z3) \ integerMulLeg(b1,x3,z2) \ reduceFromDoubleLeg(t0,b0) \ reduceFromDoubleLeg(t1,b1) \ addSub(t0,t1) \ cselect(x2,x3,regMove) \ cselect(z2,z3,regMove) \ integerSqrLeg(b0,t0) \ integerSqrLeg(b1,t1) \ reduceFromDoubleLeg(x3,b0) \ reduceFromDoubleLeg(z3,b1) \ integerMulLeg(b0,x1,z3) \ reduceFromDoubleLeg(z3,b0) \ integerSqrLeg(b0,x2) \ integerSqrLeg(b1,z2) \ reduceFromDoubleLeg(x2,b0) \ reduceFromDoubleLeg(z2,b1) \ subtraction(t0,x2,z2) \ multiplyA24Leg(t1,t0) \ additionLeg(t1,t1,z2) \ integerMulLeg(b0,x2,z2) \ integerMulLeg(b1,t0,t1) \ reduceFromDoubleLeg(x2,b0) \ reduceFromDoubleLeg(z2,b1) #define ladderStepBmi2Adx \ addSub(x2,z2) \ addSub(x3,z3) \ integerMulAdx(b0,x2,z3) \ integerMulAdx(b1,x3,z2) \ reduceFromDoubleAdx(t0,b0) \ reduceFromDoubleAdx(t1,b1) \ addSub(t0,t1) \ cselect(x2,x3,regMove) \ cselect(z2,z3,regMove) \ integerSqrAdx(b0,t0) \ integerSqrAdx(b1,t1) \ reduceFromDoubleAdx(x3,b0) \ reduceFromDoubleAdx(z3,b1) \ integerMulAdx(b0,x1,z3) \ reduceFromDoubleAdx(z3,b0) \ integerSqrAdx(b0,x2) \ integerSqrAdx(b1,z2) \ reduceFromDoubleAdx(x2,b0) \ reduceFromDoubleAdx(z2,b1) \ subtraction(t0,x2,z2) \ multiplyA24Adx(t1,t0) \ additionAdx(t1,t1,z2) \ integerMulAdx(b0,x2,z2) \ integerMulAdx(b1,t0,t1) \ reduceFromDoubleAdx(x2,b0) \ reduceFromDoubleAdx(z2,b1) #define difAddLeg \ addSub(x1,z1) \ integerMulLeg(b0,z1,ui) \ reduceFromDoubleLeg(z1,b0) \ addSub(x1,z1) \ integerSqrLeg(b0,x1) \ integerSqrLeg(b1,z1) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) \ integerMulLeg(b0,x1,z2) \ integerMulLeg(b1,z1,x2) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) #define difAddBmi2Adx \ addSub(x1,z1) \ integerMulAdx(b0,z1,ui) \ reduceFromDoubleAdx(z1,b0) \ addSub(x1,z1) \ integerSqrAdx(b0,x1) \ integerSqrAdx(b1,z1) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) \ integerMulAdx(b0,x1,z2) \ integerMulAdx(b1,z1,x2) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) #define doubleLeg \ addSub(x1,z1) \ integerSqrLeg(b0,x1) \ integerSqrLeg(b1,z1) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) \ subtraction(t0,x1,z1) \ multiplyA24Leg(t1,t0) \ additionLeg(t1,t1,z1) \ integerMulLeg(b0,x1,z1) \ integerMulLeg(b1,t0,t1) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) #define doubleBmi2Adx \ addSub(x1,z1) \ integerSqrAdx(b0,x1) \ integerSqrAdx(b1,z1) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) \ subtraction(t0,x1,z1) \ multiplyA24Adx(t1,t0) \ additionAdx(t1,t1,z1) \ integerMulAdx(b0,x1,z1) \ integerMulAdx(b1,t0,t1) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) golang-github-cloudflare-circl-1.3.7/dh/x25519/curve_amd64.s000066400000000000000000000107071454601126700232470ustar00rootroot00000000000000// +build amd64 #include "textflag.h" // Depends on circl/math/fp25519 package #include "../../math/fp25519/fp_amd64.h" #include "curve_amd64.h" // CTE_A24 is (A+2)/4 from Curve25519 #define CTE_A24 121666 #define Size 32 // multiplyA24Leg multiplies x times CTE_A24 and stores in z // Uses: AX, DX, R8-R13, FLAGS // Instr: x86_64, cmov #define multiplyA24Leg(z,x) \ MOVL $CTE_A24, AX; MULQ 0+x; MOVQ AX, R8; MOVQ DX, R9; \ MOVL $CTE_A24, AX; MULQ 8+x; MOVQ AX, R12; MOVQ DX, R10; \ MOVL $CTE_A24, AX; MULQ 16+x; MOVQ AX, R13; MOVQ DX, R11; \ MOVL $CTE_A24, AX; MULQ 24+x; \ ADDQ R12, R9; \ ADCQ R13, R10; \ ADCQ AX, R11; \ ADCQ $0, DX; \ MOVL $38, AX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ IMULQ AX, DX; \ ADDQ DX, R8; \ ADCQ $0, R9; MOVQ R9, 8+z; \ ADCQ $0, R10; MOVQ R10, 16+z; \ ADCQ $0, R11; MOVQ R11, 24+z; \ MOVQ $0, DX; \ CMOVQCS AX, DX; \ ADDQ DX, R8; MOVQ R8, 0+z; // multiplyA24Adx multiplies x times CTE_A24 and stores in z // Uses: AX, DX, R8-R12, FLAGS // Instr: x86_64, cmov, bmi2 #define multiplyA24Adx(z,x) \ MOVQ $CTE_A24, DX; \ MULXQ 0+x, R8, R10; \ MULXQ 8+x, R9, R11; ADDQ R10, R9; \ MULXQ 16+x, R10, AX; ADCQ R11, R10; \ MULXQ 24+x, R11, R12; ADCQ AX, R11; \ ;;;;;;;;;;;;;;;;;;;;; ADCQ $0, R12; \ MOVL $38, DX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ IMULQ DX, R12; \ ADDQ R12, R8; \ ADCQ $0, R9; MOVQ R9, 8+z; \ ADCQ $0, R10; MOVQ R10, 16+z; \ ADCQ $0, R11; MOVQ R11, 24+z; \ MOVQ $0, R12; \ CMOVQCS DX, R12; \ ADDQ R12, R8; MOVQ R8, 0+z; #define mulA24Legacy \ multiplyA24Leg(0(DI),0(SI)) #define mulA24Bmi2Adx \ multiplyA24Adx(0(DI),0(SI)) // func mulA24Amd64(z, x *fp255.Elt) TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 MOVQ z+0(FP), DI MOVQ x+8(FP), SI CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) // func ladderStepAmd64(w *[5]fp255.Elt, b uint) // ladderStepAmd64 calculates a point addition and doubling as follows: // (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). // work = (x1,x2,z2,x3,z3) are five fp255.Elt of 32 bytes. // stack = (t0,t1) are two fp.Elt of fp.Size bytes, and // (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. TEXT ·ladderStepAmd64(SB),NOSPLIT,$192-16 // Parameters #define regWork DI #define regMove SI #define x1 0*Size(regWork) #define x2 1*Size(regWork) #define z2 2*Size(regWork) #define x3 3*Size(regWork) #define z3 4*Size(regWork) // Local variables #define t0 0*Size(SP) #define t1 1*Size(SP) #define b0 2*Size(SP) #define b1 4*Size(SP) MOVQ w+0(FP), regWork MOVQ b+8(FP), regMove CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) #undef regWork #undef regMove #undef x1 #undef x2 #undef z2 #undef x3 #undef z3 #undef t0 #undef t1 #undef b0 #undef b1 // func diffAddAmd64(w *[5]fp255.Elt, b uint) // diffAddAmd64 calculates a differential point addition using a precomputed point. // (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) // w = (mu,x1,z1,x2,z2) are five fp.Elt, and // stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. TEXT ·diffAddAmd64(SB),NOSPLIT,$128-16 // Parameters #define regWork DI #define regSwap SI #define ui 0*Size(regWork) #define x1 1*Size(regWork) #define z1 2*Size(regWork) #define x2 3*Size(regWork) #define z2 4*Size(regWork) // Local variables #define b0 0*Size(SP) #define b1 2*Size(SP) MOVQ w+0(FP), regWork MOVQ b+8(FP), regSwap cswap(x1,x2,regSwap) cswap(z1,z2,regSwap) CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) #undef regWork #undef regSwap #undef ui #undef x1 #undef z1 #undef x2 #undef z2 #undef b0 #undef b1 // func doubleAmd64(x, z *fp255.Elt) // doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). // stack = (t0,t1) are two fp.Elt of fp.Size bytes, and // (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. TEXT ·doubleAmd64(SB),NOSPLIT,$192-16 // Parameters #define x1 0(DI) #define z1 0(SI) // Local variables #define t0 0*Size(SP) #define t1 1*Size(SP) #define b0 2*Size(SP) #define b1 4*Size(SP) MOVQ x+0(FP), DI MOVQ z+8(FP), SI CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) #undef x1 #undef z1 #undef t0 #undef t1 #undef b0 #undef b1 golang-github-cloudflare-circl-1.3.7/dh/x25519/curve_generic.go000066400000000000000000000034051454601126700241100ustar00rootroot00000000000000package x25519 import ( "encoding/binary" "math/bits" fp "github.com/cloudflare/circl/math/fp25519" ) func doubleGeneric(x, z *fp.Elt) { t0, t1 := &fp.Elt{}, &fp.Elt{} fp.AddSub(x, z) fp.Sqr(x, x) fp.Sqr(z, z) fp.Sub(t0, x, z) mulA24Generic(t1, t0) fp.Add(t1, t1, z) fp.Mul(x, x, z) fp.Mul(z, t0, t1) } func diffAddGeneric(w *[5]fp.Elt, b uint) { mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] fp.Cswap(x1, x2, b) fp.Cswap(z1, z2, b) fp.AddSub(x1, z1) fp.Mul(z1, z1, mu) fp.AddSub(x1, z1) fp.Sqr(x1, x1) fp.Sqr(z1, z1) fp.Mul(x1, x1, z2) fp.Mul(z1, z1, x2) } func ladderStepGeneric(w *[5]fp.Elt, b uint) { x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] t0 := &fp.Elt{} t1 := &fp.Elt{} fp.AddSub(x2, z2) fp.AddSub(x3, z3) fp.Mul(t0, x2, z3) fp.Mul(t1, x3, z2) fp.AddSub(t0, t1) fp.Cmov(x2, x3, b) fp.Cmov(z2, z3, b) fp.Sqr(x3, t0) fp.Sqr(z3, t1) fp.Mul(z3, x1, z3) fp.Sqr(x2, x2) fp.Sqr(z2, z2) fp.Sub(t0, x2, z2) mulA24Generic(t1, t0) fp.Add(t1, t1, z2) fp.Mul(x2, x2, z2) fp.Mul(z2, t0, t1) } func mulA24Generic(z, x *fp.Elt) { const A24 = 121666 const n = 8 var xx [4]uint64 for i := range xx { xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) } h0, l0 := bits.Mul64(xx[0], A24) h1, l1 := bits.Mul64(xx[1], A24) h2, l2 := bits.Mul64(xx[2], A24) h3, l3 := bits.Mul64(xx[3], A24) var c3 uint64 l1, c0 := bits.Add64(h0, l1, 0) l2, c1 := bits.Add64(h1, l2, c0) l3, c2 := bits.Add64(h2, l3, c1) l4, _ := bits.Add64(h3, 0, c2) _, l4 = bits.Mul64(l4, 38) l0, c0 = bits.Add64(l0, l4, 0) xx[1], c1 = bits.Add64(l1, 0, c0) xx[2], c2 = bits.Add64(l2, 0, c1) xx[3], c3 = bits.Add64(l3, 0, c2) xx[0], _ = bits.Add64(l0, (-c3)&38, 0) for i := range xx { binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) } } golang-github-cloudflare-circl-1.3.7/dh/x25519/curve_noasm.go000066400000000000000000000005701454601126700236110ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package x25519 import fp "github.com/cloudflare/circl/math/fp25519" func double(x, z *fp.Elt) { doubleGeneric(x, z) } func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } golang-github-cloudflare-circl-1.3.7/dh/x25519/curve_test.go000066400000000000000000000112171454601126700234530ustar00rootroot00000000000000package x25519 import ( "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" fp "github.com/cloudflare/circl/math/fp25519" ) func getModulus() *big.Int { p := big.NewInt(1) p.Lsh(p, 255).Sub(p, big.NewInt(19)) return p } func doubleBig(x1, z1, p *big.Int) { // Montgomery point doubling in projective (X:Z) coordinates. A24 := big.NewInt(121666) A, B, C := big.NewInt(0), big.NewInt(0), big.NewInt(0) A.Add(x1, z1).Mod(A, p) B.Sub(x1, z1).Mod(B, p) A.Mul(A, A) B.Mul(B, B) C.Sub(A, B) x1.Mul(A, B).Mod(x1, p) z1.Mul(C, A24).Add(z1, B).Mul(z1, C).Mod(z1, p) } func diffAddBig(work [5]*big.Int, p *big.Int, b uint) { // Equation 7 at https://eprint.iacr.org/2017/264 mu, x1, z1, x2, z2 := work[0], work[1], work[2], work[3], work[4] A, B := big.NewInt(0), big.NewInt(0) if b != 0 { t := new(big.Int) t.Set(x1) x1.Set(x2) x2.Set(t) t.Set(z1) z1.Set(z2) z2.Set(t) } A.Add(x1, z1) B.Sub(x1, z1) B.Mul(B, mu).Mod(B, p) x1.Add(A, B).Mod(x1, p) z1.Sub(A, B).Mod(z1, p) x1.Mul(x1, x1).Mul(x1, z2).Mod(x1, p) z1.Mul(z1, z1).Mul(z1, x2).Mod(z1, p) mu.Mod(mu, p) x2.Mod(x2, p) z2.Mod(z2, p) } func ladderStepBig(work [5]*big.Int, p *big.Int, b uint) { A24 := big.NewInt(121666) x1 := work[0] x2, z2 := work[1], work[2] x3, z3 := work[3], work[4] A, B, C, D := big.NewInt(0), big.NewInt(0), big.NewInt(0), big.NewInt(0) DA, CB, E := big.NewInt(0), big.NewInt(0), big.NewInt(0) A.Add(x2, z2).Mod(A, p) B.Sub(x2, z2).Mod(B, p) C.Add(x3, z3).Mod(C, p) D.Sub(x3, z3).Mod(D, p) DA.Mul(D, A).Mod(DA, p) CB.Mul(C, B).Mod(CB, p) if b != 0 { t := new(big.Int) t.Set(A) A.Set(C) C.Set(t) t.Set(B) B.Set(D) D.Set(t) } AA := A.Mul(A, A).Mod(A, p) BB := B.Mul(B, B).Mod(B, p) E.Sub(AA, BB) x1.Mod(x1, p) x2.Mul(AA, BB).Mod(x2, p) z2.Mul(E, A24).Add(z2, BB).Mul(z2, E).Mod(z2, p) x3.Add(DA, CB) z3.Sub(DA, CB) x3.Mul(x3, x3).Mod(x3, p) z3.Mul(z3, z3).Mul(z3, x1).Mod(z3, p) } func testMulA24(t *testing.T, f func(z, x *fp.Elt)) { const numTests = 1 << 9 var x, z fp.Elt p := getModulus() A24 := big.NewInt(121666) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) bigX := conv.BytesLe2BigInt(x[:]) f(&z, &x) got := conv.BytesLe2BigInt(z[:]) got.Mod(got, p) want := bigX.Mul(bigX, A24).Mod(bigX, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func testDouble(t *testing.T, f func(x, z *fp.Elt)) { const numTests = 1 << 9 var x, z fp.Elt p := getModulus() for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(z[:]) bigX := conv.BytesLe2BigInt(x[:]) bigZ := conv.BytesLe2BigInt(z[:]) f(&x, &z) got0 := conv.BytesLe2BigInt(x[:]) got1 := conv.BytesLe2BigInt(z[:]) got0.Mod(got0, p) got1.Mod(got1, p) doubleBig(bigX, bigZ, p) want0 := bigX want1 := bigZ if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, z) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, z) } } } func testDiffAdd(t *testing.T, f func(w *[5]fp.Elt, b uint)) { const numTests = 1 << 9 p := getModulus() var w [5]fp.Elt bigWork := [5]*big.Int{} for i := 0; i < numTests; i++ { for j := range w { _, _ = rand.Read(w[j][:]) bigWork[j] = conv.BytesLe2BigInt(w[j][:]) } b := uint(w[0][0] & 1) f(&w, b) diffAddBig(bigWork, p, b) for j := range w { got := conv.BytesLe2BigInt(w[j][:]) got.Mod(got, p) want := bigWork[j] if got.Cmp(want) != 0 { test.ReportError(t, got, want, w, b) } } } } func testLadderStep(t *testing.T, f func(w *[5]fp.Elt, b uint)) { const numTests = 1 << 9 var w [5]fp.Elt bigWork := [5]*big.Int{} p := getModulus() for i := 0; i < numTests; i++ { for j := range w { _, _ = rand.Read(w[j][:]) bigWork[j] = conv.BytesLe2BigInt(w[j][:]) } b := uint(w[0][0] & 1) f(&w, b) ladderStepBig(bigWork, p, b) for j := range bigWork { got := conv.BytesLe2BigInt(w[j][:]) got.Mod(got, p) want := bigWork[j] if got.Cmp(want) != 0 { test.ReportError(t, got, want, w, b) } } } } func TestGeneric(t *testing.T) { t.Run("Double", func(t *testing.T) { testDouble(t, doubleGeneric) }) t.Run("DiffAdd", func(t *testing.T) { testDiffAdd(t, diffAddGeneric) }) t.Run("LadderStep", func(t *testing.T) { testLadderStep(t, ladderStepGeneric) }) t.Run("MulA24", func(t *testing.T) { testMulA24(t, mulA24Generic) }) } func TestNative(t *testing.T) { t.Run("Double", func(t *testing.T) { testDouble(t, double) }) t.Run("DiffAdd", func(t *testing.T) { testDiffAdd(t, diffAdd) }) t.Run("LadderStep", func(t *testing.T) { testLadderStep(t, ladderStep) }) t.Run("MulA24", func(t *testing.T) { testMulA24(t, mulA24) }) } golang-github-cloudflare-circl-1.3.7/dh/x25519/doc.go000066400000000000000000000014111454601126700220300ustar00rootroot00000000000000/* Package x25519 provides Diffie-Hellman functions as specified in RFC-7748. Validation of public keys. The Diffie-Hellman function, as described in RFC-7748 [1], works for any public key. However, if a different protocol requires contributory behaviour [2,3], then the public keys must be validated against low-order points [3,4]. To do that, the Shared function performs this validation internally and returns false when the public key is invalid (i.e., it is a low-order point). References: - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) */ package x25519 golang-github-cloudflare-circl-1.3.7/dh/x25519/key.go000066400000000000000000000022031454601126700220530ustar00rootroot00000000000000package x25519 import ( "crypto/subtle" fp "github.com/cloudflare/circl/math/fp25519" ) // Size is the length in bytes of a X25519 key. const Size = 32 // Key represents a X25519 key. type Key [Size]byte func (k *Key) clamp(in *Key) *Key { *k = *in k[0] &= 248 k[31] = (k[31] & 127) | 64 return k } // isValidPubKey verifies if the public key is not a low-order point. func (k *Key) isValidPubKey() bool { fp.Modp((*fp.Elt)(k)) var isLowOrder int for _, P := range lowOrderPoints { isLowOrder |= subtle.ConstantTimeCompare(P[:], k[:]) } return isLowOrder == 0 } // KeyGen obtains a public key given a secret key. func KeyGen(public, secret *Key) { ladderJoye(public.clamp(secret)) } // Shared calculates Alice's shared key from Alice's secret key and Bob's // public key returning true on success. A failure case happens when the public // key is a low-order point, thus the shared key is all-zeros and the function // returns false. func Shared(shared, secret, public *Key) bool { validPk := *public validPk[31] &= (1 << (255 % 8)) - 1 ok := validPk.isValidPubKey() ladderMontgomery(shared.clamp(secret), &validPk) return ok } golang-github-cloudflare-circl-1.3.7/dh/x25519/key_test.go000066400000000000000000000111611454601126700231150ustar00rootroot00000000000000package x25519 import ( "crypto/rand" "encoding/hex" "encoding/json" "flag" "fmt" "io" "os" "testing" "github.com/cloudflare/circl/internal/test" ) func hexStr2Key(k *Key, s string) { b, err := hex.DecodeString(s) if err != nil { panic("Can't convert string to key") } copy(k[:], b) } // Indicates whether long tests should be run var runLongTest = flag.Bool("long", false, "runs longer tests") type katVector struct { Public string `json:"input"` Shared string `json:"output"` Private string `json:"scalar"` } func TestRFC7748Kat(t *testing.T) { const nameFile = "testdata/rfc7748_kat_test.json" var kat []katVector jsonFile, err := os.Open(nameFile) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", nameFile, err) } err = json.Unmarshal(input, &kat) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) } var priv, pub, got, want Key for _, v := range kat { hexStr2Key(&pub, v.Public) hexStr2Key(&priv, v.Private) Shared(&got, &priv, &pub) hexStr2Key(&want, v.Shared) if got != want { test.ReportError(t, got, want, v) } } } type katTimes struct { Times uint32 `json:"times"` Key string `json:"key"` } func TestRFC7748Times(t *testing.T) { const nameFile = "testdata/rfc7748_times_test.json" jsonFile, err := os.Open(nameFile) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", nameFile, err) } var kat []katTimes err = json.Unmarshal(input, &kat) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) } var got, want Key for _, v := range kat { if !*runLongTest && v.Times == uint32(1000000) { t.Log("Skipped one long test, add -long flag to run longer tests") continue } u := Key{9} k := u r := u for i := uint32(0); i < v.Times; i++ { Shared(&r, &k, &u) u = k k = r } got = k hexStr2Key(&want, v.Key) if got != want { test.ReportError(t, got, want, v.Times) } } } func TestBase(t *testing.T) { testTimes := 1 << 10 var got, want, secret Key gen := Key{9} for i := 0; i < testTimes; i++ { _, _ = io.ReadFull(rand.Reader, secret[:]) KeyGen(&got, &secret) Shared(&want, &secret, &gen) if got != want { test.ReportError(t, got, want, secret) } } } func TestWycheproof(t *testing.T) { // Test vectors from Wycheproof v0.4.12 const nameFile = "testdata/wycheproof_kat.json" jsonFile, err := os.Open(nameFile) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", nameFile, err) } var vecRaw []struct { TcID int `json:"tcId"` Comment string `json:"comment"` Curve string `json:"curve"` Public string `json:"public"` Private string `json:"private"` Shared string `json:"shared"` Result string `json:"result"` Flags []string `json:"flags"` } err = json.Unmarshal(input, &vecRaw) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) } var got, want, priv, pub Key for _, v := range vecRaw { hexStr2Key(&pub, v.Public) hexStr2Key(&priv, v.Private) hexStr2Key(&want, v.Shared) ok := Shared(&got, &priv, &pub) if got != want { test.ReportError(t, got, want, v.TcID, priv, pub) } if !ok && v.Result != "acceptable" { test.ReportError(t, got, want, v.TcID, priv, pub) } } } func BenchmarkX25519(b *testing.B) { var x, y, z Key _, _ = io.ReadFull(rand.Reader, x[:]) _, _ = io.ReadFull(rand.Reader, y[:]) _, _ = io.ReadFull(rand.Reader, z[:]) b.Run("KeyGen", func(b *testing.B) { for i := 0; i < b.N; i++ { KeyGen(&x, &y) } }) b.Run("Shared", func(b *testing.B) { for i := 0; i < b.N; i++ { Shared(&z, &x, &y) } }) } func Example_x25519() { var AliceSecret, BobSecret, AlicePublic, BobPublic, AliceShared, BobShared Key // Generating Alice's secret and public keys _, _ = io.ReadFull(rand.Reader, AliceSecret[:]) KeyGen(&AlicePublic, &AliceSecret) // Generating Bob's secret and public keys _, _ = io.ReadFull(rand.Reader, BobSecret[:]) KeyGen(&BobPublic, &BobSecret) // Deriving Alice's shared key okA := Shared(&AliceShared, &AliceSecret, &BobPublic) // Deriving Bob's shared key okB := Shared(&BobShared, &BobSecret, &AlicePublic) fmt.Println(AliceShared == BobShared && okA && okB) // Output: true } golang-github-cloudflare-circl-1.3.7/dh/x25519/table.go000066400000000000000000001504341454601126700223640ustar00rootroot00000000000000package x25519 import "github.com/cloudflare/circl/math/fp25519" // tableGenerator contains the set of points: // // t[i] = (xi+1)/(xi-1), // // where (xi,yi) = 2^iG and G is the generator point // Size = (256)*(256/8) = 8192 bytes. var tableGenerator = [256 * fp25519.Size]byte{ /* (2^ 0)P */ 0xf3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x5f, /* (2^ 1)P */ 0x96, 0xfe, 0xaa, 0x16, 0xf4, 0x20, 0x82, 0x6b, 0x34, 0x6a, 0x56, 0x4f, 0x2b, 0xeb, 0xeb, 0x82, 0x0f, 0x95, 0xa5, 0x75, 0xb0, 0xa5, 0xa9, 0xd5, 0xf4, 0x88, 0x24, 0x4b, 0xcf, 0xb2, 0x42, 0x51, /* (2^ 2)P */ 0x0c, 0x68, 0x69, 0x00, 0x75, 0xbc, 0xae, 0x6a, 0x41, 0x9c, 0xf9, 0xa0, 0x20, 0x78, 0xcf, 0x89, 0xf4, 0xd0, 0x56, 0x3b, 0x18, 0xd9, 0x58, 0x2a, 0xa4, 0x11, 0x60, 0xe3, 0x80, 0xca, 0x5a, 0x4b, /* (2^ 3)P */ 0x5d, 0x74, 0x29, 0x8c, 0x34, 0x32, 0x91, 0x32, 0xd7, 0x2f, 0x64, 0xe1, 0x16, 0xe6, 0xa2, 0xf4, 0x34, 0xbc, 0x67, 0xff, 0x03, 0xbb, 0x45, 0x1e, 0x4a, 0x9b, 0x2a, 0xf4, 0xd0, 0x12, 0x69, 0x30, /* (2^ 4)P */ 0x54, 0x71, 0xaf, 0xe6, 0x07, 0x65, 0x88, 0xff, 0x2f, 0xc8, 0xee, 0xdf, 0x13, 0x0e, 0xf5, 0x04, 0xce, 0xb5, 0xba, 0x2a, 0xe8, 0x2f, 0x51, 0xaa, 0x22, 0xf2, 0xd5, 0x68, 0x1a, 0x25, 0x4e, 0x17, /* (2^ 5)P */ 0x98, 0x88, 0x02, 0x82, 0x0d, 0x70, 0x96, 0xcf, 0xc5, 0x02, 0x2c, 0x0a, 0x37, 0xe3, 0x43, 0x17, 0xaa, 0x6e, 0xe8, 0xb4, 0x98, 0xec, 0x9e, 0x37, 0x2e, 0x48, 0xe0, 0x51, 0x8a, 0x88, 0x59, 0x0c, /* (2^ 6)P */ 0x89, 0xd1, 0xb5, 0x99, 0xd6, 0xf1, 0xcb, 0xfb, 0x84, 0xdc, 0x9f, 0x8e, 0xd5, 0xf0, 0xae, 0xac, 0x14, 0x76, 0x1f, 0x23, 0x06, 0x0d, 0xc2, 0xc1, 0x72, 0xf9, 0x74, 0xa2, 0x8d, 0x21, 0x38, 0x29, /* (2^ 7)P */ 0x18, 0x7f, 0x1d, 0xff, 0xbe, 0x49, 0xaf, 0xf6, 0xc2, 0xc9, 0x7a, 0x38, 0x22, 0x1c, 0x54, 0xcc, 0x6b, 0xc5, 0x15, 0x40, 0xef, 0xc9, 0xfc, 0x96, 0xa9, 0x13, 0x09, 0x69, 0x7c, 0x62, 0xc1, 0x69, /* (2^ 8)P */ 0x0e, 0xdb, 0x33, 0x47, 0x2f, 0xfd, 0x86, 0x7a, 0xe9, 0x7d, 0x08, 0x9e, 0xf2, 0xc4, 0xb8, 0xfd, 0x29, 0xa2, 0xa2, 0x8e, 0x1a, 0x4b, 0x5e, 0x09, 0x79, 0x7a, 0xb3, 0x29, 0xc8, 0xa7, 0xd7, 0x1a, /* (2^ 9)P */ 0xc0, 0xa0, 0x7e, 0xd1, 0xca, 0x89, 0x2d, 0x34, 0x51, 0x20, 0xed, 0xcc, 0xa6, 0xdd, 0xbe, 0x67, 0x74, 0x2f, 0xb4, 0x2b, 0xbf, 0x31, 0xca, 0x19, 0xbb, 0xac, 0x80, 0x49, 0xc8, 0xb4, 0xf7, 0x3d, /* (2^ 10)P */ 0x83, 0xd8, 0x0a, 0xc8, 0x4d, 0x44, 0xc6, 0xa8, 0x85, 0xab, 0xe3, 0x66, 0x03, 0x44, 0x1e, 0xb9, 0xd8, 0xf6, 0x64, 0x01, 0xa0, 0xcd, 0x15, 0xc2, 0x68, 0xe6, 0x47, 0xf2, 0x6e, 0x7c, 0x86, 0x3d, /* (2^ 11)P */ 0x8c, 0x65, 0x3e, 0xcc, 0x2b, 0x58, 0xdd, 0xc7, 0x28, 0x55, 0x0e, 0xee, 0x48, 0x47, 0x2c, 0xfd, 0x71, 0x4f, 0x9f, 0xcc, 0x95, 0x9b, 0xfd, 0xa0, 0xdf, 0x5d, 0x67, 0xb0, 0x71, 0xd8, 0x29, 0x75, /* (2^ 12)P */ 0x78, 0xbd, 0x3c, 0x2d, 0xb4, 0x68, 0xf5, 0xb8, 0x82, 0xda, 0xf3, 0x91, 0x1b, 0x01, 0x33, 0x12, 0x62, 0x3b, 0x7c, 0x4a, 0xcd, 0x6c, 0xce, 0x2d, 0x03, 0x86, 0x49, 0x9e, 0x8e, 0xfc, 0xe7, 0x75, /* (2^ 13)P */ 0xec, 0xb6, 0xd0, 0xfc, 0xf1, 0x13, 0x4f, 0x2f, 0x45, 0x7a, 0xff, 0x29, 0x1f, 0xca, 0xa8, 0xf1, 0x9b, 0xe2, 0x81, 0x29, 0xa7, 0xc1, 0x49, 0xc2, 0x6a, 0xb5, 0x83, 0x8c, 0xbb, 0x0d, 0xbe, 0x6e, /* (2^ 14)P */ 0x22, 0xb2, 0x0b, 0x17, 0x8d, 0xfa, 0x14, 0x71, 0x5f, 0x93, 0x93, 0xbf, 0xd5, 0xdc, 0xa2, 0x65, 0x9a, 0x97, 0x9c, 0xb5, 0x68, 0x1f, 0xc4, 0xbd, 0x89, 0x92, 0xce, 0xa2, 0x79, 0xef, 0x0e, 0x2f, /* (2^ 15)P */ 0xce, 0x37, 0x3c, 0x08, 0x0c, 0xbf, 0xec, 0x42, 0x22, 0x63, 0x49, 0xec, 0x09, 0xbc, 0x30, 0x29, 0x0d, 0xac, 0xfe, 0x9c, 0xc1, 0xb0, 0x94, 0xf2, 0x80, 0xbb, 0xfa, 0xed, 0x4b, 0xaa, 0x80, 0x37, /* (2^ 16)P */ 0x29, 0xd9, 0xea, 0x7c, 0x3e, 0x7d, 0xc1, 0x56, 0xc5, 0x22, 0x57, 0x2e, 0xeb, 0x4b, 0xcb, 0xe7, 0x5a, 0xe1, 0xbf, 0x2d, 0x73, 0x31, 0xe9, 0x0c, 0xf8, 0x52, 0x10, 0x62, 0xc7, 0x83, 0xb8, 0x41, /* (2^ 17)P */ 0x50, 0x53, 0xd2, 0xc3, 0xa0, 0x5c, 0xf7, 0xdb, 0x51, 0xe3, 0xb1, 0x6e, 0x08, 0xbe, 0x36, 0x29, 0x12, 0xb2, 0xa9, 0xb4, 0x3c, 0xe0, 0x36, 0xc9, 0xaa, 0x25, 0x22, 0x32, 0x82, 0xbf, 0x45, 0x1d, /* (2^ 18)P */ 0xc5, 0x4c, 0x02, 0x6a, 0x03, 0xb1, 0x1a, 0xe8, 0x72, 0x9a, 0x4c, 0x30, 0x1c, 0x20, 0x12, 0xe2, 0xfc, 0xb1, 0x32, 0x68, 0xba, 0x3f, 0xd7, 0xc5, 0x81, 0x95, 0x83, 0x4d, 0x5a, 0xdb, 0xff, 0x20, /* (2^ 19)P */ 0xad, 0x0f, 0x5d, 0xbe, 0x67, 0xd3, 0x83, 0xa2, 0x75, 0x44, 0x16, 0x8b, 0xca, 0x25, 0x2b, 0x6c, 0x2e, 0xf2, 0xaa, 0x7c, 0x46, 0x35, 0x49, 0x9d, 0x49, 0xff, 0x85, 0xee, 0x8e, 0x40, 0x66, 0x51, /* (2^ 20)P */ 0x61, 0xe3, 0xb4, 0xfa, 0xa2, 0xba, 0x67, 0x3c, 0xef, 0x5c, 0xf3, 0x7e, 0xc6, 0x33, 0xe4, 0xb3, 0x1c, 0x9b, 0x15, 0x41, 0x92, 0x72, 0x59, 0x52, 0x33, 0xab, 0xb0, 0xd5, 0x92, 0x18, 0x62, 0x6a, /* (2^ 21)P */ 0xcb, 0xcd, 0x55, 0x75, 0x38, 0x4a, 0xb7, 0x20, 0x3f, 0x92, 0x08, 0x12, 0x0e, 0xa1, 0x2a, 0x53, 0xd1, 0x1d, 0x28, 0x62, 0x77, 0x7b, 0xa1, 0xea, 0xbf, 0x44, 0x5c, 0xf0, 0x43, 0x34, 0xab, 0x61, /* (2^ 22)P */ 0xf8, 0xde, 0x24, 0x23, 0x42, 0x6c, 0x7a, 0x25, 0x7f, 0xcf, 0xe3, 0x17, 0x10, 0x6c, 0x1c, 0x13, 0x57, 0xa2, 0x30, 0xf6, 0x39, 0x87, 0x75, 0x23, 0x80, 0x85, 0xa7, 0x01, 0x7a, 0x40, 0x5a, 0x29, /* (2^ 23)P */ 0xd9, 0xa8, 0x5d, 0x6d, 0x24, 0x43, 0xc4, 0xf8, 0x5d, 0xfa, 0x52, 0x0c, 0x45, 0x75, 0xd7, 0x19, 0x3d, 0xf8, 0x1b, 0x73, 0x92, 0xfc, 0xfc, 0x2a, 0x00, 0x47, 0x2b, 0x1b, 0xe8, 0xc8, 0x10, 0x7d, /* (2^ 24)P */ 0x0b, 0xa2, 0xba, 0x70, 0x1f, 0x27, 0xe0, 0xc8, 0x57, 0x39, 0xa6, 0x7c, 0x86, 0x48, 0x37, 0x99, 0xbb, 0xd4, 0x7e, 0xcb, 0xb3, 0xef, 0x12, 0x54, 0x75, 0x29, 0xe6, 0x73, 0x61, 0xd3, 0x96, 0x31, /* (2^ 25)P */ 0xfc, 0xdf, 0xc7, 0x41, 0xd1, 0xca, 0x5b, 0xde, 0x48, 0xc8, 0x95, 0xb3, 0xd2, 0x8c, 0xcc, 0x47, 0xcb, 0xf3, 0x1a, 0xe1, 0x42, 0xd9, 0x4c, 0xa3, 0xc2, 0xce, 0x4e, 0xd0, 0xf2, 0xdb, 0x56, 0x02, /* (2^ 26)P */ 0x7f, 0x66, 0x0e, 0x4b, 0xe9, 0xb7, 0x5a, 0x87, 0x10, 0x0d, 0x85, 0xc0, 0x83, 0xdd, 0xd4, 0xca, 0x9f, 0xc7, 0x72, 0x4e, 0x8f, 0x2e, 0xf1, 0x47, 0x9b, 0xb1, 0x85, 0x8c, 0xbb, 0x87, 0x1a, 0x5f, /* (2^ 27)P */ 0xb8, 0x51, 0x7f, 0x43, 0xb6, 0xd0, 0xe9, 0x7a, 0x65, 0x90, 0x87, 0x18, 0x55, 0xce, 0xc7, 0x12, 0xee, 0x7a, 0xf7, 0x5c, 0xfe, 0x09, 0xde, 0x2a, 0x27, 0x56, 0x2c, 0x7d, 0x2f, 0x5a, 0xa0, 0x23, /* (2^ 28)P */ 0x9a, 0x16, 0x7c, 0xf1, 0x28, 0xe1, 0x08, 0x59, 0x2d, 0x85, 0xd0, 0x8a, 0xdd, 0x98, 0x74, 0xf7, 0x64, 0x2f, 0x10, 0xab, 0xce, 0xc4, 0xb4, 0x74, 0x45, 0x98, 0x13, 0x10, 0xdd, 0xba, 0x3a, 0x18, /* (2^ 29)P */ 0xac, 0xaa, 0x92, 0xaa, 0x8d, 0xba, 0x65, 0xb1, 0x05, 0x67, 0x38, 0x99, 0x95, 0xef, 0xc5, 0xd5, 0xd1, 0x40, 0xfc, 0xf8, 0x0c, 0x8f, 0x2f, 0xbe, 0x14, 0x45, 0x20, 0xee, 0x35, 0xe6, 0x01, 0x27, /* (2^ 30)P */ 0x14, 0x65, 0x15, 0x20, 0x00, 0xa8, 0x9f, 0x62, 0xce, 0xc1, 0xa8, 0x64, 0x87, 0x86, 0x23, 0xf2, 0x0e, 0x06, 0x3f, 0x0b, 0xff, 0x4f, 0x89, 0x5b, 0xfa, 0xa3, 0x08, 0xf7, 0x4c, 0x94, 0xd9, 0x60, /* (2^ 31)P */ 0x1f, 0x20, 0x7a, 0x1c, 0x1a, 0x00, 0xea, 0xae, 0x63, 0xce, 0xe2, 0x3e, 0x63, 0x6a, 0xf1, 0xeb, 0xe1, 0x07, 0x7a, 0x4c, 0x59, 0x09, 0x77, 0x6f, 0xcb, 0x08, 0x02, 0x0d, 0x15, 0x58, 0xb9, 0x79, /* (2^ 32)P */ 0xe7, 0x10, 0xd4, 0x01, 0x53, 0x5e, 0xb5, 0x24, 0x4d, 0xc8, 0xfd, 0xf3, 0xdf, 0x4e, 0xa3, 0xe3, 0xd8, 0x32, 0x40, 0x90, 0xe4, 0x68, 0x87, 0xd8, 0xec, 0xae, 0x3a, 0x7b, 0x42, 0x84, 0x13, 0x13, /* (2^ 33)P */ 0x14, 0x4f, 0x23, 0x86, 0x12, 0xe5, 0x05, 0x84, 0x29, 0xc5, 0xb4, 0xad, 0x39, 0x47, 0xdc, 0x14, 0xfd, 0x4f, 0x63, 0x50, 0xb2, 0xb5, 0xa2, 0xb8, 0x93, 0xff, 0xa7, 0xd8, 0x4a, 0xa9, 0xe2, 0x2f, /* (2^ 34)P */ 0xdd, 0xfa, 0x43, 0xe8, 0xef, 0x57, 0x5c, 0xec, 0x18, 0x99, 0xbb, 0xf0, 0x40, 0xce, 0x43, 0x28, 0x05, 0x63, 0x3d, 0xcf, 0xd6, 0x61, 0xb5, 0xa4, 0x7e, 0x77, 0xfb, 0xe8, 0xbd, 0x29, 0x36, 0x74, /* (2^ 35)P */ 0x8f, 0x73, 0xaf, 0xbb, 0x46, 0xdd, 0x3e, 0x34, 0x51, 0xa6, 0x01, 0xb1, 0x28, 0x18, 0x98, 0xed, 0x7a, 0x79, 0x2c, 0x88, 0x0b, 0x76, 0x01, 0xa4, 0x30, 0x87, 0xc8, 0x8d, 0xe2, 0x23, 0xc2, 0x1f, /* (2^ 36)P */ 0x0e, 0xba, 0x0f, 0xfc, 0x91, 0x4e, 0x60, 0x48, 0xa4, 0x6f, 0x2c, 0x05, 0x8f, 0xf7, 0x37, 0xb6, 0x9c, 0x23, 0xe9, 0x09, 0x3d, 0xac, 0xcc, 0x91, 0x7c, 0x68, 0x7a, 0x43, 0xd4, 0xee, 0xf7, 0x23, /* (2^ 37)P */ 0x00, 0xd8, 0x9b, 0x8d, 0x11, 0xb1, 0x73, 0x51, 0xa7, 0xd4, 0x89, 0x31, 0xb6, 0x41, 0xd6, 0x29, 0x86, 0xc5, 0xbb, 0x88, 0x79, 0x17, 0xbf, 0xfd, 0xf5, 0x1d, 0xd8, 0xca, 0x4f, 0x89, 0x59, 0x29, /* (2^ 38)P */ 0x99, 0xc8, 0xbb, 0xb4, 0xf3, 0x8e, 0xbc, 0xae, 0xb9, 0x92, 0x69, 0xb2, 0x5a, 0x99, 0x48, 0x41, 0xfb, 0x2c, 0xf9, 0x34, 0x01, 0x0b, 0xe2, 0x24, 0xe8, 0xde, 0x05, 0x4a, 0x89, 0x58, 0xd1, 0x40, /* (2^ 39)P */ 0xf6, 0x76, 0xaf, 0x85, 0x11, 0x0b, 0xb0, 0x46, 0x79, 0x7a, 0x18, 0x73, 0x78, 0xc7, 0xba, 0x26, 0x5f, 0xff, 0x8f, 0xab, 0x95, 0xbf, 0xc0, 0x3d, 0xd7, 0x24, 0x55, 0x94, 0xd8, 0x8b, 0x60, 0x2a, /* (2^ 40)P */ 0x02, 0x63, 0x44, 0xbd, 0x88, 0x95, 0x44, 0x26, 0x9c, 0x43, 0x88, 0x03, 0x1c, 0xc2, 0x4b, 0x7c, 0xb2, 0x11, 0xbd, 0x83, 0xf3, 0xa4, 0x98, 0x8e, 0xb9, 0x76, 0xd8, 0xc9, 0x7b, 0x8d, 0x21, 0x26, /* (2^ 41)P */ 0x8a, 0x17, 0x7c, 0x99, 0x42, 0x15, 0x08, 0xe3, 0x6f, 0x60, 0xb6, 0x6f, 0xa8, 0x29, 0x2d, 0x3c, 0x74, 0x93, 0x27, 0xfa, 0x36, 0x77, 0x21, 0x5c, 0xfa, 0xb1, 0xfe, 0x4a, 0x73, 0x05, 0xde, 0x7d, /* (2^ 42)P */ 0xab, 0x2b, 0xd4, 0x06, 0x39, 0x0e, 0xf1, 0x3b, 0x9c, 0x64, 0x80, 0x19, 0x3e, 0x80, 0xf7, 0xe4, 0x7a, 0xbf, 0x95, 0x95, 0xf8, 0x3b, 0x05, 0xe6, 0x30, 0x55, 0x24, 0xda, 0x38, 0xaf, 0x4f, 0x39, /* (2^ 43)P */ 0xf4, 0x28, 0x69, 0x89, 0x58, 0xfb, 0x8e, 0x7a, 0x3c, 0x11, 0x6a, 0xcc, 0xe9, 0x78, 0xc7, 0xfb, 0x6f, 0x59, 0xaf, 0x30, 0xe3, 0x0c, 0x67, 0x72, 0xf7, 0x6c, 0x3d, 0x1d, 0xa8, 0x22, 0xf2, 0x48, /* (2^ 44)P */ 0xa7, 0xca, 0x72, 0x0d, 0x41, 0xce, 0x1f, 0xf0, 0x95, 0x55, 0x3b, 0x21, 0xc7, 0xec, 0x20, 0x5a, 0x83, 0x14, 0xfa, 0xc1, 0x65, 0x11, 0xc2, 0x7b, 0x41, 0xa7, 0xa8, 0x1d, 0xe3, 0x9a, 0xf8, 0x07, /* (2^ 45)P */ 0xf9, 0x0f, 0x83, 0xc6, 0xb4, 0xc2, 0xd2, 0x05, 0x93, 0x62, 0x31, 0xc6, 0x0f, 0x33, 0x3e, 0xd4, 0x04, 0xa9, 0xd3, 0x96, 0x0a, 0x59, 0xa5, 0xa5, 0xb6, 0x33, 0x53, 0xa6, 0x91, 0xdb, 0x5e, 0x70, /* (2^ 46)P */ 0xf7, 0xa5, 0xb9, 0x0b, 0x5e, 0xe1, 0x8e, 0x04, 0x5d, 0xaf, 0x0a, 0x9e, 0xca, 0xcf, 0x40, 0x32, 0x0b, 0xa4, 0xc4, 0xed, 0xce, 0x71, 0x4b, 0x8f, 0x6d, 0x4a, 0x54, 0xde, 0xa3, 0x0d, 0x1c, 0x62, /* (2^ 47)P */ 0x91, 0x40, 0x8c, 0xa0, 0x36, 0x28, 0x87, 0x92, 0x45, 0x14, 0xc9, 0x10, 0xb0, 0x75, 0x83, 0xce, 0x94, 0x63, 0x27, 0x4f, 0x52, 0xeb, 0x72, 0x8a, 0x35, 0x36, 0xc8, 0x7e, 0xfa, 0xfc, 0x67, 0x26, /* (2^ 48)P */ 0x2a, 0x75, 0xe8, 0x45, 0x33, 0x17, 0x4c, 0x7f, 0xa5, 0x79, 0x70, 0xee, 0xfe, 0x47, 0x1b, 0x06, 0x34, 0xff, 0x86, 0x9f, 0xfa, 0x9a, 0xdd, 0x25, 0x9c, 0xc8, 0x5d, 0x42, 0xf5, 0xce, 0x80, 0x37, /* (2^ 49)P */ 0xe9, 0xb4, 0x3b, 0x51, 0x5a, 0x03, 0x46, 0x1a, 0xda, 0x5a, 0x57, 0xac, 0x79, 0xf3, 0x1e, 0x3e, 0x50, 0x4b, 0xa2, 0x5f, 0x1c, 0x5f, 0x8c, 0xc7, 0x22, 0x9f, 0xfd, 0x34, 0x76, 0x96, 0x1a, 0x32, /* (2^ 50)P */ 0xfa, 0x27, 0x6e, 0x82, 0xb8, 0x07, 0x67, 0x94, 0xd0, 0x6f, 0x50, 0x4c, 0xd6, 0x84, 0xca, 0x3d, 0x36, 0x14, 0xe9, 0x75, 0x80, 0x21, 0x89, 0xc1, 0x84, 0x84, 0x3b, 0x9b, 0x16, 0x84, 0x92, 0x6d, /* (2^ 51)P */ 0xdf, 0x2d, 0x3f, 0x38, 0x40, 0xe8, 0x67, 0x3a, 0x75, 0x9b, 0x4f, 0x0c, 0xa3, 0xc9, 0xee, 0x33, 0x47, 0xef, 0x83, 0xa7, 0x6f, 0xc8, 0xc7, 0x3e, 0xc4, 0xfb, 0xc9, 0xba, 0x9f, 0x44, 0xec, 0x26, /* (2^ 52)P */ 0x7d, 0x9e, 0x9b, 0xa0, 0xcb, 0x38, 0x0f, 0x5c, 0x8c, 0x47, 0xa3, 0x62, 0xc7, 0x8c, 0x16, 0x81, 0x1c, 0x12, 0xfc, 0x06, 0xd3, 0xb0, 0x23, 0x3e, 0xdd, 0xdc, 0xef, 0xa5, 0xa0, 0x8a, 0x23, 0x5a, /* (2^ 53)P */ 0xff, 0x43, 0xea, 0xc4, 0x21, 0x61, 0xa2, 0x1b, 0xb5, 0x32, 0x88, 0x7c, 0x7f, 0xc7, 0xf8, 0x36, 0x9a, 0xf9, 0xdc, 0x0a, 0x0b, 0xea, 0xfb, 0x88, 0xf9, 0xeb, 0x5b, 0xc2, 0x8e, 0x93, 0xa9, 0x5c, /* (2^ 54)P */ 0xa0, 0xcd, 0xfc, 0x51, 0x5e, 0x6a, 0x43, 0xd5, 0x3b, 0x89, 0xcd, 0xc2, 0x97, 0x47, 0xbc, 0x1d, 0x08, 0x4a, 0x22, 0xd3, 0x65, 0x6a, 0x34, 0x19, 0x66, 0xf4, 0x9a, 0x9b, 0xe4, 0x34, 0x50, 0x0f, /* (2^ 55)P */ 0x6e, 0xb9, 0xe0, 0xa1, 0x67, 0x39, 0x3c, 0xf2, 0x88, 0x4d, 0x7a, 0x86, 0xfa, 0x08, 0x8b, 0xe5, 0x79, 0x16, 0x34, 0xa7, 0xc6, 0xab, 0x2f, 0xfb, 0x46, 0x69, 0x02, 0xb6, 0x1e, 0x38, 0x75, 0x2a, /* (2^ 56)P */ 0xac, 0x20, 0x94, 0xc1, 0xe4, 0x3b, 0x0a, 0xc8, 0xdc, 0xb6, 0xf2, 0x81, 0xc6, 0xf6, 0xb1, 0x66, 0x88, 0x33, 0xe9, 0x61, 0x67, 0x03, 0xf7, 0x7c, 0xc4, 0xa4, 0x60, 0xa6, 0xd8, 0xbb, 0xab, 0x25, /* (2^ 57)P */ 0x98, 0x51, 0xfd, 0x14, 0xba, 0x12, 0xea, 0x91, 0xa9, 0xff, 0x3c, 0x4a, 0xfc, 0x50, 0x49, 0x68, 0x28, 0xad, 0xf5, 0x30, 0x21, 0x84, 0x26, 0xf8, 0x41, 0xa4, 0x01, 0x53, 0xf7, 0x88, 0xa9, 0x3e, /* (2^ 58)P */ 0x6f, 0x8c, 0x5f, 0x69, 0x9a, 0x10, 0x78, 0xc9, 0xf3, 0xc3, 0x30, 0x05, 0x4a, 0xeb, 0x46, 0x17, 0x95, 0x99, 0x45, 0xb4, 0x77, 0x6d, 0x4d, 0x44, 0xc7, 0x5c, 0x4e, 0x05, 0x8c, 0x2b, 0x95, 0x75, /* (2^ 59)P */ 0xaa, 0xd6, 0xf4, 0x15, 0x79, 0x3f, 0x70, 0xa3, 0xd8, 0x47, 0x26, 0x2f, 0x20, 0x46, 0xc3, 0x66, 0x4b, 0x64, 0x1d, 0x81, 0xdf, 0x69, 0x14, 0xd0, 0x1f, 0xd7, 0xa5, 0x81, 0x7d, 0xa4, 0xfe, 0x77, /* (2^ 60)P */ 0x81, 0xa3, 0x7c, 0xf5, 0x9e, 0x52, 0xe9, 0xc5, 0x1a, 0x88, 0x2f, 0xce, 0xb9, 0xb4, 0xee, 0x6e, 0xd6, 0x9b, 0x00, 0xe8, 0x28, 0x1a, 0xe9, 0xb6, 0xec, 0x3f, 0xfc, 0x9a, 0x3e, 0xbe, 0x80, 0x4b, /* (2^ 61)P */ 0xc5, 0xd2, 0xae, 0x26, 0xc5, 0x73, 0x37, 0x7e, 0x9d, 0xa4, 0xc9, 0x53, 0xb4, 0xfc, 0x4a, 0x1b, 0x4d, 0xb2, 0xff, 0xba, 0xd7, 0xbd, 0x20, 0xa9, 0x0e, 0x40, 0x2d, 0x12, 0x9f, 0x69, 0x54, 0x7c, /* (2^ 62)P */ 0xc8, 0x4b, 0xa9, 0x4f, 0xe1, 0xc8, 0x46, 0xef, 0x5e, 0xed, 0x52, 0x29, 0xce, 0x74, 0xb0, 0xe0, 0xd5, 0x85, 0xd8, 0xdb, 0xe1, 0x50, 0xa4, 0xbe, 0x2c, 0x71, 0x0f, 0x32, 0x49, 0x86, 0xb6, 0x61, /* (2^ 63)P */ 0xd1, 0xbd, 0xcc, 0x09, 0x73, 0x5f, 0x48, 0x8a, 0x2d, 0x1a, 0x4d, 0x7d, 0x0d, 0x32, 0x06, 0xbd, 0xf4, 0xbe, 0x2d, 0x32, 0x73, 0x29, 0x23, 0x25, 0x70, 0xf7, 0x17, 0x8c, 0x75, 0xc4, 0x5d, 0x44, /* (2^ 64)P */ 0x3c, 0x93, 0xc8, 0x7c, 0x17, 0x34, 0x04, 0xdb, 0x9f, 0x05, 0xea, 0x75, 0x21, 0xe8, 0x6f, 0xed, 0x34, 0xdb, 0x53, 0xc0, 0xfd, 0xbe, 0xfe, 0x1e, 0x99, 0xaf, 0x5d, 0xc6, 0x67, 0xe8, 0xdb, 0x4a, /* (2^ 65)P */ 0xdf, 0x09, 0x06, 0xa9, 0xa2, 0x71, 0xcd, 0x3a, 0x50, 0x40, 0xd0, 0x6d, 0x85, 0x91, 0xe9, 0xe5, 0x3c, 0xc2, 0x57, 0x81, 0x68, 0x9b, 0xc6, 0x1e, 0x4d, 0xfe, 0x5c, 0x88, 0xf6, 0x27, 0x74, 0x69, /* (2^ 66)P */ 0x51, 0xa8, 0xe1, 0x65, 0x9b, 0x7b, 0xbe, 0xd7, 0xdd, 0x36, 0xc5, 0x22, 0xd5, 0x28, 0x3d, 0xa0, 0x45, 0xb6, 0xd2, 0x8f, 0x65, 0x9d, 0x39, 0x28, 0xe1, 0x41, 0x26, 0x7c, 0xe1, 0xb7, 0xe5, 0x49, /* (2^ 67)P */ 0xa4, 0x57, 0x04, 0x70, 0x98, 0x3a, 0x8c, 0x6f, 0x78, 0x67, 0xbb, 0x5e, 0xa2, 0xf0, 0x78, 0x50, 0x0f, 0x96, 0x82, 0xc3, 0xcb, 0x3c, 0x3c, 0xd1, 0xb1, 0x84, 0xdf, 0xa7, 0x58, 0x32, 0x00, 0x2e, /* (2^ 68)P */ 0x1c, 0x6a, 0x29, 0xe6, 0x9b, 0xf3, 0xd1, 0x8a, 0xb2, 0xbf, 0x5f, 0x2a, 0x65, 0xaa, 0xee, 0xc1, 0xcb, 0xf3, 0x26, 0xfd, 0x73, 0x06, 0xee, 0x33, 0xcc, 0x2c, 0x9d, 0xa6, 0x73, 0x61, 0x25, 0x59, /* (2^ 69)P */ 0x41, 0xfc, 0x18, 0x4e, 0xaa, 0x07, 0xea, 0x41, 0x1e, 0xa5, 0x87, 0x7c, 0x52, 0x19, 0xfc, 0xd9, 0x6f, 0xca, 0x31, 0x58, 0x80, 0xcb, 0xaa, 0xbd, 0x4f, 0x69, 0x16, 0xc9, 0x2d, 0x65, 0x5b, 0x44, /* (2^ 70)P */ 0x15, 0x23, 0x17, 0xf2, 0xa7, 0xa3, 0x92, 0xce, 0x64, 0x99, 0x1b, 0xe1, 0x2d, 0x28, 0xdc, 0x1e, 0x4a, 0x31, 0x4c, 0xe0, 0xaf, 0x3a, 0x82, 0xa1, 0x86, 0xf5, 0x7c, 0x43, 0x94, 0x2d, 0x0a, 0x79, /* (2^ 71)P */ 0x09, 0xe0, 0xf6, 0x93, 0xfb, 0x47, 0xc4, 0x71, 0x76, 0x52, 0x84, 0x22, 0x67, 0xa5, 0x22, 0x89, 0x69, 0x51, 0x4f, 0x20, 0x3b, 0x90, 0x70, 0xbf, 0xfe, 0x19, 0xa3, 0x1b, 0x89, 0x89, 0x7a, 0x2f, /* (2^ 72)P */ 0x0c, 0x14, 0xe2, 0x77, 0xb5, 0x8e, 0xa0, 0x02, 0xf4, 0xdc, 0x7b, 0x42, 0xd4, 0x4e, 0x9a, 0xed, 0xd1, 0x3c, 0x32, 0xe4, 0x44, 0xec, 0x53, 0x52, 0x5b, 0x35, 0xe9, 0x14, 0x3c, 0x36, 0x88, 0x3e, /* (2^ 73)P */ 0x8c, 0x0b, 0x11, 0x77, 0x42, 0xc1, 0x66, 0xaa, 0x90, 0x33, 0xa2, 0x10, 0x16, 0x39, 0xe0, 0x1a, 0xa2, 0xc2, 0x3f, 0xc9, 0x12, 0xbd, 0x30, 0x20, 0xab, 0xc7, 0x55, 0x95, 0x57, 0x41, 0xe1, 0x3e, /* (2^ 74)P */ 0x41, 0x7d, 0x6e, 0x6d, 0x3a, 0xde, 0x14, 0x92, 0xfe, 0x7e, 0xf1, 0x07, 0x86, 0xd8, 0xcd, 0x3c, 0x17, 0x12, 0xe1, 0xf8, 0x88, 0x12, 0x4f, 0x67, 0xd0, 0x93, 0x9f, 0x32, 0x0f, 0x25, 0x82, 0x56, /* (2^ 75)P */ 0x6e, 0x39, 0x2e, 0x6d, 0x13, 0x0b, 0xf0, 0x6c, 0xbf, 0xde, 0x14, 0x10, 0x6f, 0xf8, 0x4c, 0x6e, 0x83, 0x4e, 0xcc, 0xbf, 0xb5, 0xb1, 0x30, 0x59, 0xb6, 0x16, 0xba, 0x8a, 0xb4, 0x69, 0x70, 0x04, /* (2^ 76)P */ 0x93, 0x07, 0xb2, 0x69, 0xab, 0xe4, 0x4c, 0x0d, 0x9e, 0xfb, 0xd0, 0x97, 0x1a, 0xb9, 0x4d, 0xb2, 0x1d, 0xd0, 0x00, 0x4e, 0xf5, 0x50, 0xfa, 0xcd, 0xb5, 0xdd, 0x8b, 0x36, 0x85, 0x10, 0x1b, 0x22, /* (2^ 77)P */ 0xd2, 0xd8, 0xe3, 0xb1, 0x68, 0x94, 0xe5, 0xe7, 0x93, 0x2f, 0x12, 0xbd, 0x63, 0x65, 0xc5, 0x53, 0x09, 0x3f, 0x66, 0xe0, 0x03, 0xa9, 0xe8, 0xee, 0x42, 0x3d, 0xbe, 0xcb, 0x62, 0xa6, 0xef, 0x61, /* (2^ 78)P */ 0x2a, 0xab, 0x6e, 0xde, 0xdd, 0xdd, 0xf8, 0x2c, 0x31, 0xf2, 0x35, 0x14, 0xd5, 0x0a, 0xf8, 0x9b, 0x73, 0x49, 0xf0, 0xc9, 0xce, 0xda, 0xea, 0x5d, 0x27, 0x9b, 0xd2, 0x41, 0x5d, 0x5b, 0x27, 0x29, /* (2^ 79)P */ 0x4f, 0xf1, 0xeb, 0x95, 0x08, 0x0f, 0xde, 0xcf, 0xa7, 0x05, 0x49, 0x05, 0x6b, 0xb9, 0xaa, 0xb9, 0xfd, 0x20, 0xc4, 0xa1, 0xd9, 0x0d, 0xe8, 0xca, 0xc7, 0xbb, 0x73, 0x16, 0x2f, 0xbf, 0x63, 0x0a, /* (2^ 80)P */ 0x8c, 0xbc, 0x8f, 0x95, 0x11, 0x6e, 0x2f, 0x09, 0xad, 0x2f, 0x82, 0x04, 0xe8, 0x81, 0x2a, 0x67, 0x17, 0x25, 0xd5, 0x60, 0x15, 0x35, 0xc8, 0xca, 0xf8, 0x92, 0xf1, 0xc8, 0x22, 0x77, 0x3f, 0x6f, /* (2^ 81)P */ 0xb7, 0x94, 0xe8, 0xc2, 0xcc, 0x90, 0xba, 0xf8, 0x0d, 0x9f, 0xff, 0x38, 0xa4, 0x57, 0x75, 0x2c, 0x59, 0x23, 0xe5, 0x5a, 0x85, 0x1d, 0x4d, 0x89, 0x69, 0x3d, 0x74, 0x7b, 0x15, 0x22, 0xe1, 0x68, /* (2^ 82)P */ 0xf3, 0x19, 0xb9, 0xcf, 0x70, 0x55, 0x7e, 0xd8, 0xb9, 0x8d, 0x79, 0x95, 0xcd, 0xde, 0x2c, 0x3f, 0xce, 0xa2, 0xc0, 0x10, 0x47, 0x15, 0x21, 0x21, 0xb2, 0xc5, 0x6d, 0x24, 0x15, 0xa1, 0x66, 0x3c, /* (2^ 83)P */ 0x72, 0xcb, 0x4e, 0x29, 0x62, 0xc5, 0xed, 0xcb, 0x16, 0x0b, 0x28, 0x6a, 0xc3, 0x43, 0x71, 0xba, 0x67, 0x8b, 0x07, 0xd4, 0xef, 0xc2, 0x10, 0x96, 0x1e, 0x4b, 0x6a, 0x94, 0x5d, 0x73, 0x44, 0x61, /* (2^ 84)P */ 0x50, 0x33, 0x5b, 0xd7, 0x1e, 0x11, 0x6f, 0x53, 0x1b, 0xd8, 0x41, 0x20, 0x8c, 0xdb, 0x11, 0x02, 0x3c, 0x41, 0x10, 0x0e, 0x00, 0xb1, 0x3c, 0xf9, 0x76, 0x88, 0x9e, 0x03, 0x3c, 0xfd, 0x9d, 0x14, /* (2^ 85)P */ 0x5b, 0x15, 0x63, 0x6b, 0xe4, 0xdd, 0x79, 0xd4, 0x76, 0x79, 0x83, 0x3c, 0xe9, 0x15, 0x6e, 0xb6, 0x38, 0xe0, 0x13, 0x1f, 0x3b, 0xe4, 0xfd, 0xda, 0x35, 0x0b, 0x4b, 0x2e, 0x1a, 0xda, 0xaf, 0x5f, /* (2^ 86)P */ 0x81, 0x75, 0x19, 0x17, 0xdf, 0xbb, 0x00, 0x36, 0xc2, 0xd2, 0x3c, 0xbe, 0x0b, 0x05, 0x72, 0x39, 0x86, 0xbe, 0xd5, 0xbd, 0x6d, 0x90, 0x38, 0x59, 0x0f, 0x86, 0x9b, 0x3f, 0xe4, 0xe5, 0xfc, 0x34, /* (2^ 87)P */ 0x02, 0x4d, 0xd1, 0x42, 0xcd, 0xa4, 0xa8, 0x75, 0x65, 0xdf, 0x41, 0x34, 0xc5, 0xab, 0x8d, 0x82, 0xd3, 0x31, 0xe1, 0xd2, 0xed, 0xab, 0xdc, 0x33, 0x5f, 0xd2, 0x14, 0xb8, 0x6f, 0xd7, 0xba, 0x3e, /* (2^ 88)P */ 0x0f, 0xe1, 0x70, 0x6f, 0x56, 0x6f, 0x90, 0xd4, 0x5a, 0x0f, 0x69, 0x51, 0xaa, 0xf7, 0x12, 0x5d, 0xf2, 0xfc, 0xce, 0x76, 0x6e, 0xb1, 0xad, 0x45, 0x99, 0x29, 0x23, 0xad, 0xae, 0x68, 0xf7, 0x01, /* (2^ 89)P */ 0xbd, 0xfe, 0x48, 0x62, 0x7b, 0xc7, 0x6c, 0x2b, 0xfd, 0xaf, 0x3a, 0xec, 0x28, 0x06, 0xd3, 0x3c, 0x6a, 0x48, 0xef, 0xd4, 0x80, 0x0b, 0x1c, 0xce, 0x23, 0x6c, 0xf6, 0xa6, 0x2e, 0xff, 0x3b, 0x4c, /* (2^ 90)P */ 0x5f, 0xeb, 0xea, 0x4a, 0x09, 0xc4, 0x2e, 0x3f, 0xa7, 0x2c, 0x37, 0x6e, 0x28, 0x9b, 0xb1, 0x61, 0x1d, 0x70, 0x2a, 0xde, 0x66, 0xa9, 0xef, 0x5e, 0xef, 0xe3, 0x55, 0xde, 0x65, 0x05, 0xb2, 0x23, /* (2^ 91)P */ 0x57, 0x85, 0xd5, 0x79, 0x52, 0xca, 0x01, 0xe3, 0x4f, 0x87, 0xc2, 0x27, 0xce, 0xd4, 0xb2, 0x07, 0x67, 0x1d, 0xcf, 0x9d, 0x8a, 0xcd, 0x32, 0xa5, 0x56, 0xff, 0x2b, 0x3f, 0xe2, 0xfe, 0x52, 0x2a, /* (2^ 92)P */ 0x3d, 0x66, 0xd8, 0x7c, 0xb3, 0xef, 0x24, 0x86, 0x94, 0x75, 0xbd, 0xff, 0x20, 0xac, 0xc7, 0xbb, 0x45, 0x74, 0xd3, 0x82, 0x9c, 0x5e, 0xb8, 0x57, 0x66, 0xec, 0xa6, 0x86, 0xcb, 0x52, 0x30, 0x7b, /* (2^ 93)P */ 0x1e, 0xe9, 0x25, 0x25, 0xad, 0xf0, 0x82, 0x34, 0xa0, 0xdc, 0x8e, 0xd2, 0x43, 0x80, 0xb6, 0x2c, 0x3a, 0x00, 0x1b, 0x2e, 0x05, 0x6d, 0x4f, 0xaf, 0x0a, 0x1b, 0x78, 0x29, 0x25, 0x8c, 0x5f, 0x18, /* (2^ 94)P */ 0xd6, 0xe0, 0x0c, 0xd8, 0x5b, 0xde, 0x41, 0xaa, 0xd6, 0xe9, 0x53, 0x68, 0x41, 0xb2, 0x07, 0x94, 0x3a, 0x4c, 0x7f, 0x35, 0x6e, 0xc3, 0x3e, 0x56, 0xce, 0x7b, 0x29, 0x0e, 0xdd, 0xb8, 0xc4, 0x4c, /* (2^ 95)P */ 0x0e, 0x73, 0xb8, 0xff, 0x52, 0x1a, 0xfc, 0xa2, 0x37, 0x8e, 0x05, 0x67, 0x6e, 0xf1, 0x11, 0x18, 0xe1, 0x4e, 0xdf, 0xcd, 0x66, 0xa3, 0xf9, 0x10, 0x99, 0xf0, 0xb9, 0xa0, 0xc4, 0xa0, 0xf4, 0x72, /* (2^ 96)P */ 0xa7, 0x4e, 0x3f, 0x66, 0x6f, 0xc0, 0x16, 0x8c, 0xba, 0x0f, 0x97, 0x4e, 0xf7, 0x3a, 0x3b, 0x69, 0x45, 0xc3, 0x9e, 0xd6, 0xf1, 0xe7, 0x02, 0x21, 0x89, 0x80, 0x8a, 0x96, 0xbc, 0x3c, 0xa5, 0x0b, /* (2^ 97)P */ 0x37, 0x55, 0xa1, 0xfe, 0xc7, 0x9d, 0x3d, 0xca, 0x93, 0x64, 0x53, 0x51, 0xbb, 0x24, 0x68, 0x4c, 0xb1, 0x06, 0x40, 0x84, 0x14, 0x63, 0x88, 0xb9, 0x60, 0xcc, 0x54, 0xb4, 0x2a, 0xa7, 0xd2, 0x40, /* (2^ 98)P */ 0x75, 0x09, 0x57, 0x12, 0xb7, 0xa1, 0x36, 0x59, 0x57, 0xa6, 0xbd, 0xde, 0x48, 0xd6, 0xb9, 0x91, 0xea, 0x30, 0x43, 0xb6, 0x4b, 0x09, 0x44, 0x33, 0xd0, 0x51, 0xee, 0x12, 0x0d, 0xa1, 0x6b, 0x00, /* (2^ 99)P */ 0x58, 0x5d, 0xde, 0xf5, 0x68, 0x84, 0x22, 0x19, 0xb0, 0x05, 0xcc, 0x38, 0x4c, 0x2f, 0xb1, 0x0e, 0x90, 0x19, 0x60, 0xd5, 0x9d, 0x9f, 0x03, 0xa1, 0x0b, 0x0e, 0xff, 0x4f, 0xce, 0xd4, 0x02, 0x45, /* (2^100)P */ 0x89, 0xc1, 0x37, 0x68, 0x10, 0x54, 0x20, 0xeb, 0x3c, 0xb9, 0xd3, 0x6d, 0x4c, 0x54, 0xf6, 0xd0, 0x4f, 0xd7, 0x16, 0xc4, 0x64, 0x70, 0x72, 0x40, 0xf0, 0x2e, 0x50, 0x4b, 0x11, 0xc6, 0x15, 0x6e, /* (2^101)P */ 0x6b, 0xa7, 0xb1, 0xcf, 0x98, 0xa3, 0xf2, 0x4d, 0xb1, 0xf6, 0xf2, 0x19, 0x74, 0x6c, 0x25, 0x11, 0x43, 0x60, 0x6e, 0x06, 0x62, 0x79, 0x49, 0x4a, 0x44, 0x5b, 0x35, 0x41, 0xab, 0x3a, 0x5b, 0x70, /* (2^102)P */ 0xd8, 0xb1, 0x97, 0xd7, 0x36, 0xf5, 0x5e, 0x36, 0xdb, 0xf0, 0xdd, 0x22, 0xd6, 0x6b, 0x07, 0x00, 0x88, 0x5a, 0x57, 0xe0, 0xb0, 0x33, 0xbf, 0x3b, 0x4d, 0xca, 0xe4, 0xc8, 0x05, 0xaa, 0x77, 0x37, /* (2^103)P */ 0x5f, 0xdb, 0x78, 0x55, 0xc8, 0x45, 0x27, 0x39, 0xe2, 0x5a, 0xae, 0xdb, 0x49, 0x41, 0xda, 0x6f, 0x67, 0x98, 0xdc, 0x8a, 0x0b, 0xb0, 0xf0, 0xb1, 0xa3, 0x1d, 0x6f, 0xd3, 0x37, 0x34, 0x96, 0x09, /* (2^104)P */ 0x53, 0x38, 0xdc, 0xa5, 0x90, 0x4e, 0x82, 0x7e, 0xbd, 0x5c, 0x13, 0x1f, 0x64, 0xf6, 0xb5, 0xcc, 0xcc, 0x8f, 0xce, 0x87, 0x6c, 0xd8, 0x36, 0x67, 0x9f, 0x24, 0x04, 0x66, 0xe2, 0x3c, 0x5f, 0x62, /* (2^105)P */ 0x3f, 0xf6, 0x02, 0x95, 0x05, 0xc8, 0x8a, 0xaf, 0x69, 0x14, 0x35, 0x2e, 0x0a, 0xe7, 0x05, 0x0c, 0x05, 0x63, 0x4b, 0x76, 0x9c, 0x2e, 0x29, 0x35, 0xc3, 0x3a, 0xe2, 0xc7, 0x60, 0x43, 0x39, 0x1a, /* (2^106)P */ 0x64, 0x32, 0x18, 0x51, 0x32, 0xd5, 0xc6, 0xd5, 0x4f, 0xb7, 0xc2, 0x43, 0xbd, 0x5a, 0x06, 0x62, 0x9b, 0x3f, 0x97, 0x3b, 0xd0, 0xf5, 0xfb, 0xb5, 0x5e, 0x6e, 0x20, 0x61, 0x36, 0xda, 0xa3, 0x13, /* (2^107)P */ 0xe5, 0x94, 0x5d, 0x72, 0x37, 0x58, 0xbd, 0xc6, 0xc5, 0x16, 0x50, 0x20, 0x12, 0x09, 0xe3, 0x18, 0x68, 0x3c, 0x03, 0x70, 0x15, 0xce, 0x88, 0x20, 0x87, 0x79, 0x83, 0x5c, 0x49, 0x1f, 0xba, 0x7f, /* (2^108)P */ 0x9d, 0x07, 0xf9, 0xf2, 0x23, 0x74, 0x8c, 0x5a, 0xc5, 0x3f, 0x02, 0x34, 0x7b, 0x15, 0x35, 0x17, 0x51, 0xb3, 0xfa, 0xd2, 0x9a, 0xb4, 0xf9, 0xe4, 0x3c, 0xe3, 0x78, 0xc8, 0x72, 0xff, 0x91, 0x66, /* (2^109)P */ 0x3e, 0xff, 0x5e, 0xdc, 0xde, 0x2a, 0x2c, 0x12, 0xf4, 0x6c, 0x95, 0xd8, 0xf1, 0x4b, 0xdd, 0xf8, 0xda, 0x5b, 0x9e, 0x9e, 0x5d, 0x20, 0x86, 0xeb, 0x43, 0xc7, 0x75, 0xd9, 0xb9, 0x92, 0x9b, 0x04, /* (2^110)P */ 0x5a, 0xc0, 0xf6, 0xb0, 0x30, 0x97, 0x37, 0xa5, 0x53, 0xa5, 0xf3, 0xc6, 0xac, 0xff, 0xa0, 0x72, 0x6d, 0xcd, 0x0d, 0xb2, 0x34, 0x2c, 0x03, 0xb0, 0x4a, 0x16, 0xd5, 0x88, 0xbc, 0x9d, 0x0e, 0x47, /* (2^111)P */ 0x47, 0xc0, 0x37, 0xa2, 0x0c, 0xf1, 0x9c, 0xb1, 0xa2, 0x81, 0x6c, 0x1f, 0x71, 0x66, 0x54, 0xb6, 0x43, 0x0b, 0xd8, 0x6d, 0xd1, 0x1b, 0x32, 0xb3, 0x8e, 0xbe, 0x5f, 0x0c, 0x60, 0x4f, 0xc1, 0x48, /* (2^112)P */ 0x03, 0xc8, 0xa6, 0x4a, 0x26, 0x1c, 0x45, 0x66, 0xa6, 0x7d, 0xfa, 0xa4, 0x04, 0x39, 0x6e, 0xb6, 0x95, 0x83, 0x12, 0xb3, 0xb0, 0x19, 0x5f, 0xd4, 0x10, 0xbc, 0xc9, 0xc3, 0x27, 0x26, 0x60, 0x31, /* (2^113)P */ 0x0d, 0xe1, 0xe4, 0x32, 0x48, 0xdc, 0x20, 0x31, 0xf7, 0x17, 0xc7, 0x56, 0x67, 0xc4, 0x20, 0xeb, 0x94, 0x02, 0x28, 0x67, 0x3f, 0x2e, 0xf5, 0x00, 0x09, 0xc5, 0x30, 0x47, 0xc1, 0x4f, 0x6d, 0x56, /* (2^114)P */ 0x06, 0x72, 0x83, 0xfd, 0x40, 0x5d, 0x3a, 0x7e, 0x7a, 0x54, 0x59, 0x71, 0xdc, 0x26, 0xe9, 0xc1, 0x95, 0x60, 0x8d, 0xa6, 0xfb, 0x30, 0x67, 0x21, 0xa7, 0xce, 0x69, 0x3f, 0x84, 0xc3, 0xe8, 0x22, /* (2^115)P */ 0x2b, 0x4b, 0x0e, 0x93, 0xe8, 0x74, 0xd0, 0x33, 0x16, 0x58, 0xd1, 0x84, 0x0e, 0x35, 0xe4, 0xb6, 0x65, 0x23, 0xba, 0xd6, 0x6a, 0xc2, 0x34, 0x55, 0xf3, 0xf3, 0xf1, 0x89, 0x2f, 0xc1, 0x73, 0x77, /* (2^116)P */ 0xaa, 0x62, 0x79, 0xa5, 0x4d, 0x40, 0xba, 0x8c, 0x56, 0xce, 0x99, 0x19, 0xa8, 0x97, 0x98, 0x5b, 0xfc, 0x92, 0x16, 0x12, 0x2f, 0x86, 0x8e, 0x50, 0x91, 0xc2, 0x93, 0xa0, 0x7f, 0x90, 0x81, 0x3a, /* (2^117)P */ 0x10, 0xa5, 0x25, 0x47, 0xff, 0xd0, 0xde, 0x0d, 0x03, 0xc5, 0x3f, 0x67, 0x10, 0xcc, 0xd8, 0x10, 0x89, 0x4e, 0x1f, 0x9f, 0x1c, 0x15, 0x9d, 0x5b, 0x4c, 0xa4, 0x09, 0xcb, 0xd5, 0xc1, 0xa5, 0x32, /* (2^118)P */ 0xfb, 0x41, 0x05, 0xb9, 0x42, 0xa4, 0x0a, 0x1e, 0xdb, 0x85, 0xb4, 0xc1, 0x7c, 0xeb, 0x85, 0x5f, 0xe5, 0xf2, 0x9d, 0x8a, 0xce, 0x95, 0xe5, 0xbe, 0x36, 0x22, 0x42, 0x22, 0xc7, 0x96, 0xe4, 0x25, /* (2^119)P */ 0xb9, 0xe5, 0x0f, 0xcd, 0x46, 0x3c, 0xdf, 0x5e, 0x88, 0x33, 0xa4, 0xd2, 0x7e, 0x5a, 0xe7, 0x34, 0x52, 0xe3, 0x61, 0xd7, 0x11, 0xde, 0x88, 0xe4, 0x5c, 0x54, 0x85, 0xa0, 0x01, 0x8a, 0x87, 0x0e, /* (2^120)P */ 0x04, 0xbb, 0x21, 0xe0, 0x77, 0x3c, 0x49, 0xba, 0x9a, 0x89, 0xdf, 0xc7, 0x43, 0x18, 0x4d, 0x2b, 0x67, 0x0d, 0xe8, 0x7a, 0x48, 0x7a, 0xa3, 0x9e, 0x94, 0x17, 0xe4, 0x11, 0x80, 0x95, 0xa9, 0x67, /* (2^121)P */ 0x65, 0xb0, 0x97, 0x66, 0x1a, 0x05, 0x58, 0x4b, 0xd4, 0xa6, 0x6b, 0x8d, 0x7d, 0x3f, 0xe3, 0x47, 0xc1, 0x46, 0xca, 0x83, 0xd4, 0xa8, 0x4d, 0xbb, 0x0d, 0xdb, 0xc2, 0x81, 0xa1, 0xca, 0xbe, 0x68, /* (2^122)P */ 0xa5, 0x9a, 0x98, 0x0b, 0xe9, 0x80, 0x89, 0x8d, 0x9b, 0xc9, 0x93, 0x2c, 0x4a, 0xb1, 0x5e, 0xf9, 0xa2, 0x73, 0x6e, 0x79, 0xc4, 0xc7, 0xc6, 0x51, 0x69, 0xb5, 0xef, 0xb5, 0x63, 0x83, 0x22, 0x6e, /* (2^123)P */ 0xc8, 0x24, 0xd6, 0x2d, 0xb0, 0xc0, 0xbb, 0xc6, 0xee, 0x70, 0x81, 0xec, 0x7d, 0xb4, 0x7e, 0x77, 0xa9, 0xaf, 0xcf, 0x04, 0xa0, 0x15, 0xde, 0x3c, 0x9b, 0xbf, 0x60, 0x71, 0x08, 0xbc, 0xc6, 0x1d, /* (2^124)P */ 0x02, 0x40, 0xc3, 0xee, 0x43, 0xe0, 0x07, 0x2e, 0x7f, 0xdc, 0x68, 0x7a, 0x67, 0xfc, 0xe9, 0x18, 0x9a, 0x5b, 0xd1, 0x8b, 0x18, 0x03, 0xda, 0xd8, 0x53, 0x82, 0x56, 0x00, 0xbb, 0xc3, 0xfb, 0x48, /* (2^125)P */ 0xe1, 0x4c, 0x65, 0xfb, 0x4c, 0x7d, 0x54, 0x57, 0xad, 0xe2, 0x58, 0xa0, 0x82, 0x5b, 0x56, 0xd3, 0x78, 0x44, 0x15, 0xbf, 0x0b, 0xaf, 0x3e, 0xf6, 0x18, 0xbb, 0xdf, 0x14, 0xf1, 0x1e, 0x53, 0x47, /* (2^126)P */ 0x87, 0xc5, 0x78, 0x42, 0x0a, 0x63, 0xec, 0xe1, 0xf3, 0x83, 0x8e, 0xca, 0x46, 0xd5, 0x07, 0x55, 0x2b, 0x0c, 0xdc, 0x3a, 0xc6, 0x35, 0xe1, 0x85, 0x4e, 0x84, 0x82, 0x56, 0xa8, 0xef, 0xa7, 0x0a, /* (2^127)P */ 0x15, 0xf6, 0xe1, 0xb3, 0xa8, 0x1b, 0x69, 0x72, 0xfa, 0x3f, 0xbe, 0x1f, 0x70, 0xe9, 0xb4, 0x32, 0x68, 0x78, 0xbb, 0x39, 0x2e, 0xd9, 0xb6, 0x97, 0xe8, 0x39, 0x2e, 0xa0, 0xde, 0x53, 0xfe, 0x2c, /* (2^128)P */ 0xb0, 0x52, 0xcd, 0x85, 0xcd, 0x92, 0x73, 0x68, 0x31, 0x98, 0xe2, 0x10, 0xc9, 0x66, 0xff, 0x27, 0x06, 0x2d, 0x83, 0xa9, 0x56, 0x45, 0x13, 0x97, 0xa0, 0xf8, 0x84, 0x0a, 0x36, 0xb0, 0x9b, 0x26, /* (2^129)P */ 0x5c, 0xf8, 0x43, 0x76, 0x45, 0x55, 0x6e, 0x70, 0x1b, 0x7d, 0x59, 0x9b, 0x8c, 0xa4, 0x34, 0x37, 0x72, 0xa4, 0xef, 0xc6, 0xe8, 0x91, 0xee, 0x7a, 0xe0, 0xd9, 0xa9, 0x98, 0xc1, 0xab, 0xd6, 0x5c, /* (2^130)P */ 0x1a, 0xe4, 0x3c, 0xcb, 0x06, 0xde, 0x04, 0x0e, 0x38, 0xe1, 0x02, 0x34, 0x89, 0xeb, 0xc6, 0xd8, 0x72, 0x37, 0x6e, 0x68, 0xbb, 0x59, 0x46, 0x90, 0xc8, 0xa8, 0x6b, 0x74, 0x71, 0xc3, 0x15, 0x72, /* (2^131)P */ 0xd9, 0xa2, 0xe4, 0xea, 0x7e, 0xa9, 0x12, 0xfd, 0xc5, 0xf2, 0x94, 0x63, 0x51, 0xb7, 0x14, 0x95, 0x94, 0xf2, 0x08, 0x92, 0x80, 0xd5, 0x6f, 0x26, 0xb9, 0x26, 0x9a, 0x61, 0x85, 0x70, 0x84, 0x5c, /* (2^132)P */ 0xea, 0x94, 0xd6, 0xfe, 0x10, 0x54, 0x98, 0x52, 0x54, 0xd2, 0x2e, 0x4a, 0x93, 0x5b, 0x90, 0x3c, 0x67, 0xe4, 0x3b, 0x2d, 0x69, 0x47, 0xbb, 0x10, 0xe1, 0xe9, 0xe5, 0x69, 0x2d, 0x3d, 0x3b, 0x06, /* (2^133)P */ 0xeb, 0x7d, 0xa5, 0xdd, 0xee, 0x26, 0x27, 0x47, 0x91, 0x18, 0xf4, 0x10, 0xae, 0xc4, 0xb6, 0xef, 0x14, 0x76, 0x30, 0x7b, 0x91, 0x41, 0x16, 0x2b, 0x7c, 0x5b, 0xf4, 0xc4, 0x4f, 0x55, 0x7c, 0x11, /* (2^134)P */ 0x12, 0x88, 0x9d, 0x8f, 0x11, 0xf3, 0x7c, 0xc0, 0x39, 0x79, 0x01, 0x50, 0x20, 0xd8, 0xdb, 0x01, 0x27, 0x28, 0x1b, 0x17, 0xf4, 0x03, 0xe8, 0xd7, 0xea, 0x25, 0xd2, 0x87, 0x74, 0xe8, 0x15, 0x10, /* (2^135)P */ 0x4d, 0xcc, 0x3a, 0xd2, 0xfe, 0xe3, 0x8d, 0xc5, 0x2d, 0xbe, 0xa7, 0x94, 0xc2, 0x91, 0xdb, 0x50, 0x57, 0xf4, 0x9c, 0x1c, 0x3d, 0xd4, 0x94, 0x0b, 0x4a, 0x52, 0x37, 0x6e, 0xfa, 0x40, 0x16, 0x6b, /* (2^136)P */ 0x09, 0x0d, 0xda, 0x5f, 0x6c, 0x34, 0x2f, 0x69, 0x51, 0x31, 0x4d, 0xfa, 0x59, 0x1c, 0x0b, 0x20, 0x96, 0xa2, 0x77, 0x07, 0x76, 0x6f, 0xc4, 0xb8, 0xcf, 0xfb, 0xfd, 0x3f, 0x5f, 0x39, 0x38, 0x4b, /* (2^137)P */ 0x71, 0xd6, 0x54, 0xbe, 0x00, 0x5e, 0xd2, 0x18, 0xa6, 0xab, 0xc8, 0xbe, 0x82, 0x05, 0xd5, 0x60, 0x82, 0xb9, 0x78, 0x3b, 0x26, 0x8f, 0xad, 0x87, 0x32, 0x04, 0xda, 0x9c, 0x4e, 0xf6, 0xfd, 0x50, /* (2^138)P */ 0xf0, 0xdc, 0x78, 0xc5, 0xaa, 0x67, 0xf5, 0x90, 0x3b, 0x13, 0xa3, 0xf2, 0x0e, 0x9b, 0x1e, 0xef, 0x71, 0xde, 0xd9, 0x42, 0x92, 0xba, 0xeb, 0x0e, 0xc7, 0x01, 0x31, 0xf0, 0x9b, 0x3c, 0x47, 0x15, /* (2^139)P */ 0x95, 0x80, 0xb7, 0x56, 0xae, 0xe8, 0x77, 0x7c, 0x8e, 0x07, 0x6f, 0x6e, 0x66, 0xe7, 0x78, 0xb6, 0x1f, 0xba, 0x48, 0x53, 0x61, 0xb9, 0xa0, 0x2d, 0x0b, 0x3f, 0x73, 0xff, 0xc1, 0x31, 0xf9, 0x7c, /* (2^140)P */ 0x6c, 0x36, 0x0a, 0x0a, 0xf5, 0x57, 0xb3, 0x26, 0x32, 0xd7, 0x87, 0x2b, 0xf4, 0x8c, 0x70, 0xe9, 0xc0, 0xb2, 0x1c, 0xf9, 0xa5, 0xee, 0x3a, 0xc1, 0x4c, 0xbb, 0x43, 0x11, 0x99, 0x0c, 0xd9, 0x35, /* (2^141)P */ 0xdc, 0xd9, 0xa0, 0xa9, 0x04, 0xc4, 0xc1, 0x47, 0x51, 0xd2, 0x72, 0x19, 0x45, 0x58, 0x9e, 0x65, 0x31, 0x8c, 0xb3, 0x73, 0xc4, 0xa8, 0x75, 0x38, 0x24, 0x1f, 0x56, 0x79, 0xd3, 0x9e, 0xbd, 0x1f, /* (2^142)P */ 0x8d, 0xc2, 0x1e, 0xd4, 0x6f, 0xbc, 0xfa, 0x11, 0xca, 0x2d, 0x2a, 0xcd, 0xe3, 0xdf, 0xf8, 0x7e, 0x95, 0x45, 0x40, 0x8c, 0x5d, 0x3b, 0xe7, 0x72, 0x27, 0x2f, 0xb7, 0x54, 0x49, 0xfa, 0x35, 0x61, /* (2^143)P */ 0x9c, 0xb6, 0x24, 0xde, 0xa2, 0x32, 0xfc, 0xcc, 0x88, 0x5d, 0x09, 0x1f, 0x8c, 0x69, 0x55, 0x3f, 0x29, 0xf9, 0xc3, 0x5a, 0xed, 0x50, 0x33, 0xbe, 0xeb, 0x7e, 0x47, 0xca, 0x06, 0xf8, 0x9b, 0x5e, /* (2^144)P */ 0x68, 0x9f, 0x30, 0x3c, 0xb6, 0x8f, 0xce, 0xe9, 0xf4, 0xf9, 0xe1, 0x65, 0x35, 0xf6, 0x76, 0x53, 0xf1, 0x93, 0x63, 0x5a, 0xb3, 0xcf, 0xaf, 0xd1, 0x06, 0x35, 0x62, 0xe5, 0xed, 0xa1, 0x32, 0x66, /* (2^145)P */ 0x4c, 0xed, 0x2d, 0x0c, 0x39, 0x6c, 0x7d, 0x0b, 0x1f, 0xcb, 0x04, 0xdf, 0x81, 0x32, 0xcb, 0x56, 0xc7, 0xc3, 0xec, 0x49, 0x12, 0x5a, 0x30, 0x66, 0x2a, 0xa7, 0x8c, 0xa3, 0x60, 0x8b, 0x58, 0x5d, /* (2^146)P */ 0x2d, 0xf4, 0xe5, 0xe8, 0x78, 0xbf, 0xec, 0xa6, 0xec, 0x3e, 0x8a, 0x3c, 0x4b, 0xb4, 0xee, 0x86, 0x04, 0x16, 0xd2, 0xfb, 0x48, 0x9c, 0x21, 0xec, 0x31, 0x67, 0xc3, 0x17, 0xf5, 0x1a, 0xaf, 0x1a, /* (2^147)P */ 0xe7, 0xbd, 0x69, 0x67, 0x83, 0xa2, 0x06, 0xc3, 0xdb, 0x2a, 0x1e, 0x2b, 0x62, 0x80, 0x82, 0x20, 0xa6, 0x94, 0xff, 0xfb, 0x1f, 0xf5, 0x27, 0x80, 0x6b, 0xf2, 0x24, 0x11, 0xce, 0xa1, 0xcf, 0x76, /* (2^148)P */ 0xb6, 0xab, 0x22, 0x24, 0x56, 0x00, 0xeb, 0x18, 0xc3, 0x29, 0x8c, 0x8f, 0xd5, 0xc4, 0x77, 0xf3, 0x1a, 0x56, 0x31, 0xf5, 0x07, 0xc2, 0xbb, 0x4d, 0x27, 0x8a, 0x12, 0x82, 0xf0, 0xb7, 0x53, 0x02, /* (2^149)P */ 0xe0, 0x17, 0x2c, 0xb6, 0x1c, 0x09, 0x1f, 0x3d, 0xa9, 0x28, 0x46, 0xd6, 0xab, 0xe1, 0x60, 0x48, 0x53, 0x42, 0x9d, 0x30, 0x36, 0x74, 0xd1, 0x52, 0x76, 0xe5, 0xfa, 0x3e, 0xe1, 0x97, 0x6f, 0x35, /* (2^150)P */ 0x5b, 0x53, 0x50, 0xa1, 0x1a, 0xe1, 0x51, 0xd3, 0xcc, 0x78, 0xd8, 0x1d, 0xbb, 0x45, 0x6b, 0x3e, 0x98, 0x2c, 0xd9, 0xbe, 0x28, 0x61, 0x77, 0x0c, 0xb8, 0x85, 0x28, 0x03, 0x93, 0xae, 0x34, 0x1d, /* (2^151)P */ 0xc3, 0xa4, 0x5b, 0xa8, 0x8c, 0x48, 0xa0, 0x4b, 0xce, 0xe6, 0x9c, 0x3c, 0xc3, 0x48, 0x53, 0x98, 0x70, 0xa7, 0xbd, 0x97, 0x6f, 0x4c, 0x12, 0x66, 0x4a, 0x12, 0x54, 0x06, 0x29, 0xa0, 0x81, 0x0f, /* (2^152)P */ 0xfd, 0x86, 0x9b, 0x56, 0xa6, 0x9c, 0xd0, 0x9e, 0x2d, 0x9a, 0xaf, 0x18, 0xfd, 0x09, 0x10, 0x81, 0x0a, 0xc2, 0xd8, 0x93, 0x3f, 0xd0, 0x08, 0xff, 0x6b, 0xf2, 0xae, 0x9f, 0x19, 0x48, 0xa1, 0x52, /* (2^153)P */ 0x73, 0x1b, 0x8d, 0x2d, 0xdc, 0xf9, 0x03, 0x3e, 0x70, 0x1a, 0x96, 0x73, 0x18, 0x80, 0x05, 0x42, 0x70, 0x59, 0xa3, 0x41, 0xf0, 0x87, 0xd9, 0xc0, 0x49, 0xd5, 0xc0, 0xa1, 0x15, 0x1f, 0xaa, 0x07, /* (2^154)P */ 0x24, 0x72, 0xd2, 0x8c, 0xe0, 0x6c, 0xd4, 0xdf, 0x39, 0x42, 0x4e, 0x93, 0x4f, 0x02, 0x0a, 0x6d, 0x59, 0x7b, 0x89, 0x99, 0x63, 0x7a, 0x8a, 0x80, 0xa2, 0x95, 0x3d, 0xe1, 0xe9, 0x56, 0x45, 0x0a, /* (2^155)P */ 0x45, 0x30, 0xc1, 0xe9, 0x1f, 0x99, 0x1a, 0xd2, 0xb8, 0x51, 0x77, 0xfe, 0x48, 0x85, 0x0e, 0x9b, 0x35, 0x00, 0xf3, 0x4b, 0xcb, 0x43, 0xa6, 0x5d, 0x21, 0xf7, 0x40, 0x39, 0xd6, 0x28, 0xdb, 0x77, /* (2^156)P */ 0x11, 0x90, 0xdc, 0x4a, 0x61, 0xeb, 0x5e, 0xfc, 0xeb, 0x11, 0xc4, 0xe8, 0x9a, 0x41, 0x29, 0x52, 0x74, 0xcf, 0x1d, 0x7d, 0x78, 0xe7, 0xc3, 0x9e, 0xb5, 0x4c, 0x6e, 0x21, 0x3e, 0x05, 0x0d, 0x34, /* (2^157)P */ 0xb4, 0xf2, 0x8d, 0xb4, 0x39, 0xaf, 0xc7, 0xca, 0x94, 0x0a, 0xa1, 0x71, 0x28, 0xec, 0xfa, 0xc0, 0xed, 0x75, 0xa5, 0x5c, 0x24, 0x69, 0x0a, 0x14, 0x4c, 0x3a, 0x27, 0x34, 0x71, 0xc3, 0xf1, 0x0c, /* (2^158)P */ 0xa5, 0xb8, 0x24, 0xc2, 0x6a, 0x30, 0xee, 0xc8, 0xb0, 0x30, 0x49, 0xcb, 0x7c, 0xee, 0xea, 0x57, 0x4f, 0xe7, 0xcb, 0xaa, 0xbd, 0x06, 0xe8, 0xa1, 0x7d, 0x65, 0xeb, 0x2e, 0x74, 0x62, 0x9a, 0x7d, /* (2^159)P */ 0x30, 0x48, 0x6c, 0x54, 0xef, 0xb6, 0xb6, 0x9e, 0x2e, 0x6e, 0xb3, 0xdd, 0x1f, 0xca, 0x5c, 0x88, 0x05, 0x71, 0x0d, 0xef, 0x83, 0xf3, 0xb9, 0xe6, 0x12, 0x04, 0x2e, 0x9d, 0xef, 0x4f, 0x65, 0x58, /* (2^160)P */ 0x26, 0x8e, 0x0e, 0xbe, 0xff, 0xc4, 0x05, 0xa9, 0x6e, 0x81, 0x31, 0x9b, 0xdf, 0xe5, 0x2d, 0x94, 0xe1, 0x88, 0x2e, 0x80, 0x3f, 0x72, 0x7d, 0x49, 0x8d, 0x40, 0x2f, 0x60, 0xea, 0x4d, 0x68, 0x30, /* (2^161)P */ 0x34, 0xcb, 0xe6, 0xa3, 0x78, 0xa2, 0xe5, 0x21, 0xc4, 0x1d, 0x15, 0x5b, 0x6f, 0x6e, 0xfb, 0xae, 0x15, 0xca, 0x77, 0x9d, 0x04, 0x8e, 0x0b, 0xb3, 0x81, 0x89, 0xb9, 0x53, 0xcf, 0xc9, 0xc3, 0x28, /* (2^162)P */ 0x2a, 0xdd, 0x6c, 0x55, 0x21, 0xb7, 0x7f, 0x28, 0x74, 0x22, 0x02, 0x97, 0xa8, 0x7c, 0x31, 0x0d, 0x58, 0x32, 0x54, 0x3a, 0x42, 0xc7, 0x68, 0x74, 0x2f, 0x64, 0xb5, 0x4e, 0x46, 0x11, 0x7f, 0x4a, /* (2^163)P */ 0xa6, 0x3a, 0x19, 0x4d, 0x77, 0xa4, 0x37, 0xa2, 0xa1, 0x29, 0x21, 0xa9, 0x6e, 0x98, 0x65, 0xd8, 0x88, 0x1a, 0x7c, 0xf8, 0xec, 0x15, 0xc5, 0x24, 0xeb, 0xf5, 0x39, 0x5f, 0x57, 0x03, 0x40, 0x60, /* (2^164)P */ 0x27, 0x9b, 0x0a, 0x57, 0x89, 0xf1, 0xb9, 0x47, 0x78, 0x4b, 0x5e, 0x46, 0xde, 0xce, 0x98, 0x2b, 0x20, 0x5c, 0xb8, 0xdb, 0x51, 0xf5, 0x6d, 0x02, 0x01, 0x19, 0xe2, 0x47, 0x10, 0xd9, 0xfc, 0x74, /* (2^165)P */ 0xa3, 0xbf, 0xc1, 0x23, 0x0a, 0xa9, 0xe2, 0x13, 0xf6, 0x19, 0x85, 0x47, 0x4e, 0x07, 0xb0, 0x0c, 0x44, 0xcf, 0xf6, 0x3a, 0xbe, 0xcb, 0xf1, 0x5f, 0xbe, 0x2d, 0x81, 0xbe, 0x38, 0x54, 0xfe, 0x67, /* (2^166)P */ 0xb0, 0x05, 0x0f, 0xa4, 0x4f, 0xf6, 0x3c, 0xd1, 0x87, 0x37, 0x28, 0x32, 0x2f, 0xfb, 0x4d, 0x05, 0xea, 0x2a, 0x0d, 0x7f, 0x5b, 0x91, 0x73, 0x41, 0x4e, 0x0d, 0x61, 0x1f, 0x4f, 0x14, 0x2f, 0x48, /* (2^167)P */ 0x34, 0x82, 0x7f, 0xb4, 0x01, 0x02, 0x21, 0xf6, 0x90, 0xb9, 0x70, 0x9e, 0x92, 0xe1, 0x0a, 0x5d, 0x7c, 0x56, 0x49, 0xb0, 0x55, 0xf4, 0xd7, 0xdc, 0x01, 0x6f, 0x91, 0xf0, 0xf1, 0xd0, 0x93, 0x7e, /* (2^168)P */ 0xfa, 0xb4, 0x7d, 0x8a, 0xf1, 0xcb, 0x79, 0xdd, 0x2f, 0xc6, 0x74, 0x6f, 0xbf, 0x91, 0x83, 0xbe, 0xbd, 0x91, 0x82, 0x4b, 0xd1, 0x45, 0x71, 0x02, 0x05, 0x17, 0xbf, 0x2c, 0xea, 0x73, 0x5a, 0x58, /* (2^169)P */ 0xb2, 0x0d, 0x8a, 0x92, 0x3e, 0xa0, 0x5c, 0x48, 0xe7, 0x57, 0x28, 0x74, 0xa5, 0x01, 0xfc, 0x10, 0xa7, 0x51, 0xd5, 0xd6, 0xdb, 0x2e, 0x48, 0x2f, 0x8a, 0xdb, 0x8f, 0x04, 0xb5, 0x33, 0x04, 0x0f, /* (2^170)P */ 0x47, 0x62, 0xdc, 0xd7, 0x8d, 0x2e, 0xda, 0x60, 0x9a, 0x81, 0xd4, 0x8c, 0xd3, 0xc9, 0xb4, 0x88, 0x97, 0x66, 0xf6, 0x01, 0xc0, 0x3a, 0x03, 0x13, 0x75, 0x7d, 0x36, 0x3b, 0xfe, 0x24, 0x3b, 0x27, /* (2^171)P */ 0xd4, 0xb9, 0xb3, 0x31, 0x6a, 0xf6, 0xe8, 0xc6, 0xd5, 0x49, 0xdf, 0x94, 0xa4, 0x14, 0x15, 0x28, 0xa7, 0x3d, 0xb2, 0xc8, 0xdf, 0x6f, 0x72, 0xd1, 0x48, 0xe5, 0xde, 0x03, 0xd1, 0xe7, 0x3a, 0x4b, /* (2^172)P */ 0x7e, 0x9d, 0x4b, 0xce, 0x19, 0x6e, 0x25, 0xc6, 0x1c, 0xc6, 0xe3, 0x86, 0xf1, 0x5c, 0x5c, 0xff, 0x45, 0xc1, 0x8e, 0x4b, 0xa3, 0x3c, 0xc6, 0xac, 0x74, 0x65, 0xe6, 0xfe, 0x88, 0x18, 0x62, 0x74, /* (2^173)P */ 0x1e, 0x0a, 0x29, 0x45, 0x96, 0x40, 0x6f, 0x95, 0x2e, 0x96, 0x3a, 0x26, 0xe3, 0xf8, 0x0b, 0xef, 0x7b, 0x64, 0xc2, 0x5e, 0xeb, 0x50, 0x6a, 0xed, 0x02, 0x75, 0xca, 0x9d, 0x3a, 0x28, 0x94, 0x06, /* (2^174)P */ 0xd1, 0xdc, 0xa2, 0x43, 0x36, 0x96, 0x9b, 0x76, 0x53, 0x53, 0xfc, 0x09, 0xea, 0xc8, 0xb7, 0x42, 0xab, 0x7e, 0x39, 0x13, 0xee, 0x2a, 0x00, 0x4f, 0x3a, 0xd6, 0xb7, 0x19, 0x2c, 0x5e, 0x00, 0x63, /* (2^175)P */ 0xea, 0x3b, 0x02, 0x63, 0xda, 0x36, 0x67, 0xca, 0xb7, 0x99, 0x2a, 0xb1, 0x6d, 0x7f, 0x6c, 0x96, 0xe1, 0xc5, 0x37, 0xc5, 0x90, 0x93, 0xe0, 0xac, 0xee, 0x89, 0xaa, 0xa1, 0x63, 0x60, 0x69, 0x0b, /* (2^176)P */ 0xe5, 0x56, 0x8c, 0x28, 0x97, 0x3e, 0xb0, 0xeb, 0xe8, 0x8b, 0x8c, 0x93, 0x9f, 0x9f, 0x2a, 0x43, 0x71, 0x7f, 0x71, 0x5b, 0x3d, 0xa9, 0xa5, 0xa6, 0x97, 0x9d, 0x8f, 0xe1, 0xc3, 0xb4, 0x5f, 0x1a, /* (2^177)P */ 0xce, 0xcd, 0x60, 0x1c, 0xad, 0xe7, 0x94, 0x1c, 0xa0, 0xc4, 0x02, 0xfc, 0x43, 0x2a, 0x20, 0xee, 0x20, 0x6a, 0xc4, 0x67, 0xd8, 0xe4, 0xaf, 0x8d, 0x58, 0x7b, 0xc2, 0x8a, 0x3c, 0x26, 0x10, 0x0a, /* (2^178)P */ 0x4a, 0x2a, 0x43, 0xe4, 0xdf, 0xa9, 0xde, 0xd0, 0xc5, 0x77, 0x92, 0xbe, 0x7b, 0xf8, 0x6a, 0x85, 0x1a, 0xc7, 0x12, 0xc2, 0xac, 0x72, 0x84, 0xce, 0x91, 0x1e, 0xbb, 0x9b, 0x6d, 0x1b, 0x15, 0x6f, /* (2^179)P */ 0x6a, 0xd5, 0xee, 0x7c, 0x52, 0x6c, 0x77, 0x26, 0xec, 0xfa, 0xf8, 0xfb, 0xb7, 0x1c, 0x21, 0x7d, 0xcc, 0x09, 0x46, 0xfd, 0xa6, 0x66, 0xae, 0x37, 0x42, 0x0c, 0x77, 0xd2, 0x02, 0xb7, 0x81, 0x1f, /* (2^180)P */ 0x92, 0x83, 0xc5, 0xea, 0x57, 0xb0, 0xb0, 0x2f, 0x9d, 0x4e, 0x74, 0x29, 0xfe, 0x89, 0xdd, 0xe1, 0xf8, 0xb4, 0xbe, 0x17, 0xeb, 0xf8, 0x64, 0xc9, 0x1e, 0xd4, 0xa2, 0xc9, 0x73, 0x10, 0x57, 0x29, /* (2^181)P */ 0x54, 0xe2, 0xc0, 0x81, 0x89, 0xa1, 0x48, 0xa9, 0x30, 0x28, 0xb2, 0x65, 0x9b, 0x36, 0xf6, 0x2d, 0xc6, 0xd3, 0xcf, 0x5f, 0xd7, 0xb2, 0x3e, 0xa3, 0x1f, 0xa0, 0x99, 0x41, 0xec, 0xd6, 0x8c, 0x07, /* (2^182)P */ 0x2f, 0x0d, 0x90, 0xad, 0x41, 0x4a, 0x58, 0x4a, 0x52, 0x4c, 0xc7, 0xe2, 0x78, 0x2b, 0x14, 0x32, 0x78, 0xc9, 0x31, 0x84, 0x33, 0xe8, 0xc4, 0x68, 0xc2, 0x9f, 0x68, 0x08, 0x90, 0xea, 0x69, 0x7f, /* (2^183)P */ 0x65, 0x82, 0xa3, 0x46, 0x1e, 0xc8, 0xf2, 0x52, 0xfd, 0x32, 0xa8, 0x04, 0x2d, 0x07, 0x78, 0xfd, 0x94, 0x9e, 0x35, 0x25, 0xfa, 0xd5, 0xd7, 0x8c, 0xd2, 0x29, 0xcc, 0x54, 0x74, 0x1b, 0xe7, 0x4d, /* (2^184)P */ 0xc9, 0x6a, 0xda, 0x1e, 0xad, 0x60, 0xeb, 0x42, 0x3a, 0x9c, 0xc0, 0xdb, 0xdf, 0x37, 0xad, 0x0a, 0x91, 0xc1, 0x3c, 0xe3, 0x71, 0x4b, 0x00, 0x81, 0x3c, 0x80, 0x22, 0x51, 0x34, 0xbe, 0xe6, 0x44, /* (2^185)P */ 0xdb, 0x20, 0x19, 0xba, 0x88, 0x83, 0xfe, 0x03, 0x08, 0xb0, 0x0d, 0x15, 0x32, 0x7c, 0xd5, 0xf5, 0x29, 0x0c, 0xf6, 0x1a, 0x28, 0xc4, 0xc8, 0x49, 0xee, 0x1a, 0x70, 0xde, 0x18, 0xb5, 0xed, 0x21, /* (2^186)P */ 0x99, 0xdc, 0x06, 0x8f, 0x41, 0x3e, 0xb6, 0x7f, 0xb8, 0xd7, 0x66, 0xc1, 0x99, 0x0d, 0x46, 0xa4, 0x83, 0x0a, 0x52, 0xce, 0x48, 0x52, 0xdd, 0x24, 0x58, 0x83, 0x92, 0x2b, 0x71, 0xad, 0xc3, 0x5e, /* (2^187)P */ 0x0f, 0x93, 0x17, 0xbd, 0x5f, 0x2a, 0x02, 0x15, 0xe3, 0x70, 0x25, 0xd8, 0x77, 0x4a, 0xf6, 0xa4, 0x12, 0x37, 0x78, 0x15, 0x69, 0x8d, 0xbc, 0x12, 0xbb, 0x0a, 0x62, 0xfc, 0xc0, 0x94, 0x81, 0x49, /* (2^188)P */ 0x82, 0x6c, 0x68, 0x55, 0xd2, 0xd9, 0xa2, 0x38, 0xf0, 0x21, 0x3e, 0x19, 0xd9, 0x6b, 0x5c, 0x78, 0x84, 0x54, 0x4a, 0xb2, 0x1a, 0xc8, 0xd5, 0xe4, 0x89, 0x09, 0xe2, 0xb2, 0x60, 0x78, 0x30, 0x56, /* (2^189)P */ 0xc4, 0x74, 0x4d, 0x8b, 0xf7, 0x55, 0x9d, 0x42, 0x31, 0x01, 0x35, 0x43, 0x46, 0x83, 0xf1, 0x22, 0xff, 0x1f, 0xc7, 0x98, 0x45, 0xc2, 0x60, 0x1e, 0xef, 0x83, 0x99, 0x97, 0x14, 0xf0, 0xf2, 0x59, /* (2^190)P */ 0x44, 0x4a, 0x49, 0xeb, 0x56, 0x7d, 0xa4, 0x46, 0x8e, 0xa1, 0x36, 0xd6, 0x54, 0xa8, 0x22, 0x3e, 0x3b, 0x1c, 0x49, 0x74, 0x52, 0xe1, 0x46, 0xb3, 0xe7, 0xcd, 0x90, 0x53, 0x4e, 0xfd, 0xea, 0x2c, /* (2^191)P */ 0x75, 0x66, 0x0d, 0xbe, 0x38, 0x85, 0x8a, 0xba, 0x23, 0x8e, 0x81, 0x50, 0xbb, 0x74, 0x90, 0x4b, 0xc3, 0x04, 0xd3, 0x85, 0x90, 0xb8, 0xda, 0xcb, 0xc4, 0x92, 0x61, 0xe5, 0xe0, 0x4f, 0xa2, 0x61, /* (2^192)P */ 0xcb, 0x5b, 0x52, 0xdb, 0xe6, 0x15, 0x76, 0xcb, 0xca, 0xe4, 0x67, 0xa5, 0x35, 0x8c, 0x7d, 0xdd, 0x69, 0xdd, 0xfc, 0xca, 0x3a, 0x15, 0xb4, 0xe6, 0x66, 0x97, 0x3c, 0x7f, 0x09, 0x8e, 0x66, 0x2d, /* (2^193)P */ 0xf0, 0x5e, 0xe5, 0x5c, 0x26, 0x7e, 0x7e, 0xa5, 0x67, 0xb9, 0xd4, 0x7c, 0x52, 0x4e, 0x9f, 0x5d, 0xe5, 0xd1, 0x2f, 0x49, 0x06, 0x36, 0xc8, 0xfb, 0xae, 0xf7, 0xc3, 0xb7, 0xbe, 0x52, 0x0d, 0x09, /* (2^194)P */ 0x7c, 0x4d, 0x7b, 0x1e, 0x5a, 0x51, 0xb9, 0x09, 0xc0, 0x44, 0xda, 0x99, 0x25, 0x6a, 0x26, 0x1f, 0x04, 0x55, 0xc5, 0xe2, 0x48, 0x95, 0xc4, 0xa1, 0xcc, 0x15, 0x6f, 0x12, 0x87, 0x42, 0xf0, 0x7e, /* (2^195)P */ 0x15, 0xef, 0x30, 0xbd, 0x9d, 0x65, 0xd1, 0xfe, 0x7b, 0x27, 0xe0, 0xc4, 0xee, 0xb9, 0x4a, 0x8b, 0x91, 0x32, 0xdf, 0xa5, 0x36, 0x62, 0x4d, 0x88, 0x88, 0xf7, 0x5c, 0xbf, 0xa6, 0x6e, 0xd9, 0x1f, /* (2^196)P */ 0x9a, 0x0d, 0x19, 0x1f, 0x98, 0x61, 0xa1, 0x42, 0xc1, 0x52, 0x60, 0x7e, 0x50, 0x49, 0xd8, 0x61, 0xd5, 0x2c, 0x5a, 0x28, 0xbf, 0x13, 0xe1, 0x9f, 0xd8, 0x85, 0xad, 0xdb, 0x76, 0xd6, 0x22, 0x7c, /* (2^197)P */ 0x7d, 0xd2, 0xfb, 0x2b, 0xed, 0x70, 0xe7, 0x82, 0xa5, 0xf5, 0x96, 0xe9, 0xec, 0xb2, 0x05, 0x4c, 0x50, 0x01, 0x90, 0xb0, 0xc2, 0xa9, 0x40, 0xcd, 0x64, 0xbf, 0xd9, 0x13, 0x92, 0x31, 0x95, 0x58, /* (2^198)P */ 0x08, 0x2e, 0xea, 0x3f, 0x70, 0x5d, 0xcc, 0xe7, 0x8c, 0x18, 0xe2, 0x58, 0x12, 0x49, 0x0c, 0xb5, 0xf0, 0x5b, 0x20, 0x48, 0xaa, 0x0b, 0xe3, 0xcc, 0x62, 0x2d, 0xa3, 0xcf, 0x9c, 0x65, 0x7c, 0x53, /* (2^199)P */ 0x88, 0xc0, 0xcf, 0x98, 0x3a, 0x62, 0xb6, 0x37, 0xa4, 0xac, 0xd6, 0xa4, 0x1f, 0xed, 0x9b, 0xfe, 0xb0, 0xd1, 0xa8, 0x56, 0x8e, 0x9b, 0xd2, 0x04, 0x75, 0x95, 0x51, 0x0b, 0xc4, 0x71, 0x5f, 0x72, /* (2^200)P */ 0xe6, 0x9c, 0x33, 0xd0, 0x9c, 0xf8, 0xc7, 0x28, 0x8b, 0xc1, 0xdd, 0x69, 0x44, 0xb1, 0x67, 0x83, 0x2c, 0x65, 0xa1, 0xa6, 0x83, 0xda, 0x3a, 0x88, 0x17, 0x6c, 0x4d, 0x03, 0x74, 0x19, 0x5f, 0x58, /* (2^201)P */ 0x88, 0x91, 0xb1, 0xf1, 0x66, 0xb2, 0xcf, 0x89, 0x17, 0x52, 0xc3, 0xe7, 0x63, 0x48, 0x3b, 0xe6, 0x6a, 0x52, 0xc0, 0xb4, 0xa6, 0x9d, 0x8c, 0xd8, 0x35, 0x46, 0x95, 0xf0, 0x9d, 0x5c, 0x03, 0x3e, /* (2^202)P */ 0x9d, 0xde, 0x45, 0xfb, 0x12, 0x54, 0x9d, 0xdd, 0x0d, 0xf4, 0xcf, 0xe4, 0x32, 0x45, 0x68, 0xdd, 0x1c, 0x67, 0x1d, 0x15, 0x9b, 0x99, 0x5c, 0x4b, 0x90, 0xf6, 0xe7, 0x11, 0xc8, 0x2c, 0x8c, 0x2d, /* (2^203)P */ 0x40, 0x5d, 0x05, 0x90, 0x1d, 0xbe, 0x54, 0x7f, 0x40, 0xaf, 0x4a, 0x46, 0xdf, 0xc5, 0x64, 0xa4, 0xbe, 0x17, 0xe9, 0xf0, 0x24, 0x96, 0x97, 0x33, 0x30, 0x6b, 0x35, 0x27, 0xc5, 0x8d, 0x01, 0x2c, /* (2^204)P */ 0xd4, 0xb3, 0x30, 0xe3, 0x24, 0x50, 0x41, 0xa5, 0xd3, 0x52, 0x16, 0x69, 0x96, 0x3d, 0xff, 0x73, 0xf1, 0x59, 0x9b, 0xef, 0xc4, 0x42, 0xec, 0x94, 0x5a, 0x8e, 0xd0, 0x18, 0x16, 0x20, 0x47, 0x07, /* (2^205)P */ 0x53, 0x1c, 0x41, 0xca, 0x8a, 0xa4, 0x6c, 0x4d, 0x19, 0x61, 0xa6, 0xcf, 0x2f, 0x5f, 0x41, 0x66, 0xff, 0x27, 0xe2, 0x51, 0x00, 0xd4, 0x4d, 0x9c, 0xeb, 0xf7, 0x02, 0x9a, 0xc0, 0x0b, 0x81, 0x59, /* (2^206)P */ 0x1d, 0x10, 0xdc, 0xb3, 0x71, 0xb1, 0x7e, 0x2a, 0x8e, 0xf6, 0xfe, 0x9f, 0xb9, 0x5a, 0x1c, 0x44, 0xea, 0x59, 0xb3, 0x93, 0x9b, 0x5c, 0x02, 0x32, 0x2f, 0x11, 0x9d, 0x1e, 0xa7, 0xe0, 0x8c, 0x5e, /* (2^207)P */ 0xfd, 0x03, 0x95, 0x42, 0x92, 0xcb, 0xcc, 0xbf, 0x55, 0x5d, 0x09, 0x2f, 0x75, 0xba, 0x71, 0xd2, 0x1e, 0x09, 0x2d, 0x97, 0x5e, 0xad, 0x5e, 0x34, 0xba, 0x03, 0x31, 0xa8, 0x11, 0xdf, 0xc8, 0x18, /* (2^208)P */ 0x4c, 0x0f, 0xed, 0x9a, 0x9a, 0x94, 0xcd, 0x90, 0x7e, 0xe3, 0x60, 0x66, 0xcb, 0xf4, 0xd1, 0xc5, 0x0b, 0x2e, 0xc5, 0x56, 0x2d, 0xc5, 0xca, 0xb8, 0x0d, 0x8e, 0x80, 0xc5, 0x00, 0xe4, 0x42, 0x6e, /* (2^209)P */ 0x23, 0xfd, 0xae, 0xee, 0x66, 0x69, 0xb4, 0xa3, 0xca, 0xcd, 0x9e, 0xe3, 0x0b, 0x1f, 0x4f, 0x0c, 0x1d, 0xa5, 0x83, 0xd6, 0xc9, 0xc8, 0x9d, 0x18, 0x1b, 0x35, 0x09, 0x4c, 0x05, 0x7f, 0xf2, 0x51, /* (2^210)P */ 0x82, 0x06, 0x32, 0x2a, 0xcd, 0x7c, 0x48, 0x4c, 0x96, 0x1c, 0xdf, 0xb3, 0x5b, 0xa9, 0x7e, 0x58, 0xe8, 0xb8, 0x5c, 0x55, 0x9e, 0xf7, 0xcc, 0xc8, 0x3d, 0xd7, 0x06, 0xa2, 0x29, 0xc8, 0x7d, 0x54, /* (2^211)P */ 0x06, 0x9b, 0xc3, 0x80, 0xcd, 0xa6, 0x22, 0xb8, 0xc6, 0xd4, 0x00, 0x20, 0x73, 0x54, 0x6d, 0xe9, 0x4d, 0x3b, 0x46, 0x91, 0x6f, 0x5b, 0x53, 0x28, 0x1d, 0x6e, 0x48, 0xe2, 0x60, 0x46, 0x8f, 0x22, /* (2^212)P */ 0xbf, 0x3a, 0x8d, 0xde, 0x38, 0x95, 0x79, 0x98, 0x6e, 0xca, 0xeb, 0x45, 0x00, 0x33, 0xd8, 0x8c, 0x38, 0xe7, 0x21, 0x82, 0x00, 0x2a, 0x95, 0x79, 0xbb, 0xd2, 0x5c, 0x53, 0xa7, 0xe1, 0x22, 0x43, /* (2^213)P */ 0x1c, 0x80, 0xd1, 0x19, 0x18, 0xc1, 0x14, 0xb1, 0xc7, 0x5e, 0x3f, 0x4f, 0xd8, 0xe4, 0x16, 0x20, 0x4c, 0x0f, 0x26, 0x09, 0xf4, 0x2d, 0x0e, 0xdd, 0x66, 0x72, 0x5f, 0xae, 0xc0, 0x62, 0xc3, 0x5e, /* (2^214)P */ 0xee, 0xb4, 0xb2, 0xb8, 0x18, 0x2b, 0x46, 0xc0, 0xfb, 0x1a, 0x4d, 0x27, 0x50, 0xd9, 0xc8, 0x7c, 0xd2, 0x02, 0x6b, 0x43, 0x05, 0x71, 0x5f, 0xf2, 0xd3, 0xcc, 0xf9, 0xbf, 0xdc, 0xf8, 0xbb, 0x43, /* (2^215)P */ 0xdf, 0xe9, 0x39, 0xa0, 0x67, 0x17, 0xad, 0xb6, 0x83, 0x35, 0x9d, 0xf6, 0xa8, 0x4d, 0x71, 0xb0, 0xf5, 0x31, 0x29, 0xb4, 0x18, 0xfa, 0x55, 0x5e, 0x61, 0x09, 0xc6, 0x33, 0x8f, 0x55, 0xd5, 0x4e, /* (2^216)P */ 0xdd, 0xa5, 0x47, 0xc6, 0x01, 0x79, 0xe3, 0x1f, 0x57, 0xd3, 0x81, 0x80, 0x1f, 0xdf, 0x3d, 0x59, 0xa6, 0xd7, 0x3f, 0x81, 0xfd, 0xa4, 0x49, 0x02, 0x61, 0xaf, 0x9c, 0x4e, 0x27, 0xca, 0xac, 0x69, /* (2^217)P */ 0xc9, 0x21, 0x07, 0x33, 0xea, 0xa3, 0x7b, 0x04, 0xa0, 0x1e, 0x7e, 0x0e, 0xc2, 0x3f, 0x42, 0x83, 0x60, 0x4a, 0x31, 0x01, 0xaf, 0xc0, 0xf4, 0x1d, 0x27, 0x95, 0x28, 0x89, 0xab, 0x2d, 0xa6, 0x09, /* (2^218)P */ 0x00, 0xcb, 0xc6, 0x9c, 0xa4, 0x25, 0xb3, 0xa5, 0xb6, 0x6c, 0xb5, 0x54, 0xc6, 0x5d, 0x4b, 0xe9, 0xa0, 0x94, 0xc9, 0xad, 0x79, 0x87, 0xe2, 0x3b, 0xad, 0x4a, 0x3a, 0xba, 0xf8, 0xe8, 0x96, 0x42, /* (2^219)P */ 0xab, 0x1e, 0x45, 0x1e, 0x76, 0x89, 0x86, 0x32, 0x4a, 0x59, 0x59, 0xff, 0x8b, 0x59, 0x4d, 0x2e, 0x4a, 0x08, 0xa7, 0xd7, 0x53, 0x68, 0xb9, 0x49, 0xa8, 0x20, 0x14, 0x60, 0x19, 0xa3, 0x80, 0x49, /* (2^220)P */ 0x42, 0x2c, 0x55, 0x2f, 0xe1, 0xb9, 0x65, 0x95, 0x96, 0xfe, 0x00, 0x71, 0xdb, 0x18, 0x53, 0x8a, 0xd7, 0xd0, 0xad, 0x43, 0x4d, 0x0b, 0xc9, 0x05, 0xda, 0x4e, 0x5d, 0x6a, 0xd6, 0x4c, 0x8b, 0x53, /* (2^221)P */ 0x9f, 0x03, 0x9f, 0xe8, 0xc3, 0x4f, 0xe9, 0xf4, 0x45, 0x80, 0x61, 0x6f, 0xf2, 0x9a, 0x2c, 0x59, 0x50, 0x95, 0x4b, 0xfd, 0xb5, 0x6e, 0xa3, 0x08, 0x19, 0x14, 0xed, 0xc2, 0xf6, 0xfa, 0xff, 0x25, /* (2^222)P */ 0x54, 0xd3, 0x79, 0xcc, 0x59, 0x44, 0x43, 0x34, 0x6b, 0x47, 0xd5, 0xb1, 0xb4, 0xbf, 0xec, 0xee, 0x99, 0x5d, 0x61, 0x61, 0xa0, 0x34, 0xeb, 0xdd, 0x73, 0xb7, 0x64, 0xeb, 0xcc, 0xce, 0x29, 0x51, /* (2^223)P */ 0x20, 0x35, 0x99, 0x94, 0x58, 0x21, 0x43, 0xee, 0x3b, 0x0b, 0x4c, 0xf1, 0x7c, 0x9c, 0x2f, 0x77, 0xd5, 0xda, 0xbe, 0x06, 0xe3, 0xfc, 0xe2, 0xd2, 0x97, 0x6a, 0xf0, 0x46, 0xb5, 0x42, 0x5f, 0x71, /* (2^224)P */ 0x1a, 0x5f, 0x5b, 0xda, 0xce, 0xcd, 0x4e, 0x43, 0xa9, 0x41, 0x97, 0xa4, 0x15, 0x71, 0xa1, 0x0d, 0x2e, 0xad, 0xed, 0x73, 0x7c, 0xd7, 0x0b, 0x68, 0x41, 0x90, 0xdd, 0x4e, 0x35, 0x02, 0x7c, 0x48, /* (2^225)P */ 0xc4, 0xd9, 0x0e, 0xa7, 0xf3, 0xef, 0xef, 0xb8, 0x02, 0xe3, 0x57, 0xe8, 0xa3, 0x2a, 0xa3, 0x56, 0xa0, 0xa5, 0xa2, 0x48, 0xbd, 0x68, 0x3a, 0xdf, 0x44, 0xc4, 0x76, 0x31, 0xb7, 0x50, 0xf6, 0x07, /* (2^226)P */ 0xb1, 0xcc, 0xe0, 0x26, 0x16, 0x9b, 0x8b, 0xe3, 0x36, 0xfb, 0x09, 0x8b, 0xc1, 0x53, 0xe0, 0x79, 0x64, 0x49, 0xf9, 0xc9, 0x19, 0x03, 0xd9, 0x56, 0xc4, 0xf5, 0x9f, 0xac, 0xe7, 0x41, 0xa9, 0x1c, /* (2^227)P */ 0xbb, 0xa0, 0x2f, 0x16, 0x29, 0xdf, 0xc4, 0x49, 0x05, 0x33, 0xb3, 0x82, 0x32, 0xcf, 0x88, 0x84, 0x7d, 0x43, 0xbb, 0xca, 0x14, 0xda, 0xdf, 0x95, 0x86, 0xad, 0xd5, 0x64, 0x82, 0xf7, 0x91, 0x33, /* (2^228)P */ 0x5d, 0x09, 0xb5, 0xe2, 0x6a, 0xe0, 0x9a, 0x72, 0x46, 0xa9, 0x59, 0x32, 0xd7, 0x58, 0x8a, 0xd5, 0xed, 0x21, 0x39, 0xd1, 0x62, 0x42, 0x83, 0xe9, 0x92, 0xb5, 0x4b, 0xa5, 0xfa, 0xda, 0xfe, 0x27, /* (2^229)P */ 0xbb, 0x48, 0xad, 0x29, 0xb8, 0xc5, 0x9d, 0xa9, 0x60, 0xe2, 0x9e, 0x49, 0x42, 0x57, 0x02, 0x5f, 0xfd, 0x13, 0x75, 0x5d, 0xcd, 0x8e, 0x2c, 0x80, 0x38, 0xd9, 0x6d, 0x3f, 0xef, 0xb3, 0xce, 0x78, /* (2^230)P */ 0x94, 0x5d, 0x13, 0x8a, 0x4f, 0xf4, 0x42, 0xc3, 0xa3, 0xdd, 0x8c, 0x82, 0x44, 0xdb, 0x9e, 0x7b, 0xe7, 0xcf, 0x37, 0x05, 0x1a, 0xd1, 0x36, 0x94, 0xc8, 0xb4, 0x1a, 0xec, 0x64, 0xb1, 0x64, 0x50, /* (2^231)P */ 0xfc, 0xb2, 0x7e, 0xd3, 0xcf, 0xec, 0x20, 0x70, 0xfc, 0x25, 0x0d, 0xd9, 0x3e, 0xea, 0x31, 0x1f, 0x34, 0xbb, 0xa1, 0xdf, 0x7b, 0x0d, 0x93, 0x1b, 0x44, 0x30, 0x11, 0x48, 0x7a, 0x46, 0x44, 0x53, /* (2^232)P */ 0xfb, 0x6d, 0x5e, 0xf2, 0x70, 0x31, 0x07, 0x70, 0xc8, 0x4c, 0x11, 0x50, 0x1a, 0xdc, 0x85, 0xe3, 0x00, 0x4f, 0xfc, 0xc8, 0x8a, 0x69, 0x48, 0x23, 0xd8, 0x40, 0xdd, 0x84, 0x52, 0xa5, 0x77, 0x2a, /* (2^233)P */ 0xe4, 0x6c, 0x8c, 0xc9, 0xe0, 0xaf, 0x06, 0xfe, 0xe4, 0xd6, 0xdf, 0xdd, 0x96, 0xdf, 0x35, 0xc2, 0xd3, 0x1e, 0xbf, 0x33, 0x1e, 0xd0, 0x28, 0x14, 0xaf, 0xbd, 0x00, 0x93, 0xec, 0x68, 0x57, 0x78, /* (2^234)P */ 0x3b, 0xb6, 0xde, 0x91, 0x7a, 0xe5, 0x02, 0x97, 0x80, 0x8b, 0xce, 0xe5, 0xbf, 0xb8, 0xbd, 0x61, 0xac, 0x58, 0x1d, 0x3d, 0x6f, 0x42, 0x5b, 0x64, 0xbc, 0x57, 0xa5, 0x27, 0x22, 0xa8, 0x04, 0x48, /* (2^235)P */ 0x01, 0x26, 0x4d, 0xb4, 0x8a, 0x04, 0x57, 0x8e, 0x35, 0x69, 0x3a, 0x4b, 0x1a, 0x50, 0xd6, 0x68, 0x93, 0xc2, 0xe1, 0xf9, 0xc3, 0x9e, 0x9c, 0xc3, 0xe2, 0x63, 0xde, 0xd4, 0x57, 0xf2, 0x72, 0x41, /* (2^236)P */ 0x01, 0x64, 0x0c, 0x33, 0x50, 0xb4, 0x68, 0xd3, 0x91, 0x23, 0x8f, 0x41, 0x17, 0x30, 0x0d, 0x04, 0x0d, 0xd9, 0xb7, 0x90, 0x60, 0xbb, 0x34, 0x2c, 0x1f, 0xd5, 0xdf, 0x8f, 0x22, 0x49, 0xf6, 0x16, /* (2^237)P */ 0xf5, 0x8e, 0x92, 0x2b, 0x8e, 0x81, 0xa6, 0xbe, 0x72, 0x1e, 0xc1, 0xcd, 0x91, 0xcf, 0x8c, 0xe2, 0xcd, 0x36, 0x7a, 0xe7, 0x68, 0xaa, 0x4a, 0x59, 0x0f, 0xfd, 0x7f, 0x6c, 0x80, 0x34, 0x30, 0x31, /* (2^238)P */ 0x65, 0xbd, 0x49, 0x22, 0xac, 0x27, 0x9d, 0x8a, 0x12, 0x95, 0x8e, 0x01, 0x64, 0xb4, 0xa3, 0x19, 0xc7, 0x7e, 0xb3, 0x52, 0xf3, 0xcf, 0x6c, 0xc2, 0x21, 0x7b, 0x79, 0x1d, 0x34, 0x68, 0x6f, 0x05, /* (2^239)P */ 0x27, 0x23, 0xfd, 0x7e, 0x75, 0xd6, 0x79, 0x5e, 0x15, 0xfe, 0x3a, 0x55, 0xb6, 0xbc, 0xbd, 0xfa, 0x60, 0x5a, 0xaf, 0x6e, 0x2c, 0x22, 0xe7, 0xd3, 0x3b, 0x74, 0xae, 0x4d, 0x6d, 0xc7, 0x46, 0x70, /* (2^240)P */ 0x55, 0x4a, 0x8d, 0xb1, 0x72, 0xe8, 0x0b, 0x66, 0x96, 0x14, 0x4e, 0x57, 0x18, 0x25, 0x99, 0x19, 0xbb, 0xdc, 0x2b, 0x30, 0x3a, 0x05, 0x03, 0xc1, 0x8e, 0x8e, 0x21, 0x0b, 0x80, 0xe9, 0xd8, 0x3e, /* (2^241)P */ 0x3e, 0xe0, 0x75, 0xfa, 0x39, 0x92, 0x0b, 0x7b, 0x83, 0xc0, 0x33, 0x46, 0x68, 0xfb, 0xe9, 0xef, 0x93, 0x77, 0x1a, 0x39, 0xbe, 0x5f, 0xa3, 0x98, 0x34, 0xfe, 0xd0, 0xe2, 0x0f, 0x51, 0x65, 0x60, /* (2^242)P */ 0x0c, 0xad, 0xab, 0x48, 0x85, 0x66, 0xcb, 0x55, 0x27, 0xe5, 0x87, 0xda, 0x48, 0x45, 0x58, 0xb4, 0xdd, 0xc1, 0x07, 0x01, 0xea, 0xec, 0x43, 0x2c, 0x35, 0xde, 0x72, 0x93, 0x80, 0x28, 0x60, 0x52, /* (2^243)P */ 0x1f, 0x3b, 0x21, 0xf9, 0x6a, 0xc5, 0x15, 0x34, 0xdb, 0x98, 0x7e, 0x01, 0x4d, 0x1a, 0xee, 0x5b, 0x9b, 0x70, 0xcf, 0xb5, 0x05, 0xb1, 0xf6, 0x13, 0xb6, 0x9a, 0xb2, 0x82, 0x34, 0x0e, 0xf2, 0x5f, /* (2^244)P */ 0x90, 0x6c, 0x2e, 0xcc, 0x75, 0x9c, 0xa2, 0x0a, 0x06, 0xe2, 0x70, 0x3a, 0xca, 0x73, 0x7d, 0xfc, 0x15, 0xc5, 0xb5, 0xc4, 0x8f, 0xc3, 0x9f, 0x89, 0x07, 0xc2, 0xff, 0x24, 0xb1, 0x86, 0x03, 0x25, /* (2^245)P */ 0x56, 0x2b, 0x3d, 0xae, 0xd5, 0x28, 0xea, 0x54, 0xce, 0x60, 0xde, 0xd6, 0x9d, 0x14, 0x13, 0x99, 0xc1, 0xd6, 0x06, 0x8f, 0xc5, 0x4f, 0x69, 0x16, 0xc7, 0x8f, 0x01, 0xeb, 0x75, 0x39, 0xb2, 0x46, /* (2^246)P */ 0xe2, 0xb4, 0xb7, 0xb4, 0x0f, 0x6a, 0x0a, 0x47, 0xde, 0x53, 0x72, 0x8f, 0x5a, 0x47, 0x92, 0x5d, 0xdb, 0x3a, 0xbd, 0x2f, 0xb5, 0xe5, 0xee, 0xab, 0x68, 0x69, 0x80, 0xa0, 0x01, 0x08, 0xa2, 0x7f, /* (2^247)P */ 0xd2, 0x14, 0x77, 0x9f, 0xf1, 0xfa, 0xf3, 0x76, 0xc3, 0x60, 0x46, 0x2f, 0xc1, 0x40, 0xe8, 0xb3, 0x4e, 0x74, 0x12, 0xf2, 0x8d, 0xcd, 0xb4, 0x0f, 0xd2, 0x2d, 0x3a, 0x1d, 0x25, 0x5a, 0x06, 0x4b, /* (2^248)P */ 0x4a, 0xcd, 0x77, 0x3d, 0x38, 0xde, 0xeb, 0x5c, 0xb1, 0x9c, 0x2c, 0x88, 0xdf, 0x39, 0xdf, 0x6a, 0x59, 0xf7, 0x9a, 0xb0, 0x2e, 0x24, 0xdd, 0xa2, 0x22, 0x64, 0x5f, 0x0e, 0xe5, 0xc0, 0x47, 0x31, /* (2^249)P */ 0xdb, 0x50, 0x13, 0x1d, 0x10, 0xa5, 0x4c, 0x16, 0x62, 0xc9, 0x3f, 0xc3, 0x79, 0x34, 0xd1, 0xf8, 0x08, 0xda, 0xe5, 0x13, 0x4d, 0xce, 0x40, 0xe6, 0xba, 0xf8, 0x61, 0x50, 0xc4, 0xe0, 0xde, 0x4b, /* (2^250)P */ 0xc9, 0xb1, 0xed, 0xa4, 0xc1, 0x6d, 0xc4, 0xd7, 0x8a, 0xd9, 0x7f, 0x43, 0xb6, 0xd7, 0x14, 0x55, 0x0b, 0xc0, 0xa1, 0xb2, 0x6b, 0x2f, 0x94, 0x58, 0x0e, 0x71, 0x70, 0x1d, 0xab, 0xb2, 0xff, 0x2d, /* (2^251)P */ 0x68, 0x6d, 0x8b, 0xc1, 0x2f, 0xcf, 0xdf, 0xcc, 0x67, 0x61, 0x80, 0xb7, 0xa8, 0xcb, 0xeb, 0xa8, 0xe3, 0x37, 0x29, 0x5e, 0xf9, 0x97, 0x06, 0x98, 0x8c, 0x6e, 0x12, 0xd0, 0x1c, 0xba, 0xfb, 0x02, /* (2^252)P */ 0x65, 0x45, 0xff, 0xad, 0x60, 0xc3, 0x98, 0xcb, 0x19, 0x15, 0xdb, 0x4b, 0xd2, 0x01, 0x71, 0x44, 0xd5, 0x15, 0xfb, 0x75, 0x74, 0xc8, 0xc4, 0x98, 0x7d, 0xa2, 0x22, 0x6e, 0x6d, 0xc7, 0xf8, 0x05, /* (2^253)P */ 0x94, 0xf4, 0xb9, 0xfe, 0xdf, 0xe5, 0x69, 0xab, 0x75, 0x6b, 0x40, 0x18, 0x9d, 0xc7, 0x09, 0xae, 0x1d, 0x2d, 0xa4, 0x94, 0xfb, 0x45, 0x9b, 0x19, 0x84, 0xfa, 0x2a, 0xae, 0xeb, 0x0a, 0x71, 0x79, /* (2^254)P */ 0xdf, 0xd2, 0x34, 0xf3, 0xa7, 0xed, 0xad, 0xa6, 0xb4, 0x57, 0x2a, 0xaf, 0x51, 0x9c, 0xde, 0x7b, 0xa8, 0xea, 0xdc, 0x86, 0x4f, 0xc6, 0x8f, 0xa9, 0x7b, 0xd0, 0x0e, 0xc2, 0x35, 0x03, 0xbe, 0x6b, /* (2^255)P */ 0x44, 0x43, 0x98, 0x53, 0xbe, 0xdc, 0x7f, 0x66, 0xa8, 0x49, 0x59, 0x00, 0x1c, 0xbc, 0x72, 0x07, 0x8e, 0xd6, 0xbe, 0x4e, 0x9f, 0xa4, 0x07, 0xba, 0xbf, 0x30, 0xdf, 0xba, 0x85, 0xb0, 0xa7, 0x1f, } golang-github-cloudflare-circl-1.3.7/dh/x25519/testdata/000077500000000000000000000000001454601126700225505ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/x25519/testdata/rfc7748_kat_test.json000066400000000000000000000031211454601126700264420ustar00rootroot00000000000000[ { "input": "e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c", "output": "c3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552", "scalar": "a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4" }, { "input": "e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a493", "output": "95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957", "scalar": "4b66e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba0d" }, { "input": "0900000000000000000000000000000000000000000000000000000000000000", "output": "8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a", "scalar": "77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a" }, { "input": "0900000000000000000000000000000000000000000000000000000000000000", "output": "de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f", "scalar": "5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb" }, { "input": "de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f", "output": "4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742", "scalar": "77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a" }, { "input": "8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a", "output": "4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742", "scalar": "5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb" } ] golang-github-cloudflare-circl-1.3.7/dh/x25519/testdata/rfc7748_times_test.json000066400000000000000000000005451454601126700270130ustar00rootroot00000000000000[ { "times": 1, "key": "422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079" }, { "times": 1000, "key": "684cf59ba83309552800ef566f2f4d3c1c3887c49360e3875f2eb94d99532c51" }, { "times": 1000000, "key": "7c3911e0ab2586fd864497297e575e6f3bc601c0883c30df5f4dd2d24f665424" } ] golang-github-cloudflare-circl-1.3.7/dh/x25519/testdata/wycheproof_kat.json000066400000000000000000001052521454601126700264740ustar00rootroot00000000000000[ { "tcId":1, "comment":"normal case", "curve":"curve25519", "public":"9c647d9ae589b9f58fdc3ca4947efbc915c4b2e08e744a0edf469dac59c8f85a", "private":"4852834d9d6b77dadeabaaf2e11dca66d19fe74993a7bec36c6e16a0983feaba", "shared":"87b7f212b627f7a54ca5e0bcdaddd5389d9de6156cdbcf8ebe14ffbcfb436551", "result":"valid", "flags":[ ] }, { "tcId":2, "comment":"normal case", "curve":"curve25519", "public":"9c647d9ae589b9f58fdc3ca4947efbc915c4b2e08e744a0edf469dac59c8f85a", "private":"1064a67da639a8f6df4fbea2d63358b65bca80a770712e14ea8a72df5a3313ae", "shared":"4b82bd8650ea9b81a42181840926a4ffa16434d1bf298de1db87efb5b0a9e34e", "result":"valid", "flags":[ "LowOrderPublic" ] }, { "tcId":3, "comment":"public key on twist", "curve":"curve25519", "public":"63aa40c6e38346c5caf23a6df0a5e6c80889a08647e551b3563449befcfc9733", "private":"588c061a50804ac488ad774ac716c3f5ba714b2712e048491379a500211998a8", "shared":"b1a707519495ffffb298ff941716b06dfab87cf8d91123fe2be9a233dda22212", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":4, "comment":"public key on twist", "curve":"curve25519", "public":"0f83c36fded9d32fadf4efa3ae93a90bb5cfa66893bc412c43fa7287dbb99779", "private":"b05bfd32e55325d9fd648cb302848039000b390e44d521e58aab3b29a6960ba8", "shared":"67dd4a6e165533534c0e3f172e4ab8576bca923a5f07b2c069b4c310ff2e935b", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":5, "comment":"public key on twist", "curve":"curve25519", "public":"0b8211a2b6049097f6871c6c052d3c5fc1ba17da9e32ae458403b05bb283092a", 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"comment":"edge case for shared secret", "curve":"curve25519", "public":"63e5b1fe9601fe84385d8866b0421262f78fbfa5aff9585e626679b18547d959", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":71, "comment":"edge case for shared secret", "curve":"curve25519", "public":"e428f3dac17809f827a522ce32355058d07369364aa78902ee10139b9f9dd653", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"fcffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result":"valid", "flags":[ ] }, { "tcId":72, "comment":"edge case for shared secret", "curve":"curve25519", "public":"b3b50e3ed3a407b95de942ef74575b5ab8a10c09ee103544d60bdfed8138ab2b", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"f9ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":73, "comment":"edge case for shared secret", "curve":"curve25519", "public":"213fffe93d5ea8cd242e462844029922c43c77c9e3e42f562f485d24c501a20b", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"f3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result":"valid", "flags":[ ] }, { "tcId":74, "comment":"edge case for shared secret", "curve":"curve25519", "public":"91b232a178b3cd530932441e6139418f72172292f1da4c1834fc5ebfefb51e3f", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff03", "result":"valid", "flags":[ ] }, { "tcId":75, "comment":"edge case for shared secret", "curve":"curve25519", "public":"045c6e11c5d332556c7822fe94ebf89b56a3878dc27ca079103058849fabcb4f", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"e5ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":76, "comment":"edge case for shared secret", "curve":"curve25519", "public":"1ca2190b71163539063c35773bda0c9c928e9136f0620aeb093f099197b7f74e", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"e3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":77, "comment":"edge case for shared secret", "curve":"curve25519", "public":"f76e9010ac33c5043b2d3b76a842171000c4916222e9e85897a0aec7f6350b3c", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"ddffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", "result":"valid", "flags":[ ] }, { "tcId":78, "comment":"edge case for shared secret", "curve":"curve25519", "public":"bb72688d8f8aa7a39cd6060cd5c8093cdec6fe341937c3886a99346cd07faa55", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"dbffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":79, "comment":"edge case for shared secret", "curve":"curve25519", "public":"88fddea193391c6a5933ef9b71901549447205aae9da928a6b91a352ba10f41f", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"0000000000000000000000000000000000000000000000000000000000000002", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":80, "comment":"edge case for shared secret", "curve":"curve25519", "public":"303b392f153116cad9cc682a00ccc44c95ff0d3bbe568beb6c4e739bafdc2c68", "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", "shared":"0000000000000000000000000000000000000000000000000000000000008000", "result":"acceptable", "flags":[ "Twist" ] }, { "tcId":81, "comment":"checking for overflow", "curve":"curve25519", "public":"fd300aeb40e1fa582518412b49b208a7842b1e1f056a040178ea4141534f652d", "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", "shared":"b734105dc257585d73b566ccb76f062795ccbec89128e52b02f3e59639f13c46", "result":"valid", "flags":[ ] }, { "tcId":82, "comment":"checking for overflow", "curve":"curve25519", "public":"c8ef79b514d7682677bc7931e06ee5c27c9b392b4ae9484473f554e6678ecc2e", "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", "shared":"647a46b6fc3f40d62141ee3cee706b4d7a9271593a7b143e8e2e2279883e4550", "result":"valid", "flags":[ ] }, { "tcId":83, "comment":"checking for overflow", "curve":"curve25519", "public":"64aeac2504144861532b7bbcb6c87d67dd4c1f07ebc2e06effb95aecc6170b2c", "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", "shared":"4ff03d5fb43cd8657a3cf37c138cadcecce509e4eba089d0ef40b4e4fb946155", "result":"valid", "flags":[ ] }, { "tcId":84, "comment":"checking for overflow", "curve":"curve25519", "public":"bf68e35e9bdb7eee1b50570221860f5dcdad8acbab031b14974cc49013c49831", "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", "shared":"21cee52efdbc812e1d021a4af1e1d8bc4db3c400e4d2a2c56a3926db4d99c65b", "result":"valid", "flags":[ ] }, { "tcId":85, "comment":"checking for overflow", "curve":"curve25519", "public":"5347c491331a64b43ddc683034e677f53dc32b52a52a577c15a83bf298e99f19", "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", "shared":"18cb89e4e20c0c2bd324305245266c9327690bbe79acb88f5b8fb3f74eca3e52", "result":"valid", "flags":[ ] }, { "tcId":86, "comment":"private key == -1 (mod order)", "curve":"curve25519", "public":"258e04523b8d253ee65719fc6906c657192d80717edc828fa0af21686e2faa75", "private":"a023cdd083ef5bb82f10d62e59e15a6800000000000000000000000000000050", "shared":"258e04523b8d253ee65719fc6906c657192d80717edc828fa0af21686e2faa75", "result":"valid", "flags":[ ] }, { "tcId":87, "comment":"private key == 1 (mod order) on twist", "curve":"curve25519", "public":"2eae5ec3dd494e9f2d37d258f873a8e6e9d0dbd1e383ef64d98bb91b3e0be035", "private":"58083dd261ad91eff952322ec824c682ffffffffffffffffffffffffffffff5f", "shared":"2eae5ec3dd494e9f2d37d258f873a8e6e9d0dbd1e383ef64d98bb91b3e0be035", "result":"acceptable", "flags":[ ] } ] golang-github-cloudflare-circl-1.3.7/dh/x448/000077500000000000000000000000001454601126700205715ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/x448/curve.go000066400000000000000000000066011454601126700222470ustar00rootroot00000000000000package x448 import ( fp "github.com/cloudflare/circl/math/fp448" ) // ladderJoye calculates a fixed-point multiplication with the generator point. // The algorithm is the right-to-left Joye's ladder as described // in "How to precompute a ladder" in SAC'2017. func ladderJoye(k *Key) { w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. w[1] = fp.Elt{ // x1 = S 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, } fp.SetOne(&w[2]) // z1 = 1 w[3] = fp.Elt{ // x2 = G-S 0x20, 0x27, 0x9d, 0xc9, 0x7d, 0x19, 0xb1, 0xac, 0xf8, 0xba, 0x69, 0x1c, 0xff, 0x33, 0xac, 0x23, 0x51, 0x1b, 0xce, 0x3a, 0x64, 0x65, 0xbd, 0xf1, 0x23, 0xf8, 0xc1, 0x84, 0x9d, 0x45, 0x54, 0x29, 0x67, 0xb9, 0x81, 0x1c, 0x03, 0xd1, 0xcd, 0xda, 0x7b, 0xeb, 0xff, 0x1a, 0x88, 0x03, 0xcf, 0x3a, 0x42, 0x44, 0x32, 0x01, 0x25, 0xb7, 0xfa, 0xf0, } fp.SetOne(&w[4]) // z2 = 1 const n = 448 const h = 2 swap := uint(1) for s := 0; s < n-h; s++ { i := (s + h) / 8 j := (s + h) % 8 bit := uint((k[i] >> uint(j)) & 1) copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) diffAdd(&w, swap^bit) swap = bit } for s := 0; s < h; s++ { double(&w[1], &w[2]) } toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) } // ladderMontgomery calculates a generic scalar point multiplication // The algorithm implemented is the left-to-right Montgomery's ladder. func ladderMontgomery(k, xP *Key) { w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. w[0] = *(*fp.Elt)(xP) // x1 = xP fp.SetOne(&w[1]) // x2 = 1 w[3] = *(*fp.Elt)(xP) // x3 = xP fp.SetOne(&w[4]) // z3 = 1 move := uint(0) for s := 448 - 1; s >= 0; s-- { i := s / 8 j := s % 8 bit := uint((k[i] >> uint(j)) & 1) ladderStep(&w, move^bit) move = bit } toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) } func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { fp.Inv(z, z) fp.Mul(x, x, z) _ = fp.ToBytes(k[:], x) } var lowOrderPoints = [3]fp.Elt{ { /* (0,_,1) point of order 2 on Curve448 */ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, }, { /* (1,_,1) a point of order 4 on the twist of Curve448 */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, }, { /* (-1,_,1) point of order 4 on Curve448 */ 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, }, } golang-github-cloudflare-circl-1.3.7/dh/x448/curve_amd64.go000066400000000000000000000012361454601126700232410ustar00rootroot00000000000000//go:build amd64 && !purego // +build amd64,!purego package x448 import ( fp "github.com/cloudflare/circl/math/fp448" "golang.org/x/sys/cpu" ) var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX var _ = hasBmi2Adx func double(x, z *fp.Elt) { doubleAmd64(x, z) } func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } //go:noescape func doubleAmd64(x, z *fp.Elt) //go:noescape func diffAddAmd64(w *[5]fp.Elt, b uint) //go:noescape func ladderStepAmd64(w *[5]fp.Elt, b uint) //go:noescape func mulA24Amd64(z, x *fp.Elt) golang-github-cloudflare-circl-1.3.7/dh/x448/curve_amd64.h000066400000000000000000000066431454601126700230720ustar00rootroot00000000000000#define ladderStepLeg \ addSub(x2,z2) \ addSub(x3,z3) \ integerMulLeg(b0,x2,z3) \ integerMulLeg(b1,x3,z2) \ reduceFromDoubleLeg(t0,b0) \ reduceFromDoubleLeg(t1,b1) \ addSub(t0,t1) \ cselect(x2,x3,regMove) \ cselect(z2,z3,regMove) \ integerSqrLeg(b0,t0) \ integerSqrLeg(b1,t1) \ reduceFromDoubleLeg(x3,b0) \ reduceFromDoubleLeg(z3,b1) \ integerMulLeg(b0,x1,z3) \ reduceFromDoubleLeg(z3,b0) \ integerSqrLeg(b0,x2) \ integerSqrLeg(b1,z2) \ reduceFromDoubleLeg(x2,b0) \ reduceFromDoubleLeg(z2,b1) \ subtraction(t0,x2,z2) \ multiplyA24Leg(t1,t0) \ additionLeg(t1,t1,z2) \ integerMulLeg(b0,x2,z2) \ integerMulLeg(b1,t0,t1) \ reduceFromDoubleLeg(x2,b0) \ reduceFromDoubleLeg(z2,b1) #define ladderStepBmi2Adx \ addSub(x2,z2) \ addSub(x3,z3) \ integerMulAdx(b0,x2,z3) \ integerMulAdx(b1,x3,z2) \ reduceFromDoubleAdx(t0,b0) \ reduceFromDoubleAdx(t1,b1) \ addSub(t0,t1) \ cselect(x2,x3,regMove) \ cselect(z2,z3,regMove) \ integerSqrAdx(b0,t0) \ integerSqrAdx(b1,t1) \ reduceFromDoubleAdx(x3,b0) \ reduceFromDoubleAdx(z3,b1) \ integerMulAdx(b0,x1,z3) \ reduceFromDoubleAdx(z3,b0) \ integerSqrAdx(b0,x2) \ integerSqrAdx(b1,z2) \ reduceFromDoubleAdx(x2,b0) \ reduceFromDoubleAdx(z2,b1) \ subtraction(t0,x2,z2) \ multiplyA24Adx(t1,t0) \ additionAdx(t1,t1,z2) \ integerMulAdx(b0,x2,z2) \ integerMulAdx(b1,t0,t1) \ reduceFromDoubleAdx(x2,b0) \ reduceFromDoubleAdx(z2,b1) #define difAddLeg \ addSub(x1,z1) \ integerMulLeg(b0,z1,ui) \ reduceFromDoubleLeg(z1,b0) \ addSub(x1,z1) \ integerSqrLeg(b0,x1) \ integerSqrLeg(b1,z1) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) \ integerMulLeg(b0,x1,z2) \ integerMulLeg(b1,z1,x2) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) #define difAddBmi2Adx \ addSub(x1,z1) \ integerMulAdx(b0,z1,ui) \ reduceFromDoubleAdx(z1,b0) \ addSub(x1,z1) \ integerSqrAdx(b0,x1) \ integerSqrAdx(b1,z1) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) \ integerMulAdx(b0,x1,z2) \ integerMulAdx(b1,z1,x2) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) #define doubleLeg \ addSub(x1,z1) \ integerSqrLeg(b0,x1) \ integerSqrLeg(b1,z1) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) \ subtraction(t0,x1,z1) \ multiplyA24Leg(t1,t0) \ additionLeg(t1,t1,z1) \ integerMulLeg(b0,x1,z1) \ integerMulLeg(b1,t0,t1) \ reduceFromDoubleLeg(x1,b0) \ reduceFromDoubleLeg(z1,b1) #define doubleBmi2Adx \ addSub(x1,z1) \ integerSqrAdx(b0,x1) \ integerSqrAdx(b1,z1) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) \ subtraction(t0,x1,z1) \ multiplyA24Adx(t1,t0) \ additionAdx(t1,t1,z1) \ integerMulAdx(b0,x1,z1) \ integerMulAdx(b1,t0,t1) \ reduceFromDoubleAdx(x1,b0) \ reduceFromDoubleAdx(z1,b1) golang-github-cloudflare-circl-1.3.7/dh/x448/curve_amd64.s000066400000000000000000000125361454601126700231030ustar00rootroot00000000000000// +build amd64 #include "textflag.h" // Depends on circl/math/fp448 package #include "../../math/fp448/fp_amd64.h" #include "curve_amd64.h" // CTE_A24 is (A+2)/4 from Curve448 #define CTE_A24 39082 #define Size 56 // multiplyA24Leg multiplies x times CTE_A24 and stores in z // Uses: AX, DX, R8-R15, FLAGS // Instr: x86_64, cmov, adx #define multiplyA24Leg(z,x) \ MOVQ $CTE_A24, R15; \ MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ MOVQ DX, AX; \ SHLQ $32, AX; \ ADDQ DX, R8; MOVQ $0, DX; \ ADCQ $0, R9; \ ADCQ $0, R10; \ ADCQ AX, R11; \ ADCQ $0, R12; \ ADCQ $0, R13; \ ADCQ $0, R14; \ ADCQ $0, DX; \ MOVQ DX, AX; \ SHLQ $32, AX; \ ADDQ DX, R8; \ ADCQ $0, R9; \ ADCQ $0, R10; \ ADCQ AX, R11; \ ADCQ $0, R12; \ ADCQ $0, R13; \ ADCQ $0, R14; \ MOVQ R8, 0+z; \ MOVQ R9, 8+z; \ MOVQ R10, 16+z; \ MOVQ R11, 24+z; \ MOVQ R12, 32+z; \ MOVQ R13, 40+z; \ MOVQ R14, 48+z; // multiplyA24Adx multiplies x times CTE_A24 and stores in z // Uses: AX, DX, R8-R14, FLAGS // Instr: x86_64, bmi2 #define multiplyA24Adx(z,x) \ MOVQ $CTE_A24, DX; \ MULXQ 0+x, R8, R9; \ MULXQ 8+x, AX, R10; ADDQ AX, R9; \ MULXQ 16+x, AX, R11; ADCQ AX, R10; \ MULXQ 24+x, AX, R12; ADCQ AX, R11; \ MULXQ 32+x, AX, R13; ADCQ AX, R12; \ MULXQ 40+x, AX, R14; ADCQ AX, R13; \ MULXQ 48+x, AX, DX; ADCQ AX, R14; \ ;;;;;;;;;;;;;;;;;;;; ADCQ $0, DX; \ MOVQ DX, AX; \ SHLQ $32, AX; \ ADDQ DX, R8; MOVQ $0, DX; \ ADCQ $0, R9; \ ADCQ $0, R10; \ ADCQ AX, R11; \ ADCQ $0, R12; \ ADCQ $0, R13; \ ADCQ $0, R14; \ ADCQ $0, DX; \ MOVQ DX, AX; \ SHLQ $32, AX; \ ADDQ DX, R8; \ ADCQ $0, R9; \ ADCQ $0, R10; \ ADCQ AX, R11; \ ADCQ $0, R12; \ ADCQ $0, R13; \ ADCQ $0, R14; \ MOVQ R8, 0+z; \ MOVQ R9, 8+z; \ MOVQ R10, 16+z; \ MOVQ R11, 24+z; \ MOVQ R12, 32+z; \ MOVQ R13, 40+z; \ MOVQ R14, 48+z; #define mulA24Legacy \ multiplyA24Leg(0(DI),0(SI)) #define mulA24Bmi2Adx \ multiplyA24Adx(0(DI),0(SI)) // func mulA24Amd64(z, x *fp448.Elt) TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 MOVQ z+0(FP), DI MOVQ x+8(FP), SI CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) // func ladderStepAmd64(w *[5]fp448.Elt, b uint) // ladderStepAmd64 calculates a point addition and doubling as follows: // (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). // w = {x1,x2,z2,x3,z4} are five fp255.Elt of 56 bytes. // stack = (t0,t1) are two fp.Elt of fp.Size bytes, and // (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. TEXT ·ladderStepAmd64(SB),NOSPLIT,$336-16 // Parameters #define regWork DI #define regMove SI #define x1 0*Size(regWork) #define x2 1*Size(regWork) #define z2 2*Size(regWork) #define x3 3*Size(regWork) #define z3 4*Size(regWork) // Local variables #define t0 0*Size(SP) #define t1 1*Size(SP) #define b0 2*Size(SP) #define b1 4*Size(SP) MOVQ w+0(FP), regWork MOVQ b+8(FP), regMove CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) #undef regWork #undef regMove #undef x1 #undef x2 #undef z2 #undef x3 #undef z3 #undef t0 #undef t1 #undef b0 #undef b1 // func diffAddAmd64(work *[5]fp.Elt, swap uint) // diffAddAmd64 calculates a differential point addition using a precomputed point. // (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) // work = {mu,x1,z1,x2,z2} are five fp448.Elt of 56 bytes, and // stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. // This is Equation 7 at https://eprint.iacr.org/2017/264. TEXT ·diffAddAmd64(SB),NOSPLIT,$224-16 // Parameters #define regWork DI #define regSwap SI #define ui 0*Size(regWork) #define x1 1*Size(regWork) #define z1 2*Size(regWork) #define x2 3*Size(regWork) #define z2 4*Size(regWork) // Local variables #define b0 0*Size(SP) #define b1 2*Size(SP) MOVQ w+0(FP), regWork MOVQ b+8(FP), regSwap cswap(x1,x2,regSwap) cswap(z1,z2,regSwap) CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) #undef regWork #undef regSwap #undef ui #undef x1 #undef z1 #undef x2 #undef z2 #undef b0 #undef b1 // func doubleAmd64(x, z *fp448.Elt) // doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). // stack = (t0,t1) are two fp.Elt of fp.Size bytes, and // (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. TEXT ·doubleAmd64(SB),NOSPLIT,$336-16 // Parameters #define x1 0(DI) #define z1 0(SI) // Local variables #define t0 0*Size(SP) #define t1 1*Size(SP) #define b0 2*Size(SP) #define b1 4*Size(SP) MOVQ x+0(FP), DI MOVQ z+8(FP), SI CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) #undef x1 #undef z1 #undef t0 #undef t1 #undef b0 #undef b1 golang-github-cloudflare-circl-1.3.7/dh/x448/curve_generic.go000066400000000000000000000045051454601126700237440ustar00rootroot00000000000000package x448 import ( "encoding/binary" "math/bits" "github.com/cloudflare/circl/math/fp448" ) func doubleGeneric(x, z *fp448.Elt) { t0, t1 := &fp448.Elt{}, &fp448.Elt{} fp448.AddSub(x, z) fp448.Sqr(x, x) fp448.Sqr(z, z) fp448.Sub(t0, x, z) mulA24Generic(t1, t0) fp448.Add(t1, t1, z) fp448.Mul(x, x, z) fp448.Mul(z, t0, t1) } func diffAddGeneric(w *[5]fp448.Elt, b uint) { mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] fp448.Cswap(x1, x2, b) fp448.Cswap(z1, z2, b) fp448.AddSub(x1, z1) fp448.Mul(z1, z1, mu) fp448.AddSub(x1, z1) fp448.Sqr(x1, x1) fp448.Sqr(z1, z1) fp448.Mul(x1, x1, z2) fp448.Mul(z1, z1, x2) } func ladderStepGeneric(w *[5]fp448.Elt, b uint) { x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] t0 := &fp448.Elt{} t1 := &fp448.Elt{} fp448.AddSub(x2, z2) fp448.AddSub(x3, z3) fp448.Mul(t0, x2, z3) fp448.Mul(t1, x3, z2) fp448.AddSub(t0, t1) fp448.Cmov(x2, x3, b) fp448.Cmov(z2, z3, b) fp448.Sqr(x3, t0) fp448.Sqr(z3, t1) fp448.Mul(z3, x1, z3) fp448.Sqr(x2, x2) fp448.Sqr(z2, z2) fp448.Sub(t0, x2, z2) mulA24Generic(t1, t0) fp448.Add(t1, t1, z2) fp448.Mul(x2, x2, z2) fp448.Mul(z2, t0, t1) } func mulA24Generic(z, x *fp448.Elt) { const A24 = 39082 const n = 8 var xx [7]uint64 for i := range xx { xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) } h0, l0 := bits.Mul64(xx[0], A24) h1, l1 := bits.Mul64(xx[1], A24) h2, l2 := bits.Mul64(xx[2], A24) h3, l3 := bits.Mul64(xx[3], A24) h4, l4 := bits.Mul64(xx[4], A24) h5, l5 := bits.Mul64(xx[5], A24) h6, l6 := bits.Mul64(xx[6], A24) l1, c0 := bits.Add64(h0, l1, 0) l2, c1 := bits.Add64(h1, l2, c0) l3, c2 := bits.Add64(h2, l3, c1) l4, c3 := bits.Add64(h3, l4, c2) l5, c4 := bits.Add64(h4, l5, c3) l6, c5 := bits.Add64(h5, l6, c4) l7, _ := bits.Add64(h6, 0, c5) l0, c0 = bits.Add64(l0, l7, 0) l1, c1 = bits.Add64(l1, 0, c0) l2, c2 = bits.Add64(l2, 0, c1) l3, c3 = bits.Add64(l3, l7<<32, c2) l4, c4 = bits.Add64(l4, 0, c3) l5, c5 = bits.Add64(l5, 0, c4) l6, l7 = bits.Add64(l6, 0, c5) xx[0], c0 = bits.Add64(l0, l7, 0) xx[1], c1 = bits.Add64(l1, 0, c0) xx[2], c2 = bits.Add64(l2, 0, c1) xx[3], c3 = bits.Add64(l3, l7<<32, c2) xx[4], c4 = bits.Add64(l4, 0, c3) xx[5], c5 = bits.Add64(l5, 0, c4) xx[6], _ = bits.Add64(l6, 0, c5) for i := range xx { binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) } } golang-github-cloudflare-circl-1.3.7/dh/x448/curve_noasm.go000066400000000000000000000005641454601126700234460ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package x448 import fp "github.com/cloudflare/circl/math/fp448" func double(x, z *fp.Elt) { doubleGeneric(x, z) } func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } golang-github-cloudflare-circl-1.3.7/dh/x448/curve_test.go000066400000000000000000000107461454601126700233130ustar00rootroot00000000000000package x448 import ( "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" fp "github.com/cloudflare/circl/math/fp448" ) func getModulus() *big.Int { p := big.NewInt(1) p.Lsh(p, 224) p.Sub(p, new(big.Int).SetInt64(1)) p.Lsh(p, 224) p.Sub(p, new(big.Int).SetInt64(1)) return p } func doubleBig(x1, z1, p *big.Int) { // Montgomery point doubling in projective (X:Z) coordinates. A24 := big.NewInt(39082) A, B, C := big.NewInt(0), big.NewInt(0), big.NewInt(0) A.Add(x1, z1).Mod(A, p) B.Sub(x1, z1).Mod(B, p) A.Mul(A, A) B.Mul(B, B) C.Sub(A, B) x1.Mul(A, B).Mod(x1, p) z1.Mul(C, A24).Add(z1, B).Mul(z1, C).Mod(z1, p) } // Equation 7 at https://eprint.iacr.org/2017/264 func diffAddBig(work [5]*big.Int, p *big.Int, b uint) { mu, x1, z1, x2, z2 := work[0], work[1], work[2], work[3], work[4] A, B := big.NewInt(0), big.NewInt(0) if b != 0 { t := new(big.Int) t.Set(x1) x1.Set(x2) x2.Set(t) t.Set(z1) z1.Set(z2) z2.Set(t) } A.Add(x1, z1) B.Sub(x1, z1) B.Mul(B, mu).Mod(B, p) x1.Add(A, B).Mod(x1, p) z1.Sub(A, B).Mod(z1, p) x1.Mul(x1, x1).Mul(x1, z2).Mod(x1, p) z1.Mul(z1, z1).Mul(z1, x2).Mod(z1, p) mu.Mod(mu, p) x2.Mod(x2, p) z2.Mod(z2, p) } func ladderStepBig(work [5]*big.Int, p *big.Int, b uint) { A24 := big.NewInt(39082) x1 := work[0] x2, z2 := work[1], work[2] x3, z3 := work[3], work[4] A, B, C, D := big.NewInt(0), big.NewInt(0), big.NewInt(0), big.NewInt(0) DA, CB, E := big.NewInt(0), big.NewInt(0), big.NewInt(0) A.Add(x2, z2).Mod(A, p) B.Sub(x2, z2).Mod(B, p) C.Add(x3, z3).Mod(C, p) D.Sub(x3, z3).Mod(D, p) DA.Mul(D, A).Mod(DA, p) CB.Mul(C, B).Mod(CB, p) if b != 0 { t := new(big.Int) t.Set(A) A.Set(C) C.Set(t) t.Set(B) B.Set(D) D.Set(t) } AA := A.Mul(A, A).Mod(A, p) BB := B.Mul(B, B).Mod(B, p) E.Sub(AA, BB) x1.Mod(x1, p) x2.Mul(AA, BB).Mod(x2, p) z2.Mul(E, A24).Add(z2, BB).Mul(z2, E).Mod(z2, p) x3.Add(DA, CB) z3.Sub(DA, CB) x3.Mul(x3, x3).Mod(x3, p) z3.Mul(z3, z3).Mul(z3, x1).Mod(z3, p) } type ( tDouble func(x, z *fp.Elt) tDiffAdd func(w *[5]fp.Elt, b uint) tLadderStep func(w *[5]fp.Elt, b uint) tMulA24 func(z, x *fp.Elt) ) func TestGeneric(t *testing.T) { testDouble(t, doubleGeneric) testDiffAdd(t, diffAddGeneric) testLadderStep(t, ladderStepGeneric) testMulA24(t, mulA24Generic) } func TestNative(t *testing.T) { testDouble(t, double) testDiffAdd(t, diffAdd) testLadderStep(t, ladderStep) testMulA24(t, mulA24) } func testMulA24(t *testing.T, f tMulA24) { const numTests = 1 << 9 var x, z fp.Elt p := getModulus() A24 := big.NewInt(39082) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) bigX := conv.BytesLe2BigInt(x[:]) f(&z, &x) got := conv.BytesLe2BigInt(z[:]) got.Mod(got, p) want := bigX.Mul(bigX, A24).Mod(bigX, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func testDouble(t *testing.T, f tDouble) { const numTests = 1 << 9 var x, z fp.Elt p := getModulus() for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(z[:]) bigX := conv.BytesLe2BigInt(x[:]) bigZ := conv.BytesLe2BigInt(z[:]) f(&x, &z) got0 := conv.BytesLe2BigInt(x[:]) got1 := conv.BytesLe2BigInt(z[:]) got0.Mod(got0, p) got1.Mod(got1, p) doubleBig(bigX, bigZ, p) want0 := bigX want1 := bigZ if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, z) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, z) } } } func testDiffAdd(t *testing.T, f tDiffAdd) { const numTests = 1 << 9 var w [5]fp.Elt bigWork := [5]*big.Int{} p := getModulus() for i := 0; i < numTests; i++ { for j := range w { _, _ = rand.Read(w[j][:]) bigWork[j] = conv.BytesLe2BigInt(w[j][:]) } b := uint(w[0][0] & 1) f(&w, b) diffAddBig(bigWork, p, b) for j := range bigWork { got := conv.BytesLe2BigInt(w[j][:]) got.Mod(got, p) want := bigWork[j] if got.Cmp(want) != 0 { test.ReportError(t, got, want, w, b) } } } } func testLadderStep(t *testing.T, f tLadderStep) { const numTests = 1 << 9 var w [5]fp.Elt bigWork := [5]*big.Int{} p := getModulus() for i := 0; i < numTests; i++ { for j := range w { _, _ = rand.Read(w[j][:]) bigWork[j] = conv.BytesLe2BigInt(w[j][:]) } b := uint(w[0][0] & 1) f(&w, b) ladderStepBig(bigWork, p, b) for j := range bigWork { got := conv.BytesLe2BigInt(w[j][:]) got.Mod(got, p) want := bigWork[j] if got.Cmp(want) != 0 { test.ReportError(t, got, want, w, b) } } } } golang-github-cloudflare-circl-1.3.7/dh/x448/doc.go000066400000000000000000000014051454601126700216650ustar00rootroot00000000000000/* Package x448 provides Diffie-Hellman functions as specified in RFC-7748. Validation of public keys. The Diffie-Hellman function, as described in RFC-7748 [1], works for any public key. However, if a different protocol requires contributory behaviour [2,3], then the public keys must be validated against low-order points [3,4]. To do that, the Shared function performs this validation internally and returns false when the public key is invalid (i.e., it is a low-order point). References: - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) */ package x448 golang-github-cloudflare-circl-1.3.7/dh/x448/key.go000066400000000000000000000021101454601126700217020ustar00rootroot00000000000000package x448 import ( "crypto/subtle" fp "github.com/cloudflare/circl/math/fp448" ) // Size is the length in bytes of a X448 key. const Size = 56 // Key represents a X448 key. type Key [Size]byte func (k *Key) clamp(in *Key) *Key { *k = *in k[0] &= 252 k[55] |= 128 return k } // isValidPubKey verifies if the public key is not a low-order point. func (k *Key) isValidPubKey() bool { fp.Modp((*fp.Elt)(k)) var isLowOrder int for _, P := range lowOrderPoints { isLowOrder |= subtle.ConstantTimeCompare(P[:], k[:]) } return isLowOrder == 0 } // KeyGen obtains a public key given a secret key. func KeyGen(public, secret *Key) { ladderJoye(public.clamp(secret)) } // Shared calculates Alice's shared key from Alice's secret key and Bob's // public key returning true on success. A failure case happens when the public // key is a low-order point, thus the shared key is all-zeros and the function // returns false. func Shared(shared, secret, public *Key) bool { validPk := *public ok := validPk.isValidPubKey() ladderMontgomery(shared.clamp(secret), &validPk) return ok } golang-github-cloudflare-circl-1.3.7/dh/x448/key_test.go000066400000000000000000000067111454601126700227540ustar00rootroot00000000000000package x448 import ( "crypto/rand" "encoding/hex" "encoding/json" "flag" "fmt" "io" "os" "testing" "github.com/cloudflare/circl/internal/test" ) func hexStr2Key(k *Key, s string) { b, err := hex.DecodeString(s) if err != nil { panic("Can't convert string to key") } copy(k[:], b) } // Indicates whether long tests should be run var runLongTest = flag.Bool("long", false, "runs longer tests") type katVector struct { Public string `json:"input"` Shared string `json:"output"` Private string `json:"scalar"` } func TestRFC7748Kat(t *testing.T) { const nameFile = "testdata/rfc7748_kat_test.json" var kat []katVector jsonFile, err := os.Open(nameFile) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", nameFile, err) } err = json.Unmarshal(input, &kat) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) } var priv, pub, got, want Key for _, v := range kat { hexStr2Key(&pub, v.Public) hexStr2Key(&priv, v.Private) Shared(&got, &priv, &pub) hexStr2Key(&want, v.Shared) if got != want { test.ReportError(t, got, want, v) } } } type katTimes struct { Times uint32 `json:"times"` Key string `json:"key"` } func TestRFC7748Times(t *testing.T) { const nameFile = "testdata/rfc7748_times_test.json" jsonFile, err := os.Open(nameFile) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", nameFile, err) } var kat []katTimes err = json.Unmarshal(input, &kat) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) } var got, want Key for _, v := range kat { if !*runLongTest && v.Times == uint32(1000000) { t.Log("Skipped one long test, add -long flag to run longer tests") continue } u := Key{5} k := u r := u for i := uint32(0); i < v.Times; i++ { Shared(&r, &k, &u) u = k k = r } got = k hexStr2Key(&want, v.Key) if got != want { test.ReportError(t, got, want, v.Times) } } } func TestBase(t *testing.T) { testTimes := 1 << 10 var got, want, secret Key gen := Key{5} for i := 0; i < testTimes; i++ { _, _ = io.ReadFull(rand.Reader, secret[:]) KeyGen(&got, &secret) Shared(&want, &secret, &gen) if got != want { test.ReportError(t, got, want, secret) } } } func BenchmarkX448(b *testing.B) { var x, y, z Key _, _ = io.ReadFull(rand.Reader, x[:]) _, _ = io.ReadFull(rand.Reader, y[:]) _, _ = io.ReadFull(rand.Reader, z[:]) b.Run("KeyGen", func(b *testing.B) { for i := 0; i < b.N; i++ { KeyGen(&x, &y) } }) b.Run("Shared", func(b *testing.B) { for i := 0; i < b.N; i++ { Shared(&z, &x, &y) } }) } func Example_x448() { var AliceSecret, BobSecret, AlicePublic, BobPublic, AliceShared, BobShared Key // Generating Alice's secret and public keys _, _ = io.ReadFull(rand.Reader, AliceSecret[:]) KeyGen(&AlicePublic, &AliceSecret) // Generating Bob's secret and public keys _, _ = io.ReadFull(rand.Reader, BobSecret[:]) KeyGen(&BobPublic, &BobSecret) // Deriving Alice's shared key okA := Shared(&AliceShared, &AliceSecret, &BobPublic) // Deriving Bob's shared key okB := Shared(&BobShared, &BobSecret, &AlicePublic) fmt.Println(AliceShared == BobShared && okA && okB) // Output: true } golang-github-cloudflare-circl-1.3.7/dh/x448/table.go000066400000000000000000004644271454601126700222300ustar00rootroot00000000000000package x448 import fp "github.com/cloudflare/circl/math/fp448" // tableGenerator contains the set of points: // // t[i] = (xi+1)/(xi-1), // // where (xi,yi) = 2^iG and G is the generator point // Size = (448)*(448/8) = 25088 bytes. var tableGenerator = [448 * fp.Size]byte{ /* (2^ 0)P */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, /* (2^ 1)P */ 0x37, 0xfa, 0xaa, 0x0d, 0x86, 0xa6, 0x24, 0xe9, 0x6c, 0x95, 0x08, 0x34, 0xba, 0x1a, 0x81, 0x3a, 0xae, 0x01, 0xa5, 0xa7, 0x05, 0x85, 0x96, 0x00, 0x06, 0x5a, 0xd7, 0xff, 0xee, 0x8e, 0x8f, 0x94, 0xd2, 0xdc, 0xd7, 0xfc, 0xe7, 0xe5, 0x99, 0x1d, 0x05, 0x46, 0x43, 0xe8, 0xbc, 0x12, 0xb7, 0xeb, 0x30, 0x5e, 0x7a, 0x85, 0x68, 0xed, 0x9d, 0x28, /* (2^ 2)P */ 0xf1, 0x7d, 0x08, 0x2b, 0x32, 0x4a, 0x62, 0x80, 0x36, 0xe7, 0xa4, 0x76, 0x5a, 0x2a, 0x1e, 0xf7, 0x9e, 0x3c, 0x40, 0x46, 0x9a, 0x1b, 0x61, 0xc1, 0xbf, 0x1a, 0x1b, 0xae, 0x91, 0x80, 0xa3, 0x76, 0x6c, 0xd4, 0x8f, 0xa4, 0xee, 0x26, 0x39, 0x23, 0xa4, 0x80, 0xf4, 0x66, 0x92, 0xe4, 0xe1, 0x18, 0x76, 0xc5, 0xe2, 0x19, 0x87, 0xd5, 0xc3, 0xe8, /* (2^ 3)P */ 0xfb, 0xc9, 0xf0, 0x07, 0xf2, 0x93, 0xd8, 0x50, 0x36, 0xed, 0xfb, 0xbd, 0xb2, 0xd3, 0xfc, 0xdf, 0xd5, 0x2a, 0x6e, 0x26, 0x09, 0xce, 0xd4, 0x07, 0x64, 0x9f, 0x40, 0x74, 0xad, 0x98, 0x2f, 0x1c, 0xb6, 0xdc, 0x2d, 0x42, 0xff, 0xbf, 0x97, 0xd8, 0xdb, 0xef, 0x99, 0xca, 0x73, 0x99, 0x1a, 0x04, 0x3b, 0x56, 0x2c, 0x1f, 0x87, 0x9d, 0x9f, 0x03, /* (2^ 4)P */ 0x4c, 0x35, 0x97, 0xf7, 0x81, 0x2c, 0x84, 0xa6, 0xe0, 0xcb, 0xce, 0x37, 0x4c, 0x21, 0x1c, 0x67, 0xfa, 0xab, 0x18, 0x4d, 0xef, 0xd0, 0xf0, 0x44, 0xa9, 0xfb, 0xc0, 0x8e, 0xda, 0x57, 0xa1, 0xd8, 0xeb, 0x87, 0xf4, 0x17, 0xea, 0x66, 0x0f, 0x16, 0xea, 0xcd, 0x5f, 0x3e, 0x88, 0xea, 0x09, 0x68, 0x40, 0xdf, 0x43, 0xcc, 0x54, 0x61, 0x58, 0xaa, /* (2^ 5)P */ 0x8d, 0xe7, 0x59, 0xd7, 0x5e, 0x63, 0x37, 0xa7, 0x3f, 0xd1, 0x49, 0x85, 0x01, 0xdd, 0x5e, 0xb3, 0xe6, 0x29, 0xcb, 0x25, 0x93, 0xdd, 0x08, 0x96, 0x83, 0x52, 0x76, 0x85, 0xf5, 0x5d, 0x02, 0xbf, 0xe9, 0x6d, 0x15, 0x27, 0xc1, 0x09, 0xd1, 0x14, 0x4d, 0x6e, 0xe8, 0xaf, 0x59, 0x58, 0x34, 0x9d, 0x2a, 0x99, 0x85, 0x26, 0xbe, 0x4b, 0x1e, 0xb9, /* (2^ 6)P */ 0x8d, 0xce, 0x94, 0xe2, 0x18, 0x56, 0x0d, 0x82, 0x8e, 0xdf, 0x85, 0x01, 0x8f, 0x93, 0x3c, 0xc6, 0xbd, 0x61, 0xfb, 0xf4, 0x22, 0xc5, 0x16, 0x87, 0xd1, 0xb1, 0x9e, 0x09, 0xc5, 0x83, 0x2e, 0x4a, 0x07, 0x88, 0xee, 0xe0, 0x29, 0x8d, 0x2e, 0x1f, 0x88, 0xad, 0xfd, 0x18, 0x93, 0xb7, 0xed, 0x42, 0x86, 0x78, 0xf0, 0xb8, 0x70, 0xbe, 0x01, 0x67, /* (2^ 7)P */ 0xdf, 0x62, 0x2d, 0x94, 0xc7, 0x35, 0x23, 0xda, 0x27, 0xbb, 0x2b, 0xdb, 0x30, 0x80, 0x68, 0x16, 0xa3, 0xae, 0xd7, 0xd2, 0xa7, 0x7c, 0xbf, 0x6a, 0x1d, 0x83, 0xde, 0x96, 0x0a, 0x43, 0xb6, 0x30, 0x37, 0xd6, 0xee, 0x63, 0x59, 0x9a, 0xbf, 0xa3, 0x30, 0x6c, 0xaf, 0x0c, 0xee, 0x3d, 0xcb, 0x35, 0x4b, 0x55, 0x5f, 0x84, 0x85, 0xcb, 0x4f, 0x1e, /* (2^ 8)P */ 0x9d, 0x04, 0x68, 0x89, 0xa4, 0xa9, 0x0d, 0x87, 0xc1, 0x70, 0xf1, 0xeb, 0xfb, 0x47, 0x0a, 0xf0, 0xde, 0x67, 0xb7, 0x94, 0xcd, 0x36, 0x43, 0xa5, 0x49, 0x43, 0x67, 0xc3, 0xee, 0x3c, 0x6b, 0xec, 0xd0, 0x1a, 0xf4, 0xad, 0xef, 0x06, 0x4a, 0xe8, 0x46, 0x24, 0xd7, 0x93, 0xbf, 0xf0, 0xe3, 0x81, 0x61, 0xec, 0xea, 0x64, 0xfe, 0x67, 0xeb, 0xc7, /* (2^ 9)P */ 0x95, 0x45, 0x79, 0xcf, 0x2c, 0xfd, 0x9b, 0xfe, 0x84, 0x46, 0x4b, 0x8f, 0xa1, 0xcf, 0xc3, 0x04, 0x94, 0x78, 0xdb, 0xc9, 0xa6, 0x01, 0x75, 0xa4, 0xb4, 0x93, 0x72, 0x43, 0xa7, 0x7d, 0xda, 0x31, 0x38, 0x54, 0xab, 0x4e, 0x3f, 0x89, 0xa6, 0xab, 0x57, 0xc0, 0x16, 0x65, 0xdb, 0x92, 0x96, 0xe4, 0xc8, 0xae, 0xe7, 0x4c, 0x7a, 0xeb, 0xbb, 0x5a, /* (2^ 10)P */ 0xbe, 0xfe, 0x86, 0xc3, 0x97, 0xe0, 0x6a, 0x18, 0x20, 0x21, 0xca, 0x22, 0x55, 0xa1, 0xeb, 0xf5, 0x74, 0xe5, 0xc9, 0x59, 0xa7, 0x92, 0x65, 0x15, 0x08, 0x71, 0xd1, 0x09, 0x7e, 0x83, 0xfc, 0xbc, 0x5a, 0x93, 0x38, 0x0d, 0x43, 0x42, 0xfd, 0x76, 0x30, 0xe8, 0x63, 0x60, 0x09, 0x8d, 0x6c, 0xd3, 0xf8, 0x56, 0x3d, 0x68, 0x47, 0xab, 0xa0, 0x1d, /* (2^ 11)P */ 0x38, 0x50, 0x1c, 0xb1, 0xac, 0x88, 0x8f, 0x38, 0xe3, 0x69, 0xe6, 0xfc, 0x4f, 0x8f, 0xe1, 0x9b, 0xb1, 0x1a, 0x09, 0x39, 0x19, 0xdf, 0xcd, 0x98, 0x7b, 0x64, 0x42, 0xf6, 0x11, 0xea, 0xc7, 0xe8, 0x92, 0x65, 0x00, 0x2c, 0x75, 0xb5, 0x94, 0x1e, 0x5b, 0xa6, 0x66, 0x81, 0x77, 0xf3, 0x39, 0x94, 0xac, 0xbd, 0xe4, 0x2a, 0x66, 0x84, 0x9c, 0x60, /* (2^ 12)P */ 0xb5, 0xb6, 0xd9, 0x03, 0x67, 0xa4, 0xa8, 0x0a, 0x4a, 0x2b, 0x9d, 0xfa, 0x13, 0xe1, 0x99, 0x25, 0x4a, 0x5c, 0x67, 0xb9, 0xb2, 0xb7, 0xdd, 0x1e, 0xaf, 0xeb, 0x63, 0x41, 0xb6, 0xb9, 0xa0, 0x87, 0x0a, 0xe0, 0x06, 0x07, 0xaa, 0x97, 0xf8, 0xf9, 0x38, 0x4f, 0xdf, 0x0c, 0x40, 0x7c, 0xc3, 0x98, 0xa9, 0x74, 0xf1, 0x5d, 0xda, 0xd1, 0xc0, 0x0a, /* (2^ 13)P */ 0xf2, 0x0a, 0xab, 0xab, 0x94, 0x50, 0xf0, 0xa3, 0x6f, 0xc6, 0x66, 0xba, 0xa6, 0xdc, 0x44, 0xdd, 0xd6, 0x08, 0xf4, 0xd3, 0xed, 0xb1, 0x40, 0x93, 0xee, 0xf6, 0xb8, 0x8e, 0xb4, 0x7c, 0xb9, 0x82, 0xc9, 0x9d, 0x45, 0x3b, 0x8e, 0x10, 0xcb, 0x70, 0x1e, 0xba, 0x3c, 0x62, 0x50, 0xda, 0xa9, 0x93, 0xb5, 0xd7, 0xd0, 0x6f, 0x29, 0x52, 0x95, 0xae, /* (2^ 14)P */ 0x14, 0x68, 0x69, 0x23, 0xa8, 0x44, 0x87, 0x9e, 0x22, 0x91, 0xe8, 0x92, 0xdf, 0xf7, 0xae, 0xba, 0x1c, 0x96, 0xe1, 0xc3, 0x94, 0xed, 0x6c, 0x95, 0xae, 0x96, 0xa7, 0x15, 0x9f, 0xf1, 0x17, 0x11, 0x92, 0x42, 0xd5, 0xcd, 0x18, 0xe7, 0xa9, 0xb5, 0x2f, 0xcd, 0xde, 0x6c, 0xc9, 0x7d, 0xfc, 0x7e, 0xbd, 0x7f, 0x10, 0x3d, 0x01, 0x00, 0x8d, 0x95, /* (2^ 15)P */ 0x3b, 0x76, 0x72, 0xae, 0xaf, 0x84, 0xf2, 0xf7, 0xd1, 0x6d, 0x13, 0x9c, 0x47, 0xe1, 0xb7, 0xa3, 0x19, 0x16, 0xee, 0x75, 0x45, 0xf6, 0x1a, 0x7b, 0x78, 0x49, 0x79, 0x05, 0x86, 0xf0, 0x7f, 0x9f, 0xfc, 0xc4, 0xbd, 0x86, 0xf3, 0x41, 0xa7, 0xfe, 0x01, 0xd5, 0x67, 0x16, 0x10, 0x5b, 0xa5, 0x16, 0xf3, 0x7f, 0x60, 0xce, 0xd2, 0x0c, 0x8e, 0x4b, /* (2^ 16)P */ 0x4a, 0x07, 0x99, 0x4a, 0x0f, 0x74, 0x91, 0x14, 0x68, 0xb9, 0x48, 0xb7, 0x44, 0x77, 0x9b, 0x4a, 0xe0, 0x68, 0x0e, 0x43, 0x4d, 0x98, 0x98, 0xbf, 0xa8, 0x3a, 0xb7, 0x6d, 0x2a, 0x9a, 0x77, 0x5f, 0x62, 0xf5, 0x6b, 0x4a, 0xb7, 0x7d, 0xe5, 0x09, 0x6b, 0xc0, 0x8b, 0x9c, 0x88, 0x37, 0x33, 0xf2, 0x41, 0xac, 0x22, 0x1f, 0xcf, 0x3b, 0x82, 0x34, /* (2^ 17)P */ 0x00, 0xc3, 0x78, 0x42, 0x32, 0x2e, 0xdc, 0xda, 0xb1, 0x96, 0x21, 0xa4, 0xe4, 0xbb, 0xe9, 0x9d, 0xbb, 0x0f, 0x93, 0xed, 0x26, 0x3d, 0xb5, 0xdb, 0x94, 0x31, 0x37, 0x07, 0xa2, 0xb2, 0xd5, 0x99, 0x0d, 0x93, 0xe1, 0xce, 0x3f, 0x0b, 0x96, 0x82, 0x47, 0xfe, 0x60, 0x6f, 0x8f, 0x61, 0x88, 0xd7, 0x05, 0x95, 0x0b, 0x46, 0x06, 0xb7, 0x32, 0x06, /* (2^ 18)P */ 0x44, 0xf5, 0x34, 0xdf, 0x2f, 0x9c, 0x5d, 0x9f, 0x53, 0x5c, 0x42, 0x8f, 0xc9, 0xdc, 0xd8, 0x40, 0xa2, 0xe7, 0x6a, 0x4a, 0x05, 0xf7, 0x86, 0x77, 0x2b, 0xae, 0x37, 0xed, 0x48, 0xfb, 0xf7, 0x62, 0x7c, 0x17, 0x59, 0x92, 0x41, 0x61, 0x93, 0x38, 0x30, 0xd1, 0xef, 0x54, 0x54, 0x03, 0x17, 0x57, 0x91, 0x15, 0x11, 0x33, 0xb5, 0xfa, 0xfb, 0x17, /* (2^ 19)P */ 0x29, 0xbb, 0xd4, 0xb4, 0x9c, 0xf1, 0x72, 0x94, 0xce, 0x6a, 0x29, 0xa8, 0x89, 0x18, 0x19, 0xf7, 0xb7, 0xcc, 0xee, 0x9a, 0x02, 0xe3, 0xc0, 0xb1, 0xe0, 0xee, 0x83, 0x78, 0xb4, 0x9e, 0x07, 0x87, 0xdf, 0xb0, 0x82, 0x26, 0x4e, 0xa4, 0x0c, 0x33, 0xaf, 0x40, 0x59, 0xb6, 0xdd, 0x52, 0x45, 0xf0, 0xb4, 0xf6, 0xe8, 0x4e, 0x4e, 0x79, 0x1a, 0x5d, /* (2^ 20)P */ 0x27, 0x33, 0x4d, 0x4c, 0x6b, 0x4f, 0x75, 0xb1, 0xbc, 0x1f, 0xab, 0x5b, 0x2b, 0xf0, 0x1c, 0x57, 0x86, 0xdd, 0xfd, 0x60, 0xb0, 0x8c, 0xe7, 0x9a, 0xe5, 0x5c, 0xeb, 0x11, 0x3a, 0xda, 0x22, 0x25, 0x99, 0x06, 0x8d, 0xf4, 0xaf, 0x29, 0x7a, 0xc9, 0xe5, 0xd2, 0x16, 0x9e, 0xd4, 0x63, 0x1d, 0x64, 0xa6, 0x47, 0x96, 0x37, 0x6f, 0x93, 0x2c, 0xcc, /* (2^ 21)P */ 0xc1, 0x94, 0x74, 0x86, 0x75, 0xf2, 0x91, 0x58, 0x23, 0x85, 0x63, 0x76, 0x54, 0xc7, 0xb4, 0x8c, 0xbc, 0x4e, 0xc4, 0xa7, 0xba, 0xa0, 0x55, 0x26, 0x71, 0xd5, 0x33, 0x72, 0xc9, 0xad, 0x1e, 0xf9, 0x5d, 0x78, 0x70, 0x93, 0x4e, 0x85, 0xfc, 0x39, 0x06, 0x73, 0x76, 0xff, 0xe8, 0x64, 0x69, 0x42, 0x45, 0xb2, 0x69, 0xb5, 0x32, 0xe7, 0x2c, 0xde, /* (2^ 22)P */ 0xde, 0x16, 0xd8, 0x33, 0x49, 0x32, 0xe9, 0x0e, 0x3a, 0x60, 0xee, 0x2e, 0x24, 0x75, 0xe3, 0x9c, 0x92, 0x07, 0xdb, 0xad, 0x92, 0xf5, 0x11, 0xdf, 0xdb, 0xb0, 0x17, 0x5c, 0xd6, 0x1a, 0x70, 0x00, 0xb7, 0xe2, 0x18, 0xec, 0xdc, 0xc2, 0x02, 0x93, 0xb3, 0xc8, 0x3f, 0x4f, 0x1b, 0x96, 0xe6, 0x33, 0x8c, 0xfb, 0xcc, 0xa5, 0x4e, 0xe8, 0xe7, 0x11, /* (2^ 23)P */ 0x05, 0x7a, 0x74, 0x52, 0xf8, 0xdf, 0x0d, 0x7c, 0x6a, 0x1a, 0x4e, 0x9a, 0x02, 0x1d, 0xae, 0x77, 0xf8, 0x8e, 0xf9, 0xa2, 0x38, 0x54, 0x50, 0xb2, 0x2c, 0x08, 0x9d, 0x9b, 0x9f, 0xfb, 0x2b, 0x06, 0xde, 0x9d, 0xc2, 0x03, 0x0b, 0x22, 0x2b, 0x10, 0x5b, 0x3a, 0x73, 0x29, 0x8e, 0x3e, 0x37, 0x08, 0x2c, 0x3b, 0xf8, 0x80, 0xc1, 0x66, 0x1e, 0x98, /* (2^ 24)P */ 0xd8, 0xd6, 0x3e, 0xcd, 0x63, 0x8c, 0x2b, 0x41, 0x81, 0xc0, 0x0c, 0x06, 0x87, 0xd6, 0xe7, 0x92, 0xfe, 0xf1, 0x0c, 0x4a, 0x84, 0x5b, 0xaf, 0x40, 0x53, 0x6f, 0x60, 0xd6, 0x6b, 0x76, 0x4b, 0xc2, 0xad, 0xc9, 0xb6, 0xb6, 0x6a, 0xa2, 0xb3, 0xf5, 0xf5, 0xc2, 0x55, 0x83, 0xb2, 0xd3, 0xe9, 0x41, 0x6c, 0x63, 0x51, 0xb8, 0x81, 0x74, 0xc8, 0x2c, /* (2^ 25)P */ 0xb2, 0xaf, 0x1c, 0xee, 0x07, 0xb0, 0x58, 0xa8, 0x2c, 0x6a, 0xc9, 0x2d, 0x62, 0x28, 0x75, 0x0c, 0x40, 0xb6, 0x11, 0x33, 0x96, 0x80, 0x28, 0x6d, 0xd5, 0x9e, 0x87, 0x90, 0x01, 0x66, 0x1d, 0x1c, 0xf8, 0xb4, 0x92, 0xac, 0x38, 0x18, 0x05, 0xc2, 0x4c, 0x4b, 0x54, 0x7d, 0x80, 0x46, 0x87, 0x2d, 0x99, 0x8e, 0x70, 0x80, 0x69, 0x71, 0x8b, 0xed, /* (2^ 26)P */ 0x37, 0xa7, 0x6b, 0x71, 0x36, 0x75, 0x8e, 0xff, 0x0f, 0x42, 0xda, 0x5a, 0x46, 0xa6, 0x97, 0x79, 0x7e, 0x30, 0xb3, 0x8f, 0xc7, 0x3a, 0xa0, 0xcb, 0x1d, 0x9c, 0x78, 0x77, 0x36, 0xc2, 0xe7, 0xf4, 0x2f, 0x29, 0x07, 0xb1, 0x07, 0xfd, 0xed, 0x1b, 0x39, 0x77, 0x06, 0x38, 0x77, 0x0f, 0x50, 0x31, 0x12, 0xbf, 0x92, 0xbf, 0x72, 0x79, 0x54, 0xa9, /* (2^ 27)P */ 0xbd, 0x4d, 0x46, 0x6b, 0x1a, 0x80, 0x46, 0x2d, 0xed, 0xfd, 0x64, 0x6d, 0x94, 0xbc, 0x4a, 0x6e, 0x0c, 0x12, 0xf6, 0x12, 0xab, 0x54, 0x88, 0xd3, 0x85, 0xac, 0x51, 0xae, 0x6f, 0xca, 0xc4, 0xb7, 0xec, 0x22, 0x54, 0x6d, 0x80, 0xb2, 0x1c, 0x63, 0x33, 0x76, 0x6b, 0x8e, 0x6d, 0x59, 0xcd, 0x73, 0x92, 0x5f, 0xff, 0xad, 0x10, 0x35, 0x70, 0x5f, /* (2^ 28)P */ 0xb3, 0x84, 0xde, 0xc8, 0x04, 0x43, 0x63, 0xfa, 0x29, 0xd9, 0xf0, 0x69, 0x65, 0x5a, 0x0c, 0xe8, 0x2e, 0x0b, 0xfe, 0xb0, 0x7a, 0x42, 0xb3, 0xc3, 0xfc, 0xe6, 0xb8, 0x92, 0x29, 0xae, 0xed, 0xec, 0xd5, 0xe8, 0x4a, 0xa1, 0xbd, 0x3b, 0xd3, 0xc0, 0x07, 0xab, 0x65, 0x65, 0x35, 0x9a, 0xa6, 0x5e, 0x78, 0x18, 0x76, 0x1c, 0x15, 0x49, 0xe6, 0x75, /* (2^ 29)P */ 0x45, 0xb3, 0x92, 0xa9, 0xc3, 0xb8, 0x11, 0x68, 0x64, 0x3a, 0x83, 0x5d, 0xa8, 0x94, 0x6a, 0x9d, 0xaa, 0x27, 0x9f, 0x98, 0x5d, 0xc0, 0x29, 0xf0, 0xc0, 0x4b, 0x14, 0x3c, 0x05, 0xe7, 0xf8, 0xbd, 0x38, 0x22, 0x96, 0x75, 0x65, 0x5e, 0x0d, 0x3f, 0xbb, 0x6f, 0xe8, 0x3f, 0x96, 0x76, 0x9f, 0xba, 0xd9, 0x44, 0x92, 0x96, 0x22, 0xe7, 0x52, 0xe7, /* (2^ 30)P */ 0xf4, 0xa3, 0x95, 0x90, 0x47, 0xdf, 0x7d, 0xdc, 0xf4, 0x13, 0x87, 0x67, 0x7d, 0x4f, 0x9d, 0xa0, 0x00, 0x46, 0x72, 0x08, 0xc3, 0xa2, 0x7a, 0x3e, 0xe7, 0x6d, 0x52, 0x7c, 0x11, 0x36, 0x50, 0x83, 0x89, 0x64, 0xcb, 0x1f, 0x08, 0x83, 0x46, 0xcb, 0xac, 0xa6, 0xd8, 0x9c, 0x1b, 0xe8, 0x05, 0x47, 0xc7, 0x26, 0x06, 0x83, 0x39, 0xe9, 0xb1, 0x1c, /* (2^ 31)P */ 0x11, 0xe8, 0xc8, 0x42, 0xbf, 0x30, 0x9c, 0xa3, 0xf1, 0x85, 0x96, 0x95, 0x4f, 0x4f, 0x52, 0xa2, 0xf5, 0x8b, 0x68, 0x24, 0x16, 0xac, 0x9b, 0xa9, 0x27, 0x28, 0x0e, 0x84, 0x03, 0x46, 0x22, 0x5f, 0xf7, 0x0d, 0xa6, 0x85, 0x88, 0xc1, 0x45, 0x4b, 0x85, 0x1a, 0x10, 0x7f, 0xc9, 0x94, 0x20, 0xb0, 0x04, 0x28, 0x12, 0x30, 0xb9, 0xe6, 0x40, 0x6b, /* (2^ 32)P */ 0xac, 0x1b, 0x57, 0xb6, 0x42, 0xdb, 0x81, 0x8d, 0x76, 0xfd, 0x9b, 0x1c, 0x29, 0x30, 0xd5, 0x3a, 0xcc, 0x53, 0xd9, 0x26, 0x7a, 0x0f, 0x9c, 0x2e, 0x79, 0xf5, 0x62, 0xeb, 0x61, 0x9d, 0x9b, 0x80, 0x39, 0xcd, 0x60, 0x2e, 0x1f, 0x08, 0x22, 0xbc, 0x19, 0xb3, 0x2a, 0x43, 0x44, 0xf2, 0x4e, 0x66, 0xf4, 0x36, 0xa6, 0xa7, 0xbc, 0xa4, 0x15, 0x7e, /* (2^ 33)P */ 0xc1, 0x90, 0x8a, 0xde, 0xff, 0x78, 0xc3, 0x73, 0x16, 0xee, 0x76, 0xa0, 0x84, 0x60, 0x8d, 0xe6, 0x82, 0x0f, 0xde, 0x4e, 0xc5, 0x99, 0x34, 0x06, 0x90, 0x44, 0x55, 0xf8, 0x91, 0xd8, 0xe1, 0xe4, 0x2c, 0x8a, 0xde, 0x94, 0x1e, 0x78, 0x25, 0x3d, 0xfd, 0xd8, 0x59, 0x7d, 0xaf, 0x6e, 0xbe, 0x96, 0xbe, 0x3c, 0x16, 0x23, 0x0f, 0x4c, 0xa4, 0x28, /* (2^ 34)P */ 0xba, 0x11, 0x35, 0x57, 0x03, 0xb6, 0xf4, 0x24, 0x89, 0xb8, 0x5a, 0x0d, 0x50, 0x9c, 0xaa, 0x51, 0x7f, 0xa4, 0x0e, 0xfc, 0x71, 0xb3, 0x3b, 0xf1, 0x96, 0x50, 0x23, 0x15, 0xf5, 0xf5, 0xd4, 0x23, 0xdc, 0x8b, 0x26, 0x9e, 0xae, 0xb7, 0x50, 0xcd, 0xc4, 0x25, 0xf6, 0x75, 0x40, 0x9c, 0x37, 0x79, 0x33, 0x60, 0xd4, 0x4b, 0x13, 0x32, 0xee, 0xe2, /* (2^ 35)P */ 0x43, 0xb8, 0x56, 0x59, 0xf0, 0x68, 0x23, 0xb3, 0xea, 0x70, 0x58, 0x4c, 0x1e, 0x5a, 0x16, 0x54, 0x03, 0xb2, 0xf4, 0x73, 0xb6, 0xd9, 0x5c, 0x9c, 0x6f, 0xcf, 0x82, 0x2e, 0x54, 0x15, 0x46, 0x2c, 0xa3, 0xda, 0x4e, 0x87, 0xf5, 0x2b, 0xba, 0x91, 0xa3, 0xa0, 0x89, 0xba, 0x48, 0x2b, 0xfa, 0x64, 0x02, 0x7f, 0x78, 0x03, 0xd1, 0xe8, 0x3b, 0xe9, /* (2^ 36)P */ 0x15, 0xa4, 0x71, 0xd4, 0x0c, 0x24, 0xe9, 0x07, 0xa1, 0x43, 0xf4, 0x7f, 0xbb, 0xa2, 0xa6, 0x6b, 0xfa, 0xb7, 0xea, 0x58, 0xd1, 0x96, 0xb0, 0x24, 0x5c, 0xc7, 0x37, 0x4e, 0x60, 0x0f, 0x40, 0xf2, 0x2f, 0x44, 0x70, 0xea, 0x80, 0x63, 0xfe, 0xfc, 0x46, 0x59, 0x12, 0x27, 0xb5, 0x27, 0xfd, 0xb7, 0x73, 0x0b, 0xca, 0x8b, 0xc2, 0xd3, 0x71, 0x08, /* (2^ 37)P */ 0x26, 0x0e, 0xd7, 0x52, 0x6f, 0xf1, 0xf2, 0x9d, 0xb8, 0x3d, 0xbd, 0xd4, 0x75, 0x97, 0xd8, 0xbf, 0xa8, 0x86, 0x96, 0xa5, 0x80, 0xa0, 0x45, 0x75, 0xf6, 0x77, 0x71, 0xdb, 0x77, 0x96, 0x55, 0x99, 0x31, 0xd0, 0x4f, 0x34, 0xf4, 0x35, 0x39, 0x41, 0xd3, 0x7d, 0xf7, 0xe2, 0x74, 0xde, 0xbe, 0x5b, 0x1f, 0x39, 0x10, 0x21, 0xa3, 0x4d, 0x3b, 0xc8, /* (2^ 38)P */ 0x04, 0x00, 0x2a, 0x45, 0xb2, 0xaf, 0x9b, 0x18, 0x6a, 0xeb, 0x96, 0x28, 0xa4, 0x77, 0xd0, 0x13, 0xcf, 0x17, 0x65, 0xe8, 0xc5, 0x81, 0x28, 0xad, 0x39, 0x7a, 0x0b, 0xaa, 0x55, 0x2b, 0xf3, 0xfc, 0x86, 0x40, 0xad, 0x0d, 0x1e, 0x28, 0xa2, 0x2d, 0xc5, 0xd6, 0x04, 0x15, 0xa2, 0x30, 0x3d, 0x12, 0x8e, 0xd6, 0xb5, 0xf7, 0x69, 0xbb, 0x84, 0x20, /* (2^ 39)P */ 0xd7, 0x7a, 0x77, 0x2c, 0xfb, 0x81, 0x80, 0xe9, 0x1e, 0xc6, 0x36, 0x31, 0x79, 0xc3, 0x7c, 0xa9, 0x57, 0x6b, 0xb5, 0x70, 0xfb, 0xe4, 0xa1, 0xff, 0xfd, 0x21, 0xa5, 0x7c, 0xfa, 0x44, 0xba, 0x0d, 0x96, 0x3d, 0xc4, 0x5c, 0x39, 0x52, 0x87, 0xd7, 0x22, 0x0f, 0x52, 0x88, 0x91, 0x87, 0x96, 0xac, 0xfa, 0x3b, 0xdf, 0xdc, 0x83, 0x8c, 0x99, 0x29, /* (2^ 40)P */ 0x98, 0x6b, 0x3a, 0x8d, 0x83, 0x17, 0xe1, 0x62, 0xd8, 0x80, 0x4c, 0x97, 0xce, 0x6b, 0xaa, 0x10, 0xa7, 0xc4, 0xe9, 0xeb, 0xa5, 0xfb, 0xc9, 0xdd, 0x2d, 0xeb, 0xfc, 0x9a, 0x71, 0xcd, 0x68, 0x6e, 0xc0, 0x35, 0x64, 0x62, 0x1b, 0x95, 0x12, 0xe8, 0x53, 0xec, 0xf0, 0xf4, 0x86, 0x86, 0x78, 0x18, 0xc4, 0xc6, 0xbc, 0x5a, 0x59, 0x8f, 0x7c, 0x7e, /* (2^ 41)P */ 0x7f, 0xd7, 0x1e, 0xc5, 0x83, 0xdc, 0x1f, 0xbe, 0x0b, 0xcf, 0x2e, 0x01, 0x01, 0xed, 0xac, 0x17, 0x3b, 0xed, 0xa4, 0x30, 0x96, 0x0e, 0x14, 0x7e, 0x19, 0x2b, 0xa5, 0x67, 0x1e, 0xb3, 0x34, 0x03, 0xa8, 0xbb, 0x0a, 0x7d, 0x08, 0x2d, 0xd5, 0x53, 0x19, 0x6f, 0x13, 0xd5, 0xc0, 0x90, 0x8a, 0xcc, 0xc9, 0x5c, 0xab, 0x24, 0xd7, 0x03, 0xf6, 0x57, /* (2^ 42)P */ 0x49, 0xcb, 0xb4, 0x96, 0x5f, 0xa6, 0xf8, 0x71, 0x6f, 0x59, 0xad, 0x05, 0x24, 0x2d, 0xaf, 0x67, 0xa8, 0xbe, 0x95, 0xdf, 0x0d, 0x28, 0x5a, 0x7f, 0x6e, 0x87, 0x8c, 0x6e, 0x67, 0x0c, 0xf4, 0xe0, 0x1c, 0x30, 0xc2, 0x66, 0xae, 0x20, 0xa1, 0x34, 0xec, 0x9c, 0xbc, 0xae, 0x3d, 0xa1, 0x28, 0x28, 0x95, 0x1d, 0xc9, 0x3a, 0xa8, 0xfd, 0xfc, 0xa1, /* (2^ 43)P */ 0xe2, 0x2b, 0x9d, 0xed, 0x02, 0x99, 0x67, 0xbb, 0x2e, 0x16, 0x62, 0x05, 0x70, 0xc7, 0x27, 0xb9, 0x1c, 0x3f, 0xf2, 0x11, 0x01, 0xd8, 0x51, 0xa4, 0x18, 0x92, 0xa9, 0x5d, 0xfb, 0xa9, 0xe4, 0x42, 0xba, 0x38, 0x34, 0x1a, 0x4a, 0xc5, 0x6a, 0x37, 0xde, 0xa7, 0x0c, 0xb4, 0x7e, 0x7f, 0xde, 0xa6, 0xee, 0xcd, 0x55, 0x57, 0x05, 0x06, 0xfd, 0x5d, /* (2^ 44)P */ 0x2f, 0x32, 0xcf, 0x2e, 0x2c, 0x7b, 0xbe, 0x9a, 0x0c, 0x57, 0x35, 0xf8, 0x87, 0xda, 0x9c, 0xec, 0x48, 0xf2, 0xbb, 0xe2, 0xda, 0x10, 0x58, 0x20, 0xc6, 0xd3, 0x87, 0xe9, 0xc7, 0x26, 0xd1, 0x9a, 0x46, 0x87, 0x90, 0xda, 0xdc, 0xde, 0xc3, 0xb3, 0xf2, 0xe8, 0x6f, 0x4a, 0xe6, 0xe8, 0x9d, 0x98, 0x36, 0x20, 0x03, 0x47, 0x15, 0x3f, 0x64, 0x59, /* (2^ 45)P */ 0xd4, 0x71, 0x49, 0x0a, 0x67, 0x97, 0xaa, 0x3f, 0xf4, 0x1b, 0x3a, 0x6e, 0x5e, 0x17, 0xcc, 0x0a, 0x8f, 0x81, 0x6a, 0x41, 0x38, 0x77, 0x40, 0x8a, 0x11, 0x42, 0x62, 0xd2, 0x50, 0x32, 0x79, 0x78, 0x28, 0xc2, 0x2e, 0x10, 0x01, 0x94, 0x30, 0x4f, 0x7f, 0x18, 0x17, 0x56, 0x85, 0x4e, 0xad, 0xf7, 0xcb, 0x87, 0x3c, 0x3f, 0x50, 0x2c, 0xc0, 0xba, /* (2^ 46)P */ 0xbc, 0x30, 0x8e, 0x65, 0x8e, 0x57, 0x5b, 0x38, 0x7a, 0xd4, 0x95, 0x52, 0x7a, 0x32, 0x59, 0x69, 0xcd, 0x9d, 0x47, 0x34, 0x5b, 0x55, 0xa5, 0x24, 0x60, 0xdd, 0xc0, 0xc1, 0x62, 0x73, 0x44, 0xae, 0x4c, 0x9c, 0x65, 0x55, 0x1b, 0x9d, 0x8a, 0x29, 0xb0, 0x1a, 0x52, 0xa8, 0xf1, 0xe6, 0x9a, 0xb3, 0xf6, 0xa3, 0xc9, 0x0a, 0x70, 0x7d, 0x0f, 0xee, /* (2^ 47)P */ 0x77, 0xd3, 0xe5, 0x8e, 0xfa, 0x00, 0xeb, 0x1b, 0x7f, 0xdc, 0x68, 0x3f, 0x92, 0xbd, 0xb7, 0x0b, 0xb7, 0xb5, 0x24, 0xdf, 0xc5, 0x67, 0x53, 0xd4, 0x36, 0x79, 0xc4, 0x7b, 0x57, 0xbc, 0x99, 0x97, 0x60, 0xef, 0xe4, 0x01, 0xa1, 0xa7, 0xaa, 0x12, 0x36, 0x29, 0xb1, 0x03, 0xc2, 0x83, 0x1c, 0x2b, 0x83, 0xef, 0x2e, 0x2c, 0x23, 0x92, 0xfd, 0xd1, /* (2^ 48)P */ 0x94, 0xef, 0x03, 0x59, 0xfa, 0x8a, 0x18, 0x76, 0xee, 0x58, 0x08, 0x4d, 0x44, 0xce, 0xf1, 0x52, 0x33, 0x49, 0xf6, 0x69, 0x71, 0xe3, 0xa9, 0xbc, 0x86, 0xe3, 0x43, 0xde, 0x33, 0x7b, 0x90, 0x8b, 0x3e, 0x7d, 0xd5, 0x4a, 0xf0, 0x23, 0x99, 0xa6, 0xea, 0x5f, 0x08, 0xe5, 0xb9, 0x49, 0x8b, 0x0d, 0x6a, 0x21, 0xab, 0x07, 0x62, 0xcd, 0xc4, 0xbe, /* (2^ 49)P */ 0x61, 0xbf, 0x70, 0x14, 0xfa, 0x4e, 0x9e, 0x7c, 0x0c, 0xf8, 0xb2, 0x48, 0x71, 0x62, 0x83, 0xd6, 0xd1, 0xdc, 0x9c, 0x29, 0x66, 0xb1, 0x34, 0x9c, 0x8d, 0xe6, 0x88, 0xaf, 0xbe, 0xdc, 0x4d, 0xeb, 0xb0, 0xe7, 0x28, 0xae, 0xb2, 0x05, 0x56, 0xc6, 0x0e, 0x10, 0x26, 0xab, 0x2c, 0x59, 0x72, 0x03, 0x66, 0xfe, 0x8f, 0x2c, 0x51, 0x2d, 0xdc, 0xae, /* (2^ 50)P */ 0xdc, 0x63, 0xf1, 0x8b, 0x5c, 0x65, 0x0b, 0xf1, 0xa6, 0x22, 0xe2, 0xd9, 0xdb, 0x49, 0xb1, 0x3c, 0x47, 0xc2, 0xfe, 0xac, 0x86, 0x07, 0x52, 0xec, 0xb0, 0x08, 0x69, 0xfb, 0xd1, 0x06, 0xdc, 0x48, 0x5c, 0x3d, 0xb2, 0x4d, 0xb8, 0x1a, 0x4e, 0xda, 0xb9, 0xc1, 0x2b, 0xab, 0x4b, 0x62, 0x81, 0x21, 0x9a, 0xfc, 0x3d, 0x39, 0x83, 0x11, 0x36, 0xeb, /* (2^ 51)P */ 0x94, 0xf3, 0x17, 0xef, 0xf9, 0x60, 0x54, 0xc3, 0xd7, 0x27, 0x35, 0xc5, 0x98, 0x5e, 0xf6, 0x63, 0x6c, 0xa0, 0x4a, 0xd3, 0xa3, 0x98, 0xd9, 0x42, 0xe3, 0xf1, 0xf8, 0x81, 0x96, 0xa9, 0xea, 0x6d, 0x4b, 0x8e, 0x33, 0xca, 0x94, 0x0d, 0xa0, 0xf7, 0xbb, 0x64, 0xa3, 0x36, 0x6f, 0xdc, 0x5a, 0x94, 0x42, 0xca, 0x06, 0xb2, 0x2b, 0x9a, 0x9f, 0x71, /* (2^ 52)P */ 0xec, 0xdb, 0xa6, 0x1f, 0xdf, 0x15, 0x36, 0xa3, 0xda, 0x8a, 0x7a, 0xb6, 0xa7, 0xe3, 0xaf, 0x52, 0xe0, 0x8d, 0xe8, 0xf2, 0x44, 0x20, 0xeb, 0xa1, 0x20, 0xc4, 0x65, 0x3c, 0x7c, 0x6c, 0x49, 0xed, 0x2f, 0x66, 0x23, 0x68, 0x61, 0x91, 0x40, 0x9f, 0x50, 0x19, 0xd1, 0x84, 0xa7, 0xe2, 0xed, 0x34, 0x37, 0xe3, 0xe4, 0x11, 0x7f, 0x87, 0x55, 0x0f, /* (2^ 53)P */ 0xb3, 0xa1, 0x0f, 0xb0, 0x48, 0xc0, 0x4d, 0x96, 0xa7, 0xcf, 0x5a, 0x81, 0xb8, 0x4a, 0x46, 0xef, 0x0a, 0xd3, 0x40, 0x7e, 0x02, 0xe3, 0x63, 0xaa, 0x50, 0xd1, 0x2a, 0x37, 0x22, 0x4a, 0x7f, 0x4f, 0xb6, 0xf9, 0x01, 0x82, 0x78, 0x3d, 0x93, 0x14, 0x11, 0x8a, 0x90, 0x60, 0xcd, 0x45, 0x4e, 0x7b, 0x42, 0xb9, 0x3e, 0x6e, 0x68, 0x1f, 0x36, 0x41, /* (2^ 54)P */ 0x13, 0x73, 0x0e, 0x4f, 0x79, 0x93, 0x9e, 0x29, 0x70, 0x7b, 0x4a, 0x59, 0x1a, 0x9a, 0xf4, 0x55, 0x08, 0xf0, 0xdb, 0x17, 0x58, 0xec, 0x64, 0xad, 0x7f, 0x29, 0xeb, 0x3f, 0x85, 0x4e, 0x60, 0x28, 0x98, 0x1f, 0x73, 0x4e, 0xe6, 0xa8, 0xab, 0xd5, 0xd6, 0xfc, 0xa1, 0x36, 0x6d, 0x15, 0xc6, 0x13, 0x83, 0xa0, 0xc2, 0x6e, 0xd9, 0xdb, 0xc9, 0xcc, /* (2^ 55)P */ 0xff, 0xd8, 0x52, 0xa3, 0xdc, 0x99, 0xcf, 0x3e, 0x19, 0xb3, 0x68, 0xd0, 0xb5, 0x0d, 0xb8, 0xee, 0x3f, 0xef, 0x6e, 0xc0, 0x38, 0x28, 0x44, 0x92, 0x78, 0x91, 0x1a, 0x08, 0x78, 0x6c, 0x65, 0x24, 0xf3, 0xa2, 0x3d, 0xf2, 0xe5, 0x79, 0x62, 0x69, 0x29, 0xf4, 0x22, 0xc5, 0xdb, 0x6a, 0xae, 0xf4, 0x44, 0xa3, 0x6f, 0xc7, 0x86, 0xab, 0xef, 0xef, /* (2^ 56)P */ 0xbf, 0x54, 0x9a, 0x09, 0x5d, 0x17, 0xd0, 0xde, 0xfb, 0xf5, 0xca, 0xff, 0x13, 0x20, 0x88, 0x82, 0x3a, 0xe2, 0xd0, 0x3b, 0xfb, 0x05, 0x76, 0xd1, 0xc0, 0x02, 0x71, 0x3b, 0x94, 0xe8, 0xc9, 0x84, 0xcf, 0xa4, 0xe9, 0x28, 0x7b, 0xf5, 0x09, 0xc3, 0x2b, 0x22, 0x40, 0xf1, 0x68, 0x24, 0x24, 0x7d, 0x9f, 0x6e, 0xcd, 0xfe, 0xb0, 0x19, 0x61, 0xf5, /* (2^ 57)P */ 0xe8, 0x63, 0x51, 0xb3, 0x95, 0x6b, 0x7b, 0x74, 0x92, 0x52, 0x45, 0xa4, 0xed, 0xea, 0x0e, 0x0d, 0x2b, 0x01, 0x1e, 0x2c, 0xbc, 0x91, 0x06, 0x69, 0xdb, 0x1f, 0xb5, 0x77, 0x1d, 0x56, 0xf5, 0xb4, 0x02, 0x80, 0x49, 0x56, 0x12, 0xce, 0x86, 0x05, 0xc9, 0xd9, 0xae, 0xf3, 0x6d, 0xe6, 0x3f, 0x40, 0x52, 0xe9, 0x49, 0x2b, 0x31, 0x06, 0x86, 0x14, /* (2^ 58)P */ 0xf5, 0x09, 0x3b, 0xd2, 0xff, 0xdf, 0x11, 0xa5, 0x1c, 0x99, 0xe8, 0x1b, 0xa4, 0x2c, 0x7d, 0x8e, 0xc8, 0xf7, 0x03, 0x46, 0xfa, 0xb6, 0xde, 0x73, 0x91, 0x7e, 0x5a, 0x7a, 0xd7, 0x9a, 0x5b, 0x80, 0x24, 0x62, 0x5e, 0x92, 0xf1, 0xa3, 0x45, 0xa3, 0x43, 0x92, 0x8a, 0x2a, 0x5b, 0x0c, 0xb4, 0xc8, 0xad, 0x1c, 0xb6, 0x6c, 0x5e, 0x81, 0x18, 0x91, /* (2^ 59)P */ 0x96, 0xb3, 0xca, 0x2b, 0xe3, 0x7a, 0x59, 0x72, 0x17, 0x74, 0x29, 0x21, 0xe7, 0x78, 0x07, 0xad, 0xda, 0xb6, 0xcd, 0xf9, 0x27, 0x4d, 0xc8, 0xf2, 0x98, 0x22, 0xca, 0xf2, 0x33, 0x74, 0x7a, 0xdd, 0x1e, 0x71, 0xec, 0xe3, 0x3f, 0xe2, 0xa2, 0xd2, 0x38, 0x75, 0xb0, 0xd0, 0x0a, 0xcf, 0x7d, 0x36, 0xdc, 0x49, 0x38, 0x25, 0x34, 0x4f, 0x20, 0x9a, /* (2^ 60)P */ 0x2b, 0x6e, 0x04, 0x0d, 0x4f, 0x3d, 0x3b, 0x24, 0xf6, 0x4e, 0x5e, 0x0a, 0xbd, 0x48, 0x96, 0xba, 0x81, 0x8f, 0x39, 0x82, 0x13, 0xe6, 0x72, 0xf3, 0x0f, 0xb6, 0x94, 0xf4, 0xc5, 0x90, 0x74, 0x91, 0xa8, 0xf2, 0xc9, 0xca, 0x9a, 0x4d, 0x98, 0xf2, 0xdf, 0x52, 0x4e, 0x97, 0x2f, 0xeb, 0x84, 0xd3, 0xaf, 0xc2, 0xcc, 0xfb, 0x4c, 0x26, 0x4b, 0xe4, /* (2^ 61)P */ 0x12, 0x9e, 0xfb, 0x9d, 0x78, 0x79, 0x99, 0xdd, 0xb3, 0x0b, 0x2e, 0x56, 0x41, 0x8e, 0x3f, 0x39, 0xb8, 0x97, 0x89, 0x53, 0x9b, 0x8a, 0x3c, 0x40, 0x9d, 0xa4, 0x6c, 0x2e, 0x31, 0x71, 0xc6, 0x0a, 0x41, 0xd4, 0x95, 0x06, 0x5e, 0xc1, 0xab, 0xc2, 0x14, 0xc4, 0xc7, 0x15, 0x08, 0x3a, 0xad, 0x7a, 0xb4, 0x62, 0xa3, 0x0c, 0x90, 0xf4, 0x47, 0x08, /* (2^ 62)P */ 0x7f, 0xec, 0x09, 0x82, 0xf5, 0x94, 0x09, 0x93, 0x32, 0xd3, 0xdc, 0x56, 0x80, 0x7b, 0x5b, 0x22, 0x80, 0x6a, 0x96, 0x72, 0xb1, 0xc2, 0xd9, 0xa1, 0x8b, 0x66, 0x42, 0x16, 0xe2, 0x07, 0xb3, 0x2d, 0xf1, 0x75, 0x35, 0x72, 0xc7, 0x98, 0xbe, 0x63, 0x3b, 0x20, 0x75, 0x05, 0xc1, 0x3e, 0x31, 0x5a, 0xf7, 0xaa, 0xae, 0x4b, 0xdb, 0x1d, 0xd0, 0x74, /* (2^ 63)P */ 0x36, 0x5c, 0x74, 0xe6, 0x5d, 0x59, 0x3f, 0x15, 0x4b, 0x4d, 0x4e, 0x67, 0x41, 0xfe, 0x98, 0x1f, 0x49, 0x76, 0x91, 0x0f, 0x9b, 0xf4, 0xaf, 0x86, 0xaf, 0x66, 0x19, 0xed, 0x46, 0xf1, 0x05, 0x9a, 0xcc, 0xd1, 0x14, 0x1f, 0x82, 0x12, 0x8e, 0xe6, 0xf4, 0xc3, 0x42, 0x5c, 0x4e, 0x33, 0x93, 0xbe, 0x30, 0xe7, 0x64, 0xa9, 0x35, 0x00, 0x4d, 0xf9, /* (2^ 64)P */ 0x1f, 0xc1, 0x1e, 0xb7, 0xe3, 0x7c, 0xfa, 0xa3, 0x6b, 0x76, 0xaf, 0x9c, 0x05, 0x85, 0x4a, 0xa9, 0xfb, 0xe3, 0x7e, 0xf2, 0x49, 0x56, 0xdc, 0x2f, 0x57, 0x10, 0xba, 0x37, 0xb2, 0x62, 0xf5, 0x6b, 0xe5, 0x8f, 0x0a, 0x87, 0xd1, 0x6a, 0xcb, 0x9d, 0x07, 0xd0, 0xf6, 0x38, 0x99, 0x2c, 0x61, 0x4a, 0x4e, 0xd8, 0xd2, 0x88, 0x29, 0x99, 0x11, 0x95, /* (2^ 65)P */ 0x6f, 0xdc, 0xd5, 0xd6, 0xd6, 0xa7, 0x4c, 0x46, 0x93, 0x65, 0x62, 0x23, 0x95, 0x32, 0x9c, 0xde, 0x40, 0x41, 0x68, 0x2c, 0x18, 0x4e, 0x5a, 0x8c, 0xc0, 0xc5, 0xc5, 0xea, 0x5c, 0x45, 0x0f, 0x60, 0x78, 0x39, 0xb6, 0x36, 0x23, 0x12, 0xbc, 0x21, 0x9a, 0xf8, 0x91, 0xac, 0xc4, 0x70, 0xdf, 0x85, 0x8e, 0x3c, 0xec, 0x22, 0x04, 0x98, 0xa8, 0xaa, /* (2^ 66)P */ 0xcc, 0x52, 0x10, 0x5b, 0x4b, 0x6c, 0xc5, 0xfa, 0x3e, 0xd4, 0xf8, 0x1c, 0x04, 0x14, 0x48, 0x33, 0xd9, 0xfc, 0x5f, 0xb0, 0xa5, 0x48, 0x8c, 0x45, 0x8a, 0xee, 0x3e, 0xa7, 0xc1, 0x2e, 0x34, 0xca, 0xf6, 0xc9, 0xeb, 0x10, 0xbb, 0xe1, 0x59, 0x84, 0x25, 0xe8, 0x81, 0x70, 0xc0, 0x09, 0x42, 0xa7, 0x3b, 0x0d, 0x33, 0x00, 0xb5, 0x77, 0xbe, 0x25, /* (2^ 67)P */ 0xcd, 0x1f, 0xbc, 0x7d, 0xef, 0xe5, 0xca, 0x91, 0xaf, 0xa9, 0x59, 0x6a, 0x09, 0xca, 0xd6, 0x1b, 0x3d, 0x55, 0xde, 0xa2, 0x6a, 0x80, 0xd6, 0x95, 0x47, 0xe4, 0x5f, 0x68, 0x54, 0x08, 0xdf, 0x29, 0xba, 0x2a, 0x02, 0x84, 0xe8, 0xe9, 0x00, 0x77, 0x99, 0x36, 0x03, 0xf6, 0x4a, 0x3e, 0x21, 0x81, 0x7d, 0xb8, 0xa4, 0x8a, 0xa2, 0x05, 0xef, 0xbc, /* (2^ 68)P */ 0x7c, 0x59, 0x5f, 0x66, 0xd9, 0xb7, 0x83, 0x43, 0x8a, 0xa1, 0x8d, 0x51, 0x70, 0xba, 0xf2, 0x9b, 0x95, 0xc0, 0x4b, 0x4c, 0xa0, 0x14, 0xd3, 0xa4, 0x5d, 0x4a, 0x37, 0x36, 0x97, 0x31, 0x1e, 0x12, 0xe7, 0xbb, 0x08, 0x67, 0xa5, 0x23, 0xd7, 0xfb, 0x97, 0xd8, 0x6a, 0x03, 0xb1, 0xf8, 0x7f, 0xda, 0x58, 0xd9, 0x3f, 0x73, 0x4a, 0x53, 0xe1, 0x7b, /* (2^ 69)P */ 0x55, 0x83, 0x98, 0x78, 0x6c, 0x56, 0x5e, 0xed, 0xf7, 0x23, 0x3e, 0x4c, 0x7d, 0x09, 0x2d, 0x09, 0x9c, 0x58, 0x8b, 0x32, 0xca, 0xfe, 0xbf, 0x47, 0x03, 0xeb, 0x4d, 0xe7, 0xeb, 0x9c, 0x83, 0x05, 0x68, 0xaa, 0x80, 0x89, 0x44, 0xf9, 0xd4, 0xdc, 0xdb, 0xb1, 0xdb, 0x77, 0xac, 0xf9, 0x2a, 0xae, 0x35, 0xac, 0x74, 0xb5, 0x95, 0x62, 0x18, 0x85, /* (2^ 70)P */ 0xab, 0x82, 0x7e, 0x10, 0xd7, 0xe6, 0x57, 0xd1, 0x66, 0x12, 0x31, 0x9c, 0x9c, 0xa6, 0x27, 0x59, 0x71, 0x2e, 0xeb, 0xa0, 0x68, 0xc5, 0x87, 0x51, 0xf4, 0xca, 0x3f, 0x98, 0x56, 0xb0, 0x89, 0xb1, 0xc7, 0x7b, 0x46, 0xb3, 0xae, 0x36, 0xf2, 0xee, 0x15, 0x1a, 0x60, 0xf4, 0x50, 0x76, 0x4f, 0xc4, 0x53, 0x0d, 0x36, 0x4d, 0x31, 0xb1, 0x20, 0x51, /* (2^ 71)P */ 0xf7, 0x1d, 0x8c, 0x1b, 0x5e, 0xe5, 0x02, 0x6f, 0xc5, 0xa5, 0xe0, 0x5f, 0xc6, 0xb6, 0x63, 0x43, 0xaf, 0x3c, 0x19, 0x6c, 0xf4, 0xaf, 0xa4, 0x33, 0xb1, 0x0a, 0x37, 0x3d, 0xd9, 0x4d, 0xe2, 0x29, 0x24, 0x26, 0x94, 0x7c, 0x02, 0xe4, 0xe2, 0xf2, 0xbe, 0xbd, 0xac, 0x1b, 0x48, 0xb8, 0xdd, 0xe9, 0x0d, 0x9a, 0x50, 0x1a, 0x98, 0x71, 0x6e, 0xdc, /* (2^ 72)P */ 0x9f, 0x40, 0xb1, 0xb3, 0x66, 0x28, 0x6c, 0xfe, 0xa6, 0x7d, 0xf8, 0x3e, 0xb8, 0xf3, 0xde, 0x52, 0x76, 0x52, 0xa3, 0x92, 0x98, 0x23, 0xab, 0x4f, 0x88, 0x97, 0xfc, 0x22, 0xe1, 0x6b, 0x67, 0xcd, 0x13, 0x95, 0xda, 0x65, 0xdd, 0x3b, 0x67, 0x3f, 0x5f, 0x4c, 0xf2, 0x8a, 0xad, 0x98, 0xa7, 0x94, 0x24, 0x45, 0x87, 0x11, 0x7c, 0x75, 0x79, 0x85, /* (2^ 73)P */ 0x70, 0xbf, 0xf9, 0x3b, 0xa9, 0x44, 0x57, 0x72, 0x96, 0xc9, 0xa4, 0x98, 0x65, 0xbf, 0x87, 0xb3, 0x3a, 0x39, 0x12, 0xde, 0xe5, 0x39, 0x01, 0x4f, 0xf7, 0xc0, 0x71, 0x52, 0x36, 0x85, 0xb3, 0x18, 0xf8, 0x14, 0xc0, 0x6d, 0xae, 0x9e, 0x4f, 0xb0, 0x72, 0x87, 0xac, 0x5c, 0xd1, 0x6c, 0x41, 0x6c, 0x90, 0x9d, 0x22, 0x81, 0xe4, 0x2b, 0xea, 0xe5, /* (2^ 74)P */ 0xfc, 0xea, 0x1a, 0x65, 0xd9, 0x49, 0x6a, 0x39, 0xb5, 0x96, 0x72, 0x7b, 0x32, 0xf1, 0xd0, 0xe9, 0x45, 0xd9, 0x31, 0x55, 0xc7, 0x34, 0xe9, 0x5a, 0xec, 0x73, 0x0b, 0x03, 0xc4, 0xb3, 0xe6, 0xc9, 0x5e, 0x0a, 0x17, 0xfe, 0x53, 0x66, 0x7f, 0x21, 0x18, 0x74, 0x54, 0x1b, 0xc9, 0x49, 0x16, 0xd2, 0x48, 0xaf, 0x5b, 0x47, 0x7b, 0xeb, 0xaa, 0xc9, /* (2^ 75)P */ 0x47, 0x04, 0xf5, 0x5a, 0x87, 0x77, 0x9e, 0x21, 0x34, 0x4e, 0x83, 0x88, 0xaf, 0x02, 0x1d, 0xb0, 0x5a, 0x1d, 0x1d, 0x7d, 0x8d, 0x2c, 0xd3, 0x8d, 0x63, 0xa9, 0x45, 0xfb, 0x15, 0x6d, 0x86, 0x45, 0xcd, 0x38, 0x0e, 0xf7, 0x37, 0x79, 0xed, 0x6d, 0x5a, 0xbc, 0x32, 0xcc, 0x66, 0xf1, 0x3a, 0xb2, 0x87, 0x6f, 0x70, 0x71, 0xd9, 0xf2, 0xfa, 0x7b, /* (2^ 76)P */ 0x68, 0x07, 0xdc, 0x61, 0x40, 0xe4, 0xec, 0x32, 0xc8, 0xbe, 0x66, 0x30, 0x54, 0x80, 0xfd, 0x13, 0x7a, 0xef, 0xae, 0xed, 0x2e, 0x00, 0x6d, 0x3f, 0xbd, 0xfc, 0x91, 0x24, 0x53, 0x7f, 0x63, 0x9d, 0x2e, 0xe3, 0x76, 0xe0, 0xf3, 0xe1, 0x8f, 0x7a, 0xc4, 0x77, 0x0c, 0x91, 0xc0, 0xc2, 0x18, 0x6b, 0x04, 0xad, 0xb6, 0x70, 0x9a, 0x64, 0xc5, 0x82, /* (2^ 77)P */ 0x7f, 0xea, 0x13, 0xd8, 0x9e, 0xfc, 0x5b, 0x06, 0xb5, 0x4f, 0xda, 0x38, 0xe0, 0x9c, 0xd2, 0x3a, 0xc1, 0x1c, 0x62, 0x70, 0x7f, 0xc6, 0x24, 0x0a, 0x47, 0x04, 0x01, 0xc4, 0x55, 0x09, 0xd1, 0x7a, 0x07, 0xba, 0xa3, 0x80, 0x4f, 0xc1, 0x65, 0x36, 0x6d, 0xc0, 0x10, 0xcf, 0x94, 0xa9, 0xa2, 0x01, 0x44, 0xd1, 0xf9, 0x1c, 0x4c, 0xfb, 0xf8, 0x99, /* (2^ 78)P */ 0x6c, 0xb9, 0x6b, 0xee, 0x43, 0x5b, 0xb9, 0xbb, 0xee, 0x2e, 0x52, 0xc1, 0xc6, 0xb9, 0x61, 0xd2, 0x93, 0xa5, 0xaf, 0x52, 0xf4, 0xa4, 0x1a, 0x51, 0x61, 0xa7, 0xcb, 0x9e, 0xbb, 0x56, 0x65, 0xe2, 0xbf, 0x75, 0xb9, 0x9c, 0x50, 0x96, 0x60, 0x81, 0x74, 0x47, 0xc0, 0x04, 0x88, 0x71, 0x76, 0x39, 0x9a, 0xa7, 0xb1, 0x4e, 0x43, 0x15, 0xe0, 0xbb, /* (2^ 79)P */ 0xbb, 0xce, 0xe2, 0xbb, 0xf9, 0x17, 0x0f, 0x82, 0x40, 0xad, 0x73, 0xe3, 0xeb, 0x3b, 0x06, 0x1a, 0xcf, 0x8e, 0x6e, 0x28, 0xb8, 0x26, 0xd9, 0x5b, 0xb7, 0xb3, 0xcf, 0xb4, 0x6a, 0x1c, 0xbf, 0x7f, 0xb8, 0xb5, 0x79, 0xcf, 0x45, 0x68, 0x7d, 0xc5, 0xeb, 0xf3, 0xbe, 0x39, 0x40, 0xfc, 0x07, 0x90, 0x7a, 0x62, 0xad, 0x86, 0x08, 0x71, 0x25, 0xe1, /* (2^ 80)P */ 0x9b, 0x46, 0xac, 0xef, 0xc1, 0x4e, 0xa1, 0x97, 0x95, 0x76, 0xf9, 0x1b, 0xc2, 0xb2, 0x6a, 0x41, 0xea, 0x80, 0x3d, 0xe9, 0x08, 0x52, 0x5a, 0xe3, 0xf2, 0x08, 0xc5, 0xea, 0x39, 0x3f, 0x44, 0x71, 0x4d, 0xea, 0x0d, 0x05, 0x23, 0xe4, 0x2e, 0x3c, 0x89, 0xfe, 0x12, 0x8a, 0x95, 0x42, 0x0a, 0x68, 0xea, 0x5a, 0x28, 0x06, 0x9e, 0xe3, 0x5f, 0xe0, /* (2^ 81)P */ 0x00, 0x61, 0x6c, 0x98, 0x9b, 0xe7, 0xb9, 0x06, 0x1c, 0xc5, 0x1b, 0xed, 0xbe, 0xc8, 0xb3, 0xea, 0x87, 0xf0, 0xc4, 0x24, 0x7d, 0xbb, 0x5d, 0xa4, 0x1d, 0x7a, 0x16, 0x00, 0x55, 0x94, 0x67, 0x78, 0xbd, 0x58, 0x02, 0x82, 0x90, 0x53, 0x76, 0xd4, 0x72, 0x99, 0x51, 0x6f, 0x7b, 0xcf, 0x80, 0x30, 0x31, 0x3b, 0x01, 0xc7, 0xc1, 0xef, 0xe6, 0x42, /* (2^ 82)P */ 0xe2, 0x35, 0xaf, 0x4b, 0x79, 0xc6, 0x12, 0x24, 0x99, 0xc0, 0x68, 0xb0, 0x43, 0x3e, 0xe5, 0xef, 0xe2, 0x29, 0xea, 0xb8, 0xb3, 0xbc, 0x6a, 0x53, 0x2c, 0x69, 0x18, 0x5a, 0xf9, 0x15, 0xae, 0x66, 0x58, 0x18, 0xd3, 0x2d, 0x4b, 0x00, 0xfd, 0x84, 0xab, 0x4f, 0xae, 0x70, 0x6b, 0x9e, 0x9a, 0xdf, 0x83, 0xfd, 0x2e, 0x3c, 0xcf, 0xf8, 0x88, 0x5b, /* (2^ 83)P */ 0xa4, 0x90, 0x31, 0x85, 0x13, 0xcd, 0xdf, 0x64, 0xc9, 0xa1, 0x0b, 0xe7, 0xb6, 0x73, 0x8a, 0x1b, 0x22, 0x78, 0x4c, 0xd4, 0xae, 0x48, 0x18, 0x00, 0x00, 0xa8, 0x9f, 0x06, 0xf9, 0xfb, 0x2d, 0xc3, 0xb1, 0x2a, 0xbc, 0x13, 0x99, 0x57, 0xaf, 0xf0, 0x8d, 0x61, 0x54, 0x29, 0xd5, 0xf2, 0x72, 0x00, 0x96, 0xd1, 0x85, 0x12, 0x8a, 0xf0, 0x23, 0xfb, /* (2^ 84)P */ 0x69, 0xc7, 0xdb, 0xd9, 0x92, 0x75, 0x08, 0x9b, 0xeb, 0xa5, 0x93, 0xd1, 0x1a, 0xf4, 0xf5, 0xaf, 0xe6, 0xc4, 0x4a, 0x0d, 0x35, 0x26, 0x39, 0x9d, 0xd3, 0x17, 0x3e, 0xae, 0x2d, 0xbf, 0x73, 0x9f, 0xb7, 0x74, 0x91, 0xd1, 0xd8, 0x5c, 0x14, 0xf9, 0x75, 0xdf, 0xeb, 0xc2, 0x22, 0xd8, 0x14, 0x8d, 0x86, 0x23, 0x4d, 0xd1, 0x2d, 0xdb, 0x6b, 0x42, /* (2^ 85)P */ 0x8c, 0xda, 0xc6, 0xf8, 0x71, 0xba, 0x2b, 0x06, 0x78, 0xae, 0xcc, 0x3a, 0xe3, 0xe3, 0xa1, 0x8b, 0xe2, 0x34, 0x6d, 0x28, 0x9e, 0x46, 0x13, 0x4d, 0x9e, 0xa6, 0x73, 0x49, 0x65, 0x79, 0x88, 0xb9, 0x3a, 0xd1, 0x6d, 0x2f, 0x48, 0x2b, 0x0a, 0x7f, 0x58, 0x20, 0x37, 0xf4, 0x0e, 0xbb, 0x4a, 0x95, 0x58, 0x0c, 0x88, 0x30, 0xc4, 0x74, 0xdd, 0xfd, /* (2^ 86)P */ 0x6d, 0x13, 0x4e, 0x89, 0x2d, 0xa9, 0xa3, 0xed, 0x09, 0xe3, 0x0e, 0x71, 0x3e, 0x4a, 0xab, 0x90, 0xde, 0x03, 0xeb, 0x56, 0x46, 0x60, 0x06, 0xf5, 0x71, 0xe5, 0xee, 0x9b, 0xef, 0xff, 0xc4, 0x2c, 0x9f, 0x37, 0x48, 0x45, 0x94, 0x12, 0x41, 0x81, 0x15, 0x70, 0x91, 0x99, 0x5e, 0x56, 0x6b, 0xf4, 0xa6, 0xc9, 0xf5, 0x69, 0x9d, 0x78, 0x37, 0x57, /* (2^ 87)P */ 0xf3, 0x51, 0x57, 0x7e, 0x43, 0x6f, 0xc6, 0x67, 0x59, 0x0c, 0xcf, 0x94, 0xe6, 0x3d, 0xb5, 0x07, 0xc9, 0x77, 0x48, 0xc9, 0x68, 0x0d, 0x98, 0x36, 0x62, 0x35, 0x38, 0x1c, 0xf5, 0xc5, 0xec, 0x66, 0x78, 0xfe, 0x47, 0xab, 0x26, 0xd6, 0x44, 0xb6, 0x06, 0x0f, 0x89, 0xe3, 0x19, 0x40, 0x1a, 0xe7, 0xd8, 0x65, 0x55, 0xf7, 0x1a, 0xfc, 0xa3, 0x0e, /* (2^ 88)P */ 0x0e, 0x30, 0xa6, 0xb7, 0x58, 0x60, 0x62, 0x2a, 0x6c, 0x13, 0xa8, 0x14, 0x9b, 0xb8, 0xf2, 0x70, 0xd8, 0xb1, 0x71, 0x88, 0x8c, 0x18, 0x31, 0x25, 0x93, 0x90, 0xb4, 0xc7, 0x49, 0xd8, 0xd4, 0xdb, 0x1e, 0x1e, 0x7f, 0xaa, 0xba, 0xc9, 0xf2, 0x5d, 0xa9, 0x3a, 0x43, 0xb4, 0x5c, 0xee, 0x7b, 0xc7, 0x97, 0xb7, 0x66, 0xd7, 0x23, 0xd9, 0x22, 0x59, /* (2^ 89)P */ 0x28, 0x19, 0xa6, 0xf9, 0x89, 0x20, 0x78, 0xd4, 0x6d, 0xcb, 0x79, 0x8f, 0x61, 0x6f, 0xb2, 0x5c, 0x4f, 0xa6, 0x54, 0x84, 0x95, 0x24, 0x36, 0x64, 0xcb, 0x39, 0xe7, 0x8f, 0x97, 0x9c, 0x5c, 0x3c, 0xfb, 0x51, 0x11, 0x01, 0x17, 0xdb, 0xc9, 0x9b, 0x51, 0x03, 0x9a, 0xe9, 0xe5, 0x24, 0x1e, 0xf5, 0xda, 0xe0, 0x48, 0x02, 0x23, 0xd0, 0x2c, 0x81, /* (2^ 90)P */ 0x42, 0x1b, 0xe4, 0x91, 0x85, 0x2a, 0x0c, 0xd2, 0x28, 0x66, 0x57, 0x9e, 0x33, 0x8d, 0x25, 0x71, 0x10, 0x65, 0x76, 0xa2, 0x8c, 0x21, 0x86, 0x81, 0x15, 0xc2, 0x27, 0xeb, 0x54, 0x2d, 0x4f, 0x6c, 0xe6, 0xd6, 0x24, 0x9c, 0x1a, 0x12, 0xb8, 0x81, 0xe2, 0x0a, 0xf3, 0xd3, 0xf0, 0xd3, 0xe1, 0x74, 0x1f, 0x9b, 0x11, 0x47, 0xd0, 0xcf, 0xb6, 0x54, /* (2^ 91)P */ 0x26, 0x45, 0xa2, 0x10, 0xd4, 0x2d, 0xae, 0xc0, 0xb0, 0xe8, 0x86, 0xb3, 0xc7, 0xea, 0x70, 0x87, 0x61, 0xb5, 0xa5, 0x55, 0xbe, 0x88, 0x1d, 0x7a, 0xd9, 0x6f, 0xeb, 0x83, 0xe2, 0x44, 0x7f, 0x98, 0x04, 0xd6, 0x50, 0x9d, 0xa7, 0x86, 0x66, 0x09, 0x63, 0xe1, 0xed, 0x72, 0xb1, 0xe4, 0x1d, 0x3a, 0xfd, 0x47, 0xce, 0x1c, 0xaa, 0x3b, 0x8f, 0x1b, /* (2^ 92)P */ 0xf4, 0x3c, 0x4a, 0xb6, 0xc2, 0x9c, 0xe0, 0x2e, 0xb7, 0x38, 0xea, 0x61, 0x35, 0x97, 0x10, 0x90, 0xae, 0x22, 0x48, 0xb3, 0xa9, 0xc6, 0x7a, 0xbb, 0x23, 0xf2, 0xf8, 0x1b, 0xa7, 0xa1, 0x79, 0xcc, 0xc4, 0xf8, 0x08, 0x76, 0x8a, 0x5a, 0x1c, 0x1b, 0xc5, 0x33, 0x91, 0xa9, 0xb8, 0xb9, 0xd3, 0xf8, 0x49, 0xcd, 0xe5, 0x82, 0x43, 0xf7, 0xca, 0x68, /* (2^ 93)P */ 0x38, 0xba, 0xae, 0x44, 0xfe, 0x57, 0x64, 0x56, 0x7c, 0x0e, 0x9c, 0xca, 0xff, 0xa9, 0x82, 0xbb, 0x38, 0x4a, 0xa7, 0xf7, 0x47, 0xab, 0xbe, 0x6d, 0x23, 0x0b, 0x8a, 0xed, 0xc2, 0xb9, 0x8f, 0xf1, 0xec, 0x91, 0x44, 0x73, 0x64, 0xba, 0xd5, 0x8f, 0x37, 0x38, 0x0d, 0xd5, 0xf8, 0x73, 0x57, 0xb6, 0xc2, 0x45, 0xdc, 0x25, 0xb2, 0xb6, 0xea, 0xd9, /* (2^ 94)P */ 0xbf, 0xe9, 0x1a, 0x40, 0x4d, 0xcc, 0xe6, 0x1d, 0x70, 0x1a, 0x65, 0xcc, 0x34, 0x2c, 0x37, 0x2c, 0x2d, 0x6b, 0x6d, 0xe5, 0x2f, 0x19, 0x9e, 0xe4, 0xe1, 0xaa, 0xd4, 0xab, 0x54, 0xf4, 0xa8, 0xe4, 0x69, 0x2d, 0x8e, 0x4d, 0xd7, 0xac, 0xb0, 0x5b, 0xfe, 0xe3, 0x26, 0x07, 0xc3, 0xf8, 0x1b, 0x43, 0xa8, 0x1d, 0x64, 0xa5, 0x25, 0x88, 0xbb, 0x77, /* (2^ 95)P */ 0x92, 0xcd, 0x6e, 0xa0, 0x79, 0x04, 0x18, 0xf4, 0x11, 0x58, 0x48, 0xb5, 0x3c, 0x7b, 0xd1, 0xcc, 0xd3, 0x14, 0x2c, 0xa0, 0xdd, 0x04, 0x44, 0x11, 0xb3, 0x6d, 0x2f, 0x0d, 0xf5, 0x2a, 0x75, 0x5d, 0x1d, 0xda, 0x86, 0x8d, 0x7d, 0x6b, 0x32, 0x68, 0xb6, 0x6c, 0x64, 0x9e, 0xde, 0x80, 0x88, 0xce, 0x08, 0xbf, 0x0b, 0xe5, 0x8e, 0x4f, 0x1d, 0xfb, /* (2^ 96)P */ 0xaf, 0xe8, 0x85, 0xbf, 0x7f, 0x37, 0x8d, 0x66, 0x7c, 0xd5, 0xd3, 0x96, 0xa5, 0x81, 0x67, 0x95, 0xff, 0x48, 0xde, 0xde, 0xd7, 0x7a, 0x46, 0x34, 0xb1, 0x13, 0x70, 0x29, 0xed, 0x87, 0x90, 0xb0, 0x40, 0x2c, 0xa6, 0x43, 0x6e, 0xb6, 0xbc, 0x48, 0x8a, 0xc1, 0xae, 0xb8, 0xd4, 0xe2, 0xc0, 0x32, 0xb2, 0xa6, 0x2a, 0x8f, 0xb5, 0x16, 0x9e, 0xc3, /* (2^ 97)P */ 0xff, 0x4d, 0xd2, 0xd6, 0x74, 0xef, 0x2c, 0x96, 0xc1, 0x11, 0xa8, 0xb8, 0xfe, 0x94, 0x87, 0x3e, 0xa0, 0xfb, 0x57, 0xa3, 0xfc, 0x7a, 0x7e, 0x6a, 0x59, 0x6c, 0x54, 0xbb, 0xbb, 0xa2, 0x25, 0x38, 0x1b, 0xdf, 0x5d, 0x7b, 0x94, 0x14, 0xde, 0x07, 0x6e, 0xd3, 0xab, 0x02, 0x26, 0x74, 0x16, 0x12, 0xdf, 0x2e, 0x2a, 0xa7, 0xb0, 0xe8, 0x29, 0xc0, /* (2^ 98)P */ 0x6a, 0x38, 0x0b, 0xd3, 0xba, 0x45, 0x23, 0xe0, 0x04, 0x3b, 0x83, 0x39, 0xc5, 0x11, 0xe6, 0xcf, 0x39, 0x0a, 0xb3, 0xb0, 0x3b, 0x27, 0x29, 0x63, 0x1c, 0xf3, 0x00, 0xe6, 0xd2, 0x55, 0x21, 0x1f, 0x84, 0x97, 0x9f, 0x01, 0x49, 0x43, 0x30, 0x5f, 0xe0, 0x1d, 0x24, 0xc4, 0x4e, 0xa0, 0x2b, 0x0b, 0x12, 0x55, 0xc3, 0x27, 0xae, 0x08, 0x83, 0x7c, /* (2^ 99)P */ 0x5d, 0x1a, 0xb7, 0xa9, 0xf5, 0xfd, 0xec, 0xad, 0xb7, 0x87, 0x02, 0x5f, 0x0d, 0x30, 0x4d, 0xe2, 0x65, 0x87, 0xa4, 0x41, 0x45, 0x1d, 0x67, 0xe0, 0x30, 0x5c, 0x13, 0x87, 0xf6, 0x2e, 0x08, 0xc1, 0xc7, 0x12, 0x45, 0xc8, 0x9b, 0xad, 0xb8, 0xd5, 0x57, 0xbb, 0x5c, 0x48, 0x3a, 0xe1, 0x91, 0x5e, 0xf6, 0x4d, 0x8a, 0x63, 0x75, 0x69, 0x0c, 0x01, /* (2^100)P */ 0x8f, 0x53, 0x2d, 0xa0, 0x71, 0x3d, 0xfc, 0x45, 0x10, 0x96, 0xcf, 0x56, 0xf9, 0xbb, 0x40, 0x3c, 0x86, 0x52, 0x76, 0xbe, 0x84, 0xf9, 0xa6, 0x9d, 0x3d, 0x27, 0xbe, 0xb4, 0x00, 0x49, 0x94, 0xf5, 0x5d, 0xe1, 0x62, 0x85, 0x66, 0xe5, 0xb8, 0x20, 0x2c, 0x09, 0x7d, 0x9d, 0x3d, 0x6e, 0x74, 0x39, 0xab, 0xad, 0xa0, 0x90, 0x97, 0x5f, 0xbb, 0xa7, /* (2^101)P */ 0xdb, 0x2d, 0x99, 0x08, 0x16, 0x46, 0x83, 0x7a, 0xa8, 0xea, 0x3d, 0x28, 0x5b, 0x49, 0xfc, 0xb9, 0x6d, 0x00, 0x9e, 0x54, 0x4f, 0x47, 0x64, 0x9b, 0x58, 0x4d, 0x07, 0x0c, 0x6f, 0x29, 0x56, 0x0b, 0x00, 0x14, 0x85, 0x96, 0x41, 0x04, 0xb9, 0x5c, 0xa4, 0xf6, 0x16, 0x73, 0x6a, 0xc7, 0x62, 0x0c, 0x65, 0x2f, 0x93, 0xbf, 0xf7, 0xb9, 0xb7, 0xf1, /* (2^102)P */ 0xeb, 0x6d, 0xb3, 0x46, 0x32, 0xd2, 0xcb, 0x08, 0x94, 0x14, 0xbf, 0x3f, 0xc5, 0xcb, 0x5f, 0x9f, 0x8a, 0x89, 0x0c, 0x1b, 0x45, 0xad, 0x4c, 0x50, 0xb4, 0xe1, 0xa0, 0x6b, 0x11, 0x92, 0xaf, 0x1f, 0x00, 0xcc, 0xe5, 0x13, 0x7e, 0xe4, 0x2e, 0xa0, 0x57, 0xf3, 0xa7, 0x84, 0x79, 0x7a, 0xc2, 0xb7, 0xb7, 0xfc, 0x5d, 0xa5, 0xa9, 0x64, 0xcc, 0xd8, /* (2^103)P */ 0xa9, 0xc4, 0x12, 0x8b, 0x34, 0x78, 0x3e, 0x38, 0xfd, 0x3f, 0x87, 0xfa, 0x88, 0x94, 0xd5, 0xd9, 0x7f, 0xeb, 0x58, 0xff, 0xb9, 0x45, 0xdb, 0xa1, 0xed, 0x22, 0x28, 0x1d, 0x00, 0x6d, 0x79, 0x85, 0x7a, 0x75, 0x5d, 0xf0, 0xb1, 0x9e, 0x47, 0x28, 0x8c, 0x62, 0xdf, 0xfb, 0x4c, 0x7b, 0xc5, 0x1a, 0x42, 0x95, 0xef, 0x9a, 0xb7, 0x27, 0x7e, 0xda, /* (2^104)P */ 0xca, 0xd5, 0xc0, 0x17, 0xa1, 0x66, 0x79, 0x9c, 0x2a, 0xb7, 0x0a, 0xfe, 0x62, 0xe4, 0x26, 0x78, 0x90, 0xa7, 0xcb, 0xb0, 0x4f, 0x6d, 0xf9, 0x8f, 0xf7, 0x7d, 0xac, 0xb8, 0x78, 0x1f, 0x41, 0xea, 0x97, 0x1e, 0x62, 0x97, 0x43, 0x80, 0x58, 0x80, 0xb6, 0x69, 0x7d, 0xee, 0x16, 0xd2, 0xa1, 0x81, 0xd7, 0xb1, 0x27, 0x03, 0x48, 0xda, 0xab, 0xec, /* (2^105)P */ 0x5b, 0xed, 0x40, 0x8e, 0x8c, 0xc1, 0x66, 0x90, 0x7f, 0x0c, 0xb2, 0xfc, 0xbd, 0x16, 0xac, 0x7d, 0x4c, 0x6a, 0xf9, 0xae, 0xe7, 0x4e, 0x11, 0x12, 0xe9, 0xbe, 0x17, 0x09, 0xc6, 0xc1, 0x5e, 0xb5, 0x7b, 0x50, 0x5c, 0x27, 0xfb, 0x80, 0xab, 0x01, 0xfa, 0x5b, 0x9b, 0x75, 0x16, 0x6e, 0xb2, 0x5c, 0x8c, 0x2f, 0xa5, 0x6a, 0x1a, 0x68, 0xa6, 0x90, /* (2^106)P */ 0x75, 0xfe, 0xb6, 0x96, 0x96, 0x87, 0x4c, 0x12, 0xa9, 0xd1, 0xd8, 0x03, 0xa3, 0xc1, 0x15, 0x96, 0xe8, 0xa0, 0x75, 0x82, 0xa0, 0x6d, 0xea, 0x54, 0xdc, 0x5f, 0x0d, 0x7e, 0xf6, 0x70, 0xb5, 0xdc, 0x7a, 0xf6, 0xc4, 0xd4, 0x21, 0x49, 0xf5, 0xd4, 0x14, 0x6d, 0x48, 0x1d, 0x7c, 0x99, 0x42, 0xdf, 0x78, 0x6b, 0x9d, 0xb9, 0x30, 0x3c, 0xd0, 0x29, /* (2^107)P */ 0x85, 0xd6, 0xd8, 0xf3, 0x91, 0x74, 0xdd, 0xbd, 0x72, 0x96, 0x10, 0xe4, 0x76, 0x02, 0x5a, 0x72, 0x67, 0xd3, 0x17, 0x72, 0x14, 0x9a, 0x20, 0x5b, 0x0f, 0x8d, 0xed, 0x6d, 0x4e, 0xe3, 0xd9, 0x82, 0xc2, 0x99, 0xee, 0x39, 0x61, 0x69, 0x8a, 0x24, 0x01, 0x92, 0x15, 0xe7, 0xfc, 0xf9, 0x4d, 0xac, 0xf1, 0x30, 0x49, 0x01, 0x0b, 0x6e, 0x0f, 0x20, /* (2^108)P */ 0xd8, 0x25, 0x94, 0x5e, 0x43, 0x29, 0xf5, 0xcc, 0xe8, 0xe3, 0x55, 0x41, 0x3c, 0x9f, 0x58, 0x5b, 0x00, 0xeb, 0xc5, 0xdf, 0xcf, 0xfb, 0xfd, 0x6e, 0x92, 0xec, 0x99, 0x30, 0xd6, 0x05, 0xdd, 0x80, 0x7a, 0x5d, 0x6d, 0x16, 0x85, 0xd8, 0x9d, 0x43, 0x65, 0xd8, 0x2c, 0x33, 0x2f, 0x5c, 0x41, 0xea, 0xb7, 0x95, 0x77, 0xf2, 0x9e, 0x59, 0x09, 0xe8, /* (2^109)P */ 0x00, 0xa0, 0x03, 0x80, 0xcd, 0x60, 0xe5, 0x17, 0xd4, 0x15, 0x99, 0xdd, 0x4f, 0xbf, 0x66, 0xb8, 0xc0, 0xf5, 0xf9, 0xfc, 0x6d, 0x42, 0x18, 0x34, 0x1c, 0x7d, 0x5b, 0xb5, 0x09, 0xd0, 0x99, 0x57, 0x81, 0x0b, 0x62, 0xb3, 0xa2, 0xf9, 0x0b, 0xae, 0x95, 0xb8, 0xc2, 0x3b, 0x0d, 0x5b, 0x00, 0xf1, 0xed, 0xbc, 0x05, 0x9d, 0x61, 0xbc, 0x73, 0x9d, /* (2^110)P */ 0xd4, 0xdb, 0x29, 0xe5, 0x85, 0xe9, 0xc6, 0x89, 0x2a, 0xa8, 0x54, 0xab, 0xb3, 0x7f, 0x88, 0xc0, 0x4d, 0xe0, 0xd1, 0x74, 0x6e, 0xa3, 0xa7, 0x39, 0xd5, 0xcc, 0xa1, 0x8a, 0xcb, 0x5b, 0x34, 0xad, 0x92, 0xb4, 0xd8, 0xd5, 0x17, 0xf6, 0x77, 0x18, 0x9e, 0xaf, 0x45, 0x3b, 0x03, 0xe2, 0xf8, 0x52, 0x60, 0xdc, 0x15, 0x20, 0x9e, 0xdf, 0xd8, 0x5d, /* (2^111)P */ 0x02, 0xc1, 0xac, 0x1a, 0x15, 0x8e, 0x6c, 0xf5, 0x1e, 0x1e, 0xba, 0x7e, 0xc2, 0xda, 0x7d, 0x02, 0xda, 0x43, 0xae, 0x04, 0x70, 0x28, 0x54, 0x78, 0x94, 0xf5, 0x4f, 0x07, 0x84, 0x8f, 0xed, 0xaa, 0xc0, 0xb8, 0xcd, 0x7f, 0x7e, 0x33, 0xa3, 0xbe, 0x21, 0x29, 0xc8, 0x56, 0x34, 0xc0, 0x76, 0x87, 0x8f, 0xc7, 0x73, 0x58, 0x90, 0x16, 0xfc, 0xd6, /* (2^112)P */ 0xb8, 0x3f, 0xe1, 0xdf, 0x3a, 0x91, 0x25, 0x0c, 0xf6, 0x47, 0xa8, 0x89, 0xc4, 0xc6, 0x61, 0xec, 0x86, 0x2c, 0xfd, 0xbe, 0xa4, 0x6f, 0xc2, 0xd4, 0x46, 0x19, 0x70, 0x5d, 0x09, 0x02, 0x86, 0xd3, 0x4b, 0xe9, 0x16, 0x7b, 0xf0, 0x0d, 0x6c, 0xff, 0x91, 0x05, 0xbf, 0x55, 0xb4, 0x00, 0x8d, 0xe5, 0x6d, 0x68, 0x20, 0x90, 0x12, 0xb5, 0x5c, 0x32, /* (2^113)P */ 0x80, 0x45, 0xc8, 0x51, 0x87, 0xba, 0x1c, 0x5c, 0xcf, 0x5f, 0x4b, 0x3c, 0x9e, 0x3b, 0x36, 0xd2, 0x26, 0xa2, 0x7f, 0xab, 0xb7, 0xbf, 0xda, 0x68, 0x23, 0x8f, 0xc3, 0xa0, 0xfd, 0xad, 0xf1, 0x56, 0x3b, 0xd0, 0x75, 0x2b, 0x44, 0x61, 0xd8, 0xf4, 0xf1, 0x05, 0x49, 0x53, 0x07, 0xee, 0x47, 0xef, 0xc0, 0x7c, 0x9d, 0xe4, 0x15, 0x88, 0xc5, 0x47, /* (2^114)P */ 0x2d, 0xb5, 0x09, 0x80, 0xb9, 0xd3, 0xd8, 0xfe, 0x4c, 0xd2, 0xa6, 0x6e, 0xd3, 0x75, 0xcf, 0xb0, 0x99, 0xcb, 0x50, 0x8d, 0xe9, 0x67, 0x9b, 0x20, 0xe8, 0x57, 0xd8, 0x14, 0x85, 0x73, 0x6a, 0x74, 0xe0, 0x99, 0xf0, 0x6b, 0x6e, 0x59, 0x30, 0x31, 0x33, 0x96, 0x5f, 0xa1, 0x0c, 0x1b, 0xf4, 0xca, 0x09, 0xe1, 0x9b, 0xb5, 0xcf, 0x6d, 0x0b, 0xeb, /* (2^115)P */ 0x1a, 0xde, 0x50, 0xa9, 0xac, 0x3e, 0x10, 0x43, 0x4f, 0x82, 0x4f, 0xc0, 0xfe, 0x3f, 0x33, 0xd2, 0x64, 0x86, 0x50, 0xa9, 0x51, 0x76, 0x5e, 0x50, 0x97, 0x6c, 0x73, 0x8d, 0x77, 0xa3, 0x75, 0x03, 0xbc, 0xc9, 0xfb, 0x50, 0xd9, 0x6d, 0x16, 0xad, 0x5d, 0x32, 0x3d, 0xac, 0x44, 0xdf, 0x51, 0xf7, 0x19, 0xd4, 0x0b, 0x57, 0x78, 0x0b, 0x81, 0x4e, /* (2^116)P */ 0x32, 0x24, 0xf1, 0x6c, 0x55, 0x62, 0x1d, 0xb3, 0x1f, 0xda, 0xfa, 0x6a, 0x8f, 0x98, 0x01, 0x16, 0xde, 0x44, 0x50, 0x0d, 0x2e, 0x6c, 0x0b, 0xa2, 0xd3, 0x74, 0x0e, 0xa9, 0xbf, 0x8d, 0xa9, 0xc8, 0xc8, 0x2f, 0x62, 0xc1, 0x35, 0x5e, 0xfd, 0x3a, 0xb3, 0x83, 0x2d, 0xee, 0x4e, 0xfd, 0x5c, 0x5e, 0xad, 0x85, 0xa5, 0x10, 0xb5, 0x4f, 0x34, 0xa7, /* (2^117)P */ 0xd1, 0x58, 0x6f, 0xe6, 0x54, 0x2c, 0xc2, 0xcd, 0xcf, 0x83, 0xdc, 0x88, 0x0c, 0xb9, 0xb4, 0x62, 0x18, 0x89, 0x65, 0x28, 0xe9, 0x72, 0x4b, 0x65, 0xcf, 0xd6, 0x90, 0x88, 0xd7, 0x76, 0x17, 0x4f, 0x74, 0x64, 0x1e, 0xcb, 0xd3, 0xf5, 0x4b, 0xaa, 0x2e, 0x4d, 0x2d, 0x7c, 0x13, 0x1f, 0xfd, 0xd9, 0x60, 0x83, 0x7e, 0xda, 0x64, 0x1c, 0xdc, 0x9f, /* (2^118)P */ 0xad, 0xef, 0xac, 0x1b, 0xc1, 0x30, 0x5a, 0x15, 0xc9, 0x1f, 0xac, 0xf1, 0xca, 0x44, 0x95, 0x95, 0xea, 0xf2, 0x22, 0xe7, 0x8d, 0x25, 0xf0, 0xff, 0xd8, 0x71, 0xf7, 0xf8, 0x8f, 0x8f, 0xcd, 0xf4, 0x1e, 0xfe, 0x6c, 0x68, 0x04, 0xb8, 0x78, 0xa1, 0x5f, 0xa6, 0x5d, 0x5e, 0xf9, 0x8d, 0xea, 0x80, 0xcb, 0xf3, 0x17, 0xa6, 0x03, 0xc9, 0x38, 0xd5, /* (2^119)P */ 0x79, 0x14, 0x31, 0xc3, 0x38, 0xe5, 0xaa, 0xbf, 0x17, 0xa3, 0x04, 0x4e, 0x80, 0x59, 0x9c, 0x9f, 0x19, 0x39, 0xe4, 0x2d, 0x23, 0x54, 0x4a, 0x7f, 0x3e, 0xf3, 0xd9, 0xc7, 0xba, 0x6c, 0x8f, 0x6b, 0xfa, 0x34, 0xb5, 0x23, 0x17, 0x1d, 0xff, 0x1d, 0xea, 0x1f, 0xd7, 0xba, 0x61, 0xb2, 0xe0, 0x38, 0x6a, 0xe9, 0xcf, 0x48, 0x5d, 0x6a, 0x10, 0x9c, /* (2^120)P */ 0xc8, 0xbb, 0x13, 0x1c, 0x3f, 0x3c, 0x34, 0xfd, 0xac, 0x37, 0x52, 0x44, 0x25, 0xa8, 0xde, 0x1d, 0x63, 0xf4, 0x81, 0x9a, 0xbe, 0x0b, 0x74, 0x2e, 0xc8, 0x51, 0x16, 0xd3, 0xac, 0x4a, 0xaf, 0xe2, 0x5f, 0x3a, 0x89, 0x32, 0xd1, 0x9b, 0x7c, 0x90, 0x0d, 0xac, 0xdc, 0x8b, 0x73, 0x45, 0x45, 0x97, 0xb1, 0x90, 0x2c, 0x1b, 0x31, 0xca, 0xb1, 0x94, /* (2^121)P */ 0x07, 0x28, 0xdd, 0x10, 0x14, 0xa5, 0x95, 0x7e, 0xf3, 0xe4, 0xd4, 0x14, 0xb4, 0x7e, 0x76, 0xdb, 0x42, 0xd6, 0x94, 0x3e, 0xeb, 0x44, 0x64, 0x88, 0x0d, 0xec, 0xc1, 0x21, 0xf0, 0x79, 0xe0, 0x83, 0x67, 0x55, 0x53, 0xc2, 0xf6, 0xc5, 0xc5, 0x89, 0x39, 0xe8, 0x42, 0xd0, 0x17, 0xbd, 0xff, 0x35, 0x59, 0x0e, 0xc3, 0x06, 0x86, 0xd4, 0x64, 0xcf, /* (2^122)P */ 0x91, 0xa8, 0xdb, 0x57, 0x9b, 0xe2, 0x96, 0x31, 0x10, 0x6e, 0xd7, 0x9a, 0x97, 0xb3, 0xab, 0xb5, 0x15, 0x66, 0xbe, 0xcc, 0x6d, 0x9a, 0xac, 0x06, 0xb3, 0x0d, 0xaa, 0x4b, 0x9c, 0x96, 0x79, 0x6c, 0x34, 0xee, 0x9e, 0x53, 0x4d, 0x6e, 0xbd, 0x88, 0x02, 0xbf, 0x50, 0x54, 0x12, 0x5d, 0x01, 0x02, 0x46, 0xc6, 0x74, 0x02, 0x8c, 0x24, 0xae, 0xb1, /* (2^123)P */ 0xf5, 0x22, 0xea, 0xac, 0x7d, 0x9c, 0x33, 0x8a, 0xa5, 0x36, 0x79, 0x6a, 0x4f, 0xa4, 0xdc, 0xa5, 0x73, 0x64, 0xc4, 0x6f, 0x43, 0x02, 0x3b, 0x94, 0x66, 0xd2, 0x4b, 0x4f, 0xf6, 0x45, 0x33, 0x5d, 0x10, 0x33, 0x18, 0x1e, 0xa3, 0xfc, 0xf7, 0xd2, 0xb8, 0xc8, 0xa7, 0xe0, 0x76, 0x8a, 0xcd, 0xff, 0x4f, 0x99, 0x34, 0x47, 0x84, 0x91, 0x96, 0x9f, /* (2^124)P */ 0x8a, 0x48, 0x3b, 0x48, 0x4a, 0xbc, 0xac, 0xe2, 0x80, 0xd6, 0xd2, 0x35, 0xde, 0xd0, 0x56, 0x42, 0x33, 0xb3, 0x56, 0x5a, 0xcd, 0xb8, 0x3d, 0xb5, 0x25, 0xc1, 0xed, 0xff, 0x87, 0x0b, 0x79, 0xff, 0xf2, 0x62, 0xe1, 0x76, 0xc6, 0xa2, 0x0f, 0xa8, 0x9b, 0x0d, 0xcc, 0x3f, 0x3d, 0x35, 0x27, 0x8d, 0x0b, 0x74, 0xb0, 0xc3, 0x78, 0x8c, 0xcc, 0xc8, /* (2^125)P */ 0xfc, 0x9a, 0x0c, 0xa8, 0x49, 0x42, 0xb8, 0xdf, 0xcf, 0xb3, 0x19, 0xa6, 0x64, 0x57, 0xfe, 0xe8, 0xf8, 0xa6, 0x4b, 0x86, 0xa1, 0xd5, 0x83, 0x7f, 0x14, 0x99, 0x18, 0x0c, 0x7d, 0x5b, 0xf7, 0x3d, 0xf9, 0x4b, 0x79, 0xb1, 0x86, 0x30, 0xb4, 0x5e, 0x6a, 0xe8, 0x9d, 0xfa, 0x8a, 0x41, 0xc4, 0x30, 0xfc, 0x56, 0x74, 0x14, 0x42, 0xc8, 0x96, 0x0e, /* (2^126)P */ 0xdf, 0x66, 0xec, 0xbc, 0x44, 0xdb, 0x19, 0xce, 0xd4, 0xb5, 0x49, 0x40, 0x07, 0x49, 0xe0, 0x3a, 0x61, 0x10, 0xfb, 0x7d, 0xba, 0xb1, 0xe0, 0x28, 0x5b, 0x99, 0x59, 0x96, 0xa2, 0xee, 0xe0, 0x23, 0x37, 0x39, 0x1f, 0xe6, 0x57, 0x9f, 0xf8, 0xf8, 0xdc, 0x74, 0xf6, 0x8f, 0x4f, 0x5e, 0x51, 0xa4, 0x12, 0xac, 0xbe, 0xe4, 0xf3, 0xd1, 0xf0, 0x24, /* (2^127)P */ 0x1e, 0x3e, 0x9a, 0x5f, 0xdf, 0x9f, 0xd6, 0x4e, 0x8a, 0x28, 0xc3, 0xcd, 0x96, 0x9d, 0x57, 0xc7, 0x61, 0x81, 0x90, 0xff, 0xae, 0xb1, 0x4f, 0xc2, 0x96, 0x8b, 0x1a, 0x18, 0xf4, 0x50, 0xcb, 0x31, 0xe1, 0x57, 0xf4, 0x90, 0xa8, 0xea, 0xac, 0xe7, 0x61, 0x98, 0xb6, 0x15, 0xc1, 0x7b, 0x29, 0xa4, 0xc3, 0x18, 0xef, 0xb9, 0xd8, 0xdf, 0xf6, 0xac, /* (2^128)P */ 0xca, 0xa8, 0x6c, 0xf1, 0xb4, 0xca, 0xfe, 0x31, 0xee, 0x48, 0x38, 0x8b, 0x0e, 0xbb, 0x7a, 0x30, 0xaa, 0xf9, 0xee, 0x27, 0x53, 0x24, 0xdc, 0x2e, 0x15, 0xa6, 0x48, 0x8f, 0xa0, 0x7e, 0xf1, 0xdc, 0x93, 0x87, 0x39, 0xeb, 0x7f, 0x38, 0x92, 0x92, 0x4c, 0x29, 0xe9, 0x57, 0xd8, 0x59, 0xfc, 0xe9, 0x9c, 0x44, 0xc0, 0x65, 0xcf, 0xac, 0x4b, 0xdc, /* (2^129)P */ 0xa3, 0xd0, 0x37, 0x8f, 0x86, 0x2f, 0xc6, 0x47, 0x55, 0x46, 0x65, 0x26, 0x4b, 0x91, 0xe2, 0x18, 0x5c, 0x4f, 0x23, 0xc1, 0x37, 0x29, 0xb9, 0xc1, 0x27, 0xc5, 0x3c, 0xbf, 0x7e, 0x23, 0xdb, 0x73, 0x99, 0xbd, 0x1b, 0xb2, 0x31, 0x68, 0x3a, 0xad, 0xb7, 0xb0, 0x10, 0xc5, 0xe5, 0x11, 0x51, 0xba, 0xa7, 0x60, 0x66, 0x54, 0xf0, 0x08, 0xd7, 0x69, /* (2^130)P */ 0x89, 0x41, 0x79, 0xcc, 0xeb, 0x0a, 0xf5, 0x4b, 0xa3, 0x4c, 0xce, 0x52, 0xb0, 0xa7, 0xe4, 0x41, 0x75, 0x7d, 0x04, 0xbb, 0x09, 0x4c, 0x50, 0x9f, 0xdf, 0xea, 0x74, 0x61, 0x02, 0xad, 0xb4, 0x9d, 0xb7, 0x05, 0xb9, 0xea, 0xeb, 0x91, 0x35, 0xe7, 0x49, 0xea, 0xd3, 0x4f, 0x3c, 0x60, 0x21, 0x7a, 0xde, 0xc7, 0xe2, 0x5a, 0xee, 0x8e, 0x93, 0xc7, /* (2^131)P */ 0x00, 0xe8, 0xed, 0xd0, 0xb3, 0x0d, 0xaf, 0xb2, 0xde, 0x2c, 0xf6, 0x00, 0xe2, 0xea, 0x6d, 0xf8, 0x0e, 0xd9, 0x67, 0x59, 0xa9, 0x50, 0xbb, 0x17, 0x8f, 0xff, 0xb1, 0x9f, 0x17, 0xb6, 0xf2, 0xb5, 0xba, 0x80, 0xf7, 0x0f, 0xba, 0xd5, 0x09, 0x43, 0xaa, 0x4e, 0x3a, 0x67, 0x6a, 0x89, 0x9b, 0x18, 0x65, 0x35, 0xf8, 0x3a, 0x49, 0x91, 0x30, 0x51, /* (2^132)P */ 0x8d, 0x25, 0xe9, 0x0e, 0x7d, 0x50, 0x76, 0xe4, 0x58, 0x7e, 0xb9, 0x33, 0xe6, 0x65, 0x90, 0xc2, 0x50, 0x9d, 0x50, 0x2e, 0x11, 0xad, 0xd5, 0x43, 0x52, 0x32, 0x41, 0x4f, 0x7b, 0xb6, 0xa0, 0xec, 0x81, 0x75, 0x36, 0x7c, 0x77, 0x85, 0x59, 0x70, 0xe4, 0xf9, 0xef, 0x66, 0x8d, 0x35, 0xc8, 0x2a, 0x6e, 0x5b, 0xc6, 0x0d, 0x0b, 0x29, 0x60, 0x68, /* (2^133)P */ 0xf8, 0xce, 0xb0, 0x3a, 0x56, 0x7d, 0x51, 0x9a, 0x25, 0x73, 0xea, 0xdd, 0xe4, 0xe0, 0x0e, 0xf0, 0x07, 0xc0, 0x31, 0x00, 0x73, 0x35, 0xd0, 0x39, 0xc4, 0x9b, 0xb7, 0x95, 0xe0, 0x62, 0x70, 0x36, 0x0b, 0xcb, 0xa0, 0x42, 0xde, 0x51, 0xcf, 0x41, 0xe0, 0xb8, 0xb4, 0xc0, 0xe5, 0x46, 0x99, 0x9f, 0x02, 0x7f, 0x14, 0x8c, 0xc1, 0x4e, 0xef, 0xe8, /* (2^134)P */ 0x10, 0x01, 0x57, 0x0a, 0xbe, 0x8b, 0x18, 0xc8, 0xca, 0x00, 0x28, 0x77, 0x4a, 0x9a, 0xc7, 0x55, 0x2a, 0xcc, 0x0c, 0x7b, 0xb9, 0xe9, 0xc8, 0x97, 0x7c, 0x02, 0xe3, 0x09, 0x2f, 0x62, 0x30, 0xb8, 0x40, 0x09, 0x65, 0xe9, 0x55, 0x63, 0xb5, 0x07, 0xca, 0x9f, 0x00, 0xdf, 0x9d, 0x5c, 0xc7, 0xee, 0x57, 0xa5, 0x90, 0x15, 0x1e, 0x22, 0xa0, 0x12, /* (2^135)P */ 0x71, 0x2d, 0xc9, 0xef, 0x27, 0xb9, 0xd8, 0x12, 0x43, 0x6b, 0xa8, 0xce, 0x3b, 0x6d, 0x6e, 0x91, 0x43, 0x23, 0xbc, 0x32, 0xb3, 0xbf, 0xe1, 0xc7, 0x39, 0xcf, 0x7c, 0x42, 0x4c, 0xb1, 0x30, 0xe2, 0xdd, 0x69, 0x06, 0xe5, 0xea, 0xf0, 0x2a, 0x16, 0x50, 0x71, 0xca, 0x92, 0xdf, 0xc1, 0xcc, 0xec, 0xe6, 0x54, 0x07, 0xf3, 0x18, 0x8d, 0xd8, 0x29, /* (2^136)P */ 0x98, 0x51, 0x48, 0x8f, 0xfa, 0x2e, 0x5e, 0x67, 0xb0, 0xc6, 0x17, 0x12, 0xb6, 0x7d, 0xc9, 0xad, 0x81, 0x11, 0xad, 0x0c, 0x1c, 0x2d, 0x45, 0xdf, 0xac, 0x66, 0xbd, 0x08, 0x6f, 0x7c, 0xc7, 0x06, 0x6e, 0x19, 0x08, 0x39, 0x64, 0xd7, 0xe4, 0xd1, 0x11, 0x5f, 0x1c, 0xf4, 0x67, 0xc3, 0x88, 0x6a, 0xe6, 0x07, 0xa3, 0x83, 0xd7, 0xfd, 0x2a, 0xf9, /* (2^137)P */ 0x87, 0xed, 0xeb, 0xd9, 0xdf, 0xff, 0x43, 0x8b, 0xaa, 0x20, 0x58, 0xb0, 0xb4, 0x6b, 0x14, 0xb8, 0x02, 0xc5, 0x40, 0x20, 0x22, 0xbb, 0xf7, 0xb4, 0xf3, 0x05, 0x1e, 0x4d, 0x94, 0xff, 0xe3, 0xc5, 0x22, 0x82, 0xfe, 0xaf, 0x90, 0x42, 0x98, 0x6b, 0x76, 0x8b, 0x3e, 0x89, 0x3f, 0x42, 0x2a, 0xa7, 0x26, 0x00, 0xda, 0x5c, 0xa2, 0x2b, 0xec, 0xdd, /* (2^138)P */ 0x5c, 0x21, 0x16, 0x0d, 0x46, 0xb8, 0xd0, 0xa7, 0x88, 0xe7, 0x25, 0xcb, 0x3e, 0x50, 0x73, 0x61, 0xe7, 0xaf, 0x5a, 0x3f, 0x47, 0x8b, 0x3d, 0x97, 0x79, 0x2c, 0xe6, 0x6d, 0x95, 0x74, 0x65, 0x70, 0x36, 0xfd, 0xd1, 0x9e, 0x13, 0x18, 0x63, 0xb1, 0x2d, 0x0b, 0xb5, 0x36, 0x3e, 0xe7, 0x35, 0x42, 0x3b, 0xe6, 0x1f, 0x4d, 0x9d, 0x59, 0xa2, 0x43, /* (2^139)P */ 0x8c, 0x0c, 0x7c, 0x24, 0x9e, 0xe0, 0xf8, 0x05, 0x1c, 0x9e, 0x1f, 0x31, 0xc0, 0x70, 0xb3, 0xfb, 0x4e, 0xf8, 0x0a, 0x57, 0xb7, 0x49, 0xb5, 0x73, 0xa1, 0x5f, 0x9b, 0x6a, 0x07, 0x6c, 0x87, 0x71, 0x87, 0xd4, 0xbe, 0x98, 0x1e, 0x98, 0xee, 0x52, 0xc1, 0x7b, 0x95, 0x0f, 0x28, 0x32, 0x36, 0x28, 0xd0, 0x3a, 0x0f, 0x7d, 0x2a, 0xa9, 0x62, 0xb9, /* (2^140)P */ 0x97, 0xe6, 0x18, 0x77, 0xf9, 0x34, 0xac, 0xbc, 0xe0, 0x62, 0x9f, 0x42, 0xde, 0xbd, 0x2f, 0xf7, 0x1f, 0xb7, 0x14, 0x52, 0x8a, 0x79, 0xb2, 0x3f, 0xd2, 0x95, 0x71, 0x01, 0xe8, 0xaf, 0x8c, 0xa4, 0xa4, 0xa7, 0x27, 0xf3, 0x5c, 0xdf, 0x3e, 0x57, 0x7a, 0xf1, 0x76, 0x49, 0xe6, 0x42, 0x3f, 0x8f, 0x1e, 0x63, 0x4a, 0x65, 0xb5, 0x41, 0xf5, 0x02, /* (2^141)P */ 0x72, 0x85, 0xc5, 0x0b, 0xe1, 0x47, 0x64, 0x02, 0xc5, 0x4d, 0x81, 0x69, 0xb2, 0xcf, 0x0f, 0x6c, 0xd4, 0x6d, 0xd0, 0xc7, 0xb4, 0x1c, 0xd0, 0x32, 0x59, 0x89, 0xe2, 0xe0, 0x96, 0x8b, 0x12, 0x98, 0xbf, 0x63, 0x7a, 0x4c, 0x76, 0x7e, 0x58, 0x17, 0x8f, 0x5b, 0x0a, 0x59, 0x65, 0x75, 0xbc, 0x61, 0x1f, 0xbe, 0xc5, 0x6e, 0x0a, 0x57, 0x52, 0x70, /* (2^142)P */ 0x92, 0x1c, 0x77, 0xbb, 0x62, 0x02, 0x6c, 0x25, 0x9c, 0x66, 0x07, 0x83, 0xab, 0xcc, 0x80, 0x5d, 0xd2, 0x76, 0x0c, 0xa4, 0xc5, 0xb4, 0x8a, 0x68, 0x23, 0x31, 0x32, 0x29, 0x8a, 0x47, 0x92, 0x12, 0x80, 0xb3, 0xfa, 0x18, 0xe4, 0x8d, 0xc0, 0x4d, 0xfe, 0x97, 0x5f, 0x72, 0x41, 0xb5, 0x5c, 0x7a, 0xbd, 0xf0, 0xcf, 0x5e, 0x97, 0xaa, 0x64, 0x32, /* (2^143)P */ 0x35, 0x3f, 0x75, 0xc1, 0x7a, 0x75, 0x7e, 0xa9, 0xc6, 0x0b, 0x4e, 0x32, 0x62, 0xec, 0xe3, 0x5c, 0xfb, 0x01, 0x43, 0xb6, 0xd4, 0x5b, 0x75, 0xd2, 0xee, 0x7f, 0x5d, 0x23, 0x2b, 0xb3, 0x54, 0x34, 0x4c, 0xd3, 0xb4, 0x32, 0x84, 0x81, 0xb5, 0x09, 0x76, 0x19, 0xda, 0x58, 0xda, 0x7c, 0xdb, 0x2e, 0xdd, 0x4c, 0x8e, 0xdd, 0x5d, 0x89, 0x10, 0x10, /* (2^144)P */ 0x57, 0x25, 0x6a, 0x08, 0x37, 0x92, 0xa8, 0xdf, 0x24, 0xef, 0x8f, 0x33, 0x34, 0x52, 0xa4, 0x4c, 0xf0, 0x77, 0x9f, 0x69, 0x77, 0xd5, 0x8f, 0xd2, 0x9a, 0xb3, 0xb6, 0x1d, 0x2d, 0xa6, 0xf7, 0x1f, 0xda, 0xd7, 0xcb, 0x75, 0x11, 0xc3, 0x6b, 0xc0, 0x38, 0xb1, 0xd5, 0x2d, 0x96, 0x84, 0x16, 0xfa, 0x26, 0xb9, 0xcc, 0x3f, 0x16, 0x47, 0x23, 0x74, /* (2^145)P */ 0x9b, 0x61, 0x2a, 0x1c, 0xdd, 0x39, 0xa5, 0xfa, 0x1c, 0x7d, 0x63, 0x50, 0xca, 0xe6, 0x9d, 0xfa, 0xb7, 0xc4, 0x4c, 0x6a, 0x97, 0x5f, 0x36, 0x4e, 0x47, 0xdd, 0x17, 0xf7, 0xf9, 0x19, 0xce, 0x75, 0x17, 0xad, 0xce, 0x2a, 0xf3, 0xfe, 0x27, 0x8f, 0x3e, 0x48, 0xc0, 0x60, 0x87, 0x24, 0x19, 0xae, 0x59, 0xe4, 0x5a, 0x00, 0x2a, 0xba, 0xa2, 0x1f, /* (2^146)P */ 0x26, 0x88, 0x42, 0x60, 0x9f, 0x6e, 0x2c, 0x7c, 0x39, 0x0f, 0x47, 0x6a, 0x0e, 0x02, 0xbb, 0x4b, 0x34, 0x29, 0x55, 0x18, 0x36, 0xcf, 0x3b, 0x47, 0xf1, 0x2e, 0xfc, 0x6e, 0x94, 0xff, 0xe8, 0x6b, 0x06, 0xd2, 0xba, 0x77, 0x5e, 0x60, 0xd7, 0x19, 0xef, 0x02, 0x9d, 0x3a, 0xc2, 0xb7, 0xa9, 0xd8, 0x57, 0xee, 0x7e, 0x2b, 0xf2, 0x6d, 0x28, 0xda, /* (2^147)P */ 0xdf, 0xd9, 0x92, 0x11, 0x98, 0x23, 0xe2, 0x45, 0x2f, 0x74, 0x70, 0xee, 0x0e, 0x55, 0x65, 0x79, 0x86, 0x38, 0x17, 0x92, 0x85, 0x87, 0x99, 0x50, 0xd9, 0x7c, 0xdb, 0xa1, 0x10, 0xec, 0x30, 0xb7, 0x40, 0xa3, 0x23, 0x9b, 0x0e, 0x27, 0x49, 0x29, 0x03, 0x94, 0xff, 0x53, 0xdc, 0xd7, 0xed, 0x49, 0xa9, 0x5a, 0x3b, 0xee, 0xd7, 0xc7, 0x65, 0xaf, /* (2^148)P */ 0xa0, 0xbd, 0xbe, 0x03, 0xee, 0x0c, 0xbe, 0x32, 0x00, 0x7b, 0x52, 0xcb, 0x92, 0x29, 0xbf, 0xa0, 0xc6, 0xd9, 0xd2, 0xd6, 0x15, 0xe8, 0x3a, 0x75, 0x61, 0x65, 0x56, 0xae, 0xad, 0x3c, 0x2a, 0x64, 0x14, 0x3f, 0x8e, 0xc1, 0x2d, 0x0c, 0x8d, 0x20, 0xdb, 0x58, 0x4b, 0xe5, 0x40, 0x15, 0x4b, 0xdc, 0xa8, 0xbd, 0xef, 0x08, 0xa7, 0xd1, 0xf4, 0xb0, /* (2^149)P */ 0xa9, 0x0f, 0x05, 0x94, 0x66, 0xac, 0x1f, 0x65, 0x3f, 0xe1, 0xb8, 0xe1, 0x34, 0x5e, 0x1d, 0x8f, 0xe3, 0x93, 0x03, 0x15, 0xff, 0xb6, 0x65, 0xb6, 0x6e, 0xc0, 0x2f, 0xd4, 0x2e, 0xb9, 0x2c, 0x13, 0x3c, 0x99, 0x1c, 0xb5, 0x87, 0xba, 0x79, 0xcb, 0xf0, 0x18, 0x06, 0x86, 0x04, 0x14, 0x25, 0x09, 0xcd, 0x1c, 0x14, 0xda, 0x35, 0xd0, 0x38, 0x3b, /* (2^150)P */ 0x1b, 0x04, 0xa3, 0x27, 0xb4, 0xd3, 0x37, 0x48, 0x1e, 0x8f, 0x69, 0xd3, 0x5a, 0x2f, 0x20, 0x02, 0x36, 0xbe, 0x06, 0x7b, 0x6b, 0x6c, 0x12, 0x5b, 0x80, 0x74, 0x44, 0xe6, 0xf8, 0xf5, 0x95, 0x59, 0x29, 0xab, 0x51, 0x47, 0x83, 0x28, 0xe0, 0xad, 0xde, 0xaa, 0xd3, 0xb1, 0x1a, 0xcb, 0xa3, 0xcd, 0x8b, 0x6a, 0xb1, 0xa7, 0x0a, 0xd1, 0xf9, 0xbe, /* (2^151)P */ 0xce, 0x2f, 0x85, 0xca, 0x74, 0x6d, 0x49, 0xb8, 0xce, 0x80, 0x44, 0xe0, 0xda, 0x5b, 0xcf, 0x2f, 0x79, 0x74, 0xfe, 0xb4, 0x2c, 0x99, 0x20, 0x6e, 0x09, 0x04, 0xfb, 0x6d, 0x57, 0x5b, 0x95, 0x0c, 0x45, 0xda, 0x4f, 0x7f, 0x63, 0xcc, 0x85, 0x5a, 0x67, 0x50, 0x68, 0x71, 0xb4, 0x67, 0xb1, 0x2e, 0xc1, 0x1c, 0xdc, 0xff, 0x2a, 0x7c, 0x10, 0x5e, /* (2^152)P */ 0xa6, 0xde, 0xf3, 0xd4, 0x22, 0x30, 0x24, 0x9e, 0x0b, 0x30, 0x54, 0x59, 0x7e, 0xa2, 0xeb, 0x89, 0x54, 0x65, 0x3e, 0x40, 0xd1, 0xde, 0xe6, 0xee, 0x4d, 0xbf, 0x5e, 0x40, 0x1d, 0xee, 0x4f, 0x68, 0xd9, 0xa7, 0x2f, 0xb3, 0x64, 0xb3, 0xf5, 0xc8, 0xd3, 0xaa, 0x70, 0x70, 0x3d, 0xef, 0xd3, 0x95, 0x54, 0xdb, 0x3e, 0x94, 0x95, 0x92, 0x1f, 0x45, /* (2^153)P */ 0x22, 0x80, 0x1d, 0x9d, 0x96, 0xa5, 0x78, 0x6f, 0xe0, 0x1e, 0x1b, 0x66, 0x42, 0xc8, 0xae, 0x9e, 0x46, 0x45, 0x08, 0x41, 0xdf, 0x80, 0xae, 0x6f, 0xdb, 0x15, 0x5a, 0x21, 0x31, 0x7a, 0xd0, 0xf2, 0x54, 0x15, 0x88, 0xd3, 0x0f, 0x7f, 0x14, 0x5a, 0x14, 0x97, 0xab, 0xf4, 0x58, 0x6a, 0x9f, 0xea, 0x74, 0xe5, 0x6b, 0x90, 0x59, 0x2b, 0x48, 0xd9, /* (2^154)P */ 0x12, 0x24, 0x04, 0xf5, 0x50, 0xc2, 0x8c, 0xb0, 0x7c, 0x46, 0x98, 0xd5, 0x24, 0xad, 0xf6, 0x72, 0xdc, 0x82, 0x1a, 0x60, 0xc1, 0xeb, 0x48, 0xef, 0x7f, 0x6e, 0xe6, 0xcc, 0xdb, 0x7b, 0xae, 0xbe, 0x5e, 0x1e, 0x5c, 0xe6, 0x0a, 0x70, 0xdf, 0xa4, 0xa3, 0x85, 0x1b, 0x1b, 0x7f, 0x72, 0xb9, 0x96, 0x6f, 0xdc, 0x03, 0x76, 0x66, 0xfb, 0xa0, 0x33, /* (2^155)P */ 0x37, 0x40, 0xbb, 0xbc, 0x68, 0x58, 0x86, 0xca, 0xbb, 0xa5, 0x24, 0x76, 0x3d, 0x48, 0xd1, 0xad, 0xb4, 0xa8, 0xcf, 0xc3, 0xb6, 0xa8, 0xba, 0x1a, 0x3a, 0xbe, 0x33, 0x75, 0x04, 0x5c, 0x13, 0x8c, 0x0d, 0x70, 0x8d, 0xa6, 0x4e, 0x2a, 0xeb, 0x17, 0x3c, 0x22, 0xdd, 0x3e, 0x96, 0x40, 0x11, 0x9e, 0x4e, 0xae, 0x3d, 0xf8, 0x91, 0xd7, 0x50, 0xc8, /* (2^156)P */ 0xd8, 0xca, 0xde, 0x19, 0xcf, 0x00, 0xe4, 0x73, 0x18, 0x7f, 0x9b, 0x9f, 0xf4, 0x5b, 0x49, 0x49, 0x99, 0xdc, 0xa4, 0x46, 0x21, 0xb5, 0xd7, 0x3e, 0xb7, 0x47, 0x1b, 0xa9, 0x9f, 0x4c, 0x69, 0x7d, 0xec, 0x33, 0xd6, 0x1c, 0x51, 0x7f, 0x47, 0x74, 0x7a, 0x6c, 0xf3, 0xd2, 0x2e, 0xbf, 0xdf, 0x6c, 0x9e, 0x77, 0x3b, 0x34, 0xf6, 0x73, 0x80, 0xed, /* (2^157)P */ 0x16, 0xfb, 0x16, 0xc3, 0xc2, 0x83, 0xe4, 0xf4, 0x03, 0x7f, 0x52, 0xb0, 0x67, 0x51, 0x7b, 0x24, 0x5a, 0x51, 0xd3, 0xb6, 0x4e, 0x59, 0x76, 0xcd, 0x08, 0x7b, 0x1d, 0x7a, 0x9c, 0x65, 0xae, 0xce, 0xaa, 0xd2, 0x1c, 0x85, 0x66, 0x68, 0x06, 0x15, 0xa8, 0x06, 0xe6, 0x16, 0x37, 0xf4, 0x49, 0x9e, 0x0f, 0x50, 0x37, 0xb1, 0xb2, 0x93, 0x70, 0x43, /* (2^158)P */ 0x18, 0x3a, 0x16, 0xe5, 0x8d, 0xc8, 0x35, 0xd6, 0x7b, 0x09, 0xec, 0x61, 0x5f, 0x5c, 0x2a, 0x19, 0x96, 0x2e, 0xc3, 0xfd, 0xab, 0xe6, 0x23, 0xae, 0xab, 0xc5, 0xcb, 0xb9, 0x7b, 0x2d, 0x34, 0x51, 0xb9, 0x41, 0x9e, 0x7d, 0xca, 0xda, 0x25, 0x45, 0x14, 0xb0, 0xc7, 0x4d, 0x26, 0x2b, 0xfe, 0x43, 0xb0, 0x21, 0x5e, 0xfa, 0xdc, 0x7c, 0xf9, 0x5a, /* (2^159)P */ 0x94, 0xad, 0x42, 0x17, 0xf5, 0xcd, 0x1c, 0x0d, 0xf6, 0x41, 0xd2, 0x55, 0xbb, 0x50, 0xf1, 0xc6, 0xbc, 0xa6, 0xc5, 0x3a, 0xfd, 0x9b, 0x75, 0x3e, 0xf6, 0x1a, 0xa7, 0xb2, 0x6e, 0x64, 0x12, 0xdc, 0x3c, 0xe5, 0xf6, 0xfc, 0x3b, 0xfa, 0x43, 0x81, 0xd4, 0xa5, 0xee, 0xf5, 0x9c, 0x47, 0x2f, 0xd0, 0x9c, 0xde, 0xa1, 0x48, 0x91, 0x9a, 0x34, 0xc1, /* (2^160)P */ 0x37, 0x1b, 0xb3, 0x88, 0xc9, 0x98, 0x4e, 0xfb, 0x84, 0x4f, 0x2b, 0x0a, 0xb6, 0x8f, 0x35, 0x15, 0xcd, 0x61, 0x7a, 0x5f, 0x5c, 0xa0, 0xca, 0x23, 0xa0, 0x93, 0x1f, 0xcc, 0x3c, 0x39, 0x3a, 0x24, 0xa7, 0x49, 0xad, 0x8d, 0x59, 0xcc, 0x94, 0x5a, 0x16, 0xf5, 0x70, 0xe8, 0x52, 0x1e, 0xee, 0x20, 0x30, 0x17, 0x7e, 0xf0, 0x4c, 0x93, 0x06, 0x5a, /* (2^161)P */ 0x81, 0xba, 0x3b, 0xd7, 0x3e, 0xb4, 0x32, 0x3a, 0x22, 0x39, 0x2a, 0xfc, 0x19, 0xd9, 0xd2, 0xf6, 0xc5, 0x79, 0x6c, 0x0e, 0xde, 0xda, 0x01, 0xff, 0x52, 0xfb, 0xb6, 0x95, 0x4e, 0x7a, 0x10, 0xb8, 0x06, 0x86, 0x3c, 0xcd, 0x56, 0xd6, 0x15, 0xbf, 0x6e, 0x3e, 0x4f, 0x35, 0x5e, 0xca, 0xbc, 0xa5, 0x95, 0xa2, 0xdf, 0x2d, 0x1d, 0xaf, 0x59, 0xf9, /* (2^162)P */ 0x69, 0xe5, 0xe2, 0xfa, 0xc9, 0x7f, 0xdd, 0x09, 0xf5, 0x6b, 0x4e, 0x2e, 0xbe, 0xb4, 0xbf, 0x3e, 0xb2, 0xf2, 0x81, 0x30, 0xe1, 0x07, 0xa8, 0x0d, 0x2b, 0xd2, 0x5a, 0x55, 0xbe, 0x4b, 0x86, 0x5d, 0xb0, 0x5e, 0x7c, 0x8f, 0xc1, 0x3c, 0x81, 0x4c, 0xf7, 0x6d, 0x7d, 0xe6, 0x4f, 0x8a, 0x85, 0xc2, 0x2f, 0x28, 0xef, 0x8c, 0x69, 0xc2, 0xc2, 0x1a, /* (2^163)P */ 0xd9, 0xe4, 0x0e, 0x1e, 0xc2, 0xf7, 0x2f, 0x9f, 0xa1, 0x40, 0xfe, 0x46, 0x16, 0xaf, 0x2e, 0xd1, 0xec, 0x15, 0x9b, 0x61, 0x92, 0xce, 0xfc, 0x10, 0x43, 0x1d, 0x00, 0xf6, 0xbe, 0x20, 0x80, 0x80, 0x6f, 0x3c, 0x16, 0x94, 0x59, 0xba, 0x03, 0x53, 0x6e, 0xb6, 0xdd, 0x25, 0x7b, 0x86, 0xbf, 0x96, 0xf4, 0x2f, 0xa1, 0x96, 0x8d, 0xf9, 0xb3, 0x29, /* (2^164)P */ 0x3b, 0x04, 0x60, 0x6e, 0xce, 0xab, 0xd2, 0x63, 0x18, 0x53, 0x88, 0x16, 0x4a, 0x6a, 0xab, 0x72, 0x03, 0x68, 0xa5, 0xd4, 0x0d, 0xb2, 0x82, 0x81, 0x1f, 0x2b, 0x5c, 0x75, 0xe8, 0xd2, 0x1d, 0x7f, 0xe7, 0x1b, 0x35, 0x02, 0xde, 0xec, 0xbd, 0xcb, 0xc7, 0x01, 0xd3, 0x95, 0x61, 0xfe, 0xb2, 0x7a, 0x66, 0x09, 0x4c, 0x6d, 0xfd, 0x39, 0xf7, 0x52, /* (2^165)P */ 0x42, 0xc1, 0x5f, 0xf8, 0x35, 0x52, 0xc1, 0xfe, 0xc5, 0x11, 0x80, 0x1c, 0x11, 0x46, 0x31, 0x11, 0xbe, 0xd0, 0xc4, 0xb6, 0x07, 0x13, 0x38, 0xa0, 0x8d, 0x65, 0xf0, 0x56, 0x9e, 0x16, 0xbf, 0x9d, 0xcd, 0x51, 0x34, 0xf9, 0x08, 0x48, 0x7b, 0x76, 0x0c, 0x7b, 0x30, 0x07, 0xa8, 0x76, 0xaf, 0xa3, 0x29, 0x38, 0xb0, 0x58, 0xde, 0x72, 0x4b, 0x45, /* (2^166)P */ 0xd4, 0x16, 0xa7, 0xc0, 0xb4, 0x9f, 0xdf, 0x1a, 0x37, 0xc8, 0x35, 0xed, 0xc5, 0x85, 0x74, 0x64, 0x09, 0x22, 0xef, 0xe9, 0x0c, 0xaf, 0x12, 0x4c, 0x9e, 0xf8, 0x47, 0x56, 0xe0, 0x7f, 0x4e, 0x24, 0x6b, 0x0c, 0xe7, 0xad, 0xc6, 0x47, 0x1d, 0xa4, 0x0d, 0x86, 0x89, 0x65, 0xe8, 0x5f, 0x71, 0xc7, 0xe9, 0xcd, 0xec, 0x6c, 0x62, 0xc7, 0xe3, 0xb3, /* (2^167)P */ 0xb5, 0xea, 0x86, 0xe3, 0x15, 0x18, 0x3f, 0x6d, 0x7b, 0x05, 0x95, 0x15, 0x53, 0x26, 0x1c, 0xeb, 0xbe, 0x7e, 0x16, 0x42, 0x4b, 0xa2, 0x3d, 0xdd, 0x0e, 0xff, 0xba, 0x67, 0xb5, 0xae, 0x7a, 0x17, 0xde, 0x23, 0xad, 0x14, 0xcc, 0xd7, 0xaf, 0x57, 0x01, 0xe0, 0xdd, 0x48, 0xdd, 0xd7, 0xe3, 0xdf, 0xe9, 0x2d, 0xda, 0x67, 0xa4, 0x9f, 0x29, 0x04, /* (2^168)P */ 0x16, 0x53, 0xe6, 0x9c, 0x4e, 0xe5, 0x1e, 0x70, 0x81, 0x25, 0x02, 0x9b, 0x47, 0x6d, 0xd2, 0x08, 0x73, 0xbe, 0x0a, 0xf1, 0x7b, 0xeb, 0x24, 0xeb, 0x38, 0x23, 0x5c, 0xb6, 0x3e, 0xce, 0x1e, 0xe3, 0xbc, 0x82, 0x35, 0x1f, 0xaf, 0x3a, 0x3a, 0xe5, 0x4e, 0xc1, 0xca, 0xbf, 0x47, 0xb4, 0xbb, 0xbc, 0x5f, 0xea, 0xc6, 0xca, 0xf3, 0xa0, 0xa2, 0x73, /* (2^169)P */ 0xef, 0xa4, 0x7a, 0x4e, 0xe4, 0xc7, 0xb6, 0x43, 0x2e, 0xa5, 0xe4, 0xa5, 0xba, 0x1e, 0xa5, 0xfe, 0x9e, 0xce, 0xa9, 0x80, 0x04, 0xcb, 0x4f, 0xd8, 0x74, 0x05, 0x48, 0xfa, 0x99, 0x11, 0x5d, 0x97, 0x3b, 0x07, 0x0d, 0xdd, 0xe6, 0xb1, 0x74, 0x87, 0x1a, 0xd3, 0x26, 0xb7, 0x8f, 0xe1, 0x63, 0x3d, 0xec, 0x53, 0x93, 0xb0, 0x81, 0x78, 0x34, 0xa4, /* (2^170)P */ 0xe1, 0xe7, 0xd4, 0x58, 0x9d, 0x0e, 0x8b, 0x65, 0x66, 0x37, 0x16, 0x48, 0x6f, 0xaa, 0x42, 0x37, 0x77, 0xad, 0xb1, 0x56, 0x48, 0xdf, 0x65, 0x36, 0x30, 0xb8, 0x00, 0x12, 0xd8, 0x32, 0x28, 0x7f, 0xc1, 0x71, 0xeb, 0x93, 0x0f, 0x48, 0x04, 0xe1, 0x5a, 0x6a, 0x96, 0xc1, 0xca, 0x89, 0x6d, 0x1b, 0x82, 0x4c, 0x18, 0x6d, 0x55, 0x4b, 0xea, 0xfd, /* (2^171)P */ 0x62, 0x1a, 0x53, 0xb4, 0xb1, 0xbe, 0x6f, 0x15, 0x18, 0x88, 0xd4, 0x66, 0x61, 0xc7, 0x12, 0x69, 0x02, 0xbd, 0x03, 0x23, 0x2b, 0xef, 0xf9, 0x54, 0xa4, 0x85, 0xa8, 0xe3, 0xb7, 0xbd, 0xa9, 0xa3, 0xf3, 0x2a, 0xdd, 0xf1, 0xd4, 0x03, 0x0f, 0xa9, 0xa1, 0xd8, 0xa3, 0xcd, 0xb2, 0x71, 0x90, 0x4b, 0x35, 0x62, 0xf2, 0x2f, 0xce, 0x67, 0x1f, 0xaa, /* (2^172)P */ 0x9e, 0x1e, 0xcd, 0x43, 0x7e, 0x87, 0x37, 0x94, 0x3a, 0x97, 0x4c, 0x7e, 0xee, 0xc9, 0x37, 0x85, 0xf1, 0xd9, 0x4f, 0xbf, 0xf9, 0x6f, 0x39, 0x9a, 0x39, 0x87, 0x2e, 0x25, 0x84, 0x42, 0xc3, 0x80, 0xcb, 0x07, 0x22, 0xae, 0x30, 0xd5, 0x50, 0xa1, 0x23, 0xcc, 0x31, 0x81, 0x9d, 0xf1, 0x30, 0xd9, 0x2b, 0x73, 0x41, 0x16, 0x50, 0xab, 0x2d, 0xa2, /* (2^173)P */ 0xa4, 0x69, 0x4f, 0xa1, 0x4e, 0xb9, 0xbf, 0x14, 0xe8, 0x2b, 0x04, 0x93, 0xb7, 0x6e, 0x9f, 0x7d, 0x73, 0x0a, 0xc5, 0x14, 0xb8, 0xde, 0x8c, 0xc1, 0xfe, 0xc0, 0xa7, 0xa4, 0xcc, 0x42, 0x42, 0x81, 0x15, 0x65, 0x8a, 0x80, 0xb9, 0xde, 0x1f, 0x60, 0x33, 0x0e, 0xcb, 0xfc, 0xe0, 0xdb, 0x83, 0xa1, 0xe5, 0xd0, 0x16, 0x86, 0x2c, 0xe2, 0x87, 0xed, /* (2^174)P */ 0x7a, 0xc0, 0xeb, 0x6b, 0xf6, 0x0d, 0x4c, 0x6d, 0x1e, 0xdb, 0xab, 0xe7, 0x19, 0x45, 0xc6, 0xe3, 0xb2, 0x06, 0xbb, 0xbc, 0x70, 0x99, 0x83, 0x33, 0xeb, 0x28, 0xc8, 0x77, 0xf6, 0x4d, 0x01, 0xb7, 0x59, 0xa0, 0xd2, 0xb3, 0x2a, 0x72, 0x30, 0xe7, 0x11, 0x39, 0xb6, 0x41, 0x29, 0x65, 0x5a, 0x14, 0xb9, 0x86, 0x08, 0xe0, 0x7d, 0x32, 0x8c, 0xf0, /* (2^175)P */ 0x5c, 0x11, 0x30, 0x9e, 0x05, 0x27, 0xf5, 0x45, 0x0f, 0xb3, 0xc9, 0x75, 0xc3, 0xd7, 0xe1, 0x82, 0x3b, 0x8e, 0x87, 0x23, 0x00, 0x15, 0x19, 0x07, 0xd9, 0x21, 0x53, 0xc7, 0xf1, 0xa3, 0xbf, 0x70, 0x64, 0x15, 0x18, 0xca, 0x23, 0x9e, 0xd3, 0x08, 0xc3, 0x2a, 0x8b, 0xe5, 0x83, 0x04, 0x89, 0x14, 0xfd, 0x28, 0x25, 0x1c, 0xe3, 0x26, 0xa7, 0x22, /* (2^176)P */ 0xdc, 0xd4, 0x75, 0x60, 0x99, 0x94, 0xea, 0x09, 0x8e, 0x8a, 0x3c, 0x1b, 0xf9, 0xbd, 0x33, 0x0d, 0x51, 0x3d, 0x12, 0x6f, 0x4e, 0x72, 0xe0, 0x17, 0x20, 0xe9, 0x75, 0xe6, 0x3a, 0xb2, 0x13, 0x83, 0x4e, 0x7a, 0x08, 0x9e, 0xd1, 0x04, 0x5f, 0x6b, 0x42, 0x0b, 0x76, 0x2a, 0x2d, 0x77, 0x53, 0x6c, 0x65, 0x6d, 0x8e, 0x25, 0x3c, 0xb6, 0x8b, 0x69, /* (2^177)P */ 0xb9, 0x49, 0x28, 0xd0, 0xdc, 0x6c, 0x8f, 0x4c, 0xc9, 0x14, 0x8a, 0x38, 0xa3, 0xcb, 0xc4, 0x9d, 0x53, 0xcf, 0xe9, 0xe3, 0xcf, 0xe0, 0xb1, 0xf2, 0x1b, 0x4c, 0x7f, 0x83, 0x2a, 0x7a, 0xe9, 0x8b, 0x3b, 0x86, 0x61, 0x30, 0xe9, 0x99, 0xbd, 0xba, 0x19, 0x6e, 0x65, 0x2a, 0x12, 0x3e, 0x9c, 0xa8, 0xaf, 0xc3, 0xcf, 0xf8, 0x1f, 0x77, 0x86, 0xea, /* (2^178)P */ 0x30, 0xde, 0xe7, 0xff, 0x54, 0xf7, 0xa2, 0x59, 0xf6, 0x0b, 0xfb, 0x7a, 0xf2, 0x39, 0xf0, 0xdb, 0x39, 0xbc, 0xf0, 0xfa, 0x60, 0xeb, 0x6b, 0x4f, 0x47, 0x17, 0xc8, 0x00, 0x65, 0x6d, 0x25, 0x1c, 0xd0, 0x48, 0x56, 0x53, 0x45, 0x11, 0x30, 0x02, 0x49, 0x20, 0x27, 0xac, 0xf2, 0x4c, 0xac, 0x64, 0x3d, 0x52, 0xb8, 0x89, 0xe0, 0x93, 0x16, 0x0f, /* (2^179)P */ 0x84, 0x09, 0xba, 0x40, 0xb2, 0x2f, 0xa3, 0xa8, 0xc2, 0xba, 0x46, 0x33, 0x05, 0x9d, 0x62, 0xad, 0xa1, 0x3c, 0x33, 0xef, 0x0d, 0xeb, 0xf0, 0x77, 0x11, 0x5a, 0xb0, 0x21, 0x9c, 0xdf, 0x55, 0x24, 0x25, 0x35, 0x51, 0x61, 0x92, 0xf0, 0xb1, 0xce, 0xf5, 0xd4, 0x7b, 0x6c, 0x21, 0x9d, 0x56, 0x52, 0xf8, 0xa1, 0x4c, 0xe9, 0x27, 0x55, 0xac, 0x91, /* (2^180)P */ 0x03, 0x3e, 0x30, 0xd2, 0x0a, 0xfa, 0x7d, 0x82, 0x3d, 0x1f, 0x8b, 0xcb, 0xb6, 0x04, 0x5c, 0xcc, 0x8b, 0xda, 0xe2, 0x68, 0x74, 0x08, 0x8c, 0x44, 0x83, 0x57, 0x6d, 0x6f, 0x80, 0xb0, 0x7e, 0xa9, 0x82, 0x91, 0x7b, 0x4c, 0x37, 0x97, 0xd1, 0x63, 0xd1, 0xbd, 0x45, 0xe6, 0x8a, 0x86, 0xd6, 0x89, 0x54, 0xfd, 0xd2, 0xb1, 0xd7, 0x54, 0xad, 0xaf, /* (2^181)P */ 0x8b, 0x33, 0x62, 0x49, 0x9f, 0x63, 0xf9, 0x87, 0x42, 0x58, 0xbf, 0xb3, 0xe6, 0x68, 0x02, 0x60, 0x5c, 0x76, 0x62, 0xf7, 0x61, 0xd7, 0x36, 0x31, 0xf7, 0x9c, 0xb5, 0xe5, 0x13, 0x6c, 0xea, 0x78, 0xae, 0xcf, 0xde, 0xbf, 0xb6, 0xeb, 0x4f, 0xc8, 0x2a, 0xb4, 0x9a, 0x9f, 0xf3, 0xd1, 0x6a, 0xec, 0x0c, 0xbd, 0x85, 0x98, 0x40, 0x06, 0x1c, 0x2a, /* (2^182)P */ 0x74, 0x3b, 0xe7, 0x81, 0xd5, 0xae, 0x54, 0x56, 0x03, 0xe8, 0x97, 0x16, 0x76, 0xcf, 0x24, 0x96, 0x96, 0x5b, 0xcc, 0x09, 0xab, 0x23, 0x6f, 0x54, 0xae, 0x8f, 0xe4, 0x12, 0xcb, 0xfd, 0xbc, 0xac, 0x93, 0x45, 0x3d, 0x68, 0x08, 0x22, 0x59, 0xc6, 0xf0, 0x47, 0x19, 0x8c, 0x79, 0x93, 0x1e, 0x0e, 0x30, 0xb0, 0x94, 0xfb, 0x17, 0x1d, 0x5a, 0x12, /* (2^183)P */ 0x85, 0xff, 0x40, 0x18, 0x85, 0xff, 0x44, 0x37, 0x69, 0x23, 0x4d, 0x34, 0xe1, 0xeb, 0xa3, 0x1b, 0x55, 0x40, 0xc1, 0x64, 0xf4, 0xd4, 0x13, 0x0a, 0x9f, 0xb9, 0x19, 0xfc, 0x88, 0x7d, 0xc0, 0x72, 0xcf, 0x69, 0x2f, 0xd2, 0x0c, 0x82, 0x0f, 0xda, 0x08, 0xba, 0x0f, 0xaa, 0x3b, 0xe9, 0xe5, 0x83, 0x7a, 0x06, 0xe8, 0x1b, 0x38, 0x43, 0xc3, 0x54, /* (2^184)P */ 0x14, 0xaa, 0xb3, 0x6e, 0xe6, 0x28, 0xee, 0xc5, 0x22, 0x6c, 0x7c, 0xf9, 0xa8, 0x71, 0xcc, 0xfe, 0x68, 0x7e, 0xd3, 0xb8, 0x37, 0x96, 0xca, 0x0b, 0xd9, 0xb6, 0x06, 0xa9, 0xf6, 0x71, 0xe8, 0x31, 0xf7, 0xd8, 0xf1, 0x5d, 0xab, 0xb9, 0xf0, 0x5c, 0x98, 0xcf, 0x22, 0xa2, 0x2a, 0xf6, 0xd0, 0x59, 0xf0, 0x9d, 0xd9, 0x6a, 0x4f, 0x59, 0x57, 0xad, /* (2^185)P */ 0xd7, 0x2b, 0x3d, 0x38, 0x4c, 0x2e, 0x23, 0x4d, 0x49, 0xa2, 0x62, 0x62, 0xf9, 0x0f, 0xde, 0x08, 0xf3, 0x86, 0x71, 0xb6, 0xc7, 0xf9, 0x85, 0x9c, 0x33, 0xa1, 0xcf, 0x16, 0xaa, 0x60, 0xb9, 0xb7, 0xea, 0xed, 0x01, 0x1c, 0x59, 0xdb, 0x3f, 0x3f, 0x97, 0x2e, 0xf0, 0x09, 0x9f, 0x10, 0x85, 0x5f, 0x53, 0x39, 0xf3, 0x13, 0x40, 0x56, 0x95, 0xf9, /* (2^186)P */ 0xb4, 0xe3, 0xda, 0xc6, 0x1f, 0x78, 0x8e, 0xac, 0xd4, 0x20, 0x1d, 0xa0, 0xbf, 0x4c, 0x09, 0x16, 0xa7, 0x30, 0xb5, 0x8d, 0x9e, 0xa1, 0x5f, 0x6d, 0x52, 0xf4, 0x71, 0xb6, 0x32, 0x2d, 0x21, 0x51, 0xc6, 0xfc, 0x2f, 0x08, 0xf4, 0x13, 0x6c, 0x55, 0xba, 0x72, 0x81, 0x24, 0x49, 0x0e, 0x4f, 0x06, 0x36, 0x39, 0x6a, 0xc5, 0x81, 0xfc, 0xeb, 0xb2, /* (2^187)P */ 0x7d, 0x8d, 0xc8, 0x6c, 0xea, 0xb4, 0xb9, 0xe8, 0x40, 0xc9, 0x69, 0xc9, 0x30, 0x05, 0xfd, 0x34, 0x46, 0xfd, 0x94, 0x05, 0x16, 0xf5, 0x4b, 0x13, 0x3d, 0x24, 0x1a, 0xd6, 0x64, 0x2b, 0x9c, 0xe2, 0xa5, 0xd9, 0x98, 0xe0, 0xe8, 0xf4, 0xbc, 0x2c, 0xbd, 0xa2, 0x56, 0xe3, 0x9e, 0x14, 0xdb, 0xbf, 0x05, 0xbf, 0x9a, 0x13, 0x5d, 0xf7, 0x91, 0xa3, /* (2^188)P */ 0x8b, 0xcb, 0x27, 0xf3, 0x15, 0x26, 0x05, 0x40, 0x0f, 0xa6, 0x15, 0x13, 0x71, 0x95, 0xa2, 0xc6, 0x38, 0x04, 0x67, 0xf8, 0x9a, 0x83, 0x06, 0xaa, 0x25, 0x36, 0x72, 0x01, 0x6f, 0x74, 0x5f, 0xe5, 0x6e, 0x44, 0x99, 0xce, 0x13, 0xbc, 0x82, 0xc2, 0x0d, 0xa4, 0x98, 0x50, 0x38, 0xf3, 0xa2, 0xc5, 0xe5, 0x24, 0x1f, 0x6f, 0x56, 0x3e, 0x07, 0xb2, /* (2^189)P */ 0xbd, 0x0f, 0x32, 0x60, 0x07, 0xb1, 0xd7, 0x0b, 0x11, 0x07, 0x57, 0x02, 0x89, 0xe8, 0x8b, 0xe8, 0x5a, 0x1f, 0xee, 0x54, 0x6b, 0xff, 0xb3, 0x04, 0x07, 0x57, 0x13, 0x0b, 0x94, 0xa8, 0x4d, 0x81, 0xe2, 0x17, 0x16, 0x45, 0xd4, 0x4b, 0xf7, 0x7e, 0x64, 0x66, 0x20, 0xe8, 0x0b, 0x26, 0xfd, 0xa9, 0x8a, 0x47, 0x52, 0x89, 0x14, 0xd0, 0xd1, 0xa1, /* (2^190)P */ 0xdc, 0x03, 0xe6, 0x20, 0x44, 0x47, 0x8f, 0x04, 0x16, 0x24, 0x22, 0xc1, 0x55, 0x5c, 0xbe, 0x43, 0xc3, 0x92, 0xc5, 0x54, 0x3d, 0x5d, 0xd1, 0x05, 0x9c, 0xc6, 0x7c, 0xbf, 0x23, 0x84, 0x1a, 0xba, 0x4f, 0x1f, 0xfc, 0xa1, 0xae, 0x1a, 0x64, 0x02, 0x51, 0xf1, 0xcb, 0x7a, 0x20, 0xce, 0xb2, 0x34, 0x3c, 0xca, 0xe0, 0xe4, 0xba, 0x22, 0xd4, 0x7b, /* (2^191)P */ 0xca, 0xfd, 0xca, 0xd7, 0xde, 0x61, 0xae, 0xf0, 0x79, 0x0c, 0x20, 0xab, 0xbc, 0x6f, 0x4d, 0x61, 0xf0, 0xc7, 0x9c, 0x8d, 0x4b, 0x52, 0xf3, 0xb9, 0x48, 0x63, 0x0b, 0xb6, 0xd2, 0x25, 0x9a, 0x96, 0x72, 0xc1, 0x6b, 0x0c, 0xb5, 0xfb, 0x71, 0xaa, 0xad, 0x47, 0x5b, 0xe7, 0xc0, 0x0a, 0x55, 0xb2, 0xd4, 0x16, 0x2f, 0xb1, 0x01, 0xfd, 0xce, 0x27, /* (2^192)P */ 0x64, 0x11, 0x4b, 0xab, 0x57, 0x09, 0xc6, 0x49, 0x4a, 0x37, 0xc3, 0x36, 0xc4, 0x7b, 0x81, 0x1f, 0x42, 0xed, 0xbb, 0xe0, 0xa0, 0x8d, 0x51, 0xe6, 0xca, 0x8b, 0xb9, 0xcd, 0x99, 0x2d, 0x91, 0x53, 0xa9, 0x47, 0xcb, 0x32, 0xc7, 0xa4, 0x92, 0xec, 0x46, 0x74, 0x44, 0x6d, 0x71, 0x9f, 0x6d, 0x0c, 0x69, 0xa4, 0xf8, 0xbe, 0x9f, 0x7f, 0xa0, 0xd7, /* (2^193)P */ 0x5f, 0x33, 0xb6, 0x91, 0xc8, 0xa5, 0x3f, 0x5d, 0x7f, 0x38, 0x6e, 0x74, 0x20, 0x4a, 0xd6, 0x2b, 0x98, 0x2a, 0x41, 0x4b, 0x83, 0x64, 0x0b, 0x92, 0x7a, 0x06, 0x1e, 0xc6, 0x2c, 0xf6, 0xe4, 0x91, 0xe5, 0xb1, 0x2e, 0x6e, 0x4e, 0xa8, 0xc8, 0x14, 0x32, 0x57, 0x44, 0x1c, 0xe4, 0xb9, 0x7f, 0x54, 0x51, 0x08, 0x81, 0xaa, 0x4e, 0xce, 0xa1, 0x5d, /* (2^194)P */ 0x5c, 0xd5, 0x9b, 0x5e, 0x7c, 0xb5, 0xb1, 0x52, 0x73, 0x00, 0x41, 0x56, 0x79, 0x08, 0x7e, 0x07, 0x28, 0x06, 0xa6, 0xfb, 0x7f, 0x69, 0xbd, 0x7a, 0x3c, 0xae, 0x9f, 0x39, 0xbb, 0x54, 0xa2, 0x79, 0xb9, 0x0e, 0x7f, 0xbb, 0xe0, 0xe6, 0xb7, 0x27, 0x64, 0x38, 0x45, 0xdb, 0x84, 0xe4, 0x61, 0x72, 0x3f, 0xe2, 0x24, 0xfe, 0x7a, 0x31, 0x9a, 0xc9, /* (2^195)P */ 0xa1, 0xd2, 0xa4, 0xee, 0x24, 0x96, 0xe5, 0x5b, 0x79, 0x78, 0x3c, 0x7b, 0x82, 0x3b, 0x8b, 0x58, 0x0b, 0xa3, 0x63, 0x2d, 0xbc, 0x75, 0x46, 0xe8, 0x83, 0x1a, 0xc0, 0x2a, 0x92, 0x61, 0xa8, 0x75, 0x37, 0x3c, 0xbf, 0x0f, 0xef, 0x8f, 0x6c, 0x97, 0x75, 0x10, 0x05, 0x7a, 0xde, 0x23, 0xe8, 0x2a, 0x35, 0xeb, 0x41, 0x64, 0x7d, 0xcf, 0xe0, 0x52, /* (2^196)P */ 0x4a, 0xd0, 0x49, 0x93, 0xae, 0xf3, 0x24, 0x8c, 0xe1, 0x09, 0x98, 0x45, 0xd8, 0xb9, 0xfe, 0x8e, 0x8c, 0xa8, 0x2c, 0xc9, 0x9f, 0xce, 0x01, 0xdc, 0x38, 0x11, 0xab, 0x85, 0xb9, 0xe8, 0x00, 0x51, 0xfd, 0x82, 0xe1, 0x9b, 0x4e, 0xfc, 0xb5, 0x2a, 0x0f, 0x8b, 0xda, 0x4e, 0x02, 0xca, 0xcc, 0xe3, 0x91, 0xc4, 0xe0, 0xcf, 0x7b, 0xd6, 0xe6, 0x6a, /* (2^197)P */ 0xfe, 0x11, 0xd7, 0xaa, 0xe3, 0x0c, 0x52, 0x2e, 0x04, 0xe0, 0xe0, 0x61, 0xc8, 0x05, 0xd7, 0x31, 0x4c, 0xc3, 0x9b, 0x2d, 0xce, 0x59, 0xbe, 0x12, 0xb7, 0x30, 0x21, 0xfc, 0x81, 0xb8, 0x5e, 0x57, 0x73, 0xd0, 0xad, 0x8e, 0x9e, 0xe4, 0xeb, 0xcd, 0xcf, 0xd2, 0x0f, 0x01, 0x35, 0x16, 0xed, 0x7a, 0x43, 0x8e, 0x42, 0xdc, 0xea, 0x4c, 0xa8, 0x7c, /* (2^198)P */ 0x37, 0x26, 0xcc, 0x76, 0x0b, 0xe5, 0x76, 0xdd, 0x3e, 0x19, 0x3c, 0xc4, 0x6c, 0x7f, 0xd0, 0x03, 0xc1, 0xb8, 0x59, 0x82, 0xca, 0x36, 0xc1, 0xe4, 0xc8, 0xb2, 0x83, 0x69, 0x9c, 0xc5, 0x9d, 0x12, 0x82, 0x1c, 0xea, 0xb2, 0x84, 0x9f, 0xf3, 0x52, 0x6b, 0xbb, 0xd8, 0x81, 0x56, 0x83, 0x04, 0x66, 0x05, 0x22, 0x49, 0x37, 0x93, 0xb1, 0xfd, 0xd5, /* (2^199)P */ 0xaf, 0x96, 0xbf, 0x03, 0xbe, 0xe6, 0x5d, 0x78, 0x19, 0xba, 0x37, 0x46, 0x0a, 0x2b, 0x52, 0x7c, 0xd8, 0x51, 0x9e, 0x3d, 0x29, 0x42, 0xdb, 0x0e, 0x31, 0x20, 0x94, 0xf8, 0x43, 0x9a, 0x2d, 0x22, 0xd3, 0xe3, 0xa1, 0x79, 0x68, 0xfb, 0x2d, 0x7e, 0xd6, 0x79, 0xda, 0x0b, 0xc6, 0x5b, 0x76, 0x68, 0xf0, 0xfe, 0x72, 0x59, 0xbb, 0xa1, 0x9c, 0x74, /* (2^200)P */ 0x0a, 0xd9, 0xec, 0xc5, 0xbd, 0xf0, 0xda, 0xcf, 0x82, 0xab, 0x46, 0xc5, 0x32, 0x13, 0xdc, 0x5b, 0xac, 0xc3, 0x53, 0x9a, 0x7f, 0xef, 0xa5, 0x40, 0x5a, 0x1f, 0xc1, 0x12, 0x91, 0x54, 0x83, 0x6a, 0xb0, 0x9a, 0x85, 0x4d, 0xbf, 0x36, 0x8e, 0xd3, 0xa2, 0x2b, 0xe5, 0xd6, 0xc6, 0xe1, 0x58, 0x5b, 0x82, 0x9b, 0xc8, 0xf2, 0x03, 0xba, 0xf5, 0x92, /* (2^201)P */ 0xfb, 0x21, 0x7e, 0xde, 0xe7, 0xb4, 0xc0, 0x56, 0x86, 0x3a, 0x5b, 0x78, 0xf8, 0xf0, 0xf4, 0xe7, 0x5c, 0x00, 0xd2, 0xd7, 0xd6, 0xf8, 0x75, 0x5e, 0x0f, 0x3e, 0xd1, 0x4b, 0x77, 0xd8, 0xad, 0xb0, 0xc9, 0x8b, 0x59, 0x7d, 0x30, 0x76, 0x64, 0x7a, 0x76, 0xd9, 0x51, 0x69, 0xfc, 0xbd, 0x8e, 0xb5, 0x55, 0xe0, 0xd2, 0x07, 0x15, 0xa9, 0xf7, 0xa4, /* (2^202)P */ 0xaa, 0x2d, 0x2f, 0x2b, 0x3c, 0x15, 0xdd, 0xcd, 0xe9, 0x28, 0x82, 0x4f, 0xa2, 0xaa, 0x31, 0x48, 0xcc, 0xfa, 0x07, 0x73, 0x8a, 0x34, 0x74, 0x0d, 0xab, 0x1a, 0xca, 0xd2, 0xbf, 0x3a, 0xdb, 0x1a, 0x5f, 0x50, 0x62, 0xf4, 0x6b, 0x83, 0x38, 0x43, 0x96, 0xee, 0x6b, 0x39, 0x1e, 0xf0, 0x17, 0x80, 0x1e, 0x9b, 0xed, 0x2b, 0x2f, 0xcc, 0x65, 0xf7, /* (2^203)P */ 0x03, 0xb3, 0x23, 0x9c, 0x0d, 0xd1, 0xeb, 0x7e, 0x34, 0x17, 0x8a, 0x4c, 0xde, 0x54, 0x39, 0xc4, 0x11, 0x82, 0xd3, 0xa4, 0x00, 0x32, 0x95, 0x9c, 0xa6, 0x64, 0x76, 0x6e, 0xd6, 0x53, 0x27, 0xb4, 0x6a, 0x14, 0x8c, 0x54, 0xf6, 0x58, 0x9e, 0x22, 0x4a, 0x55, 0x18, 0x77, 0xd0, 0x08, 0x6b, 0x19, 0x8a, 0xb5, 0xe7, 0x19, 0xb8, 0x60, 0x92, 0xb1, /* (2^204)P */ 0x66, 0xec, 0xf3, 0x12, 0xde, 0x67, 0x7f, 0xd4, 0x5b, 0xf6, 0x70, 0x64, 0x0a, 0xb5, 0xc2, 0xf9, 0xb3, 0x64, 0xab, 0x56, 0x46, 0xc7, 0x93, 0xc2, 0x8b, 0x2d, 0xd0, 0xd6, 0x39, 0x3b, 0x1f, 0xcd, 0xb3, 0xac, 0xcc, 0x2c, 0x27, 0x6a, 0xbc, 0xb3, 0x4b, 0xa8, 0x3c, 0x69, 0x20, 0xe2, 0x18, 0x35, 0x17, 0xe1, 0x8a, 0xd3, 0x11, 0x74, 0xaa, 0x4d, /* (2^205)P */ 0x96, 0xc4, 0x16, 0x7e, 0xfd, 0xf5, 0xd0, 0x7d, 0x1f, 0x32, 0x1b, 0xdb, 0xa6, 0xfd, 0x51, 0x75, 0x4d, 0xd7, 0x00, 0xe5, 0x7f, 0x58, 0x5b, 0xeb, 0x4b, 0x6a, 0x78, 0xfe, 0xe5, 0xd6, 0x8f, 0x99, 0x17, 0xca, 0x96, 0x45, 0xf7, 0x52, 0xdf, 0x84, 0x06, 0x77, 0xb9, 0x05, 0x63, 0x5d, 0xe9, 0x91, 0xb1, 0x4b, 0x82, 0x5a, 0xdb, 0xd7, 0xca, 0x69, /* (2^206)P */ 0x02, 0xd3, 0x38, 0x38, 0x87, 0xea, 0xbd, 0x9f, 0x11, 0xca, 0xf3, 0x21, 0xf1, 0x9b, 0x35, 0x97, 0x98, 0xff, 0x8e, 0x6d, 0x3d, 0xd6, 0xb2, 0xfa, 0x68, 0xcb, 0x7e, 0x62, 0x85, 0xbb, 0xc7, 0x5d, 0xee, 0x32, 0x30, 0x2e, 0x71, 0x96, 0x63, 0x43, 0x98, 0xc4, 0xa7, 0xde, 0x60, 0xb2, 0xd9, 0x43, 0x4a, 0xfa, 0x97, 0x2d, 0x5f, 0x21, 0xd4, 0xfe, /* (2^207)P */ 0x3b, 0x20, 0x29, 0x07, 0x07, 0xb5, 0x78, 0xc3, 0xc7, 0xab, 0x56, 0xba, 0x40, 0xde, 0x1d, 0xcf, 0xc3, 0x00, 0x56, 0x21, 0x0c, 0xc8, 0x42, 0xd9, 0x0e, 0xcd, 0x02, 0x7c, 0x07, 0xb9, 0x11, 0xd7, 0x96, 0xaf, 0xff, 0xad, 0xc5, 0xba, 0x30, 0x6d, 0x82, 0x3a, 0xbf, 0xef, 0x7b, 0xf7, 0x0a, 0x74, 0xbd, 0x31, 0x0c, 0xe4, 0xec, 0x1a, 0xe5, 0xc5, /* (2^208)P */ 0xcc, 0xf2, 0x28, 0x16, 0x12, 0xbf, 0xef, 0x85, 0xbc, 0xf7, 0xcb, 0x9f, 0xdb, 0xa8, 0xb2, 0x49, 0x53, 0x48, 0xa8, 0x24, 0xa8, 0x68, 0x8d, 0xbb, 0x21, 0x0a, 0x5a, 0xbd, 0xb2, 0x91, 0x61, 0x47, 0xc4, 0x43, 0x08, 0xa6, 0x19, 0xef, 0x8e, 0x88, 0x39, 0xc6, 0x33, 0x30, 0xf3, 0x0e, 0xc5, 0x92, 0x66, 0xd6, 0xfe, 0xc5, 0x12, 0xd9, 0x4c, 0x2d, /* (2^209)P */ 0x30, 0x34, 0x07, 0xbf, 0x9c, 0x5a, 0x4e, 0x65, 0xf1, 0x39, 0x35, 0x38, 0xae, 0x7b, 0x55, 0xac, 0x6a, 0x92, 0x24, 0x7e, 0x50, 0xd3, 0xba, 0x78, 0x51, 0xfe, 0x4d, 0x32, 0x05, 0x11, 0xf5, 0x52, 0xf1, 0x31, 0x45, 0x39, 0x98, 0x7b, 0x28, 0x56, 0xc3, 0x5d, 0x4f, 0x07, 0x6f, 0x84, 0xb8, 0x1a, 0x58, 0x0b, 0xc4, 0x7c, 0xc4, 0x8d, 0x32, 0x8e, /* (2^210)P */ 0x7e, 0xaf, 0x98, 0xce, 0xc5, 0x2b, 0x9d, 0xf6, 0xfa, 0x2c, 0xb6, 0x2a, 0x5a, 0x1d, 0xc0, 0x24, 0x8d, 0xa4, 0xce, 0xb1, 0x12, 0x01, 0xf9, 0x79, 0xc6, 0x79, 0x38, 0x0c, 0xd4, 0x07, 0xc9, 0xf7, 0x37, 0xa1, 0x0b, 0xfe, 0x72, 0xec, 0x5d, 0xd6, 0xb0, 0x1c, 0x70, 0xbe, 0x70, 0x01, 0x13, 0xe0, 0x86, 0x95, 0xc7, 0x2e, 0x12, 0x3b, 0xe6, 0xa6, /* (2^211)P */ 0x24, 0x82, 0x67, 0xe0, 0x14, 0x7b, 0x56, 0x08, 0x38, 0x44, 0xdb, 0xa0, 0x3a, 0x05, 0x47, 0xb2, 0xc0, 0xac, 0xd1, 0xcc, 0x3f, 0x82, 0xb8, 0x8a, 0x88, 0xbc, 0xf5, 0x33, 0xa1, 0x35, 0x0f, 0xf6, 0xe2, 0xef, 0x6c, 0xf7, 0x37, 0x9e, 0xe8, 0x10, 0xca, 0xb0, 0x8e, 0x80, 0x86, 0x00, 0x23, 0xd0, 0x4a, 0x76, 0x9f, 0xf7, 0x2c, 0x52, 0x15, 0x0e, /* (2^212)P */ 0x5e, 0x49, 0xe1, 0x2c, 0x9a, 0x01, 0x76, 0xa6, 0xb3, 0x07, 0x5b, 0xa4, 0x07, 0xef, 0x1d, 0xc3, 0x6a, 0xbb, 0x64, 0xbe, 0x71, 0x15, 0x6e, 0x32, 0x31, 0x46, 0x9a, 0x9e, 0x8f, 0x45, 0x73, 0xce, 0x0b, 0x94, 0x1a, 0x52, 0x07, 0xf4, 0x50, 0x30, 0x49, 0x53, 0x50, 0xfb, 0x71, 0x1f, 0x5a, 0x03, 0xa9, 0x76, 0xf2, 0x8f, 0x42, 0xff, 0xed, 0xed, /* (2^213)P */ 0xed, 0x08, 0xdb, 0x91, 0x1c, 0xee, 0xa2, 0xb4, 0x47, 0xa2, 0xfa, 0xcb, 0x03, 0xd1, 0xff, 0x8c, 0xad, 0x64, 0x50, 0x61, 0xcd, 0xfc, 0x88, 0xa0, 0x31, 0x95, 0x30, 0xb9, 0x58, 0xdd, 0xd7, 0x43, 0xe4, 0x46, 0xc2, 0x16, 0xd9, 0x72, 0x4a, 0x56, 0x51, 0x70, 0x85, 0xf1, 0xa1, 0x80, 0x40, 0xd5, 0xba, 0x67, 0x81, 0xda, 0xcd, 0x03, 0xea, 0x51, /* (2^214)P */ 0x42, 0x50, 0xf0, 0xef, 0x37, 0x61, 0x72, 0x85, 0xe1, 0xf1, 0xff, 0x6f, 0x3d, 0xe8, 0x7b, 0x21, 0x5c, 0xe5, 0x50, 0x03, 0xde, 0x00, 0xc1, 0xf7, 0x3a, 0x55, 0x12, 0x1c, 0x9e, 0x1e, 0xce, 0xd1, 0x2f, 0xaf, 0x05, 0x70, 0x5b, 0x47, 0xf2, 0x04, 0x7a, 0x89, 0xbc, 0x78, 0xa6, 0x65, 0x6c, 0xaa, 0x3c, 0xa2, 0x3c, 0x8b, 0x5c, 0xa9, 0x22, 0x48, /* (2^215)P */ 0x7e, 0x8c, 0x8f, 0x2f, 0x60, 0xe3, 0x5a, 0x94, 0xd4, 0xce, 0xdd, 0x9d, 0x83, 0x3b, 0x77, 0x78, 0x43, 0x1d, 0xfd, 0x8f, 0xc8, 0xe8, 0x02, 0x90, 0xab, 0xf6, 0xc9, 0xfc, 0xf1, 0x63, 0xaa, 0x5f, 0x42, 0xf1, 0x78, 0x34, 0x64, 0x16, 0x75, 0x9c, 0x7d, 0xd0, 0xe4, 0x74, 0x5a, 0xa8, 0xfb, 0xcb, 0xac, 0x20, 0xa3, 0xc2, 0xa6, 0x20, 0xf8, 0x1b, /* (2^216)P */ 0x00, 0x4f, 0x1e, 0x56, 0xb5, 0x34, 0xb2, 0x87, 0x31, 0xe5, 0xee, 0x8d, 0xf1, 0x41, 0x67, 0xb7, 0x67, 0x3a, 0x54, 0x86, 0x5c, 0xf0, 0x0b, 0x37, 0x2f, 0x1b, 0x92, 0x5d, 0x58, 0x93, 0xdc, 0xd8, 0x58, 0xcc, 0x9e, 0x67, 0xd0, 0x97, 0x3a, 0xaf, 0x49, 0x39, 0x2d, 0x3b, 0xd8, 0x98, 0xfb, 0x76, 0x6b, 0xe7, 0xaf, 0xc3, 0x45, 0x44, 0x53, 0x94, /* (2^217)P */ 0x30, 0xbd, 0x90, 0x75, 0xd3, 0xbd, 0x3b, 0x58, 0x27, 0x14, 0x9f, 0x6b, 0xd4, 0x31, 0x99, 0xcd, 0xde, 0x3a, 0x21, 0x1e, 0xb4, 0x02, 0xe4, 0x33, 0x04, 0x02, 0xb0, 0x50, 0x66, 0x68, 0x90, 0xdd, 0x7b, 0x69, 0x31, 0xd9, 0xcf, 0x68, 0x73, 0xf1, 0x60, 0xdd, 0xc8, 0x1d, 0x5d, 0xe3, 0xd6, 0x5b, 0x2a, 0xa4, 0xea, 0xc4, 0x3f, 0x08, 0xcd, 0x9c, /* (2^218)P */ 0x6b, 0x1a, 0xbf, 0x55, 0xc1, 0x1b, 0x0c, 0x05, 0x09, 0xdf, 0xf5, 0x5e, 0xa3, 0x77, 0x95, 0xe9, 0xdf, 0x19, 0xdd, 0xc7, 0x94, 0xcb, 0x06, 0x73, 0xd0, 0x88, 0x02, 0x33, 0x94, 0xca, 0x7a, 0x2f, 0x8e, 0x3d, 0x72, 0x61, 0x2d, 0x4d, 0xa6, 0x61, 0x1f, 0x32, 0x5e, 0x87, 0x53, 0x36, 0x11, 0x15, 0x20, 0xb3, 0x5a, 0x57, 0x51, 0x93, 0x20, 0xd8, /* (2^219)P */ 0xb7, 0x56, 0xf4, 0xab, 0x7d, 0x0c, 0xfb, 0x99, 0x1a, 0x30, 0x29, 0xb0, 0x75, 0x2a, 0xf8, 0x53, 0x71, 0x23, 0xbd, 0xa7, 0xd8, 0x0a, 0xe2, 0x27, 0x65, 0xe9, 0x74, 0x26, 0x98, 0x4a, 0x69, 0x19, 0xb2, 0x4d, 0x0a, 0x17, 0x98, 0xb2, 0xa9, 0x57, 0x4e, 0xf6, 0x86, 0xc8, 0x01, 0xa4, 0xc6, 0x98, 0xad, 0x5a, 0x90, 0x2c, 0x05, 0x46, 0x64, 0xb7, /* (2^220)P */ 0x7b, 0x91, 0xdf, 0xfc, 0xf8, 0x1c, 0x8c, 0x15, 0x9e, 0xf7, 0xd5, 0xa8, 0xe8, 0xe7, 0xe3, 0xa3, 0xb0, 0x04, 0x74, 0xfa, 0x78, 0xfb, 0x26, 0xbf, 0x67, 0x42, 0xf9, 0x8c, 0x9b, 0xb4, 0x69, 0x5b, 0x02, 0x13, 0x6d, 0x09, 0x6c, 0xd6, 0x99, 0x61, 0x7b, 0x89, 0x4a, 0x67, 0x75, 0xa3, 0x98, 0x13, 0x23, 0x1d, 0x18, 0x24, 0x0e, 0xef, 0x41, 0x79, /* (2^221)P */ 0x86, 0x33, 0xab, 0x08, 0xcb, 0xbf, 0x1e, 0x76, 0x3c, 0x0b, 0xbd, 0x30, 0xdb, 0xe9, 0xa3, 0x35, 0x87, 0x1b, 0xe9, 0x07, 0x00, 0x66, 0x7f, 0x3b, 0x35, 0x0c, 0x8a, 0x3f, 0x61, 0xbc, 0xe0, 0xae, 0xf6, 0xcc, 0x54, 0xe1, 0x72, 0x36, 0x2d, 0xee, 0x93, 0x24, 0xf8, 0xd7, 0xc5, 0xf9, 0xcb, 0xb0, 0xe5, 0x88, 0x0d, 0x23, 0x4b, 0x76, 0x15, 0xa2, /* (2^222)P */ 0x37, 0xdb, 0x83, 0xd5, 0x6d, 0x06, 0x24, 0x37, 0x1b, 0x15, 0x85, 0x15, 0xe2, 0xc0, 0x4e, 0x02, 0xa9, 0x6d, 0x0a, 0x3a, 0x94, 0x4a, 0x6f, 0x49, 0x00, 0x01, 0x72, 0xbb, 0x60, 0x14, 0x35, 0xae, 0xb4, 0xc6, 0x01, 0x0a, 0x00, 0x9e, 0xc3, 0x58, 0xc5, 0xd1, 0x5e, 0x30, 0x73, 0x96, 0x24, 0x85, 0x9d, 0xf0, 0xf9, 0xec, 0x09, 0xd3, 0xe7, 0x70, /* (2^223)P */ 0xf3, 0xbd, 0x96, 0x87, 0xe9, 0x71, 0xbd, 0xd6, 0xa2, 0x45, 0xeb, 0x0a, 0xcd, 0x2c, 0xf1, 0x72, 0xa6, 0x31, 0xa9, 0x6f, 0x09, 0xa1, 0x5e, 0xdd, 0xc8, 0x8d, 0x0d, 0xbc, 0x5a, 0x8d, 0xb1, 0x2c, 0x9a, 0xcc, 0x37, 0x74, 0xc2, 0xa9, 0x4e, 0xd6, 0xc0, 0x3c, 0xa0, 0x23, 0xb0, 0xa0, 0x77, 0x14, 0x80, 0x45, 0x71, 0x6a, 0x2d, 0x41, 0xc3, 0x82, /* (2^224)P */ 0x37, 0x44, 0xec, 0x8a, 0x3e, 0xc1, 0x0c, 0xa9, 0x12, 0x9c, 0x08, 0x88, 0xcb, 0xd9, 0xf8, 0xba, 0x00, 0xd6, 0xc3, 0xdf, 0xef, 0x7a, 0x44, 0x7e, 0x25, 0x69, 0xc9, 0xc1, 0x46, 0xe5, 0x20, 0x9e, 0xcc, 0x0b, 0x05, 0x3e, 0xf4, 0x78, 0x43, 0x0c, 0xa6, 0x2f, 0xc1, 0xfa, 0x70, 0xb2, 0x3c, 0x31, 0x7a, 0x63, 0x58, 0xab, 0x17, 0xcf, 0x4c, 0x4f, /* (2^225)P */ 0x2b, 0x08, 0x31, 0x59, 0x75, 0x8b, 0xec, 0x0a, 0xa9, 0x79, 0x70, 0xdd, 0xf1, 0x11, 0xc3, 0x11, 0x1f, 0xab, 0x37, 0xaa, 0x26, 0xea, 0x53, 0xc4, 0x79, 0xa7, 0x91, 0x00, 0xaa, 0x08, 0x42, 0xeb, 0x8b, 0x8b, 0xe8, 0xc3, 0x2f, 0xb8, 0x78, 0x90, 0x38, 0x0e, 0x8a, 0x42, 0x0c, 0x0f, 0xbf, 0x3e, 0xf8, 0xd8, 0x07, 0xcf, 0x6a, 0x34, 0xc9, 0xfa, /* (2^226)P */ 0x11, 0xe0, 0x76, 0x4d, 0x23, 0xc5, 0xa6, 0xcc, 0x9f, 0x9a, 0x2a, 0xde, 0x3a, 0xb5, 0x92, 0x39, 0x19, 0x8a, 0xf1, 0x8d, 0xf9, 0x4d, 0xc9, 0xb4, 0x39, 0x9f, 0x57, 0xd8, 0x72, 0xab, 0x1d, 0x61, 0x6a, 0xb2, 0xff, 0x52, 0xba, 0x54, 0x0e, 0xfb, 0x83, 0x30, 0x8a, 0xf7, 0x3b, 0xf4, 0xd8, 0xae, 0x1a, 0x94, 0x3a, 0xec, 0x63, 0xfe, 0x6e, 0x7c, /* (2^227)P */ 0xdc, 0x70, 0x8e, 0x55, 0x44, 0xbf, 0xd2, 0x6a, 0xa0, 0x14, 0x61, 0x89, 0xd5, 0x55, 0x45, 0x3c, 0xf6, 0x40, 0x0d, 0x83, 0x85, 0x44, 0xb4, 0x62, 0x56, 0xfe, 0x60, 0xd7, 0x07, 0x1d, 0x47, 0x30, 0x3b, 0x73, 0xa4, 0xb5, 0xb7, 0xea, 0xac, 0xda, 0xf1, 0x17, 0xaa, 0x60, 0xdf, 0xe9, 0x84, 0xda, 0x31, 0x32, 0x61, 0xbf, 0xd0, 0x7e, 0x8a, 0x02, /* (2^228)P */ 0xb9, 0x51, 0xb3, 0x89, 0x21, 0x5d, 0xa2, 0xfe, 0x79, 0x2a, 0xb3, 0x2a, 0x3b, 0xe6, 0x6f, 0x2b, 0x22, 0x03, 0xea, 0x7b, 0x1f, 0xaf, 0x85, 0xc3, 0x38, 0x55, 0x5b, 0x8e, 0xb4, 0xaa, 0x77, 0xfe, 0x03, 0x6e, 0xda, 0x91, 0x24, 0x0c, 0x48, 0x39, 0x27, 0x43, 0x16, 0xd2, 0x0a, 0x0d, 0x43, 0xa3, 0x0e, 0xca, 0x45, 0xd1, 0x7f, 0xf5, 0xd3, 0x16, /* (2^229)P */ 0x3d, 0x32, 0x9b, 0x38, 0xf8, 0x06, 0x93, 0x78, 0x5b, 0x50, 0x2b, 0x06, 0xd8, 0x66, 0xfe, 0xab, 0x9b, 0x58, 0xc7, 0xd1, 0x4d, 0xd5, 0xf8, 0x3b, 0x10, 0x7e, 0x85, 0xde, 0x58, 0x4e, 0xdf, 0x53, 0xd9, 0x58, 0xe0, 0x15, 0x81, 0x9f, 0x1a, 0x78, 0xfc, 0x9f, 0x10, 0xc2, 0x23, 0xd6, 0x78, 0xd1, 0x9d, 0xd2, 0xd5, 0x1c, 0x53, 0xe2, 0xc9, 0x76, /* (2^230)P */ 0x98, 0x1e, 0x38, 0x7b, 0x71, 0x18, 0x4b, 0x15, 0xaf, 0xa1, 0xa6, 0x98, 0xcb, 0x26, 0xa3, 0xc8, 0x07, 0x46, 0xda, 0x3b, 0x70, 0x65, 0xec, 0x7a, 0x2b, 0x34, 0x94, 0xa8, 0xb6, 0x14, 0xf8, 0x1a, 0xce, 0xf7, 0xc8, 0x60, 0xf3, 0x88, 0xf4, 0x33, 0x60, 0x7b, 0xd1, 0x02, 0xe7, 0xda, 0x00, 0x4a, 0xea, 0xd2, 0xfd, 0x88, 0xd2, 0x99, 0x28, 0xf3, /* (2^231)P */ 0x28, 0x24, 0x1d, 0x26, 0xc2, 0xeb, 0x8b, 0x3b, 0xb4, 0x6b, 0xbe, 0x6b, 0x77, 0xff, 0xf3, 0x21, 0x3b, 0x26, 0x6a, 0x8c, 0x8e, 0x2a, 0x44, 0xa8, 0x01, 0x2b, 0x71, 0xea, 0x64, 0x30, 0xfd, 0xfd, 0x95, 0xcb, 0x39, 0x38, 0x48, 0xfa, 0x96, 0x97, 0x8c, 0x2f, 0x33, 0xca, 0x03, 0xe6, 0xd7, 0x94, 0x55, 0x6c, 0xc3, 0xb3, 0xa8, 0xf7, 0xae, 0x8c, /* (2^232)P */ 0xea, 0x62, 0x8a, 0xb4, 0xeb, 0x74, 0xf7, 0xb8, 0xae, 0xc5, 0x20, 0x71, 0x06, 0xd6, 0x7c, 0x62, 0x9b, 0x69, 0x74, 0xef, 0xa7, 0x6d, 0xd6, 0x8c, 0x37, 0xb9, 0xbf, 0xcf, 0xeb, 0xe4, 0x2f, 0x04, 0x02, 0x21, 0x7d, 0x75, 0x6b, 0x92, 0x48, 0xf8, 0x70, 0xad, 0x69, 0xe2, 0xea, 0x0e, 0x88, 0x67, 0x72, 0xcc, 0x2d, 0x10, 0xce, 0x2d, 0xcf, 0x65, /* (2^233)P */ 0x49, 0xf3, 0x57, 0x64, 0xe5, 0x5c, 0xc5, 0x65, 0x49, 0x97, 0xc4, 0x8a, 0xcc, 0xa9, 0xca, 0x94, 0x7b, 0x86, 0x88, 0xb6, 0x51, 0x27, 0x69, 0xa5, 0x0f, 0x8b, 0x06, 0x59, 0xa0, 0x94, 0xef, 0x63, 0x1a, 0x01, 0x9e, 0x4f, 0xd2, 0x5a, 0x93, 0xc0, 0x7c, 0xe6, 0x61, 0x77, 0xb6, 0xf5, 0x40, 0xd9, 0x98, 0x43, 0x5b, 0x56, 0x68, 0xe9, 0x37, 0x8f, /* (2^234)P */ 0xee, 0x87, 0xd2, 0x05, 0x1b, 0x39, 0x89, 0x10, 0x07, 0x6d, 0xe8, 0xfd, 0x8b, 0x4d, 0xb2, 0xa7, 0x7b, 0x1e, 0xa0, 0x6c, 0x0d, 0x3d, 0x3d, 0x49, 0xba, 0x61, 0x36, 0x1f, 0xc2, 0x84, 0x4a, 0xcc, 0x87, 0xa9, 0x1b, 0x23, 0x04, 0xe2, 0x3e, 0x97, 0xe1, 0xdb, 0xd5, 0x5a, 0xe8, 0x41, 0x6b, 0xe5, 0x5a, 0xa1, 0x99, 0xe5, 0x7b, 0xa7, 0xe0, 0x3b, /* (2^235)P */ 0xea, 0xa3, 0x6a, 0xdd, 0x77, 0x7f, 0x77, 0x41, 0xc5, 0x6a, 0xe4, 0xaf, 0x11, 0x5f, 0x88, 0xa5, 0x10, 0xee, 0xd0, 0x8c, 0x0c, 0xb4, 0xa5, 0x2a, 0xd0, 0xd8, 0x1d, 0x47, 0x06, 0xc0, 0xd5, 0xce, 0x51, 0x54, 0x9b, 0x2b, 0xe6, 0x2f, 0xe7, 0xe7, 0x31, 0x5f, 0x5c, 0x23, 0x81, 0x3e, 0x03, 0x93, 0xaa, 0x2d, 0x71, 0x84, 0xa0, 0x89, 0x32, 0xa6, /* (2^236)P */ 0x55, 0xa3, 0x13, 0x92, 0x4e, 0x93, 0x7d, 0xec, 0xca, 0x57, 0xfb, 0x37, 0xae, 0xd2, 0x18, 0x2e, 0x54, 0x05, 0x6c, 0xd1, 0x28, 0xca, 0x90, 0x40, 0x82, 0x2e, 0x79, 0xc6, 0x5a, 0xc7, 0xdd, 0x84, 0x93, 0xdf, 0x15, 0xb8, 0x1f, 0xb1, 0xf9, 0xaf, 0x2c, 0xe5, 0x32, 0xcd, 0xc2, 0x99, 0x6d, 0xac, 0x85, 0x5c, 0x63, 0xd3, 0xe2, 0xff, 0x24, 0xda, /* (2^237)P */ 0x2d, 0x8d, 0xfd, 0x65, 0xcc, 0xe5, 0x02, 0xa0, 0xe5, 0xb9, 0xec, 0x59, 0x09, 0x50, 0x27, 0xb7, 0x3d, 0x2a, 0x79, 0xb2, 0x76, 0x5d, 0x64, 0x95, 0xf8, 0xc5, 0xaf, 0x8a, 0x62, 0x11, 0x5c, 0x56, 0x1c, 0x05, 0x64, 0x9e, 0x5e, 0xbd, 0x54, 0x04, 0xe6, 0x9e, 0xab, 0xe6, 0x22, 0x7e, 0x42, 0x54, 0xb5, 0xa5, 0xd0, 0x8d, 0x28, 0x6b, 0x0f, 0x0b, /* (2^238)P */ 0x2d, 0xb2, 0x8c, 0x59, 0x10, 0x37, 0x84, 0x3b, 0x9b, 0x65, 0x1b, 0x0f, 0x10, 0xf9, 0xea, 0x60, 0x1b, 0x02, 0xf5, 0xee, 0x8b, 0xe6, 0x32, 0x7d, 0x10, 0x7f, 0x5f, 0x8c, 0x72, 0x09, 0x4e, 0x1f, 0x29, 0xff, 0x65, 0xcb, 0x3e, 0x3a, 0xd2, 0x96, 0x50, 0x1e, 0xea, 0x64, 0x99, 0xb5, 0x4c, 0x7a, 0x69, 0xb8, 0x95, 0xae, 0x48, 0xc0, 0x7c, 0xb1, /* (2^239)P */ 0xcd, 0x7c, 0x4f, 0x3e, 0xea, 0xf3, 0x90, 0xcb, 0x12, 0x76, 0xd1, 0x17, 0xdc, 0x0d, 0x13, 0x0f, 0xfd, 0x4d, 0xb5, 0x1f, 0xe4, 0xdd, 0xf2, 0x4d, 0x58, 0xea, 0xa5, 0x66, 0x92, 0xcf, 0xe5, 0x54, 0xea, 0x9b, 0x35, 0x83, 0x1a, 0x44, 0x8e, 0x62, 0x73, 0x45, 0x98, 0xa3, 0x89, 0x95, 0x52, 0x93, 0x1a, 0x8d, 0x63, 0x0f, 0xc2, 0x57, 0x3c, 0xb1, /* (2^240)P */ 0x72, 0xb4, 0xdf, 0x51, 0xb7, 0xf6, 0x52, 0xa2, 0x14, 0x56, 0xe5, 0x0a, 0x2e, 0x75, 0x81, 0x02, 0xee, 0x93, 0x48, 0x0a, 0x92, 0x4e, 0x0c, 0x0f, 0xdf, 0x09, 0x89, 0x99, 0xf6, 0xf9, 0x22, 0xa2, 0x32, 0xf8, 0xb0, 0x76, 0x0c, 0xb2, 0x4d, 0x6e, 0xbe, 0x83, 0x35, 0x61, 0x44, 0xd2, 0x58, 0xc7, 0xdd, 0x14, 0xcf, 0xc3, 0x4b, 0x7c, 0x07, 0xee, /* (2^241)P */ 0x8b, 0x03, 0xee, 0xcb, 0xa7, 0x2e, 0x28, 0xbd, 0x97, 0xd1, 0x4c, 0x2b, 0xd1, 0x92, 0x67, 0x5b, 0x5a, 0x12, 0xbf, 0x29, 0x17, 0xfc, 0x50, 0x09, 0x74, 0x76, 0xa2, 0xd4, 0x82, 0xfd, 0x2c, 0x0c, 0x90, 0xf7, 0xe7, 0xe5, 0x9a, 0x2c, 0x16, 0x40, 0xb9, 0x6c, 0xd9, 0xe0, 0x22, 0x9e, 0xf8, 0xdd, 0x73, 0xe4, 0x7b, 0x9e, 0xbe, 0x4f, 0x66, 0x22, /* (2^242)P */ 0xa4, 0x10, 0xbe, 0xb8, 0x83, 0x3a, 0x77, 0x8e, 0xea, 0x0a, 0xc4, 0x97, 0x3e, 0xb6, 0x6c, 0x81, 0xd7, 0x65, 0xd9, 0xf7, 0xae, 0xe6, 0xbe, 0xab, 0x59, 0x81, 0x29, 0x4b, 0xff, 0xe1, 0x0f, 0xc3, 0x2b, 0xad, 0x4b, 0xef, 0xc4, 0x50, 0x9f, 0x88, 0x31, 0xf2, 0xde, 0x80, 0xd6, 0xf4, 0x20, 0x9c, 0x77, 0x9b, 0xbe, 0xbe, 0x08, 0xf5, 0xf0, 0x95, /* (2^243)P */ 0x0e, 0x7c, 0x7b, 0x7c, 0xb3, 0xd8, 0x83, 0xfc, 0x8c, 0x75, 0x51, 0x74, 0x1b, 0xe1, 0x6d, 0x11, 0x05, 0x46, 0x24, 0x0d, 0xa4, 0x2b, 0x32, 0xfd, 0x2c, 0x4e, 0x21, 0xdf, 0x39, 0x6b, 0x96, 0xfc, 0xff, 0x92, 0xfc, 0x35, 0x0d, 0x9a, 0x4b, 0xc0, 0x70, 0x46, 0x32, 0x7d, 0xc0, 0xc4, 0x04, 0xe0, 0x2d, 0x83, 0xa7, 0x00, 0xc7, 0xcb, 0xb4, 0x8f, /* (2^244)P */ 0xa9, 0x5a, 0x7f, 0x0e, 0xdd, 0x2c, 0x85, 0xaa, 0x4d, 0xac, 0xde, 0xb3, 0xb6, 0xaf, 0xe6, 0xd1, 0x06, 0x7b, 0x2c, 0xa4, 0x01, 0x19, 0x22, 0x7d, 0x78, 0xf0, 0x3a, 0xea, 0x89, 0xfe, 0x21, 0x61, 0x6d, 0xb8, 0xfe, 0xa5, 0x2a, 0xab, 0x0d, 0x7b, 0x51, 0x39, 0xb6, 0xde, 0xbc, 0xf0, 0xc5, 0x48, 0xd7, 0x09, 0x82, 0x6e, 0x66, 0x75, 0xc5, 0xcd, /* (2^245)P */ 0xee, 0xdf, 0x2b, 0x6c, 0xa8, 0xde, 0x61, 0xe1, 0x27, 0xfa, 0x2a, 0x0f, 0x68, 0xe7, 0x7a, 0x9b, 0x13, 0xe9, 0x56, 0xd2, 0x1c, 0x3d, 0x2f, 0x3c, 0x7a, 0xf6, 0x6f, 0x45, 0xee, 0xe8, 0xf4, 0xa0, 0xa6, 0xe8, 0xa5, 0x27, 0xee, 0xf2, 0x85, 0xa9, 0xd5, 0x0e, 0xa9, 0x26, 0x60, 0xfe, 0xee, 0xc7, 0x59, 0x99, 0x5e, 0xa3, 0xdf, 0x23, 0x36, 0xd5, /* (2^246)P */ 0x15, 0x66, 0x6f, 0xd5, 0x78, 0xa4, 0x0a, 0xf7, 0xb1, 0xe8, 0x75, 0x6b, 0x48, 0x7d, 0xa6, 0x4d, 0x3d, 0x36, 0x9b, 0xc7, 0xcc, 0x68, 0x9a, 0xfe, 0x2f, 0x39, 0x2a, 0x51, 0x31, 0x39, 0x7d, 0x73, 0x6f, 0xc8, 0x74, 0x72, 0x6f, 0x6e, 0xda, 0x5f, 0xad, 0x48, 0xc8, 0x40, 0xe1, 0x06, 0x01, 0x36, 0xa1, 0x88, 0xc8, 0x99, 0x9c, 0xd1, 0x11, 0x8f, /* (2^247)P */ 0xab, 0xc5, 0xcb, 0xcf, 0xbd, 0x73, 0x21, 0xd0, 0x82, 0xb1, 0x2e, 0x2d, 0xd4, 0x36, 0x1b, 0xed, 0xa9, 0x8a, 0x26, 0x79, 0xc4, 0x17, 0xae, 0xe5, 0x09, 0x0a, 0x0c, 0xa4, 0x21, 0xa0, 0x6e, 0xdd, 0x62, 0x8e, 0x44, 0x62, 0xcc, 0x50, 0xff, 0x93, 0xb3, 0x9a, 0x72, 0x8c, 0x3f, 0xa1, 0xa6, 0x4d, 0x87, 0xd5, 0x1c, 0x5a, 0xc0, 0x0b, 0x1a, 0xd6, /* (2^248)P */ 0x67, 0x36, 0x6a, 0x1f, 0x96, 0xe5, 0x80, 0x20, 0xa9, 0xe8, 0x0b, 0x0e, 0x21, 0x29, 0x3f, 0xc8, 0x0a, 0x6d, 0x27, 0x47, 0xca, 0xd9, 0x05, 0x55, 0xbf, 0x11, 0xcf, 0x31, 0x7a, 0x37, 0xc7, 0x90, 0xa9, 0xf4, 0x07, 0x5e, 0xd5, 0xc3, 0x92, 0xaa, 0x95, 0xc8, 0x23, 0x2a, 0x53, 0x45, 0xe3, 0x3a, 0x24, 0xe9, 0x67, 0x97, 0x3a, 0x82, 0xf9, 0xa6, /* (2^249)P */ 0x92, 0x9e, 0x6d, 0x82, 0x67, 0xe9, 0xf9, 0x17, 0x96, 0x2c, 0xa7, 0xd3, 0x89, 0xf9, 0xdb, 0xd8, 0x20, 0xc6, 0x2e, 0xec, 0x4a, 0x76, 0x64, 0xbf, 0x27, 0x40, 0xe2, 0xb4, 0xdf, 0x1f, 0xa0, 0xef, 0x07, 0x80, 0xfb, 0x8e, 0x12, 0xf8, 0xb8, 0xe1, 0xc6, 0xdf, 0x7c, 0x69, 0x35, 0x5a, 0xe1, 0x8e, 0x5d, 0x69, 0x84, 0x56, 0xb6, 0x31, 0x1c, 0x0b, /* (2^250)P */ 0xd6, 0x94, 0x5c, 0xef, 0xbb, 0x46, 0x45, 0x44, 0x5b, 0xa1, 0xae, 0x03, 0x65, 0xdd, 0xb5, 0x66, 0x88, 0x35, 0x29, 0x95, 0x16, 0x54, 0xa6, 0xf5, 0xc9, 0x78, 0x34, 0xe6, 0x0f, 0xc4, 0x2b, 0x5b, 0x79, 0x51, 0x68, 0x48, 0x3a, 0x26, 0x87, 0x05, 0x70, 0xaf, 0x8b, 0xa6, 0xc7, 0x2e, 0xb3, 0xa9, 0x10, 0x01, 0xb0, 0xb9, 0x31, 0xfd, 0xdc, 0x80, /* (2^251)P */ 0x25, 0xf2, 0xad, 0xd6, 0x75, 0xa3, 0x04, 0x05, 0x64, 0x8a, 0x97, 0x60, 0x27, 0x2a, 0xe5, 0x6d, 0xb0, 0x73, 0xf4, 0x07, 0x2a, 0x9d, 0xe9, 0x46, 0xb4, 0x1c, 0x51, 0xf8, 0x63, 0x98, 0x7e, 0xe5, 0x13, 0x51, 0xed, 0x98, 0x65, 0x98, 0x4f, 0x8f, 0xe7, 0x7e, 0x72, 0xd7, 0x64, 0x11, 0x2f, 0xcd, 0x12, 0xf8, 0xc4, 0x63, 0x52, 0x0f, 0x7f, 0xc4, /* (2^252)P */ 0x5c, 0xd9, 0x85, 0x63, 0xc7, 0x8a, 0x65, 0x9a, 0x25, 0x83, 0x31, 0x73, 0x49, 0xf0, 0x93, 0x96, 0x70, 0x67, 0x6d, 0xb1, 0xff, 0x95, 0x54, 0xe4, 0xf8, 0x15, 0x6c, 0x5f, 0xbd, 0xf6, 0x0f, 0x38, 0x7b, 0x68, 0x7d, 0xd9, 0x3d, 0xf0, 0xa9, 0xa0, 0xe4, 0xd1, 0xb6, 0x34, 0x6d, 0x14, 0x16, 0xc2, 0x4c, 0x30, 0x0e, 0x67, 0xd3, 0xbe, 0x2e, 0xc0, /* (2^253)P */ 0x06, 0x6b, 0x52, 0xc8, 0x14, 0xcd, 0xae, 0x03, 0x93, 0xea, 0xc1, 0xf2, 0xf6, 0x8b, 0xc5, 0xb6, 0xdc, 0x82, 0x42, 0x29, 0x94, 0xe0, 0x25, 0x6c, 0x3f, 0x9f, 0x5d, 0xe4, 0x96, 0xf6, 0x8e, 0x3f, 0xf9, 0x72, 0xc4, 0x77, 0x60, 0x8b, 0xa4, 0xf9, 0xa8, 0xc3, 0x0a, 0x81, 0xb1, 0x97, 0x70, 0x18, 0xab, 0xea, 0x37, 0x8a, 0x08, 0xc7, 0xe2, 0x95, /* (2^254)P */ 0x94, 0x49, 0xd9, 0x5f, 0x76, 0x72, 0x82, 0xad, 0x2d, 0x50, 0x1a, 0x7a, 0x5b, 0xe6, 0x95, 0x1e, 0x95, 0x65, 0x87, 0x1c, 0x52, 0xd7, 0x44, 0xe6, 0x9b, 0x56, 0xcd, 0x6f, 0x05, 0xff, 0x67, 0xc5, 0xdb, 0xa2, 0xac, 0xe4, 0xa2, 0x28, 0x63, 0x5f, 0xfb, 0x0c, 0x3b, 0xf1, 0x87, 0xc3, 0x36, 0x78, 0x3f, 0x77, 0xfa, 0x50, 0x85, 0xf9, 0xd7, 0x82, /* (2^255)P */ 0x64, 0xc0, 0xe0, 0xd8, 0x2d, 0xed, 0xcb, 0x6a, 0xfd, 0xcd, 0xbc, 0x7e, 0x9f, 0xc8, 0x85, 0xe9, 0xc1, 0x7c, 0x0f, 0xe5, 0x18, 0xea, 0xd4, 0x51, 0xad, 0x59, 0x13, 0x75, 0xd9, 0x3d, 0xd4, 0x8a, 0xb2, 0xbe, 0x78, 0x52, 0x2b, 0x52, 0x94, 0x37, 0x41, 0xd6, 0xb4, 0xb6, 0x45, 0x20, 0x76, 0xe0, 0x1f, 0x31, 0xdb, 0xb1, 0xa1, 0x43, 0xf0, 0x18, /* (2^256)P */ 0x74, 0xa9, 0xa4, 0xa9, 0xdd, 0x6e, 0x3e, 0x68, 0xe5, 0xc3, 0x2e, 0x92, 0x17, 0xa4, 0xcb, 0x80, 0xb1, 0xf0, 0x06, 0x93, 0xef, 0xe6, 0x00, 0xe6, 0x3b, 0xb1, 0x32, 0x65, 0x7b, 0x83, 0xb6, 0x8a, 0x49, 0x1b, 0x14, 0x89, 0xee, 0xba, 0xf5, 0x6a, 0x8d, 0x36, 0xef, 0xb0, 0xd8, 0xb2, 0x16, 0x99, 0x17, 0x35, 0x02, 0x16, 0x55, 0x58, 0xdd, 0x82, /* (2^257)P */ 0x36, 0x95, 0xe8, 0xf4, 0x36, 0x42, 0xbb, 0xc5, 0x3e, 0xfa, 0x30, 0x84, 0x9e, 0x59, 0xfd, 0xd2, 0x95, 0x42, 0xf8, 0x64, 0xd9, 0xb9, 0x0e, 0x9f, 0xfa, 0xd0, 0x7b, 0x20, 0x31, 0x77, 0x48, 0x29, 0x4d, 0xd0, 0x32, 0x57, 0x56, 0x30, 0xa6, 0x17, 0x53, 0x04, 0xbf, 0x08, 0x28, 0xec, 0xb8, 0x46, 0xc1, 0x03, 0x89, 0xdc, 0xed, 0xa0, 0x35, 0x53, /* (2^258)P */ 0xc5, 0x7f, 0x9e, 0xd8, 0xc5, 0xba, 0x5f, 0x68, 0xc8, 0x23, 0x75, 0xea, 0x0d, 0xd9, 0x5a, 0xfd, 0x61, 0x1a, 0xa3, 0x2e, 0x45, 0x63, 0x14, 0x55, 0x86, 0x21, 0x29, 0xbe, 0xef, 0x5e, 0x50, 0xe5, 0x18, 0x59, 0xe7, 0xe3, 0xce, 0x4d, 0x8c, 0x15, 0x8f, 0x89, 0x66, 0x44, 0x52, 0x3d, 0xfa, 0xc7, 0x9a, 0x59, 0x90, 0x8e, 0xc0, 0x06, 0x3f, 0xc9, /* (2^259)P */ 0x8e, 0x04, 0xd9, 0x16, 0x50, 0x1d, 0x8c, 0x9f, 0xd5, 0xe3, 0xce, 0xfd, 0x47, 0x04, 0x27, 0x4d, 0xc2, 0xfa, 0x71, 0xd9, 0x0b, 0xb8, 0x65, 0xf4, 0x11, 0xf3, 0x08, 0xee, 0x81, 0xc8, 0x67, 0x99, 0x0b, 0x8d, 0x77, 0xa3, 0x4f, 0xb5, 0x9b, 0xdb, 0x26, 0xf1, 0x97, 0xeb, 0x04, 0x54, 0xeb, 0x80, 0x08, 0x1d, 0x1d, 0xf6, 0x3d, 0x1f, 0x5a, 0xb8, /* (2^260)P */ 0xb7, 0x9c, 0x9d, 0xee, 0xb9, 0x5c, 0xad, 0x0d, 0x9e, 0xfd, 0x60, 0x3c, 0x27, 0x4e, 0xa2, 0x95, 0xfb, 0x64, 0x7e, 0x79, 0x64, 0x87, 0x10, 0xb4, 0x73, 0xe0, 0x9d, 0x46, 0x4d, 0x3d, 0xee, 0x83, 0xe4, 0x16, 0x88, 0x97, 0xe6, 0x4d, 0xba, 0x70, 0xb6, 0x96, 0x7b, 0xff, 0x4b, 0xc8, 0xcf, 0x72, 0x83, 0x3e, 0x5b, 0x24, 0x2e, 0x57, 0xf1, 0x82, /* (2^261)P */ 0x30, 0x71, 0x40, 0x51, 0x4f, 0x44, 0xbb, 0xc7, 0xf0, 0x54, 0x6e, 0x9d, 0xeb, 0x15, 0xad, 0xf8, 0x61, 0x43, 0x5a, 0xef, 0xc0, 0xb1, 0x57, 0xae, 0x03, 0x40, 0xe8, 0x68, 0x6f, 0x03, 0x20, 0x4f, 0x8a, 0x51, 0x2a, 0x9e, 0xd2, 0x45, 0xaf, 0xb4, 0xf5, 0xd4, 0x95, 0x7f, 0x3d, 0x3d, 0xb7, 0xb6, 0x28, 0xc5, 0x08, 0x8b, 0x44, 0xd6, 0x3f, 0xe7, /* (2^262)P */ 0xa9, 0x52, 0x04, 0x67, 0xcb, 0x20, 0x63, 0xf8, 0x18, 0x01, 0x44, 0x21, 0x6a, 0x8a, 0x83, 0x48, 0xd4, 0xaf, 0x23, 0x0f, 0x35, 0x8d, 0xe5, 0x5a, 0xc4, 0x7c, 0x55, 0x46, 0x19, 0x5f, 0x35, 0xe0, 0x5d, 0x97, 0x4c, 0x2d, 0x04, 0xed, 0x59, 0xd4, 0xb0, 0xb2, 0xc6, 0xe3, 0x51, 0xe1, 0x38, 0xc6, 0x30, 0x49, 0x8f, 0xae, 0x61, 0x64, 0xce, 0xa8, /* (2^263)P */ 0x9b, 0x64, 0x83, 0x3c, 0xd3, 0xdf, 0xb9, 0x27, 0xe7, 0x5b, 0x7f, 0xeb, 0xf3, 0x26, 0xcf, 0xb1, 0x8f, 0xaf, 0x26, 0xc8, 0x48, 0xce, 0xa1, 0xac, 0x7d, 0x10, 0x34, 0x28, 0xe1, 0x1f, 0x69, 0x03, 0x64, 0x77, 0x61, 0xdd, 0x4a, 0x9b, 0x18, 0x47, 0xf8, 0xca, 0x63, 0xc9, 0x03, 0x2d, 0x20, 0x2a, 0x69, 0x6e, 0x42, 0xd0, 0xe7, 0xaa, 0xb5, 0xf3, /* (2^264)P */ 0xea, 0x31, 0x0c, 0x57, 0x0f, 0x3e, 0xe3, 0x35, 0xd8, 0x30, 0xa5, 0x6f, 0xdd, 0x95, 0x43, 0xc6, 0x66, 0x07, 0x4f, 0x34, 0xc3, 0x7e, 0x04, 0x10, 0x2d, 0xc4, 0x1c, 0x94, 0x52, 0x2e, 0x5b, 0x9a, 0x65, 0x2f, 0x91, 0xaa, 0x4f, 0x3c, 0xdc, 0x23, 0x18, 0xe1, 0x4f, 0x85, 0xcd, 0xf4, 0x8c, 0x51, 0xf7, 0xab, 0x4f, 0xdc, 0x15, 0x5c, 0x9e, 0xc5, /* (2^265)P */ 0x54, 0x57, 0x23, 0x17, 0xe7, 0x82, 0x2f, 0x04, 0x7d, 0xfe, 0xe7, 0x1f, 0xa2, 0x57, 0x79, 0xe9, 0x58, 0x9b, 0xbe, 0xc6, 0x16, 0x4a, 0x17, 0x50, 0x90, 0x4a, 0x34, 0x70, 0x87, 0x37, 0x01, 0x26, 0xd8, 0xa3, 0x5f, 0x07, 0x7c, 0xd0, 0x7d, 0x05, 0x8a, 0x93, 0x51, 0x2f, 0x99, 0xea, 0xcf, 0x00, 0xd8, 0xc7, 0xe6, 0x9b, 0x8c, 0x62, 0x45, 0x87, /* (2^266)P */ 0xc3, 0xfd, 0x29, 0x66, 0xe7, 0x30, 0x29, 0x77, 0xe0, 0x0d, 0x63, 0x5b, 0xe6, 0x90, 0x1a, 0x1e, 0x99, 0xc2, 0xa7, 0xab, 0xff, 0xa7, 0xbd, 0x79, 0x01, 0x97, 0xfd, 0x27, 0x1b, 0x43, 0x2b, 0xe6, 0xfe, 0x5e, 0xf1, 0xb9, 0x35, 0x38, 0x08, 0x25, 0x55, 0x90, 0x68, 0x2e, 0xc3, 0x67, 0x39, 0x9f, 0x2b, 0x2c, 0x70, 0x48, 0x8c, 0x47, 0xee, 0x56, /* (2^267)P */ 0xf7, 0x32, 0x70, 0xb5, 0xe6, 0x42, 0xfd, 0x0a, 0x39, 0x9b, 0x07, 0xfe, 0x0e, 0xf4, 0x47, 0xba, 0x6a, 0x3f, 0xf5, 0x2c, 0x15, 0xf3, 0x60, 0x3f, 0xb1, 0x83, 0x7b, 0x2e, 0x34, 0x58, 0x1a, 0x6e, 0x4a, 0x49, 0x05, 0x45, 0xca, 0xdb, 0x00, 0x01, 0x0c, 0x42, 0x5e, 0x60, 0x40, 0x5f, 0xd9, 0xc7, 0x3a, 0x9e, 0x1c, 0x8d, 0xab, 0x11, 0x55, 0x65, /* (2^268)P */ 0x87, 0x40, 0xb7, 0x0d, 0xaa, 0x34, 0x89, 0x90, 0x75, 0x6d, 0xa2, 0xfe, 0x3b, 0x6d, 0x5c, 0x39, 0x98, 0x10, 0x9e, 0x15, 0xc5, 0x35, 0xa2, 0x27, 0x23, 0x0a, 0x2d, 0x60, 0xe2, 0xa8, 0x7f, 0x3e, 0x77, 0x8f, 0xcc, 0x44, 0xcc, 0x30, 0x28, 0xe2, 0xf0, 0x04, 0x8c, 0xee, 0xe4, 0x5f, 0x68, 0x8c, 0xdf, 0x70, 0xbf, 0x31, 0xee, 0x2a, 0xfc, 0xce, /* (2^269)P */ 0x92, 0xf2, 0xa0, 0xd9, 0x58, 0x3b, 0x7c, 0x1a, 0x99, 0x46, 0x59, 0x54, 0x60, 0x06, 0x8d, 0x5e, 0xf0, 0x22, 0xa1, 0xed, 0x92, 0x8a, 0x4d, 0x76, 0x95, 0x05, 0x0b, 0xff, 0xfc, 0x9a, 0xd1, 0xcc, 0x05, 0xb9, 0x5e, 0x99, 0xe8, 0x2a, 0x76, 0x7b, 0xfd, 0xa6, 0xe2, 0xd1, 0x1a, 0xd6, 0x76, 0x9f, 0x2f, 0x0e, 0xd1, 0xa8, 0x77, 0x5a, 0x40, 0x5a, /* (2^270)P */ 0xff, 0xf9, 0x3f, 0xa9, 0xa6, 0x6c, 0x6d, 0x03, 0x8b, 0xa7, 0x10, 0x5d, 0x3f, 0xec, 0x3e, 0x1c, 0x0b, 0x6b, 0xa2, 0x6a, 0x22, 0xa9, 0x28, 0xd0, 0x66, 0xc9, 0xc2, 0x3d, 0x47, 0x20, 0x7d, 0xa6, 0x1d, 0xd8, 0x25, 0xb5, 0xf2, 0xf9, 0x70, 0x19, 0x6b, 0xf8, 0x43, 0x36, 0xc5, 0x1f, 0xe4, 0x5a, 0x4c, 0x13, 0xe4, 0x6d, 0x08, 0x0b, 0x1d, 0xb1, /* (2^271)P */ 0x3f, 0x20, 0x9b, 0xfb, 0xec, 0x7d, 0x31, 0xc5, 0xfc, 0x88, 0x0b, 0x30, 0xed, 0x36, 0xc0, 0x63, 0xb1, 0x7d, 0x10, 0xda, 0xb6, 0x2e, 0xad, 0xf3, 0xec, 0x94, 0xe7, 0xec, 0xb5, 0x9c, 0xfe, 0xf5, 0x35, 0xf0, 0xa2, 0x2d, 0x7f, 0xca, 0x6b, 0x67, 0x1a, 0xf6, 0xb3, 0xda, 0x09, 0x2a, 0xaa, 0xdf, 0xb1, 0xca, 0x9b, 0xfb, 0xeb, 0xb3, 0xcd, 0xc0, /* (2^272)P */ 0xcd, 0x4d, 0x89, 0x00, 0xa4, 0x3b, 0x48, 0xf0, 0x76, 0x91, 0x35, 0xa5, 0xf8, 0xc9, 0xb6, 0x46, 0xbc, 0xf6, 0x9a, 0x45, 0x47, 0x17, 0x96, 0x80, 0x5b, 0x3a, 0x28, 0x33, 0xf9, 0x5a, 0xef, 0x43, 0x07, 0xfe, 0x3b, 0xf4, 0x8e, 0x19, 0xce, 0xd2, 0x94, 0x4b, 0x6d, 0x8e, 0x67, 0x20, 0xc7, 0x4f, 0x2f, 0x59, 0x8e, 0xe1, 0xa1, 0xa9, 0xf9, 0x0e, /* (2^273)P */ 0xdc, 0x7b, 0xb5, 0x50, 0x2e, 0xe9, 0x7e, 0x8b, 0x78, 0xa1, 0x38, 0x96, 0x22, 0xc3, 0x61, 0x67, 0x6d, 0xc8, 0x58, 0xed, 0x41, 0x1d, 0x5d, 0x86, 0x98, 0x7f, 0x2f, 0x1b, 0x8d, 0x3e, 0xaa, 0xc1, 0xd2, 0x0a, 0xf3, 0xbf, 0x95, 0x04, 0xf3, 0x10, 0x3c, 0x2b, 0x7f, 0x90, 0x46, 0x04, 0xaa, 0x6a, 0xa9, 0x35, 0x76, 0xac, 0x49, 0xb5, 0x00, 0x45, /* (2^274)P */ 0xb1, 0x93, 0x79, 0x84, 0x4a, 0x2a, 0x30, 0x78, 0x16, 0xaa, 0xc5, 0x74, 0x06, 0xce, 0xa5, 0xa7, 0x32, 0x86, 0xe0, 0xf9, 0x10, 0xd2, 0x58, 0x76, 0xfb, 0x66, 0x49, 0x76, 0x3a, 0x90, 0xba, 0xb5, 0xcc, 0x99, 0xcd, 0x09, 0xc1, 0x9a, 0x74, 0x23, 0xdf, 0x0c, 0xfe, 0x99, 0x52, 0x80, 0xa3, 0x7c, 0x1c, 0x71, 0x5f, 0x2c, 0x49, 0x57, 0xf4, 0xf9, /* (2^275)P */ 0x6d, 0xbf, 0x52, 0xe6, 0x25, 0x98, 0xed, 0xcf, 0xe3, 0xbc, 0x08, 0xa2, 0x1a, 0x90, 0xae, 0xa0, 0xbf, 0x07, 0x15, 0xad, 0x0a, 0x9f, 0x3e, 0x47, 0x44, 0xc2, 0x10, 0x46, 0xa6, 0x7a, 0x9e, 0x2f, 0x57, 0xbc, 0xe2, 0xf0, 0x1d, 0xd6, 0x9a, 0x06, 0xed, 0xfc, 0x54, 0x95, 0x92, 0x15, 0xa2, 0xf7, 0x8d, 0x6b, 0xef, 0xb2, 0x05, 0xed, 0x5c, 0x63, /* (2^276)P */ 0xbc, 0x0b, 0x27, 0x3a, 0x3a, 0xf8, 0xe1, 0x48, 0x02, 0x7e, 0x27, 0xe6, 0x81, 0x62, 0x07, 0x73, 0x74, 0xe5, 0x52, 0xd7, 0xf8, 0x26, 0xca, 0x93, 0x4d, 0x3e, 0x9b, 0x55, 0x09, 0x8e, 0xe3, 0xd7, 0xa6, 0xe3, 0xb6, 0x2a, 0xa9, 0xb3, 0xb0, 0xa0, 0x8c, 0x01, 0xbb, 0x07, 0x90, 0x78, 0x6d, 0x6d, 0xe9, 0xf0, 0x7a, 0x90, 0xbd, 0xdc, 0x0c, 0x36, /* (2^277)P */ 0x7f, 0x20, 0x12, 0x0f, 0x40, 0x00, 0x53, 0xd8, 0x0c, 0x27, 0x47, 0x47, 0x22, 0x80, 0xfb, 0x62, 0xe4, 0xa7, 0xf7, 0xbd, 0x42, 0xa5, 0xc3, 0x2b, 0xb2, 0x7f, 0x50, 0xcc, 0xe2, 0xfb, 0xd5, 0xc0, 0x63, 0xdd, 0x24, 0x5f, 0x7c, 0x08, 0x91, 0xbf, 0x6e, 0x47, 0x44, 0xd4, 0x6a, 0xc0, 0xc3, 0x09, 0x39, 0x27, 0xdd, 0xc7, 0xca, 0x06, 0x29, 0x55, /* (2^278)P */ 0x76, 0x28, 0x58, 0xb0, 0xd2, 0xf3, 0x0f, 0x04, 0xe9, 0xc9, 0xab, 0x66, 0x5b, 0x75, 0x51, 0xdc, 0xe5, 0x8f, 0xe8, 0x1f, 0xdb, 0x03, 0x0f, 0xb0, 0x7d, 0xf9, 0x20, 0x64, 0x89, 0xe9, 0xdc, 0xe6, 0x24, 0xc3, 0xd5, 0xd2, 0x41, 0xa6, 0xe4, 0xe3, 0xc4, 0x79, 0x7c, 0x0f, 0xa1, 0x61, 0x2f, 0xda, 0xa4, 0xc9, 0xfd, 0xad, 0x5c, 0x65, 0x6a, 0xf3, /* (2^279)P */ 0xd5, 0xab, 0x72, 0x7a, 0x3b, 0x59, 0xea, 0xcf, 0xd5, 0x17, 0xd2, 0xb2, 0x5f, 0x2d, 0xab, 0xad, 0x9e, 0x88, 0x64, 0x55, 0x96, 0x6e, 0xf3, 0x44, 0xa9, 0x11, 0xf5, 0xf8, 0x3a, 0xf1, 0xcd, 0x79, 0x4c, 0x99, 0x6d, 0x23, 0x6a, 0xa0, 0xc2, 0x1a, 0x19, 0x45, 0xb5, 0xd8, 0x95, 0x2f, 0x49, 0xe9, 0x46, 0x39, 0x26, 0x60, 0x04, 0x15, 0x8b, 0xcc, /* (2^280)P */ 0x66, 0x0c, 0xf0, 0x54, 0x41, 0x02, 0x91, 0xab, 0xe5, 0x85, 0x8a, 0x44, 0xa6, 0x34, 0x96, 0x32, 0xc0, 0xdf, 0x6c, 0x41, 0x39, 0xd4, 0xc6, 0xe1, 0xe3, 0x81, 0xb0, 0x4c, 0x34, 0x4f, 0xe5, 0xf4, 0x35, 0x46, 0x1f, 0xeb, 0x75, 0xfd, 0x43, 0x37, 0x50, 0x99, 0xab, 0xad, 0xb7, 0x8c, 0xa1, 0x57, 0xcb, 0xe6, 0xce, 0x16, 0x2e, 0x85, 0xcc, 0xf9, /* (2^281)P */ 0x63, 0xd1, 0x3f, 0x9e, 0xa2, 0x17, 0x2e, 0x1d, 0x3e, 0xce, 0x48, 0x2d, 0xbb, 0x8f, 0x69, 0xc9, 0xa6, 0x3d, 0x4e, 0xfe, 0x09, 0x56, 0xb3, 0x02, 0x5f, 0x99, 0x97, 0x0c, 0x54, 0xda, 0x32, 0x97, 0x9b, 0xf4, 0x95, 0xf1, 0xad, 0xe3, 0x2b, 0x04, 0xa7, 0x9b, 0x3f, 0xbb, 0xe7, 0x87, 0x2e, 0x1f, 0x8b, 0x4b, 0x7a, 0xa4, 0x43, 0x0c, 0x0f, 0x35, /* (2^282)P */ 0x05, 0xdc, 0xe0, 0x2c, 0xa1, 0xc1, 0xd0, 0xf1, 0x1f, 0x4e, 0xc0, 0x6c, 0x35, 0x7b, 0xca, 0x8f, 0x8b, 0x02, 0xb1, 0xf7, 0xd6, 0x2e, 0xe7, 0x93, 0x80, 0x85, 0x18, 0x88, 0x19, 0xb9, 0xb4, 0x4a, 0xbc, 0xeb, 0x5a, 0x78, 0x38, 0xed, 0xc6, 0x27, 0x2a, 0x74, 0x76, 0xf0, 0x1b, 0x79, 0x92, 0x2f, 0xd2, 0x81, 0x98, 0xdf, 0xa9, 0x50, 0x19, 0xeb, /* (2^283)P */ 0xb5, 0xe7, 0xb4, 0x11, 0x3a, 0x81, 0xb6, 0xb4, 0xf8, 0xa2, 0xb3, 0x6c, 0xfc, 0x9d, 0xe0, 0xc0, 0xe0, 0x59, 0x7f, 0x05, 0x37, 0xef, 0x2c, 0xa9, 0x3a, 0x24, 0xac, 0x7b, 0x25, 0xa0, 0x55, 0xd2, 0x44, 0x82, 0x82, 0x6e, 0x64, 0xa3, 0x58, 0xc8, 0x67, 0xae, 0x26, 0xa7, 0x0f, 0x42, 0x63, 0xe1, 0x93, 0x01, 0x52, 0x19, 0xaf, 0x49, 0x3e, 0x33, /* (2^284)P */ 0x05, 0x85, 0xe6, 0x66, 0xaf, 0x5f, 0xdf, 0xbf, 0x9d, 0x24, 0x62, 0x60, 0x90, 0xe2, 0x4c, 0x7d, 0x4e, 0xc3, 0x74, 0x5d, 0x4f, 0x53, 0xf3, 0x63, 0x13, 0xf4, 0x74, 0x28, 0x6b, 0x7d, 0x57, 0x0c, 0x9d, 0x84, 0xa7, 0x1a, 0xff, 0xa0, 0x79, 0xdf, 0xfc, 0x65, 0x98, 0x8e, 0x22, 0x0d, 0x62, 0x7e, 0xf2, 0x34, 0x60, 0x83, 0x05, 0x14, 0xb1, 0xc1, /* (2^285)P */ 0x64, 0x22, 0xcc, 0xdf, 0x5c, 0xbc, 0x88, 0x68, 0x4c, 0xd9, 0xbc, 0x0e, 0xc9, 0x8b, 0xb4, 0x23, 0x52, 0xad, 0xb0, 0xb3, 0xf1, 0x17, 0xd8, 0x15, 0x04, 0x6b, 0x99, 0xf0, 0xc4, 0x7d, 0x48, 0x22, 0x4a, 0xf8, 0x6f, 0xaa, 0x88, 0x0d, 0xc5, 0x5e, 0xa9, 0x1c, 0x61, 0x3d, 0x95, 0xa9, 0x7b, 0x6a, 0x79, 0x33, 0x0a, 0x2b, 0x99, 0xe3, 0x4e, 0x48, /* (2^286)P */ 0x6b, 0x9b, 0x6a, 0x2a, 0xf1, 0x60, 0x31, 0xb4, 0x73, 0xd1, 0x87, 0x45, 0x9c, 0x15, 0x58, 0x4b, 0x91, 0x6d, 0x94, 0x1c, 0x41, 0x11, 0x4a, 0x83, 0xec, 0xaf, 0x65, 0xbc, 0x34, 0xaa, 0x26, 0xe2, 0xaf, 0xed, 0x46, 0x05, 0x4e, 0xdb, 0xc6, 0x4e, 0x10, 0x28, 0x4e, 0x72, 0xe5, 0x31, 0xa3, 0x20, 0xd7, 0xb1, 0x96, 0x64, 0xf6, 0xce, 0x08, 0x08, /* (2^287)P */ 0x16, 0xa9, 0x5c, 0x9f, 0x9a, 0xb4, 0xb8, 0xc8, 0x32, 0x78, 0xc0, 0x3a, 0xd9, 0x5f, 0x94, 0xac, 0x3a, 0x42, 0x1f, 0x43, 0xd6, 0x80, 0x47, 0x2c, 0xdc, 0x76, 0x27, 0xfa, 0x50, 0xe5, 0xa1, 0xe4, 0xc3, 0xcb, 0x61, 0x31, 0xe1, 0x2e, 0xde, 0x81, 0x3b, 0x77, 0x1c, 0x39, 0x3c, 0xdb, 0xda, 0x87, 0x4b, 0x84, 0x12, 0xeb, 0xdd, 0x54, 0xbf, 0xe7, /* (2^288)P */ 0xbf, 0xcb, 0x73, 0x21, 0x3d, 0x7e, 0x13, 0x8c, 0xa6, 0x34, 0x21, 0x2b, 0xa5, 0xe4, 0x9f, 0x8e, 0x9c, 0x01, 0x9c, 0x43, 0xd9, 0xc7, 0xb9, 0xf1, 0xbe, 0x7f, 0x45, 0x51, 0x97, 0xa1, 0x8e, 0x01, 0xf8, 0xbd, 0xd2, 0xbf, 0x81, 0x3a, 0x8b, 0xab, 0xe4, 0x89, 0xb7, 0xbd, 0xf2, 0xcd, 0xa9, 0x8a, 0x8a, 0xde, 0xfb, 0x8a, 0x55, 0x12, 0x7b, 0x17, /* (2^289)P */ 0x1b, 0x95, 0x58, 0x4d, 0xe6, 0x51, 0x31, 0x52, 0x1c, 0xd8, 0x15, 0x84, 0xb1, 0x0d, 0x36, 0x25, 0x88, 0x91, 0x46, 0x71, 0x42, 0x56, 0xe2, 0x90, 0x08, 0x9e, 0x77, 0x1b, 0xee, 0x22, 0x3f, 0xec, 0xee, 0x8c, 0x7b, 0x2e, 0x79, 0xc4, 0x6c, 0x07, 0xa1, 0x7e, 0x52, 0xf5, 0x26, 0x5c, 0x84, 0x2a, 0x50, 0x6e, 0x82, 0xb3, 0x76, 0xda, 0x35, 0x16, /* (2^290)P */ 0x0a, 0x6f, 0x99, 0x87, 0xc0, 0x7d, 0x8a, 0xb2, 0xca, 0xae, 0xe8, 0x65, 0x98, 0x0f, 0xb3, 0x44, 0xe1, 0xdc, 0x52, 0x79, 0x75, 0xec, 0x8f, 0x95, 0x87, 0x45, 0xd1, 0x32, 0x18, 0x55, 0x15, 0xce, 0x64, 0x9b, 0x08, 0x4f, 0x2c, 0xea, 0xba, 0x1c, 0x57, 0x06, 0x63, 0xc8, 0xb1, 0xfd, 0xc5, 0x67, 0xe7, 0x1f, 0x87, 0x9e, 0xde, 0x72, 0x7d, 0xec, /* (2^291)P */ 0x36, 0x8b, 0x4d, 0x2c, 0xc2, 0x46, 0xe8, 0x96, 0xac, 0x0b, 0x8c, 0xc5, 0x09, 0x10, 0xfc, 0xf2, 0xda, 0xea, 0x22, 0xb2, 0xd3, 0x89, 0xeb, 0xb2, 0x85, 0x0f, 0xff, 0x59, 0x50, 0x2c, 0x99, 0x5a, 0x1f, 0xec, 0x2a, 0x6f, 0xec, 0xcf, 0xe9, 0xce, 0x12, 0x6b, 0x19, 0xd8, 0xde, 0x9b, 0xce, 0x0e, 0x6a, 0xaa, 0xe1, 0x32, 0xea, 0x4c, 0xfe, 0x92, /* (2^292)P */ 0x5f, 0x17, 0x70, 0x53, 0x26, 0x03, 0x0b, 0xab, 0xd1, 0xc1, 0x42, 0x0b, 0xab, 0x2b, 0x3d, 0x31, 0xa4, 0xd5, 0x2b, 0x5e, 0x00, 0xd5, 0x9a, 0x22, 0x34, 0xe0, 0x53, 0x3f, 0x59, 0x7f, 0x2c, 0x6d, 0x72, 0x9a, 0xa4, 0xbe, 0x3d, 0x42, 0x05, 0x1b, 0xf2, 0x7f, 0x88, 0x56, 0xd1, 0x7c, 0x7d, 0x6b, 0x9f, 0x43, 0xfe, 0x65, 0x19, 0xae, 0x9c, 0x4c, /* (2^293)P */ 0xf3, 0x7c, 0x20, 0xa9, 0xfc, 0xf2, 0xf2, 0x3b, 0x3c, 0x57, 0x41, 0x94, 0xe5, 0xcc, 0x6a, 0x37, 0x5d, 0x09, 0xf2, 0xab, 0xc2, 0xca, 0x60, 0x38, 0x6b, 0x7a, 0xe1, 0x78, 0x2b, 0xc1, 0x1d, 0xe8, 0xfd, 0xbc, 0x3d, 0x5c, 0xa2, 0xdb, 0x49, 0x20, 0x79, 0xe6, 0x1b, 0x9b, 0x65, 0xd9, 0x6d, 0xec, 0x57, 0x1d, 0xd2, 0xe9, 0x90, 0xeb, 0x43, 0x7b, /* (2^294)P */ 0x2a, 0x8b, 0x2e, 0x19, 0x18, 0x10, 0xb8, 0x83, 0xe7, 0x7d, 0x2d, 0x9a, 0x3a, 0xe5, 0xd1, 0xe4, 0x7c, 0x38, 0xe5, 0x59, 0x2a, 0x6e, 0xd9, 0x01, 0x29, 0x3d, 0x23, 0xf7, 0x52, 0xba, 0x61, 0x04, 0x9a, 0xde, 0xc4, 0x31, 0x50, 0xeb, 0x1b, 0xaa, 0xde, 0x39, 0x58, 0xd8, 0x1b, 0x1e, 0xfc, 0x57, 0x9a, 0x28, 0x43, 0x9e, 0x97, 0x5e, 0xaa, 0xa3, /* (2^295)P */ 0x97, 0x0a, 0x74, 0xc4, 0x39, 0x99, 0x6b, 0x40, 0xc7, 0x3e, 0x8c, 0xa7, 0xb1, 0x4e, 0x9a, 0x59, 0x6e, 0x1c, 0xfe, 0xfc, 0x2a, 0x5e, 0x73, 0x2b, 0x8c, 0xa9, 0x71, 0xf5, 0xda, 0x6b, 0x15, 0xab, 0xf7, 0xbe, 0x2a, 0x44, 0x5f, 0xba, 0xae, 0x67, 0x93, 0xc5, 0x86, 0xc1, 0xb8, 0xdf, 0xdc, 0xcb, 0xd7, 0xff, 0xb1, 0x71, 0x7c, 0x6f, 0x88, 0xf8, /* (2^296)P */ 0x3f, 0x89, 0xb1, 0xbf, 0x24, 0x16, 0xac, 0x56, 0xfe, 0xdf, 0x94, 0x71, 0xbf, 0xd6, 0x57, 0x0c, 0xb4, 0x77, 0x37, 0xaa, 0x2a, 0x70, 0x76, 0x49, 0xaf, 0x0c, 0x97, 0x8e, 0x78, 0x2a, 0x67, 0xc9, 0x3b, 0x3d, 0x5b, 0x01, 0x2f, 0xda, 0xd5, 0xa8, 0xde, 0x02, 0xa9, 0xac, 0x76, 0x00, 0x0b, 0x46, 0xc6, 0x2d, 0xdc, 0x08, 0xf4, 0x10, 0x2c, 0xbe, /* (2^297)P */ 0xcb, 0x07, 0xf9, 0x91, 0xc6, 0xd5, 0x3e, 0x54, 0x63, 0xae, 0xfc, 0x10, 0xbe, 0x3a, 0x20, 0x73, 0x4e, 0x65, 0x0e, 0x2d, 0x86, 0x77, 0x83, 0x9d, 0xe2, 0x0a, 0xe9, 0xac, 0x22, 0x52, 0x76, 0xd4, 0x6e, 0xfa, 0xe0, 0x09, 0xef, 0x78, 0x82, 0x9f, 0x26, 0xf9, 0x06, 0xb5, 0xe7, 0x05, 0x0e, 0xf2, 0x46, 0x72, 0x93, 0xd3, 0x24, 0xbd, 0x87, 0x60, /* (2^298)P */ 0x14, 0x55, 0x84, 0x7b, 0x6c, 0x60, 0x80, 0x73, 0x8c, 0xbe, 0x2d, 0xd6, 0x69, 0xd6, 0x17, 0x26, 0x44, 0x9f, 0x88, 0xa2, 0x39, 0x7c, 0x89, 0xbc, 0x6d, 0x9e, 0x46, 0xb6, 0x68, 0x66, 0xea, 0xdc, 0x31, 0xd6, 0x21, 0x51, 0x9f, 0x28, 0x28, 0xaf, 0x9e, 0x47, 0x2c, 0x4c, 0x8f, 0xf3, 0xaf, 0x1f, 0xe4, 0xab, 0xac, 0xe9, 0x0c, 0x91, 0x3a, 0x61, /* (2^299)P */ 0xb0, 0x37, 0x55, 0x4b, 0xe9, 0xc3, 0xb1, 0xce, 0x42, 0xe6, 0xc5, 0x11, 0x7f, 0x2c, 0x11, 0xfc, 0x4e, 0x71, 0x17, 0x00, 0x74, 0x7f, 0xbf, 0x07, 0x4d, 0xfd, 0x40, 0xb2, 0x87, 0xb0, 0xef, 0x1f, 0x35, 0x2c, 0x2d, 0xd7, 0xe1, 0xe4, 0xad, 0x0e, 0x7f, 0x63, 0x66, 0x62, 0x23, 0x41, 0xf6, 0xc1, 0x14, 0xa6, 0xd7, 0xa9, 0x11, 0x56, 0x9d, 0x1b, /* (2^300)P */ 0x02, 0x82, 0x42, 0x18, 0x4f, 0x1b, 0xc9, 0x5d, 0x78, 0x5f, 0xee, 0xed, 0x01, 0x49, 0x8f, 0xf2, 0xa0, 0xe2, 0x6e, 0xbb, 0x6b, 0x04, 0x8d, 0xb2, 0x41, 0xae, 0xc8, 0x1b, 0x59, 0x34, 0xb8, 0x2a, 0xdb, 0x1f, 0xd2, 0x52, 0xdf, 0x3f, 0x35, 0x00, 0x8b, 0x61, 0xbc, 0x97, 0xa0, 0xc4, 0x77, 0xd1, 0xe4, 0x2c, 0x59, 0x68, 0xff, 0x30, 0xf2, 0xe2, /* (2^301)P */ 0x79, 0x08, 0xb1, 0xdb, 0x55, 0xae, 0xd0, 0xed, 0xda, 0xa0, 0xec, 0x6c, 0xae, 0x68, 0xf2, 0x0b, 0x61, 0xb3, 0xf5, 0x21, 0x69, 0x87, 0x0b, 0x03, 0xea, 0x8a, 0x15, 0xd9, 0x7e, 0xca, 0xf7, 0xcd, 0xf3, 0x33, 0xb3, 0x4c, 0x5b, 0x23, 0x4e, 0x6f, 0x90, 0xad, 0x91, 0x4b, 0x4f, 0x46, 0x37, 0xe5, 0xe8, 0xb7, 0xeb, 0xd5, 0xca, 0x34, 0x4e, 0x23, /* (2^302)P */ 0x09, 0x02, 0xdd, 0xfd, 0x70, 0xac, 0x56, 0x80, 0x36, 0x5e, 0x49, 0xd0, 0x3f, 0xc2, 0xe0, 0xba, 0x46, 0x7f, 0x5c, 0xf7, 0xc5, 0xbd, 0xd5, 0x55, 0x7d, 0x3f, 0xd5, 0x7d, 0x06, 0xdf, 0x27, 0x20, 0x4f, 0xe9, 0x30, 0xec, 0x1b, 0xa0, 0x0c, 0xd4, 0x2c, 0xe1, 0x2b, 0x65, 0x73, 0xea, 0x75, 0x35, 0xe8, 0xe6, 0x56, 0xd6, 0x07, 0x15, 0x99, 0xdf, /* (2^303)P */ 0x4e, 0x10, 0xb7, 0xd0, 0x63, 0x8c, 0xcf, 0x16, 0x00, 0x7c, 0x58, 0xdf, 0x86, 0xdc, 0x4e, 0xca, 0x9c, 0x40, 0x5a, 0x42, 0xfd, 0xec, 0x98, 0xa4, 0x42, 0x53, 0xae, 0x16, 0x9d, 0xfd, 0x75, 0x5a, 0x12, 0x56, 0x1e, 0xc6, 0x57, 0xcc, 0x79, 0x27, 0x96, 0x00, 0xcf, 0x80, 0x4f, 0x8a, 0x36, 0x5c, 0xbb, 0xe9, 0x12, 0xdb, 0xb6, 0x2b, 0xad, 0x96, /* (2^304)P */ 0x92, 0x32, 0x1f, 0xfd, 0xc6, 0x02, 0x94, 0x08, 0x1b, 0x60, 0x6a, 0x9f, 0x8b, 0xd6, 0xc8, 0xad, 0xd5, 0x1b, 0x27, 0x4e, 0xa4, 0x4d, 0x4a, 0x00, 0x10, 0x5f, 0x86, 0x11, 0xf5, 0xe3, 0x14, 0x32, 0x43, 0xee, 0xb9, 0xc7, 0xab, 0xf4, 0x6f, 0xe5, 0x66, 0x0c, 0x06, 0x0d, 0x96, 0x79, 0x28, 0xaf, 0x45, 0x2b, 0x56, 0xbe, 0xe4, 0x4a, 0x52, 0xd6, /* (2^305)P */ 0x15, 0x16, 0x69, 0xef, 0x60, 0xca, 0x82, 0x25, 0x0f, 0xc6, 0x30, 0xa0, 0x0a, 0xd1, 0x83, 0x29, 0xcd, 0xb6, 0x89, 0x6c, 0xf5, 0xb2, 0x08, 0x38, 0xe6, 0xca, 0x6b, 0x19, 0x93, 0xc6, 0x5f, 0x75, 0x8e, 0x60, 0x34, 0x23, 0xc4, 0x13, 0x17, 0x69, 0x55, 0xcc, 0x72, 0x9c, 0x2b, 0x6c, 0x80, 0xf4, 0x4b, 0x8b, 0xb6, 0x97, 0x65, 0x07, 0xb6, 0xfb, /* (2^306)P */ 0x01, 0x99, 0x74, 0x28, 0xa6, 0x67, 0xa3, 0xe5, 0x25, 0xfb, 0xdf, 0x82, 0x93, 0xe7, 0x35, 0x74, 0xce, 0xe3, 0x15, 0x1c, 0x1d, 0x79, 0x52, 0x84, 0x08, 0x04, 0x2f, 0x5c, 0xb8, 0xcd, 0x7f, 0x89, 0xb0, 0x39, 0x93, 0x63, 0xc9, 0x5d, 0x06, 0x01, 0x59, 0xf7, 0x7e, 0xf1, 0x4c, 0x3d, 0x12, 0x8d, 0x69, 0x1d, 0xb7, 0x21, 0x5e, 0x88, 0x82, 0xa2, /* (2^307)P */ 0x8e, 0x69, 0xaf, 0x9a, 0x41, 0x0d, 0x9d, 0xcf, 0x8e, 0x8d, 0x5c, 0x51, 0x6e, 0xde, 0x0e, 0x48, 0x23, 0x89, 0xe5, 0x37, 0x80, 0xd6, 0x9d, 0x72, 0x32, 0x26, 0x38, 0x2d, 0x63, 0xa0, 0xfa, 0xd3, 0x40, 0xc0, 0x8c, 0x68, 0x6f, 0x2b, 0x1e, 0x9a, 0x39, 0x51, 0x78, 0x74, 0x9a, 0x7b, 0x4a, 0x8f, 0x0c, 0xa0, 0x88, 0x60, 0xa5, 0x21, 0xcd, 0xc7, /* (2^308)P */ 0x3a, 0x7f, 0x73, 0x14, 0xbf, 0x89, 0x6a, 0x4c, 0x09, 0x5d, 0xf2, 0x93, 0x20, 0x2d, 0xc4, 0x29, 0x86, 0x06, 0x95, 0xab, 0x22, 0x76, 0x4c, 0x54, 0xe1, 0x7e, 0x80, 0x6d, 0xab, 0x29, 0x61, 0x87, 0x77, 0xf6, 0xc0, 0x3e, 0xda, 0xab, 0x65, 0x7e, 0x39, 0x12, 0xa1, 0x6b, 0x42, 0xf7, 0xc5, 0x97, 0x77, 0xec, 0x6f, 0x22, 0xbe, 0x44, 0xc7, 0x03, /* (2^309)P */ 0xa5, 0x23, 0x90, 0x41, 0xa3, 0xc5, 0x3e, 0xe0, 0xa5, 0x32, 0x49, 0x1f, 0x39, 0x78, 0xb1, 0xd8, 0x24, 0xea, 0xd4, 0x87, 0x53, 0x42, 0x51, 0xf4, 0xd9, 0x46, 0x25, 0x2f, 0x62, 0xa9, 0x90, 0x9a, 0x4a, 0x25, 0x8a, 0xd2, 0x10, 0xe7, 0x3c, 0xbc, 0x58, 0x8d, 0x16, 0x14, 0x96, 0xa4, 0x6f, 0xf8, 0x12, 0x69, 0x91, 0x73, 0xe2, 0xfa, 0xf4, 0x57, /* (2^310)P */ 0x51, 0x45, 0x3f, 0x96, 0xdc, 0x97, 0x38, 0xa6, 0x01, 0x63, 0x09, 0xea, 0xc2, 0x13, 0x30, 0xb0, 0x00, 0xb8, 0x0a, 0xce, 0xd1, 0x8f, 0x3e, 0x69, 0x62, 0x46, 0x33, 0x9c, 0xbf, 0x4b, 0xcb, 0x0c, 0x90, 0x1c, 0x45, 0xcf, 0x37, 0x5b, 0xf7, 0x4b, 0x5e, 0x95, 0xc3, 0x28, 0x9f, 0x08, 0x83, 0x53, 0x74, 0xab, 0x0c, 0xb4, 0xc0, 0xa1, 0xbc, 0x89, /* (2^311)P */ 0x06, 0xb1, 0x51, 0x15, 0x65, 0x60, 0x21, 0x17, 0x7a, 0x20, 0x65, 0xee, 0x12, 0x35, 0x4d, 0x46, 0xf4, 0xf8, 0xd0, 0xb1, 0xca, 0x09, 0x30, 0x08, 0x89, 0x23, 0x3b, 0xe7, 0xab, 0x8b, 0x77, 0xa6, 0xad, 0x25, 0xdd, 0xea, 0x3c, 0x7d, 0xa5, 0x24, 0xb3, 0xe8, 0xfa, 0xfb, 0xc9, 0xf2, 0x71, 0xe9, 0xfa, 0xf2, 0xdc, 0x54, 0xdd, 0x55, 0x2e, 0x2f, /* (2^312)P */ 0x7f, 0x96, 0x96, 0xfb, 0x52, 0x86, 0xcf, 0xea, 0x62, 0x18, 0xf1, 0x53, 0x1f, 0x61, 0x2a, 0x9f, 0x8c, 0x51, 0xca, 0x2c, 0xde, 0x6d, 0xce, 0xab, 0x58, 0x32, 0x0b, 0x33, 0x9b, 0x99, 0xb4, 0x5c, 0x88, 0x2a, 0x76, 0xcc, 0x3e, 0x54, 0x1e, 0x9d, 0xa2, 0x89, 0xe4, 0x19, 0xba, 0x80, 0xc8, 0x39, 0x32, 0x7f, 0x0f, 0xc7, 0x84, 0xbb, 0x43, 0x56, /* (2^313)P */ 0x9b, 0x07, 0xb4, 0x42, 0xa9, 0xa0, 0x78, 0x4f, 0x28, 0x70, 0x2b, 0x7e, 0x61, 0xe0, 0xdd, 0x02, 0x98, 0xfc, 0xed, 0x31, 0x80, 0xf1, 0x15, 0x52, 0x89, 0x23, 0xcd, 0x5d, 0x2b, 0xc5, 0x19, 0x32, 0xfb, 0x70, 0x50, 0x7a, 0x97, 0x6b, 0x42, 0xdb, 0xca, 0xdb, 0xc4, 0x59, 0x99, 0xe0, 0x12, 0x1f, 0x17, 0xba, 0x8b, 0xf0, 0xc4, 0x38, 0x5d, 0x27, /* (2^314)P */ 0x29, 0x1d, 0xdc, 0x2b, 0xf6, 0x5b, 0x04, 0x61, 0x36, 0x76, 0xa0, 0x56, 0x36, 0x6e, 0xd7, 0x24, 0x4d, 0xe7, 0xef, 0x44, 0xd2, 0xd5, 0x07, 0xcd, 0xc4, 0x9d, 0x80, 0x48, 0xc3, 0x38, 0xcf, 0xd8, 0xa3, 0xdd, 0xb2, 0x5e, 0xb5, 0x70, 0x15, 0xbb, 0x36, 0x85, 0x8a, 0xd7, 0xfb, 0x56, 0x94, 0x73, 0x9c, 0x81, 0xbe, 0xb1, 0x44, 0x28, 0xf1, 0x37, /* (2^315)P */ 0xbf, 0xcf, 0x5c, 0xd2, 0xe2, 0xea, 0xc2, 0xcd, 0x70, 0x7a, 0x9d, 0xcb, 0x81, 0xc1, 0xe9, 0xf1, 0x56, 0x71, 0x52, 0xf7, 0x1b, 0x87, 0xc6, 0xd8, 0xcc, 0xb2, 0x69, 0xf3, 0xb0, 0xbd, 0xba, 0x83, 0x12, 0x26, 0xc4, 0xce, 0x72, 0xde, 0x3b, 0x21, 0x28, 0x9e, 0x5a, 0x94, 0xf5, 0x04, 0xa3, 0xc8, 0x0f, 0x5e, 0xbc, 0x71, 0xf9, 0x0d, 0xce, 0xf5, /* (2^316)P */ 0x93, 0x97, 0x00, 0x85, 0xf4, 0xb4, 0x40, 0xec, 0xd9, 0x2b, 0x6c, 0xd6, 0x63, 0x9e, 0x93, 0x0a, 0x5a, 0xf4, 0xa7, 0x9a, 0xe3, 0x3c, 0xf0, 0x55, 0xd1, 0x96, 0x6c, 0xf5, 0x2a, 0xce, 0xd7, 0x95, 0x72, 0xbf, 0xc5, 0x0c, 0xce, 0x79, 0xa2, 0x0a, 0x78, 0xe0, 0x72, 0xd0, 0x66, 0x28, 0x05, 0x75, 0xd3, 0x23, 0x09, 0x91, 0xed, 0x7e, 0xc4, 0xbc, /* (2^317)P */ 0x77, 0xc2, 0x9a, 0xf7, 0xa6, 0xe6, 0x18, 0xb4, 0xe7, 0xf6, 0xda, 0xec, 0x44, 0x6d, 0xfb, 0x08, 0xee, 0x65, 0xa8, 0x92, 0x85, 0x1f, 0xba, 0x38, 0x93, 0x20, 0x5c, 0x4d, 0xd2, 0x18, 0x0f, 0x24, 0xbe, 0x1a, 0x96, 0x44, 0x7d, 0xeb, 0xb3, 0xda, 0x95, 0xf4, 0xaf, 0x6c, 0x06, 0x0f, 0x47, 0x37, 0xc8, 0x77, 0x63, 0xe1, 0x29, 0xef, 0xff, 0xa5, /* (2^318)P */ 0x16, 0x12, 0xd9, 0x47, 0x90, 0x22, 0x9b, 0x05, 0xf2, 0xa5, 0x9a, 0xae, 0x83, 0x98, 0xb5, 0xac, 0xab, 0x29, 0xaa, 0xdc, 0x5f, 0xde, 0xcd, 0xf7, 0x42, 0xad, 0x3b, 0x96, 0xd6, 0x3e, 0x6e, 0x52, 0x47, 0xb1, 0xab, 0x51, 0xde, 0x49, 0x7c, 0x87, 0x8d, 0x86, 0xe2, 0x70, 0x13, 0x21, 0x51, 0x1c, 0x0c, 0x25, 0xc1, 0xb0, 0xe6, 0x19, 0xcf, 0x12, /* (2^319)P */ 0xf0, 0xbc, 0x97, 0x8f, 0x4b, 0x2f, 0xd1, 0x1f, 0x8c, 0x57, 0xed, 0x3c, 0xf4, 0x26, 0x19, 0xbb, 0x60, 0xca, 0x24, 0xc5, 0xd9, 0x97, 0xe2, 0x5f, 0x76, 0x49, 0x39, 0x7e, 0x2d, 0x12, 0x21, 0x98, 0xda, 0xe6, 0xdb, 0xd2, 0xd8, 0x9f, 0x18, 0xd8, 0x83, 0x6c, 0xba, 0x89, 0x8d, 0x29, 0xfa, 0x46, 0x33, 0x8c, 0x28, 0xdf, 0x6a, 0xb3, 0x69, 0x28, /* (2^320)P */ 0x86, 0x17, 0xbc, 0xd6, 0x7c, 0xba, 0x1e, 0x83, 0xbb, 0x84, 0xb5, 0x8c, 0xad, 0xdf, 0xa1, 0x24, 0x81, 0x70, 0x40, 0x0f, 0xad, 0xad, 0x3b, 0x23, 0xd0, 0x93, 0xa0, 0x49, 0x5c, 0x4b, 0x51, 0xbe, 0x20, 0x49, 0x4e, 0xda, 0x2d, 0xd3, 0xad, 0x1b, 0x74, 0x08, 0x41, 0xf0, 0xef, 0x19, 0xe9, 0x45, 0x5d, 0x02, 0xae, 0x26, 0x25, 0xd9, 0xd1, 0xc2, /* (2^321)P */ 0x48, 0x81, 0x3e, 0xb2, 0x83, 0xf8, 0x4d, 0xb3, 0xd0, 0x4c, 0x75, 0xb3, 0xa0, 0x52, 0x26, 0xf2, 0xaf, 0x5d, 0x36, 0x70, 0x72, 0xd6, 0xb7, 0x88, 0x08, 0x69, 0xbd, 0x15, 0x25, 0xb1, 0x45, 0x1b, 0xb7, 0x0b, 0x5f, 0x71, 0x5d, 0x83, 0x49, 0xb9, 0x84, 0x3b, 0x7c, 0xc1, 0x50, 0x93, 0x05, 0x53, 0xe0, 0x61, 0xea, 0xc1, 0xef, 0xdb, 0x82, 0x97, /* (2^322)P */ 0x00, 0xd5, 0xc3, 0x3a, 0x4d, 0x8a, 0x23, 0x7a, 0xef, 0xff, 0x37, 0xef, 0xf3, 0xbc, 0xa9, 0xb6, 0xae, 0xd7, 0x3a, 0x7b, 0xfd, 0x3e, 0x8e, 0x9b, 0xab, 0x44, 0x54, 0x60, 0x28, 0x6c, 0xbf, 0x15, 0x24, 0x4a, 0x56, 0x60, 0x7f, 0xa9, 0x7a, 0x28, 0x59, 0x2c, 0x8a, 0xd1, 0x7d, 0x6b, 0x00, 0xfd, 0xa5, 0xad, 0xbc, 0x19, 0x3f, 0xcb, 0x73, 0xe0, /* (2^323)P */ 0xcf, 0x9e, 0x66, 0x06, 0x4d, 0x2b, 0xf5, 0x9c, 0xc2, 0x9d, 0x9e, 0xed, 0x5a, 0x5c, 0x2d, 0x00, 0xbf, 0x29, 0x90, 0x88, 0xe4, 0x5d, 0xfd, 0xe2, 0xf0, 0x38, 0xec, 0x4d, 0x26, 0xea, 0x54, 0xf0, 0x3c, 0x84, 0x10, 0x6a, 0xf9, 0x66, 0x9c, 0xe7, 0x21, 0xfd, 0x0f, 0xc7, 0x13, 0x50, 0x81, 0xb6, 0x50, 0xf9, 0x04, 0x7f, 0xa4, 0x37, 0x85, 0x14, /* (2^324)P */ 0xdb, 0x87, 0x49, 0xc7, 0xa8, 0x39, 0x0c, 0x32, 0x98, 0x0c, 0xb9, 0x1a, 0x1b, 0x4d, 0xe0, 0x8a, 0x9a, 0x8e, 0x8f, 0xab, 0x5a, 0x17, 0x3d, 0x04, 0x21, 0xce, 0x3e, 0x2c, 0xf9, 0xa3, 0x97, 0xe4, 0x77, 0x95, 0x0e, 0xb6, 0xa5, 0x15, 0xad, 0x3a, 0x1e, 0x46, 0x53, 0x17, 0x09, 0x83, 0x71, 0x4e, 0x86, 0x38, 0xd5, 0x23, 0x44, 0x16, 0x8d, 0xc8, /* (2^325)P */ 0x05, 0x5e, 0x99, 0x08, 0xbb, 0xc3, 0xc0, 0xb7, 0x6c, 0x12, 0xf2, 0xf3, 0xf4, 0x7c, 0x6a, 0x4d, 0x9e, 0xeb, 0x3d, 0xb9, 0x63, 0x94, 0xce, 0x81, 0xd8, 0x11, 0xcb, 0x55, 0x69, 0x4a, 0x20, 0x0b, 0x4c, 0x2e, 0x14, 0xb8, 0xd4, 0x6a, 0x7c, 0xf0, 0xed, 0xfc, 0x8f, 0xef, 0xa0, 0xeb, 0x6c, 0x01, 0xe2, 0xdc, 0x10, 0x22, 0xa2, 0x01, 0x85, 0x64, /* (2^326)P */ 0x58, 0xe1, 0x9c, 0x27, 0x55, 0xc6, 0x25, 0xa6, 0x7d, 0x67, 0x88, 0x65, 0x99, 0x6c, 0xcb, 0xdb, 0x27, 0x4f, 0x44, 0x29, 0xf5, 0x4a, 0x23, 0x10, 0xbc, 0x03, 0x3f, 0x36, 0x1e, 0xef, 0xb0, 0xba, 0x75, 0xe8, 0x74, 0x5f, 0x69, 0x3e, 0x26, 0x40, 0xb4, 0x2f, 0xdc, 0x43, 0xbf, 0xa1, 0x8b, 0xbd, 0xca, 0x6e, 0xc1, 0x6e, 0x21, 0x79, 0xa0, 0xd0, /* (2^327)P */ 0x78, 0x93, 0x4a, 0x2d, 0x22, 0x6e, 0x6e, 0x7d, 0x74, 0xd2, 0x66, 0x58, 0xce, 0x7b, 0x1d, 0x97, 0xb1, 0xf2, 0xda, 0x1c, 0x79, 0xfb, 0xba, 0xd1, 0xc0, 0xc5, 0x6e, 0xc9, 0x11, 0x89, 0xd2, 0x41, 0x8d, 0x70, 0xb9, 0xcc, 0xea, 0x6a, 0xb3, 0x45, 0xb6, 0x05, 0x2e, 0xf2, 0x17, 0xf1, 0x27, 0xb8, 0xed, 0x06, 0x1f, 0xdb, 0x9d, 0x1f, 0x69, 0x28, /* (2^328)P */ 0x93, 0x12, 0xa8, 0x11, 0xe1, 0x92, 0x30, 0x8d, 0xac, 0xe1, 0x1c, 0x60, 0x7c, 0xed, 0x2d, 0x2e, 0xd3, 0x03, 0x5c, 0x9c, 0xc5, 0xbd, 0x64, 0x4a, 0x8c, 0xba, 0x76, 0xfe, 0xc6, 0xc1, 0xea, 0xc2, 0x4f, 0xbe, 0x70, 0x3d, 0x64, 0xcf, 0x8e, 0x18, 0xcb, 0xcd, 0x57, 0xa7, 0xf7, 0x36, 0xa9, 0x6b, 0x3e, 0xb8, 0x69, 0xee, 0x47, 0xa2, 0x7e, 0xb2, /* (2^329)P */ 0x96, 0xaf, 0x3a, 0xf5, 0xed, 0xcd, 0xaf, 0xf7, 0x82, 0xaf, 0x59, 0x62, 0x0b, 0x36, 0x85, 0xf9, 0xaf, 0xd6, 0x38, 0xff, 0x87, 0x2e, 0x1d, 0x6c, 0x8b, 0xaf, 0x3b, 0xdf, 0x28, 0xa2, 0xd6, 0x4d, 0x80, 0x92, 0xc3, 0x0f, 0x34, 0xa8, 0xae, 0x69, 0x5d, 0x7b, 0x9d, 0xbc, 0xf5, 0xfd, 0x1d, 0xb1, 0x96, 0x55, 0x86, 0xe1, 0x5c, 0xb6, 0xac, 0xb9, /* (2^330)P */ 0x50, 0x9e, 0x37, 0x28, 0x7d, 0xa8, 0x33, 0x63, 0xda, 0x3f, 0x20, 0x98, 0x0e, 0x09, 0xa8, 0x77, 0x3b, 0x7a, 0xfc, 0x16, 0x85, 0x44, 0x64, 0x77, 0x65, 0x68, 0x92, 0x41, 0xc6, 0x1f, 0xdf, 0x27, 0xf9, 0xec, 0xa0, 0x61, 0x22, 0xea, 0x19, 0xe7, 0x75, 0x8b, 0x4e, 0xe5, 0x0f, 0xb7, 0xf7, 0xd2, 0x53, 0xf4, 0xdd, 0x4a, 0xaa, 0x78, 0x40, 0xb7, /* (2^331)P */ 0xd4, 0x89, 0xe3, 0x79, 0xba, 0xb6, 0xc3, 0xda, 0xe6, 0x78, 0x65, 0x7d, 0x6e, 0x22, 0x62, 0xb1, 0x3d, 0xea, 0x90, 0x84, 0x30, 0x5e, 0xd4, 0x39, 0x84, 0x78, 0xd9, 0x75, 0xd6, 0xce, 0x2a, 0x11, 0x29, 0x69, 0xa4, 0x5e, 0xaa, 0x2a, 0x98, 0x5a, 0xe5, 0x91, 0x8f, 0xb2, 0xfb, 0xda, 0x97, 0xe8, 0x83, 0x6f, 0x04, 0xb9, 0x5d, 0xaf, 0xe1, 0x9b, /* (2^332)P */ 0x8b, 0xe4, 0xe1, 0x48, 0x9c, 0xc4, 0x83, 0x89, 0xdf, 0x65, 0xd3, 0x35, 0x55, 0x13, 0xf4, 0x1f, 0x36, 0x92, 0x33, 0x38, 0xcb, 0xed, 0x15, 0xe6, 0x60, 0x2d, 0x25, 0xf5, 0x36, 0x60, 0x3a, 0x37, 0x9b, 0x71, 0x9d, 0x42, 0xb0, 0x14, 0xc8, 0xba, 0x62, 0xa3, 0x49, 0xb0, 0x88, 0xc1, 0x72, 0x73, 0xdd, 0x62, 0x40, 0xa9, 0x62, 0x88, 0x99, 0xca, /* (2^333)P */ 0x47, 0x7b, 0xea, 0xda, 0x46, 0x2f, 0x45, 0xc6, 0xe3, 0xb4, 0x4d, 0x8d, 0xac, 0x0b, 0x54, 0x22, 0x06, 0x31, 0x16, 0x66, 0x3e, 0xe4, 0x38, 0x12, 0xcd, 0xf3, 0xe7, 0x99, 0x37, 0xd9, 0x62, 0x24, 0x4b, 0x05, 0xf2, 0x58, 0xe6, 0x29, 0x4b, 0x0d, 0xf6, 0xc1, 0xba, 0xa0, 0x1e, 0x0f, 0xcb, 0x1f, 0xc6, 0x2b, 0x19, 0xfc, 0x82, 0x01, 0xd0, 0x86, /* (2^334)P */ 0xa2, 0xae, 0x77, 0x20, 0xfb, 0xa8, 0x18, 0xb4, 0x61, 0xef, 0xe8, 0x52, 0x79, 0xbb, 0x86, 0x90, 0x5d, 0x2e, 0x76, 0xed, 0x66, 0x60, 0x5d, 0x00, 0xb5, 0xa4, 0x00, 0x40, 0x89, 0xec, 0xd1, 0xd2, 0x0d, 0x26, 0xb9, 0x30, 0xb2, 0xd2, 0xb8, 0xe8, 0x0e, 0x56, 0xf9, 0x67, 0x94, 0x2e, 0x62, 0xe1, 0x79, 0x48, 0x2b, 0xa9, 0xfa, 0xea, 0xdb, 0x28, /* (2^335)P */ 0x35, 0xf1, 0xb0, 0x43, 0xbd, 0x27, 0xef, 0x18, 0x44, 0xa2, 0x04, 0xb4, 0x69, 0xa1, 0x97, 0x1f, 0x8c, 0x04, 0x82, 0x9b, 0x00, 0x6d, 0xf8, 0xbf, 0x7d, 0xc1, 0x5b, 0xab, 0xe8, 0xb2, 0x34, 0xbd, 0xaf, 0x7f, 0xb2, 0x0d, 0xf3, 0xed, 0xfc, 0x5b, 0x50, 0xee, 0xe7, 0x4a, 0x20, 0xd9, 0xf5, 0xc6, 0x9a, 0x97, 0x6d, 0x07, 0x2f, 0xb9, 0x31, 0x02, /* (2^336)P */ 0xf9, 0x54, 0x4a, 0xc5, 0x61, 0x7e, 0x1d, 0xa6, 0x0e, 0x1a, 0xa8, 0xd3, 0x8c, 0x36, 0x7d, 0xf1, 0x06, 0xb1, 0xac, 0x93, 0xcd, 0xe9, 0x8f, 0x61, 0x6c, 0x5d, 0x03, 0x23, 0xdf, 0x85, 0x53, 0x39, 0x63, 0x5e, 0xeb, 0xf3, 0xd3, 0xd3, 0x75, 0x97, 0x9b, 0x62, 0x9b, 0x01, 0xb3, 0x19, 0xd8, 0x2b, 0x36, 0xf2, 0x2c, 0x2c, 0x6f, 0x36, 0xc6, 0x3c, /* (2^337)P */ 0x05, 0x74, 0x43, 0x10, 0xb6, 0xb0, 0xf8, 0xbf, 0x02, 0x46, 0x9a, 0xee, 0xc1, 0xaf, 0xc1, 0xe5, 0x5a, 0x2e, 0xbb, 0xe1, 0xdc, 0xc6, 0xce, 0x51, 0x29, 0x50, 0xbf, 0x1b, 0xde, 0xff, 0xba, 0x4d, 0x8d, 0x8b, 0x7e, 0xe7, 0xbd, 0x5b, 0x8f, 0xbe, 0xe3, 0x75, 0x71, 0xff, 0x37, 0x05, 0x5a, 0x10, 0xeb, 0x54, 0x7e, 0x44, 0x72, 0x2c, 0xd4, 0xfc, /* (2^338)P */ 0x03, 0x12, 0x1c, 0xb2, 0x08, 0x90, 0xa1, 0x2d, 0x50, 0xa0, 0xad, 0x7f, 0x8d, 0xa6, 0x97, 0xc1, 0xbd, 0xdc, 0xc3, 0xa7, 0xad, 0x31, 0xdf, 0xb8, 0x03, 0x84, 0xc3, 0xb9, 0x29, 0x3d, 0x92, 0x2e, 0xc3, 0x90, 0x07, 0xe8, 0xa7, 0xc7, 0xbc, 0x61, 0xe9, 0x3e, 0xa0, 0x35, 0xda, 0x1d, 0xab, 0x48, 0xfe, 0x50, 0xc9, 0x25, 0x59, 0x23, 0x69, 0x3f, /* (2^339)P */ 0x8e, 0x91, 0xab, 0x6b, 0x91, 0x4f, 0x89, 0x76, 0x67, 0xad, 0xb2, 0x65, 0x9d, 0xad, 0x02, 0x36, 0xdc, 0xac, 0x96, 0x93, 0x97, 0x21, 0x14, 0xd0, 0xe8, 0x11, 0x60, 0x1e, 0xeb, 0x96, 0x06, 0xf2, 0x53, 0xf2, 0x6d, 0xb7, 0x93, 0x6f, 0x26, 0x91, 0x23, 0xe3, 0x34, 0x04, 0x92, 0x91, 0x37, 0x08, 0x50, 0xd6, 0x28, 0x09, 0x27, 0xa1, 0x0c, 0x00, /* (2^340)P */ 0x1f, 0xbb, 0x21, 0x26, 0x33, 0xcb, 0xa4, 0xd1, 0xee, 0x85, 0xf9, 0xd9, 0x3c, 0x90, 0xc3, 0xd1, 0x26, 0xa2, 0x25, 0x93, 0x43, 0x61, 0xed, 0x91, 0x6e, 0x54, 0x03, 0x2e, 0x42, 0x9d, 0xf7, 0xa6, 0x02, 0x0f, 0x2f, 0x9c, 0x7a, 0x8d, 0x12, 0xc2, 0x18, 0xfc, 0x41, 0xff, 0x85, 0x26, 0x1a, 0x44, 0x55, 0x0b, 0x89, 0xab, 0x6f, 0x62, 0x33, 0x8c, /* (2^341)P */ 0xe0, 0x3c, 0x5d, 0x70, 0x64, 0x87, 0x81, 0x35, 0xf2, 0x37, 0xa6, 0x24, 0x3e, 0xe0, 0x62, 0xd5, 0x71, 0xe7, 0x93, 0xfb, 0xac, 0xc3, 0xe7, 0xc7, 0x04, 0xe2, 0x70, 0xd3, 0x29, 0x5b, 0x21, 0xbf, 0xf4, 0x26, 0x5d, 0xf3, 0x95, 0xb4, 0x2a, 0x6a, 0x07, 0x55, 0xa6, 0x4b, 0x3b, 0x15, 0xf2, 0x25, 0x8a, 0x95, 0x3f, 0x63, 0x2f, 0x7a, 0x23, 0x96, /* (2^342)P */ 0x0d, 0x3d, 0xd9, 0x13, 0xa7, 0xb3, 0x5e, 0x67, 0xf7, 0x02, 0x23, 0xee, 0x84, 0xff, 0x99, 0xda, 0xb9, 0x53, 0xf8, 0xf0, 0x0e, 0x39, 0x2f, 0x3c, 0x64, 0x34, 0xe3, 0x09, 0xfd, 0x2b, 0x33, 0xc7, 0xfe, 0x62, 0x2b, 0x84, 0xdf, 0x2b, 0xd2, 0x7c, 0x26, 0x01, 0x70, 0x66, 0x5b, 0x85, 0xc2, 0xbe, 0x88, 0x37, 0xf1, 0x30, 0xac, 0xb8, 0x76, 0xa3, /* (2^343)P */ 0x6e, 0x01, 0xf0, 0x55, 0x35, 0xe4, 0xbd, 0x43, 0x62, 0x9d, 0xd6, 0x11, 0xef, 0x6f, 0xb8, 0x8c, 0xaa, 0x98, 0x87, 0xc6, 0x6d, 0xc4, 0xcc, 0x74, 0x92, 0x53, 0x4a, 0xdf, 0xe4, 0x08, 0x89, 0x17, 0xd0, 0x0f, 0xf4, 0x00, 0x60, 0x78, 0x08, 0x44, 0xb5, 0xda, 0x18, 0xed, 0x98, 0xc8, 0x61, 0x3d, 0x39, 0xdb, 0xcf, 0x1d, 0x49, 0x40, 0x65, 0x75, /* (2^344)P */ 0x8e, 0x10, 0xae, 0x5f, 0x06, 0xd2, 0x95, 0xfd, 0x20, 0x16, 0x49, 0x5b, 0x57, 0xbe, 0x22, 0x8b, 0x43, 0xfb, 0xe6, 0xcc, 0x26, 0xa5, 0x5d, 0xd3, 0x68, 0xc5, 0xf9, 0x5a, 0x86, 0x24, 0x87, 0x27, 0x05, 0xfd, 0xe2, 0xff, 0xb3, 0xa3, 0x7b, 0x37, 0x59, 0xc5, 0x4e, 0x14, 0x94, 0xf9, 0x3b, 0xcb, 0x7c, 0xed, 0xca, 0x1d, 0xb2, 0xac, 0x05, 0x4a, /* (2^345)P */ 0xf4, 0xd1, 0x81, 0xeb, 0x89, 0xbf, 0xfe, 0x1e, 0x41, 0x92, 0x29, 0xee, 0xe1, 0x43, 0xf5, 0x86, 0x1d, 0x2f, 0xbb, 0x1e, 0x84, 0x5d, 0x7b, 0x8d, 0xd5, 0xda, 0xee, 0x1e, 0x8a, 0xd0, 0x27, 0xf2, 0x60, 0x51, 0x59, 0x82, 0xf4, 0x84, 0x2b, 0x5b, 0x14, 0x2d, 0x81, 0x82, 0x3e, 0x2b, 0xb4, 0x6d, 0x51, 0x4f, 0xc5, 0xcb, 0xbf, 0x74, 0xe3, 0xb4, /* (2^346)P */ 0x19, 0x2f, 0x22, 0xb3, 0x04, 0x5f, 0x81, 0xca, 0x05, 0x60, 0xb9, 0xaa, 0xee, 0x0e, 0x2f, 0x48, 0x38, 0xf9, 0x91, 0xb4, 0x66, 0xe4, 0x57, 0x28, 0x54, 0x10, 0xe9, 0x61, 0x9d, 0xd4, 0x90, 0x75, 0xb1, 0x39, 0x23, 0xb6, 0xfc, 0x82, 0xe0, 0xfa, 0xbb, 0x5c, 0x6e, 0xc3, 0x44, 0x13, 0x00, 0x83, 0x55, 0x9e, 0x8e, 0x10, 0x61, 0x81, 0x91, 0x04, /* (2^347)P */ 0x5f, 0x2a, 0xd7, 0x81, 0xd9, 0x9c, 0xbb, 0x79, 0xbc, 0x62, 0x56, 0x98, 0x03, 0x5a, 0x18, 0x85, 0x2a, 0x9c, 0xd0, 0xfb, 0xd2, 0xb1, 0xaf, 0xef, 0x0d, 0x24, 0xc5, 0xfa, 0x39, 0xbb, 0x6b, 0xed, 0xa4, 0xdf, 0xe4, 0x87, 0xcd, 0x41, 0xd3, 0x72, 0x32, 0xc6, 0x28, 0x21, 0xb1, 0xba, 0x8b, 0xa3, 0x91, 0x79, 0x76, 0x22, 0x25, 0x10, 0x61, 0xd1, /* (2^348)P */ 0x73, 0xb5, 0x32, 0x97, 0xdd, 0xeb, 0xdd, 0x22, 0x22, 0xf1, 0x33, 0x3c, 0x77, 0x56, 0x7d, 0x6b, 0x48, 0x2b, 0x05, 0x81, 0x03, 0x03, 0x91, 0x9a, 0xe3, 0x5e, 0xd4, 0xee, 0x3f, 0xf8, 0xbb, 0x50, 0x21, 0x32, 0x4c, 0x4a, 0x58, 0x49, 0xde, 0x0c, 0xde, 0x30, 0x82, 0x3d, 0x92, 0xf0, 0x6c, 0xcc, 0x32, 0x3e, 0xd2, 0x78, 0x8a, 0x6e, 0x2c, 0xd0, /* (2^349)P */ 0xf0, 0xf7, 0xa1, 0x0b, 0xc1, 0x74, 0x85, 0xa8, 0xe9, 0xdd, 0x48, 0xa1, 0xc0, 0x16, 0xd8, 0x2b, 0x61, 0x08, 0xc2, 0x2b, 0x30, 0x26, 0x79, 0xce, 0x9e, 0xfd, 0x39, 0xd7, 0x81, 0xa4, 0x63, 0x8c, 0xd5, 0x74, 0xa0, 0x88, 0xfa, 0x03, 0x30, 0xe9, 0x7f, 0x2b, 0xc6, 0x02, 0xc9, 0x5e, 0xe4, 0xd5, 0x4d, 0x92, 0xd0, 0xf6, 0xf2, 0x5b, 0x79, 0x08, /* (2^350)P */ 0x34, 0x89, 0x81, 0x43, 0xd1, 0x94, 0x2c, 0x10, 0x54, 0x9b, 0xa0, 0xe5, 0x44, 0xe8, 0xc2, 0x2f, 0x3e, 0x0e, 0x74, 0xae, 0xba, 0xe2, 0xac, 0x85, 0x6b, 0xd3, 0x5c, 0x97, 0xf7, 0x90, 0xf1, 0x12, 0xc0, 0x03, 0xc8, 0x1f, 0x37, 0x72, 0x8c, 0x9b, 0x9c, 0x17, 0x96, 0x9d, 0xc7, 0xbf, 0xa3, 0x3f, 0x44, 0x3d, 0x87, 0x81, 0xbd, 0x81, 0xa6, 0x5f, /* (2^351)P */ 0xe4, 0xff, 0x78, 0x62, 0x82, 0x5b, 0x76, 0x58, 0xf5, 0x5b, 0xa6, 0xc4, 0x53, 0x11, 0x3b, 0x7b, 0xaa, 0x67, 0xf8, 0xea, 0x3b, 0x5d, 0x9a, 0x2e, 0x04, 0xeb, 0x4a, 0x24, 0xfb, 0x56, 0xf0, 0xa8, 0xd4, 0x14, 0xed, 0x0f, 0xfd, 0xc5, 0x26, 0x17, 0x2a, 0xf0, 0xb9, 0x13, 0x8c, 0xbd, 0x65, 0x14, 0x24, 0x95, 0x27, 0x12, 0x63, 0x2a, 0x09, 0x18, /* (2^352)P */ 0xe1, 0x5c, 0xe7, 0xe0, 0x00, 0x6a, 0x96, 0xf2, 0x49, 0x6a, 0x39, 0xa5, 0xe0, 0x17, 0x79, 0x4a, 0x63, 0x07, 0x62, 0x09, 0x61, 0x1b, 0x6e, 0xa9, 0xb5, 0x62, 0xb7, 0xde, 0xdf, 0x80, 0x4c, 0x5a, 0x99, 0x73, 0x59, 0x9d, 0xfb, 0xb1, 0x5e, 0xbe, 0xb8, 0xb7, 0x63, 0x93, 0xe8, 0xad, 0x5e, 0x1f, 0xae, 0x59, 0x1c, 0xcd, 0xb4, 0xc2, 0xb3, 0x8a, /* (2^353)P */ 0x78, 0x53, 0xa1, 0x4c, 0x70, 0x9c, 0x63, 0x7e, 0xb3, 0x12, 0x40, 0x5f, 0xbb, 0x23, 0xa7, 0xf7, 0x77, 0x96, 0x5b, 0x4d, 0x91, 0x10, 0x52, 0x85, 0x9e, 0xa5, 0x38, 0x0b, 0xfd, 0x25, 0x01, 0x4b, 0xfa, 0x4d, 0xd3, 0x3f, 0x78, 0x74, 0x42, 0xff, 0x62, 0x2d, 0x27, 0xdc, 0x9d, 0xd1, 0x29, 0x76, 0x2e, 0x78, 0xb3, 0x35, 0xfa, 0x15, 0xd5, 0x38, /* (2^354)P */ 0x8b, 0xc7, 0x43, 0xce, 0xf0, 0x5e, 0xf1, 0x0d, 0x02, 0x38, 0xe8, 0x82, 0xc9, 0x25, 0xad, 0x2d, 0x27, 0xa4, 0x54, 0x18, 0xb2, 0x30, 0x73, 0xa4, 0x41, 0x08, 0xe4, 0x86, 0xe6, 0x8c, 0xe9, 0x2a, 0x34, 0xb3, 0xd6, 0x61, 0x8f, 0x66, 0x26, 0x08, 0xb6, 0x06, 0x33, 0xaa, 0x12, 0xac, 0x72, 0xec, 0x2e, 0x52, 0xa3, 0x25, 0x3e, 0xd7, 0x62, 0xe8, /* (2^355)P */ 0xc4, 0xbb, 0x89, 0xc8, 0x40, 0xcc, 0x84, 0xec, 0x4a, 0xd9, 0xc4, 0x55, 0x78, 0x00, 0xcf, 0xd8, 0xe9, 0x24, 0x59, 0xdc, 0x5e, 0xf0, 0x66, 0xa1, 0x83, 0xae, 0x97, 0x18, 0xc5, 0x54, 0x27, 0xa2, 0x21, 0x52, 0x03, 0x31, 0x5b, 0x11, 0x67, 0xf6, 0x12, 0x00, 0x87, 0x2f, 0xff, 0x59, 0x70, 0x8f, 0x6d, 0x71, 0xab, 0xab, 0x24, 0xb8, 0xba, 0x35, /* (2^356)P */ 0x69, 0x43, 0xa7, 0x14, 0x06, 0x96, 0xe9, 0xc2, 0xe3, 0x2b, 0x45, 0x22, 0xc0, 0xd0, 0x2f, 0x34, 0xd1, 0x01, 0x99, 0xfc, 0x99, 0x38, 0xa1, 0x25, 0x2e, 0x59, 0x6c, 0x27, 0xc9, 0xeb, 0x7b, 0xdc, 0x4e, 0x26, 0x68, 0xba, 0xfa, 0xec, 0x02, 0x05, 0x64, 0x80, 0x30, 0x20, 0x5c, 0x26, 0x7f, 0xaf, 0x95, 0x17, 0x3d, 0x5c, 0x9e, 0x96, 0x96, 0xaf, /* (2^357)P */ 0xa6, 0xba, 0x21, 0x29, 0x32, 0xe2, 0x98, 0xde, 0x9b, 0x6d, 0x0b, 0x44, 0x91, 0xa8, 0x3e, 0xd4, 0xb8, 0x04, 0x6c, 0xf6, 0x04, 0x39, 0xbd, 0x52, 0x05, 0x15, 0x27, 0x78, 0x8e, 0x55, 0xac, 0x79, 0xc5, 0xe6, 0x00, 0x7f, 0x90, 0xa2, 0xdd, 0x07, 0x13, 0xe0, 0x24, 0x70, 0x5c, 0x0f, 0x4d, 0xa9, 0xf9, 0xae, 0xcb, 0x34, 0x10, 0x9d, 0x89, 0x9d, /* (2^358)P */ 0x12, 0xe0, 0xb3, 0x9f, 0xc4, 0x96, 0x1d, 0xcf, 0xed, 0x99, 0x64, 0x28, 0x8d, 0xc7, 0x31, 0x82, 0xee, 0x5e, 0x75, 0x48, 0xff, 0x3a, 0xf2, 0x09, 0x34, 0x03, 0x93, 0x52, 0x19, 0xb2, 0xc5, 0x81, 0x93, 0x45, 0x5e, 0x59, 0x21, 0x2b, 0xec, 0x89, 0xba, 0x36, 0x6e, 0xf9, 0x82, 0x75, 0x7e, 0x82, 0x3f, 0xaa, 0xe2, 0xe3, 0x3b, 0x94, 0xfd, 0x98, /* (2^359)P */ 0x7c, 0xdb, 0x75, 0x31, 0x61, 0xfb, 0x15, 0x28, 0x94, 0xd7, 0xc3, 0x5a, 0xa9, 0xa1, 0x0a, 0x66, 0x0f, 0x2b, 0x13, 0x3e, 0x42, 0xb5, 0x28, 0x3a, 0xca, 0x83, 0xf3, 0x61, 0x22, 0xf4, 0x40, 0xc5, 0xdf, 0xe7, 0x31, 0x9f, 0x7e, 0x51, 0x75, 0x06, 0x9d, 0x51, 0xc8, 0xe7, 0x9f, 0xc3, 0x71, 0x4f, 0x3d, 0x5b, 0xfb, 0xe9, 0x8e, 0x08, 0x40, 0x8e, /* (2^360)P */ 0xf7, 0x31, 0xad, 0x50, 0x5d, 0x25, 0x93, 0x73, 0x68, 0xf6, 0x7c, 0x89, 0x5a, 0x3d, 0x9f, 0x9b, 0x05, 0x82, 0xe7, 0x70, 0x4b, 0x19, 0xaa, 0xcf, 0xff, 0xde, 0x50, 0x8f, 0x2f, 0x69, 0xd3, 0xf0, 0x99, 0x51, 0x6b, 0x9d, 0xb6, 0x56, 0x6f, 0xf8, 0x4c, 0x74, 0x8b, 0x4c, 0x91, 0xf9, 0xa9, 0xb1, 0x3e, 0x07, 0xdf, 0x0b, 0x27, 0x8a, 0xb1, 0xed, /* (2^361)P */ 0xfb, 0x67, 0xd9, 0x48, 0xd2, 0xe4, 0x44, 0x9b, 0x43, 0x15, 0x8a, 0xeb, 0x00, 0x53, 0xad, 0x25, 0xc7, 0x7e, 0x19, 0x30, 0x87, 0xb7, 0xd5, 0x5f, 0x04, 0xf8, 0xaa, 0xdd, 0x57, 0xae, 0x34, 0x75, 0xe2, 0x84, 0x4b, 0x54, 0x60, 0x37, 0x95, 0xe4, 0xd3, 0xec, 0xac, 0xef, 0x47, 0x31, 0xa3, 0xc8, 0x31, 0x22, 0xdb, 0x26, 0xe7, 0x6a, 0xb5, 0xad, /* (2^362)P */ 0x44, 0x09, 0x5c, 0x95, 0xe4, 0x72, 0x3c, 0x1a, 0xd1, 0xac, 0x42, 0x51, 0x99, 0x6f, 0xfa, 0x1f, 0xf2, 0x22, 0xbe, 0xff, 0x7b, 0x66, 0xf5, 0x6c, 0xb3, 0x66, 0xc7, 0x4d, 0x78, 0x31, 0x83, 0x80, 0xf5, 0x41, 0xe9, 0x7f, 0xbe, 0xf7, 0x23, 0x49, 0x6b, 0x84, 0x4e, 0x7e, 0x47, 0x07, 0x6e, 0x74, 0xdf, 0xe5, 0x9d, 0x9e, 0x56, 0x2a, 0xc0, 0xbc, /* (2^363)P */ 0xac, 0x10, 0x80, 0x8c, 0x7c, 0xfa, 0x83, 0xdf, 0xb3, 0xd0, 0xc4, 0xbe, 0xfb, 0x9f, 0xac, 0xc9, 0xc3, 0x40, 0x95, 0x0b, 0x09, 0x23, 0xda, 0x63, 0x67, 0xcf, 0xe7, 0x9f, 0x7d, 0x7b, 0x6b, 0xe2, 0xe6, 0x6d, 0xdb, 0x87, 0x9e, 0xa6, 0xff, 0x6d, 0xab, 0xbd, 0xfb, 0x54, 0x84, 0x68, 0xcf, 0x89, 0xf1, 0xd0, 0xe2, 0x85, 0x61, 0xdc, 0x22, 0xd1, /* (2^364)P */ 0xa8, 0x48, 0xfb, 0x8c, 0x6a, 0x63, 0x01, 0x72, 0x43, 0x43, 0xeb, 0x21, 0xa3, 0x00, 0x8a, 0xc0, 0x87, 0x51, 0x9e, 0x86, 0x75, 0x16, 0x79, 0xf9, 0x6b, 0x11, 0x80, 0x62, 0xc2, 0x9d, 0xb8, 0x8c, 0x30, 0x8e, 0x8d, 0x03, 0x52, 0x7e, 0x31, 0x59, 0x38, 0xf9, 0x25, 0xc7, 0x0f, 0xc7, 0xa8, 0x2b, 0x5c, 0x80, 0xfa, 0x90, 0xa2, 0x63, 0xca, 0xe7, /* (2^365)P */ 0xf1, 0x5d, 0xb5, 0xd9, 0x20, 0x10, 0x7d, 0x0f, 0xc5, 0x50, 0x46, 0x07, 0xff, 0x02, 0x75, 0x2b, 0x4a, 0xf3, 0x39, 0x91, 0x72, 0xb7, 0xd5, 0xcc, 0x38, 0xb8, 0xe7, 0x36, 0x26, 0x5e, 0x11, 0x97, 0x25, 0xfb, 0x49, 0x68, 0xdc, 0xb4, 0x46, 0x87, 0x5c, 0xc2, 0x7f, 0xaa, 0x7d, 0x36, 0x23, 0xa6, 0xc6, 0x53, 0xec, 0xbc, 0x57, 0x47, 0xc1, 0x2b, /* (2^366)P */ 0x25, 0x5d, 0x7d, 0x95, 0xda, 0x0b, 0x8f, 0x78, 0x1e, 0x19, 0x09, 0xfa, 0x67, 0xe0, 0xa0, 0x17, 0x24, 0x76, 0x6c, 0x30, 0x1f, 0x62, 0x3d, 0xbe, 0x45, 0x70, 0xcc, 0xb6, 0x1e, 0x68, 0x06, 0x25, 0x68, 0x16, 0x1a, 0x33, 0x3f, 0x90, 0xc7, 0x78, 0x2d, 0x98, 0x3c, 0x2f, 0xb9, 0x2d, 0x94, 0x0b, 0xfb, 0x49, 0x56, 0x30, 0xd7, 0xc1, 0xe6, 0x48, /* (2^367)P */ 0x7a, 0xd1, 0xe0, 0x8e, 0x67, 0xfc, 0x0b, 0x50, 0x1f, 0x84, 0x98, 0xfa, 0xaf, 0xae, 0x2e, 0x31, 0x27, 0xcf, 0x3f, 0xf2, 0x6e, 0x8d, 0x81, 0x8f, 0xd2, 0x5f, 0xde, 0xd3, 0x5e, 0xe9, 0xe7, 0x13, 0x48, 0x83, 0x5a, 0x4e, 0x84, 0xd1, 0x58, 0xcf, 0x6b, 0x84, 0xdf, 0x13, 0x1d, 0x91, 0x85, 0xe8, 0xcb, 0x29, 0x79, 0xd2, 0xca, 0xac, 0x6a, 0x93, /* (2^368)P */ 0x53, 0x82, 0xce, 0x61, 0x96, 0x88, 0x6f, 0xe1, 0x4a, 0x4c, 0x1e, 0x30, 0x73, 0xe8, 0x74, 0xde, 0x40, 0x2b, 0xe0, 0xc4, 0xb5, 0xd8, 0x7c, 0x15, 0xe7, 0xe1, 0xb1, 0xe0, 0xd6, 0x88, 0xb1, 0x6a, 0x57, 0x19, 0x6a, 0x22, 0x66, 0x57, 0xf6, 0x8d, 0xfd, 0xc0, 0xf2, 0xa3, 0x03, 0x56, 0xfb, 0x2e, 0x75, 0x5e, 0xc7, 0x8e, 0x22, 0x96, 0x5c, 0x06, /* (2^369)P */ 0x98, 0x7e, 0xbf, 0x3e, 0xbf, 0x24, 0x9d, 0x15, 0xd3, 0xf6, 0xd3, 0xd2, 0xf0, 0x11, 0xf2, 0xdb, 0x36, 0x23, 0x38, 0xf7, 0x1d, 0x71, 0x20, 0xd2, 0x54, 0x7f, 0x1e, 0x24, 0x8f, 0xe2, 0xaa, 0xf7, 0x3f, 0x6b, 0x41, 0x4e, 0xdc, 0x0e, 0xec, 0xe8, 0x35, 0x0a, 0x08, 0x6d, 0x89, 0x5b, 0x32, 0x91, 0x01, 0xb6, 0xe0, 0x2c, 0xc6, 0xa1, 0xbe, 0xb4, /* (2^370)P */ 0x29, 0xf2, 0x1e, 0x1c, 0xdc, 0x68, 0x8a, 0x43, 0x87, 0x2c, 0x48, 0xb3, 0x9e, 0xed, 0xd2, 0x82, 0x46, 0xac, 0x2f, 0xef, 0x93, 0x34, 0x37, 0xca, 0x64, 0x8d, 0xc9, 0x06, 0x90, 0xbb, 0x78, 0x0a, 0x3c, 0x4c, 0xcf, 0x35, 0x7a, 0x0f, 0xf7, 0xa7, 0xf4, 0x2f, 0x45, 0x69, 0x3f, 0xa9, 0x5d, 0xce, 0x7b, 0x8a, 0x84, 0xc3, 0xae, 0xf4, 0xda, 0xd5, /* (2^371)P */ 0xca, 0xba, 0x95, 0x43, 0x05, 0x7b, 0x06, 0xd9, 0x5c, 0x0a, 0x18, 0x5f, 0x6a, 0x6a, 0xce, 0xc0, 0x3d, 0x95, 0x51, 0x0e, 0x1a, 0xbe, 0x85, 0x7a, 0xf2, 0x69, 0xec, 0xc0, 0x8c, 0xca, 0xa3, 0x32, 0x0a, 0x76, 0x50, 0xc6, 0x76, 0x61, 0x00, 0x89, 0xbf, 0x6e, 0x0f, 0x48, 0x90, 0x31, 0x93, 0xec, 0x34, 0x70, 0xf0, 0xc3, 0x8d, 0xf0, 0x0f, 0xb5, /* (2^372)P */ 0xbe, 0x23, 0xe2, 0x18, 0x99, 0xf1, 0xed, 0x8a, 0xf6, 0xc9, 0xac, 0xb8, 0x1e, 0x9a, 0x3c, 0x15, 0xae, 0xd7, 0x6d, 0xb3, 0x04, 0xee, 0x5b, 0x0d, 0x1e, 0x79, 0xb7, 0xf9, 0xf9, 0x8d, 0xad, 0xf9, 0x8f, 0x5a, 0x6a, 0x7b, 0xd7, 0x9b, 0xca, 0x62, 0xfe, 0x9c, 0xc0, 0x6f, 0x6d, 0x9d, 0x76, 0xa3, 0x69, 0xb9, 0x4c, 0xa1, 0xc4, 0x0c, 0x76, 0xaa, /* (2^373)P */ 0x1c, 0x06, 0xfe, 0x3f, 0x45, 0x70, 0xcd, 0x97, 0xa9, 0xa2, 0xb1, 0xd3, 0xf2, 0xa5, 0x0c, 0x49, 0x2c, 0x75, 0x73, 0x1f, 0xcf, 0x00, 0xaf, 0xd5, 0x2e, 0xde, 0x0d, 0x8f, 0x8f, 0x7c, 0xc4, 0x58, 0xce, 0xd4, 0xf6, 0x24, 0x19, 0x2e, 0xd8, 0xc5, 0x1d, 0x1a, 0x3f, 0xb8, 0x4f, 0xbc, 0x7d, 0xbd, 0x68, 0xe3, 0x81, 0x98, 0x1b, 0xa8, 0xc9, 0xd9, /* (2^374)P */ 0x39, 0x95, 0x78, 0x24, 0x6c, 0x38, 0xe4, 0xe7, 0xd0, 0x8d, 0xb9, 0x38, 0x71, 0x5e, 0xc1, 0x62, 0x80, 0xcc, 0xcb, 0x8c, 0x97, 0xca, 0xf8, 0xb9, 0xd9, 0x9c, 0xce, 0x72, 0x7b, 0x70, 0xee, 0x5f, 0xea, 0xa2, 0xdf, 0xa9, 0x14, 0x10, 0xf9, 0x6e, 0x59, 0x9f, 0x9c, 0xe0, 0x0c, 0xb2, 0x07, 0x97, 0xcd, 0xd2, 0x89, 0x16, 0xfd, 0x9c, 0xa8, 0xa5, /* (2^375)P */ 0x5a, 0x61, 0xf1, 0x59, 0x7c, 0x38, 0xda, 0xe2, 0x85, 0x99, 0x68, 0xe9, 0xc9, 0xf7, 0x32, 0x7e, 0xc4, 0xca, 0xb7, 0x11, 0x08, 0x69, 0x2b, 0x66, 0x02, 0xf7, 0x2e, 0x18, 0xc3, 0x8e, 0xe1, 0xf9, 0xc5, 0x19, 0x9a, 0x0a, 0x9c, 0x07, 0xba, 0xc7, 0x9c, 0x03, 0x34, 0x89, 0x99, 0x67, 0x0b, 0x16, 0x4b, 0x07, 0x36, 0x16, 0x36, 0x2c, 0xe2, 0xa1, /* (2^376)P */ 0x70, 0x10, 0x91, 0x27, 0xa8, 0x24, 0x8e, 0x29, 0x04, 0x6f, 0x79, 0x1f, 0xd3, 0xa5, 0x68, 0xd3, 0x0b, 0x7d, 0x56, 0x4d, 0x14, 0x57, 0x7b, 0x2e, 0x00, 0x9f, 0x9a, 0xfd, 0x6c, 0x63, 0x18, 0x81, 0xdb, 0x9d, 0xb7, 0xd7, 0xa4, 0x1e, 0xe8, 0x40, 0xf1, 0x4c, 0xa3, 0x01, 0xd5, 0x4b, 0x75, 0xea, 0xdd, 0x97, 0xfd, 0x5b, 0xb2, 0x66, 0x6a, 0x24, /* (2^377)P */ 0x72, 0x11, 0xfe, 0x73, 0x1b, 0xd3, 0xea, 0x7f, 0x93, 0x15, 0x15, 0x05, 0xfe, 0x40, 0xe8, 0x28, 0xd8, 0x50, 0x47, 0x66, 0xfa, 0xb7, 0xb5, 0x04, 0xba, 0x35, 0x1e, 0x32, 0x9f, 0x5f, 0x32, 0xba, 0x3d, 0xd1, 0xed, 0x9a, 0x76, 0xca, 0xa3, 0x3e, 0x77, 0xd8, 0xd8, 0x7c, 0x5f, 0x68, 0x42, 0xb5, 0x86, 0x7f, 0x3b, 0xc9, 0xc1, 0x89, 0x64, 0xda, /* (2^378)P */ 0xd5, 0xd4, 0x17, 0x31, 0xfc, 0x6a, 0xfd, 0xb8, 0xe8, 0xe5, 0x3e, 0x39, 0x06, 0xe4, 0xd1, 0x90, 0x2a, 0xca, 0xf6, 0x54, 0x6c, 0x1b, 0x2f, 0x49, 0x97, 0xb1, 0x2a, 0x82, 0x43, 0x3d, 0x1f, 0x8b, 0xe2, 0x47, 0xc5, 0x24, 0xa8, 0xd5, 0x53, 0x29, 0x7d, 0xc6, 0x87, 0xa6, 0x25, 0x3a, 0x64, 0xdd, 0x71, 0x08, 0x9e, 0xcd, 0xe9, 0x45, 0xc7, 0xba, /* (2^379)P */ 0x37, 0x72, 0x6d, 0x13, 0x7a, 0x8d, 0x04, 0x31, 0xe6, 0xe3, 0x9e, 0x36, 0x71, 0x3e, 0xc0, 0x1e, 0xe3, 0x71, 0xd3, 0x49, 0x4e, 0x4a, 0x36, 0x42, 0x68, 0x68, 0x61, 0xc7, 0x3c, 0xdb, 0x81, 0x49, 0xf7, 0x91, 0x4d, 0xea, 0x4c, 0x4f, 0x98, 0xc6, 0x7e, 0x60, 0x84, 0x4b, 0x6a, 0x37, 0xbb, 0x52, 0xf7, 0xce, 0x02, 0xe4, 0xad, 0xd1, 0x3c, 0xa7, /* (2^380)P */ 0x51, 0x06, 0x2d, 0xf8, 0x08, 0xe8, 0xf1, 0x0c, 0xe5, 0xa9, 0xac, 0x29, 0x73, 0x3b, 0xed, 0x98, 0x5f, 0x55, 0x08, 0x38, 0x51, 0x44, 0x36, 0x5d, 0xea, 0xc3, 0xb8, 0x0e, 0xa0, 0x4f, 0xd2, 0x79, 0xe9, 0x98, 0xc3, 0xf5, 0x00, 0xb9, 0x26, 0x27, 0x42, 0xa8, 0x07, 0xc1, 0x12, 0x31, 0xc1, 0xc3, 0x3c, 0x3b, 0x7a, 0x72, 0x97, 0xc2, 0x70, 0x3a, /* (2^381)P */ 0xf4, 0xb2, 0xba, 0x32, 0xbc, 0xa9, 0x2f, 0x87, 0xc7, 0x3c, 0x45, 0xcd, 0xae, 0xe2, 0x13, 0x6d, 0x3a, 0xf2, 0xf5, 0x66, 0x97, 0x29, 0xaf, 0x53, 0x9f, 0xda, 0xea, 0x14, 0xdf, 0x04, 0x98, 0x19, 0x95, 0x9e, 0x2a, 0x00, 0x5c, 0x9d, 0x1d, 0xf0, 0x39, 0x23, 0xff, 0xfc, 0xca, 0x36, 0xb7, 0xde, 0xdf, 0x37, 0x78, 0x52, 0x21, 0xfa, 0x19, 0x10, /* (2^382)P */ 0x50, 0x20, 0x73, 0x74, 0x62, 0x21, 0xf2, 0xf7, 0x9b, 0x66, 0x85, 0x34, 0x74, 0xd4, 0x9d, 0x60, 0xd7, 0xbc, 0xc8, 0x46, 0x3b, 0xb8, 0x80, 0x42, 0x15, 0x0a, 0x6c, 0x35, 0x1a, 0x69, 0xf0, 0x1d, 0x4b, 0x29, 0x54, 0x5a, 0x9a, 0x48, 0xec, 0x9f, 0x37, 0x74, 0x91, 0xd0, 0xd1, 0x9e, 0x00, 0xc2, 0x76, 0x56, 0xd6, 0xa0, 0x15, 0x14, 0x83, 0x59, /* (2^383)P */ 0xc2, 0xf8, 0x22, 0x20, 0x23, 0x07, 0xbd, 0x1d, 0x6f, 0x1e, 0x8c, 0x56, 0x06, 0x6a, 0x4b, 0x9f, 0xe2, 0xa9, 0x92, 0x46, 0x4b, 0x46, 0x59, 0xd7, 0xe1, 0xda, 0x14, 0x98, 0x07, 0x65, 0x7e, 0x28, 0x20, 0xf2, 0x9d, 0x4f, 0x36, 0x5c, 0x92, 0xe0, 0x9d, 0xfe, 0x3e, 0xda, 0xe4, 0x47, 0x19, 0x3c, 0x00, 0x7f, 0x22, 0xf2, 0x9e, 0x51, 0xae, 0x4d, /* (2^384)P */ 0xbe, 0x8c, 0x1b, 0x10, 0xb6, 0xad, 0xcc, 0xcc, 0xd8, 0x5e, 0x21, 0xa6, 0xfb, 0xf1, 0xf6, 0xbd, 0x0a, 0x24, 0x67, 0xb4, 0x57, 0x7a, 0xbc, 0xe8, 0xe9, 0xff, 0xee, 0x0a, 0x1f, 0xee, 0xbd, 0xc8, 0x44, 0xed, 0x2b, 0xbb, 0x55, 0x1f, 0xdd, 0x7c, 0xb3, 0xeb, 0x3f, 0x63, 0xa1, 0x28, 0x91, 0x21, 0xab, 0x71, 0xc6, 0x4c, 0xd0, 0xe9, 0xb0, 0x21, /* (2^385)P */ 0xad, 0xc9, 0x77, 0x2b, 0xee, 0x89, 0xa4, 0x7b, 0xfd, 0xf9, 0xf6, 0x14, 0xe4, 0xed, 0x1a, 0x16, 0x9b, 0x78, 0x41, 0x43, 0xa8, 0x83, 0x72, 0x06, 0x2e, 0x7c, 0xdf, 0xeb, 0x7e, 0xdd, 0xd7, 0x8b, 0xea, 0x9a, 0x2b, 0x03, 0xba, 0x57, 0xf3, 0xf1, 0xd9, 0xe5, 0x09, 0xc5, 0x98, 0x61, 0x1c, 0x51, 0x6d, 0x5d, 0x6e, 0xfb, 0x5e, 0x95, 0x9f, 0xb5, /* (2^386)P */ 0x23, 0xe2, 0x1e, 0x95, 0xa3, 0x5e, 0x42, 0x10, 0xc7, 0xc3, 0x70, 0xbf, 0x4b, 0x6b, 0x83, 0x36, 0x93, 0xb7, 0x68, 0x47, 0x88, 0x3a, 0x10, 0x88, 0x48, 0x7f, 0x8c, 0xae, 0x54, 0x10, 0x02, 0xa4, 0x52, 0x8f, 0x8d, 0xf7, 0x26, 0x4f, 0x50, 0xc3, 0x6a, 0xe2, 0x4e, 0x3b, 0x4c, 0xb9, 0x8a, 0x14, 0x15, 0x6d, 0x21, 0x29, 0xb3, 0x6e, 0x4e, 0xd0, /* (2^387)P */ 0x4c, 0x8a, 0x18, 0x3f, 0xb7, 0x20, 0xfd, 0x3e, 0x54, 0xca, 0x68, 0x3c, 0xea, 0x6f, 0xf4, 0x6b, 0xa2, 0xbd, 0x01, 0xbd, 0xfe, 0x08, 0xa8, 0xd8, 0xc2, 0x20, 0x36, 0x05, 0xcd, 0xe9, 0xf3, 0x9e, 0xfa, 0x85, 0x66, 0x8f, 0x4b, 0x1d, 0x8c, 0x64, 0x4f, 0xb8, 0xc6, 0x0f, 0x5b, 0x57, 0xd8, 0x24, 0x19, 0x5a, 0x14, 0x4b, 0x92, 0xd3, 0x96, 0xbc, /* (2^388)P */ 0xa9, 0x3f, 0xc9, 0x6c, 0xca, 0x64, 0x1e, 0x6f, 0xdf, 0x65, 0x7f, 0x9a, 0x47, 0x6b, 0x8a, 0x60, 0x31, 0xa6, 0x06, 0xac, 0x69, 0x30, 0xe6, 0xea, 0x63, 0x42, 0x26, 0x5f, 0xdb, 0xd0, 0xf2, 0x8e, 0x34, 0x0a, 0x3a, 0xeb, 0xf3, 0x79, 0xc8, 0xb7, 0x60, 0x56, 0x5c, 0x37, 0x95, 0x71, 0xf8, 0x7f, 0x49, 0x3e, 0x9e, 0x01, 0x26, 0x1e, 0x80, 0x9f, /* (2^389)P */ 0xf8, 0x16, 0x9a, 0xaa, 0xb0, 0x28, 0xb5, 0x8e, 0xd0, 0x60, 0xe5, 0x26, 0xa9, 0x47, 0xc4, 0x5c, 0xa9, 0x39, 0xfe, 0x0a, 0xd8, 0x07, 0x2b, 0xb3, 0xce, 0xf1, 0xea, 0x1a, 0xf4, 0x7b, 0x98, 0x31, 0x3d, 0x13, 0x29, 0x80, 0xe8, 0x0d, 0xcf, 0x56, 0x39, 0x86, 0x50, 0x0c, 0xb3, 0x18, 0xf4, 0xc5, 0xca, 0xf2, 0x6f, 0xcd, 0x8d, 0xd5, 0x02, 0xb0, /* (2^390)P */ 0xbf, 0x39, 0x3f, 0xac, 0x6d, 0x1a, 0x6a, 0xe4, 0x42, 0x24, 0xd6, 0x41, 0x9d, 0xb9, 0x5b, 0x46, 0x73, 0x93, 0x76, 0xaa, 0xb7, 0x37, 0x36, 0xa6, 0x09, 0xe5, 0x04, 0x3b, 0x66, 0xc4, 0x29, 0x3e, 0x41, 0xc2, 0xcb, 0xe5, 0x17, 0xd7, 0x34, 0x67, 0x1d, 0x2c, 0x12, 0xec, 0x24, 0x7a, 0x40, 0xa2, 0x45, 0x41, 0xf0, 0x75, 0xed, 0x43, 0x30, 0xc9, /* (2^391)P */ 0x80, 0xf6, 0x47, 0x5b, 0xad, 0x54, 0x02, 0xbc, 0xdd, 0xa4, 0xb2, 0xd7, 0x42, 0x95, 0xf2, 0x0d, 0x1b, 0xef, 0x37, 0xa7, 0xb4, 0x34, 0x04, 0x08, 0x71, 0x1b, 0xd3, 0xdf, 0xa1, 0xf0, 0x2b, 0xfa, 0xc0, 0x1f, 0xf3, 0x44, 0xb5, 0xc6, 0x47, 0x3d, 0x65, 0x67, 0x45, 0x4d, 0x2f, 0xde, 0x52, 0x73, 0xfc, 0x30, 0x01, 0x6b, 0xc1, 0x03, 0xd8, 0xd7, /* (2^392)P */ 0x1c, 0x67, 0x55, 0x3e, 0x01, 0x17, 0x0f, 0x3e, 0xe5, 0x34, 0x58, 0xfc, 0xcb, 0x71, 0x24, 0x74, 0x5d, 0x36, 0x1e, 0x89, 0x2a, 0x63, 0xf8, 0xf8, 0x9f, 0x50, 0x9f, 0x32, 0x92, 0x29, 0xd8, 0x1a, 0xec, 0x76, 0x57, 0x6c, 0x67, 0x12, 0x6a, 0x6e, 0xef, 0x97, 0x1f, 0xc3, 0x77, 0x60, 0x3c, 0x22, 0xcb, 0xc7, 0x04, 0x1a, 0x89, 0x2d, 0x10, 0xa6, /* (2^393)P */ 0x12, 0xf5, 0xa9, 0x26, 0x16, 0xd9, 0x3c, 0x65, 0x5d, 0x83, 0xab, 0xd1, 0x70, 0x6b, 0x1c, 0xdb, 0xe7, 0x86, 0x0d, 0xfb, 0xe7, 0xf8, 0x2a, 0x58, 0x6e, 0x7a, 0x66, 0x13, 0x53, 0x3a, 0x6f, 0x8d, 0x43, 0x5f, 0x14, 0x23, 0x14, 0xff, 0x3d, 0x52, 0x7f, 0xee, 0xbd, 0x7a, 0x34, 0x8b, 0x35, 0x24, 0xc3, 0x7a, 0xdb, 0xcf, 0x22, 0x74, 0x9a, 0x8f, /* (2^394)P */ 0xdb, 0x20, 0xfc, 0xe5, 0x39, 0x4e, 0x7d, 0x78, 0xee, 0x0b, 0xbf, 0x1d, 0x80, 0xd4, 0x05, 0x4f, 0xb9, 0xd7, 0x4e, 0x94, 0x88, 0x9a, 0x50, 0x78, 0x1a, 0x70, 0x8c, 0xcc, 0x25, 0xb6, 0x61, 0x09, 0xdc, 0x7b, 0xea, 0x3f, 0x7f, 0xea, 0x2a, 0x0d, 0x47, 0x1c, 0x8e, 0xa6, 0x5b, 0xd2, 0xa3, 0x61, 0x93, 0x3c, 0x68, 0x9f, 0x8b, 0xea, 0xb0, 0xcb, /* (2^395)P */ 0xff, 0x54, 0x02, 0x19, 0xae, 0x8b, 0x4c, 0x2c, 0x3a, 0xe0, 0xe4, 0xac, 0x87, 0xf7, 0x51, 0x45, 0x41, 0x43, 0xdc, 0xaa, 0xcd, 0xcb, 0xdc, 0x40, 0xe3, 0x44, 0x3b, 0x1d, 0x9e, 0x3d, 0xb9, 0x82, 0xcc, 0x7a, 0xc5, 0x12, 0xf8, 0x1e, 0xdd, 0xdb, 0x8d, 0xb0, 0x2a, 0xe8, 0xe6, 0x6c, 0x94, 0x3b, 0xb7, 0x2d, 0xba, 0x79, 0x3b, 0xb5, 0x86, 0xfb, /* (2^396)P */ 0x82, 0x88, 0x13, 0xdd, 0x6c, 0xcd, 0x85, 0x2b, 0x90, 0x86, 0xb7, 0xac, 0x16, 0xa6, 0x6e, 0x6a, 0x94, 0xd8, 0x1e, 0x4e, 0x41, 0x0f, 0xce, 0x81, 0x6a, 0xa8, 0x26, 0x56, 0x43, 0x52, 0x52, 0xe6, 0xff, 0x88, 0xcf, 0x47, 0x05, 0x1d, 0xff, 0xf3, 0xa0, 0x10, 0xb2, 0x97, 0x87, 0xeb, 0x47, 0xbb, 0xfa, 0x1f, 0xe8, 0x4c, 0xce, 0xc4, 0xcd, 0x93, /* (2^397)P */ 0xf4, 0x11, 0xf5, 0x8d, 0x89, 0x29, 0x79, 0xb3, 0x59, 0x0b, 0x29, 0x7d, 0x9c, 0x12, 0x4a, 0x65, 0x72, 0x3a, 0xf9, 0xec, 0x37, 0x18, 0x86, 0xef, 0x44, 0x07, 0x25, 0x74, 0x76, 0x53, 0xed, 0x51, 0x01, 0xc6, 0x28, 0xc5, 0xc3, 0x4a, 0x0f, 0x99, 0xec, 0xc8, 0x40, 0x5a, 0x83, 0x30, 0x79, 0xa2, 0x3e, 0x63, 0x09, 0x2d, 0x6f, 0x23, 0x54, 0x1c, /* (2^398)P */ 0x5c, 0x6f, 0x3b, 0x1c, 0x30, 0x77, 0x7e, 0x87, 0x66, 0x83, 0x2e, 0x7e, 0x85, 0x50, 0xfd, 0xa0, 0x7a, 0xc2, 0xf5, 0x0f, 0xc1, 0x64, 0xe7, 0x0b, 0xbd, 0x59, 0xa7, 0xe7, 0x65, 0x53, 0xc3, 0xf5, 0x55, 0x5b, 0xe1, 0x82, 0x30, 0x5a, 0x61, 0xcd, 0xa0, 0x89, 0x32, 0xdb, 0x87, 0xfc, 0x21, 0x8a, 0xab, 0x6d, 0x82, 0xa8, 0x42, 0x81, 0x4f, 0xf2, /* (2^399)P */ 0xb3, 0xeb, 0x88, 0x18, 0xf6, 0x56, 0x96, 0xbf, 0xba, 0x5d, 0x71, 0xa1, 0x5a, 0xd1, 0x04, 0x7b, 0xd5, 0x46, 0x01, 0x74, 0xfe, 0x15, 0x25, 0xb7, 0xff, 0x0c, 0x24, 0x47, 0xac, 0xfd, 0xab, 0x47, 0x32, 0xe1, 0x6a, 0x4e, 0xca, 0xcf, 0x7f, 0xdd, 0xf8, 0xd2, 0x4b, 0x3b, 0xf5, 0x17, 0xba, 0xba, 0x8b, 0xa1, 0xec, 0x28, 0x3f, 0x97, 0xab, 0x2a, /* (2^400)P */ 0x51, 0x38, 0xc9, 0x5e, 0xc6, 0xb3, 0x64, 0xf2, 0x24, 0x4d, 0x04, 0x7d, 0xc8, 0x39, 0x0c, 0x4a, 0xc9, 0x73, 0x74, 0x1b, 0x5c, 0xb2, 0xc5, 0x41, 0x62, 0xa0, 0x4c, 0x6d, 0x8d, 0x91, 0x9a, 0x7b, 0x88, 0xab, 0x9c, 0x7e, 0x23, 0xdb, 0x6f, 0xb5, 0x72, 0xd6, 0x47, 0x40, 0xef, 0x22, 0x58, 0x62, 0x19, 0x6c, 0x38, 0xba, 0x5b, 0x00, 0x30, 0x9f, /* (2^401)P */ 0x65, 0xbb, 0x3b, 0x9b, 0xe9, 0xae, 0xbf, 0xbe, 0xe4, 0x13, 0x95, 0xf3, 0xe3, 0x77, 0xcb, 0xe4, 0x9a, 0x22, 0xb5, 0x4a, 0x08, 0x9d, 0xb3, 0x9e, 0x27, 0xe0, 0x15, 0x6c, 0x9f, 0x7e, 0x9a, 0x5e, 0x15, 0x45, 0x25, 0x8d, 0x01, 0x0a, 0xd2, 0x2b, 0xbd, 0x48, 0x06, 0x0d, 0x18, 0x97, 0x4b, 0xdc, 0xbc, 0xf0, 0xcd, 0xb2, 0x52, 0x3c, 0xac, 0xf5, /* (2^402)P */ 0x3e, 0xed, 0x47, 0x6b, 0x5c, 0xf6, 0x76, 0xd0, 0xe9, 0x15, 0xa3, 0xcb, 0x36, 0x00, 0x21, 0xa3, 0x79, 0x20, 0xa5, 0x3e, 0x88, 0x03, 0xcb, 0x7e, 0x63, 0xbb, 0xed, 0xa9, 0x13, 0x35, 0x16, 0xaf, 0x2e, 0xb4, 0x70, 0x14, 0x93, 0xfb, 0xc4, 0x9b, 0xd8, 0xb1, 0xbe, 0x43, 0xd1, 0x85, 0xb8, 0x97, 0xef, 0xea, 0x88, 0xa1, 0x25, 0x52, 0x62, 0x75, /* (2^403)P */ 0x8e, 0x4f, 0xaa, 0x23, 0x62, 0x7e, 0x2b, 0x37, 0x89, 0x00, 0x11, 0x30, 0xc5, 0x33, 0x4a, 0x89, 0x8a, 0xe2, 0xfc, 0x5c, 0x6a, 0x75, 0xe5, 0xf7, 0x02, 0x4a, 0x9b, 0xf7, 0xb5, 0x6a, 0x85, 0x31, 0xd3, 0x5a, 0xcf, 0xc3, 0xf8, 0xde, 0x2f, 0xcf, 0xb5, 0x24, 0xf4, 0xe3, 0xa1, 0xad, 0x42, 0xae, 0x09, 0xb9, 0x2e, 0x04, 0x2d, 0x01, 0x22, 0x3f, /* (2^404)P */ 0x41, 0x16, 0xfb, 0x7d, 0x50, 0xfd, 0xb5, 0xba, 0x88, 0x24, 0xba, 0xfd, 0x3d, 0xb2, 0x90, 0x15, 0xb7, 0xfa, 0xa2, 0xe1, 0x4c, 0x7d, 0xb9, 0xc6, 0xff, 0x81, 0x57, 0xb6, 0xc2, 0x9e, 0xcb, 0xc4, 0x35, 0xbd, 0x01, 0xb7, 0xaa, 0xce, 0xd0, 0xe9, 0xb5, 0xd6, 0x72, 0xbf, 0xd2, 0xee, 0xc7, 0xac, 0x94, 0xff, 0x29, 0x57, 0x02, 0x49, 0x09, 0xad, /* (2^405)P */ 0x27, 0xa5, 0x78, 0x1b, 0xbf, 0x6b, 0xaf, 0x0b, 0x8c, 0xd9, 0xa8, 0x37, 0xb0, 0x67, 0x18, 0xb6, 0xc7, 0x05, 0x8a, 0x67, 0x03, 0x30, 0x62, 0x6e, 0x56, 0x82, 0xa9, 0x54, 0x3e, 0x0c, 0x4e, 0x07, 0xe1, 0x5a, 0x38, 0xed, 0xfa, 0xc8, 0x55, 0x6b, 0x08, 0xa3, 0x6b, 0x64, 0x2a, 0x15, 0xd6, 0x39, 0x6f, 0x47, 0x99, 0x42, 0x3f, 0x33, 0x84, 0x8f, /* (2^406)P */ 0xbc, 0x45, 0x29, 0x81, 0x0e, 0xa4, 0xc5, 0x72, 0x3a, 0x10, 0xe1, 0xc4, 0x1e, 0xda, 0xc3, 0xfe, 0xb0, 0xce, 0xd2, 0x13, 0x34, 0x67, 0x21, 0xc6, 0x7e, 0xf9, 0x8c, 0xff, 0x39, 0x50, 0xae, 0x92, 0x60, 0x35, 0x2f, 0x8b, 0x6e, 0xc9, 0xc1, 0x27, 0x3a, 0x94, 0x66, 0x3e, 0x26, 0x84, 0x93, 0xc8, 0x6c, 0xcf, 0xd2, 0x03, 0xa1, 0x10, 0xcf, 0xb7, /* (2^407)P */ 0x64, 0xda, 0x19, 0xf6, 0xc5, 0x73, 0x17, 0x44, 0x88, 0x81, 0x07, 0x0d, 0x34, 0xb2, 0x75, 0xf9, 0xd9, 0xe2, 0xe0, 0x8b, 0x71, 0xcf, 0x72, 0x34, 0x83, 0xb4, 0xce, 0xfc, 0xd7, 0x29, 0x09, 0x5a, 0x98, 0xbf, 0x14, 0xac, 0x77, 0x55, 0x38, 0x47, 0x5b, 0x0f, 0x40, 0x24, 0xe5, 0xa5, 0xa6, 0xac, 0x2d, 0xa6, 0xff, 0x9c, 0x73, 0xfe, 0x5c, 0x7e, /* (2^408)P */ 0x1e, 0x33, 0xcc, 0x68, 0xb2, 0xbc, 0x8c, 0x93, 0xaf, 0xcc, 0x38, 0xf8, 0xd9, 0x16, 0x72, 0x50, 0xac, 0xd9, 0xb5, 0x0b, 0x9a, 0xbe, 0x46, 0x7a, 0xf1, 0xee, 0xf1, 0xad, 0xec, 0x5b, 0x59, 0x27, 0x9c, 0x05, 0xa3, 0x87, 0xe0, 0x37, 0x2c, 0x83, 0xce, 0xb3, 0x65, 0x09, 0x8e, 0xc3, 0x9c, 0xbf, 0x6a, 0xa2, 0x00, 0xcc, 0x12, 0x36, 0xc5, 0x95, /* (2^409)P */ 0x36, 0x11, 0x02, 0x14, 0x9c, 0x3c, 0xeb, 0x2f, 0x23, 0x5b, 0x6b, 0x2b, 0x08, 0x54, 0x53, 0xac, 0xb2, 0xa3, 0xe0, 0x26, 0x62, 0x3c, 0xe4, 0xe1, 0x81, 0xee, 0x13, 0x3e, 0xa4, 0x97, 0xef, 0xf9, 0x92, 0x27, 0x01, 0xce, 0x54, 0x8b, 0x3e, 0x31, 0xbe, 0xa7, 0x88, 0xcf, 0x47, 0x99, 0x3c, 0x10, 0x6f, 0x60, 0xb3, 0x06, 0x4e, 0xee, 0x1b, 0xf0, /* (2^410)P */ 0x59, 0x49, 0x66, 0xcf, 0x22, 0xe6, 0xf6, 0x73, 0xfe, 0xa3, 0x1c, 0x09, 0xfa, 0x5f, 0x65, 0xa8, 0xf0, 0x82, 0xc2, 0xef, 0x16, 0x63, 0x6e, 0x79, 0x69, 0x51, 0x39, 0x07, 0x65, 0xc4, 0x81, 0xec, 0x73, 0x0f, 0x15, 0x93, 0xe1, 0x30, 0x33, 0xe9, 0x37, 0x86, 0x42, 0x4c, 0x1f, 0x9b, 0xad, 0xee, 0x3f, 0xf1, 0x2a, 0x8e, 0x6a, 0xa3, 0xc8, 0x35, /* (2^411)P */ 0x1e, 0x49, 0xf1, 0xdd, 0xd2, 0x9c, 0x8e, 0x78, 0xb2, 0x06, 0xe4, 0x6a, 0xab, 0x3a, 0xdc, 0xcd, 0xf4, 0xeb, 0xe1, 0xe7, 0x2f, 0xaa, 0xeb, 0x40, 0x31, 0x9f, 0xb9, 0xab, 0x13, 0xa9, 0x78, 0xbf, 0x38, 0x89, 0x0e, 0x85, 0x14, 0x8b, 0x46, 0x76, 0x14, 0xda, 0xcf, 0x33, 0xc8, 0x79, 0xd3, 0xd5, 0xa3, 0x6a, 0x69, 0x45, 0x70, 0x34, 0xc3, 0xe9, /* (2^412)P */ 0x5e, 0xe7, 0x78, 0xe9, 0x24, 0xcc, 0xe9, 0xf4, 0xc8, 0x6b, 0xe0, 0xfb, 0x3a, 0xbe, 0xcc, 0x42, 0x4a, 0x00, 0x22, 0xf8, 0xe6, 0x32, 0xbe, 0x6d, 0x18, 0x55, 0x60, 0xe9, 0x72, 0x69, 0x50, 0x56, 0xca, 0x04, 0x18, 0x38, 0xa1, 0xee, 0xd8, 0x38, 0x3c, 0xa7, 0x70, 0xe2, 0xb9, 0x4c, 0xa0, 0xc8, 0x89, 0x72, 0xcf, 0x49, 0x7f, 0xdf, 0xbc, 0x67, /* (2^413)P */ 0x1d, 0x17, 0xcb, 0x0b, 0xbd, 0xb2, 0x36, 0xe3, 0xa8, 0x99, 0x31, 0xb6, 0x26, 0x9c, 0x0c, 0x74, 0xaf, 0x4d, 0x24, 0x61, 0xcf, 0x31, 0x7b, 0xed, 0xdd, 0xc3, 0xf6, 0x32, 0x70, 0xfe, 0x17, 0xf6, 0x51, 0x37, 0x65, 0xce, 0x5d, 0xaf, 0xa5, 0x2f, 0x2a, 0xfe, 0x00, 0x71, 0x7c, 0x50, 0xbe, 0x21, 0xc7, 0xed, 0xc6, 0xfc, 0x67, 0xcf, 0x9c, 0xdd, /* (2^414)P */ 0x26, 0x3e, 0xf8, 0xbb, 0xd0, 0xb1, 0x01, 0xd8, 0xeb, 0x0b, 0x62, 0x87, 0x35, 0x4c, 0xde, 0xca, 0x99, 0x9c, 0x6d, 0xf7, 0xb6, 0xf0, 0x57, 0x0a, 0x52, 0x29, 0x6a, 0x3f, 0x26, 0x31, 0x04, 0x07, 0x2a, 0xc9, 0xfa, 0x9b, 0x0e, 0x62, 0x8e, 0x72, 0xf2, 0xad, 0xce, 0xb6, 0x35, 0x7a, 0xc1, 0xae, 0x35, 0xc7, 0xa3, 0x14, 0xcf, 0x0c, 0x28, 0xb7, /* (2^415)P */ 0xa6, 0xf1, 0x32, 0x3a, 0x20, 0xd2, 0x24, 0x97, 0xcf, 0x5d, 0x37, 0x99, 0xaf, 0x33, 0x7a, 0x5b, 0x7a, 0xcc, 0x4e, 0x41, 0x38, 0xb1, 0x4e, 0xad, 0xc9, 0xd9, 0x71, 0x7e, 0xb2, 0xf5, 0xd5, 0x01, 0x6c, 0x4d, 0xfd, 0xa1, 0xda, 0x03, 0x38, 0x9b, 0x3d, 0x92, 0x92, 0xf2, 0xca, 0xbf, 0x1f, 0x24, 0xa4, 0xbb, 0x30, 0x6a, 0x74, 0x56, 0xc8, 0xce, /* (2^416)P */ 0x27, 0xf4, 0xed, 0xc9, 0xc3, 0xb1, 0x79, 0x85, 0xbe, 0xf6, 0xeb, 0xf3, 0x55, 0xc7, 0xaa, 0xa6, 0xe9, 0x07, 0x5d, 0xf4, 0xeb, 0xa6, 0x81, 0xe3, 0x0e, 0xcf, 0xa3, 0xc1, 0xef, 0xe7, 0x34, 0xb2, 0x03, 0x73, 0x8a, 0x91, 0xf1, 0xad, 0x05, 0xc7, 0x0b, 0x43, 0x99, 0x12, 0x31, 0xc8, 0xc7, 0xc5, 0xa4, 0x3d, 0xcd, 0xe5, 0x4e, 0x6d, 0x24, 0xdd, /* (2^417)P */ 0x61, 0x54, 0xd0, 0x95, 0x2c, 0x45, 0x75, 0xac, 0xb5, 0x1a, 0x9d, 0x11, 0xeb, 0xed, 0x6b, 0x57, 0xa3, 0xe6, 0xcd, 0x77, 0xd4, 0x83, 0x8e, 0x39, 0xf1, 0x0f, 0x98, 0xcb, 0x40, 0x02, 0x6e, 0x10, 0x82, 0x9e, 0xb4, 0x93, 0x76, 0xd7, 0x97, 0xa3, 0x53, 0x12, 0x86, 0xc6, 0x15, 0x78, 0x73, 0x93, 0xe7, 0x7f, 0xcf, 0x1f, 0xbf, 0xcd, 0xd2, 0x7a, /* (2^418)P */ 0xc2, 0x21, 0xdc, 0xd5, 0x69, 0xff, 0xca, 0x49, 0x3a, 0xe1, 0xc3, 0x69, 0x41, 0x56, 0xc1, 0x76, 0x63, 0x24, 0xbd, 0x64, 0x1b, 0x3d, 0x92, 0xf9, 0x13, 0x04, 0x25, 0xeb, 0x27, 0xa6, 0xef, 0x39, 0x3a, 0x80, 0xe0, 0xf8, 0x27, 0xee, 0xc9, 0x49, 0x77, 0xef, 0x3f, 0x29, 0x3d, 0x5e, 0xe6, 0x66, 0x83, 0xd1, 0xf6, 0xfe, 0x9d, 0xbc, 0xf1, 0x96, /* (2^419)P */ 0x6b, 0xc6, 0x99, 0x26, 0x3c, 0xf3, 0x63, 0xf9, 0xc7, 0x29, 0x8c, 0x52, 0x62, 0x2d, 0xdc, 0x8a, 0x66, 0xce, 0x2c, 0xa7, 0xe4, 0xf0, 0xd7, 0x37, 0x17, 0x1e, 0xe4, 0xa3, 0x53, 0x7b, 0x29, 0x8e, 0x60, 0x99, 0xf9, 0x0c, 0x7c, 0x6f, 0xa2, 0xcc, 0x9f, 0x80, 0xdd, 0x5e, 0x46, 0xaa, 0x0d, 0x6c, 0xc9, 0x6c, 0xf7, 0x78, 0x5b, 0x38, 0xe3, 0x24, /* (2^420)P */ 0x4b, 0x75, 0x6a, 0x2f, 0x08, 0xe1, 0x72, 0x76, 0xab, 0x82, 0x96, 0xdf, 0x3b, 0x1f, 0x9b, 0xd8, 0xed, 0xdb, 0xcd, 0x15, 0x09, 0x5a, 0x1e, 0xb7, 0xc5, 0x26, 0x72, 0x07, 0x0c, 0x50, 0xcd, 0x3b, 0x4d, 0x3f, 0xa2, 0x67, 0xc2, 0x02, 0x61, 0x2e, 0x68, 0xe9, 0x6f, 0xf0, 0x21, 0x2a, 0xa7, 0x3b, 0x88, 0x04, 0x11, 0x64, 0x49, 0x0d, 0xb4, 0x46, /* (2^421)P */ 0x63, 0x85, 0xf3, 0xc5, 0x2b, 0x5a, 0x9f, 0xf0, 0x17, 0xcb, 0x45, 0x0a, 0xf3, 0x6e, 0x7e, 0xb0, 0x7c, 0xbc, 0xf0, 0x4f, 0x3a, 0xb0, 0xbc, 0x36, 0x36, 0x52, 0x51, 0xcb, 0xfe, 0x9a, 0xcb, 0xe8, 0x7e, 0x4b, 0x06, 0x7f, 0xaa, 0x35, 0xc8, 0x0e, 0x7a, 0x30, 0xa3, 0xb1, 0x09, 0xbb, 0x86, 0x4c, 0xbe, 0xb8, 0xbd, 0xe0, 0x32, 0xa5, 0xd4, 0xf7, /* (2^422)P */ 0x7d, 0x50, 0x37, 0x68, 0x4e, 0x22, 0xb2, 0x2c, 0xd5, 0x0f, 0x2b, 0x6d, 0xb1, 0x51, 0xf2, 0x82, 0xe9, 0x98, 0x7c, 0x50, 0xc7, 0x96, 0x7e, 0x0e, 0xdc, 0xb1, 0x0e, 0xb2, 0x63, 0x8c, 0x30, 0x37, 0x72, 0x21, 0x9c, 0x61, 0xc2, 0xa7, 0x33, 0xd9, 0xb2, 0x63, 0x93, 0xd1, 0x6b, 0x6a, 0x73, 0xa5, 0x58, 0x80, 0xff, 0x04, 0xc7, 0x83, 0x21, 0x29, /* (2^423)P */ 0x29, 0x04, 0xbc, 0x99, 0x39, 0xc9, 0x58, 0xc9, 0x6b, 0x17, 0xe8, 0x90, 0xb3, 0xe6, 0xa9, 0xb6, 0x28, 0x9b, 0xcb, 0x3b, 0x28, 0x90, 0x68, 0x71, 0xff, 0xcf, 0x08, 0x78, 0xc9, 0x8d, 0xa8, 0x4e, 0x43, 0xd1, 0x1c, 0x9e, 0xa4, 0xe3, 0xdf, 0xbf, 0x92, 0xf4, 0xf9, 0x41, 0xba, 0x4d, 0x1c, 0xf9, 0xdd, 0x74, 0x76, 0x1c, 0x6e, 0x3e, 0x94, 0x87, /* (2^424)P */ 0xe4, 0xda, 0xc5, 0xd7, 0xfb, 0x87, 0xc5, 0x4d, 0x6b, 0x19, 0xaa, 0xb9, 0xbc, 0x8c, 0xf2, 0x8a, 0xd8, 0x5d, 0xdb, 0x4d, 0xef, 0xa6, 0xf2, 0x65, 0xf1, 0x22, 0x9c, 0xf1, 0x46, 0x30, 0x71, 0x7c, 0xe4, 0x53, 0x8e, 0x55, 0x2e, 0x9c, 0x9a, 0x31, 0x2a, 0xc3, 0xab, 0x0f, 0xde, 0xe4, 0xbe, 0xd8, 0x96, 0x50, 0x6e, 0x0c, 0x54, 0x49, 0xe6, 0xec, /* (2^425)P */ 0x3c, 0x1d, 0x5a, 0xa5, 0xda, 0xad, 0xdd, 0xc2, 0xae, 0xac, 0x6f, 0x86, 0x75, 0x31, 0x91, 0x64, 0x45, 0x9d, 0xa4, 0xf0, 0x81, 0xf1, 0x0e, 0xba, 0x74, 0xaf, 0x7b, 0xcd, 0x6f, 0xfe, 0xac, 0x4e, 0xdb, 0x4e, 0x45, 0x35, 0x36, 0xc5, 0xc0, 0x6c, 0x3d, 0x64, 0xf4, 0xd8, 0x07, 0x62, 0xd1, 0xec, 0xf3, 0xfc, 0x93, 0xc9, 0x28, 0x0c, 0x2c, 0xf3, /* (2^426)P */ 0x0c, 0x69, 0x2b, 0x5c, 0xb6, 0x41, 0x69, 0xf1, 0xa4, 0xf1, 0x5b, 0x75, 0x4c, 0x42, 0x8b, 0x47, 0xeb, 0x69, 0xfb, 0xa8, 0xe6, 0xf9, 0x7b, 0x48, 0x50, 0xaf, 0xd3, 0xda, 0xb2, 0x35, 0x10, 0xb5, 0x5b, 0x40, 0x90, 0x39, 0xc9, 0x07, 0x06, 0x73, 0x26, 0x20, 0x95, 0x01, 0xa4, 0x2d, 0xf0, 0xe7, 0x2e, 0x00, 0x7d, 0x41, 0x09, 0x68, 0x13, 0xc4, /* (2^427)P */ 0xbe, 0x38, 0x78, 0xcf, 0xc9, 0x4f, 0x36, 0xca, 0x09, 0x61, 0x31, 0x3c, 0x57, 0x2e, 0xec, 0x17, 0xa4, 0x7d, 0x19, 0x2b, 0x9b, 0x5b, 0xbe, 0x8f, 0xd6, 0xc5, 0x2f, 0x86, 0xf2, 0x64, 0x76, 0x17, 0x00, 0x6e, 0x1a, 0x8c, 0x67, 0x1b, 0x68, 0xeb, 0x15, 0xa2, 0xd6, 0x09, 0x91, 0xdd, 0x23, 0x0d, 0x98, 0xb2, 0x10, 0x19, 0x55, 0x9b, 0x63, 0xf2, /* (2^428)P */ 0x51, 0x1f, 0x93, 0xea, 0x2a, 0x3a, 0xfa, 0x41, 0xc0, 0x57, 0xfb, 0x74, 0xa6, 0x65, 0x09, 0x56, 0x14, 0xb6, 0x12, 0xaa, 0xb3, 0x1a, 0x8d, 0x3b, 0x76, 0x91, 0x7a, 0x23, 0x56, 0x9c, 0x6a, 0xc0, 0xe0, 0x3c, 0x3f, 0xb5, 0x1a, 0xf4, 0x57, 0x71, 0x93, 0x2b, 0xb1, 0xa7, 0x70, 0x57, 0x22, 0x80, 0xf5, 0xb8, 0x07, 0x77, 0x87, 0x0c, 0xbe, 0x83, /* (2^429)P */ 0x07, 0x9b, 0x0e, 0x52, 0x38, 0x63, 0x13, 0x86, 0x6a, 0xa6, 0xb4, 0xd2, 0x60, 0x68, 0x9a, 0x99, 0x82, 0x0a, 0x04, 0x5f, 0x89, 0x7a, 0x1a, 0x2a, 0xae, 0x2d, 0x35, 0x0c, 0x1e, 0xad, 0xef, 0x4f, 0x9a, 0xfc, 0xc8, 0xd9, 0xcf, 0x9d, 0x48, 0x71, 0xa5, 0x55, 0x79, 0x73, 0x39, 0x1b, 0xd8, 0x73, 0xec, 0x9b, 0x03, 0x16, 0xd8, 0x82, 0xf7, 0x67, /* (2^430)P */ 0x52, 0x67, 0x42, 0x21, 0xc9, 0x40, 0x78, 0x82, 0x2b, 0x95, 0x2d, 0x20, 0x92, 0xd1, 0xe2, 0x61, 0x25, 0xb0, 0xc6, 0x9c, 0x20, 0x59, 0x8e, 0x28, 0x6f, 0xf3, 0xfd, 0xd3, 0xc1, 0x32, 0x43, 0xc9, 0xa6, 0x08, 0x7a, 0x77, 0x9c, 0x4c, 0x8c, 0x33, 0x71, 0x13, 0x69, 0xe3, 0x52, 0x30, 0xa7, 0xf5, 0x07, 0x67, 0xac, 0xad, 0x46, 0x8a, 0x26, 0x25, /* (2^431)P */ 0xda, 0x86, 0xc4, 0xa2, 0x71, 0x56, 0xdd, 0xd2, 0x48, 0xd3, 0xde, 0x42, 0x63, 0x01, 0xa7, 0x2c, 0x92, 0x83, 0x6f, 0x2e, 0xd8, 0x1e, 0x3f, 0xc1, 0xc5, 0x42, 0x4e, 0x34, 0x19, 0x54, 0x6e, 0x35, 0x2c, 0x51, 0x2e, 0xfd, 0x0f, 0x9a, 0x45, 0x66, 0x5e, 0x4a, 0x83, 0xda, 0x0a, 0x53, 0x68, 0x63, 0xfa, 0xce, 0x47, 0x20, 0xd3, 0x34, 0xba, 0x0d, /* (2^432)P */ 0xd0, 0xe9, 0x64, 0xa4, 0x61, 0x4b, 0x86, 0xe5, 0x93, 0x6f, 0xda, 0x0e, 0x31, 0x7e, 0x6e, 0xe3, 0xc6, 0x73, 0xd8, 0xa3, 0x08, 0x57, 0x52, 0xcd, 0x51, 0x63, 0x1d, 0x9f, 0x93, 0x00, 0x62, 0x91, 0x26, 0x21, 0xa7, 0xdd, 0x25, 0x0f, 0x09, 0x0d, 0x35, 0xad, 0xcf, 0x11, 0x8e, 0x6e, 0xe8, 0xae, 0x1d, 0x95, 0xcb, 0x88, 0xf8, 0x70, 0x7b, 0x91, /* (2^433)P */ 0x0c, 0x19, 0x5c, 0xd9, 0x8d, 0xda, 0x9d, 0x2c, 0x90, 0x54, 0x65, 0xe8, 0xb6, 0x35, 0x50, 0xae, 0xea, 0xae, 0x43, 0xb7, 0x1e, 0x99, 0x8b, 0x4c, 0x36, 0x4e, 0xe4, 0x1e, 0xc4, 0x64, 0x43, 0xb6, 0xeb, 0xd4, 0xe9, 0x60, 0x22, 0xee, 0xcf, 0xb8, 0x52, 0x1b, 0xf0, 0x04, 0xce, 0xbc, 0x2b, 0xf0, 0xbe, 0xcd, 0x44, 0x74, 0x1e, 0x1f, 0x63, 0xf9, /* (2^434)P */ 0xe1, 0x3f, 0x95, 0x94, 0xb2, 0xb6, 0x31, 0xa9, 0x1b, 0xdb, 0xfd, 0x0e, 0xdb, 0xdd, 0x1a, 0x22, 0x78, 0x60, 0x9f, 0x75, 0x5f, 0x93, 0x06, 0x0c, 0xd8, 0xbb, 0xa2, 0x85, 0x2b, 0x5e, 0xc0, 0x9b, 0xa8, 0x5d, 0xaf, 0x93, 0x91, 0x91, 0x47, 0x41, 0x1a, 0xfc, 0xb4, 0x51, 0x85, 0xad, 0x69, 0x4d, 0x73, 0x69, 0xd5, 0x4e, 0x82, 0xfb, 0x66, 0xcb, /* (2^435)P */ 0x7c, 0xbe, 0xc7, 0x51, 0xc4, 0x74, 0x6e, 0xab, 0xfd, 0x41, 0x4f, 0x76, 0x4f, 0x24, 0x03, 0xd6, 0x2a, 0xb7, 0x42, 0xb4, 0xda, 0x41, 0x2c, 0x82, 0x48, 0x4c, 0x7f, 0x6f, 0x25, 0x5d, 0x36, 0xd4, 0x69, 0xf5, 0xef, 0x02, 0x81, 0xea, 0x6f, 0x19, 0x69, 0xe8, 0x6f, 0x5b, 0x2f, 0x14, 0x0e, 0x6f, 0x89, 0xb4, 0xb5, 0xd8, 0xae, 0xef, 0x7b, 0x87, /* (2^436)P */ 0xe9, 0x91, 0xa0, 0x8b, 0xc9, 0xe0, 0x01, 0x90, 0x37, 0xc1, 0x6f, 0xdc, 0x5e, 0xf7, 0xbf, 0x43, 0x00, 0xaa, 0x10, 0x76, 0x76, 0x18, 0x6e, 0x19, 0x1e, 0x94, 0x50, 0x11, 0x0a, 0xd1, 0xe2, 0xdb, 0x08, 0x21, 0xa0, 0x1f, 0xdb, 0x54, 0xfe, 0xea, 0x6e, 0xa3, 0x68, 0x56, 0x87, 0x0b, 0x22, 0x4e, 0x66, 0xf3, 0x82, 0x82, 0x00, 0xcd, 0xd4, 0x12, /* (2^437)P */ 0x25, 0x8e, 0x24, 0x77, 0x64, 0x4c, 0xe0, 0xf8, 0x18, 0xc0, 0xdc, 0xc7, 0x1b, 0x35, 0x65, 0xde, 0x67, 0x41, 0x5e, 0x6f, 0x90, 0x82, 0xa7, 0x2e, 0x6d, 0xf1, 0x47, 0xb4, 0x92, 0x9c, 0xfd, 0x6a, 0x9a, 0x41, 0x36, 0x20, 0x24, 0x58, 0xc3, 0x59, 0x07, 0x9a, 0xfa, 0x9f, 0x03, 0xcb, 0xc7, 0x69, 0x37, 0x60, 0xe1, 0xab, 0x13, 0x72, 0xee, 0xa2, /* (2^438)P */ 0x74, 0x78, 0xfb, 0x13, 0xcb, 0x8e, 0x37, 0x1a, 0xf6, 0x1d, 0x17, 0x83, 0x06, 0xd4, 0x27, 0x06, 0x21, 0xe8, 0xda, 0xdf, 0x6b, 0xf3, 0x83, 0x6b, 0x34, 0x8a, 0x8c, 0xee, 0x01, 0x05, 0x5b, 0xed, 0xd3, 0x1b, 0xc9, 0x64, 0x83, 0xc9, 0x49, 0xc2, 0x57, 0x1b, 0xdd, 0xcf, 0xf1, 0x9d, 0x63, 0xee, 0x1c, 0x0d, 0xa0, 0x0a, 0x73, 0x1f, 0x5b, 0x32, /* (2^439)P */ 0x29, 0xce, 0x1e, 0xc0, 0x6a, 0xf5, 0xeb, 0x99, 0x5a, 0x39, 0x23, 0xe9, 0xdd, 0xac, 0x44, 0x88, 0xbc, 0x80, 0x22, 0xde, 0x2c, 0xcb, 0xa8, 0x3b, 0xff, 0xf7, 0x6f, 0xc7, 0x71, 0x72, 0xa8, 0xa3, 0xf6, 0x4d, 0xc6, 0x75, 0xda, 0x80, 0xdc, 0xd9, 0x30, 0xd9, 0x07, 0x50, 0x5a, 0x54, 0x7d, 0xda, 0x39, 0x6f, 0x78, 0x94, 0xbf, 0x25, 0x98, 0xdc, /* (2^440)P */ 0x01, 0x26, 0x62, 0x44, 0xfb, 0x0f, 0x11, 0x72, 0x73, 0x0a, 0x16, 0xc7, 0x16, 0x9c, 0x9b, 0x37, 0xd8, 0xff, 0x4f, 0xfe, 0x57, 0xdb, 0xae, 0xef, 0x7d, 0x94, 0x30, 0x04, 0x70, 0x83, 0xde, 0x3c, 0xd4, 0xb5, 0x70, 0xda, 0xa7, 0x55, 0xc8, 0x19, 0xe1, 0x36, 0x15, 0x61, 0xe7, 0x3b, 0x7d, 0x85, 0xbb, 0xf3, 0x42, 0x5a, 0x94, 0xf4, 0x53, 0x2a, /* (2^441)P */ 0x14, 0x60, 0xa6, 0x0b, 0x83, 0xe1, 0x23, 0x77, 0xc0, 0xce, 0x50, 0xed, 0x35, 0x8d, 0x98, 0x99, 0x7d, 0xf5, 0x8d, 0xce, 0x94, 0x25, 0xc8, 0x0f, 0x6d, 0xfa, 0x4a, 0xa4, 0x3a, 0x1f, 0x66, 0xfb, 0x5a, 0x64, 0xaf, 0x8b, 0x54, 0x54, 0x44, 0x3f, 0x5b, 0x88, 0x61, 0xe4, 0x48, 0x45, 0x26, 0x20, 0xbe, 0x0d, 0x06, 0xbb, 0x65, 0x59, 0xe1, 0x36, /* (2^442)P */ 0xb7, 0x98, 0xce, 0xa3, 0xe3, 0xee, 0x11, 0x1b, 0x9e, 0x24, 0x59, 0x75, 0x31, 0x37, 0x44, 0x6f, 0x6b, 0x9e, 0xec, 0xb7, 0x44, 0x01, 0x7e, 0xab, 0xbb, 0x69, 0x5d, 0x11, 0xb0, 0x30, 0x64, 0xea, 0x91, 0xb4, 0x7a, 0x8c, 0x02, 0x4c, 0xb9, 0x10, 0xa7, 0xc7, 0x79, 0xe6, 0xdc, 0x77, 0xe3, 0xc8, 0xef, 0x3e, 0xf9, 0x38, 0x81, 0xce, 0x9a, 0xb2, /* (2^443)P */ 0x91, 0x12, 0x76, 0xd0, 0x10, 0xb4, 0xaf, 0xe1, 0x89, 0x3a, 0x93, 0x6b, 0x5c, 0x19, 0x5f, 0x24, 0xed, 0x04, 0x92, 0xc7, 0xf0, 0x00, 0x08, 0xc1, 0x92, 0xff, 0x90, 0xdb, 0xb2, 0xbf, 0xdf, 0x49, 0xcd, 0xbd, 0x5c, 0x6e, 0xbf, 0x16, 0xbb, 0x61, 0xf9, 0x20, 0x33, 0x35, 0x93, 0x11, 0xbc, 0x59, 0x69, 0xce, 0x18, 0x9f, 0xf8, 0x7b, 0xa1, 0x6e, /* (2^444)P */ 0xa1, 0xf4, 0xaf, 0xad, 0xf8, 0xe6, 0x99, 0xd2, 0xa1, 0x4d, 0xde, 0x56, 0xc9, 0x7b, 0x0b, 0x11, 0x3e, 0xbf, 0x89, 0x1a, 0x9a, 0x90, 0xe5, 0xe2, 0xa6, 0x37, 0x88, 0xa1, 0x68, 0x59, 0xae, 0x8c, 0xec, 0x02, 0x14, 0x8d, 0xb7, 0x2e, 0x25, 0x75, 0x7f, 0x76, 0x1a, 0xd3, 0x4d, 0xad, 0x8a, 0x00, 0x6c, 0x96, 0x49, 0xa4, 0xc3, 0x2e, 0x5c, 0x7b, /* (2^445)P */ 0x26, 0x53, 0xf7, 0xda, 0xa8, 0x01, 0x14, 0xb1, 0x63, 0xe3, 0xc3, 0x89, 0x88, 0xb0, 0x85, 0x40, 0x2b, 0x26, 0x9a, 0x10, 0x1a, 0x70, 0x33, 0xf4, 0x50, 0x9d, 0x4d, 0xd8, 0x64, 0xc6, 0x0f, 0xe1, 0x17, 0xc8, 0x10, 0x4b, 0xfc, 0xa0, 0xc9, 0xba, 0x2c, 0x98, 0x09, 0xf5, 0x84, 0xb6, 0x7c, 0x4e, 0xa3, 0xe3, 0x81, 0x1b, 0x32, 0x60, 0x02, 0xdd, /* (2^446)P */ 0xa3, 0xe5, 0x86, 0xd4, 0x43, 0xa8, 0xd1, 0x98, 0x9d, 0x9d, 0xdb, 0x04, 0xcf, 0x6e, 0x35, 0x05, 0x30, 0x53, 0x3b, 0xbc, 0x90, 0x00, 0x4a, 0xc5, 0x40, 0x2a, 0x0f, 0xde, 0x1a, 0xd7, 0x36, 0x27, 0x44, 0x62, 0xa6, 0xac, 0x9d, 0xd2, 0x70, 0x69, 0x14, 0x39, 0x9b, 0xd1, 0xc3, 0x0a, 0x3a, 0x82, 0x0e, 0xf1, 0x94, 0xd7, 0x42, 0x94, 0xd5, 0x7d, /* (2^447)P */ 0x04, 0xc0, 0x6e, 0x12, 0x90, 0x70, 0xf9, 0xdf, 0xf7, 0xc9, 0x86, 0xc0, 0xe6, 0x92, 0x8b, 0x0a, 0xa1, 0xc1, 0x3b, 0xcc, 0x33, 0xb7, 0xf0, 0xeb, 0x51, 0x50, 0x80, 0x20, 0x69, 0x1c, 0x4f, 0x89, 0x05, 0x1e, 0xe4, 0x7a, 0x0a, 0xc2, 0xf0, 0xf5, 0x78, 0x91, 0x76, 0x34, 0x45, 0xdc, 0x24, 0x53, 0x24, 0x98, 0xe2, 0x73, 0x6f, 0xe6, 0x46, 0x67, } golang-github-cloudflare-circl-1.3.7/dh/x448/testdata/000077500000000000000000000000001454601126700224025ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/dh/x448/testdata/rfc7748_kat_test.json000066400000000000000000000046611454601126700263060ustar00rootroot00000000000000[ { "input": "06fce640fa3487bfda5f6cf2d5263f8aad88334cbd07437f020f08f9814dc031ddbdc38c19c6da2583fa5429db94ada18aa7a7fb4ef8a086", "output": "ce3e4ff95a60dc6697da1db1d85e6afbdf79b50a2412d7546d5f239fe14fbaadeb445fc66a01b0779d98223961111e21766282f73dd96b6f", "scalar": "3d262fddf9ec8e88495266fea19a34d28882acef045104d0d1aae121700a779c984c24f8cdd78fbff44943eba368f54b29259a4f1c600ad3" }, { "input": "0fbcc2f993cd56d3305b0b7d9e55d4c1a8fb5dbb52f8e9a1e9b6201b165d015894e56c4d3570bee52fe205e28a78b91cdfbde71ce8d157db", "output": "884a02576239ff7a2f2f63b2db6a9ff37047ac13568e1e30fe63c4a7ad1b3ee3a5700df34321d62077e63633c575c1c954514e99da7c179d", "scalar": "203d494428b8399352665ddca42f9de8fef600908e0d461cb021f8c538345dd77c3e4806e25f46d3315c44e0a5b4371282dd2c8d5be3095f" }, { "input": "0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "output": "9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0", "scalar": "9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b" }, { "input": "0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "output": "3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609", "scalar": "1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d" }, { "input": "3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609", "output": "07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d", "scalar": "9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b" }, { "input": "9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0", "output": "07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d", "scalar": "1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d" } ] golang-github-cloudflare-circl-1.3.7/dh/x448/testdata/rfc7748_times_test.json000066400000000000000000000007651454601126700266510ustar00rootroot00000000000000[ { "times": 1, "key": "3f482c8a9f19b01e6c46ee9711d9dc14fd4bf67af30765c2ae2b846a4d23a8cd0db897086239492caf350b51f833868b9bc2b3bca9cf4113" }, { "times": 1000, "key": "aa3b4749d55b9daf1e5b00288826c467274ce3ebbdd5c17b975e09d4af6c67cf10d087202db88286e2b79fceea3ec353ef54faa26e219f38" }, { "times": 1000000, "key": "077f453681caca3693198420bbe515cae0002472519b3e67661a7e89cab94695c8f4bcd66e61b9b9c946da8d524de3d69bd9d9d66b997e37" } ] golang-github-cloudflare-circl-1.3.7/doc.go000066400000000000000000000006371454601126700205710ustar00rootroot00000000000000// Package circl provides a collection of cryptographic primitives. The goal // of this module is to be used as a tool for experimental deployment of // cryptographic algorithms targeting Post-Quantum (PQ) and Elliptic // Curve Cryptography (ECC). // // Following blog post describes ideas behind CIRCL in more details: // https://blog.cloudflare.com/introducing-circl/ package circl // github.com/cloudflare/circl golang-github-cloudflare-circl-1.3.7/ecc/000077500000000000000000000000001454601126700202215ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ecc/bls12381/000077500000000000000000000000001454601126700214005ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ecc/bls12381/constants.go000066400000000000000000000416011454601126700237450ustar00rootroot00000000000000package bls12381 import ( "errors" "github.com/cloudflare/circl/ecc/bls12381/ff" ) // Scalar represents positive integers in the range 0 <= x < Order. type Scalar = ff.Scalar const ScalarSize = ff.ScalarSize // Order returns the order of the pairing groups, returned as a big-endian slice. // // Order = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 func Order() []byte { return ff.ScalarOrder() } var ( bls12381 struct { // Let z be the BLS12 parameter. minusZ [8]byte // (-z), (integer big-endian). oneMinusZ [8]byte // (1-z), (integer big-endian). g1Check [16]byte // (z^2-1)/3, (integer big-endian). } g1Params struct{ b, _3b, genX, genY ff.Fp } g2Params struct{ b, _3b, genX, genY ff.Fp2 } // g1Isog11 is an isogeny of degree 11 from g1Iso(a,b) to G1 and is given // by rational maps: // g1Iso(a,b) --> G1 // (x,y,z) |-> (x,y,1) // (xNum/xDen, y * yNum/yDen, 1) // (xNum*yDen, y * yNum*xDen, z*xDen*yDen) // such that // xNum = \sum ai * x^i * z^(n-1-i), for 0 <= i < n, and n=12. // xDen = \sum bi * x^i * z^(n-1-i), for 0 <= i < n, and n=11. // yNum = \sum ci * x^i * z^(n-1-i), for 0 <= i < n, and n=16. // yDen = \sum di * x^i * z^(n-1-i), for 0 <= i < n, and n=16. g1Isog11 struct { a, b ff.Fp xNum [12]ff.Fp xDen [11]ff.Fp yNum [16]ff.Fp yDen [16]ff.Fp } // g2Isog3 is an isogeny of degree 3 from g2Iso(a,b) to G2 and is given // by rational maps: // g2Iso(a,b) --> G2 // (x,y,z) |-> (x,y,1) // (xNum/xDen, y * yNum/yDen, 1) // (xNum*yDen, y * yNum*xDen, z*xDen*yDen) // such that // xNum = \sum ai * x^i * z^(n-1-i), for 0 <= i < n, and n=4. // xDen = \sum bi * x^i * z^(n-1-i), for 0 <= i < n, and n=3. // yNum = \sum ci * x^i * z^(n-1-i), for 0 <= i < n, and n=4. // yDen = \sum di * x^i * z^(n-1-i), for 0 <= i < n, and n=4. g2Isog3 struct { a, b ff.Fp2 xNum [4]ff.Fp2 xDen [3]ff.Fp2 yNum [4]ff.Fp2 yDen [4]ff.Fp2 } g1sswu struct { Z ff.Fp // Z = 11. c1 [48]byte // integer c1 = (p - 3) / 4 (big-endian) c2 ff.Fp } g2sswu struct { Z ff.Fp2 // -(2 + I) c1 [95]byte // integer c1 = (p^2 - 9) / 16 (big-endian) c2 ff.Fp2 // sqrt(-1) c3 ff.Fp2 // sqrt(c2) c4 ff.Fp2 // sqrt(Z^3 / c3) c5 ff.Fp2 // sqrt(Z^3 / (c2 * c3)) } g1Sigma struct { beta0 ff.Fp // beta0 = F(2)^(2*(p-1)/3) where F = GF(p). beta1 ff.Fp // beta1 = F(2)^(1*(p-1)/3) where F = GF(p). } g2Psi struct { alpha ff.Fp2 // alpha = w^2/Frob(w^2) beta ff.Fp2 // beta = w^3/Frob(w^3) } ) var ( errInputLength = errors.New("incorrect input length") errEncoding = errors.New("incorrect encoding") ) func headerEncoding(isCompressed, isInfinity, isBigYCoord byte) byte { return (isBigYCoord&0x1)<<5 | (isInfinity&0x1)<<6 | (isCompressed&0x1)<<7 } func err(e error) { if e != nil { panic(e) } } func init() { bls12381.oneMinusZ = [8]byte{ // (big-endian) 0xd2, 0x01, 0x00, 0x00, 0x00, 0x01, 0x00, 0x01, } bls12381.minusZ = [8]byte{ // (big-endian) 0xd2, 0x01, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, } bls12381.g1Check = [16]byte{ // (big-endian) 0x39, 0x6c, 0x8c, 0x00, 0x55, 0x55, 0xe1, 0x56, 0x00, 0x00, 0x00, 0x00, 0x55, 0x55, 0x55, 0x55, } initG1Params() initG2Params() initG1Isog11() initG2Isog3() initG1sswu() initG2sswu() initSigma() initPsi() } func initG1Params() { g1Params.b.SetUint64(4) g1Params._3b.SetUint64(12) err(g1Params.genX.SetString("0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb")) err(g1Params.genY.SetString("0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1")) } func initG2Params() { g2Params.b[0].SetUint64(4) g2Params.b[1].SetUint64(4) g2Params._3b[0].SetUint64(12) g2Params._3b[1].SetUint64(12) err(g2Params.genX[0].SetString("0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8")) err(g2Params.genX[1].SetString("0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e")) err(g2Params.genY[0].SetString("0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801")) err(g2Params.genY[1].SetString("0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be")) } func initG1Isog11() { err(g1Isog11.a.SetString("0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1d")) err(g1Isog11.b.SetString("0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0")) err(g1Isog11.xNum[0].SetString("0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7")) err(g1Isog11.xNum[1].SetString("0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bb")) err(g1Isog11.xNum[2].SetString("0x0d54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0")) err(g1Isog11.xNum[3].SetString("0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861")) err(g1Isog11.xNum[4].SetString("0x0e99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9")) err(g1Isog11.xNum[5].SetString("0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983")) err(g1Isog11.xNum[6].SetString("0x0d6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84")) err(g1Isog11.xNum[7].SetString("0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88e")) err(g1Isog11.xNum[8].SetString("0x080d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317")) err(g1Isog11.xNum[9].SetString("0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9e")) err(g1Isog11.xNum[10].SetString("0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7b")) err(g1Isog11.xNum[11].SetString("0x06e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229")) err(g1Isog11.xDen[0].SetString("0x08ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1c")) err(g1Isog11.xDen[1].SetString("0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bff")) err(g1Isog11.xDen[2].SetString("0x0b2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19")) err(g1Isog11.xDen[3].SetString("0x03425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8")) err(g1Isog11.xDen[4].SetString("0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21e")) err(g1Isog11.xDen[5].SetString("0x0e7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5")) err(g1Isog11.xDen[6].SetString("0x0772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3a")) err(g1Isog11.xDen[7].SetString("0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5e")) err(g1Isog11.xDen[8].SetString("0x0a10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641")) err(g1Isog11.xDen[9].SetString("0x095fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0a")) g1Isog11.xDen[10].SetOne() err(g1Isog11.yNum[0].SetString("0x090d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33")) err(g1Isog11.yNum[1].SetString("0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696")) err(g1Isog11.yNum[2].SetString("0x00cc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6")) err(g1Isog11.yNum[3].SetString("0x01f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cb")) err(g1Isog11.yNum[4].SetString("0x08cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedb")) err(g1Isog11.yNum[5].SetString("0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0")) err(g1Isog11.yNum[6].SetString("0x04ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2")) err(g1Isog11.yNum[7].SetString("0x0987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29")) err(g1Isog11.yNum[8].SetString("0x09fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587")) err(g1Isog11.yNum[9].SetString("0x0e1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30")) err(g1Isog11.yNum[10].SetString("0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132")) err(g1Isog11.yNum[11].SetString("0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8e")) err(g1Isog11.yNum[12].SetString("0x0b182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8")) err(g1Isog11.yNum[13].SetString("0x0245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133")) err(g1Isog11.yNum[14].SetString("0x05c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224b")) err(g1Isog11.yNum[15].SetString("0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604")) err(g1Isog11.yDen[0].SetString("0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1")) err(g1Isog11.yDen[1].SetString("0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03d")) err(g1Isog11.yDen[2].SetString("0x058df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2")) err(g1Isog11.yDen[3].SetString("0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416")) err(g1Isog11.yDen[4].SetString("0x0be0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001d")) err(g1Isog11.yDen[5].SetString("0x08d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7ac")) err(g1Isog11.yDen[6].SetString("0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775c")) err(g1Isog11.yDen[7].SetString("0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9")) err(g1Isog11.yDen[8].SetString("0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4a")) err(g1Isog11.yDen[9].SetString("0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55")) err(g1Isog11.yDen[10].SetString("0x04d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8")) err(g1Isog11.yDen[11].SetString("0x0accbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092")) err(g1Isog11.yDen[12].SetString("0x0ad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345cc")) err(g1Isog11.yDen[13].SetString("0x02660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7")) err(g1Isog11.yDen[14].SetString("0x0e0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8f")) g1Isog11.yDen[15].SetOne() } func initG2Isog3() { err(g2Isog3.a.SetString("0x00", "0xF0")) err(g2Isog3.b.SetString("0x03F4", "0x03F4")) err(g2Isog3.xNum[0].SetString( "0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6", "0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6", )) err(g2Isog3.xNum[1].SetString( "0x00", "0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71a", )) err(g2Isog3.xNum[2].SetString( "0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71e", "0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38d", )) err(g2Isog3.xNum[3].SetString( "0x171d6541fa38ccfaed6dea691f5fb614cb14b4e7f4e810aa22d6108f142b85757098e38d0f671c7188e2aaaaaaaa5ed1", "0x00", )) err(g2Isog3.xDen[0].SetString( "0x00", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa63", )) err(g2Isog3.xDen[1].SetString( "0x0c", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa9f", )) g2Isog3.xDen[2].SetOne() err(g2Isog3.yNum[0].SetString( "0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706", "0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706", )) err(g2Isog3.yNum[1].SetString( "0x00", "0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97be", )) err(g2Isog3.yNum[2].SetString( "0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71c", "0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38f", )) err(g2Isog3.yNum[3].SetString( "0x124c9ad43b6cf79bfbf7043de3811ad0761b0f37a1e26286b0e977c69aa274524e79097a56dc4bd9e1b371c71c718b10", "0x00", )) err(g2Isog3.yDen[0].SetString( "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb", )) err(g2Isog3.yDen[1].SetString( "0x00", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa9d3", )) err(g2Isog3.yDen[2].SetString( "0x12", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa99", )) g2Isog3.yDen[3].SetOne() } func initG1sswu() { g1sswu.Z.SetUint64(11) g1sswu.c1 = [48]byte{ // (big-endian) 0x06, 0x80, 0x44, 0x7a, 0x8e, 0x5f, 0xf9, 0xa6, 0x92, 0xc6, 0xe9, 0xed, 0x90, 0xd2, 0xeb, 0x35, 0xd9, 0x1d, 0xd2, 0xe1, 0x3c, 0xe1, 0x44, 0xaf, 0xd9, 0xcc, 0x34, 0xa8, 0x3d, 0xac, 0x3d, 0x89, 0x07, 0xaa, 0xff, 0xff, 0xac, 0x54, 0xff, 0xff, 0xee, 0x7f, 0xbf, 0xff, 0xff, 0xff, 0xea, 0xaa, } err(g1sswu.c2.SetString("0x3d689d1e0e762cef9f2bec6130316806b4c80eda6fc10ce77ae83eab1ea8b8b8a407c9c6db195e06f2dbeabc2baeff5")) } func initG2sswu() { g2sswu.Z[1].SetUint64(1) g2sswu.Z[0].SetUint64(2) g2sswu.Z.Neg() g2sswu.c1 = [95]byte{ // (big-endian) 0x2a, 0x43, 0x7a, 0x4b, 0x8c, 0x35, 0xfc, 0x74, 0xbd, 0x27, 0x8e, 0xaa, 0x22, 0xf2, 0x5e, 0x9e, 0x2d, 0xc9, 0x0e, 0x50, 0xe7, 0x04, 0x6b, 0x46, 0x6e, 0x59, 0xe4, 0x93, 0x49, 0xe8, 0xbd, 0x05, 0x0a, 0x62, 0xcf, 0xd1, 0x6d, 0xdc, 0xa6, 0xef, 0x53, 0x14, 0x93, 0x30, 0x97, 0x8e, 0xf0, 0x11, 0xd6, 0x86, 0x19, 0xc8, 0x61, 0x85, 0xc7, 0xb2, 0x92, 0xe8, 0x5a, 0x87, 0x09, 0x1a, 0x04, 0x96, 0x6b, 0xf9, 0x1e, 0xd3, 0xe7, 0x1b, 0x74, 0x31, 0x62, 0xc3, 0x38, 0x36, 0x21, 0x13, 0xcf, 0xd7, 0xce, 0xd6, 0xb1, 0xd7, 0x63, 0x82, 0xea, 0xb2, 0x6a, 0xa0, 0x00, 0x01, 0xc7, 0x18, 0xe3, } err(g2sswu.c2.SetString("0x00", "0x01")) err(g2sswu.c3.SetString( "0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2", "0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09", )) err(g2sswu.c4.SetString( "0x699be3b8c6870965e5bf892ad5d2cc7b0e85a117402dfd83b7f4a947e02d978498255a2aaec0ac627b5afbdf1bf1c90", "0x8157cd83046453f5dd0972b6e3949e4288020b5b8a9cc99ca07e27089a2ce2436d965026adad3ef7baba37f2183e9b5", )) err(g2sswu.c5.SetString( "0xf5d0d63d2797471e6d39f306cc0dc0ab85de3bd9f39ce46f3649ac0de9e844417cc8de88716c1fd323fa68040801aea", "0xab1c2ffdd6c253ca155231eb3e71ba044fd562f6f72bc5bad5ec46a0b7a3b0247cf08ce6c6317f40edbc653a72dee17", )) } func initSigma() { err(g1Sigma.beta0.SetString("0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac")) err(g1Sigma.beta1.SetString("0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe")) } func initPsi() { // ratioKummer sets z = t/Frob(t) if it falls in Fp2, panics otherwise. ratioKummer := func(z *ff.Fp2, t *ff.Fp12) { var r ff.Fp12 r.Frob(t) r.Inv(&r) r.Mul(t, &r) if r[1].IsZero() != 1 || r[0][1].IsZero() != 1 || r[0][2].IsZero() != 1 { err(errors.New("failure of result to be in Fp2")) } *z = r[0][0] } w := &ff.Fp12{} w[1].SetOne() wsq := &ff.Fp12{} wsq.Sqr(w) ratioKummer(&g2Psi.alpha, wsq) wcube := &ff.Fp12{} wcube.Mul(wsq, w) ratioKummer(&g2Psi.beta, wcube) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/doc.go000066400000000000000000000051331454601126700224760ustar00rootroot00000000000000// Package bls12381 provides bilinear pairings using the BLS12-381 curve. // // A pairing system consists of three groups G1 and G2 (additive notation) and // Gt (multiplicative notation) of the same order. // Scalars can be used interchangeably between groups. // // These groups have the same order equal to: // // Order = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 // // # Serialization Format // // Elements of G1 and G2 can be encoded in uncompressed form (the x-coordinate // followed by the y-coordinate) or in compressed form (just the x-coordinate). // G1 elements occupy 96 bytes in uncompressed form, and 48 bytes in compressed // form. G2 elements occupy 192 bytes in uncompressed form, and 96 bytes in // compressed form. // // The most-significant three bits of a G1 or G2 encoding should be masked away // before the coordinates are interpreted. These bits are used to unambiguously // represent the underlying element: // // * The most significant bit, when set, indicates that the point is in // compressed form. Otherwise, the point is in uncompressed form. // // * The second-most significant bit indicates that the point is at infinity. // If this bit is set, the remaining bits of the group element's encoding // should be set to zero. // // * The third-most significant bit is set if (and only if) this point is in // compressed form AND it is not the point at infinity AND its y-coordinate // is the lexicographically largest of the two associated with the encoded // x-coordinate. // // |----------------------------------------------------| // | Serialization Format | // |-----|-------|-------|---------------|--------------| // | MSB | MSB-1 | MSB-2 | Description | Encoding | // |-----|-------|-------|---------------|--------------| // | 0 | X | X | Uncompressed | e || x || y | // | 1 | X | X | Compressed | e || x | // |-----|-------|-------|---------------|--------------| // | X | 0 | X | Non-Infinity | e || x || y | // | X | 1 | X | Infinity | e || 0 || 0 | // |-----|-------|-------|---------------|--------------| // | | | | Compressed, | | // | 1 | 0 | 1 | Non-Infinity, | e || x | // | | | | Big y-coord | | // |-----|-------|-------|---------------|--------------| // | | | | Compressed, | | // | 1 | 0 | 0 | Non-Infinity, | e || x | // | | | | Small y-coord | | // |----------------------------------------------------| package bls12381 golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ec2.go000066400000000000000000000101351454601126700224000ustar00rootroot00000000000000package bls12381 import "github.com/cloudflare/circl/ecc/bls12381/ff" func doubleAndLine(P *G2, l *line) { // Reference: // "Faster Pairing Computations on Curves with High-Degree Twists" by // Costello-Lange-Naehrig. [Sec. 5] (eprint.iacr.org/2009/615). // "Complete addition formulas for prime order elliptic curves" by // Costello-Renes-Batina. [Alg.9] (eprint.iacr.org/2015/1060). var R G2 X, Y, Z := &P.x, &P.y, &P.z X3, Y3, Z3 := &R.x, &R.y, &R.z isDoubLine := l != nil _3B := &g2Params._3b var A, B, C, D, E, F, G, T ff.Fp2 B.Sqr(Y) // 1. B = Y1^2 C.Sqr(Z) // 2. C = Z1^2 D.Mul(_3B, &C) // 3. D = 3b*C F.Add(Y, Z) // 4. F = (Y1+Z1) F.Sqr(&F) // F = (Y1+Z1)^2 F.Sub(&F, &B) // F = (Y1+Z1)^2-B F.Sub(&F, &C) // F = (Y1+Z1)^2-B-C if isDoubLine { A.Sqr(X) // 5. A = X1^2 E.Add(X, Y) // E = (X1+Y1) E.Sqr(&E) // E = (X1+Y1)^2 E.Sub(&E, &A) // E = (X1+Y1)^2-A E.Sub(&E, &B) // E = (X1+Y1)^2-A-B = 2X*Y l[0].Add(&A, &A) // 5a. l0 = 2A l[0].Add(&l[0], &A) // l0 = 3A = 3X1^2 l[1] = F // 5b. l1 = F l[1].Neg() // l1 = -F = -2Y1Z1 l[2].Sub(&D, &B) // 5c. l2 = D-B = 3b*Z1^2-Y1^2 } else { E.Mul(X, Y) // 5. E = X*Y E.Add(&E, &E) // E = 2X*Y } T.Add(&D, &D) // 6. T = 2D G.Add(&T, &D) // 7. G = 3D X3.Sub(&B, &G) // 8. X3 = (B-G) X3.Mul(X3, &E) // X3 = E*(B-G) T.Sqr(&T) // 9 . T = 4D^2 Y3.Add(&B, &G) // 10. Y3 = (B+G) Y3.Sqr(Y3) // Y3 = (B+G)^2 Y3.Sub(Y3, &T) // Y3 = (B+G)^2-4D^2 Y3.Sub(Y3, &T) // Y3 = (B+G)^2-8D^2 Y3.Sub(Y3, &T) // Y3 = (B+G)^2-12D^2 Z3.Mul(&B, &F) // 11. Z3 = B*F Z3.Add(Z3, Z3) // Z3 = 2B*F Z3.Add(Z3, Z3) // Z3 = 4B*F *P = R } func addAndLine(PQ, P, Q *G2, l *line) { // Reference: // "Faster Pairing Computations on Curves with High-Degree Twists" by // Costello-Lange-Naehrig. [Sec. 5] (eprint.iacr.org/2009/615). // "Complete addition formulas for prime order elliptic curves" by // Costello-Renes-Batina. [Alg.7] (eprint.iacr.org/2015/1060). var R G2 X1, Y1, Z1 := &P.x, &P.y, &P.z X2, Y2, Z2 := &Q.x, &Q.y, &Q.z X3, Y3, Z3 := &R.x, &R.y, &R.z _3B := &g2Params._3b isAddLine := l != nil var X1X2, Y1Y2, Z1Z2, _3bZ1Z2 ff.Fp2 var A, B, C, D, E, F, G ff.Fp2 t0, t1 := &ff.Fp2{}, &ff.Fp2{} X1X2.Mul(X1, X2) Y1Y2.Mul(Y1, Y2) Z1Z2.Mul(Z1, Z2) _3bZ1Z2.Mul(&Z1Z2, _3B) A.Add(&X1X2, &X1X2) // A = 2X1X2 A.Add(&A, &X1X2) // = 3X1X2 B.Add(&Y1Y2, &_3bZ1Z2) // B = Y1Y2+3bZ1Z2 C.Sub(&Y1Y2, &_3bZ1Z2) // C = Y1Y2-3bZ1Z2 t0.Add(X1, Y1) // t0 = (X1 + Y1) D.Add(X2, Y2) // D = (X2 + Y2) D.Mul(&D, t0) // = X1X2 + X1Y2 + X2Y1 + Y1Y2 D.Sub(&D, &X1X2) // = X1Y2 + X2Y1 + Y1Y2 D.Sub(&D, &Y1Y2) // = X1Y2 + X2Y1 if isAddLine { var EE, FF ff.Fp2 t0.Mul(Y1, Z2) // t0 = Y1Z2 t1.Mul(Y2, Z1) // t1 = Y2Z1 E.Add(t0, t1) // E = Y1Z2 + Y2Z1 EE.Sub(t0, t1) // EE = Y1Z2 - Y2Z1 t0.Mul(X1, Z2) // t0 = X1Z2 t1.Mul(X2, Z1) // t1 = X2Z1 F.Add(t0, t1) // F = X1Z2 + X2Z1 FF.Sub(t0, t1) // FF = X1Z2 - X2Z1 l[0].Mul(&EE, Z2) // l0 = (Y1Z2 - Y2Z1)*Z2 l[0].Neg() // = -(Y1Z2 - Y2Z1)*Z2 l[1].Mul(&FF, Z2) // l1 = (X1Z2 - X2Z1)*Z2 t0.Mul(&FF, Y2) // t0 = (X1Z2 - X2Z1)*Y2 l[2].Mul(&EE, X2) // l2 = (Y1Z2 - Y2Z1)*X2 l[2].Sub(&l[2], t0) // = (Y1Z2 - Y2Z1)*X2 - (X1Z2 - X2Z1)*Y2 } else { t0.Add(Y1, Z1) // t0 = (Y1 + Z1) t1.Add(Y2, Z2) // t1 = (Y2 + Z2) E.Mul(t0, t1) // E = Y1Y2 + Y1Z2 + Y2Z1 + Z1Z2 E.Sub(&E, &Y1Y2) // = Y1Z2 + Y2Z1 + Z1Z2 E.Sub(&E, &Z1Z2) // = Y1Z2 + Y2Z1 t0.Add(X1, Z1) // t0 = (X1 + Z1) t1.Add(X2, Z2) // t1 = (X2 + Z2) F.Mul(t0, t1) // F = X1X2 + X1Z2 + X2Z1 + Z1Z2 F.Sub(&F, &X1X2) // = X1Z2 + X2Z1 + Z1Z2 F.Sub(&F, &Z1Z2) // = X1Z2 + X2Z1 } G.Mul(&F, _3B) // G = 3b*F t0.Mul(&E, &G) // t0 = E*G X3.Mul(&D, &C) // X3 = D*C X3.Sub(X3, t0) // = D*C - E*G t0.Mul(&A, &G) // t0 = A*G Y3.Mul(&B, &C) // Y3 = B*C Y3.Add(Y3, t0) // = B*C + A*G t0.Mul(&A, &D) // t0 = A*D Z3.Mul(&E, &B) // Z3 = E*B Z3.Add(Z3, t0) // = E*B + A*D *PQ = R } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/encoding_test.go000066400000000000000000000034641454601126700245630ustar00rootroot00000000000000package bls12381 import ( "bytes" "io" "os" "testing" "github.com/cloudflare/circl/internal/test" ) func isEqual(p, q interface{}) bool { switch P := p.(type) { case *G1: return P.IsEqual(q.(*G1)) case *G2: return P.IsEqual(q.(*G2)) default: panic("bad type") } } func addGenerator(p interface{}) { switch P := p.(type) { case *G1: P.Add(P, G1Generator()) case *G2: P.Add(P, G2Generator()) default: panic("bad type") } } func testSerialVector(t *testing.T, file io.Reader, v *serialVector) { var bP []byte bQ := make([]byte, v.length) v.P.SetIdentity() for i := 0; i < 1000; i++ { n, err := file.Read(bQ) if n != v.length || err != nil { t.Fatalf("error reading %v file: %v", v.fileName, err) } test.CheckNoErr(t, v.Q.SetBytes(bQ), "failed deserialization") if !isEqual(v.P, v.Q) { test.ReportError(t, v.P, v.Q, i) } if v.compressed { bP = v.P.BytesCompressed() } else { bP = v.P.Bytes() } if !bytes.Equal(bP, bQ) { test.ReportError(t, bP, bQ, i) } addGenerator(v.P) } } type serialVector struct { fileName string length int compressed bool P, Q interface { SetIdentity() SetBytes([]byte) error Bytes() []byte BytesCompressed() []byte } } func TestSerializationVector(t *testing.T) { for _, vv := range []serialVector{ {"g1_uncompressed", G1Size, false, new(G1), new(G1)}, {"g1_compressed", G1SizeCompressed, true, new(G1), new(G1)}, {"g2_uncompressed", G2Size, false, new(G2), new(G2)}, {"g2_compressed", G2SizeCompressed, true, new(G2), new(G2)}, } { v := vv file, err := os.Open("testdata/" + v.fileName + "_valid_test_vectors.dat") if err != nil { t.Fatalf("file %v can not be opened: %v", v.fileName, err) } defer file.Close() t.Run(v.fileName[:7], func(t *testing.T) { testSerialVector(t, file, &v) }) } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/000077500000000000000000000000001454601126700217735ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/common.go000066400000000000000000000040221454601126700236100ustar00rootroot00000000000000// Package ff provides finite fields of characteristic P381. package ff import ( "crypto/rand" "crypto/subtle" "errors" "io" "math/big" "github.com/cloudflare/circl/internal/conv" ) var ( errInputLength = errors.New("incorrect input length") errInputRange = errors.New("value out of range [0,order)") errInputString = errors.New("invalid string") ) func errFirst(e ...error) (err error) { for i := 0; i < len(e); i++ { if e[i] != nil { return e[i] } } return } func setString(in string, order []byte) ([]uint64, error) { inBig, ok := new(big.Int).SetString(in, 0) if !ok { return nil, errInputString } if inBig.Sign() < 0 || inBig.Cmp(new(big.Int).SetBytes(order)) >= 0 { return nil, errInputRange } inBytes := inBig.FillBytes(make([]byte, len(order))) return setBytesBounded(inBytes, order) } func setBytesBounded(in []byte, order []byte) ([]uint64, error) { if isLessThan(in, order) == 0 { return nil, errInputRange } return conv.BytesBe2Uint64Le(in), nil } func setBytesUnbounded(in []byte, order []byte) []uint64 { inBig := new(big.Int).SetBytes(in) inBig.Mod(inBig, new(big.Int).SetBytes(order)) inBytes := inBig.FillBytes(make([]byte, len(order))) return conv.BytesBe2Uint64Le(inBytes) } // isLessThan returns 1 if 0 <= x < y, otherwise 0. Assumes that slices have the same length. func isLessThan(x, y []byte) int { i := 0 for i < len(x)-1 && x[i] == y[i] { i++ } return 1 - subtle.ConstantTimeLessOrEq(int(y[i]), int(x[i])) } func randomInt(out []uint64, rnd io.Reader, order []byte) error { r, err := rand.Int(rnd, new(big.Int).SetBytes(order)) if err == nil { conv.BigInt2Uint64Le(out, r) } return err } // ctUint64Eq returns 1 if the two slices have equal contents and 0 otherwise. func ctUint64Eq(x, y []uint64) (b int) { if len(x) == len(y) { var v uint64 for i := 0; i < len(x); i++ { v |= x[i] ^ y[i] } return subtle.ConstantTimeEq(int32(v>>32), 0) & subtle.ConstantTimeEq(int32(v), 0) } return } func cselectU64(z *uint64, b, x, y uint64) { *z = (x &^ (-b)) | (y & (-b)) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/cyclo6.go000066400000000000000000000052461454601126700235300ustar00rootroot00000000000000package ff // Cyclo6 represents an element of the 6th cyclotomic group. type Cyclo6 Fp12 func (z Cyclo6) String() string { return (Fp12)(z).String() } func (z Cyclo6) IsEqual(x *Cyclo6) int { return (Fp12)(z).IsEqual((*Fp12)(x)) } func (z Cyclo6) IsIdentity() int { i := &Fp12{}; i.SetOne(); return z.IsEqual((*Cyclo6)(i)) } func (z *Cyclo6) Frob(x *Cyclo6) { (*Fp12)(z).Frob((*Fp12)(x)) } func (z *Cyclo6) Mul(x, y *Cyclo6) { (*Fp12)(z).Mul((*Fp12)(x), (*Fp12)(y)) } func (z *Cyclo6) Sqr(x *Cyclo6) { (*Fp12)(z).Sqr((*Fp12)(x)) } func (z *Cyclo6) Inv(x *Cyclo6) { *z = *x; z[1].Neg() } func (z *Cyclo6) exp(x *Cyclo6, n []byte) { (*Fp12)(z).Exp((*Fp12)(x), n) } // PowToX computes z = x^paramX, where paramX is the parameter of the BLS curve. func (z *Cyclo6) PowToX(x *Cyclo6) { t := new(Cyclo6) *t = *x const lenX = 64 for i := lenX - 2; i >= 0; i-- { t.Sqr(t) // paramX is -2 ^ 63 - 2 ^ 62 - 2 ^ 60 - 2 ^ 57 - 2 ^ 48 - 2 ^ 16 if (i == 62) || (i == 60) || (i == 57) || (i == 48) || (i == 16) { t.Mul(t, x) } } z.Inv(t) } // EasyExponentiation calculates g = f^(p^6-1)(p^2+1), where g becomes an // element of the 6-th cyclotomic group. func EasyExponentiation(g *Cyclo6, f *Fp12) { var t0, t1, p Fp12 p.Frob(f) // p = f^(p) p.Frob(&p) // p = f^(p^2) t0.Mul(&p, f) // t0 = f^(p^2 + 1) t1.Frob(&t0) // t1 = f^(p^2 + 1)*(p) t1.Frob(&t1) // t1 = f^(p^2 + 1)*(p^2) t1.Frob(&t1) // t1 = f^(p^2 + 1)*(p^3) t1.Frob(&t1) // t1 = f^(p^2 + 1)*(p^4) t1.Frob(&t1) // t1 = f^(p^2 + 1)*(p^5) t1.Frob(&t1) // t1 = f^(p^2 + 1)*(p^6) t0.Inv(&t0) // t0 = f^-(p^2 + 1) t0.Mul(&t0, &t1) // t0 = f^(p^2 + 1)*(p^6 - 1) *g = (Cyclo6)(t0) } // HardExponentiation calculates u = g^(Cy_6(p)/r), where u is a root of unity. func HardExponentiation(u *URoot, g *Cyclo6) { var t0, t1, _g, g3 Cyclo6 var c, a0, a1, a2, a3 Cyclo6 _g.Inv(g) // _g = g^-1 g3.Sqr(g) // g3 = g^2 g3.Mul(&g3, g) // g3 = g^3 t0.PowToX(g) // t0 = g^x t0.Mul(&t0, &_g) // t0 = g^(x-1) t1.PowToX(&t0) // t1 = g^(x-1)*x t0.Inv(&t0) // t0 = g^-(x-1) a3.Mul(&t1, &t0) // a3 = g^(x-1)*(x-1) a2.Frob(&a3) // a2 = a3*p a1.Frob(&a2) // a1 = a2*p = a3*p^2 t0.Inv(&a3) // t0 = -a3 a1.Mul(&a1, &t0) // a1 = a3*p^2-a3 a0.Frob(&a1) // a0 = a3*p^3-a3*p a0.Mul(&a0, &g3) // a0 = a3*p^3-a3*p+3 c.PowToX(&a3) // c = g^(a3*x) c.Mul(&c, &a2) // c = g^(a3*x+a2) c.PowToX(&c) // c = g^(a3*x+a2)*x = g^(a3*x^2+a2*x) c.Mul(&c, &a1) // c = g^(a3*x^2+a2*x+a1) c.PowToX(&c) // c = g^(a3*x^2+a2*x+a1)*x = g^(a3*x^3+a2*x^2+a1*x) c.Mul(&c, &a0) // c = g^(a3*x^3+a2*x^2+a1*x+a0) *u = (URoot)(c) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/cyclo6_test.go000066400000000000000000000047031454601126700245640ustar00rootroot00000000000000package ff import ( "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) func randomCyclo6(t testing.TB) *Cyclo6 { c := &Cyclo6{} EasyExponentiation(c, randomFp12(t)) return c } // phi6primeSq evaluates the 6-th cyclotomic polynomial, \phi_6(x) = x^2-x+1, at p^2. func phi6primeSq() []byte { one := big.NewInt(1) p := new(big.Int).SetBytes(fpOrder[:]) // p p2 := new(big.Int).Mul(p, p) // p^2 p4 := new(big.Int).Sub(p2, one) // p^2 - 1 p4.Mul(p4, p2) // p^4 - p^2 p4.Add(p4, one) // p^4 - p^2 + 1 return p4.Bytes() } func TestCyclo6(t *testing.T) { const testTimes = 1 << 10 t.Run("no_alias", func(t *testing.T) { var want, got Cyclo6 x := randomCyclo6(t) got = *x got.Sqr(&got) want = *x want.Mul(&want, &want) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } }) t.Run("order", func(t *testing.T) { cyclo6Order := phi6primeSq() var z Cyclo6 for i := 0; i < 16; i++ { x := randomCyclo6(t) z.exp(x, cyclo6Order) // x^phi6primeSq = 1 got := z.IsIdentity() want := 1 if got != want { test.ReportError(t, got, want, x, z) } } }) t.Run("mul_inv", func(t *testing.T) { var z Cyclo6 for i := 0; i < testTimes; i++ { x := randomCyclo6(t) y := randomCyclo6(t) // x*y*x^1 = y z.Inv(x) z.Mul(&z, y) z.Mul(&z, x) got := z want := y if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("mul_sqr", func(t *testing.T) { var want, got Cyclo6 for i := 0; i < testTimes; i++ { x := randomCyclo6(t) // x*x = x^2 got.Mul(x, x) want.Sqr(x) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } } }) t.Run("invFp12_vs_invCyclo6", func(t *testing.T) { var want, got Fp12 var y Cyclo6 for i := 0; i < testTimes; i++ { x := randomCyclo6(t) y.Inv(x) got = (Fp12)(y) want.Inv((*Fp12)(x)) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } } }) } func BenchmarkCyclo6(b *testing.B) { x := randomCyclo6(b) y := randomCyclo6(b) z := randomCyclo6(b) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sqr(x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Inv(x) } }) b.Run("PowToX", func(b *testing.B) { for i := 0; i < b.N; i++ { z.PowToX(x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/doc.go000066400000000000000000000036531454601126700230760ustar00rootroot00000000000000// Package ff provides finite fields and groups useful for the BLS12-381 curve. // // # Fp // // Fp are elements of the prime field GF(p), where // // p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab // // The binary representation takes FpSize = 48 bytes encoded in big-endian form. // // # Fp2 // // Fp2 are elements of the finite field GF(p^2) = Fp[u]/(u^2+1) represented as // // (a[1]u + a[0]) in Fp2, where a[0],a[1] in Fp // // The binary representation takes Fp2Size = 96 bytes encoded as a[1] || a[0] // all in big-endian form. // // # Fp4 // // Fp4 is GF(p^4)=Fp2[t]/(t^2-(u+1)). We use the representation a[1]v+a[0]. // There is no fixed external form. // // # Fp6 // // Fp6 are elements of the finite field GF(p^6) = Fp2[v]/(v^3-u-1) represented as // // (a[2]v^2 + a[1]v + a[0]) in Fp6, where a[0],a[1],a[2] in Fp2 // // The binary representation takes Fp6Size = 288 bytes encoded as a[2] || a[1] || a[0] // all in big-endian form. // // # Fp12 // // Fp12 are elements of the finite field GF(p^12) = Fp6[w]/(w^2-v) represented as // // (a[1]w + a[0]) in Fp12, where a[0],a[1] in Fp6 // // The binary representation takes Fp12Size = 576 bytes encoded as a[1] || a[0] // all in big-endian form. // // We can also represent this field via Fp4[w]/(w^3-t). This is the struct Fp12alt, // used to accelerate the pairing calculation. // // # Scalar // // Scalar are elements of the prime field GF(r), where // // r = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 // // The binary representation takes ScalarSize = 32 bytes encoded in big-endian form. // // # Groups // // Cyclo6 are elements of the 6th cyclotomic group contained in Fp12. // For efficient arithmetic see Granger-Scott "Faster Squaring in the Cyclotomic Subgroup of Sixth // Degree Extensions" (https://eprint.iacr.org/2009/565). // // URoot are elements of the r-roots of unity group contained in Fp12. package ff golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp.go000066400000000000000000000164371454601126700227420ustar00rootroot00000000000000package ff import ( "io" "github.com/cloudflare/circl/internal/conv" ) // FpSize is the length in bytes of an Fp element. const FpSize = 48 // fpMont represents an element in the Montgomery domain (little-endian). type fpMont = [FpSize / 8]uint64 // fpRaw represents an element in the integers domain (little-endian). type fpRaw = [FpSize / 8]uint64 // Fp represents prime field elements as positive integers less than FpOrder. type Fp struct{ i fpMont } func (z Fp) String() string { x := z.fromMont(); return conv.Uint64Le2Hex(x[:]) } func (z *Fp) SetUint64(n uint64) { z.toMont(&fpRaw{n}) } func (z *Fp) SetOne() { z.SetUint64(1) } func (z *Fp) Random(r io.Reader) error { return randomInt(z.i[:], r, fpOrder[:]) } // IsNegative returns 0 if the least absolute residue for z is in [0,(p-1)/2], // and 1 otherwise. Equivalently, this function returns 1 if z is // lexicographically larger than -z. func (z Fp) IsNegative() int { b, _ := z.MarshalBinary() return 1 - isLessThan(b, fpOrderPlus1Div2[:]) } // IsZero returns 1 if z == 0 and 0 otherwise. func (z Fp) IsZero() int { return ctUint64Eq(z.i[:], (&fpMont{})[:]) } // IsEqual returns 1 if z == x and 0 otherwise. func (z Fp) IsEqual(x *Fp) int { return ctUint64Eq(z.i[:], x.i[:]) } func (z *Fp) Neg() { fiatFpMontSub(&z.i, &fpMont{}, &z.i) } func (z *Fp) Add(x, y *Fp) { fiatFpMontAdd(&z.i, &x.i, &y.i) } func (z *Fp) Sub(x, y *Fp) { fiatFpMontSub(&z.i, &x.i, &y.i) } func (z *Fp) Mul(x, y *Fp) { fiatFpMontMul(&z.i, &x.i, &y.i) } func (z *Fp) Sqr(x *Fp) { fiatFpMontSquare(&z.i, &x.i) } func (z *Fp) toMont(in *fpRaw) { fiatFpMontMul(&z.i, in, &fpRSquare) } func (z Fp) fromMont() (out fpRaw) { fiatFpMontMul(&out, &z.i, &fpMont{1}); return } func (z Fp) Sgn0() int { return int(z.fromMont()[0]) & 1 } // Sqrt returns 1 and sets z=sqrt(x) only if x is a quadratic-residue; otherwise, returns 0 and z is unmodified. func (z *Fp) Sqrt(x *Fp) int { var y, y2 Fp y.ExpVarTime(x, fpOrderPlus1Div4[:]) y2.Sqr(&y) isQR := y2.IsEqual(x) z.CMov(z, &y, isQR) return isQR } // CMov sets z=x if b == 0 and z=y if b == 1. Its behavior is undefined if b takes any other value. func (z *Fp) CMov(x, y *Fp, b int) { mask := -uint64(b & 0x1) for i := 0; i < FpSize/8; i++ { z.i[i] = (x.i[i] &^ mask) | (y.i[i] & mask) } } // FpOrder is the order of the base field for towering returned as a big-endian slice. // // FpOrder = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab. func FpOrder() []byte { o := fpOrder; return o[:] } // ExpVarTime calculates z=x^n, where n is the exponent in big-endian order. func (z *Fp) ExpVarTime(x *Fp, n []byte) { zz := new(Fp) zz.SetOne() N := 8 * len(n) for i := 0; i < N; i++ { zz.Sqr(zz) bit := 0x1 & (n[i/8] >> uint(7-i%8)) if bit != 0 { zz.Mul(zz, x) } } *z = *zz } // SetBytes assigns to z the number modulo FpOrder stored in the slice // (in big-endian order). func (z *Fp) SetBytes(data []byte) { in64 := setBytesUnbounded(data, fpOrder[:]) s := &fpRaw{} copy(s[:], in64[:FpSize/8]) z.toMont(s) } // MarshalBinary returns a slice of FpSize bytes that contains the minimal // residue of z such that 0 <= z < FpOrder (in big-endian order). func (z *Fp) MarshalBinary() ([]byte, error) { x := z.fromMont() return conv.Uint64Le2BytesBe(x[:]), nil } // UnmarshalBinary reconstructs a Fp from a slice that must have at least // FpSize bytes and contain a number (in big-endian order) from 0 // to FpOrder-1. func (z *Fp) UnmarshalBinary(b []byte) error { if len(b) < FpSize { return errInputLength } in64, err := setBytesBounded(b[:FpSize], fpOrder[:]) if err == nil { s := &fpRaw{} copy(s[:], in64[:FpSize/8]) z.toMont(s) } return err } // SetString reconstructs a Fp from a numeric string from 0 to FpOrder-1. func (z *Fp) SetString(s string) error { in64, err := setString(s, fpOrder[:]) if err == nil { s := &fpRaw{} copy(s[:], in64[:FpSize/8]) z.toMont(s) } return err } func fiatFpMontCmovznzU64(z *uint64, b, x, y uint64) { cselectU64(z, b, x, y) } func (z *Fp) Inv(x *Fp) { // Addition chain found using mmcloughlin/addchain: v0.3.0 // McLoughlin, Michael Ben. (2021). https://doi.org/10.5281/zenodo.4758226 var i2, i4, i8, i9, i11, i13, i17, i20, i25, i26, i52, i54, i55, i77, i79, i86, i93, i103, i105, i119, i123, i137, i149, i151, i169, i177, i191, i195, i208, i215, i225, i229, i235, i245, i255 Fp i2.Sqr(x) i4.Sqr(&i2) i8.Sqr(&i4) i9.Mul(&i8, x) i11.Mul(&i9, &i2) i13.Mul(&i11, &i2) i17.Mul(&i13, &i4) i20.Mul(&i11, &i9) i25.Mul(&i17, &i8) i26.Mul(&i25, x) i52.Sqr(&i26) i54.Mul(&i52, &i2) i55.Mul(&i54, x) i77.Mul(&i52, &i25) i79.Mul(&i77, &i2) i86.Mul(&i77, &i8) i93.Mul(&i86, &i8) i103.Mul(&i77, &i26) i105.Mul(&i103, &i2) i119.Mul(&i93, &i26) i123.Mul(&i119, &i4) i137.Mul(&i86, &i52) i149.Mul(&i123, &i26) i151.Mul(&i149, &i2) i169.Mul(&i149, &i20) i177.Mul(&i169, &i8) i191.Mul(&i137, &i54) i195.Mul(&i191, &i4) i208.Mul(&i195, &i13) i215.Mul(&i195, &i20) i225.Mul(&i208, &i17) i229.Mul(&i225, &i4) i235.Mul(&i215, &i20) i245.Mul(&i225, &i20) i255.Mul(&i235, &i20) z.Mul(&i225, &i191) for _, s := range []struct { l int x *Fp }{ {8, &i17}, {11, &i245}, {11, &i229}, {8, &i255}, {7, &i77}, {9, &i105}, {10, &i177}, {7, &i93}, {9, &i123}, {6, &i25}, {11, &i105}, {9, &i235}, {10, &i215}, {6, &i25}, {10, &i119}, {9, &i151}, {11, &i79}, {10, &i225}, {9, &i137}, {9, &i191}, {8, &i103}, {10, &i195}, {9, &i149}, {12, &i123}, {5, &i11}, {11, &i123}, {7, &i9}, {13, &i245}, {9, &i191}, {8, &i255}, {8, &i235}, {11, &i169}, {8, &i255}, {8, &i255}, {6, &i55}, {10, &i255}, {9, &i255}, {8, &i255}, {8, &i255}, {8, &i255}, {7, &i86}, {9, &i169}, } { for i := 0; i < s.l; i++ { z.Sqr(z) } z.Mul(z, s.x) } } var ( // fpOrder is the order of the Fp field (big-endian). fpOrder = [FpSize]byte{ 0x1a, 0x01, 0x11, 0xea, 0x39, 0x7f, 0xe6, 0x9a, 0x4b, 0x1b, 0xa7, 0xb6, 0x43, 0x4b, 0xac, 0xd7, 0x64, 0x77, 0x4b, 0x84, 0xf3, 0x85, 0x12, 0xbf, 0x67, 0x30, 0xd2, 0xa0, 0xf6, 0xb0, 0xf6, 0x24, 0x1e, 0xab, 0xff, 0xfe, 0xb1, 0x53, 0xff, 0xff, 0xb9, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xaa, 0xab, } // fpOrderPlus1Div2 is the half of (fpOrder plus one) used for lexicographically order (big-endian). fpOrderPlus1Div2 = [FpSize]byte{ 0x0d, 0x00, 0x88, 0xf5, 0x1c, 0xbf, 0xf3, 0x4d, 0x25, 0x8d, 0xd3, 0xdb, 0x21, 0xa5, 0xd6, 0x6b, 0xb2, 0x3b, 0xa5, 0xc2, 0x79, 0xc2, 0x89, 0x5f, 0xb3, 0x98, 0x69, 0x50, 0x7b, 0x58, 0x7b, 0x12, 0x0f, 0x55, 0xff, 0xff, 0x58, 0xa9, 0xff, 0xff, 0xdc, 0xff, 0x7f, 0xff, 0xff, 0xff, 0xd5, 0x56, } // fpOrderPlus1Div4 is (fpOrder plus one) divided by four used for square-roots (big-endian). fpOrderPlus1Div4 = [FpSize]byte{ 0x06, 0x80, 0x44, 0x7a, 0x8e, 0x5f, 0xf9, 0xa6, 0x92, 0xc6, 0xe9, 0xed, 0x90, 0xd2, 0xeb, 0x35, 0xd9, 0x1d, 0xd2, 0xe1, 0x3c, 0xe1, 0x44, 0xaf, 0xd9, 0xcc, 0x34, 0xa8, 0x3d, 0xac, 0x3d, 0x89, 0x07, 0xaa, 0xff, 0xff, 0xac, 0x54, 0xff, 0xff, 0xee, 0x7f, 0xbf, 0xff, 0xff, 0xff, 0xea, 0xab, } // fpRSquare is R^2 mod fpOrder, where R=2^384 (little-endian). fpRSquare = fpMont{ 0xf4df1f341c341746, 0x0a76e6a609d104f1, 0x8de5476c4c95b6d5, 0x67eb88a9939d83c0, 0x9a793e85b519952d, 0x11988fe592cae3aa, } ) golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp12.go000066400000000000000000000065111454601126700230750ustar00rootroot00000000000000package ff import ( "crypto/subtle" "fmt" ) // Fp12Size is the length in bytes of an Fp12 element. const Fp12Size = 2 * Fp6Size // Fp12 represents an element of the field Fp12 = Fp6[w]/(w^2-v)., where v in Fp6. type Fp12 [2]Fp6 func (z Fp12) String() string { return fmt.Sprintf("0: %v\n1: %v", z[0], z[1]) } func (z *Fp12) SetOne() { z[0].SetOne(); z[1] = Fp6{} } func (z Fp12) IsZero() int { return z.IsEqual(&Fp12{}) } func (z Fp12) IsEqual(x *Fp12) int { return z[0].IsEqual(&x[0]) & z[1].IsEqual(&x[1]) } func (z *Fp12) MulBeta() { t := z[0]; z[0].Sub(&z[0], &z[1]); z[1].Add(&t, &z[1]) } func (z *Fp12) Frob(x *Fp12) { z[0].Frob(&x[0]); z[1].Frob(&x[1]); z[1].Mul(&z[1], &Fp6{frob12W1}) } func (z *Fp12) Cjg() { z[1].Neg() } func (z *Fp12) Neg() { z[0].Neg(); z[1].Neg() } func (z *Fp12) Add(x, y *Fp12) { z[0].Add(&x[0], &y[0]); z[1].Add(&x[1], &y[1]) } func (z *Fp12) Sub(x, y *Fp12) { z[0].Sub(&x[0], &y[0]); z[1].Sub(&x[1], &y[1]) } func (z *Fp12) Mul(x, y *Fp12) { var x0y0, x1y1, sx, sy, k Fp6 x0y0.Mul(&x[0], &y[0]) x1y1.Mul(&x[1], &y[1]) sx.Add(&x[0], &x[1]) sy.Add(&y[0], &y[1]) k.Mul(&sx, &sy) z[1].Sub(&k, &x0y0) z[1].Sub(&z[1], &x1y1) x1y1.MulBeta() z[0].Add(&x0y0, &x1y1) } func (z *Fp12) Sqr(x *Fp12) { var x02, x12, k Fp6 x02.Sqr(&x[0]) x12.Sqr(&x[1]) x12.MulBeta() k.Mul(&x[0], &x[1]) z[0].Add(&x02, &x12) z[1].Add(&k, &k) } func (z *Fp12) Inv(x *Fp12) { var x02, x12, den Fp6 x02.Sqr(&x[0]) x12.Sqr(&x[1]) x12.MulBeta() den.Sub(&x02, &x12) den.Inv(&den) z[0].Mul(&x[0], &den) z[1].Mul(&x[1], &den) z[1].Neg() } func (z *Fp12) CMov(x, y *Fp12, b int) { z[0].CMov(&x[0], &y[0], b) z[1].CMov(&x[1], &y[1], b) } // Exp calculates z=x^n, where n is the exponent in big-endian order. func (z *Fp12) Exp(x *Fp12, n []byte) { zz := new(Fp12) zz.SetOne() T := new(Fp12) var mults [16]Fp12 mults[0].SetOne() mults[1] = *x for i := 1; i < 8; i++ { mults[2*i] = mults[i] mults[2*i].Sqr(&mults[2*i]) mults[2*i+1].Mul(&mults[2*i], x) } N := 8 * len(n) for i := 0; i < N; i += 4 { zz.Sqr(zz) zz.Sqr(zz) zz.Sqr(zz) zz.Sqr(zz) idx := 0xf & (n[i/8] >> uint(4-i%8)) for j := 0; j < 16; j++ { T.CMov(T, &mults[j], subtle.ConstantTimeByteEq(idx, uint8(j))) } zz.Mul(zz, T) } *z = *zz } func (z *Fp12) UnmarshalBinary(b []byte) error { if len(b) < Fp12Size { return errInputLength } return errFirst( z[1].UnmarshalBinary(b[:Fp6Size]), z[0].UnmarshalBinary(b[Fp6Size:2*Fp6Size]), ) } func (z Fp12) MarshalBinary() (b []byte, e error) { var b0, b1 []byte if b1, e = z[1].MarshalBinary(); e == nil { if b0, e = z[0].MarshalBinary(); e == nil { return append(b1, b0...), e } } return } // frob12W1 is Fp2 = [toMont(frob12W1_0), toMont(frob12W1_1) ], where // // frob12W1_0 = 0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8 // frob12W1_1 = 0xfc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3 var frob12W1 = Fp2{ Fp{fpMont{ // (little-endian) 0x07089552b319d465, 0xc6695f92b50a8313, 0x97e83cccd117228f, 0xa35baecab2dc29ee, 0x1ce393ea5daace4d, 0x08f2220fb0fb66eb, }}, Fp{fpMont{ // (little-endian) 0xb2f66aad4ce5d646, 0x5842a06bfc497cec, 0xcf4895d42599d394, 0xc11b9cba40a8e8d0, 0x2e3813cbe5a0de89, 0x110eefda88847faf, }}, } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp12_test.go000066400000000000000000000042441454601126700241350ustar00rootroot00000000000000package ff import ( "testing" "github.com/cloudflare/circl/internal/test" ) func randomFp12(t testing.TB) *Fp12 { return &Fp12{*randomFp6(t), *randomFp6(t)} } func TestFp12(t *testing.T) { const testTimes = 1 << 8 t.Run("no_alias", func(t *testing.T) { var want, got Fp12 x := randomFp12(t) got = *x got.Sqr(&got) want = *x want.Mul(&want, &want) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } }) t.Run("mul_inv", func(t *testing.T) { var z Fp12 for i := 0; i < testTimes; i++ { x := randomFp12(t) y := randomFp12(t) // x*y*x^1 - y = 0 z.Inv(x) z.Mul(&z, y) z.Mul(&z, x) z.Sub(&z, y) got := z.IsZero() want := 1 if got != want { test.ReportError(t, got, want, x, y) } } }) t.Run("mul_sqr", func(t *testing.T) { var l0, l1, r0, r1 Fp12 for i := 0; i < testTimes; i++ { x := randomFp12(t) y := randomFp12(t) // (x+y)(x-y) = (x^2-y^2) l0.Add(x, y) l1.Sub(x, y) l0.Mul(&l0, &l1) r0.Sqr(x) r1.Sqr(y) r0.Sub(&r0, &r1) got := &l0 want := &r0 if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("marshal", func(t *testing.T) { var b Fp12 for i := 0; i < testTimes; i++ { a := randomFp12(t) s, err := a.MarshalBinary() test.CheckNoErr(t, err, "MarshalBinary failed") err = b.UnmarshalBinary(s) test.CheckNoErr(t, err, "UnmarshalBinary failed") if b.IsEqual(a) == 0 { test.ReportError(t, a, b) } } }) t.Run("frobenius", func(t *testing.T) { var got, want Fp12 p := FpOrder() for i := 0; i < testTimes; i++ { x := randomFp12(t) // Frob(x) == x^p got.Frob(x) want.Exp(x, p) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } } }) } func BenchmarkFp12(b *testing.B) { x := randomFp12(b) y := randomFp12(b) z := randomFp12(b) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Add(x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sqr(x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Inv(x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp12cubic.go000066400000000000000000000067041454601126700241070ustar00rootroot00000000000000package ff import "fmt" // Fp12Cubic represents elements of Fp4[w]/w^3-t type Fp12Cubic [3]Fp4 // LineValue a represents a[0]+a[1]*w^2+a[2]*w^3, with all values in Fp2. // This lets us shave off a number of Fp2 multiplications. type LineValue [3]Fp2 func (z Fp12Cubic) String() string { return fmt.Sprintf("%s + ( %s )*w + ( %s )*w^2", z[0], z[1], z[2]) } func (z Fp12Cubic) IsEqual(x *Fp12Cubic) int { return z[0].IsEqual(&x[0]) & z[1].IsEqual(&x[1]) & z[2].IsEqual(&x[2]) } func (z *Fp12Cubic) FromFp12(x *Fp12) { // To understand this function, write everything in Fp2[w]/(w^6-(u+1)). // v = w^2 // t = w^3 z[0][0] = x[0][0] // w^0 z[1][0] = x[1][0] // w^1 z[2][0] = x[0][1] // w^2 z[0][1] = x[1][1] // w^3 z[1][1] = x[0][2] // w^4 z[2][1] = x[1][2] // w^5 } func (z *Fp12) FromFp12Alt(x *Fp12Cubic) { z[0][0] = x[0][0] // w^0 z[1][0] = x[1][0] // w^1 z[0][1] = x[2][0] // w^2 z[1][1] = x[0][1] // w^3 z[0][2] = x[1][1] // w^4 z[1][2] = x[2][1] // w^5 } func (z *Fp12Cubic) Add(x *Fp12Cubic, y *Fp12Cubic) { z[0].Add(&x[0], &y[0]) z[1].Add(&x[1], &y[1]) z[2].Add(&x[2], &y[2]) } func (z *Fp12Cubic) SetOne() { z[0].SetOne() z[1] = Fp4{} z[2] = Fp4{} } func (z *Fp12Cubic) Mul(x *Fp12Cubic, y *Fp12Cubic) { // This is a Karatsuba like technique: compute x_iy_i, then // subtract the terms from expressions like (x0+x1)(y0+y1). // See Multiplication and Squaring in Pairing Friendly Fields // for more. var v0, v1, v2, p0, p1, p2, tx, ty Fp4 v0.Mul(&x[0], &y[0]) v1.Mul(&x[1], &y[1]) v2.Mul(&x[2], &y[2]) tx.Add(&x[1], &x[2]) ty.Add(&y[1], &y[2]) p0.Mul(&tx, &ty) tx.Add(&x[0], &x[1]) ty.Add(&y[0], &y[1]) p1.Mul(&tx, &ty) tx.Add(&x[0], &x[2]) ty.Add(&y[0], &y[2]) p2.Mul(&tx, &ty) z[0].Sub(&p0, &v1) z[0].Sub(&z[0], &v2) z[0].mulT(&z[0]) z[0].Add(&z[0], &v0) z[1].Sub(&p1, &v0) z[1].Sub(&z[1], &v1) tx.mulT(&v2) z[1].Add(&z[1], &tx) z[2].Sub(&p2, &v0) z[2].Add(&z[2], &v1) z[2].Sub(&z[2], &v2) } func (z *Fp12Cubic) Sqr(x *Fp12Cubic) { // The Chung-Hasan asymmetric squaring formula. // We keep the same notation as in Multiplication // and Squaring on Pairing-Friendly Fields to make // it easier to compare. var s0, s1, s2, s3, s4, t Fp4 s0.Sqr(&x[0]) // x0^2 s1.Mul(&x[0], &x[1]) s1.Add(&s1, &s1) // 2x0x1 t.Add(&x[0], &x[2]) t.Sub(&t, &x[1]) s2.Sqr(&t) // (x0-x1+x2)^2 s3.Mul(&x[1], &x[2]) s3.Add(&s3, &s3) // 2x1x2 s4.Sqr(&x[2]) // x2^2 z[0].mulT(&s3) z[0].Add(&z[0], &s0) z[1].mulT(&s4) z[1].Add(&z[1], &s1) z[2].Add(&s1, &s2) z[2].Add(&z[2], &s3) z[2].Sub(&z[2], &s0) z[2].Sub(&z[2], &s4) } func (z *Fp12Cubic) MulLine(x *Fp12Cubic, y *LineValue) { // Values produced by evaluating a line function // do not have a linear term, and the quadratic term is // in Fp2. // We copy the Mul method, but remove any multiplies by y1, // and strength reduce multiplies by y2. var y0 Fp4 var y2 Fp2 var v0, v2, p0, p1, p2, tx, ty Fp4 y0[0] = y[0] y0[1] = y[2] y2 = y[1] v0.Mul(&x[0], &y0) v2.mulSubfield(&x[2], &y2) tx.Add(&x[1], &x[2]) p0.mulSubfield(&tx, &y2) tx.Add(&x[0], &x[1]) p1.Mul(&tx, &y0) tx.Add(&x[0], &x[2]) ty = y0 ty[0].Add(&ty[0], &y2) p2.Mul(&tx, &ty) z[0].Sub(&p0, &v2) z[0].mulT(&z[0]) z[0].Add(&z[0], &v0) z[1].Sub(&p1, &v0) tx.mulT(&v2) z[1].Add(&z[1], &tx) z[2].Sub(&p2, &v0) z[2].Sub(&z[2], &v2) } func (z *LineValue) IsZero() int { return z[0].IsZero() & z[1].IsZero() & z[2].IsZero() } func (z *LineValue) SetOne() { z[0].SetOne() z[1] = Fp2{} z[2] = Fp2{} } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp12cubic_test.go000066400000000000000000000030731454601126700251420ustar00rootroot00000000000000package ff import ( "testing" "github.com/cloudflare/circl/internal/test" ) func TestFP12CubicAdd(t *testing.T) { const testTimes = 1 << 8 for i := 0; i < testTimes; i++ { var xalt, yalt, zalt Fp12Cubic var z, zcmp Fp12 x := randomFp12(t) y := randomFp12(t) xalt.FromFp12(x) yalt.FromFp12(y) zalt.Add(&xalt, &yalt) z.Add(x, y) zcmp.FromFp12Alt(&zalt) if z.IsEqual(&zcmp) == 0 { test.ReportError(t, z, zcmp, x, y) } } } func TestFP12CubicMul(t *testing.T) { const testTimes = 1 << 8 for i := 0; i < testTimes; i++ { var xalt, yalt, zalt Fp12Cubic var z, zcmp Fp12 x := randomFp12(t) y := randomFp12(t) xalt.FromFp12(x) yalt.FromFp12(y) zalt.Mul(&xalt, &yalt) z.Mul(x, y) zcmp.FromFp12Alt(&zalt) if z.IsEqual(&zcmp) == 0 { test.ReportError(t, z, zcmp, x, y) } } } func TestFP12AltSqr(t *testing.T) { const testTimes = 1 << 8 for i := 0; i < testTimes; i++ { var xalt, zalt Fp12Cubic var z, zcmp Fp12 x := randomFp12(t) xalt.FromFp12(x) zalt.Sqr(&xalt) z.Sqr(x) zcmp.FromFp12Alt(&zalt) if z.IsEqual(&zcmp) == 0 { test.ReportError(t, z, zcmp, x) } } } func TestFP12CubicLine(t *testing.T) { const testTimes = 1 << 8 for i := 0; i < testTimes; i++ { var x, y, z, zcmp Fp12Cubic var yline LineValue xnorm := randomFp12(t) x.FromFp12(xnorm) yline[0] = *randomFp2(t) yline[1] = *randomFp2(t) yline[2] = *randomFp2(t) y[0][0] = yline[0] y[0][1] = yline[2] y[2][0] = yline[1] zcmp.Mul(&x, &y) z.MulLine(&x, &yline) if z.IsEqual(&zcmp) == 0 { test.ReportError(t, z, zcmp, x) } } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp2.go000066400000000000000000000122051454601126700230110ustar00rootroot00000000000000package ff import "fmt" // Fp2Size is the length in bytes of an Fp2 element. const Fp2Size = 2 * FpSize type Fp2 [2]Fp func (z Fp2) String() string { return fmt.Sprintf("0: %v\n1: %v", z[0], z[1]) } func (z *Fp2) SetOne() { z[0].SetOne(); z[1] = Fp{} } // IsNegative returns 1 if z is lexicographically larger than -z; otherwise returns 0. func (z Fp2) IsNegative() int { return z[1].IsNegative() | (z[1].IsZero() & z[0].IsNegative()) } func (z Fp2) IsZero() int { return z.IsEqual(&Fp2{}) } func (z Fp2) IsEqual(x *Fp2) int { return z[0].IsEqual(&x[0]) & z[1].IsEqual(&x[1]) } func (z *Fp2) MulBeta() { t := z[0]; z[0].Sub(&z[0], &z[1]); z[1].Add(&t, &z[1]) } func (z *Fp2) Frob(x *Fp2) { *z = *x; z.Cjg() } func (z *Fp2) Cjg() { z[1].Neg() } func (z *Fp2) Neg() { z[0].Neg(); z[1].Neg() } func (z *Fp2) Add(x, y *Fp2) { z[0].Add(&x[0], &y[0]); z[1].Add(&x[1], &y[1]) } func (z *Fp2) Sub(x, y *Fp2) { z[0].Sub(&x[0], &y[0]); z[1].Sub(&x[1], &y[1]) } func (z *Fp2) Mul(x, y *Fp2) { var x0y0, x1y1, sx, sy, k Fp x0y0.Mul(&x[0], &y[0]) x1y1.Mul(&x[1], &y[1]) sx.Add(&x[0], &x[1]) sy.Add(&y[0], &y[1]) k.Mul(&sx, &sy) z[0].Sub(&x0y0, &x1y1) z[1].Sub(&k, &x0y0) z[1].Sub(&z[1], &x1y1) } func (z *Fp2) Sqr(x *Fp2) { var x02, x12, k Fp x02.Sqr(&x[0]) x12.Sqr(&x[1]) k.Mul(&x[0], &x[1]) z[0].Sub(&x02, &x12) z[1].Add(&k, &k) } func (z *Fp2) Inv(x *Fp2) { var x02, x12, den Fp x02.Sqr(&x[0]) x12.Sqr(&x[1]) den.Add(&x02, &x12) den.Inv(&den) z[0].Mul(&x[0], &den) z[1].Mul(&x[1], &den) z[1].Neg() } func (z Fp2) Sgn0() int { s0, s1 := z[0].Sgn0(), z[1].Sgn0() z0 := z[0].IsZero() return s0 | (z0 & s1) } func (z *Fp2) UnmarshalBinary(b []byte) error { if len(b) < Fp2Size { return errInputLength } return errFirst( z[1].UnmarshalBinary(b[:FpSize]), z[0].UnmarshalBinary(b[FpSize:2*FpSize]), ) } func (z Fp2) MarshalBinary() (b []byte, e error) { var b0, b1 []byte if b1, e = z[1].MarshalBinary(); e == nil { if b0, e = z[0].MarshalBinary(); e == nil { return append(b1, b0...), e } } return } // SetString reconstructs a Fp2 element as s0+s1*i, where s0 and s1 are numeric // strings from 0 to FpOrder-1. func (z *Fp2) SetString(s0, s1 string) (err error) { if err = z[0].SetString(s0); err == nil { err = z[1].SetString(s1) } return } func (z *Fp2) CMov(x, y *Fp2, b int) { z[0].CMov(&x[0], &y[0], b) z[1].CMov(&x[1], &y[1], b) } // ExpVarTime calculates z=x^n, where n is the exponent in big-endian order. func (z *Fp2) ExpVarTime(x *Fp2, n []byte) { zz := new(Fp2) zz.SetOne() N := 8 * len(n) for i := 0; i < N; i++ { zz.Sqr(zz) bit := 0x1 & (n[i/8] >> uint(7-i%8)) if bit != 0 { zz.Mul(zz, x) } } *z = *zz } // Sqrt returns 1 and sets z=sqrt(x) only if x is a quadratic-residue; otherwise, returns 0 and z is unmodified. func (z *Fp2) Sqrt(x *Fp2) int { // "Square-root for q = p^2 = 9 (mod 16)" Appendix I.3 of Hashing to elliptic curves. // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-I.3 var t, tv1, tv2, tv3, tv4 Fp2 tv1.ExpVarTime(x, fp2SqrtConst.c4[:]) tv2.Mul(&fp2SqrtConst.c1, &tv1) tv3.Mul(&fp2SqrtConst.c2, &tv1) tv4.Mul(&fp2SqrtConst.c3, &tv1) t.Sqr(&tv1) e1 := t.IsEqual(x) z.CMov(z, &tv1, e1) t.Sqr(&tv2) e2 := t.IsEqual(x) z.CMov(z, &tv2, e2) t.Sqr(&tv3) e3 := t.IsEqual(x) z.CMov(z, &tv3, e3) t.Sqr(&tv4) e4 := t.IsEqual(x) z.CMov(z, &tv4, e4) return e1 | e2 | e3 | e4 } var fp2SqrtConst = struct { // "Square-root for q = p^2 = 9 (mod 16)" Appendix I.3 of Hashing to elliptic curves. // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-I.3 c1 Fp2 // c1 = sqrt( -1) = u c2 Fp2 // c2 = sqrt( c1) c3 Fp2 // c3 = sqrt(-c1) c4 [95]byte // c4 = (p^2 + 7) / 16 (big-endian) }{ c1: Fp2{ // (little-endian) Fp{fpMont{}}, Fp{fpMont{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493}}, }, c2: Fp2{ // (little-endian) Fp{fpMont{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8}}, Fp{fpMont{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2}}, }, c3: Fp2{ // (little-endian) Fp{fpMont{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2}}, Fp{fpMont{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2}}, }, c4: [95]byte{ // (big-endian) 0x2a, 0x43, 0x7a, 0x4b, 0x8c, 0x35, 0xfc, 0x74, 0xbd, 0x27, 0x8e, 0xaa, 0x22, 0xf2, 0x5e, 0x9e, 0x2d, 0xc9, 0x0e, 0x50, 0xe7, 0x04, 0x6b, 0x46, 0x6e, 0x59, 0xe4, 0x93, 0x49, 0xe8, 0xbd, 0x05, 0x0a, 0x62, 0xcf, 0xd1, 0x6d, 0xdc, 0xa6, 0xef, 0x53, 0x14, 0x93, 0x30, 0x97, 0x8e, 0xf0, 0x11, 0xd6, 0x86, 0x19, 0xc8, 0x61, 0x85, 0xc7, 0xb2, 0x92, 0xe8, 0x5a, 0x87, 0x09, 0x1a, 0x04, 0x96, 0x6b, 0xf9, 0x1e, 0xd3, 0xe7, 0x1b, 0x74, 0x31, 0x62, 0xc3, 0x38, 0x36, 0x21, 0x13, 0xcf, 0xd7, 0xce, 0xd6, 0xb1, 0xd7, 0x63, 0x82, 0xea, 0xb2, 0x6a, 0xa0, 0x00, 0x01, 0xc7, 0x18, 0xe4, }, } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp2_test.go000066400000000000000000000056411454601126700240560ustar00rootroot00000000000000package ff import ( "fmt" "testing" "github.com/cloudflare/circl/internal/test" ) func randomFp2(t testing.TB) *Fp2 { return &Fp2{*randomFp(t), *randomFp(t)} } func TestFp2(t *testing.T) { const testTimes = 1 << 9 t.Run("no_alias", func(t *testing.T) { var want, got Fp2 x := randomFp2(t) got = *x got.Sqr(&got) want = *x want.Mul(&want, &want) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } }) t.Run("mul_inv", func(t *testing.T) { var z Fp2 for i := 0; i < testTimes; i++ { x := randomFp2(t) y := randomFp2(t) // x*y*x^1 - y = 0 z.Inv(x) z.Mul(&z, y) z.Mul(&z, x) z.Sub(&z, y) got := z.IsZero() want := 1 if got != want { test.ReportError(t, got, want, x, y, z) } } }) t.Run("mul_sqr", func(t *testing.T) { var l0, l1, r0, r1 Fp2 for i := 0; i < testTimes; i++ { x := randomFp2(t) y := randomFp2(t) // (x+y)(x-y) = (x^2-y^2) l0.Add(x, y) l1.Sub(x, y) l0.Mul(&l0, &l1) r0.Sqr(x) r1.Sqr(y) r0.Sub(&r0, &r1) got := &l0 want := &r0 if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("sqrt", func(t *testing.T) { var r, notRoot, got Fp2 // Check when x has square-root. for i := 0; i < testTimes; i++ { x := randomFp2(t) x.Sqr(x) // let x is QR and r = sqrt(x); check (+r)^2 = (-r)^2 = x. isQR := r.Sqrt(x) test.CheckOk(isQR == 1, fmt.Sprintf("should be a QR: %v", x), t) rNeg := r rNeg.Neg() want := x for _, root := range []*Fp2{&r, &rNeg} { got.Sqr(root) if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, root) } } } // Check when x has not square-root. var uPlus1 Fp2 uPlus1[0].SetUint64(1) uPlus1[1].SetUint64(1) for i := 0; i < testTimes; i++ { want := randomFp2(t) x := randomFp2(t) x.Sqr(x) x.Mul(x, &uPlus1) // x = (u+1)*(x^2), since u+1 is not QR in Fp2. // let x is not QR and r = sqrt(x); check that r was not modified. got := want isQR := got.Sqrt(x) test.CheckOk(isQR == 0, fmt.Sprintf("shouldn't be a QR: %v", x), t) if got.IsEqual(want) != 1 { test.ReportError(t, got, want, x, notRoot) } } }) t.Run("marshal", func(t *testing.T) { var b Fp2 for i := 0; i < testTimes; i++ { a := randomFp2(t) s, err := a.MarshalBinary() test.CheckNoErr(t, err, "MarshalBinary failed") err = b.UnmarshalBinary(s) test.CheckNoErr(t, err, "UnmarshalBinary failed") if b.IsEqual(a) == 0 { test.ReportError(t, a, b) } } }) } func BenchmarkFp2(b *testing.B) { x := randomFp2(b) y := randomFp2(b) z := randomFp2(b) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Add(x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sqr(x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Inv(x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp4.go000066400000000000000000000035461454601126700230230ustar00rootroot00000000000000package ff import "fmt" // Fp4Size is the size of an Fp4 element const Fp4Size = 4 * FpSize // Fp4 is obtained by adjoining t, the square root of u+1 to Fp2 type Fp4 [2]Fp2 func (z Fp4) String() string { return fmt.Sprintf("%s + ( %s )*t", z[0], z[1]) } func (z *Fp4) SetOne() { z[0].SetOne() z[1] = Fp2{} } func (z *Fp4) IsZero() int { return z.IsEqual(&Fp4{}) } func (z *Fp4) IsEqual(x *Fp4) int { return z[0].IsEqual(&x[0]) & z[1].IsEqual(&x[1]) } func (z *Fp4) Neg() { z[0].Neg() z[1].Neg() } func (z *Fp4) Add(x *Fp4, y *Fp4) { z[0].Add(&x[0], &y[0]) z[1].Add(&x[1], &y[1]) } func (z *Fp4) Sub(x *Fp4, y *Fp4) { z[0].Sub(&x[0], &y[0]) z[1].Sub(&x[1], &y[1]) } func (z *Fp4) Mul(x *Fp4, y *Fp4) { var x0y0, x1y1, sx, sy, k Fp2 x0y0.Mul(&x[0], &y[0]) x1y1.Mul(&x[1], &y[1]) sx.Add(&x[0], &x[1]) sy.Add(&y[0], &y[1]) k.Mul(&sx, &sy) k.Sub(&k, &x0y0) k.Sub(&k, &x1y1) // k is x0y1+x1y0 computed as (x0+x1)(y0+y1)-x0y0-x1y1 z[1] = k // Multiply x1y1 by u+1 z[0][1].Add(&x1y1[0], &x1y1[1]) z[0][0].Sub(&x1y1[0], &x1y1[1]) z[0].Add(&z[0], &x0y0) } func (z *Fp4) Sqr(x *Fp4) { var x0s, x1s, sx, k Fp2 x0s.Sqr(&x[0]) x1s.Sqr(&x[1]) sx.Add(&x[0], &x[1]) k.Sqr(&sx) k.Sub(&k, &x0s) k.Sub(&k, &x1s) z[1] = k // Multiplying x1s by u+1 z[0][1].Add(&x1s[0], &x1s[1]) z[0][0].Sub(&x1s[0], &x1s[1]) z[0].Add(&z[0], &x0s) } func (z *Fp4) Inv(x *Fp4) { // Compute the inverse via conjugation var denom, x0sqr, x1sqr Fp2 x0sqr.Sqr(&x[0]) x1sqr.Sqr(&x[1]) denom[1].Add(&x1sqr[0], &x1sqr[1]) denom[0].Sub(&x1sqr[0], &x1sqr[1]) denom.Sub(&x0sqr, &denom) denom.Inv(&denom) z[0] = x[0] z[1].Sub(&z[1], &x[1]) z.mulSubfield(z, &denom) } func (z *Fp4) mulSubfield(x *Fp4, y *Fp2) { z[0].Mul(&x[0], y) z[1].Mul(&x[1], y) } func (z *Fp4) mulT(x *Fp4) { var t Fp4 t[1] = x[0] t[0][1].Add(&x[1][0], &x[1][1]) t[0][0].Sub(&x[1][0], &x[1][1]) *z = t } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp6.go000066400000000000000000000114711454601126700230210ustar00rootroot00000000000000package ff import "fmt" // Fp6Size is the length in bytes of an Fp6 element. const Fp6Size = 3 * Fp2Size type Fp6 [3]Fp2 func (z Fp6) String() string { return fmt.Sprintf("\n0: %v\n1: %v\n2: %v", z[0], z[1], z[2]) } func (z *Fp6) SetOne() { z[0].SetOne(); z[1] = Fp2{}; z[2] = Fp2{} } func (z Fp6) IsZero() int { return z.IsEqual(&Fp6{}) } func (z Fp6) IsEqual(x *Fp6) int { return z[0].IsEqual(&x[0]) & z[1].IsEqual(&x[1]) & z[2].IsEqual(&x[2]) } func (z *Fp6) Neg() { z[0].Neg(); z[1].Neg(); z[2].Neg() } func (z *Fp6) Add(x, y *Fp6) { z[0].Add(&x[0], &y[0]); z[1].Add(&x[1], &y[1]); z[2].Add(&x[2], &y[2]) } func (z *Fp6) Sub(x, y *Fp6) { z[0].Sub(&x[0], &y[0]); z[1].Sub(&x[1], &y[1]); z[2].Sub(&x[2], &y[2]) } func (z *Fp6) MulBeta() { t := z[2] t.MulBeta() z[2] = z[1] z[1] = z[0] z[0] = t } func (z *Fp6) Mul(x, y *Fp6) { // https://ia.cr/2006/224 (Sec3.1) // z = x*y mod (v^3-B) // | v^4 | v^3 || v^2 | v^1 | v^0 | // |-----|-----||-------|-------|-------| // | | || -c2 | -c1 | +c0 | // | | -c2 || +c1 | -c0 | | // | +c2 | -c1 || -c0 | | | // | | +c5 || +c4 | +c3 | | // |-----|-----||-------|-------|-------| // | | || | B(+c2)| B(-c2)| // | | || | | B(-c1)| // | | || | | B(+c5)| aL, aM, aH := &x[0], &x[1], &x[2] bL, bM, bH := &y[0], &y[1], &y[2] aLM, aLH, aMH := &Fp2{}, &Fp2{}, &Fp2{} bLM, bLH, bMH := &Fp2{}, &Fp2{}, &Fp2{} aLM.Add(aL, aM) aLH.Add(aL, aH) aMH.Add(aM, aH) bLM.Add(bL, bM) bLH.Add(bL, bH) bMH.Add(bM, bH) c0, c1, c2 := &Fp2{}, &Fp2{}, &Fp2{} c5, c3, c4 := &z[0], &z[1], &z[2] c0.Mul(aL, bL) c1.Mul(aM, bM) c2.Mul(aH, bH) c3.Mul(aLM, bLM) c4.Mul(aLH, bLH) c5.Mul(aMH, bMH) z[2].Add(c4, c1) // c4+c1 z[2].Sub(&z[2], c0) // c4+c1-c0 z[2].Sub(&z[2], c2) // z2 = c4+c1-c0-c2 c2.MulBeta() // Bc2 c2.Sub(c2, c0) // Bc2-c0 z[1].Sub(c3, c1) // c3-c1 z[1].Add(&z[1], c2) // z1 = Bc2-c0+c3-c1 z[0].Sub(c5, c1) // c5-c1 z[0].MulBeta() // B(c5-c1) z[0].Sub(&z[0], c2) // z0 = B(c5-c1)-Bc2+c0 = B(c5-c1-c2)+c0 } func (z *Fp6) Sqr(x *Fp6) { // z = x^2 mod (v^3-B) // z0 = B(2x1*x2) + x0^2 // z1 = B(x2^2) + 2x0*x1 // z2 = 2x0*x2 + x1^2 aL, aM, aH := &x[0], &x[1], &x[2] c0, c2, c4 := &z[0], &z[1], &z[2] c3, c5, tt := &Fp2{}, &Fp2{}, &Fp2{} tt.Add(aL, aH) tt.Sub(tt, aM) c3.Mul(aL, aM) c5.Mul(aM, aH) c0.Sqr(aL) c2.Sqr(aH) c4.Sqr(tt) c5.Add(c5, c5) // 2c5 c3.Add(c3, c3) // 2c3 tt.Add(c3, c5) // 2c3+2c5 z[2].Add(tt, c4) // 2c3+2c5+c4 z[2].Sub(&z[2], c0) // 2c3+2c5+c4-c0 z[2].Sub(&z[2], c2) // z2 = 2c3+2c5+c4-c0-c2 c5.MulBeta() // B(2c5) z[0].Add(c5, c0) // z0 = B(2c5)+c0 c2.MulBeta() // B(c2) z[1].Add(c2, c3) // z1 = B(c2)+2c3 } func (z *Fp6) Inv(x *Fp6) { aL, aM, aH := &x[0], &x[1], &x[2] c0, c1, c2 := &Fp2{}, &Fp2{}, &Fp2{} t0, t1, t2 := &Fp2{}, &Fp2{}, &Fp2{} c0.Sqr(aL) c1.Sqr(aH) c2.Sqr(aM) t0.Mul(aM, aH) t1.Mul(aL, aM) t2.Mul(aL, aH) t0.MulBeta() c0.Sub(c0, t0) // c0 = aL^2 - B(aM*AH) c1.MulBeta() c1.Sub(c1, t1) // c1 = B(aH^2) - aL*AM c2.Sub(c2, t2) // c1 = aM^2 - aL*AH t0.Mul(aM, c2) t1.Mul(aH, c1) t2.Mul(aL, c0) t0.Add(t0, t1) t0.MulBeta() t0.Add(t0, t2) t0.Inv(t0) // den = B(aL*c2 + aM*c1) + aLc0 z[0].Mul(c0, t0) // z0 = c0/den z[1].Mul(c1, t0) // z1 = c1/den z[2].Mul(c2, t0) // z2 = c2/den } func (z *Fp6) Frob(x *Fp6) { z[0].Frob(&x[0]) z[1].Frob(&x[1]) z[2].Frob(&x[2]) z[1].Mul(&z[1], &Fp2{Fp{}, frob6V1}) z[2].Mul(&z[2], &Fp2{frob6V2, Fp{}}) } func (z *Fp6) CMov(x, y *Fp6, b int) { z[0].CMov(&x[0], &y[0], b) z[1].CMov(&x[1], &y[1], b) z[2].CMov(&x[2], &y[2], b) } func (z Fp6) MarshalBinary() (b []byte, e error) { var b0, b1, b2 []byte if b2, e = z[2].MarshalBinary(); e == nil { if b1, e = z[1].MarshalBinary(); e == nil { if b0, e = z[0].MarshalBinary(); e == nil { return append(append(b2, b1...), b0...), e } } } return } func (z *Fp6) UnmarshalBinary(b []byte) error { if len(b) < Fp6Size { return errInputLength } return errFirst( z[2].UnmarshalBinary(b[0*Fp2Size:1*Fp2Size]), z[1].UnmarshalBinary(b[1*Fp2Size:2*Fp2Size]), z[0].UnmarshalBinary(b[2*Fp2Size:3*Fp2Size]), ) } var ( // frob6V1 is toMont(v) = 2**384 * v mod fpPrime, where // v = 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac frob6V1 = Fp{fpMont{ 0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741, }} // frob6V2 is toMont(v) = 2**384 * v mod fpPrime, where // v = 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad frob6V2 = Fp{fpMont{ 0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a, }} ) golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp6_test.go000066400000000000000000000041701454601126700240560ustar00rootroot00000000000000package ff import ( "testing" "github.com/cloudflare/circl/internal/test" ) func randomFp6(t testing.TB) *Fp6 { return &Fp6{*randomFp2(t), *randomFp2(t), *randomFp2(t)} } // expVarTime calculates z=x^n, where n is the exponent in big-endian order. func expVarTime(z, x *Fp6, n []byte) { zz := new(Fp6) zz.SetOne() N := 8 * len(n) for i := 0; i < N; i++ { zz.Sqr(zz) bit := 0x1 & (n[i/8] >> uint(7-i%8)) if bit != 0 { zz.Mul(zz, x) } } *z = *zz } func TestFp6(t *testing.T) { const testTimes = 1 << 10 t.Run("no_alias", func(t *testing.T) { var want, got Fp6 x := randomFp6(t) got = *x got.Sqr(&got) want = *x want.Mul(&want, &want) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } }) t.Run("mul_inv", func(t *testing.T) { var z Fp6 for i := 0; i < testTimes; i++ { x := randomFp6(t) y := randomFp6(t) // x*y*x^1 - y = 0 z.Inv(x) z.Mul(&z, y) z.Mul(&z, x) z.Sub(&z, y) got := z.IsZero() want := 1 if got != want { test.ReportError(t, got, want, x, y) } } }) t.Run("mul_sqr", func(t *testing.T) { var l0, l1, r0, r1 Fp6 for i := 0; i < testTimes; i++ { x := randomFp6(t) y := randomFp6(t) // (x+y)(x-y) = (x^2-y^2) l0.Add(x, y) l1.Sub(x, y) l0.Mul(&l0, &l1) r0.Sqr(x) r1.Sqr(y) r0.Sub(&r0, &r1) got := &l0 want := &r0 if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("frobenius", func(t *testing.T) { var got, want Fp6 p := FpOrder() for i := 0; i < testTimes; i++ { x := randomFp6(t) // Frob(x) == x^p got.Frob(x) expVarTime(&want, x, p) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } } }) } func BenchmarkFp6(b *testing.B) { x := randomFp6(b) y := randomFp6(b) z := randomFp6(b) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Add(x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sqr(x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Inv(x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fpMont381.go000066400000000000000000001333761454601126700240360ustar00rootroot00000000000000// Code generated by gen.go using fiat-crypto. // // Autogenerated: './word_by_word_montgomery' --output fpMont381.go --lang Go --package-name ff --doc-prepend-header 'Code generated by gen.go using fiat-crypto.' --package-case lowerCamelCase --public-function-case lowerCamelCase --public-type-case lowerCamelCase --doc-newline-before-package-declaration --no-primitives --widen-carry --no-field-element-typedefs --relax-primitive-carry-to-bitwidth 64 FpMont 64 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab add sub mul square // // curve description: FpMont // // machine_wordsize = 64 (from "64") // // requested operations: add, sub, mul, square // // m = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab (from "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab") // // // // NOTE: In addition to the bounds specified above each function, all // // functions synthesized for this Montgomery arithmetic require the // // input to be strictly less than the prime modulus (m), and also // // require the input to be in the unique saturated representation. // // All functions also ensure that these two properties are true of // // return values. // // // // Computed values: // // eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) // // bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) + (z[32] << 256) + (z[33] << 0x108) + (z[34] << 0x110) + (z[35] << 0x118) + (z[36] << 0x120) + (z[37] << 0x128) + (z[38] << 0x130) + (z[39] << 0x138) + (z[40] << 0x140) + (z[41] << 0x148) + (z[42] << 0x150) + (z[43] << 0x158) + (z[44] << 0x160) + (z[45] << 0x168) + (z[46] << 0x170) + (z[47] << 0x178) // // twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) in // // if x1 & (2^384-1) < 2^383 then x1 & (2^384-1) else (x1 & (2^384-1)) - 2^384 package ff import "math/bits" // The function fiatFpMontAdd adds two field elements in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // 0 ≤ eval arg2 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatFpMontAdd(out1 *[6]uint64, arg1 *[6]uint64, arg2 *[6]uint64) { var x1 uint64 var x2 uint64 x1, x2 = bits.Add64(arg1[0], arg2[0], uint64(0x0)) var x3 uint64 var x4 uint64 x3, x4 = bits.Add64(arg1[1], arg2[1], uint64(x2)) var x5 uint64 var x6 uint64 x5, x6 = bits.Add64(arg1[2], arg2[2], uint64(x4)) var x7 uint64 var x8 uint64 x7, x8 = bits.Add64(arg1[3], arg2[3], uint64(x6)) var x9 uint64 var x10 uint64 x9, x10 = bits.Add64(arg1[4], arg2[4], uint64(x8)) var x11 uint64 var x12 uint64 x11, x12 = bits.Add64(arg1[5], arg2[5], uint64(x10)) var x13 uint64 var x14 uint64 x13, x14 = bits.Sub64(x1, 0xb9feffffffffaaab, uint64(uint64(0x0))) var x15 uint64 var x16 uint64 x15, x16 = bits.Sub64(x3, 0x1eabfffeb153ffff, uint64(x14)) var x17 uint64 var x18 uint64 x17, x18 = bits.Sub64(x5, 0x6730d2a0f6b0f624, uint64(x16)) var x19 uint64 var x20 uint64 x19, x20 = bits.Sub64(x7, 0x64774b84f38512bf, uint64(x18)) var x21 uint64 var x22 uint64 x21, x22 = bits.Sub64(x9, 0x4b1ba7b6434bacd7, uint64(x20)) var x23 uint64 var x24 uint64 x23, x24 = bits.Sub64(x11, 0x1a0111ea397fe69a, uint64(x22)) var x26 uint64 _, x26 = bits.Sub64(x12, uint64(0x0), uint64(x24)) var x27 uint64 fiatFpMontCmovznzU64(&x27, x26, x13, x1) var x28 uint64 fiatFpMontCmovznzU64(&x28, x26, x15, x3) var x29 uint64 fiatFpMontCmovznzU64(&x29, x26, x17, x5) var x30 uint64 fiatFpMontCmovznzU64(&x30, x26, x19, x7) var x31 uint64 fiatFpMontCmovznzU64(&x31, x26, x21, x9) var x32 uint64 fiatFpMontCmovznzU64(&x32, x26, x23, x11) out1[0] = x27 out1[1] = x28 out1[2] = x29 out1[3] = x30 out1[4] = x31 out1[5] = x32 } // The function fiatFpMontSub subtracts two field elements in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // 0 ≤ eval arg2 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatFpMontSub(out1 *[6]uint64, arg1 *[6]uint64, arg2 *[6]uint64) { var x1 uint64 var x2 uint64 x1, x2 = bits.Sub64(arg1[0], arg2[0], uint64(0x0)) var x3 uint64 var x4 uint64 x3, x4 = bits.Sub64(arg1[1], arg2[1], uint64(x2)) var x5 uint64 var x6 uint64 x5, x6 = bits.Sub64(arg1[2], arg2[2], uint64(x4)) var x7 uint64 var x8 uint64 x7, x8 = bits.Sub64(arg1[3], arg2[3], uint64(x6)) var x9 uint64 var x10 uint64 x9, x10 = bits.Sub64(arg1[4], arg2[4], uint64(x8)) var x11 uint64 var x12 uint64 x11, x12 = bits.Sub64(arg1[5], arg2[5], uint64(x10)) var x13 uint64 fiatFpMontCmovznzU64(&x13, x12, uint64(0x0), 0xffffffffffffffff) var x14 uint64 var x15 uint64 x14, x15 = bits.Add64(x1, (x13 & 0xb9feffffffffaaab), uint64(0x0)) var x16 uint64 var x17 uint64 x16, x17 = bits.Add64(x3, (x13 & 0x1eabfffeb153ffff), uint64(x15)) var x18 uint64 var x19 uint64 x18, x19 = bits.Add64(x5, (x13 & 0x6730d2a0f6b0f624), uint64(x17)) var x20 uint64 var x21 uint64 x20, x21 = bits.Add64(x7, (x13 & 0x64774b84f38512bf), uint64(x19)) var x22 uint64 var x23 uint64 x22, x23 = bits.Add64(x9, (x13 & 0x4b1ba7b6434bacd7), uint64(x21)) var x24 uint64 x24, _ = bits.Add64(x11, (x13 & 0x1a0111ea397fe69a), uint64(x23)) out1[0] = x14 out1[1] = x16 out1[2] = x18 out1[3] = x20 out1[4] = x22 out1[5] = x24 } // The function fiatFpMontMul multiplies two field elements in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // 0 ≤ eval arg2 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatFpMontMul(out1 *[6]uint64, arg1 *[6]uint64, arg2 *[6]uint64) { x1 := arg1[1] x2 := arg1[2] x3 := arg1[3] x4 := arg1[4] x5 := arg1[5] x6 := arg1[0] var x7 uint64 var x8 uint64 x8, x7 = bits.Mul64(x6, arg2[5]) var x9 uint64 var x10 uint64 x10, x9 = bits.Mul64(x6, arg2[4]) var x11 uint64 var x12 uint64 x12, x11 = bits.Mul64(x6, arg2[3]) var x13 uint64 var x14 uint64 x14, x13 = bits.Mul64(x6, arg2[2]) var x15 uint64 var x16 uint64 x16, x15 = bits.Mul64(x6, arg2[1]) var x17 uint64 var x18 uint64 x18, x17 = bits.Mul64(x6, arg2[0]) var x19 uint64 var x20 uint64 x19, x20 = bits.Add64(x18, x15, uint64(0x0)) var x21 uint64 var x22 uint64 x21, x22 = bits.Add64(x16, x13, uint64(x20)) var x23 uint64 var x24 uint64 x23, x24 = bits.Add64(x14, x11, uint64(x22)) var x25 uint64 var x26 uint64 x25, x26 = bits.Add64(x12, x9, uint64(x24)) var x27 uint64 var x28 uint64 x27, x28 = bits.Add64(x10, x7, uint64(x26)) x29 := (x28 + x8) var x30 uint64 _, x30 = bits.Mul64(x17, 0x89f3fffcfffcfffd) var x32 uint64 var x33 uint64 x33, x32 = bits.Mul64(x30, 0x1a0111ea397fe69a) var x34 uint64 var x35 uint64 x35, x34 = bits.Mul64(x30, 0x4b1ba7b6434bacd7) var x36 uint64 var x37 uint64 x37, x36 = bits.Mul64(x30, 0x64774b84f38512bf) var x38 uint64 var x39 uint64 x39, x38 = bits.Mul64(x30, 0x6730d2a0f6b0f624) var x40 uint64 var x41 uint64 x41, x40 = bits.Mul64(x30, 0x1eabfffeb153ffff) var x42 uint64 var x43 uint64 x43, x42 = bits.Mul64(x30, 0xb9feffffffffaaab) var x44 uint64 var x45 uint64 x44, x45 = bits.Add64(x43, x40, uint64(0x0)) var x46 uint64 var x47 uint64 x46, x47 = bits.Add64(x41, x38, uint64(x45)) var x48 uint64 var x49 uint64 x48, x49 = bits.Add64(x39, x36, uint64(x47)) var x50 uint64 var x51 uint64 x50, x51 = bits.Add64(x37, x34, uint64(x49)) var x52 uint64 var x53 uint64 x52, x53 = bits.Add64(x35, x32, uint64(x51)) x54 := (x53 + x33) var x56 uint64 _, x56 = bits.Add64(x17, x42, uint64(0x0)) var x57 uint64 var x58 uint64 x57, x58 = bits.Add64(x19, x44, uint64(x56)) var x59 uint64 var x60 uint64 x59, x60 = bits.Add64(x21, x46, uint64(x58)) var x61 uint64 var x62 uint64 x61, x62 = bits.Add64(x23, x48, uint64(x60)) var x63 uint64 var x64 uint64 x63, x64 = bits.Add64(x25, x50, uint64(x62)) var x65 uint64 var x66 uint64 x65, x66 = bits.Add64(x27, x52, uint64(x64)) var x67 uint64 var x68 uint64 x67, x68 = bits.Add64(x29, x54, uint64(x66)) var x69 uint64 var x70 uint64 x70, x69 = bits.Mul64(x1, arg2[5]) var x71 uint64 var x72 uint64 x72, x71 = bits.Mul64(x1, arg2[4]) var x73 uint64 var x74 uint64 x74, x73 = bits.Mul64(x1, arg2[3]) var x75 uint64 var x76 uint64 x76, x75 = bits.Mul64(x1, arg2[2]) var x77 uint64 var x78 uint64 x78, x77 = bits.Mul64(x1, arg2[1]) var x79 uint64 var x80 uint64 x80, x79 = bits.Mul64(x1, arg2[0]) var x81 uint64 var x82 uint64 x81, x82 = bits.Add64(x80, x77, uint64(0x0)) var x83 uint64 var x84 uint64 x83, x84 = bits.Add64(x78, x75, uint64(x82)) var x85 uint64 var x86 uint64 x85, x86 = bits.Add64(x76, x73, uint64(x84)) var x87 uint64 var x88 uint64 x87, x88 = bits.Add64(x74, x71, uint64(x86)) var x89 uint64 var x90 uint64 x89, x90 = bits.Add64(x72, x69, uint64(x88)) x91 := (x90 + x70) var x92 uint64 var x93 uint64 x92, x93 = bits.Add64(x57, x79, uint64(0x0)) var x94 uint64 var x95 uint64 x94, x95 = bits.Add64(x59, x81, uint64(x93)) var x96 uint64 var x97 uint64 x96, x97 = bits.Add64(x61, x83, uint64(x95)) var x98 uint64 var x99 uint64 x98, x99 = bits.Add64(x63, x85, uint64(x97)) var x100 uint64 var x101 uint64 x100, x101 = bits.Add64(x65, x87, uint64(x99)) var x102 uint64 var x103 uint64 x102, x103 = bits.Add64(x67, x89, uint64(x101)) var x104 uint64 var x105 uint64 x104, x105 = bits.Add64(x68, x91, uint64(x103)) var x106 uint64 _, x106 = bits.Mul64(x92, 0x89f3fffcfffcfffd) var x108 uint64 var x109 uint64 x109, x108 = bits.Mul64(x106, 0x1a0111ea397fe69a) var x110 uint64 var x111 uint64 x111, x110 = bits.Mul64(x106, 0x4b1ba7b6434bacd7) var x112 uint64 var x113 uint64 x113, x112 = bits.Mul64(x106, 0x64774b84f38512bf) var x114 uint64 var x115 uint64 x115, x114 = bits.Mul64(x106, 0x6730d2a0f6b0f624) var x116 uint64 var x117 uint64 x117, x116 = bits.Mul64(x106, 0x1eabfffeb153ffff) var x118 uint64 var x119 uint64 x119, x118 = bits.Mul64(x106, 0xb9feffffffffaaab) var x120 uint64 var x121 uint64 x120, x121 = bits.Add64(x119, x116, uint64(0x0)) var x122 uint64 var x123 uint64 x122, x123 = bits.Add64(x117, x114, uint64(x121)) var x124 uint64 var x125 uint64 x124, x125 = bits.Add64(x115, x112, uint64(x123)) var x126 uint64 var x127 uint64 x126, x127 = bits.Add64(x113, x110, uint64(x125)) var x128 uint64 var x129 uint64 x128, x129 = bits.Add64(x111, x108, uint64(x127)) x130 := (x129 + x109) var x132 uint64 _, x132 = bits.Add64(x92, x118, uint64(0x0)) var x133 uint64 var x134 uint64 x133, x134 = bits.Add64(x94, x120, uint64(x132)) var x135 uint64 var x136 uint64 x135, x136 = bits.Add64(x96, x122, uint64(x134)) var x137 uint64 var x138 uint64 x137, x138 = bits.Add64(x98, x124, uint64(x136)) var x139 uint64 var x140 uint64 x139, x140 = bits.Add64(x100, x126, uint64(x138)) var x141 uint64 var x142 uint64 x141, x142 = bits.Add64(x102, x128, uint64(x140)) var x143 uint64 var x144 uint64 x143, x144 = bits.Add64(x104, x130, uint64(x142)) x145 := (x144 + x105) var x146 uint64 var x147 uint64 x147, x146 = bits.Mul64(x2, arg2[5]) var x148 uint64 var x149 uint64 x149, x148 = bits.Mul64(x2, arg2[4]) var x150 uint64 var x151 uint64 x151, x150 = bits.Mul64(x2, arg2[3]) var x152 uint64 var x153 uint64 x153, x152 = bits.Mul64(x2, arg2[2]) var x154 uint64 var x155 uint64 x155, x154 = bits.Mul64(x2, arg2[1]) var x156 uint64 var x157 uint64 x157, x156 = bits.Mul64(x2, arg2[0]) var x158 uint64 var x159 uint64 x158, x159 = bits.Add64(x157, x154, uint64(0x0)) var x160 uint64 var x161 uint64 x160, x161 = bits.Add64(x155, x152, uint64(x159)) var x162 uint64 var x163 uint64 x162, x163 = bits.Add64(x153, x150, uint64(x161)) var x164 uint64 var x165 uint64 x164, x165 = bits.Add64(x151, x148, uint64(x163)) var x166 uint64 var x167 uint64 x166, x167 = bits.Add64(x149, x146, uint64(x165)) x168 := (x167 + x147) var x169 uint64 var x170 uint64 x169, x170 = bits.Add64(x133, x156, uint64(0x0)) var x171 uint64 var x172 uint64 x171, x172 = bits.Add64(x135, x158, uint64(x170)) var x173 uint64 var x174 uint64 x173, x174 = bits.Add64(x137, x160, uint64(x172)) var x175 uint64 var x176 uint64 x175, x176 = bits.Add64(x139, x162, uint64(x174)) var x177 uint64 var x178 uint64 x177, x178 = bits.Add64(x141, x164, uint64(x176)) var x179 uint64 var x180 uint64 x179, x180 = bits.Add64(x143, x166, uint64(x178)) var x181 uint64 var x182 uint64 x181, x182 = bits.Add64(x145, x168, uint64(x180)) var x183 uint64 _, x183 = bits.Mul64(x169, 0x89f3fffcfffcfffd) var x185 uint64 var x186 uint64 x186, x185 = bits.Mul64(x183, 0x1a0111ea397fe69a) var x187 uint64 var x188 uint64 x188, x187 = bits.Mul64(x183, 0x4b1ba7b6434bacd7) var x189 uint64 var x190 uint64 x190, x189 = bits.Mul64(x183, 0x64774b84f38512bf) var x191 uint64 var x192 uint64 x192, x191 = bits.Mul64(x183, 0x6730d2a0f6b0f624) var x193 uint64 var x194 uint64 x194, x193 = bits.Mul64(x183, 0x1eabfffeb153ffff) var x195 uint64 var x196 uint64 x196, x195 = bits.Mul64(x183, 0xb9feffffffffaaab) var x197 uint64 var x198 uint64 x197, x198 = bits.Add64(x196, x193, uint64(0x0)) var x199 uint64 var x200 uint64 x199, x200 = bits.Add64(x194, x191, uint64(x198)) var x201 uint64 var x202 uint64 x201, x202 = bits.Add64(x192, x189, uint64(x200)) var x203 uint64 var x204 uint64 x203, x204 = bits.Add64(x190, x187, uint64(x202)) var x205 uint64 var x206 uint64 x205, x206 = bits.Add64(x188, x185, uint64(x204)) x207 := (x206 + x186) var x209 uint64 _, x209 = bits.Add64(x169, x195, uint64(0x0)) var x210 uint64 var x211 uint64 x210, x211 = bits.Add64(x171, x197, uint64(x209)) var x212 uint64 var x213 uint64 x212, x213 = bits.Add64(x173, x199, uint64(x211)) var x214 uint64 var x215 uint64 x214, x215 = bits.Add64(x175, x201, uint64(x213)) var x216 uint64 var x217 uint64 x216, x217 = bits.Add64(x177, x203, uint64(x215)) var x218 uint64 var x219 uint64 x218, x219 = bits.Add64(x179, x205, uint64(x217)) var x220 uint64 var x221 uint64 x220, x221 = bits.Add64(x181, x207, uint64(x219)) x222 := (x221 + x182) var x223 uint64 var x224 uint64 x224, x223 = bits.Mul64(x3, arg2[5]) var x225 uint64 var x226 uint64 x226, x225 = bits.Mul64(x3, arg2[4]) var x227 uint64 var x228 uint64 x228, x227 = bits.Mul64(x3, arg2[3]) var x229 uint64 var x230 uint64 x230, x229 = bits.Mul64(x3, arg2[2]) var x231 uint64 var x232 uint64 x232, x231 = bits.Mul64(x3, arg2[1]) var x233 uint64 var x234 uint64 x234, x233 = bits.Mul64(x3, arg2[0]) var x235 uint64 var x236 uint64 x235, x236 = bits.Add64(x234, x231, uint64(0x0)) var x237 uint64 var x238 uint64 x237, x238 = bits.Add64(x232, x229, uint64(x236)) var x239 uint64 var x240 uint64 x239, x240 = bits.Add64(x230, x227, uint64(x238)) var x241 uint64 var x242 uint64 x241, x242 = bits.Add64(x228, x225, uint64(x240)) var x243 uint64 var x244 uint64 x243, x244 = bits.Add64(x226, x223, uint64(x242)) x245 := (x244 + x224) var x246 uint64 var x247 uint64 x246, x247 = bits.Add64(x210, x233, uint64(0x0)) var x248 uint64 var x249 uint64 x248, x249 = bits.Add64(x212, x235, uint64(x247)) var x250 uint64 var x251 uint64 x250, x251 = bits.Add64(x214, x237, uint64(x249)) var x252 uint64 var x253 uint64 x252, x253 = bits.Add64(x216, x239, uint64(x251)) var x254 uint64 var x255 uint64 x254, x255 = bits.Add64(x218, x241, uint64(x253)) var x256 uint64 var x257 uint64 x256, x257 = bits.Add64(x220, x243, uint64(x255)) var x258 uint64 var x259 uint64 x258, x259 = bits.Add64(x222, x245, uint64(x257)) var x260 uint64 _, x260 = bits.Mul64(x246, 0x89f3fffcfffcfffd) var x262 uint64 var x263 uint64 x263, x262 = bits.Mul64(x260, 0x1a0111ea397fe69a) var x264 uint64 var x265 uint64 x265, x264 = bits.Mul64(x260, 0x4b1ba7b6434bacd7) var x266 uint64 var x267 uint64 x267, x266 = bits.Mul64(x260, 0x64774b84f38512bf) var x268 uint64 var x269 uint64 x269, x268 = bits.Mul64(x260, 0x6730d2a0f6b0f624) var x270 uint64 var x271 uint64 x271, x270 = bits.Mul64(x260, 0x1eabfffeb153ffff) var x272 uint64 var x273 uint64 x273, x272 = bits.Mul64(x260, 0xb9feffffffffaaab) var x274 uint64 var x275 uint64 x274, x275 = bits.Add64(x273, x270, uint64(0x0)) var x276 uint64 var x277 uint64 x276, x277 = bits.Add64(x271, x268, uint64(x275)) var x278 uint64 var x279 uint64 x278, x279 = bits.Add64(x269, x266, uint64(x277)) var x280 uint64 var x281 uint64 x280, x281 = bits.Add64(x267, x264, uint64(x279)) var x282 uint64 var x283 uint64 x282, x283 = bits.Add64(x265, x262, uint64(x281)) x284 := (x283 + x263) var x286 uint64 _, x286 = bits.Add64(x246, x272, uint64(0x0)) var x287 uint64 var x288 uint64 x287, x288 = bits.Add64(x248, x274, uint64(x286)) var x289 uint64 var x290 uint64 x289, x290 = bits.Add64(x250, x276, uint64(x288)) var x291 uint64 var x292 uint64 x291, x292 = bits.Add64(x252, x278, uint64(x290)) var x293 uint64 var x294 uint64 x293, x294 = bits.Add64(x254, x280, uint64(x292)) var x295 uint64 var x296 uint64 x295, x296 = bits.Add64(x256, x282, uint64(x294)) var x297 uint64 var x298 uint64 x297, x298 = bits.Add64(x258, x284, uint64(x296)) x299 := (x298 + x259) var x300 uint64 var x301 uint64 x301, x300 = bits.Mul64(x4, arg2[5]) var x302 uint64 var x303 uint64 x303, x302 = bits.Mul64(x4, arg2[4]) var x304 uint64 var x305 uint64 x305, x304 = bits.Mul64(x4, arg2[3]) var x306 uint64 var x307 uint64 x307, x306 = bits.Mul64(x4, arg2[2]) var x308 uint64 var x309 uint64 x309, x308 = bits.Mul64(x4, arg2[1]) var x310 uint64 var x311 uint64 x311, x310 = bits.Mul64(x4, arg2[0]) var x312 uint64 var x313 uint64 x312, x313 = bits.Add64(x311, x308, uint64(0x0)) var x314 uint64 var x315 uint64 x314, x315 = bits.Add64(x309, x306, uint64(x313)) var x316 uint64 var x317 uint64 x316, x317 = bits.Add64(x307, x304, uint64(x315)) var x318 uint64 var x319 uint64 x318, x319 = bits.Add64(x305, x302, uint64(x317)) var x320 uint64 var x321 uint64 x320, x321 = bits.Add64(x303, x300, uint64(x319)) x322 := (x321 + x301) var x323 uint64 var x324 uint64 x323, x324 = bits.Add64(x287, x310, uint64(0x0)) var x325 uint64 var x326 uint64 x325, x326 = bits.Add64(x289, x312, uint64(x324)) var x327 uint64 var x328 uint64 x327, x328 = bits.Add64(x291, x314, uint64(x326)) var x329 uint64 var x330 uint64 x329, x330 = bits.Add64(x293, x316, uint64(x328)) var x331 uint64 var x332 uint64 x331, x332 = bits.Add64(x295, x318, uint64(x330)) var x333 uint64 var x334 uint64 x333, x334 = bits.Add64(x297, x320, uint64(x332)) var x335 uint64 var x336 uint64 x335, x336 = bits.Add64(x299, x322, uint64(x334)) var x337 uint64 _, x337 = bits.Mul64(x323, 0x89f3fffcfffcfffd) var x339 uint64 var x340 uint64 x340, x339 = bits.Mul64(x337, 0x1a0111ea397fe69a) var x341 uint64 var x342 uint64 x342, x341 = bits.Mul64(x337, 0x4b1ba7b6434bacd7) var x343 uint64 var x344 uint64 x344, x343 = bits.Mul64(x337, 0x64774b84f38512bf) var x345 uint64 var x346 uint64 x346, x345 = bits.Mul64(x337, 0x6730d2a0f6b0f624) var x347 uint64 var x348 uint64 x348, x347 = bits.Mul64(x337, 0x1eabfffeb153ffff) var x349 uint64 var x350 uint64 x350, x349 = bits.Mul64(x337, 0xb9feffffffffaaab) var x351 uint64 var x352 uint64 x351, x352 = bits.Add64(x350, x347, uint64(0x0)) var x353 uint64 var x354 uint64 x353, x354 = bits.Add64(x348, x345, uint64(x352)) var x355 uint64 var x356 uint64 x355, x356 = bits.Add64(x346, x343, uint64(x354)) var x357 uint64 var x358 uint64 x357, x358 = bits.Add64(x344, x341, uint64(x356)) var x359 uint64 var x360 uint64 x359, x360 = bits.Add64(x342, x339, uint64(x358)) x361 := (x360 + x340) var x363 uint64 _, x363 = bits.Add64(x323, x349, uint64(0x0)) var x364 uint64 var x365 uint64 x364, x365 = bits.Add64(x325, x351, uint64(x363)) var x366 uint64 var x367 uint64 x366, x367 = bits.Add64(x327, x353, uint64(x365)) var x368 uint64 var x369 uint64 x368, x369 = bits.Add64(x329, x355, uint64(x367)) var x370 uint64 var x371 uint64 x370, x371 = bits.Add64(x331, x357, uint64(x369)) var x372 uint64 var x373 uint64 x372, x373 = bits.Add64(x333, x359, uint64(x371)) var x374 uint64 var x375 uint64 x374, x375 = bits.Add64(x335, x361, uint64(x373)) x376 := (x375 + x336) var x377 uint64 var x378 uint64 x378, x377 = bits.Mul64(x5, arg2[5]) var x379 uint64 var x380 uint64 x380, x379 = bits.Mul64(x5, arg2[4]) var x381 uint64 var x382 uint64 x382, x381 = bits.Mul64(x5, arg2[3]) var x383 uint64 var x384 uint64 x384, x383 = bits.Mul64(x5, arg2[2]) var x385 uint64 var x386 uint64 x386, x385 = bits.Mul64(x5, arg2[1]) var x387 uint64 var x388 uint64 x388, x387 = bits.Mul64(x5, arg2[0]) var x389 uint64 var x390 uint64 x389, x390 = bits.Add64(x388, x385, uint64(0x0)) var x391 uint64 var x392 uint64 x391, x392 = bits.Add64(x386, x383, uint64(x390)) var x393 uint64 var x394 uint64 x393, x394 = bits.Add64(x384, x381, uint64(x392)) var x395 uint64 var x396 uint64 x395, x396 = bits.Add64(x382, x379, uint64(x394)) var x397 uint64 var x398 uint64 x397, x398 = bits.Add64(x380, x377, uint64(x396)) x399 := (x398 + x378) var x400 uint64 var x401 uint64 x400, x401 = bits.Add64(x364, x387, uint64(0x0)) var x402 uint64 var x403 uint64 x402, x403 = bits.Add64(x366, x389, uint64(x401)) var x404 uint64 var x405 uint64 x404, x405 = bits.Add64(x368, x391, uint64(x403)) var x406 uint64 var x407 uint64 x406, x407 = bits.Add64(x370, x393, uint64(x405)) var x408 uint64 var x409 uint64 x408, x409 = bits.Add64(x372, x395, uint64(x407)) var x410 uint64 var x411 uint64 x410, x411 = bits.Add64(x374, x397, uint64(x409)) var x412 uint64 var x413 uint64 x412, x413 = bits.Add64(x376, x399, uint64(x411)) var x414 uint64 _, x414 = bits.Mul64(x400, 0x89f3fffcfffcfffd) var x416 uint64 var x417 uint64 x417, x416 = bits.Mul64(x414, 0x1a0111ea397fe69a) var x418 uint64 var x419 uint64 x419, x418 = bits.Mul64(x414, 0x4b1ba7b6434bacd7) var x420 uint64 var x421 uint64 x421, x420 = bits.Mul64(x414, 0x64774b84f38512bf) var x422 uint64 var x423 uint64 x423, x422 = bits.Mul64(x414, 0x6730d2a0f6b0f624) var x424 uint64 var x425 uint64 x425, x424 = bits.Mul64(x414, 0x1eabfffeb153ffff) var x426 uint64 var x427 uint64 x427, x426 = bits.Mul64(x414, 0xb9feffffffffaaab) var x428 uint64 var x429 uint64 x428, x429 = bits.Add64(x427, x424, uint64(0x0)) var x430 uint64 var x431 uint64 x430, x431 = bits.Add64(x425, x422, uint64(x429)) var x432 uint64 var x433 uint64 x432, x433 = bits.Add64(x423, x420, uint64(x431)) var x434 uint64 var x435 uint64 x434, x435 = bits.Add64(x421, x418, uint64(x433)) var x436 uint64 var x437 uint64 x436, x437 = bits.Add64(x419, x416, uint64(x435)) x438 := (x437 + x417) var x440 uint64 _, x440 = bits.Add64(x400, x426, uint64(0x0)) var x441 uint64 var x442 uint64 x441, x442 = bits.Add64(x402, x428, uint64(x440)) var x443 uint64 var x444 uint64 x443, x444 = bits.Add64(x404, x430, uint64(x442)) var x445 uint64 var x446 uint64 x445, x446 = bits.Add64(x406, x432, uint64(x444)) var x447 uint64 var x448 uint64 x447, x448 = bits.Add64(x408, x434, uint64(x446)) var x449 uint64 var x450 uint64 x449, x450 = bits.Add64(x410, x436, uint64(x448)) var x451 uint64 var x452 uint64 x451, x452 = bits.Add64(x412, x438, uint64(x450)) x453 := (x452 + x413) var x454 uint64 var x455 uint64 x454, x455 = bits.Sub64(x441, 0xb9feffffffffaaab, uint64(uint64(0x0))) var x456 uint64 var x457 uint64 x456, x457 = bits.Sub64(x443, 0x1eabfffeb153ffff, uint64(x455)) var x458 uint64 var x459 uint64 x458, x459 = bits.Sub64(x445, 0x6730d2a0f6b0f624, uint64(x457)) var x460 uint64 var x461 uint64 x460, x461 = bits.Sub64(x447, 0x64774b84f38512bf, uint64(x459)) var x462 uint64 var x463 uint64 x462, x463 = bits.Sub64(x449, 0x4b1ba7b6434bacd7, uint64(x461)) var x464 uint64 var x465 uint64 x464, x465 = bits.Sub64(x451, 0x1a0111ea397fe69a, uint64(x463)) var x467 uint64 _, x467 = bits.Sub64(x453, uint64(0x0), uint64(x465)) var x468 uint64 fiatFpMontCmovznzU64(&x468, x467, x454, x441) var x469 uint64 fiatFpMontCmovznzU64(&x469, x467, x456, x443) var x470 uint64 fiatFpMontCmovznzU64(&x470, x467, x458, x445) var x471 uint64 fiatFpMontCmovznzU64(&x471, x467, x460, x447) var x472 uint64 fiatFpMontCmovznzU64(&x472, x467, x462, x449) var x473 uint64 fiatFpMontCmovznzU64(&x473, x467, x464, x451) out1[0] = x468 out1[1] = x469 out1[2] = x470 out1[3] = x471 out1[4] = x472 out1[5] = x473 } // The function fiatFpMontSquare squares a field element in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatFpMontSquare(out1 *[6]uint64, arg1 *[6]uint64) { x1 := arg1[1] x2 := arg1[2] x3 := arg1[3] x4 := arg1[4] x5 := arg1[5] x6 := arg1[0] var x7 uint64 var x8 uint64 x8, x7 = bits.Mul64(x6, arg1[5]) var x9 uint64 var x10 uint64 x10, x9 = bits.Mul64(x6, arg1[4]) var x11 uint64 var x12 uint64 x12, x11 = bits.Mul64(x6, arg1[3]) var x13 uint64 var x14 uint64 x14, x13 = bits.Mul64(x6, arg1[2]) var x15 uint64 var x16 uint64 x16, x15 = bits.Mul64(x6, arg1[1]) var x17 uint64 var x18 uint64 x18, x17 = bits.Mul64(x6, arg1[0]) var x19 uint64 var x20 uint64 x19, x20 = bits.Add64(x18, x15, uint64(0x0)) var x21 uint64 var x22 uint64 x21, x22 = bits.Add64(x16, x13, uint64(x20)) var x23 uint64 var x24 uint64 x23, x24 = bits.Add64(x14, x11, uint64(x22)) var x25 uint64 var x26 uint64 x25, x26 = bits.Add64(x12, x9, uint64(x24)) var x27 uint64 var x28 uint64 x27, x28 = bits.Add64(x10, x7, uint64(x26)) x29 := (x28 + x8) var x30 uint64 _, x30 = bits.Mul64(x17, 0x89f3fffcfffcfffd) var x32 uint64 var x33 uint64 x33, x32 = bits.Mul64(x30, 0x1a0111ea397fe69a) var x34 uint64 var x35 uint64 x35, x34 = bits.Mul64(x30, 0x4b1ba7b6434bacd7) var x36 uint64 var x37 uint64 x37, x36 = bits.Mul64(x30, 0x64774b84f38512bf) var x38 uint64 var x39 uint64 x39, x38 = bits.Mul64(x30, 0x6730d2a0f6b0f624) var x40 uint64 var x41 uint64 x41, x40 = bits.Mul64(x30, 0x1eabfffeb153ffff) var x42 uint64 var x43 uint64 x43, x42 = bits.Mul64(x30, 0xb9feffffffffaaab) var x44 uint64 var x45 uint64 x44, x45 = bits.Add64(x43, x40, uint64(0x0)) var x46 uint64 var x47 uint64 x46, x47 = bits.Add64(x41, x38, uint64(x45)) var x48 uint64 var x49 uint64 x48, x49 = bits.Add64(x39, x36, uint64(x47)) var x50 uint64 var x51 uint64 x50, x51 = bits.Add64(x37, x34, uint64(x49)) var x52 uint64 var x53 uint64 x52, x53 = bits.Add64(x35, x32, uint64(x51)) x54 := (x53 + x33) var x56 uint64 _, x56 = bits.Add64(x17, x42, uint64(0x0)) var x57 uint64 var x58 uint64 x57, x58 = bits.Add64(x19, x44, uint64(x56)) var x59 uint64 var x60 uint64 x59, x60 = bits.Add64(x21, x46, uint64(x58)) var x61 uint64 var x62 uint64 x61, x62 = bits.Add64(x23, x48, uint64(x60)) var x63 uint64 var x64 uint64 x63, x64 = bits.Add64(x25, x50, uint64(x62)) var x65 uint64 var x66 uint64 x65, x66 = bits.Add64(x27, x52, uint64(x64)) var x67 uint64 var x68 uint64 x67, x68 = bits.Add64(x29, x54, uint64(x66)) var x69 uint64 var x70 uint64 x70, x69 = bits.Mul64(x1, arg1[5]) var x71 uint64 var x72 uint64 x72, x71 = bits.Mul64(x1, arg1[4]) var x73 uint64 var x74 uint64 x74, x73 = bits.Mul64(x1, arg1[3]) var x75 uint64 var x76 uint64 x76, x75 = bits.Mul64(x1, arg1[2]) var x77 uint64 var x78 uint64 x78, x77 = bits.Mul64(x1, arg1[1]) var x79 uint64 var x80 uint64 x80, x79 = bits.Mul64(x1, arg1[0]) var x81 uint64 var x82 uint64 x81, x82 = bits.Add64(x80, x77, uint64(0x0)) var x83 uint64 var x84 uint64 x83, x84 = bits.Add64(x78, x75, uint64(x82)) var x85 uint64 var x86 uint64 x85, x86 = bits.Add64(x76, x73, uint64(x84)) var x87 uint64 var x88 uint64 x87, x88 = bits.Add64(x74, x71, uint64(x86)) var x89 uint64 var x90 uint64 x89, x90 = bits.Add64(x72, x69, uint64(x88)) x91 := (x90 + x70) var x92 uint64 var x93 uint64 x92, x93 = bits.Add64(x57, x79, uint64(0x0)) var x94 uint64 var x95 uint64 x94, x95 = bits.Add64(x59, x81, uint64(x93)) var x96 uint64 var x97 uint64 x96, x97 = bits.Add64(x61, x83, uint64(x95)) var x98 uint64 var x99 uint64 x98, x99 = bits.Add64(x63, x85, uint64(x97)) var x100 uint64 var x101 uint64 x100, x101 = bits.Add64(x65, x87, uint64(x99)) var x102 uint64 var x103 uint64 x102, x103 = bits.Add64(x67, x89, uint64(x101)) var x104 uint64 var x105 uint64 x104, x105 = bits.Add64(x68, x91, uint64(x103)) var x106 uint64 _, x106 = bits.Mul64(x92, 0x89f3fffcfffcfffd) var x108 uint64 var x109 uint64 x109, x108 = bits.Mul64(x106, 0x1a0111ea397fe69a) var x110 uint64 var x111 uint64 x111, x110 = bits.Mul64(x106, 0x4b1ba7b6434bacd7) var x112 uint64 var x113 uint64 x113, x112 = bits.Mul64(x106, 0x64774b84f38512bf) var x114 uint64 var x115 uint64 x115, x114 = bits.Mul64(x106, 0x6730d2a0f6b0f624) var x116 uint64 var x117 uint64 x117, x116 = bits.Mul64(x106, 0x1eabfffeb153ffff) var x118 uint64 var x119 uint64 x119, x118 = bits.Mul64(x106, 0xb9feffffffffaaab) var x120 uint64 var x121 uint64 x120, x121 = bits.Add64(x119, x116, uint64(0x0)) var x122 uint64 var x123 uint64 x122, x123 = bits.Add64(x117, x114, uint64(x121)) var x124 uint64 var x125 uint64 x124, x125 = bits.Add64(x115, x112, uint64(x123)) var x126 uint64 var x127 uint64 x126, x127 = bits.Add64(x113, x110, uint64(x125)) var x128 uint64 var x129 uint64 x128, x129 = bits.Add64(x111, x108, uint64(x127)) x130 := (x129 + x109) var x132 uint64 _, x132 = bits.Add64(x92, x118, uint64(0x0)) var x133 uint64 var x134 uint64 x133, x134 = bits.Add64(x94, x120, uint64(x132)) var x135 uint64 var x136 uint64 x135, x136 = bits.Add64(x96, x122, uint64(x134)) var x137 uint64 var x138 uint64 x137, x138 = bits.Add64(x98, x124, uint64(x136)) var x139 uint64 var x140 uint64 x139, x140 = bits.Add64(x100, x126, uint64(x138)) var x141 uint64 var x142 uint64 x141, x142 = bits.Add64(x102, x128, uint64(x140)) var x143 uint64 var x144 uint64 x143, x144 = bits.Add64(x104, x130, uint64(x142)) x145 := (x144 + x105) var x146 uint64 var x147 uint64 x147, x146 = bits.Mul64(x2, arg1[5]) var x148 uint64 var x149 uint64 x149, x148 = bits.Mul64(x2, arg1[4]) var x150 uint64 var x151 uint64 x151, x150 = bits.Mul64(x2, arg1[3]) var x152 uint64 var x153 uint64 x153, x152 = bits.Mul64(x2, arg1[2]) var x154 uint64 var x155 uint64 x155, x154 = bits.Mul64(x2, arg1[1]) var x156 uint64 var x157 uint64 x157, x156 = bits.Mul64(x2, arg1[0]) var x158 uint64 var x159 uint64 x158, x159 = bits.Add64(x157, x154, uint64(0x0)) var x160 uint64 var x161 uint64 x160, x161 = bits.Add64(x155, x152, uint64(x159)) var x162 uint64 var x163 uint64 x162, x163 = bits.Add64(x153, x150, uint64(x161)) var x164 uint64 var x165 uint64 x164, x165 = bits.Add64(x151, x148, uint64(x163)) var x166 uint64 var x167 uint64 x166, x167 = bits.Add64(x149, x146, uint64(x165)) x168 := (x167 + x147) var x169 uint64 var x170 uint64 x169, x170 = bits.Add64(x133, x156, uint64(0x0)) var x171 uint64 var x172 uint64 x171, x172 = bits.Add64(x135, x158, uint64(x170)) var x173 uint64 var x174 uint64 x173, x174 = bits.Add64(x137, x160, uint64(x172)) var x175 uint64 var x176 uint64 x175, x176 = bits.Add64(x139, x162, uint64(x174)) var x177 uint64 var x178 uint64 x177, x178 = bits.Add64(x141, x164, uint64(x176)) var x179 uint64 var x180 uint64 x179, x180 = bits.Add64(x143, x166, uint64(x178)) var x181 uint64 var x182 uint64 x181, x182 = bits.Add64(x145, x168, uint64(x180)) var x183 uint64 _, x183 = bits.Mul64(x169, 0x89f3fffcfffcfffd) var x185 uint64 var x186 uint64 x186, x185 = bits.Mul64(x183, 0x1a0111ea397fe69a) var x187 uint64 var x188 uint64 x188, x187 = bits.Mul64(x183, 0x4b1ba7b6434bacd7) var x189 uint64 var x190 uint64 x190, x189 = bits.Mul64(x183, 0x64774b84f38512bf) var x191 uint64 var x192 uint64 x192, x191 = bits.Mul64(x183, 0x6730d2a0f6b0f624) var x193 uint64 var x194 uint64 x194, x193 = bits.Mul64(x183, 0x1eabfffeb153ffff) var x195 uint64 var x196 uint64 x196, x195 = bits.Mul64(x183, 0xb9feffffffffaaab) var x197 uint64 var x198 uint64 x197, x198 = bits.Add64(x196, x193, uint64(0x0)) var x199 uint64 var x200 uint64 x199, x200 = bits.Add64(x194, x191, uint64(x198)) var x201 uint64 var x202 uint64 x201, x202 = bits.Add64(x192, x189, uint64(x200)) var x203 uint64 var x204 uint64 x203, x204 = bits.Add64(x190, x187, uint64(x202)) var x205 uint64 var x206 uint64 x205, x206 = bits.Add64(x188, x185, uint64(x204)) x207 := (x206 + x186) var x209 uint64 _, x209 = bits.Add64(x169, x195, uint64(0x0)) var x210 uint64 var x211 uint64 x210, x211 = bits.Add64(x171, x197, uint64(x209)) var x212 uint64 var x213 uint64 x212, x213 = bits.Add64(x173, x199, uint64(x211)) var x214 uint64 var x215 uint64 x214, x215 = bits.Add64(x175, x201, uint64(x213)) var x216 uint64 var x217 uint64 x216, x217 = bits.Add64(x177, x203, uint64(x215)) var x218 uint64 var x219 uint64 x218, x219 = bits.Add64(x179, x205, uint64(x217)) var x220 uint64 var x221 uint64 x220, x221 = bits.Add64(x181, x207, uint64(x219)) x222 := (x221 + x182) var x223 uint64 var x224 uint64 x224, x223 = bits.Mul64(x3, arg1[5]) var x225 uint64 var x226 uint64 x226, x225 = bits.Mul64(x3, arg1[4]) var x227 uint64 var x228 uint64 x228, x227 = bits.Mul64(x3, arg1[3]) var x229 uint64 var x230 uint64 x230, x229 = bits.Mul64(x3, arg1[2]) var x231 uint64 var x232 uint64 x232, x231 = bits.Mul64(x3, arg1[1]) var x233 uint64 var x234 uint64 x234, x233 = bits.Mul64(x3, arg1[0]) var x235 uint64 var x236 uint64 x235, x236 = bits.Add64(x234, x231, uint64(0x0)) var x237 uint64 var x238 uint64 x237, x238 = bits.Add64(x232, x229, uint64(x236)) var x239 uint64 var x240 uint64 x239, x240 = bits.Add64(x230, x227, uint64(x238)) var x241 uint64 var x242 uint64 x241, x242 = bits.Add64(x228, x225, uint64(x240)) var x243 uint64 var x244 uint64 x243, x244 = bits.Add64(x226, x223, uint64(x242)) x245 := (x244 + x224) var x246 uint64 var x247 uint64 x246, x247 = bits.Add64(x210, x233, uint64(0x0)) var x248 uint64 var x249 uint64 x248, x249 = bits.Add64(x212, x235, uint64(x247)) var x250 uint64 var x251 uint64 x250, x251 = bits.Add64(x214, x237, uint64(x249)) var x252 uint64 var x253 uint64 x252, x253 = bits.Add64(x216, x239, uint64(x251)) var x254 uint64 var x255 uint64 x254, x255 = bits.Add64(x218, x241, uint64(x253)) var x256 uint64 var x257 uint64 x256, x257 = bits.Add64(x220, x243, uint64(x255)) var x258 uint64 var x259 uint64 x258, x259 = bits.Add64(x222, x245, uint64(x257)) var x260 uint64 _, x260 = bits.Mul64(x246, 0x89f3fffcfffcfffd) var x262 uint64 var x263 uint64 x263, x262 = bits.Mul64(x260, 0x1a0111ea397fe69a) var x264 uint64 var x265 uint64 x265, x264 = bits.Mul64(x260, 0x4b1ba7b6434bacd7) var x266 uint64 var x267 uint64 x267, x266 = bits.Mul64(x260, 0x64774b84f38512bf) var x268 uint64 var x269 uint64 x269, x268 = bits.Mul64(x260, 0x6730d2a0f6b0f624) var x270 uint64 var x271 uint64 x271, x270 = bits.Mul64(x260, 0x1eabfffeb153ffff) var x272 uint64 var x273 uint64 x273, x272 = bits.Mul64(x260, 0xb9feffffffffaaab) var x274 uint64 var x275 uint64 x274, x275 = bits.Add64(x273, x270, uint64(0x0)) var x276 uint64 var x277 uint64 x276, x277 = bits.Add64(x271, x268, uint64(x275)) var x278 uint64 var x279 uint64 x278, x279 = bits.Add64(x269, x266, uint64(x277)) var x280 uint64 var x281 uint64 x280, x281 = bits.Add64(x267, x264, uint64(x279)) var x282 uint64 var x283 uint64 x282, x283 = bits.Add64(x265, x262, uint64(x281)) x284 := (x283 + x263) var x286 uint64 _, x286 = bits.Add64(x246, x272, uint64(0x0)) var x287 uint64 var x288 uint64 x287, x288 = bits.Add64(x248, x274, uint64(x286)) var x289 uint64 var x290 uint64 x289, x290 = bits.Add64(x250, x276, uint64(x288)) var x291 uint64 var x292 uint64 x291, x292 = bits.Add64(x252, x278, uint64(x290)) var x293 uint64 var x294 uint64 x293, x294 = bits.Add64(x254, x280, uint64(x292)) var x295 uint64 var x296 uint64 x295, x296 = bits.Add64(x256, x282, uint64(x294)) var x297 uint64 var x298 uint64 x297, x298 = bits.Add64(x258, x284, uint64(x296)) x299 := (x298 + x259) var x300 uint64 var x301 uint64 x301, x300 = bits.Mul64(x4, arg1[5]) var x302 uint64 var x303 uint64 x303, x302 = bits.Mul64(x4, arg1[4]) var x304 uint64 var x305 uint64 x305, x304 = bits.Mul64(x4, arg1[3]) var x306 uint64 var x307 uint64 x307, x306 = bits.Mul64(x4, arg1[2]) var x308 uint64 var x309 uint64 x309, x308 = bits.Mul64(x4, arg1[1]) var x310 uint64 var x311 uint64 x311, x310 = bits.Mul64(x4, arg1[0]) var x312 uint64 var x313 uint64 x312, x313 = bits.Add64(x311, x308, uint64(0x0)) var x314 uint64 var x315 uint64 x314, x315 = bits.Add64(x309, x306, uint64(x313)) var x316 uint64 var x317 uint64 x316, x317 = bits.Add64(x307, x304, uint64(x315)) var x318 uint64 var x319 uint64 x318, x319 = bits.Add64(x305, x302, uint64(x317)) var x320 uint64 var x321 uint64 x320, x321 = bits.Add64(x303, x300, uint64(x319)) x322 := (x321 + x301) var x323 uint64 var x324 uint64 x323, x324 = bits.Add64(x287, x310, uint64(0x0)) var x325 uint64 var x326 uint64 x325, x326 = bits.Add64(x289, x312, uint64(x324)) var x327 uint64 var x328 uint64 x327, x328 = bits.Add64(x291, x314, uint64(x326)) var x329 uint64 var x330 uint64 x329, x330 = bits.Add64(x293, x316, uint64(x328)) var x331 uint64 var x332 uint64 x331, x332 = bits.Add64(x295, x318, uint64(x330)) var x333 uint64 var x334 uint64 x333, x334 = bits.Add64(x297, x320, uint64(x332)) var x335 uint64 var x336 uint64 x335, x336 = bits.Add64(x299, x322, uint64(x334)) var x337 uint64 _, x337 = bits.Mul64(x323, 0x89f3fffcfffcfffd) var x339 uint64 var x340 uint64 x340, x339 = bits.Mul64(x337, 0x1a0111ea397fe69a) var x341 uint64 var x342 uint64 x342, x341 = bits.Mul64(x337, 0x4b1ba7b6434bacd7) var x343 uint64 var x344 uint64 x344, x343 = bits.Mul64(x337, 0x64774b84f38512bf) var x345 uint64 var x346 uint64 x346, x345 = bits.Mul64(x337, 0x6730d2a0f6b0f624) var x347 uint64 var x348 uint64 x348, x347 = bits.Mul64(x337, 0x1eabfffeb153ffff) var x349 uint64 var x350 uint64 x350, x349 = bits.Mul64(x337, 0xb9feffffffffaaab) var x351 uint64 var x352 uint64 x351, x352 = bits.Add64(x350, x347, uint64(0x0)) var x353 uint64 var x354 uint64 x353, x354 = bits.Add64(x348, x345, uint64(x352)) var x355 uint64 var x356 uint64 x355, x356 = bits.Add64(x346, x343, uint64(x354)) var x357 uint64 var x358 uint64 x357, x358 = bits.Add64(x344, x341, uint64(x356)) var x359 uint64 var x360 uint64 x359, x360 = bits.Add64(x342, x339, uint64(x358)) x361 := (x360 + x340) var x363 uint64 _, x363 = bits.Add64(x323, x349, uint64(0x0)) var x364 uint64 var x365 uint64 x364, x365 = bits.Add64(x325, x351, uint64(x363)) var x366 uint64 var x367 uint64 x366, x367 = bits.Add64(x327, x353, uint64(x365)) var x368 uint64 var x369 uint64 x368, x369 = bits.Add64(x329, x355, uint64(x367)) var x370 uint64 var x371 uint64 x370, x371 = bits.Add64(x331, x357, uint64(x369)) var x372 uint64 var x373 uint64 x372, x373 = bits.Add64(x333, x359, uint64(x371)) var x374 uint64 var x375 uint64 x374, x375 = bits.Add64(x335, x361, uint64(x373)) x376 := (x375 + x336) var x377 uint64 var x378 uint64 x378, x377 = bits.Mul64(x5, arg1[5]) var x379 uint64 var x380 uint64 x380, x379 = bits.Mul64(x5, arg1[4]) var x381 uint64 var x382 uint64 x382, x381 = bits.Mul64(x5, arg1[3]) var x383 uint64 var x384 uint64 x384, x383 = bits.Mul64(x5, arg1[2]) var x385 uint64 var x386 uint64 x386, x385 = bits.Mul64(x5, arg1[1]) var x387 uint64 var x388 uint64 x388, x387 = bits.Mul64(x5, arg1[0]) var x389 uint64 var x390 uint64 x389, x390 = bits.Add64(x388, x385, uint64(0x0)) var x391 uint64 var x392 uint64 x391, x392 = bits.Add64(x386, x383, uint64(x390)) var x393 uint64 var x394 uint64 x393, x394 = bits.Add64(x384, x381, uint64(x392)) var x395 uint64 var x396 uint64 x395, x396 = bits.Add64(x382, x379, uint64(x394)) var x397 uint64 var x398 uint64 x397, x398 = bits.Add64(x380, x377, uint64(x396)) x399 := (x398 + x378) var x400 uint64 var x401 uint64 x400, x401 = bits.Add64(x364, x387, uint64(0x0)) var x402 uint64 var x403 uint64 x402, x403 = bits.Add64(x366, x389, uint64(x401)) var x404 uint64 var x405 uint64 x404, x405 = bits.Add64(x368, x391, uint64(x403)) var x406 uint64 var x407 uint64 x406, x407 = bits.Add64(x370, x393, uint64(x405)) var x408 uint64 var x409 uint64 x408, x409 = bits.Add64(x372, x395, uint64(x407)) var x410 uint64 var x411 uint64 x410, x411 = bits.Add64(x374, x397, uint64(x409)) var x412 uint64 var x413 uint64 x412, x413 = bits.Add64(x376, x399, uint64(x411)) var x414 uint64 _, x414 = bits.Mul64(x400, 0x89f3fffcfffcfffd) var x416 uint64 var x417 uint64 x417, x416 = bits.Mul64(x414, 0x1a0111ea397fe69a) var x418 uint64 var x419 uint64 x419, x418 = bits.Mul64(x414, 0x4b1ba7b6434bacd7) var x420 uint64 var x421 uint64 x421, x420 = bits.Mul64(x414, 0x64774b84f38512bf) var x422 uint64 var x423 uint64 x423, x422 = bits.Mul64(x414, 0x6730d2a0f6b0f624) var x424 uint64 var x425 uint64 x425, x424 = bits.Mul64(x414, 0x1eabfffeb153ffff) var x426 uint64 var x427 uint64 x427, x426 = bits.Mul64(x414, 0xb9feffffffffaaab) var x428 uint64 var x429 uint64 x428, x429 = bits.Add64(x427, x424, uint64(0x0)) var x430 uint64 var x431 uint64 x430, x431 = bits.Add64(x425, x422, uint64(x429)) var x432 uint64 var x433 uint64 x432, x433 = bits.Add64(x423, x420, uint64(x431)) var x434 uint64 var x435 uint64 x434, x435 = bits.Add64(x421, x418, uint64(x433)) var x436 uint64 var x437 uint64 x436, x437 = bits.Add64(x419, x416, uint64(x435)) x438 := (x437 + x417) var x440 uint64 _, x440 = bits.Add64(x400, x426, uint64(0x0)) var x441 uint64 var x442 uint64 x441, x442 = bits.Add64(x402, x428, uint64(x440)) var x443 uint64 var x444 uint64 x443, x444 = bits.Add64(x404, x430, uint64(x442)) var x445 uint64 var x446 uint64 x445, x446 = bits.Add64(x406, x432, uint64(x444)) var x447 uint64 var x448 uint64 x447, x448 = bits.Add64(x408, x434, uint64(x446)) var x449 uint64 var x450 uint64 x449, x450 = bits.Add64(x410, x436, uint64(x448)) var x451 uint64 var x452 uint64 x451, x452 = bits.Add64(x412, x438, uint64(x450)) x453 := (x452 + x413) var x454 uint64 var x455 uint64 x454, x455 = bits.Sub64(x441, 0xb9feffffffffaaab, uint64(uint64(0x0))) var x456 uint64 var x457 uint64 x456, x457 = bits.Sub64(x443, 0x1eabfffeb153ffff, uint64(x455)) var x458 uint64 var x459 uint64 x458, x459 = bits.Sub64(x445, 0x6730d2a0f6b0f624, uint64(x457)) var x460 uint64 var x461 uint64 x460, x461 = bits.Sub64(x447, 0x64774b84f38512bf, uint64(x459)) var x462 uint64 var x463 uint64 x462, x463 = bits.Sub64(x449, 0x4b1ba7b6434bacd7, uint64(x461)) var x464 uint64 var x465 uint64 x464, x465 = bits.Sub64(x451, 0x1a0111ea397fe69a, uint64(x463)) var x467 uint64 _, x467 = bits.Sub64(x453, uint64(0x0), uint64(x465)) var x468 uint64 fiatFpMontCmovznzU64(&x468, x467, x454, x441) var x469 uint64 fiatFpMontCmovznzU64(&x469, x467, x456, x443) var x470 uint64 fiatFpMontCmovznzU64(&x470, x467, x458, x445) var x471 uint64 fiatFpMontCmovznzU64(&x471, x467, x460, x447) var x472 uint64 fiatFpMontCmovznzU64(&x472, x467, x462, x449) var x473 uint64 fiatFpMontCmovznzU64(&x473, x467, x464, x451) out1[0] = x468 out1[1] = x469 out1[2] = x470 out1[3] = x471 out1[4] = x472 out1[5] = x473 } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/fp_test.go000066400000000000000000000056051454601126700237740ustar00rootroot00000000000000package ff import ( "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/internal/test" ) func randomFp(t testing.TB) *Fp { t.Helper() f := new(Fp) err := f.Random(rand.Reader) if err != nil { t.Error(err) } return f } func TestFp(t *testing.T) { const testTimes = 1 << 10 t.Run("no_alias", func(t *testing.T) { var want, got Fp x := randomFp(t) got = *x got.Sqr(&got) want = *x want.Mul(&want, &want) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } }) t.Run("mul_inv", func(t *testing.T) { var z Fp for i := 0; i < testTimes; i++ { x := randomFp(t) y := randomFp(t) // x*y*x^1 - y = 0 z.Inv(x) z.Mul(&z, y) z.Mul(&z, x) z.Sub(&z, y) got := z.IsZero() want := 1 if got != want { test.ReportError(t, got, want, x, y) } } }) t.Run("mul_sqr", func(t *testing.T) { var l0, l1, r0, r1 Fp for i := 0; i < testTimes; i++ { x := randomFp(t) y := randomFp(t) // (x+y)(x-y) = (x^2-y^2) l0.Add(x, y) l1.Sub(x, y) l0.Mul(&l0, &l1) r0.Sqr(x) r1.Sqr(y) r0.Sub(&r0, &r1) got := &l0 want := &r0 if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("sqrt", func(t *testing.T) { var r, notRoot, got Fp // Check when x has square-root. for i := 0; i < testTimes; i++ { x := randomFp(t) x.Sqr(x) // let x is QR and r = sqrt(x); check (+r)^2 = (-r)^2 = x. isQR := r.Sqrt(x) test.CheckOk(isQR == 1, fmt.Sprintf("should be a QR: %v", x), t) rNeg := r rNeg.Neg() want := x for _, root := range []*Fp{&r, &rNeg} { got.Sqr(root) if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, root) } } } // Check when x has not square-root. for i := 0; i < testTimes; i++ { want := randomFp(t) x := randomFp(t) x.Sqr(x) x.Add(x, x) // x = 2*(x^2), since 2 is not QR in Fp. // let x is not QR and r = sqrt(x); check that r was not modified. got := want isQR := got.Sqrt(x) test.CheckOk(isQR == 0, fmt.Sprintf("shouldn't be a QR: %v", x), t) if got.IsEqual(want) != 1 { test.ReportError(t, got, want, x, notRoot) } } }) t.Run("marshal", func(t *testing.T) { var b Fp for i := 0; i < testTimes; i++ { a := randomFp(t) s, err := a.MarshalBinary() test.CheckNoErr(t, err, "MarshalBinary failed") err = b.UnmarshalBinary(s) test.CheckNoErr(t, err, "UnmarshalBinary failed") if b.IsEqual(a) == 0 { test.ReportError(t, a, b) } } }) } func BenchmarkFp(b *testing.B) { x := randomFp(b) y := randomFp(b) z := randomFp(b) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Add(x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sqr(x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Inv(x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/gen.go000066400000000000000000000045251454601126700231010ustar00rootroot00000000000000//go:build ignore // +build ignore // Code Generation using fiat-crypto // // Download and unpack `ExtractionOCaml-Ubuntu LTS` from // https://github.com/mit-plv/fiat-crypto/suites/3241842351/artifacts/75305272 // // Then run this program specifying the path to the word_by_word_montgomery binary. // $ FIAT_BINARY= go run gen.go // // References: // [1] Erbsen et al. "Simple High-Level Code For Cryptographic Arithmetic – With // Proofs, Without Compromises" https://github.com/mit-plv/fiat-crypto package main import ( "log" "os" "os/exec" "strings" "text/template" ) const ( packName = "ff" headerCIRCL = "Code generated by gen.go using fiat-crypto." ) var ( FIAT_BINARY = "./word_by_word_montgomery" FIAT_PARAMS = []string{ "--output", "{{.Name}}.go", "--lang", "Go", "--package-name", "{{.PackageName}}", "--doc-prepend-header", "{{.Header}}", "--package-case", "lowerCamelCase", "--public-function-case", "lowerCamelCase", "--public-type-case", "lowerCamelCase", "--doc-newline-before-package-declaration", "--no-primitives", "--widen-carry", "--no-field-element-typedefs", "--relax-primitive-carry-to-bitwidth", "64", "{{.Prefix}}", "64", "{{.Prime}}", "add", "sub", "mul", "square", } ) var fields = []struct{ Prefix, Name, Prime, Header, PackageName string }{ { Prefix: "FpMont", Name: "fpMont381", Prime: "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab", Header: headerCIRCL, PackageName: packName, }, { Prefix: "ScMont", Name: "scMont255", Prime: "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", Header: headerCIRCL, PackageName: packName, }, } func main() { if s := os.Getenv("FIAT_BINARY"); s != "" { FIAT_BINARY = s } var err error t := template.New("params") buf := new(strings.Builder) for _, f := range fields { params := []string{} for _, p := range FIAT_PARAMS { buf.Reset() t = template.Must(t.Parse(p)) err = t.Execute(buf, f) if err != nil { log.Fatalf("executing template:", err) } params = append(params, buf.String()) } cmd := exec.Command(FIAT_BINARY, params...) out, err := cmd.CombinedOutput() if len(out) != 0 || err != nil { log.Fatalf("command output: %s\n command error: %v\n", out, err) } } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/scMont255.go000066400000000000000000000570001454601126700240230ustar00rootroot00000000000000// Code generated by gen.go using fiat-crypto. // // Autogenerated: './word_by_word_montgomery' --output scMont255.go --lang Go --package-name ff --doc-prepend-header 'Code generated by gen.go using fiat-crypto.' --package-case lowerCamelCase --public-function-case lowerCamelCase --public-type-case lowerCamelCase --doc-newline-before-package-declaration --no-primitives --widen-carry --no-field-element-typedefs --relax-primitive-carry-to-bitwidth 64 ScMont 64 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 add sub mul square // // curve description: ScMont // // machine_wordsize = 64 (from "64") // // requested operations: add, sub, mul, square // // m = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 (from "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001") // // // // NOTE: In addition to the bounds specified above each function, all // // functions synthesized for this Montgomery arithmetic require the // // input to be strictly less than the prime modulus (m), and also // // require the input to be in the unique saturated representation. // // All functions also ensure that these two properties are true of // // return values. // // // // Computed values: // // eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) // // bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) // // twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in // // if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 package ff import "math/bits" // The function fiatScMontAdd adds two field elements in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // 0 ≤ eval arg2 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatScMontAdd(out1 *[4]uint64, arg1 *[4]uint64, arg2 *[4]uint64) { var x1 uint64 var x2 uint64 x1, x2 = bits.Add64(arg1[0], arg2[0], uint64(0x0)) var x3 uint64 var x4 uint64 x3, x4 = bits.Add64(arg1[1], arg2[1], uint64(x2)) var x5 uint64 var x6 uint64 x5, x6 = bits.Add64(arg1[2], arg2[2], uint64(x4)) var x7 uint64 var x8 uint64 x7, x8 = bits.Add64(arg1[3], arg2[3], uint64(x6)) var x9 uint64 var x10 uint64 x9, x10 = bits.Sub64(x1, 0xffffffff00000001, uint64(uint64(0x0))) var x11 uint64 var x12 uint64 x11, x12 = bits.Sub64(x3, 0x53bda402fffe5bfe, uint64(x10)) var x13 uint64 var x14 uint64 x13, x14 = bits.Sub64(x5, 0x3339d80809a1d805, uint64(x12)) var x15 uint64 var x16 uint64 x15, x16 = bits.Sub64(x7, 0x73eda753299d7d48, uint64(x14)) var x18 uint64 _, x18 = bits.Sub64(x8, uint64(0x0), uint64(x16)) var x19 uint64 fiatScMontCmovznzU64(&x19, x18, x9, x1) var x20 uint64 fiatScMontCmovznzU64(&x20, x18, x11, x3) var x21 uint64 fiatScMontCmovznzU64(&x21, x18, x13, x5) var x22 uint64 fiatScMontCmovznzU64(&x22, x18, x15, x7) out1[0] = x19 out1[1] = x20 out1[2] = x21 out1[3] = x22 } // The function fiatScMontSub subtracts two field elements in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // 0 ≤ eval arg2 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatScMontSub(out1 *[4]uint64, arg1 *[4]uint64, arg2 *[4]uint64) { var x1 uint64 var x2 uint64 x1, x2 = bits.Sub64(arg1[0], arg2[0], uint64(0x0)) var x3 uint64 var x4 uint64 x3, x4 = bits.Sub64(arg1[1], arg2[1], uint64(x2)) var x5 uint64 var x6 uint64 x5, x6 = bits.Sub64(arg1[2], arg2[2], uint64(x4)) var x7 uint64 var x8 uint64 x7, x8 = bits.Sub64(arg1[3], arg2[3], uint64(x6)) var x9 uint64 fiatScMontCmovznzU64(&x9, x8, uint64(0x0), 0xffffffffffffffff) var x10 uint64 var x11 uint64 x10, x11 = bits.Add64(x1, (x9 & 0xffffffff00000001), uint64(0x0)) var x12 uint64 var x13 uint64 x12, x13 = bits.Add64(x3, (x9 & 0x53bda402fffe5bfe), uint64(x11)) var x14 uint64 var x15 uint64 x14, x15 = bits.Add64(x5, (x9 & 0x3339d80809a1d805), uint64(x13)) var x16 uint64 x16, _ = bits.Add64(x7, (x9 & 0x73eda753299d7d48), uint64(x15)) out1[0] = x10 out1[1] = x12 out1[2] = x14 out1[3] = x16 } // The function fiatScMontMul multiplies two field elements in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // 0 ≤ eval arg2 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatScMontMul(out1 *[4]uint64, arg1 *[4]uint64, arg2 *[4]uint64) { x1 := arg1[1] x2 := arg1[2] x3 := arg1[3] x4 := arg1[0] var x5 uint64 var x6 uint64 x6, x5 = bits.Mul64(x4, arg2[3]) var x7 uint64 var x8 uint64 x8, x7 = bits.Mul64(x4, arg2[2]) var x9 uint64 var x10 uint64 x10, x9 = bits.Mul64(x4, arg2[1]) var x11 uint64 var x12 uint64 x12, x11 = bits.Mul64(x4, arg2[0]) var x13 uint64 var x14 uint64 x13, x14 = bits.Add64(x12, x9, uint64(0x0)) var x15 uint64 var x16 uint64 x15, x16 = bits.Add64(x10, x7, uint64(x14)) var x17 uint64 var x18 uint64 x17, x18 = bits.Add64(x8, x5, uint64(x16)) x19 := (x18 + x6) var x20 uint64 _, x20 = bits.Mul64(x11, 0xfffffffeffffffff) var x22 uint64 var x23 uint64 x23, x22 = bits.Mul64(x20, 0x73eda753299d7d48) var x24 uint64 var x25 uint64 x25, x24 = bits.Mul64(x20, 0x3339d80809a1d805) var x26 uint64 var x27 uint64 x27, x26 = bits.Mul64(x20, 0x53bda402fffe5bfe) var x28 uint64 var x29 uint64 x29, x28 = bits.Mul64(x20, 0xffffffff00000001) var x30 uint64 var x31 uint64 x30, x31 = bits.Add64(x29, x26, uint64(0x0)) var x32 uint64 var x33 uint64 x32, x33 = bits.Add64(x27, x24, uint64(x31)) var x34 uint64 var x35 uint64 x34, x35 = bits.Add64(x25, x22, uint64(x33)) x36 := (x35 + x23) var x38 uint64 _, x38 = bits.Add64(x11, x28, uint64(0x0)) var x39 uint64 var x40 uint64 x39, x40 = bits.Add64(x13, x30, uint64(x38)) var x41 uint64 var x42 uint64 x41, x42 = bits.Add64(x15, x32, uint64(x40)) var x43 uint64 var x44 uint64 x43, x44 = bits.Add64(x17, x34, uint64(x42)) var x45 uint64 var x46 uint64 x45, x46 = bits.Add64(x19, x36, uint64(x44)) var x47 uint64 var x48 uint64 x48, x47 = bits.Mul64(x1, arg2[3]) var x49 uint64 var x50 uint64 x50, x49 = bits.Mul64(x1, arg2[2]) var x51 uint64 var x52 uint64 x52, x51 = bits.Mul64(x1, arg2[1]) var x53 uint64 var x54 uint64 x54, x53 = bits.Mul64(x1, arg2[0]) var x55 uint64 var x56 uint64 x55, x56 = bits.Add64(x54, x51, uint64(0x0)) var x57 uint64 var x58 uint64 x57, x58 = bits.Add64(x52, x49, uint64(x56)) var x59 uint64 var x60 uint64 x59, x60 = bits.Add64(x50, x47, uint64(x58)) x61 := (x60 + x48) var x62 uint64 var x63 uint64 x62, x63 = bits.Add64(x39, x53, uint64(0x0)) var x64 uint64 var x65 uint64 x64, x65 = bits.Add64(x41, x55, uint64(x63)) var x66 uint64 var x67 uint64 x66, x67 = bits.Add64(x43, x57, uint64(x65)) var x68 uint64 var x69 uint64 x68, x69 = bits.Add64(x45, x59, uint64(x67)) var x70 uint64 var x71 uint64 x70, x71 = bits.Add64(x46, x61, uint64(x69)) var x72 uint64 _, x72 = bits.Mul64(x62, 0xfffffffeffffffff) var x74 uint64 var x75 uint64 x75, x74 = bits.Mul64(x72, 0x73eda753299d7d48) var x76 uint64 var x77 uint64 x77, x76 = bits.Mul64(x72, 0x3339d80809a1d805) var x78 uint64 var x79 uint64 x79, x78 = bits.Mul64(x72, 0x53bda402fffe5bfe) var x80 uint64 var x81 uint64 x81, x80 = bits.Mul64(x72, 0xffffffff00000001) var x82 uint64 var x83 uint64 x82, x83 = bits.Add64(x81, x78, uint64(0x0)) var x84 uint64 var x85 uint64 x84, x85 = bits.Add64(x79, x76, uint64(x83)) var x86 uint64 var x87 uint64 x86, x87 = bits.Add64(x77, x74, uint64(x85)) x88 := (x87 + x75) var x90 uint64 _, x90 = bits.Add64(x62, x80, uint64(0x0)) var x91 uint64 var x92 uint64 x91, x92 = bits.Add64(x64, x82, uint64(x90)) var x93 uint64 var x94 uint64 x93, x94 = bits.Add64(x66, x84, uint64(x92)) var x95 uint64 var x96 uint64 x95, x96 = bits.Add64(x68, x86, uint64(x94)) var x97 uint64 var x98 uint64 x97, x98 = bits.Add64(x70, x88, uint64(x96)) x99 := (x98 + x71) var x100 uint64 var x101 uint64 x101, x100 = bits.Mul64(x2, arg2[3]) var x102 uint64 var x103 uint64 x103, x102 = bits.Mul64(x2, arg2[2]) var x104 uint64 var x105 uint64 x105, x104 = bits.Mul64(x2, arg2[1]) var x106 uint64 var x107 uint64 x107, x106 = bits.Mul64(x2, arg2[0]) var x108 uint64 var x109 uint64 x108, x109 = bits.Add64(x107, x104, uint64(0x0)) var x110 uint64 var x111 uint64 x110, x111 = bits.Add64(x105, x102, uint64(x109)) var x112 uint64 var x113 uint64 x112, x113 = bits.Add64(x103, x100, uint64(x111)) x114 := (x113 + x101) var x115 uint64 var x116 uint64 x115, x116 = bits.Add64(x91, x106, uint64(0x0)) var x117 uint64 var x118 uint64 x117, x118 = bits.Add64(x93, x108, uint64(x116)) var x119 uint64 var x120 uint64 x119, x120 = bits.Add64(x95, x110, uint64(x118)) var x121 uint64 var x122 uint64 x121, x122 = bits.Add64(x97, x112, uint64(x120)) var x123 uint64 var x124 uint64 x123, x124 = bits.Add64(x99, x114, uint64(x122)) var x125 uint64 _, x125 = bits.Mul64(x115, 0xfffffffeffffffff) var x127 uint64 var x128 uint64 x128, x127 = bits.Mul64(x125, 0x73eda753299d7d48) var x129 uint64 var x130 uint64 x130, x129 = bits.Mul64(x125, 0x3339d80809a1d805) var x131 uint64 var x132 uint64 x132, x131 = bits.Mul64(x125, 0x53bda402fffe5bfe) var x133 uint64 var x134 uint64 x134, x133 = bits.Mul64(x125, 0xffffffff00000001) var x135 uint64 var x136 uint64 x135, x136 = bits.Add64(x134, x131, uint64(0x0)) var x137 uint64 var x138 uint64 x137, x138 = bits.Add64(x132, x129, uint64(x136)) var x139 uint64 var x140 uint64 x139, x140 = bits.Add64(x130, x127, uint64(x138)) x141 := (x140 + x128) var x143 uint64 _, x143 = bits.Add64(x115, x133, uint64(0x0)) var x144 uint64 var x145 uint64 x144, x145 = bits.Add64(x117, x135, uint64(x143)) var x146 uint64 var x147 uint64 x146, x147 = bits.Add64(x119, x137, uint64(x145)) var x148 uint64 var x149 uint64 x148, x149 = bits.Add64(x121, x139, uint64(x147)) var x150 uint64 var x151 uint64 x150, x151 = bits.Add64(x123, x141, uint64(x149)) x152 := (x151 + x124) var x153 uint64 var x154 uint64 x154, x153 = bits.Mul64(x3, arg2[3]) var x155 uint64 var x156 uint64 x156, x155 = bits.Mul64(x3, arg2[2]) var x157 uint64 var x158 uint64 x158, x157 = bits.Mul64(x3, arg2[1]) var x159 uint64 var x160 uint64 x160, x159 = bits.Mul64(x3, arg2[0]) var x161 uint64 var x162 uint64 x161, x162 = bits.Add64(x160, x157, uint64(0x0)) var x163 uint64 var x164 uint64 x163, x164 = bits.Add64(x158, x155, uint64(x162)) var x165 uint64 var x166 uint64 x165, x166 = bits.Add64(x156, x153, uint64(x164)) x167 := (x166 + x154) var x168 uint64 var x169 uint64 x168, x169 = bits.Add64(x144, x159, uint64(0x0)) var x170 uint64 var x171 uint64 x170, x171 = bits.Add64(x146, x161, uint64(x169)) var x172 uint64 var x173 uint64 x172, x173 = bits.Add64(x148, x163, uint64(x171)) var x174 uint64 var x175 uint64 x174, x175 = bits.Add64(x150, x165, uint64(x173)) var x176 uint64 var x177 uint64 x176, x177 = bits.Add64(x152, x167, uint64(x175)) var x178 uint64 _, x178 = bits.Mul64(x168, 0xfffffffeffffffff) var x180 uint64 var x181 uint64 x181, x180 = bits.Mul64(x178, 0x73eda753299d7d48) var x182 uint64 var x183 uint64 x183, x182 = bits.Mul64(x178, 0x3339d80809a1d805) var x184 uint64 var x185 uint64 x185, x184 = bits.Mul64(x178, 0x53bda402fffe5bfe) var x186 uint64 var x187 uint64 x187, x186 = bits.Mul64(x178, 0xffffffff00000001) var x188 uint64 var x189 uint64 x188, x189 = bits.Add64(x187, x184, uint64(0x0)) var x190 uint64 var x191 uint64 x190, x191 = bits.Add64(x185, x182, uint64(x189)) var x192 uint64 var x193 uint64 x192, x193 = bits.Add64(x183, x180, uint64(x191)) x194 := (x193 + x181) var x196 uint64 _, x196 = bits.Add64(x168, x186, uint64(0x0)) var x197 uint64 var x198 uint64 x197, x198 = bits.Add64(x170, x188, uint64(x196)) var x199 uint64 var x200 uint64 x199, x200 = bits.Add64(x172, x190, uint64(x198)) var x201 uint64 var x202 uint64 x201, x202 = bits.Add64(x174, x192, uint64(x200)) var x203 uint64 var x204 uint64 x203, x204 = bits.Add64(x176, x194, uint64(x202)) x205 := (x204 + x177) var x206 uint64 var x207 uint64 x206, x207 = bits.Sub64(x197, 0xffffffff00000001, uint64(uint64(0x0))) var x208 uint64 var x209 uint64 x208, x209 = bits.Sub64(x199, 0x53bda402fffe5bfe, uint64(x207)) var x210 uint64 var x211 uint64 x210, x211 = bits.Sub64(x201, 0x3339d80809a1d805, uint64(x209)) var x212 uint64 var x213 uint64 x212, x213 = bits.Sub64(x203, 0x73eda753299d7d48, uint64(x211)) var x215 uint64 _, x215 = bits.Sub64(x205, uint64(0x0), uint64(x213)) var x216 uint64 fiatScMontCmovznzU64(&x216, x215, x206, x197) var x217 uint64 fiatScMontCmovznzU64(&x217, x215, x208, x199) var x218 uint64 fiatScMontCmovznzU64(&x218, x215, x210, x201) var x219 uint64 fiatScMontCmovznzU64(&x219, x215, x212, x203) out1[0] = x216 out1[1] = x217 out1[2] = x218 out1[3] = x219 } // The function fiatScMontSquare squares a field element in the Montgomery domain. // // Preconditions: // // 0 ≤ eval arg1 < m // // Postconditions: // // eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m // 0 ≤ eval out1 < m // // Input Bounds: // // arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // // Output Bounds: // // out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] func fiatScMontSquare(out1 *[4]uint64, arg1 *[4]uint64) { x1 := arg1[1] x2 := arg1[2] x3 := arg1[3] x4 := arg1[0] var x5 uint64 var x6 uint64 x6, x5 = bits.Mul64(x4, arg1[3]) var x7 uint64 var x8 uint64 x8, x7 = bits.Mul64(x4, arg1[2]) var x9 uint64 var x10 uint64 x10, x9 = bits.Mul64(x4, arg1[1]) var x11 uint64 var x12 uint64 x12, x11 = bits.Mul64(x4, arg1[0]) var x13 uint64 var x14 uint64 x13, x14 = bits.Add64(x12, x9, uint64(0x0)) var x15 uint64 var x16 uint64 x15, x16 = bits.Add64(x10, x7, uint64(x14)) var x17 uint64 var x18 uint64 x17, x18 = bits.Add64(x8, x5, uint64(x16)) x19 := (x18 + x6) var x20 uint64 _, x20 = bits.Mul64(x11, 0xfffffffeffffffff) var x22 uint64 var x23 uint64 x23, x22 = bits.Mul64(x20, 0x73eda753299d7d48) var x24 uint64 var x25 uint64 x25, x24 = bits.Mul64(x20, 0x3339d80809a1d805) var x26 uint64 var x27 uint64 x27, x26 = bits.Mul64(x20, 0x53bda402fffe5bfe) var x28 uint64 var x29 uint64 x29, x28 = bits.Mul64(x20, 0xffffffff00000001) var x30 uint64 var x31 uint64 x30, x31 = bits.Add64(x29, x26, uint64(0x0)) var x32 uint64 var x33 uint64 x32, x33 = bits.Add64(x27, x24, uint64(x31)) var x34 uint64 var x35 uint64 x34, x35 = bits.Add64(x25, x22, uint64(x33)) x36 := (x35 + x23) var x38 uint64 _, x38 = bits.Add64(x11, x28, uint64(0x0)) var x39 uint64 var x40 uint64 x39, x40 = bits.Add64(x13, x30, uint64(x38)) var x41 uint64 var x42 uint64 x41, x42 = bits.Add64(x15, x32, uint64(x40)) var x43 uint64 var x44 uint64 x43, x44 = bits.Add64(x17, x34, uint64(x42)) var x45 uint64 var x46 uint64 x45, x46 = bits.Add64(x19, x36, uint64(x44)) var x47 uint64 var x48 uint64 x48, x47 = bits.Mul64(x1, arg1[3]) var x49 uint64 var x50 uint64 x50, x49 = bits.Mul64(x1, arg1[2]) var x51 uint64 var x52 uint64 x52, x51 = bits.Mul64(x1, arg1[1]) var x53 uint64 var x54 uint64 x54, x53 = bits.Mul64(x1, arg1[0]) var x55 uint64 var x56 uint64 x55, x56 = bits.Add64(x54, x51, uint64(0x0)) var x57 uint64 var x58 uint64 x57, x58 = bits.Add64(x52, x49, uint64(x56)) var x59 uint64 var x60 uint64 x59, x60 = bits.Add64(x50, x47, uint64(x58)) x61 := (x60 + x48) var x62 uint64 var x63 uint64 x62, x63 = bits.Add64(x39, x53, uint64(0x0)) var x64 uint64 var x65 uint64 x64, x65 = bits.Add64(x41, x55, uint64(x63)) var x66 uint64 var x67 uint64 x66, x67 = bits.Add64(x43, x57, uint64(x65)) var x68 uint64 var x69 uint64 x68, x69 = bits.Add64(x45, x59, uint64(x67)) var x70 uint64 var x71 uint64 x70, x71 = bits.Add64(x46, x61, uint64(x69)) var x72 uint64 _, x72 = bits.Mul64(x62, 0xfffffffeffffffff) var x74 uint64 var x75 uint64 x75, x74 = bits.Mul64(x72, 0x73eda753299d7d48) var x76 uint64 var x77 uint64 x77, x76 = bits.Mul64(x72, 0x3339d80809a1d805) var x78 uint64 var x79 uint64 x79, x78 = bits.Mul64(x72, 0x53bda402fffe5bfe) var x80 uint64 var x81 uint64 x81, x80 = bits.Mul64(x72, 0xffffffff00000001) var x82 uint64 var x83 uint64 x82, x83 = bits.Add64(x81, x78, uint64(0x0)) var x84 uint64 var x85 uint64 x84, x85 = bits.Add64(x79, x76, uint64(x83)) var x86 uint64 var x87 uint64 x86, x87 = bits.Add64(x77, x74, uint64(x85)) x88 := (x87 + x75) var x90 uint64 _, x90 = bits.Add64(x62, x80, uint64(0x0)) var x91 uint64 var x92 uint64 x91, x92 = bits.Add64(x64, x82, uint64(x90)) var x93 uint64 var x94 uint64 x93, x94 = bits.Add64(x66, x84, uint64(x92)) var x95 uint64 var x96 uint64 x95, x96 = bits.Add64(x68, x86, uint64(x94)) var x97 uint64 var x98 uint64 x97, x98 = bits.Add64(x70, x88, uint64(x96)) x99 := (x98 + x71) var x100 uint64 var x101 uint64 x101, x100 = bits.Mul64(x2, arg1[3]) var x102 uint64 var x103 uint64 x103, x102 = bits.Mul64(x2, arg1[2]) var x104 uint64 var x105 uint64 x105, x104 = bits.Mul64(x2, arg1[1]) var x106 uint64 var x107 uint64 x107, x106 = bits.Mul64(x2, arg1[0]) var x108 uint64 var x109 uint64 x108, x109 = bits.Add64(x107, x104, uint64(0x0)) var x110 uint64 var x111 uint64 x110, x111 = bits.Add64(x105, x102, uint64(x109)) var x112 uint64 var x113 uint64 x112, x113 = bits.Add64(x103, x100, uint64(x111)) x114 := (x113 + x101) var x115 uint64 var x116 uint64 x115, x116 = bits.Add64(x91, x106, uint64(0x0)) var x117 uint64 var x118 uint64 x117, x118 = bits.Add64(x93, x108, uint64(x116)) var x119 uint64 var x120 uint64 x119, x120 = bits.Add64(x95, x110, uint64(x118)) var x121 uint64 var x122 uint64 x121, x122 = bits.Add64(x97, x112, uint64(x120)) var x123 uint64 var x124 uint64 x123, x124 = bits.Add64(x99, x114, uint64(x122)) var x125 uint64 _, x125 = bits.Mul64(x115, 0xfffffffeffffffff) var x127 uint64 var x128 uint64 x128, x127 = bits.Mul64(x125, 0x73eda753299d7d48) var x129 uint64 var x130 uint64 x130, x129 = bits.Mul64(x125, 0x3339d80809a1d805) var x131 uint64 var x132 uint64 x132, x131 = bits.Mul64(x125, 0x53bda402fffe5bfe) var x133 uint64 var x134 uint64 x134, x133 = bits.Mul64(x125, 0xffffffff00000001) var x135 uint64 var x136 uint64 x135, x136 = bits.Add64(x134, x131, uint64(0x0)) var x137 uint64 var x138 uint64 x137, x138 = bits.Add64(x132, x129, uint64(x136)) var x139 uint64 var x140 uint64 x139, x140 = bits.Add64(x130, x127, uint64(x138)) x141 := (x140 + x128) var x143 uint64 _, x143 = bits.Add64(x115, x133, uint64(0x0)) var x144 uint64 var x145 uint64 x144, x145 = bits.Add64(x117, x135, uint64(x143)) var x146 uint64 var x147 uint64 x146, x147 = bits.Add64(x119, x137, uint64(x145)) var x148 uint64 var x149 uint64 x148, x149 = bits.Add64(x121, x139, uint64(x147)) var x150 uint64 var x151 uint64 x150, x151 = bits.Add64(x123, x141, uint64(x149)) x152 := (x151 + x124) var x153 uint64 var x154 uint64 x154, x153 = bits.Mul64(x3, arg1[3]) var x155 uint64 var x156 uint64 x156, x155 = bits.Mul64(x3, arg1[2]) var x157 uint64 var x158 uint64 x158, x157 = bits.Mul64(x3, arg1[1]) var x159 uint64 var x160 uint64 x160, x159 = bits.Mul64(x3, arg1[0]) var x161 uint64 var x162 uint64 x161, x162 = bits.Add64(x160, x157, uint64(0x0)) var x163 uint64 var x164 uint64 x163, x164 = bits.Add64(x158, x155, uint64(x162)) var x165 uint64 var x166 uint64 x165, x166 = bits.Add64(x156, x153, uint64(x164)) x167 := (x166 + x154) var x168 uint64 var x169 uint64 x168, x169 = bits.Add64(x144, x159, uint64(0x0)) var x170 uint64 var x171 uint64 x170, x171 = bits.Add64(x146, x161, uint64(x169)) var x172 uint64 var x173 uint64 x172, x173 = bits.Add64(x148, x163, uint64(x171)) var x174 uint64 var x175 uint64 x174, x175 = bits.Add64(x150, x165, uint64(x173)) var x176 uint64 var x177 uint64 x176, x177 = bits.Add64(x152, x167, uint64(x175)) var x178 uint64 _, x178 = bits.Mul64(x168, 0xfffffffeffffffff) var x180 uint64 var x181 uint64 x181, x180 = bits.Mul64(x178, 0x73eda753299d7d48) var x182 uint64 var x183 uint64 x183, x182 = bits.Mul64(x178, 0x3339d80809a1d805) var x184 uint64 var x185 uint64 x185, x184 = bits.Mul64(x178, 0x53bda402fffe5bfe) var x186 uint64 var x187 uint64 x187, x186 = bits.Mul64(x178, 0xffffffff00000001) var x188 uint64 var x189 uint64 x188, x189 = bits.Add64(x187, x184, uint64(0x0)) var x190 uint64 var x191 uint64 x190, x191 = bits.Add64(x185, x182, uint64(x189)) var x192 uint64 var x193 uint64 x192, x193 = bits.Add64(x183, x180, uint64(x191)) x194 := (x193 + x181) var x196 uint64 _, x196 = bits.Add64(x168, x186, uint64(0x0)) var x197 uint64 var x198 uint64 x197, x198 = bits.Add64(x170, x188, uint64(x196)) var x199 uint64 var x200 uint64 x199, x200 = bits.Add64(x172, x190, uint64(x198)) var x201 uint64 var x202 uint64 x201, x202 = bits.Add64(x174, x192, uint64(x200)) var x203 uint64 var x204 uint64 x203, x204 = bits.Add64(x176, x194, uint64(x202)) x205 := (x204 + x177) var x206 uint64 var x207 uint64 x206, x207 = bits.Sub64(x197, 0xffffffff00000001, uint64(uint64(0x0))) var x208 uint64 var x209 uint64 x208, x209 = bits.Sub64(x199, 0x53bda402fffe5bfe, uint64(x207)) var x210 uint64 var x211 uint64 x210, x211 = bits.Sub64(x201, 0x3339d80809a1d805, uint64(x209)) var x212 uint64 var x213 uint64 x212, x213 = bits.Sub64(x203, 0x73eda753299d7d48, uint64(x211)) var x215 uint64 _, x215 = bits.Sub64(x205, uint64(0x0), uint64(x213)) var x216 uint64 fiatScMontCmovznzU64(&x216, x215, x206, x197) var x217 uint64 fiatScMontCmovznzU64(&x217, x215, x208, x199) var x218 uint64 fiatScMontCmovznzU64(&x218, x215, x210, x201) var x219 uint64 fiatScMontCmovznzU64(&x219, x215, x212, x203) out1[0] = x216 out1[1] = x217 out1[2] = x218 out1[3] = x219 } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/scalar.go000066400000000000000000000102751454601126700235740ustar00rootroot00000000000000package ff import ( "io" "github.com/cloudflare/circl/internal/conv" ) // ScalarSize is the length in bytes of a Scalar. const ScalarSize = 32 // scMont represents an element in the Montgomery domain (little-endian). type scMont = [ScalarSize / 8]uint64 // scRaw represents a scalar in the integers domain (little-endian). type scRaw = [ScalarSize / 8]uint64 // Scalar represents positive integers less than ScalarOrder. type Scalar struct{ i scMont } func (z Scalar) String() string { x := z.fromMont(); return conv.Uint64Le2Hex(x[:]) } func (z *Scalar) Set(x *Scalar) { z.i = x.i } func (z *Scalar) SetUint64(n uint64) { z.toMont(&scRaw{n}) } func (z *Scalar) SetOne() { z.SetUint64(1) } func (z *Scalar) Random(r io.Reader) error { return randomInt(z.i[:], r, scOrder[:]) } func (z Scalar) IsZero() int { return ctUint64Eq(z.i[:], (&scMont{})[:]) } func (z Scalar) IsEqual(x *Scalar) int { return ctUint64Eq(z.i[:], x.i[:]) } func (z *Scalar) Neg() { fiatScMontSub(&z.i, &scMont{}, &z.i) } func (z *Scalar) Add(x, y *Scalar) { fiatScMontAdd(&z.i, &x.i, &y.i) } func (z *Scalar) Sub(x, y *Scalar) { fiatScMontSub(&z.i, &x.i, &y.i) } func (z *Scalar) Mul(x, y *Scalar) { fiatScMontMul(&z.i, &x.i, &y.i) } func (z *Scalar) Sqr(x *Scalar) { fiatScMontSquare(&z.i, &x.i) } func (z *Scalar) Inv(x *Scalar) { z.expVarTime(x, scOrderMinus2[:]) } func (z *Scalar) toMont(in *scRaw) { fiatScMontMul(&z.i, in, &scRSquare) } func (z Scalar) fromMont() (out scRaw) { fiatScMontMul(&out, &z.i, &scMont{1}); return } // ScalarOrder is the order of the scalar field of the pairing groups, order is // returned as a big-endian slice. // // ScalarOrder = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 func ScalarOrder() []byte { o := scOrder; return o[:] } // exp calculates z=x^n, where n is in big-endian order. func (z *Scalar) expVarTime(x *Scalar, n []byte) { zz := new(Scalar) zz.SetOne() N := 8 * len(n) for i := 0; i < N; i++ { zz.Sqr(zz) bit := 0x1 & (n[i/8] >> uint(7-i%8)) if bit != 0 { zz.Mul(zz, x) } } z.Set(zz) } // SetBytes assigns to z the number modulo ScalarOrder stored in the slice // (in big-endian order). func (z *Scalar) SetBytes(data []byte) { in64 := setBytesUnbounded(data, scOrder[:]) s := &scRaw{} copy(s[:], in64[:ScalarSize/8]) z.toMont(s) } // MarshalBinary returns a slice of ScalarSize bytes that contains the minimal // residue of z such that 0 <= z < ScalarOrder (in big-endian order). func (z *Scalar) MarshalBinary() ([]byte, error) { x := z.fromMont() return conv.Uint64Le2BytesBe(x[:]), nil } // UnmarshalBinary reconstructs a Scalar from a slice that must have at least // ScalarSize bytes and contain a number (in big-endian order) from 0 // to ScalarOrder-1. func (z *Scalar) UnmarshalBinary(data []byte) error { if len(data) < ScalarSize { return errInputLength } in64, err := setBytesBounded(data[:ScalarSize], scOrder[:]) if err == nil { s := &scRaw{} copy(s[:], in64[:ScalarSize/8]) z.toMont(s) } return err } // SetString reconstructs a Fp from a numeric string from 0 to ScalarOrder-1. func (z *Scalar) SetString(s string) error { in64, err := setString(s, scOrder[:]) if err == nil { s := &scRaw{} copy(s[:], in64[:ScalarSize/8]) z.toMont(s) } return err } func fiatScMontCmovznzU64(z *uint64, b, x, y uint64) { cselectU64(z, b, x, y) } var ( // scOrder is the order of the Scalar field (big-endian). scOrder = [ScalarSize]byte{ 0x73, 0xed, 0xa7, 0x53, 0x29, 0x9d, 0x7d, 0x48, 0x33, 0x39, 0xd8, 0x08, 0x09, 0xa1, 0xd8, 0x05, 0x53, 0xbd, 0xa4, 0x02, 0xff, 0xfe, 0x5b, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, } // scOrderMinus2 is the scOrder minus two used for inversion (big-endian). scOrderMinus2 = [ScalarSize]byte{ 0x73, 0xed, 0xa7, 0x53, 0x29, 0x9d, 0x7d, 0x48, 0x33, 0x39, 0xd8, 0x08, 0x09, 0xa1, 0xd8, 0x05, 0x53, 0xbd, 0xa4, 0x02, 0xff, 0xfe, 0x5b, 0xfe, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, } // scRSquare is R^2 mod scOrder, where R=2^256 (little-endian). scRSquare = scMont{ 0xc999e990f3f29c6d, 0x2b6cedcb87925c23, 0x05d314967254398f, 0x0748d9d99f59ff11, } ) golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/scalar_test.go000066400000000000000000000054001454601126700246250ustar00rootroot00000000000000package ff_test import ( "bytes" "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/ecc/bls12381/ff" "github.com/cloudflare/circl/internal/test" ) func randomScalar(t testing.TB) *ff.Scalar { t.Helper() s := new(ff.Scalar) err := s.Random(rand.Reader) if err != nil { t.Error(err) } return s } func TestScalar(t *testing.T) { const testTimes = 1 << 10 t.Run("marshal", func(t *testing.T) { for i := 0; i < testTimes; i++ { var y ff.Scalar x := randomScalar(t) bytes, err := x.MarshalBinary() if err != nil { test.ReportError(t, x, y, x) } err = y.UnmarshalBinary(bytes) if err != nil { test.ReportError(t, x, y, x) } if x.IsEqual(&y) == 0 { test.ReportError(t, x, y, x) } } }) t.Run("no_alias", func(t *testing.T) { var want, got ff.Scalar x := randomScalar(t) got.Set(x) got.Sqr(&got) want.Set(x) want.Mul(&want, &want) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } }) t.Run("mul_inv", func(t *testing.T) { var z ff.Scalar for i := 0; i < testTimes; i++ { x := randomScalar(t) y := randomScalar(t) // x*y*x^1 - y = 0 z.Inv(x) z.Mul(&z, y) z.Mul(&z, x) z.Sub(&z, y) got := z.IsZero() want := 1 if got != want { test.ReportError(t, got, want, x, y) } } }) t.Run("mul_sqr", func(t *testing.T) { var l0, l1, r0, r1 ff.Scalar for i := 0; i < testTimes; i++ { x := randomScalar(t) y := randomScalar(t) // (x+y)(x-y) = (x^2-y^2) l0.Add(x, y) l1.Sub(x, y) l0.Mul(&l0, &l1) r0.Sqr(x) r1.Sqr(y) r0.Sub(&r0, &r1) got := &l0 want := &r0 if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("bytes", func(t *testing.T) { var data [100]byte _, _ = rand.Read(data[:]) var a, b ff.Scalar var bigA, bigOrder big.Int bigOrder.SetBytes(ff.ScalarOrder()) for i := 0; i < 100; i++ { a.SetBytes(data[:i]) bigA.SetBytes(data[:i]) bigA.Mod(&bigA, &bigOrder) bytesA := bigA.Bytes() b.SetBytes(bytesA) if a.IsEqual(&b) == 0 { test.ReportError(t, a, b) } got, err := a.MarshalBinary() test.CheckNoErr(t, err, "MarshalBinary failed") want, err := b.MarshalBinary() test.CheckNoErr(t, err, "MarshalBinary failed") if !bytes.Equal(got, want) { test.ReportError(t, got, want) } } }) } func BenchmarkScalar(b *testing.B) { x := randomScalar(b) y := randomScalar(b) z := randomScalar(b) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Add(x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sqr(x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Inv(x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/uroot.go000066400000000000000000000021201454601126700234650ustar00rootroot00000000000000package ff // URootSize is the length in bytes of a root of unit. const URootSize = Fp12Size // URoot represents an n-th root of unit, that is an element x in Cyclo6 such // that x^n=1, where n = ScalarOrder(). type URoot Cyclo6 func (z URoot) String() string { return (Cyclo6)(z).String() } func (z *URoot) UnmarshalBinary(b []byte) error { return (*Fp12)(z).UnmarshalBinary(b) } func (z URoot) MarshalBinary() ([]byte, error) { return (Fp12)(z).MarshalBinary() } func (z *URoot) SetIdentity() { (*Fp12)(z).SetOne() } func (z URoot) IsEqual(x *URoot) int { return (Cyclo6)(z).IsEqual((*Cyclo6)(x)) } func (z URoot) IsIdentity() int { i := &URoot{}; i.SetIdentity(); return z.IsEqual(i) } func (z *URoot) Exp(x *URoot, n []byte) { (*Cyclo6)(z).exp((*Cyclo6)(x), n) } func (z *URoot) Mul(x, y *URoot) { (*Cyclo6)(z).Mul((*Cyclo6)(x), (*Cyclo6)(y)) } func (z *URoot) Sqr(x *URoot) { (*Cyclo6)(z).Sqr((*Cyclo6)(x)) } func (z *URoot) Inv(x *URoot) { (*Cyclo6)(z).Inv((*Cyclo6)(x)) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/ff/uroot_test.go000066400000000000000000000032301454601126700245270ustar00rootroot00000000000000package ff import ( "testing" "github.com/cloudflare/circl/internal/test" ) func randomURoot(t testing.TB) *URoot { u := &URoot{} HardExponentiation(u, randomCyclo6(t)) return u } func TestURoot(t *testing.T) { const testTimes = 1 << 8 t.Run("no_alias", func(t *testing.T) { var want, got URoot x := randomURoot(t) got = *x got.Sqr(&got) want = *x want.Mul(&want, &want) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } }) t.Run("order", func(t *testing.T) { order := ScalarOrder() var z URoot for i := 0; i < 16; i++ { x := randomURoot(t) (*Cyclo6)(&z).exp((*Cyclo6)(x), order) // x^order = 1 got := z.IsIdentity() want := 1 if got != want { test.ReportError(t, got, want, x, z) } } }) t.Run("mul_inv", func(t *testing.T) { var z URoot for i := 0; i < testTimes; i++ { x := randomURoot(t) y := randomURoot(t) // x*y*x^1 = y z.Inv(x) z.Mul(&z, y) z.Mul(&z, x) got := z want := y if got.IsEqual(want) == 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("mul_sqr", func(t *testing.T) { var want, got URoot for i := 0; i < testTimes; i++ { x := randomURoot(t) // x*x = x^2 got.Mul(x, x) want.Sqr(x) if got.IsEqual(&want) == 0 { test.ReportError(t, got, want, x) } } }) } func BenchmarkURoot(b *testing.B) { x := randomURoot(b) y := randomURoot(b) z := randomURoot(b) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sqr(x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Inv(x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/g1.go000066400000000000000000000263761454601126700222540ustar00rootroot00000000000000package bls12381 import ( "crypto" _ "crypto/sha256" "crypto/subtle" "fmt" "math/big" "github.com/cloudflare/circl/ecc/bls12381/ff" "github.com/cloudflare/circl/expander" ) // G1Size is the length in bytes of an element in G1 in uncompressed form.. const G1Size = 2 * ff.FpSize // G1SizeCompressed is the length in bytes of an element in G1 in compressed form. const G1SizeCompressed = ff.FpSize // G1 is a point in the BLS12 curve over Fp. type G1 struct{ x, y, z ff.Fp } func (g G1) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v", g.x, g.y, g.z) } // Bytes serializes a G1 element in uncompressed form. func (g G1) Bytes() []byte { return g.encodeBytes(false) } // Bytes serializes a G1 element in compressed form. func (g G1) BytesCompressed() []byte { return g.encodeBytes(true) } // SetBytes sets g to the value in bytes, and returns a non-nil error if not in G1. func (g *G1) SetBytes(b []byte) error { if len(b) < G1SizeCompressed { return errInputLength } isCompressed := int((b[0] >> 7) & 0x1) isInfinity := int((b[0] >> 6) & 0x1) isBigYCoord := int((b[0] >> 5) & 0x1) if isInfinity == 1 { l := G1Size if isCompressed == 1 { l = G1SizeCompressed } zeros := make([]byte, l-1) if (b[0]&0x1F) != 0 || subtle.ConstantTimeCompare(b[1:], zeros) != 1 { return errEncoding } g.SetIdentity() return nil } x := (&[ff.FpSize]byte{})[:] copy(x, b) x[0] &= 0x1F if err := g.x.UnmarshalBinary(x); err != nil { return err } if isCompressed == 1 { x3b := &ff.Fp{} x3b.Sqr(&g.x) x3b.Mul(x3b, &g.x) x3b.Add(x3b, &g1Params.b) if g.y.Sqrt(x3b) == 0 { return errEncoding } if g.y.IsNegative() != isBigYCoord { g.y.Neg() } } else { if len(b) < G1Size { return errInputLength } if err := g.y.UnmarshalBinary(b[ff.FpSize:G1Size]); err != nil { return err } } g.z.SetOne() if !g.IsOnG1() { return errEncoding } return nil } func (g G1) encodeBytes(compressed bool) []byte { g.toAffine() var isCompressed, isInfinity, isBigYCoord byte if compressed { isCompressed = 1 } if g.z.IsZero() == 1 { isInfinity = 1 } if isCompressed == 1 && isInfinity == 0 { isBigYCoord = byte(g.y.IsNegative()) } bytes, _ := g.x.MarshalBinary() if isCompressed == 0 { yBytes, _ := g.y.MarshalBinary() bytes = append(bytes, yBytes...) } if isInfinity == 1 { l := len(bytes) for i := 0; i < l; i++ { bytes[i] = 0 } } bytes[0] = bytes[0]&0x1F | headerEncoding(isCompressed, isInfinity, isBigYCoord) return bytes } // Neg inverts g. func (g *G1) Neg() { g.y.Neg() } // SetIdentity assigns g to the identity element. func (g *G1) SetIdentity() { g.x = ff.Fp{}; g.y.SetOne(); g.z = ff.Fp{} } // isValidProjective returns true if the point is not a projective point. func (g *G1) isValidProjective() bool { return (g.x.IsZero() & g.y.IsZero() & g.z.IsZero()) != 1 } // IsOnG1 returns true if the point is in the group G1. func (g *G1) IsOnG1() bool { return g.isValidProjective() && g.isOnCurve() && g.isRTorsion() } // IsIdentity return true if the point is the identity of G1. func (g *G1) IsIdentity() bool { return g.isValidProjective() && (g.z.IsZero() == 1) } // cmov sets g to P if b == 1 func (g *G1) cmov(P *G1, b int) { (&g.x).CMov(&g.x, &P.x, b) (&g.y).CMov(&g.y, &P.y, b) (&g.z).CMov(&g.z, &P.z, b) } // sigma is an edomorphism defined by (x, y) → (βx, y) for some β ∈ Fp of // multiplicative order 3. func (g *G1) sigma(P *G1) { *g = *P; g.x.Mul(&g.x, &g1Sigma.beta0) } // sigma2 is sigma(sigma(P)). func (g *G1) sigma2(P *G1) { *g = *P; g.x.Mul(&g.x, &g1Sigma.beta1) } // isRTorsion returns true if point is in the r-torsion subgroup. func (g *G1) isRTorsion() bool { // Bowe, "Faster Subgroup Checks for BLS12-381" (https://eprint.iacr.org/2019/814) Q, _2sP, ssP := &G1{}, &G1{}, &G1{} coef := bls12381.g1Check[:] _2sP.sigma(g) // s(P) _2sP.Double() // 2*s(P) ssP.sigma2(g) // s(s(P)) Q.Add(g, ssP) // P + s(s(P)) Q.Neg() // -P - s(s(P)) Q.Add(Q, _2sP) // 2*s(P) - P - s(s(P)) Q.scalarMultShort(coef, Q) // coef * [2*s(P) - P - s(s(P))] ssP.Neg() // -s(s(P)) Q.Add(Q, ssP) // coef * [2*s(P) - P - s(s(P))] - s(s(P)) return Q.IsIdentity() } // clearCofactor maps g to a point in the r-torsion subgroup. // // This method multiplies g times (1-z) rather than (z-1)^2/3, where z is the // BLS12 parameter. This is enough to remove points of order // // h \in {3, 11, 10177, 859267, 52437899}, // // and because there are no points of order h^2. See Section 5 of Wahby-Boneh // "Fast and simple constant-time hashing to the BLS12-381 elliptic curve" at // https://eprint.iacr.org/2019/403 func (g *G1) clearCofactor() { g.scalarMultShort(bls12381.oneMinusZ[:], g) } // Double updates g = 2g. func (g *G1) Double() { // Reference: // "Complete addition formulas for prime order elliptic curves" by // Costello-Renes-Batina. [Alg.9] (eprint.iacr.org/2015/1060). var R G1 X, Y, Z := &g.x, &g.y, &g.z X3, Y3, Z3 := &R.x, &R.y, &R.z var f0, f1, f2 ff.Fp t0, t1, t2 := &f0, &f1, &f2 _3B := &g1Params._3b t0.Sqr(Y) // 1. t0 = Y * Y Z3.Add(t0, t0) // 2. Z3 = t0 + t0 Z3.Add(Z3, Z3) // 3. Z3 = Z3 + Z3 Z3.Add(Z3, Z3) // 4. Z3 = Z3 + Z3 t1.Mul(Y, Z) // 5. t1 = Y * Z t2.Sqr(Z) // 6. t2 = Z * Z t2.Mul(_3B, t2) // 7. t2 = b3 * t2 X3.Mul(t2, Z3) // 8. X3 = t2 * Z3 Y3.Add(t0, t2) // 9. Y3 = t0 + t2 Z3.Mul(t1, Z3) // 10. Z3 = t1 * Z3 t1.Add(t2, t2) // 11. t1 = t2 + t2 t2.Add(t1, t2) // 12. t2 = t1 + t2 t0.Sub(t0, t2) // 13. t0 = t0 - t2 Y3.Mul(t0, Y3) // 14. Y3 = t0 * Y3 Y3.Add(X3, Y3) // 15. Y3 = X3 + Y3 t1.Mul(X, Y) // 16. t1 = X * Y X3.Mul(t0, t1) // 17. X3 = t0 * t1 X3.Add(X3, X3) // 18. X3 = X3 + X3 *g = R } // Add updates g=P+Q. func (g *G1) Add(P, Q *G1) { // Reference: // "Complete addition formulas for prime order elliptic curves" by // Costello-Renes-Batina. [Alg.7] (eprint.iacr.org/2015/1060). var R G1 X1, Y1, Z1 := &P.x, &P.y, &P.z X2, Y2, Z2 := &Q.x, &Q.y, &Q.z X3, Y3, Z3 := &R.x, &R.y, &R.z _3B := &g1Params._3b var f0, f1, f2, f3, f4 ff.Fp t0, t1, t2, t3, t4 := &f0, &f1, &f2, &f3, &f4 t0.Mul(X1, X2) // 1. t0 = X1 * X2 t1.Mul(Y1, Y2) // 2. t1 = Y1 * Y2 t2.Mul(Z1, Z2) // 3. t2 = Z1 * Z2 t3.Add(X1, Y1) // 4. t3 = X1 + Y1 t4.Add(X2, Y2) // 5. t4 = X2 + Y2 t3.Mul(t3, t4) // 6. t3 = t3 * t4 t4.Add(t0, t1) // 7. t4 = t0 + t1 t3.Sub(t3, t4) // 8. t3 = t3 - t4 t4.Add(Y1, Z1) // 9. t4 = Y1 + Z1 X3.Add(Y2, Z2) // 10. X3 = Y2 + Z2 t4.Mul(t4, X3) // 11. t4 = t4 * X3 X3.Add(t1, t2) // 12. X3 = t1 + t2 t4.Sub(t4, X3) // 13. t4 = t4 - X3 X3.Add(X1, Z1) // 14. X3 = X1 + Z1 Y3.Add(X2, Z2) // 15. Y3 = X2 + Z2 X3.Mul(X3, Y3) // 16. X3 = X3 * Y3 Y3.Add(t0, t2) // 17. Y3 = t0 + t2 Y3.Sub(X3, Y3) // 18. Y3 = X3 - Y3 X3.Add(t0, t0) // 19. X3 = t0 + t0 t0.Add(X3, t0) // 20. t0 = X3 + t0 t2.Mul(_3B, t2) // 21. t2 = b3 * t2 Z3.Add(t1, t2) // 22. Z3 = t1 + t2 t1.Sub(t1, t2) // 23. t1 = t1 - t2 Y3.Mul(_3B, Y3) // 24. Y3 = b3 * Y3 X3.Mul(t4, Y3) // 25. X3 = t4 * Y3 t2.Mul(t3, t1) // 26. t2 = t3 * t1 X3.Sub(t2, X3) // 27. X3 = t2 - X3 Y3.Mul(Y3, t0) // 28. Y3 = Y3 * t0 t1.Mul(t1, Z3) // 29. t1 = t1 * Z3 Y3.Add(t1, Y3) // 30. Y3 = t1 + Y3 t0.Mul(t0, t3) // 31. t0 = t0 * t3 Z3.Mul(Z3, t4) // 32. Z3 = Z3 * t4 Z3.Add(Z3, t0) // 33. Z3 = Z3 + t0 *g = R } // ScalarMult calculates g = kP. func (g *G1) ScalarMult(k *Scalar, P *G1) { b, _ := k.MarshalBinary(); g.scalarMult(b, P) } // scalarMult calculates g = kP, where k is the scalar in big-endian order. func (g *G1) scalarMult(k []byte, P *G1) { var Q G1 Q.SetIdentity() T := &G1{} var mults [16]G1 mults[0].SetIdentity() mults[1] = *P for i := 1; i < 8; i++ { mults[2*i] = mults[i] mults[2*i].Double() mults[2*i+1].Add(&mults[2*i], P) } N := 8 * len(k) for i := 0; i < N; i += 4 { Q.Double() Q.Double() Q.Double() Q.Double() idx := 0xf & (k[i/8] >> uint(4-i%8)) for j := 0; j < 16; j++ { T.cmov(&mults[j], subtle.ConstantTimeByteEq(idx, uint8(j))) } Q.Add(&Q, T) } *g = Q } // scalarMultShort multiplies by a short, constant scalar k, where k is the // scalar in big-endian order. Runtime depends on the scalar. func (g *G1) scalarMultShort(k []byte, P *G1) { // Since the scalar is short and low Hamming weight not much helps. var Q G1 Q.SetIdentity() N := 8 * len(k) for i := 0; i < N; i++ { Q.Double() bit := 0x1 & (k[i/8] >> uint(7-i%8)) if bit != 0 { Q.Add(&Q, P) } } *g = Q } // IsEqual returns true if g and p are equivalent. func (g *G1) IsEqual(p *G1) bool { var lx, rx, ly, ry ff.Fp lx.Mul(&g.x, &p.z) // lx = x1*z2 rx.Mul(&p.x, &g.z) // rx = x2*z1 lx.Sub(&lx, &rx) // lx = lx-rx ly.Mul(&g.y, &p.z) // ly = y1*z2 ry.Mul(&p.y, &g.z) // ry = y2*z1 ly.Sub(&ly, &ry) // ly = ly-ry return g.isValidProjective() && p.isValidProjective() && lx.IsZero() == 1 && ly.IsZero() == 1 } // isOnCurve returns true if g is a valid point on the curve. func (g *G1) isOnCurve() bool { var x3, z3, y2 ff.Fp y2.Sqr(&g.y) // y2 = y^2 y2.Mul(&y2, &g.z) // y2 = y^2*z x3.Sqr(&g.x) // x3 = x^2 x3.Mul(&x3, &g.x) // x3 = x^3 z3.Sqr(&g.z) // z3 = z^2 z3.Mul(&z3, &g.z) // z3 = z^3 z3.Mul(&z3, &g1Params.b) // z3 = 4*z^3 x3.Add(&x3, &z3) // x3 = x^3 + 4*z^3 y2.Sub(&y2, &x3) // y2 = y^2*z - (x^3 + 4*z^3) return y2.IsZero() == 1 } // toAffine updates g with its affine representation. func (g *G1) toAffine() { if g.z.IsZero() != 1 { var invZ ff.Fp invZ.Inv(&g.z) g.x.Mul(&g.x, &invZ) g.y.Mul(&g.y, &invZ) g.z.SetOne() } } // EncodeToCurve is a non-uniform encoding from an input byte string (and // an optional domain separation tag) to elements in G1. This function must not // be used as a hash function, otherwise use G1.Hash instead. func (g *G1) Encode(input, dst []byte) { const L = 64 pseudo := expander.NewExpanderMD(crypto.SHA256, dst).Expand(input, L) bu := new(big.Int).SetBytes(pseudo) bu.Mod(bu, new(big.Int).SetBytes(ff.FpOrder())) var u ff.Fp u.SetBytes(pseudo[:L]) var q isogG1Point q.sswu(&u) g.evalIsogG1(&q) g.clearCofactor() } // Hash produces an element of G1 from the hash of an input byte string and // an optional domain separation tag. This function is safe to use when a // random oracle returning points in G1 be required. func (g *G1) Hash(input, dst []byte) { const L = 64 pseudo := expander.NewExpanderMD(crypto.SHA256, dst).Expand(input, 2*L) var u0, u1 ff.Fp u0.SetBytes(pseudo[0*L : 1*L]) u1.SetBytes(pseudo[1*L : 2*L]) var q0, q1 isogG1Point q0.sswu(&u0) q1.sswu(&u1) var p0, p1 G1 p0.evalIsogG1(&q0) p1.evalIsogG1(&q1) g.Add(&p0, &p1) g.clearCofactor() } // G1Generator returns the generator point of G1. func G1Generator() *G1 { var G G1 G.x = g1Params.genX G.y = g1Params.genY G.z.SetOne() return &G } // affinize converts an entire slice to affine at once func affinize(points []*G1) { if len(points) == 0 { return } ws := make([]ff.Fp, len(points)+1) ws[0].SetOne() for i := 0; i < len(points); i++ { ws[i+1].Mul(&ws[i], &points[i].z) } w := &ff.Fp{} w.Inv(&ws[len(points)]) zinv := &ff.Fp{} for i := len(points) - 1; i >= 0; i-- { zinv.Mul(w, &ws[i]) w.Mul(w, &points[i].z) points[i].x.Mul(&points[i].x, zinv) points[i].y.Mul(&points[i].y, zinv) points[i].z.SetOne() } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/g1Isog.go000066400000000000000000000111601454601126700230570ustar00rootroot00000000000000package bls12381 import ( "fmt" "github.com/cloudflare/circl/ecc/bls12381/ff" ) type isogG1Point struct{ x, y, z ff.Fp } func (p isogG1Point) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v", p.x, p.y, p.z) } // IsOnCurve returns true if g is a valid point on the curve. func (p *isogG1Point) IsOnCurve() bool { var x2, x3, z2, z3, y2 ff.Fp y2.Sqr(&p.y) // y2 = y^2 y2.Mul(&y2, &p.z) // y2 = y^2*z z2.Sqr(&p.z) // z2 = z^2 z3.Mul(&z2, &p.z) // z3 = z^3 z3.Mul(&z3, &g1Isog11.b) // z3 = B*z^3 x2.Sqr(&p.x) // x2 = x^2 x3.Mul(&z2, &g1Isog11.a) // x3 = A*z^2 x3.Add(&x3, &x2) // x3 = x^2 + A*z^2 x3.Mul(&x3, &p.x) // x3 = x^3 + A*x*z^2 x3.Add(&x3, &z3) // x3 = x^3 + A*x*z^2 + Bz^3 return y2.IsEqual(&x3) == 1 && *p != isogG1Point{} } // sswu implements the Simplified Shallue-van de Woestijne-Ulas method for // mapping a field element to a point on the isogenous curve. func (p *isogG1Point) sswu(u *ff.Fp) { // Method in Appendix-G.2.1 of // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11 tv1, tv2, tv3, tv4 := &ff.Fp{}, &ff.Fp{}, &ff.Fp{}, &ff.Fp{} xd, x1n, gxd, gx1 := &ff.Fp{}, &ff.Fp{}, &ff.Fp{}, &ff.Fp{} y, y1, x2n, y2, xn := &ff.Fp{}, &ff.Fp{}, &ff.Fp{}, &ff.Fp{}, &ff.Fp{} tv1.Sqr(u) // 1. tv1 = u^2 tv3.Mul(&g1sswu.Z, tv1) // 2. tv3 = Z * tv1 tv2.Sqr(tv3) // 3. tv2 = tv3^2 xd.Add(tv2, tv3) // 4. xd = tv2 + tv3 tv4.SetOne() // 5. tv4 = 1 x1n.Add(xd, tv4) // x1n = xd + tv4 x1n.Mul(x1n, &g1Isog11.b) // 6. x1n = x1n * B xd.Mul(&g1Isog11.a, xd) // 7. xd = A * xd xd.Neg() // xd = -xd e1 := xd.IsZero() // 8. e1 = xd == 0 tv4.Mul(&g1sswu.Z, &g1Isog11.a) // 9. tv4 = Z * A xd.CMov(xd, tv4, e1) // xd = CMOV(xd, tv4, e1) tv2.Sqr(xd) // 10. tv2 = xd^2 gxd.Mul(tv2, xd) // 11. gxd = tv2 * xd tv2.Mul(&g1Isog11.a, tv2) // 12. tv2 = A * tv2 gx1.Sqr(x1n) // 13. gx1 = x1n^2 gx1.Add(gx1, tv2) // 14. gx1 = gx1 + tv2 gx1.Mul(gx1, x1n) // 15. gx1 = gx1 * x1n tv2.Mul(&g1Isog11.b, gxd) // 16. tv2 = B * gxd gx1.Add(gx1, tv2) // 17. gx1 = gx1 + tv2 tv4.Sqr(gxd) // 18. tv4 = gxd^2 tv2.Mul(gx1, gxd) // 19. tv2 = gx1 * gxd tv4.Mul(tv4, tv2) // 20. tv4 = tv4 * tv2 y1.ExpVarTime(tv4, g1sswu.c1[:]) // 21. y1 = tv4^c1 y1.Mul(y1, tv2) // 22. y1 = y1 * tv2 x2n.Mul(tv3, x1n) // 23. x2n = tv3 * x1n y2.Mul(y1, &g1sswu.c2) // 24. y2 = y1 * c2 y2.Mul(y2, tv1) // 25. y2 = y2 * tv1 y2.Mul(y2, u) // 26. y2 = y2 * u tv2.Sqr(y1) // 27. tv2 = y1^2 tv2.Mul(tv2, gxd) // 28. tv2 = tv2 * gxd e2 := tv2.IsEqual(gx1) // 29. e2 = tv2 == gx1 xn.CMov(x2n, x1n, e2) // 30. xn = CMOV(x2n, x1n, e2) y.CMov(y2, y1, e2) // 31. y = CMOV(y2, y1, e2) e3 := u.Sgn0() ^ y.Sgn0() // 32. e3 = sgn0(u) == sgn0(y) *tv1 = *y // 33. tv1 = y tv1.Neg() // tv1 = -y y.CMov(tv1, y, ^e3) // y = CMOV(tv1, y, e3) p.x = *xn // 34. return p.y.Mul(y, xd) // (x,y) = (xn/xd, y/1) p.z = *xd // (X,Y,Z) = (xn, y*xd, xd) } // evalIsogG1 calculates g = g1Isog11(p), where g1Isog11 is an isogeny of // degree 11 to the curve used in G1. func (g *G1) evalIsogG1(p *isogG1Point) { x, y, z := &p.x, &p.y, &p.z t, zi := &ff.Fp{}, &ff.Fp{} xNum, xDen, yNum, yDen := &ff.Fp{}, &ff.Fp{}, &ff.Fp{}, &ff.Fp{} ixn := len(g1Isog11.xNum) - 1 ixd := len(g1Isog11.xDen) - 1 iyn := len(g1Isog11.yNum) - 1 iyd := len(g1Isog11.yDen) - 1 *xNum = g1Isog11.xNum[ixn] *xDen = g1Isog11.xDen[ixd] *yNum = g1Isog11.yNum[iyn] *yDen = g1Isog11.yDen[iyd] *zi = *z for (ixn | ixd | iyn | iyd) != 0 { if ixn > 0 { ixn-- t.Mul(zi, &g1Isog11.xNum[ixn]) xNum.Mul(xNum, x) xNum.Add(xNum, t) } if ixd > 0 { ixd-- t.Mul(zi, &g1Isog11.xDen[ixd]) xDen.Mul(xDen, x) xDen.Add(xDen, t) } if iyn > 0 { iyn-- t.Mul(zi, &g1Isog11.yNum[iyn]) yNum.Mul(yNum, x) yNum.Add(yNum, t) } if iyd > 0 { iyd-- t.Mul(zi, &g1Isog11.yDen[iyd]) yDen.Mul(yDen, x) yDen.Add(yDen, t) } zi.Mul(zi, z) } g.x.Mul(xNum, yDen) g.y.Mul(yNum, xDen) g.y.Mul(&g.y, y) g.z.Mul(xDen, yDen) g.z.Mul(&g.z, z) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/g1_test.go000066400000000000000000000146321454601126700233030ustar00rootroot00000000000000package bls12381 import ( "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/ecc/bls12381/ff" "github.com/cloudflare/circl/internal/test" ) func randomScalar(t testing.TB) *Scalar { s := &Scalar{} err := s.Random(rand.Reader) test.CheckNoErr(t, err, "random scalar") return s } func randomG1(t testing.TB) *G1 { P := &G1{} u := &ff.Fp{} r := &isogG1Point{} err := u.Random(rand.Reader) test.CheckNoErr(t, err, "random fp") r.sswu(u) P.evalIsogG1(r) P.clearCofactor() got := P.IsOnG1() want := true if got != want { test.ReportError(t, got, want, "point not in G1", u) } return P } func TestG1Add(t *testing.T) { const testTimes = 1 << 6 var Q, R G1 for i := 0; i < testTimes; i++ { P := randomG1(t) Q = *P R = *P R.Add(&R, &R) R.Neg() Q.Double() Q.Neg() got := R want := Q if !got.IsEqual(&want) { test.ReportError(t, got, want, P) } } } func TestG1ScalarMult(t *testing.T) { const testTimes = 1 << 6 var Q G1 for i := 0; i < testTimes; i++ { P := randomG1(t) k := randomScalar(t) Q.ScalarMult(k, P) Q.toAffine() got := Q.IsOnG1() want := true if got != want { test.ReportError(t, got, want, P, k) } } } func TestG1Hash(t *testing.T) { const testTimes = 1 << 8 for _, e := range [...]struct { Name string Enc func(p *G1, input, dst []byte) }{ {"Encode", func(p *G1, input, dst []byte) { p.Encode(input, dst) }}, {"Hash", func(p *G1, input, dst []byte) { p.Hash(input, dst) }}, } { var msg, dst [4]byte var p G1 t.Run(e.Name, func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(msg[:]) _, _ = rand.Read(dst[:]) e.Enc(&p, msg[:], dst[:]) got := p.isRTorsion() want := true if got != want { test.ReportError(t, got, want, e.Name, msg, dst) } } }) } } func BenchmarkG1(b *testing.B) { P := randomG1(b) Q := randomG1(b) k := randomScalar(b) var msg, dst [4]byte _, _ = rand.Read(msg[:]) _, _ = rand.Read(dst[:]) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Add(P, Q) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ScalarMult(k, P) } }) b.Run("Hash", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Hash(msg[:], dst[:]) } }) } func TestG1Serial(t *testing.T) { mustOk := "must be ok" mustErr := "must be an error" t.Run("valid", func(t *testing.T) { testTimes := 1 << 6 var got, want G1 want.SetIdentity() for i := 0; i < testTimes; i++ { for _, b := range [][]byte{want.Bytes(), want.BytesCompressed()} { err := got.SetBytes(b) test.CheckNoErr(t, err, fmt.Sprintf("failure to deserialize: (P:%v b:%x)", want, b)) if !got.IsEqual(&want) { test.ReportError(t, got, want, b) } } want = *randomG1(t) } }) t.Run("badLength", func(t *testing.T) { q := new(G1) p := randomG1(t) b := p.Bytes() test.CheckIsErr(t, q.SetBytes(b[:0]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:1]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:G1Size-1]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:G1SizeCompressed]), mustErr) test.CheckNoErr(t, q.SetBytes(b), mustOk) test.CheckNoErr(t, q.SetBytes(append(b, 0)), mustOk) b = p.BytesCompressed() test.CheckIsErr(t, q.SetBytes(b[:0]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:1]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:G1SizeCompressed-1]), mustErr) test.CheckNoErr(t, q.SetBytes(b), mustOk) test.CheckNoErr(t, q.SetBytes(append(b, 0)), mustOk) }) t.Run("badInfinity", func(t *testing.T) { var badInf, p G1 badInf.SetIdentity() b := badInf.Bytes() b[0] |= 0x1F err := p.SetBytes(b) test.CheckIsErr(t, err, mustErr) b[0] &= 0xE0 b[1] = 0xFF err = p.SetBytes(b) test.CheckIsErr(t, err, mustErr) }) t.Run("badCoords", func(t *testing.T) { bad := (&[ff.FpSize]byte{})[:] for i := range bad { bad[i] = 0xFF } var e ff.Fp _ = e.Random(rand.Reader) good, err := e.MarshalBinary() test.CheckNoErr(t, err, mustOk) // bad x, good y b := append(bad, good...) b[0] = b[0]&0x1F | headerEncoding(0, 0, 0) test.CheckIsErr(t, new(G1).SetBytes(b), mustErr) // good x, bad y b = append(good, bad...) b[0] = b[0]&0x1F | headerEncoding(0, 0, 0) test.CheckIsErr(t, new(G1).SetBytes(b), mustErr) }) t.Run("noQR", func(t *testing.T) { var x ff.Fp x.SetUint64(1) // Let x=1, so x^3+4 = 5, which is not QR. b, err := x.MarshalBinary() test.CheckNoErr(t, err, mustOk) b[0] = b[0]&0x1F | headerEncoding(1, 0, 0) test.CheckIsErr(t, new(G1).SetBytes(b), mustErr) }) t.Run("notInG1", func(t *testing.T) { // p=(0,1) is not on curve. var x, y ff.Fp y.SetUint64(1) bx, err := x.MarshalBinary() test.CheckNoErr(t, err, mustOk) by, err := y.MarshalBinary() test.CheckNoErr(t, err, mustOk) b := append(bx, by...) b[0] = b[0]&0x1F | headerEncoding(0, 0, 0) test.CheckIsErr(t, new(G1).SetBytes(b), mustErr) }) } func TestG1Affinize(t *testing.T) { N := 20 testTimes := 1 << 6 g1 := make([]*G1, N) g2 := make([]*G1, N) for i := 0; i < testTimes; i++ { for j := 0; j < N; j++ { g1[j] = randomG1(t) g2[j] = &G1{} *g2[j] = *g1[j] } affinize(g2) for j := 0; j < N; j++ { g1[j].toAffine() if !g1[j].IsEqual(g2[j]) { t.Fatal("failure to preserve points") } if g2[j].z.IsEqual(&g1[j].z) != 1 { t.Fatal("failure to make affine") } } } } func TestG1Torsion(t *testing.T) { if !G1Generator().isRTorsion() { t.Fatalf("G1 generator is not r-torsion") } } func TestG1Bytes(t *testing.T) { got := new(G1) id := new(G1) id.SetIdentity() g := G1Generator() minusG := G1Generator() minusG.Neg() type testCase struct { header byte length int point *G1 toBytes func(G1) []byte } for i, v := range []testCase{ {headerEncoding(0, 0, 0), G1Size, randomG1(t), (G1).Bytes}, {headerEncoding(0, 0, 0), G1Size, g, (G1).Bytes}, {headerEncoding(1, 0, 0), G1SizeCompressed, g, (G1).BytesCompressed}, {headerEncoding(1, 0, 1), G1SizeCompressed, minusG, (G1).BytesCompressed}, {headerEncoding(0, 1, 0), G1Size, id, (G1).Bytes}, {headerEncoding(1, 1, 0), G1SizeCompressed, id, (G1).BytesCompressed}, } { b := v.toBytes(*v.point) test.CheckOk(len(b) == v.length, fmt.Sprintf("bad encoding size (case:%v point:%v b:%x)", i, v.point, b), t) test.CheckOk(b[0]&0xE0 == v.header, fmt.Sprintf("bad encoding header (case:%v point:%v b:%x)", i, v.point, b), t) err := got.SetBytes(b) want := v.point if err != nil || !got.IsEqual(want) { test.ReportError(t, got, want, i, b) } } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/g2.go000066400000000000000000000211701454601126700222400ustar00rootroot00000000000000package bls12381 import ( "crypto" "crypto/subtle" "fmt" "github.com/cloudflare/circl/ecc/bls12381/ff" "github.com/cloudflare/circl/expander" ) // G2Size is the length in bytes of an element in G2 in uncompressed form.. const G2Size = 2 * ff.Fp2Size // G2SizeCompressed is the length in bytes of an element in G2 in compressed form. const G2SizeCompressed = ff.Fp2Size // G2 is a point in the twist of the BLS12 curve over Fp2. type G2 struct{ x, y, z ff.Fp2 } func (g G2) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v", g.x, g.y, g.z) } // Bytes serializes a G2 element in uncompressed form. func (g G2) Bytes() []byte { return g.encodeBytes(false) } // Bytes serializes a G2 element in compressed form. func (g G2) BytesCompressed() []byte { return g.encodeBytes(true) } // SetBytes sets g to the value in bytes, and returns a non-nil error if not in G2. func (g *G2) SetBytes(b []byte) error { if len(b) < G2SizeCompressed { return errInputLength } isCompressed := int((b[0] >> 7) & 0x1) isInfinity := int((b[0] >> 6) & 0x1) isBigYCoord := int((b[0] >> 5) & 0x1) if isInfinity == 1 { l := G2Size if isCompressed == 1 { l = G2SizeCompressed } zeros := make([]byte, l-1) if (b[0]&0x1F) != 0 || subtle.ConstantTimeCompare(b[1:], zeros) != 1 { return errEncoding } g.SetIdentity() return nil } x := (&[ff.Fp2Size]byte{})[:] copy(x, b) x[0] &= 0x1F if err := g.x.UnmarshalBinary(x); err != nil { return err } if isCompressed == 1 { x3b := &ff.Fp2{} x3b.Sqr(&g.x) x3b.Mul(x3b, &g.x) x3b.Add(x3b, &g2Params.b) if g.y.Sqrt(x3b) == 0 { return errEncoding } if g.y.IsNegative() != isBigYCoord { g.y.Neg() } } else { if len(b) < G2Size { return errInputLength } if err := g.y.UnmarshalBinary(b[ff.Fp2Size:G2Size]); err != nil { return err } } g.z.SetOne() if !g.IsOnG2() { return errEncoding } return nil } func (g G2) encodeBytes(compressed bool) []byte { g.toAffine() var isCompressed, isInfinity, isBigYCoord byte if compressed { isCompressed = 1 } if g.z.IsZero() == 1 { isInfinity = 1 } if isCompressed == 1 && isInfinity == 0 { isBigYCoord = byte(g.y.IsNegative()) } bytes, _ := g.x.MarshalBinary() if isCompressed == 0 { yBytes, _ := g.y.MarshalBinary() bytes = append(bytes, yBytes...) } if isInfinity == 1 { l := len(bytes) for i := 0; i < l; i++ { bytes[i] = 0 } } bytes[0] = bytes[0]&0x1F | headerEncoding(isCompressed, isInfinity, isBigYCoord) return bytes } // Neg inverts g. func (g *G2) Neg() { g.y.Neg() } // SetIdentity assigns g to the identity element. func (g *G2) SetIdentity() { g.x = ff.Fp2{}; g.y.SetOne(); g.z = ff.Fp2{} } // isValidProjective returns true if the point is not a projective point. func (g *G2) isValidProjective() bool { return (g.x.IsZero() & g.y.IsZero() & g.z.IsZero()) != 1 } // IsOnG2 returns true if the point is in the group G2. func (g *G2) IsOnG2() bool { return g.isValidProjective() && g.isOnCurve() && g.isRTorsion() } // IsIdentity return true if the point is the identity of G2. func (g *G2) IsIdentity() bool { return g.isValidProjective() && (g.z.IsZero() == 1) } // cmov sets g to P if b == 1 func (g *G2) cmov(P *G2, b int) { (&g.x).CMov(&g.x, &P.x, b) (&g.y).CMov(&g.y, &P.y, b) (&g.z).CMov(&g.z, &P.z, b) } // isRTorsion returns true if point is in the r-torsion subgroup. func (g *G2) isRTorsion() bool { // Bowe, "Faster Subgroup Checks for BLS12-381" (https://eprint.iacr.org/2019/814) _z := bls12381.minusZ[:] Q := *g Q.psi() // Q = \psi(g) Q.scalarMultShort(_z, &Q) // Q = -[z]\psi(g) Q.Add(&Q, g) // Q = -[z]\psi(g)+g Q.psi() // Q = -[z]\psi^2(g)+\psi(g) Q.psi() // Q = -[z]\psi^3(g)+\psi^2(g) return Q.IsEqual(g) // Equivalent to verification equation in paper } // psi is the Galbraith-Scott endomorphism. See https://eprint.iacr.org/2008/117. func (g *G2) psi() { g.x.Frob(&g.x) g.y.Frob(&g.y) g.z.Frob(&g.z) g.x.Mul(&g2Psi.alpha, &g.x) g.y.Mul(&g2Psi.beta, &g.y) } // clearCofactor maps g to a point in the r-torsion subgroup. // // This method multiplies g times a multiple of the cofactor as proposed by // Fuentes-Knapp-Rodríguez at https://doi.org/10.1007/978-3-642-28496-0_25. // // The explicit formulas for BLS curves are in Section 4.1 of Budroni-Pintore // "Efficient hash maps to G2 on BLS curves" at https://eprint.iacr.org/2017/419 // // h(a)P = [x^2-x-1]P + [x-1]ψ(P) + ψ^2(2P) func (g *G2) clearCofactor() { x := bls12381.minusZ[:] xP, psiP := &G2{}, &G2{} _2P := *g _2P.Double() // 2P _2P.psi() // ψ(2P) _2P.psi() // ψ^2(2P) xP.scalarMultShort(x, g) // -xP xP.Add(xP, g) // -xP + P = [-x+1]P *psiP = *xP // psiP.psi() // ψ(-xP + P) = [-x+1]ψ(P) xP.scalarMultShort(x, xP) // x^2P - xP = [x^2-x]P g.Add(g, psiP) // P + [-x+1]ψ(P) g.Neg() // -P + [x-1]ψ(P) g.Add(g, xP) // [x^2-x-1]P + [x-1]ψ(P) g.Add(g, &_2P) // [x^2-x-1]P + [x-1]ψ(P) + 2ψ^2(P) } // Double updates g = 2g. func (g *G2) Double() { doubleAndLine(g, nil) } // Add updates g=P+Q. func (g *G2) Add(P, Q *G2) { addAndLine(g, P, Q, nil) } // ScalarMult calculates g = kP. func (g *G2) ScalarMult(k *Scalar, P *G2) { b, _ := k.MarshalBinary(); g.scalarMult(b, P) } // scalarMult calculates g = kP, where k is the scalar in big-endian order. func (g *G2) scalarMult(k []byte, P *G2) { var Q G2 Q.SetIdentity() T := &G2{} var mults [16]G2 mults[0].SetIdentity() mults[1] = *P for i := 1; i < 8; i++ { mults[2*i] = mults[i] mults[2*i].Double() mults[2*i+1].Add(&mults[2*i], P) } N := 8 * len(k) for i := 0; i < N; i += 4 { Q.Double() Q.Double() Q.Double() Q.Double() idx := 0xf & (k[i/8] >> uint(4-i%8)) for j := 0; j < 16; j++ { T.cmov(&mults[j], subtle.ConstantTimeByteEq(idx, uint8(j))) } Q.Add(&Q, T) } *g = Q } // scalarMultShort multiplies by a short, constant scalar k, where k is the // scalar in big-endian order. Runtime depends on the scalar. func (g *G2) scalarMultShort(k []byte, P *G2) { // Since the scalar is short and low Hamming weight not much helps. var Q G2 Q.SetIdentity() N := 8 * len(k) for i := 0; i < N; i++ { Q.Double() bit := 0x1 & (k[i/8] >> uint(7-i%8)) if bit != 0 { Q.Add(&Q, P) } } *g = Q } // IsEqual returns true if g and p are equivalent. func (g *G2) IsEqual(p *G2) bool { var lx, rx, ly, ry ff.Fp2 lx.Mul(&g.x, &p.z) // lx = x1*z2 rx.Mul(&p.x, &g.z) // rx = x2*z1 lx.Sub(&lx, &rx) // lx = lx-rx ly.Mul(&g.y, &p.z) // ly = y1*z2 ry.Mul(&p.y, &g.z) // ry = y2*z1 ly.Sub(&ly, &ry) // ly = ly-ry return lx.IsZero() == 1 && ly.IsZero() == 1 } // EncodeToCurve is a non-uniform encoding from an input byte string (and // an optional domain separation tag) to elements in G2. This function must not // be used as a hash function, otherwise use G2.Hash instead. func (g *G2) Encode(input, dst []byte) { const L = 64 pseudo := expander.NewExpanderMD(crypto.SHA256, dst).Expand(input, 2*L) var u ff.Fp2 u[0].SetBytes(pseudo[0*L : 1*L]) u[1].SetBytes(pseudo[1*L : 2*L]) var q isogG2Point q.sswu(&u) g.evalIsogG2(&q) g.clearCofactor() } // Hash produces an element of G2 from the hash of an input byte string and // an optional domain separation tag. This function is safe to use when a // random oracle returning points in G2 be required. func (g *G2) Hash(input, dst []byte) { const L = 64 pseudo := expander.NewExpanderMD(crypto.SHA256, dst).Expand(input, 4*L) var u0, u1 ff.Fp2 u0[0].SetBytes(pseudo[0*L : 1*L]) u0[1].SetBytes(pseudo[1*L : 2*L]) u1[0].SetBytes(pseudo[2*L : 3*L]) u1[1].SetBytes(pseudo[3*L : 4*L]) var q0, q1 isogG2Point q0.sswu(&u0) q1.sswu(&u1) var p0, p1 G2 p0.evalIsogG2(&q0) p1.evalIsogG2(&q1) g.Add(&p0, &p1) g.clearCofactor() } // isOnCurve returns true if g is a valid point on the curve. func (g *G2) isOnCurve() bool { var x3, z3, y2 ff.Fp2 y2.Sqr(&g.y) // y2 = y^2 y2.Mul(&y2, &g.z) // y2 = y^2*z x3.Sqr(&g.x) // x3 = x^2 x3.Mul(&x3, &g.x) // x3 = x^3 z3.Sqr(&g.z) // z3 = z^2 z3.Mul(&z3, &g.z) // z3 = z^3 z3.Mul(&z3, &g2Params.b) // z3 = (4+4i)*z^3 x3.Add(&x3, &z3) // x3 = x^3 + (4+4i)*z^3 y2.Sub(&y2, &x3) // y2 = y^2*z - (x^3 + (4+4i)*z^3) return y2.IsZero() == 1 } // toAffine updates g with its affine representation. func (g *G2) toAffine() { if g.z.IsZero() != 1 { var invZ ff.Fp2 invZ.Inv(&g.z) g.x.Mul(&g.x, &invZ) g.y.Mul(&g.y, &invZ) g.z.SetOne() } } // G2Generator returns the generator point of G2. func G2Generator() *G2 { var G G2 G.x = g2Params.genX G.y = g2Params.genY G.z.SetOne() return &G } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/g2Isog.go000066400000000000000000000150411454601126700230620ustar00rootroot00000000000000package bls12381 import ( "fmt" "github.com/cloudflare/circl/ecc/bls12381/ff" ) type isogG2Point struct{ x, y, z ff.Fp2 } func (p isogG2Point) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v", p.x, p.y, p.z) } // IsOnCurve returns true if g is a valid point on the curve. func (p *isogG2Point) IsOnCurve() bool { var x2, x3, z2, z3, y2 ff.Fp2 y2.Sqr(&p.y) // y2 = y^2 y2.Mul(&y2, &p.z) // y2 = y^2*z z2.Sqr(&p.z) // z2 = z^2 z3.Mul(&z2, &p.z) // z3 = z^3 z3.Mul(&z3, &g2Isog3.b) // z3 = B*z^3 x2.Sqr(&p.x) // x2 = x^2 x3.Mul(&z2, &g2Isog3.a) // x3 = A*z^2 x3.Add(&x3, &x2) // x3 = x^2 + A*z^2 x3.Mul(&x3, &p.x) // x3 = x^3 + A*x*z^2 x3.Add(&x3, &z3) // x3 = x^3 + A*x*z^2 + Bz^3 return y2.IsEqual(&x3) == 1 && *p != isogG2Point{} } // sswu implements the Simplified Shallue-van de Woestijne-Ulas method for // mapping a field element to a point on the isogenous curve. func (p *isogG2Point) sswu(u *ff.Fp2) { // Method in Appendix-G.2.3 of // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11 tv1, tv2, tv3, tv4 := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{} tv5, xd, x1n, gxd := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{} gx1, y, xn, gx2 := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{} tv1.Sqr(u) // 1. tv1 = u^2 tv3.Mul(&g2sswu.Z, tv1) // 2. tv3 = Z * tv1 tv5.Sqr(tv3) // 3. tv5 = tv3^2 xd.Add(tv5, tv3) // 4. xd = tv5 + tv3 tv2.SetOne() // 5. tv2 = 1 x1n.Add(xd, tv2) // x1n = xd + tv2 x1n.Mul(x1n, &g2Isog3.b) // 6. x1n = x1n * B xd.Mul(&g2Isog3.a, xd) // 7. xd = A * xd xd.Neg() // xd = -xd e1 := xd.IsZero() // 8. e1 = xd == 0 tv2.Mul(&g2sswu.Z, &g2Isog3.a) // 9. tv2 = Z * A xd.CMov(xd, tv2, e1) // xd = CMOV(xd, tv2, e1) tv2.Sqr(xd) // 10. tv2 = xd^2 gxd.Mul(tv2, xd) // 11. gxd = tv2 * xd tv2.Mul(&g2Isog3.a, tv2) // 12. tv2 = A * tv2 gx1.Sqr(x1n) // 13. gx1 = x1n^2 gx1.Add(gx1, tv2) // 14. gx1 = gx1 + tv2 gx1.Mul(gx1, x1n) // 15. gx1 = gx1 * x1n tv2.Mul(&g2Isog3.b, gxd) // 16. tv2 = B * gxd gx1.Add(gx1, tv2) // 17. gx1 = gx1 + tv2 tv4.Sqr(gxd) // 18. tv4 = gxd^2 tv2.Mul(tv4, gxd) // 19. tv2 = tv4 * gxd tv4.Sqr(tv4) // 20. tv4 = tv4^2 tv2.Mul(tv2, tv4) // 21. tv2 = tv2 * tv4 tv2.Mul(tv2, gx1) // 22. tv2 = tv2 * gx1 tv4.Sqr(tv4) // 23. tv4 = tv4^2 tv4.Mul(tv2, tv4) // 24. tv4 = tv2 * tv4 y.ExpVarTime(tv4, g2sswu.c1[:]) // 25. y = tv4^c1 y.Mul(y, tv2) // 26. y = y * tv2 tv4.Mul(y, &g2sswu.c2) // 27. tv4 = y * c2 tv2.Sqr(tv4) // 28. tv2 = tv4^2 tv2.Mul(tv2, gxd) // 29. tv2 = tv2 * gxd e2 := tv2.IsEqual(gx1) // 30. e2 = tv2 == gx1 y.CMov(y, tv4, e2) // 31. y = CMOV(y, tv4, e2) tv4.Mul(y, &g2sswu.c3) // 32. tv4 = y * c3 tv2.Sqr(tv4) // 33. tv2 = tv4^2 tv2.Mul(tv2, gxd) // 34. tv2 = tv2 * gxd e3 := tv2.IsEqual(gx1) // 35. e3 = tv2 == gx1 y.CMov(y, tv4, e3) // 36. y = CMOV(y, tv4, e3) tv4.Mul(tv4, &g2sswu.c2) // 37. tv4 = tv4 * c2 tv2.Sqr(tv4) // 38. tv2 = tv4^2 tv2.Mul(tv2, gxd) // 39. tv2 = tv2 * gxd e4 := tv2.IsEqual(gx1) // 40. e4 = tv2 == gx1 y.CMov(y, tv4, e4) // 41. y = CMOV(y, tv4, e4) gx2.Mul(gx1, tv5) // 42. gx2 = gx1 * tv5 gx2.Mul(gx2, tv3) // 43. gx2 = gx2 * tv3 tv5.Mul(y, tv1) // 44. tv5 = y * tv1 tv5.Mul(tv5, u) // 45. tv5 = tv5 * u tv1.Mul(tv5, &g2sswu.c4) // 46. tv1 = tv5 * c4 tv4.Mul(tv1, &g2sswu.c2) // 47. tv4 = tv1 * c2 tv2.Sqr(tv4) // 48. tv2 = tv4^2 tv2.Mul(tv2, gxd) // 49. tv2 = tv2 * gxd e5 := tv2.IsEqual(gx2) // 50. e5 = tv2 == gx2 tv1.CMov(tv1, tv4, e5) // 51. tv1 = CMOV(tv1, tv4, e5) tv4.Mul(tv5, &g2sswu.c5) // 52. tv4 = tv5 * c5 tv2.Sqr(tv4) // 53. tv2 = tv4^2 tv2.Mul(tv2, gxd) // 54. tv2 = tv2 * gxd e6 := tv2.IsEqual(gx2) // 55. e6 = tv2 == gx2 tv1.CMov(tv1, tv4, e6) // 56. tv1 = CMOV(tv1, tv4, e6) tv4.Mul(tv4, &g2sswu.c2) // 57. tv4 = tv4 * c2 tv2.Sqr(tv4) // 58. tv2 = tv4^2 tv2.Mul(tv2, gxd) // 59. tv2 = tv2 * gxd e7 := tv2.IsEqual(gx2) // 60. e7 = tv2 == gx2 tv1.CMov(tv1, tv4, e7) // 61. tv1 = CMOV(tv1, tv4, e7) tv2.Sqr(y) // 62. tv2 = y^2 tv2.Mul(tv2, gxd) // 63. tv2 = tv2 * gxd e8 := tv2.IsEqual(gx1) // 64. e8 = tv2 == gx1 y.CMov(tv1, y, e8) // 65. y = CMOV(tv1, y, e8) tv2.Mul(tv3, x1n) // 66. tv2 = tv3 * x1n xn.CMov(tv2, x1n, e8) // 67. xn = CMOV(tv2, x1n, e8) e9 := 1 ^ u.Sgn0() ^ y.Sgn0() // 68. e9 = sgn0(u) == sgn0(y) *tv1 = *y // 69. tv1 = y tv1.Neg() // tv1 = -y y.CMov(tv1, y, e9) // y = CMOV(tv1, y, e9) p.x = *xn // 70. return p.y.Mul(y, xd) // (x,y) = (xn/xd, y/1) p.z = *xd // (X,Y,Z) = (xn, y*xd, xd) } // evalIsogG2 calculates g = g2Isog3(p), where g2Isog3 is an isogeny of // degree 3 to the curve used in G2. func (g *G2) evalIsogG2(p *isogG2Point) { x, y, z := &p.x, &p.y, &p.z t, zi := &ff.Fp2{}, &ff.Fp2{} xNum, xDen, yNum, yDen := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{} ixn := len(g2Isog3.xNum) - 1 ixd := len(g2Isog3.xDen) - 1 iyn := len(g2Isog3.yNum) - 1 iyd := len(g2Isog3.yDen) - 1 *xNum = g2Isog3.xNum[ixn] *xDen = g2Isog3.xDen[ixd] *yNum = g2Isog3.yNum[iyn] *yDen = g2Isog3.yDen[iyd] *zi = *z for (ixn | ixd | iyn | iyd) != 0 { if ixn > 0 { ixn-- t.Mul(zi, &g2Isog3.xNum[ixn]) xNum.Mul(xNum, x) xNum.Add(xNum, t) } if ixd > 0 { ixd-- t.Mul(zi, &g2Isog3.xDen[ixd]) xDen.Mul(xDen, x) xDen.Add(xDen, t) } if iyn > 0 { iyn-- t.Mul(zi, &g2Isog3.yNum[iyn]) yNum.Mul(yNum, x) yNum.Add(yNum, t) } if iyd > 0 { iyd-- t.Mul(zi, &g2Isog3.yDen[iyd]) yDen.Mul(yDen, x) yDen.Add(yDen, t) } zi.Mul(zi, z) } g.x.Mul(xNum, yDen) g.y.Mul(yNum, xDen) g.y.Mul(&g.y, y) g.z.Mul(xDen, yDen) g.z.Mul(&g.z, z) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/g2_test.go000066400000000000000000000133371454601126700233050ustar00rootroot00000000000000package bls12381 import ( "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/ecc/bls12381/ff" "github.com/cloudflare/circl/internal/test" ) func randomG2(t testing.TB) *G2 { var P G2 k := randomScalar(t) P.ScalarMult(k, G2Generator()) if !P.isOnCurve() { t.Helper() t.Fatal("not on curve") } return &P } func TestG2Add(t *testing.T) { const testTimes = 1 << 6 var Q, R G2 for i := 0; i < testTimes; i++ { P := randomG2(t) Q = *P R = *P R.Add(&R, &R) R.Neg() Q.Double() Q.Neg() got := R want := Q if !got.IsEqual(&want) { test.ReportError(t, got, want, P) } } } func TestG2ScalarMult(t *testing.T) { const testTimes = 1 << 6 var Q G2 for i := 0; i < testTimes; i++ { P := randomG2(t) k := randomScalar(t) Q.ScalarMult(k, P) Q.toAffine() got := Q.IsOnG2() want := true if got != want { test.ReportError(t, got, want, P) } } } func TestG2Hash(t *testing.T) { const testTimes = 1 << 8 for _, e := range [...]struct { Name string Enc func(p *G2, input, dst []byte) }{ {"Encode", func(p *G2, input, dst []byte) { p.Encode(input, dst) }}, {"Hash", func(p *G2, input, dst []byte) { p.Hash(input, dst) }}, } { var msg, dst [4]byte var p G2 t.Run(e.Name, func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(msg[:]) _, _ = rand.Read(dst[:]) e.Enc(&p, msg[:], dst[:]) got := p.isRTorsion() want := true if got != want { test.ReportError(t, got, want, e.Name, msg, dst) } } }) } } func TestG2Serial(t *testing.T) { mustOk := "must be ok" mustErr := "must be an error" t.Run("valid", func(t *testing.T) { testTimes := 1 << 6 var got, want G2 want.SetIdentity() for i := 0; i < testTimes; i++ { for _, b := range [][]byte{want.Bytes(), want.BytesCompressed()} { err := got.SetBytes(b) test.CheckNoErr(t, err, fmt.Sprintf("failure to deserialize: (P:%v b:%x)", want, b)) if !got.IsEqual(&want) { test.ReportError(t, got, want, b) } } want = *randomG2(t) } }) t.Run("badLength", func(t *testing.T) { q := new(G2) p := randomG2(t) b := p.Bytes() test.CheckIsErr(t, q.SetBytes(b[:0]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:1]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:G2Size-1]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:G2SizeCompressed]), mustErr) test.CheckNoErr(t, q.SetBytes(b), mustOk) test.CheckNoErr(t, q.SetBytes(append(b, 0)), mustOk) b = p.BytesCompressed() test.CheckIsErr(t, q.SetBytes(b[:0]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:1]), mustErr) test.CheckIsErr(t, q.SetBytes(b[:G2SizeCompressed-1]), mustErr) test.CheckNoErr(t, q.SetBytes(b), mustOk) test.CheckNoErr(t, q.SetBytes(append(b, 0)), mustOk) }) t.Run("badInfinity", func(t *testing.T) { var badInf, p G2 badInf.SetIdentity() b := badInf.Bytes() b[0] |= 0x1F err := p.SetBytes(b) test.CheckIsErr(t, err, mustErr) b[0] &= 0xE0 b[1] = 0xFF err = p.SetBytes(b) test.CheckIsErr(t, err, mustErr) }) t.Run("badCoords", func(t *testing.T) { bad := (&[ff.Fp2Size]byte{})[:] for i := range bad { bad[i] = 0xFF } var e ff.Fp2 _ = e[0].Random(rand.Reader) _ = e[1].Random(rand.Reader) good, err := e.MarshalBinary() test.CheckNoErr(t, err, mustOk) // bad x, good y b := append(bad, good...) b[0] = b[0]&0x1F | headerEncoding(0, 0, 0) test.CheckIsErr(t, new(G2).SetBytes(b), mustErr) // good x, bad y b = append(good, bad...) b[0] = b[0]&0x1F | headerEncoding(0, 0, 0) test.CheckIsErr(t, new(G2).SetBytes(b), mustErr) }) t.Run("noQR", func(t *testing.T) { var x ff.Fp2 // Let x=0, so x^3+4*(u+1) = 4*(u+1), which is not QR because (u+1) is not. b, err := x.MarshalBinary() test.CheckNoErr(t, err, mustOk) b[0] = b[0]&0x1F | headerEncoding(1, 0, 0) test.CheckIsErr(t, new(G2).SetBytes(b), mustErr) }) t.Run("notInG2", func(t *testing.T) { // p=(0,1) is not on curve. var x, y ff.Fp2 y[0].SetUint64(1) bx, err := x.MarshalBinary() test.CheckNoErr(t, err, mustOk) by, err := y.MarshalBinary() test.CheckNoErr(t, err, mustOk) b := append(bx, by...) b[0] = b[0]&0x1F | headerEncoding(0, 0, 0) test.CheckIsErr(t, new(G2).SetBytes(b), mustErr) }) } func BenchmarkG2(b *testing.B) { P := randomG2(b) Q := randomG2(b) k := randomScalar(b) var msg, dst [4]byte _, _ = rand.Read(msg[:]) _, _ = rand.Read(dst[:]) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Add(P, Q) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ScalarMult(k, P) } }) b.Run("Hash", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Hash(msg[:], dst[:]) } }) } func TestG2Torsion(t *testing.T) { if !G2Generator().isRTorsion() { t.Fatalf("G2 generator is not r-torsion") } } func TestG2Bytes(t *testing.T) { got := new(G2) id := new(G2) id.SetIdentity() g := G2Generator() minusG := G2Generator() minusG.Neg() type testCase struct { header byte length int point *G2 toBytes func(G2) []byte } for i, v := range []testCase{ {headerEncoding(0, 0, 0), G2Size, randomG2(t), (G2).Bytes}, {headerEncoding(0, 0, 0), G2Size, g, (G2).Bytes}, {headerEncoding(1, 0, 0), G2SizeCompressed, g, (G2).BytesCompressed}, {headerEncoding(1, 0, 1), G2SizeCompressed, minusG, (G2).BytesCompressed}, {headerEncoding(0, 1, 0), G2Size, id, (G2).Bytes}, {headerEncoding(1, 1, 0), G2SizeCompressed, id, (G2).BytesCompressed}, } { b := v.toBytes(*v.point) test.CheckOk(len(b) == v.length, fmt.Sprintf("bad encoding size (case:%v point:%v b:%x)", i, v.point, b), t) test.CheckOk(b[0]&0xE0 == v.header, fmt.Sprintf("bad encoding header (case:%v point:%v b:%x)", i, v.point, b), t) err := got.SetBytes(b) want := v.point if err != nil || !got.IsEqual(want) { test.ReportError(t, got, want, i, b) } } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/gt.go000066400000000000000000000020711454601126700223410ustar00rootroot00000000000000package bls12381 import "github.com/cloudflare/circl/ecc/bls12381/ff" // GtSize is the length in bytes of an element in Gt. const GtSize = ff.URootSize // Gt represents an element of the output (multiplicative) group of a pairing. type Gt struct{ i ff.URoot } func (z Gt) String() string { return z.i.String() } func (z *Gt) UnmarshalBinary(b []byte) error { return z.i.UnmarshalBinary(b) } func (z Gt) MarshalBinary() ([]byte, error) { return z.i.MarshalBinary() } func (z *Gt) SetIdentity() { z.i.SetIdentity() } func (z Gt) IsEqual(x *Gt) bool { return z.i.IsEqual(&x.i) == 1 } func (z Gt) IsIdentity() bool { i := &Gt{}; i.SetIdentity(); return z.IsEqual(i) } func (z *Gt) Mul(x, y *Gt) { z.i.Mul(&x.i, &y.i) } func (z *Gt) Sqr(x *Gt) { z.i.Sqr(&x.i) } func (z *Gt) Inv(x *Gt) { z.i.Inv(&x.i) } // Exp calculates z=x^n, where n is the exponent in big-endian order. func (z *Gt) Exp(x *Gt, n *Scalar) { b, _ := n.MarshalBinary(); z.i.Exp(&x.i, b) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/gt_test.go000066400000000000000000000007331454601126700234030ustar00rootroot00000000000000package bls12381 import ( "crypto/rand" "testing" ) func BenchmarkGt(b *testing.B) { sc := &Scalar{} err := sc.Random(rand.Reader) if err != nil { b.Fatal(err) } g1 := G1Generator() g2 := G2Generator() e1 := Pair(g1, g2) g1.ScalarMult(sc, g1) e2 := Pair(g1, g2) e3 := &Gt{} b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { e3.Mul(e1, e2) } }) b.Run("Exp", func(b *testing.B) { for i := 0; i < b.N; i++ { e3.Exp(e1, sc) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/hash_test.go000066400000000000000000000060671454601126700237220ustar00rootroot00000000000000package bls12381 import ( "encoding/hex" "encoding/json" "io" "os" "path/filepath" "strings" "testing" "github.com/cloudflare/circl/ecc/bls12381/ff" "github.com/cloudflare/circl/internal/test" ) type vectorHash struct { SuiteID string `json:"ciphersuite"` CurveName string `json:"curve"` DST string `json:"dst"` IsRandomOracle bool `json:"randomOracle"` Vectors []struct { P point `json:"P"` Msg string `json:"msg"` } `json:"vectors"` Field struct { M string `json:"m"` P string `json:"p"` } `json:"field"` } type elm string func (e elm) toBytes(t *testing.T) (out []byte) { var buf [ff.FpSize]byte for _, s := range strings.Split(string(e), ",") { x, err := hex.DecodeString(s[2:]) if err != nil { t.Fatal(err) } copy(buf[ff.FpSize-len(x):ff.FpSize], x) out = append(append([]byte{}, buf[:]...), out...) } return } type point struct { X elm `json:"x"` Y elm `json:"y"` } func (p point) toBytes(t *testing.T) []byte { return append(p.X.toBytes(t), p.Y.toBytes(t)...) } type hasher interface { Encode(_, _ []byte) Hash(_, _ []byte) SetBytes([]byte) error IsEqualTo(_ hasher) bool IsRTorsion() bool } type g1Hasher struct{ *G1 } func (g g1Hasher) IsEqualTo(x hasher) bool { return g.IsEqual(x.(g1Hasher).G1) } func (g g1Hasher) IsRTorsion() bool { return g.IsOnG1() } type g2Hasher struct{ *G2 } func (g g2Hasher) IsEqualTo(x hasher) bool { return g.IsEqual(x.(g2Hasher).G2) } func (g g2Hasher) IsRTorsion() bool { return g.IsOnG2() } func (v *vectorHash) test(t *testing.T) { var got, want hasher if v.Field.M == "0x1" { got, want = g1Hasher{new(G1)}, g1Hasher{new(G1)} } else if v.Field.M == "0x2" { got, want = g2Hasher{new(G2)}, g2Hasher{new(G2)} } dst := []byte(v.DST) doHash := got.Encode if v.IsRandomOracle { doHash = got.Hash } for i, vi := range v.Vectors { input := []byte(vi.Msg) doHash(input, dst) err := want.SetBytes(vi.P.toBytes(t)) test.CheckNoErr(t, err, "bad deserialization") if !got.IsEqualTo(want) || !got.IsRTorsion() { test.ReportError(t, got, want, v.SuiteID, i) } } } func readFile(t *testing.T, fileName string) *vectorHash { jsonFile, err := os.Open(fileName) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", fileName, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) } v := new(vectorHash) err = json.Unmarshal(input, v) if err != nil { t.Fatalf("File %v can not be parsed. Error: %v", fileName, err) } return v } func TestHashVectors(t *testing.T) { // Test vectors from draft-irtf-cfrg-hash-to-curve: // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11 // // JSON files can be found at: // https://github.com/cfrg/draft-irtf-cfrg-hash-to-curve/tree/draft-irtf-cfrg-hash-to-curve-10/poc/vectors fileNames, err := filepath.Glob("./testdata/BLS12381*.json") if err != nil { t.Fatal(err) } for _, fileName := range fileNames { v := readFile(t, fileName) t.Run(v.SuiteID, v.test) } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/pair.go000066400000000000000000000050641454601126700226670ustar00rootroot00000000000000package bls12381 import "github.com/cloudflare/circl/ecc/bls12381/ff" // Pair calculates the ate-pairing of P and Q. func Pair(P *G1, Q *G2) *Gt { P.toAffine() mi := &ff.Fp12{} miller(mi, P, Q) e := &Gt{} finalExp(e, mi) return e } func miller(f *ff.Fp12, P *G1, Q *G2) { g := &ff.LineValue{} acc := &ff.Fp12Cubic{} acc.SetOne() T := &G2{} *T = *Q l := &line{} const lenX = 64 for i := lenX - 2; i >= 0; i-- { acc.Sqr(acc) doubleAndLine(T, l) evalLine(g, l, P) acc.MulLine(acc, g) // paramX is -2 ^ 63 - 2 ^ 62 - 2 ^ 60 - 2 ^ 57 - 2 ^ 48 - 2 ^ 16 if (i == 62) || (i == 60) || (i == 57) || (i == 48) || (i == 16) { addAndLine(T, T, Q, l) evalLine(g, l, P) acc.MulLine(acc, g) } } f.FromFp12Alt(acc) f.Cjg() // inverts f as paramX is negative. } // line contains the coefficients of a sparse element of Fp12. // Evaluating the line on P' = (xP',yP') results in // // f = evalLine(P') = l[0]*xP' + l[1]*yP' + l[2] \in Fp12. type line [3]ff.Fp2 // evalLine updates f = f * line(P'), where f lives in Fp12 = Fp6[w]/(w^2-v) // and P' is the image of P on the twist curve. func evalLine(f *ff.LineValue, l *line, P *G1) { // Send P \in E to the twist // E --> E' // (xP,yP) |-> (xP*w^2,yP*w^3) = (xP',yP') // // f = line(P') = l[0]*xP' + l[1]*yP' + l[2] \in Fp12. // = l[0]*xP*w^2 + l[1]*yP*w^3 + l[2] \in Fp12. // First perform the products: l[0]*xP and l[1]*yP \in Fp2. var xP, yP ff.Fp2 xP[0] = P.x yP[0] = P.y f[1].Mul(&l[0], &xP) f[2].Mul(&l[1], &yP) f[0] = l[2] if f.IsZero() == 1 { f.SetOne() } } func finalExp(g *Gt, f *ff.Fp12) { c := &ff.Cyclo6{} ff.EasyExponentiation(c, f) ff.HardExponentiation(&g.i, c) } // ProdPair calculates the product of pairings, i.e., \Prod_i pair(Pi,Qi)^ni. func ProdPair(P []*G1, Q []*G2, n []*Scalar) *Gt { if len(P) != len(Q) || len(P) != len(n) { panic("mismatch length of inputs") } ei := new(ff.Fp12) mi := new(ff.Fp12) out := new(ff.Fp12) out.SetOne() affinize(P) for i := range P { miller(mi, P[i], Q[i]) nb, _ := n[i].MarshalBinary() ei.Exp(mi, nb) out.Mul(out, ei) } e := &Gt{} finalExp(e, out) return e } // ProdPairFrac computes the product e(P, Q)^sign where sign is 1 or -1 func ProdPairFrac(P []*G1, Q []*G2, signs []int) *Gt { if len(P) != len(Q) || len(P) != len(signs) { panic("mismatch length of inputs") } mi := new(ff.Fp12) out := new(ff.Fp12) out.SetOne() affinize(P) for i := range P { g := *P[i] if signs[i] == -1 { g.Neg() } miller(mi, &g, Q[i]) out.Mul(mi, out) } e := &Gt{} finalExp(e, out) return e } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/pair_test.go000066400000000000000000000065731454601126700237340ustar00rootroot00000000000000package bls12381 import ( "fmt" "math/rand" "testing" "github.com/cloudflare/circl/ecc/bls12381/ff" "github.com/cloudflare/circl/internal/test" ) func TestProdPair(t *testing.T) { const testTimes = 1 << 5 const N = 3 listG1 := [N]*G1{} listG2 := [N]*G2{} listSc := [N]*Scalar{} var ePQn, got Gt for i := 0; i < testTimes; i++ { got.SetIdentity() for j := 0; j < N; j++ { listG1[j] = randomG1(t) listG2[j] = randomG2(t) listSc[j] = randomScalar(t) ePQ := Pair(listG1[j], listG2[j]) ePQn.Exp(ePQ, listSc[j]) got.Mul(&got, &ePQn) } want := ProdPair(listG1[:], listG2[:], listSc[:]) if !got.IsEqual(want) { test.ReportError(t, got, want) } } } func TestProdPairFrac(t *testing.T) { const testTimes = 1 << 5 const N = 5 listG1 := [N]*G1{} listG2 := [N]*G2{} listSc := [N]*Scalar{} listSigns := [N]int{} var ePQn, got Gt for i := 0; i < testTimes; i++ { got.SetIdentity() for j := 0; j < N; j++ { listG1[j] = randomG1(t) listG2[j] = randomG2(t) listSc[j] = &Scalar{} coin := rand.Int31n(2) //nolint switch coin { case 0: listSc[j].SetOne() listSc[j].Neg() listSigns[j] = -1 case 1: listSc[j].SetOne() listSigns[j] = 1 } ePQ := Pair(listG1[j], listG2[j]) ePQn.Exp(ePQ, listSc[j]) got.Mul(&got, &ePQn) } want := ProdPairFrac(listG1[:], listG2[:], listSigns[:]) if !got.IsEqual(want) { test.ReportError(t, got, want) } } } func TestPairBilinear(t *testing.T) { testTimes := 1 << 5 for i := 0; i < testTimes; i++ { g1 := G1Generator() g2 := G2Generator() a := randomScalar(t) b := randomScalar(t) ab := &Scalar{} ab.Mul(a, b) p := &G1{} q := &G2{} p.ScalarMult(a, g1) q.ScalarMult(b, g2) lhs := Pair(p, q) tmp := Pair(g1, g2) rhs := &Gt{} rhs.Exp(tmp, ab) if !lhs.IsEqual(rhs) { test.ReportError(t, lhs, rhs) } } } func TestPairIdentity(t *testing.T) { g1id := &G1{} g2id := &G2{} g1 := G1Generator() g2 := G2Generator() g1id.SetIdentity() g2id.SetIdentity() one := &Gt{} one.SetIdentity() ans := Pair(g1id, g2) if !ans.IsEqual(one) { test.ReportError(t, ans, one) } ans = Pair(g1, g2id) if !ans.IsEqual(one) { test.ReportError(t, ans, one) } } func BenchmarkMiller(b *testing.B) { g1 := G1Generator() g2 := G2Generator() mi := new(ff.Fp12) b.ResetTimer() for i := 0; i < b.N; i++ { miller(mi, g1, g2) } } func BenchmarkFinalExpo(b *testing.B) { g1 := G1Generator() g2 := G2Generator() mi := new(ff.Fp12) miller(mi, g1, g2) c := &ff.Cyclo6{} u := &ff.URoot{} g := &Gt{} ff.EasyExponentiation(c, mi) b.Run("EasyExp", func(b *testing.B) { for i := 0; i < b.N; i++ { ff.EasyExponentiation(c, mi) } }) b.Run("HardExp", func(b *testing.B) { for i := 0; i < b.N; i++ { ff.HardExponentiation(u, c) } }) b.Run("FinalExp", func(b *testing.B) { for i := 0; i < b.N; i++ { finalExp(g, mi) } }) } func BenchmarkPair(b *testing.B) { g1 := G1Generator() g2 := G2Generator() const N = 3 listG1 := [N]*G1{} listG2 := [N]*G2{} listExp := [N]*Scalar{} for i := 0; i < N; i++ { listG1[i] = new(G1) *listG1[i] = *g1 listG2[i] = new(G2) *listG2[i] = *g2 listExp[i] = randomScalar(b) } b.Run("Pair", func(b *testing.B) { for i := 0; i < b.N; i++ { Pair(g1, g2) } }) b.Run(fmt.Sprintf("ProdPair%v", N), func(b *testing.B) { for i := 0; i < b.N; i++ { ProdPair(listG1[:], listG2[:], listExp[:]) } }) } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/psi_test.go000066400000000000000000000042311454601126700235610ustar00rootroot00000000000000package bls12381 import ( "testing" "github.com/cloudflare/circl/ecc/bls12381/ff" ) func checkE(t *testing.T, x *ff.Fp12, y *ff.Fp12) { four := &ff.Fp12{} four[0][0][0].SetUint64(4) xcube := &ff.Fp12{} xcube.Mul(x, x) xcube.Mul(xcube, x) ysq := &ff.Fp12{} ysq.Mul(y, y) check := &ff.Fp12{} check.Add(xcube, four) if check.IsEqual(ysq) != 1 { t.Log("failure of isogeny to E to verify") t.Fail() } } func checkEprime(t *testing.T, x *ff.Fp12, y *ff.Fp12) { four := &ff.Fp12{} four[0][0][0].SetUint64(4) ysq := &ff.Fp12{} xcube := &ff.Fp12{} uplusOne := &ff.Fp12{} uplusOne[0][0][1].SetOne() uplusOne[0][0][0].SetOne() b := &ff.Fp12{} b.Mul(uplusOne, four) check := &ff.Fp12{} ysq.Mul(y, y) xcube.Mul(x, x) xcube.Mul(x, xcube) check.Add(xcube, b) if check.IsEqual(ysq) != 1 { t.Log("failure to return to original curve") t.Fail() } } func TestPsi(t *testing.T) { xp12 := &ff.Fp12{} yp12 := &ff.Fp12{} Q := &G2{} P := randomG2(t) *Q = *P P.toAffine() Q.psi() Q.toAffine() w := &ff.Fp12{} w[1].SetOne() wsq := &ff.Fp12{} wsq.Sqr(w) wcube := &ff.Fp12{} wcube.Mul(wsq, w) wsqInv := &ff.Fp12{} wsqInv.Inv(wsq) wcubInv := &ff.Fp12{} wcubInv.Inv(wcube) uplusOne := &ff.Fp12{} uplusOne[0][0][1].SetOne() uplusOne[0][0][0].SetOne() wsix := &ff.Fp12{} wsix.Mul(wcube, wcube) if wsix.IsEqual(uplusOne) != 1 { t.Log("w^6 is not u+1") t.Fail() } xp12[0][0] = P.x yp12[0][0] = P.y // E' is yp^2=xp^3+4(u+1) t.Log("testing input") checkEprime(t, xp12, yp12) // let x12 = xp/w^2 // let y12 = yp/w^3 // Then y12^2=x12^3+4 x12 := &ff.Fp12{} y12 := &ff.Fp12{} x12.Mul(xp12, wsqInv) y12.Mul(yp12, wcubInv) t.Log("testing intermediate") checkE(t, x12, y12) // Do Frobenius x12.Frob(x12) y12.Frob(y12) t.Log("testing post frobenius") checkE(t, x12, y12) // And return to original x12.Mul(x12, wsq) y12.Mul(y12, wcube) // Now we should have y^2=x^3+4(u+1) checkEprime(t, x12, y12) qx12 := &ff.Fp12{} qx12[0][0] = Q.x qy12 := &ff.Fp12{} qy12[0][0] = Q.y if x12.IsEqual(qx12) != 1 { t.Log("failure in evaluation of x") t.Fail() } if y12.IsEqual(qy12) != 1 { t.Log("failure in evaluation of y") t.Fail() } } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/testdata/000077500000000000000000000000001454601126700232115ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ecc/bls12381/testdata/BLS12381G1_XMD-SHA-256_SSWU_NU_.json000066400000000000000000000105161454601126700303730ustar00rootroot00000000000000{ "L": "0x40", "Z": "0xb", "ciphersuite": "BLS12381G1_XMD:SHA-256_SSWU_NU_", "curve": "BLS12-381 G1", "dst": "QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_NU_", "expand": "XMD", "field": { "m": "0x1", "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab" }, "hash": "sha256", "k": "0x80", "map": { "name": "SSWU" }, "randomOracle": false, "vectors": [ { "P": { "x": "0x184bb665c37ff561a89ec2122dd343f20e0f4cbcaec84e3c3052ea81d1834e192c426074b02ed3dca4e7676ce4ce48ba", "y": "0x04407b8d35af4dacc809927071fc0405218f1401a6d15af775810e4e460064bcc9468beeba82fdc751be70476c888bf3" }, "Q": { "x": 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"a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "u": [ "0x0dd824886d2123a96447f6c56e3a3fa992fbfefdba17b6673f9f630ff19e4d326529db37e1c1be43f905bf9202e0278d" ] } ] } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/testdata/BLS12381G1_XMD-SHA-256_SSWU_RO_.json000066400000000000000000000141441454601126700303720ustar00rootroot00000000000000{ "L": "0x40", "Z": "0xb", "ciphersuite": "BLS12381G1_XMD:SHA-256_SSWU_RO_", "curve": "BLS12-381 G1", "dst": "QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_RO_", "expand": "XMD", "field": { "m": "0x1", "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab" }, "hash": "sha256", "k": "0x80", "map": { "name": "SSWU" }, "randomOracle": true, "vectors": [ { "P": { "x": "0x052926add2207b76ca4fa57a8734416c8dc95e24501772c814278700eed6d1e4e8cf62d9c09db0fac349612b759e79a1", "y": "0x08ba738453bfed09cb546dbb0783dbb3a5f1f566ed67bb6be0e8c67e2e81a4cc68ee29813bb7994998f3eae0c9c6a265" }, "Q0": { "x": "0x11a3cce7e1d90975990066b2f2643b9540fa40d6137780df4e753a8054d07580db3b7f1f03396333d4a359d1fe3766fe", "y": "0x0eeaf6d794e479e270da10fdaf768db4c96b650a74518fc67b04b03927754bac66f3ac720404f339ecdcc028afa091b7" }, "Q1": { "x": "0x160003aaf1632b13396dbad518effa00fff532f604de1a7fc2082ff4cb0afa2d63b2c32da1bef2bf6c5ca62dc6b72f9c", "y": "0x0d8bb2d14e20cf9f6036152ed386d79189415b6d015a20133acb4e019139b94e9c146aaad5817f866c95d609a361735e" }, "msg": "", "u": [ "0x0ba14bd907ad64a016293ee7c2d276b8eae71f25a4b941eece7b0d89f17f75cb3ae5438a614fb61d6835ad59f29c564f", "0x019b9bd7979f12657976de2884c7cce192b82c177c80e0ec604436a7f538d231552f0d96d9f7babe5fa3b19b3ff25ac9" ] }, { "P": { "x": "0x03567bc5ef9c690c2ab2ecdf6a96ef1c139cc0b2f284dca0a9a7943388a49a3aee664ba5379a7655d3c68900be2f6903", "y": "0x0b9c15f3fe6e5cf4211f346271d7b01c8f3b28be689c8429c85b67af215533311f0b8dfaaa154fa6b88176c229f2885d" }, "Q0": { "x": "0x125435adce8e1cbd1c803e7123f45392dc6e326d292499c2c45c5865985fd74fe8f042ecdeeec5ecac80680d04317d80", "y": "0x0e8828948c989126595ee30e4f7c931cbd6f4570735624fd25aef2fa41d3f79cfb4b4ee7b7e55a8ce013af2a5ba20bf2" }, "Q1": { "x": "0x11def93719829ecda3b46aa8c31fc3ac9c34b428982b898369608e4f042babee6c77ab9218aad5c87ba785481eff8ae4", "y": "0x0007c9cef122ccf2efd233d6eb9bfc680aa276652b0661f4f820a653cec1db7ff69899f8e52b8e92b025a12c822a6ce6" }, "msg": "abc", "u": [ 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"0x028e6d0169a72cfedb737be45db6c401d3adfb12c58c619c82b93a5dfcccef12290de530b0480575ddc8397cda0bbebf" }, "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "u": [ "0x0a8ffa7447f6be1c5a2ea4b959c9454b431e29ccc0802bc052413a9c5b4f9aac67a93431bd480d15be1e057c8a08e8c6", "0x05d487032f602c90fa7625dbafe0f4a49ef4a6b0b33d7bb349ff4cf5410d297fd6241876e3e77b651cfc8191e40a68b7" ] } ] } golang-github-cloudflare-circl-1.3.7/ecc/bls12381/testdata/BLS12381G2_XMD-SHA-256_SSWU_NU_.json000066400000000000000000000156731454601126700304050ustar00rootroot00000000000000{ "L": "0x40", "Z": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9,0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa", "ciphersuite": "BLS12381G2_XMD:SHA-256_SSWU_NU_", "curve": "BLS12-381 G2", "dst": "QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_NU_", "expand": "XMD", "field": { "m": "0x2", "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab" }, "hash": "sha256", "k": "0x80", "map": { "name": "SSWU" }, "randomOracle": false, "vectors": [ { "P": { "x": "0x00e7f4568a82b4b7dc1f14c6aaa055edf51502319c723c4dc2688c7fe5944c213f510328082396515734b6612c4e7bb7,0x126b855e9e69b1f691f816e48ac6977664d24d99f8724868a184186469ddfd4617367e94527d4b74fc86413483afb35b", "y": 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TP v,'L#m6ݦH%p5~)‰r (ŊX  :7iƤSjJ|X!(u,wj{̳ݟmQ %")9<;Pz{3iC-)7`jJ#כ߀PE0>0md` 6 ׇt zk;8 F2kj4 n6 ΄~G58Ǘ7 GB39-HdXEotc|"+J Qk"V+4;d%j4hġU;lׇcu yqy@k sZp+*,q)P5##6B䠒 0\Ͷ[ Abp2|u3D3?G_mRxs{d{BD(z=ӓY]㗾T f ڼd豐K8mr%Ѳc;-I/jrI8'=YG'h{f)z1F"T'?s2 l}]b u7x~EQ RUSd˷OB?y'M9tbPqӕjVǙ4pA*6L\X  FƳ[$?o=J"d|j6C{IQp:N | VLB;JC=`P8V*CHY2ޠu v-.} Y鋆9EUV̚:>)O!rvS2k[k&ɇm'Mv˼ FAM$ik'<'pJ:Vnp rV h6|Gogw< h vXSW->gfA"q..~ S@O!t=9  y_89A#h[tg2nm4%Y /G3W}Iܮ%?ަJ!0VTga{;\ǵKu+L8:]!^C-w67f\nM=»h~TݐXǼ`R ޸p|_a/- =}38sRUy⦷7Ij"w |h7VVmt y @ns҇δi6 /U abe Y[:PA>|b|;_mZ˼ 6_{32{Xt0wu`BKbWX{M1Dmڔ3Yգ=Ӱs(bk wѹf OaGXy?Dh(:AJ 2Ev;ĽA5a(CEbzo0B4@~(F,QR~JΪs]O33-$ӤL8}&|:iL4|ϥDE  UЩtQ0^[{PGzPW`p-4kmbu1!aR}^UZΪ]>kEHyZ@C;~P%\~ 󉍕Gnܼ~ꇑ?VA4 5-.R'xݿwlܯc"= K SQ2qcF Xn쭹 :xS+91*WB͸34t^.^UCÁ?*󿺍dW , -f&sOs}/: K5ᘺ42<tm}F )rcS6dfc;E#},O-PʱrCs D[$%KUXsiW]{ SڙK[EoU@X^1.Q$ m? qdz\l+L.}^USIɂ8VnjJ *΢f?eO!MHeIv;'&41ΰSㄺT.2]s׳z,T3Kq94=O_mĜOf}h=h"dܖ \jp[qg&f8}+7`zX'[#7.g7Чo54~/Lw4X=&^ /Rzc4xC|J -4ǍyuLz̍t?">D~l:b~sſ.d,X~^trDsa*q /q ?1> 7 want := 1 - (encR[31] >> 7) encQ[31] &= 0x7F encR[31] &= 0x7F if encQ != encR { test.ReportError(t, encQ, encR, P, k) } if got != want { test.ReportError(t, got, want, P, k) } } }) } func BenchmarkCurve(b *testing.B) { var P, Q, R Point var k [32]byte _, _ = rand.Read(k[:]) P.ScalarBaseMult(&k) _, _ = rand.Read(k[:]) Q.ScalarBaseMult(&k) _, _ = rand.Read(k[:]) R.ScalarBaseMult(&k) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Add(&Q, &R) } }) b.Run("Double", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Add(&Q, &Q) } }) b.Run("ScalarBaseMult", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ScalarBaseMult(&k) } }) b.Run("ScalarMult", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ScalarMult(&k, &Q) } }) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/doc.go000066400000000000000000000005751454601126700224600ustar00rootroot00000000000000// Package fourq provides elliptic curve operations over FourQ curve. // // FourQ is a high-speed elliptic curve at the 128-bit security level. This package // contains an AMD64-optimized implementation. In particular, this package does // not implement FourQ's endomorphisms or lattice reduction techniques. // // References: // - https://eprint.iacr.org/2015/565 package fourq golang-github-cloudflare-circl-1.3.7/ecc/fourq/fp.go000066400000000000000000000041721454601126700223150ustar00rootroot00000000000000package fourq import ( "math/big" "github.com/cloudflare/circl/internal/conv" ) var modulusP = Fp{ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, } // SizeFp is the length in bytes to represent an element in the base field. const SizeFp = 16 // Fp is an element (in littleEndian order) of prime field GF(2^127-1). type Fp [SizeFp]byte func (f *Fp) String() string { return conv.BytesLe2Hex(f[:]) } func (f *Fp) isZero() bool { fpMod(f); return *f == Fp{} } func (f *Fp) toBigInt() *big.Int { fpMod(f); return conv.BytesLe2BigInt(f[:]) } func (f *Fp) setBigInt(b *big.Int) { conv.BigInt2BytesLe((*f)[:], b); fpMod(f) } func (f *Fp) toBytes(buf []byte) { if len(buf) == SizeFp { fpMod(f) copy(buf, f[:]) } } func (f *Fp) fromBytes(buf []byte) bool { if len(buf) == SizeFp { if (buf[SizeFp-1] >> 7) == 0 { copy(f[:], buf) fpMod(f) return true } } return false } func fpNeg(c, a *Fp) { fpSub(c, &modulusP, a) } // fqSgn returns the sign of an element. // // -1 if x > (p+1)/2 // 0 if x == 0 // +1 if x > (p+1)/2. func fpSgn(c *Fp) int { s := 0 if !c.isZero() { b := int(c[SizeFp-1]>>6) & 0x1 s = 1 - (b << 1) } return s } // fpTwo1251 sets c = a^(2^125-1). func fpTwo1251(c, a *Fp) { t1, t2, t3, t4, t5 := &Fp{}, &Fp{}, &Fp{}, &Fp{}, &Fp{} fpSqr(t2, a) fpMul(t2, t2, a) fpSqr(t3, t2) fpSqr(t3, t3) fpMul(t3, t3, t2) fpSqr(t4, t3) fpSqr(t4, t4) fpSqr(t4, t4) fpSqr(t4, t4) fpMul(t4, t4, t3) fpSqr(t5, t4) for i := 0; i < 7; i++ { fpSqr(t5, t5) } fpMul(t5, t5, t4) fpSqr(t2, t5) for i := 0; i < 15; i++ { fpSqr(t2, t2) } fpMul(t2, t2, t5) fpSqr(t1, t2) for i := 0; i < 31; i++ { fpSqr(t1, t1) } fpMul(t1, t1, t2) for i := 0; i < 32; i++ { fpSqr(t1, t1) } fpMul(t1, t2, t1) for i := 0; i < 16; i++ { fpSqr(t1, t1) } fpMul(t1, t1, t5) for i := 0; i < 8; i++ { fpSqr(t1, t1) } fpMul(t1, t1, t4) for i := 0; i < 4; i++ { fpSqr(t1, t1) } fpMul(t1, t1, t3) fpSqr(t1, t1) fpMul(c, a, t1) } // fpInv sets z to a^(-1) mod p. func fpInv(z, a *Fp) { t := &Fp{} fpTwo1251(t, a) fpSqr(t, t) fpSqr(t, t) fpMul(z, t, a) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/fp_amd64.go000066400000000000000000000005551454601126700233110ustar00rootroot00000000000000//go:build amd64 && !purego // +build amd64,!purego package fourq import ( "golang.org/x/sys/cpu" ) var hasBMI2 = cpu.X86.HasBMI2 //nolint //go:noescape func fpMod(c *Fp) //go:noescape func fpAdd(c, a, b *Fp) //go:noescape func fpSub(c, a, b *Fp) //go:noescape func fpMul(c, a, b *Fp) //go:noescape func fpSqr(c, a *Fp) //go:noescape func fpHlf(c, a *Fp) golang-github-cloudflare-circl-1.3.7/ecc/fourq/fp_amd64.h000066400000000000000000000034511454601126700231310ustar00rootroot00000000000000// CHECK_BMI2 triggers bmi2 if supported, // otherwise it fallbacks to legacy code. #define CHECK_BMI2(label, legacy, bmi2) \ CMPB ·hasBMI2(SB), $0 \ JE label \ bmi2 \ RET \ label: \ legacy \ RET #define _fpReduce(c0, c1) \ BTRQ $63, c1 \ ADCQ $0, c0 \ ADCQ $0, c1 // _fpMod: c = c mod p // Uses: AX, DX, FLAGS // Instr: x86_64 #define _fpMod(c) \ MOVQ 0+c, AX \ MOVQ 8+c, DX \ SUBQ ·modulusP+0(SB), AX \ SBBQ ·modulusP+8(SB), DX \ BTRQ $63, DX \ SBBQ $0, AX \ SBBQ $0, DX \ _fpReduce(AX, DX) \ _fpReduce(AX, DX) \ MOVQ AX, 0+c \ MOVQ DX, 8+c // _fpAdd: c = a + b // Uses: AX, DX, FLAGS // Instr: x86_64 #define _fpAdd(c,a,b) \ MOVQ 0+a, AX \ MOVQ 8+a, DX \ ADDQ 0+b, AX \ ADCQ 8+b, DX \ _fpReduce(AX, DX) \ MOVQ AX, 0+c \ MOVQ DX, 8+c // _fpSub: c = a - b // Uses: AX, DX, FLAGS // Instr: x86_64 #define _fpSub(c,a,b) \ MOVQ 0+a, AX \ MOVQ 8+a, DX \ SUBQ 0+b, AX \ SBBQ 8+b, DX \ BTRQ $63, DX \ SBBQ $0, AX \ SBBQ $0, DX \ MOVQ AX, 0+c \ MOVQ DX, 8+c #define _fpMulLeg(C2, C1, C0, a, b) \ MOVQ $0, C2 \ MOVQ 0+b, CX \ MOVQ 0+a, AX \ MULQ CX \ MOVQ AX, C0 \ MOVQ DX, C1 \ MOVQ 8+a, AX \ MULQ CX \ SHLQ $1,DX \ ADDQ DX,C0 \ ADCQ AX, C1 \ ADCQ $0, C2 \ MOVQ 8+b, CX \ MOVQ 0+a, AX \ MULQ CX \ SHLQ $1,DX \ ADDQ DX,C0 \ ADCQ AX, C1 \ ADCQ $0, C2 \ MOVQ 8+a, AX \ MULQ CX \ SHLQ $1,AX,DX \ SHLQ $1,AX \ ADDQ AX,C0 \ ADCQ DX, C1 \ ADCQ $0, C2 golang-github-cloudflare-circl-1.3.7/ecc/fourq/fp_amd64.s000066400000000000000000000032641454601126700231460ustar00rootroot00000000000000// +build amd64,!purego #include "textflag.h" #include "fp_amd64.h" // fpModp sets e to zero if it is equal to p. This is the only case where c // will not naturally be reduced to canonical form. // func fpMod(c *fp) TEXT ·fpMod(SB),0,$0-8 MOVQ c+0(FP), DI _fpMod(0(DI)) RET // func fpAdd(c, a, b *fp) TEXT ·fpAdd(SB),0,$0-24 MOVQ c+0(FP), DI MOVQ a+8(FP), SI MOVQ b+16(FP), BX _fpAdd(0(DI), 0(SI), 0(BX)) RET // func fpSub(c, a, b *fp) TEXT ·fpSub(SB),0,$0-24 MOVQ c+0(FP), DI MOVQ a+8(FP), SI MOVQ b+16(FP), BX _fpSub(0(DI), 0(SI), 0(BX)) RET // func fpHlf(c, a *fp) TEXT ·fpHlf(SB),0,$0-16 MOVQ a+8(FP), DI MOVQ 0(DI), AX MOVQ 8(DI), BX SHLQ $1, BX SHRQ $1, AX, BX SHRQ $1, BX, AX SHRQ $1, BX MOVQ c+0(FP), DI MOVQ AX, 0(DI) MOVQ BX, 8(DI) RET // func fpMul(c, a, b *fp) TEXT ·fpMul(SB),0,$0-24 MOVQ a+8(FP), DI MOVQ b+16(FP), SI _fpMulLeg(R10, R9, R8, 0(DI), 0(SI)) SHLQ $1, R10 BTRQ $63, R9 ADCQ R10, R8 ADCQ $0, R9 _fpReduce(R8, R9) MOVQ c+0(FP), DI MOVQ R8, 0(DI) MOVQ R9, 8(DI) RET // func fpSqr(c, a *fp) TEXT ·fpSqr(SB),0,$0-16 MOVQ a+8(FP), DI MOVQ $0, CX MOVQ 0(DI), AX MULQ 0(DI) MOVQ AX, R8 MOVQ DX, R9 MOVQ 0(DI), AX MULQ 8(DI) SHLQ $1, DX ADDQ DX, R8 ADCQ AX, R9 ADCQ $0, CX ADDQ DX, R8 ADCQ AX, R9 ADCQ $0, CX MOVQ 8(DI), AX MULQ 8(DI) SHLQ $1, DX SHLQ $1, AX ADCQ $0, DX ADDQ AX, R8 ADCQ DX, R9 ADCQ $0, CX SHLQ $1, CX BTRQ $63, R9 ADCQ CX, R8 ADCQ $0, R9 _fpReduce(R8, R9) MOVQ c+0(FP), DI MOVQ R8, 0(DI) MOVQ R9, 8(DI) RET golang-github-cloudflare-circl-1.3.7/ecc/fourq/fp_generic.go000066400000000000000000000046371454601126700240170ustar00rootroot00000000000000//go:build go1.12 // +build go1.12 package fourq import ( "encoding/binary" "math/bits" ) func fpModGeneric(c *Fp) { fpSubGeneric(c, c, &modulusP) } func fpAddGeneric(c, a, b *Fp) { a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) b0 := binary.LittleEndian.Uint64(b[0*8 : 1*8]) b1 := binary.LittleEndian.Uint64(b[1*8 : 2*8]) c0, x := bits.Add64(a0, b0, 0) c1, _ := bits.Add64(a1, b1, x) c1, x = bits.Add64(c1, c1, 0) c0, x = bits.Add64(c0, 0, x) c1, _ = bits.Add64(c1>>1, 0, x) binary.LittleEndian.PutUint64(c[0*8:1*8], c0) binary.LittleEndian.PutUint64(c[1*8:2*8], c1) } func fpSubGeneric(c, a, b *Fp) { a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) b0 := binary.LittleEndian.Uint64(b[0*8 : 1*8]) b1 := binary.LittleEndian.Uint64(b[1*8 : 2*8]) c0, x := bits.Sub64(a0, b0, 0) c1, _ := bits.Sub64(a1, b1, x) c1, x = bits.Add64(c1, c1, 0) c0, x = bits.Sub64(c0, 0, x) c1, _ = bits.Sub64(c1>>1, 0, x) binary.LittleEndian.PutUint64(c[0*8:1*8], c0) binary.LittleEndian.PutUint64(c[1*8:2*8], c1) } func fpMulGeneric(c, a, b *Fp) { a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) b0 := binary.LittleEndian.Uint64(b[0*8 : 1*8]) b1 := binary.LittleEndian.Uint64(b[1*8 : 2*8]) c1, c0 := bits.Mul64(a0, b0) hi, lo := bits.Mul64(a0, b1) c0, x := bits.Add64(c0, hi<<1, 0) c1, x = bits.Add64(c1, lo, x) c2, _ := bits.Add64(0, 0, x) hi, lo = bits.Mul64(a1, b0) c0, x = bits.Add64(c0, hi<<1, 0) c1, x = bits.Add64(c1, lo, x) c2, _ = bits.Add64(c2, 0, x) hi, lo = bits.Mul64(a1, b1) lo, x = bits.Add64(lo, lo, 0) hi, _ = bits.Add64(hi, hi, x) c0, x = bits.Add64(c0, lo, 0) c1, x = bits.Add64(c1, hi, x) c2, _ = bits.Add64(c2, 0, x) c1, x = bits.Add64(c1, c1, 0) c0, x = bits.Add64(c0, c2<<1, x) c1, _ = bits.Add64(c1>>1, 0, x) c1, x = bits.Add64(c1, c1, 0) c0, x = bits.Add64(c0, 0, x) c1, _ = bits.Add64(c1>>1, 0, x) binary.LittleEndian.PutUint64(c[0*8:1*8], c0) binary.LittleEndian.PutUint64(c[1*8:2*8], c1) } func fpSqrGeneric(c, a *Fp) { fpMulGeneric(c, a, a) } func fpHlfGeneric(c, a *Fp) { a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) hlf := a0 & 0x1 c0 := (a1 << 63) | (a0 >> 1) c1 := (hlf << 62) | (a1 >> 1) binary.LittleEndian.PutUint64(c[0*8:1*8], c0) binary.LittleEndian.PutUint64(c[1*8:2*8], c1) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/fp_noasm.go000066400000000000000000000005441454601126700235110ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package fourq func fpMod(c *Fp) { fpModGeneric(c) } func fpAdd(c, a, b *Fp) { fpAddGeneric(c, a, b) } func fpSub(c, a, b *Fp) { fpSubGeneric(c, a, b) } func fpMul(c, a, b *Fp) { fpMulGeneric(c, a, b) } func fpSqr(c, a *Fp) { fpSqrGeneric(c, a) } func fpHlf(c, a *Fp) { fpHlfGeneric(c, a) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/fp_test.go000066400000000000000000000153071454601126700233560ustar00rootroot00000000000000package fourq import ( "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) type ( tFpAdd = func(z, x, y *Fp) tFpSub = func(z, x, y *Fp) tFpMul = func(z, x, y *Fp) tFpSqr = func(z, x *Fp) tFpHlf = func(z, x *Fp) tFpModp = func(z *Fp) ) func getModulus() *big.Int { p := big.NewInt(1) return p.Lsh(p, 127).Sub(p, big.NewInt(1)) } func TestFpSign(t *testing.T) { const testTimes = 1 << 9 P := getModulus() x := &Fp{} var P1div2 big.Int P1div2.Add(P, big.NewInt(1)).Rsh(&P1div2, 1) // (p+1)/2 // Verifying Sign(0) = 0 x.setBigInt(big.NewInt(0)) got := fpSgn(x) want := 0 if got != want { test.ReportError(t, got, want, x) } // Verifying Sign(P) = 0 x.setBigInt(P) got = fpSgn(x) want = 0 if got != want { test.ReportError(t, got, want, x) } // Verifying Sign( (p+1)/2 ) = -1 x.setBigInt(&P1div2) got = fpSgn(x) want = -1 if got != want { test.ReportError(t, got, want, x) } // Verifying x be a non-zero positive for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, &P1div2) x.setBigInt(bigX) got = fpSgn(x) want = 1 if got != want { test.ReportError(t, got, want, x) } } // Verifying x be a non-zero negative for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, &P1div2) bigX.Add(bigX, &P1div2) x.setBigInt(bigX) got = fpSgn(x) want = -1 if got != want { test.ReportError(t, got, want, x) } } } func TestFpIsZero(t *testing.T) { P := getModulus() x := &Fp{} // Verifying x=0 x.setBigInt(big.NewInt(0)) got := x.isZero() want := true if got != want { test.ReportError(t, got, want, x) } // Verifying x=P goes to 0 x.setBigInt(P) got = x.isZero() want = true if got != want { test.ReportError(t, got, want, x) } // Verifying x!=0 _, _ = rand.Read(x[:]) got = x.isZero() want = false if got != want { test.ReportError(t, got, want, x) } } func testFpModp(t *testing.T, f tFpModp) { const testTimes = 1 << 9 P := getModulus() x := &Fp{} var bigX big.Int // Verifying x=P goes to 0 bigX.Set(P) x.setBigInt(&bigX) f(x) got := x.toBigInt() want := big.NewInt(0) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } // Verifying x=P+1 goes to 1 bigX.Add(P, big.NewInt(1)) x.setBigInt(&bigX) f(x) got = x.toBigInt() want = big.NewInt(1) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) bigX := x.toBigInt() fpMod(x) got := x.toBigInt() want := bigX.Mod(bigX, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestFpNeg(t *testing.T) { const testTimes = 1 << 9 P := getModulus() x, z := &Fp{}, &Fp{} for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX) fpNeg(z, x) got := z.toBigInt() want := bigX.Neg(bigX) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func testFpHlf(t *testing.T, f tFpHlf) { const testTimes = 1 << 9 P := getModulus() x, z := &Fp{}, &Fp{} invTwo := big.NewInt(2) invTwo.ModInverse(invTwo, P) for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX) f(z, x) got := z.toBigInt() want := bigX.Mul(bigX, invTwo) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func testFpAdd(t *testing.T, f tFpAdd) { const testTimes = 1 << 9 P := getModulus() x, y, z := &Fp{}, &Fp{}, &Fp{} for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, P) bigY, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX) y.setBigInt(bigY) f(z, x, y) got := z.toBigInt() want := bigX.Add(bigX, bigY) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testFpSub(t *testing.T, f tFpSub) { const testTimes = 1 << 9 P := getModulus() x, y, z := &Fp{}, &Fp{}, &Fp{} for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, P) bigY, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX) y.setBigInt(bigY) f(z, x, y) got := z.toBigInt() want := bigX.Sub(bigX, bigY) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testFpMul(t *testing.T, f tFpMul) { const testTimes = 1 << 9 P := getModulus() x, y, z := &Fp{}, &Fp{}, &Fp{} for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, P) bigY, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX) y.setBigInt(bigY) f(z, x, y) got := z.toBigInt() want := bigX.Mul(bigX, bigY) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testFpSqr(t *testing.T, f tFpSqr) { const testTimes = 1 << 9 P := getModulus() x, z := &Fp{}, &Fp{} for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX) f(z, x) got := z.toBigInt() want := bigX.Mul(bigX, bigX) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestFpInv(t *testing.T) { const testTimes = 1 << 9 P := getModulus() x, z := &Fp{}, &Fp{} for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX) fpInv(z, x) got := z.toBigInt() want := bigX.ModInverse(bigX, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestFpGeneric(t *testing.T) { t.Run("Add", func(t *testing.T) { testFpAdd(t, fpAddGeneric) }) t.Run("Sub", func(t *testing.T) { testFpSub(t, fpSubGeneric) }) t.Run("Mul", func(t *testing.T) { testFpMul(t, fpMulGeneric) }) t.Run("Sqr", func(t *testing.T) { testFpSqr(t, fpSqrGeneric) }) t.Run("Hlf", func(t *testing.T) { testFpHlf(t, fpHlfGeneric) }) t.Run("Modp", func(t *testing.T) { testFpModp(t, fpModGeneric) }) } func TestFpNative(t *testing.T) { t.Run("Add", func(t *testing.T) { testFpAdd(t, fpAdd) }) t.Run("Sub", func(t *testing.T) { testFpSub(t, fpSub) }) t.Run("Mul", func(t *testing.T) { testFpMul(t, fpMul) }) t.Run("Sqr", func(t *testing.T) { testFpSqr(t, fpSqr) }) t.Run("Hlf", func(t *testing.T) { testFpHlf(t, fpHlf) }) t.Run("Modp", func(t *testing.T) { testFpModp(t, fpMod) }) } func BenchmarkFp(b *testing.B) { x, y, z := &Fp{}, &Fp{}, &Fp{} p := getModulus() n, _ := rand.Int(rand.Reader, p) x.setBigInt(n) n, _ = rand.Int(rand.Reader, p) y.setBigInt(n) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { fpAdd(z, x, y) } }) b.Run("Sub", func(b *testing.B) { for i := 0; i < b.N; i++ { fpSub(z, x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { fpMul(z, x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { fpSqr(z, x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { fpInv(z, x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/fq.go000066400000000000000000000050171454601126700223150ustar00rootroot00000000000000package fourq import ( "crypto/subtle" "math/big" ) // Fq implements operations of a field of size q=p^2 as a quadratic // extension of the base field where i^2=-1. // An element in Fq is represented as f[0]+f[1]*i, where f[0],f[1] are in Fp. type Fq [2]Fp func (e *Fq) String() string { return e[1].String() + " *i+ " + e[0].String() } func (e *Fq) toBigInt() (f0, f1 *big.Int) { return e[0].toBigInt(), e[1].toBigInt() } func (e *Fq) setBigInt(f0, f1 *big.Int) { e[0].setBigInt(f0); e[1].setBigInt(f1) } func (e *Fq) setZero() { var z Fp; e[0] = z; e[1] = z } func (e *Fq) setOne() { e.setZero(); e[0][0] = 1 } func (e *Fq) isZero() bool { return e[0].isZero() && e[1].isZero() } func (e *Fq) toBytes(buf []byte) { if len(buf) == 2*SizeFp { e[0].toBytes(buf[:SizeFp]) e[1].toBytes(buf[SizeFp:]) } } func (e *Fq) fromBytes(buf []byte) bool { if len(buf) == 2*SizeFp { return e[0].fromBytes(buf[:SizeFp]) && e[1].fromBytes(buf[SizeFp:]) } return false } func fqSgn(c *Fq) int { s0 := fpSgn(&c[0]) s1 := fpSgn(&c[1]) return subtle.ConstantTimeSelect(s0&0x1, s0, s1) } func fqCopy(c, a *Fq) { *c = *a } func fqNeg(c, a *Fq) { fpNeg(&c[0], &a[0]); fpNeg(&c[1], &a[1]) } // fqSqrt calculates c = sqrt(u/v) such that sgn(c)=s. func fqSqrt(c, u, v *Fq, s int) { t0, t1, t, r := &Fp{}, &Fp{}, &Fp{}, &Fp{} a, b, g := &Fp{}, &Fp{}, &Fp{} // a = u0*v0 + u1*v1 fpMul(a, &u[0], &v[0]) fpMul(t0, &u[1], &v[1]) fpAdd(a, a, t0) // b = v0^2 + v1^2 fpSqr(b, &v[0]) fpSqr(t0, &v[1]) fpAdd(b, b, t0) // g = u1*v0 - u0*v1 fpMul(g, &u[1], &v[0]) fpMul(t0, &u[0], &v[1]) fpSub(g, g, t0) // t = 2(a + sqrt(a^2+g^2)) = 2*(a + (a^2+g^2)^(2^125)) // if t=0; then t = 2*(a - (a^2+g^2)^(2^125)) fpSqr(t0, a) fpSqr(t1, g) fpAdd(t0, t0, t1) for i := 0; i < 125; i++ { fpSqr(t0, t0) } fpAdd(t, a, t0) if t.isZero() { fpSub(t, a, t0) } fpAdd(t, t, t) // r = (t*b^3)^(2^125-1) fpSqr(r, b) fpMul(r, r, b) fpMul(r, r, t) fpTwo1251(r, r) // x0 = (r*b*t)/2 // x1 = (r*b*g) fpMul(&c[1], r, b) fpMul(&c[0], &c[1], t) fpHlf(&c[0], &c[0]) fpMul(&c[1], &c[1], g) // if b*(2*x0)^2 == t then (x0,x1) <- (x1,x0) fpAdd(t0, &c[0], &c[0]) fpSqr(t0, t0) fpMul(t0, t0, b) fpSub(t0, t0, t) if !t0.isZero() { *t0 = c[0] c[0] = c[1] c[1] = *t0 } if fqSgn(c) != s { fqNeg(c, c) } } func fqInv(c, a *Fq) { t1, t2 := &Fp{}, &Fp{} fpSqr(t1, &a[0]) fpSqr(t2, &a[1]) fpAdd(t1, t1, t2) fpInv(t1, t1) fpMul(&c[0], &a[0], t1) fpNeg(t1, t1) fpMul(&c[1], &a[1], t1) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/fq_amd64.go000066400000000000000000000004101454601126700233000ustar00rootroot00000000000000//go:build amd64 && !purego // +build amd64,!purego package fourq //go:noescape func fqCmov(c, a *Fq, b int) //go:noescape func fqAdd(c, a, b *Fq) //go:noescape func fqSub(c, a, b *Fq) //go:noescape func fqMul(c, a, b *Fq) //go:noescape func fqSqr(c, a *Fq) golang-github-cloudflare-circl-1.3.7/ecc/fourq/fq_amd64.h000066400000000000000000000110401454601126700231230ustar00rootroot00000000000000#include "fp_amd64.h" #define _fqAdd(c,a,b) \ _fpAdd( 0+c, 0+a, 0+b) \ _fpAdd(16+c,16+a,16+b) #define _fqSub(c,a,b) \ _fpSub( 0+c, 0+a, 0+b) \ _fpSub(16+c,16+a,16+b) #define _fqMulBmi2(c, a, b) \ MOVL $0, R15 \ \ // T0 = a0 * b0, R11:R10:R9:R8 <- 0+ra:8+ra * 0+rb:8+rb MOVQ 0+b, DX \ MULXQ 0+a, R8, R9 \ MULXQ 8+a, R10, AX \ ADDQ R10, R9 \ MOVQ 8+b, DX \ MULXQ 8+a, R10, R11 \ ADCQ AX, R10 \ MULXQ 0+a, DX, AX \ ADCQ $0, R11 \ ADDQ DX, R9 \ \ \ // T1 = a1 * b1, R15:R14:R13:R12 <- 16+ra:24+ra * 16+rb:24+rb MOVQ 16+b, DX \ MULXQ 16+a, R12, R13 \ ADCQ AX, R10 \ MULXQ 24+a, R14, AX \ ADCQ $0, R11 \ MOVQ 24+b, DX \ ADDQ R14, R13 \ MULXQ 24+a, R14, R15 \ ADCQ AX, R14 \ ADCQ $0, R15 \ MULXQ 16+a, DX, AX \ ADDQ DX, R13 \ ADCQ AX, R14 \ ADCQ $0, R15 \ \ \ // c0 = T0 - T1 = a0*b0 - a1*b1 SUBQ R12, R8 \ SBBQ R13, R9 \ SBBQ R14, R10 \ SBBQ R15, R11 \ \ SHLQ $1, R10, R11 \ SHLQ $1, R9, R10 \ MOVQ 16+b, DX \ BTRQ $63, R9 \ \ \ // T0 = a0 * b1, R15:R14:R13:R12 <- 0+ra:8+ra * 16+rb:24+rb MULXQ 0+a, R12, R13 \ BTRQ $63, R11 \ SBBQ $0, R10 \ SBBQ $0, R11 \ MULXQ 8+a, R14, AX \ ADDQ R14, R13 \ MOVQ 24+b, DX \ MULXQ 8+a, R14, R15 \ ADCQ AX, R14 \ ADCQ $0, R15 \ MULXQ 0+a, DX, AX \ ADDQ DX, R13 \ ADCQ AX, R14 \ ADCQ $0, R15 \ \ \ // Reducing and storing c0 ADDQ R8, R10 \ ADCQ R9, R11 \ BTRQ $63, R11 \ ADCQ $0, R10 \ ADCQ $0, R11 \ \ \ // T1 = a1 * b0, R12:R11:R10:R9 <- 16+ra:24+ra * 0+rb:8+rb MOVQ 0+b, DX \ MULXQ 16+a, R8, R9 \ MOVQ R10, 0+c \ MULXQ 24+a, R10, AX \ ADDQ R10, R9 \ MOVQ 8+b, DX \ MOVQ R11, 8+c \ MULXQ 24+a, R10, R11 \ ADCQ AX, R10 \ ADCQ $0, R11 \ MULXQ 16+a, DX, AX \ ADDQ DX, R9 \ ADCQ AX, R10 \ ADCQ $0, R11 \ \ \ // c1 = T0 + T1 = a0*b1 + a1*b0 ADDQ R12, R8 \ ADCQ R13, R9 \ ADCQ R14, R10 \ ADCQ R15, R11 \ \ \ // Reducing and storing c1 SHLQ $1, R10, R11 \ SHLQ $1, R9, R10 \ BTRQ $63, R9 \ BTRQ $63, R11 \ ADCQ R10, R8 \ ADCQ R11, R9 \ BTRQ $63, R9 \ ADCQ $0, R8 \ ADCQ $0, R9 \ MOVQ R8, 16+c \ MOVQ R9, 24+c #define _fqMulLeg(c, a, b) \ _fpMulLeg(R10, R9, R8, 0+a, 0+b) \ _fpMulLeg(R13,R12,R11,16+a,16+b) \ MOVQ $0,R14 \ SUBQ R11, R8 \ SBBQ R12, R9 \ SBBQ R13,R10 \ SBBQ $0,R14 \ SHLQ $1,R10 \ BTRQ $63, R9 \ ADCQ R10, R8 \ ADCQ R14, R9 \ MOVQ R8, R14 \ MOVQ R9, R15 \ _fpMulLeg(R10, R9, R8, 0+a,16+b) \ _fpMulLeg(R13,R12,R11,16+a, 0+b) \ ADDQ R11, R8 \ ADCQ R12, R9 \ ADCQ R13,R10 \ SHLQ $1,R10 \ BTRQ $63, R9 \ ADCQ R10, R8 \ ADCQ $0, R9 \ MOVQ R14, 0+c \ MOVQ R15, 8+c \ MOVQ R8,16+c \ MOVQ R9,24+c #define _fqSqrBmi2(c,a) \ \ // t0 = R9:R8 = a0 + a1, R14:CX = a1 MOVQ 0+a, R10 \ MOVQ 16+a, R14 \ SUBQ R14, R10 \ MOVQ 8+a, R11 \ MOVQ 24+a, CX \ SBBQ CX, R11 \ \ BTRQ $63, R11 \ SBBQ $0, R10 \ \ \ // t1 = R11:R10 = a0 - a1 MOVQ R10, DX \ MOVQ 0+a, R8 \ ADDQ R14, R8 \ MOVQ 8+a, R9 \ ADCQ CX, R9 \ \ \ // c0 = t0 * t1 = (a0 + a1)*(a0 - a1), CX:R14:R13:R12 <- R9:R8 * R11:R10 MULXQ R8, R12, R13 \ SBBQ $0, R11 \ MULXQ R9, R14, AX \ MOVQ R11, DX \ ADDQ R14, R13 \ MULXQ R9, R14, CX \ MOVQ 8+a, R9 \ ADCQ AX, R14 \ ADCQ $0, CX \ MULXQ R8, DX, AX \ MOVQ 0+a, R8 \ ADDQ DX, R13 \ ADCQ AX, R14 \ ADCQ $0, CX \ \ \ // t2 = R9:R8 = 2*a0 ADDQ R8, R8 \ ADCQ R9, R9 \ \ \ // Reducing and storing c0 SHLQ $1, R14, CX \ SHLQ $1, R13, R14 \ BTRQ $63, R13 \ BTRQ $63, CX \ ADCQ R14, R12 \ ADCQ CX, R13 \ BTRQ $63, R13 \ ADCQ $0, R12 \ ADCQ $0, R13 \ MOVQ R12, 0+c \ MOVQ R13, 8+c \ \ \ // c1 = 2a0 * a1, CX:R14:R11:R10 <- R9:R8 * 16+ra:24+ra MOVQ 16+a, DX \ MULXQ R8, R10, R11 \ MULXQ R9, R14, AX \ ADDQ R14, R11 \ MOVQ 24+a, DX \ MULXQ R9, R14, CX \ ADCQ AX, R14 \ ADCQ $0, CX \ MULXQ R8, DX, AX \ ADDQ DX, R11 \ ADCQ AX, R14 \ ADCQ $0, CX \ \ \ // Reduce and store c1 SHLQ $1, R14, CX \ SHLQ $1, R11, R14 \ BTRQ $63, R11 \ BTRQ $63, CX \ ADCQ R14, R10 \ ADCQ CX, R11 \ BTRQ $63, R11 \ ADCQ $0, R10 \ ADCQ $0, R11 \ MOVQ R10, 16+c \ MOVQ R11, 24+c #define _fqSqrLeg(c,a) _fqMulLeg(c,a,a) golang-github-cloudflare-circl-1.3.7/ecc/fourq/fq_amd64.s000066400000000000000000000024501454601126700231430ustar00rootroot00000000000000// +build amd64,!purego #include "fq_amd64.h" #define fqMulLegacy \ _fqMulLeg(0(DI),0(SI),0(BX)) #define fqMulBmi2 \ _fqMulBmi2(0(DI),0(SI),0(BX)) #define fqSqrLegacy \ _fqSqrLeg(0(DI),0(SI)) #define fqSqrBmi2 \ _fqSqrBmi2(0(DI),0(SI)) // func fqCmov(c, a *fq, b int) TEXT ·fqCmov(SB),0,$0-24 MOVQ c+0(FP), DI MOVQ a+8(FP), SI MOVQ b+16(FP), BX TESTQ BX, BX MOVQ 0(DI), AX; MOVQ 0(SI), DX; CMOVQNE DX, AX; MOVQ AX, 0(DI); MOVQ 8(DI), AX; MOVQ 8(SI), DX; CMOVQNE DX, AX; MOVQ AX, 8(DI); MOVQ 16(DI), AX; MOVQ 16(SI), DX; CMOVQNE DX, AX; MOVQ AX, 16(DI); MOVQ 24(DI), AX; MOVQ 24(SI), DX; CMOVQNE DX, AX; MOVQ AX, 24(DI); RET // func fqAdd(c, a, b *fq) TEXT ·fqAdd(SB),0,$0-24 MOVQ c+0(FP), DI MOVQ a+8(FP), SI MOVQ b+16(FP), BX _fqAdd(0(DI), 0(SI), 0(BX)) RET // func fqSub(c, a, b *fq) TEXT ·fqSub(SB),0,$0-24 MOVQ c+0(FP), DI MOVQ a+8(FP), SI MOVQ b+16(FP), BX _fqSub(0(DI), 0(SI), 0(BX)) RET // func fqMul(c, a, b *fq) TEXT ·fqMul(SB),0,$0-24 MOVQ c+0(FP), DI MOVQ a+8(FP), SI MOVQ b+16(FP), BX CHECK_BMI2(LFQMUL, fqMulLegacy, fqMulBmi2) RET // func fqSqr(c, a *fq) TEXT ·fqSqr(SB),0,$0-16 MOVQ c+0(FP), DI MOVQ a+8(FP), SI CHECK_BMI2(LFQSQR, fqSqrLegacy, fqSqrBmi2) RET golang-github-cloudflare-circl-1.3.7/ecc/fourq/fq_generic.go000066400000000000000000000013101454601126700240010ustar00rootroot00000000000000package fourq func fqAddGeneric(c, a, b *Fq) { fpAddGeneric(&c[0], &a[0], &b[0]) fpAddGeneric(&c[1], &a[1], &b[1]) } func fqSubGeneric(c, a, b *Fq) { fpSubGeneric(&c[0], &a[0], &b[0]) fpSubGeneric(&c[1], &a[1], &b[1]) } func fqMulGeneric(c, a, b *Fq) { var a0b0, a0b1, a1b0, a1b1 Fp fpMulGeneric(&a0b0, &a[0], &b[0]) fpMulGeneric(&a0b1, &a[0], &b[1]) fpMulGeneric(&a1b0, &a[1], &b[0]) fpMulGeneric(&a1b1, &a[1], &b[1]) fpSubGeneric(&c[0], &a0b0, &a1b1) fpAddGeneric(&c[1], &a0b1, &a1b0) } func fqSqrGeneric(c, a *Fq) { var aa0, a01, aa1 Fp fpSqrGeneric(&aa0, &a[0]) fpMulGeneric(&a01, &a[0], &a[1]) fpSqrGeneric(&aa1, &a[1]) fpSubGeneric(&c[0], &aa0, &aa1) fpAddGeneric(&c[1], &a01, &a01) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/fq_noasm.go000066400000000000000000000006361454601126700235140ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package fourq import "crypto/subtle" func fqCmov(c, a *Fq, b int) { subtle.ConstantTimeCopy(b, c[0][:], a[0][:]) subtle.ConstantTimeCopy(b, c[1][:], a[1][:]) } func fqAdd(c, a, b *Fq) { fqAddGeneric(c, a, b) } func fqSub(c, a, b *Fq) { fqSubGeneric(c, a, b) } func fqMul(c, a, b *Fq) { fqMulGeneric(c, a, b) } func fqSqr(c, a *Fq) { fqSqrGeneric(c, a) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/fq_test.go000066400000000000000000000176411454601126700233620ustar00rootroot00000000000000package fourq import ( "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) type ( tFqAdd = func(z, x, y *Fq) tFqSub = func(z, x, y *Fq) tFqMul = func(z, x, y *Fq) tFqSqr = func(z, x *Fq) ) func TestFqOne(t *testing.T) { x := &Fq{} x.setOne() got0, got1 := x.toBigInt() want0, want1 := big.NewInt(1), big.NewInt(0) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x) } } func TestFqSign(t *testing.T) { testTimes := 1 << 9 x := &Fq{} P := getModulus() var P1div2 big.Int P1div2.Add(P, big.NewInt(1)).Rsh(&P1div2, 1) // (p+1)/2 // Verifying Sign(0) = 0 x.setBigInt(big.NewInt(0), big.NewInt(0)) got := fqSgn(x) want := 0 if got != want { test.ReportError(t, got, want, x) } // Verifying Sign(P) = 0 x.setBigInt(P, P) got = fqSgn(x) want = 0 if got != want { test.ReportError(t, got, want, x) } // Verifying Sign( (p+1)/2 ) = -1 x.setBigInt(&P1div2, &P1div2) got = fqSgn(x) want = -1 if got != want { test.ReportError(t, got, want, x) } // Verifying x be a non-zero positive for i := 0; i < testTimes; i++ { bigX1, _ := rand.Int(rand.Reader, &P1div2) x.setBigInt(P, bigX1) got = fqSgn(x) want = 1 if got != want { test.ReportError(t, got, want, x) } } // Verifying x be a non-zero positive for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, &P1div2) bigX1, _ := rand.Int(rand.Reader, &P1div2) x.setBigInt(bigX0, bigX1) got = fqSgn(x) want = 1 if got != want { test.ReportError(t, got, want, x) } } // Verifying x be a non-zero negative for i := 0; i < testTimes; i++ { bigX1, _ := rand.Int(rand.Reader, &P1div2) bigX1.Add(bigX1, &P1div2) x.setBigInt(P, bigX1) got = fqSgn(x) want = -1 if got != want { test.ReportError(t, got, want, x) } } // Verifying x be a non-zero negative for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, &P1div2) bigX1, _ := rand.Int(rand.Reader, &P1div2) bigX0.Add(bigX0, &P1div2) bigX1.Add(bigX1, &P1div2) x.setBigInt(bigX0, bigX1) got = fqSgn(x) want = -1 if got != want { test.ReportError(t, got, want, x) } } } func TestFqIsZero(t *testing.T) { x := &Fq{} P := getModulus() // Verifying x=0 x.setBigInt(big.NewInt(0), big.NewInt(0)) got := x.isZero() want := true if got != want { test.ReportError(t, got, want, x) } // Verifying x=P goes to 0 x.setBigInt(P, P) got = x.isZero() want = true if got != want { test.ReportError(t, got, want, x) } // Verifying x!=0 bigX0, _ := rand.Int(rand.Reader, P) bigX1, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX0, bigX1) got = x.isZero() want = false if got != want { test.ReportError(t, got, want, x) } } func TestFqNeg(t *testing.T) { testTimes := 1 << 9 x, z := &Fq{}, &Fq{} P := getModulus() for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, P) bigX1, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX0, bigX1) fqNeg(z, x) got0, got1 := z.toBigInt() want0 := bigX0.Neg(bigX0) want1 := bigX1.Neg(bigX1) want0 = want0.Mod(want0, P) want1 = want1.Mod(want1, P) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x) } } } func testFqAdd(t *testing.T, f tFqAdd) { testTimes := 1 << 9 x, y, z := &Fq{}, &Fq{}, &Fq{} P := getModulus() for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, P) bigX1, _ := rand.Int(rand.Reader, P) bigY0, _ := rand.Int(rand.Reader, P) bigY1, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX0, bigX1) y.setBigInt(bigY0, bigY1) f(z, x, y) got0, got1 := z.toBigInt() want0 := bigX0.Add(bigX0, bigY0) want1 := bigX1.Add(bigX1, bigY1) want0 = want0.Mod(want0, P) want1 = want1.Mod(want1, P) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, y) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, y) } } } func testFqSub(t *testing.T, f tFqSub) { testTimes := 1 << 9 x, y, z := &Fq{}, &Fq{}, &Fq{} P := getModulus() for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, P) bigX1, _ := rand.Int(rand.Reader, P) bigY0, _ := rand.Int(rand.Reader, P) bigY1, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX0, bigX1) y.setBigInt(bigY0, bigY1) f(z, x, y) got0, got1 := z.toBigInt() want0 := bigX0.Sub(bigX0, bigY0) want1 := bigX1.Sub(bigX1, bigY1) want0 = want0.Mod(want0, P) want1 = want1.Mod(want1, P) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, y) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, y) } } } func testFqMul(t *testing.T, f tFqMul) { testTimes := 1 << 9 x, y, z := &Fq{}, &Fq{}, &Fq{} P := getModulus() for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, P) bigX1, _ := rand.Int(rand.Reader, P) bigY0, _ := rand.Int(rand.Reader, P) bigY1, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX0, bigX1) y.setBigInt(bigY0, bigY1) f(z, x, y) got0, got1 := z.toBigInt() x0y0 := new(big.Int).Mul(bigX0, bigY0) x0y1 := new(big.Int).Mul(bigX0, bigY1) x1y0 := new(big.Int).Mul(bigX1, bigY0) x1y1 := new(big.Int).Mul(bigX1, bigY1) want0 := x0y0.Sub(x0y0, x1y1) want1 := x1y0.Add(x1y0, x0y1) want0 = want0.Mod(want0, P) want1 = want1.Mod(want1, P) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, y) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, y) } } } func testFqSqr(t *testing.T, f tFqSqr) { testTimes := 1 << 9 x, z := &Fq{}, &Fq{} P := getModulus() for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, P) bigX1, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX0, bigX1) f(z, x) got0, got1 := z.toBigInt() x0x0 := new(big.Int).Mul(bigX0, bigX0) x0x1 := new(big.Int).Mul(bigX0, bigX1) x1x1 := new(big.Int).Mul(bigX1, bigX1) want0 := x0x0.Sub(x0x0, x1x1) want1 := x0x1.Lsh(x0x1, 1) want0 = want0.Mod(want0, P) want1 = want1.Mod(want1, P) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x) } } } func TestFqInv(t *testing.T) { testTimes := 1 << 9 x, z := &Fq{}, &Fq{} P := getModulus() for i := 0; i < testTimes; i++ { bigX0, _ := rand.Int(rand.Reader, P) bigX1, _ := rand.Int(rand.Reader, P) x.setBigInt(bigX0, bigX1) fqInv(z, x) got0, got1 := z.toBigInt() x0x0 := new(big.Int).Mul(bigX0, bigX0) x1x1 := new(big.Int).Mul(bigX1, bigX1) inv := x0x0.Add(x0x0, x1x1) inv.ModInverse(inv, P) want0 := bigX0.Mul(bigX0, inv) want1 := bigX1.Mul(bigX1, inv).Neg(bigX1) want0 = want0.Mod(want0, P) want1 = want1.Mod(want1, P) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x) } } } func TestFqGeneric(t *testing.T) { t.Run("Add", func(t *testing.T) { testFqAdd(t, fqAddGeneric) }) t.Run("Sub", func(t *testing.T) { testFqSub(t, fqSubGeneric) }) t.Run("Mul", func(t *testing.T) { testFqMul(t, fqMulGeneric) }) t.Run("Sqr", func(t *testing.T) { testFqSqr(t, fqSqrGeneric) }) } func TestFqNative(t *testing.T) { t.Run("Add", func(t *testing.T) { testFqAdd(t, fqAdd) }) t.Run("Sub", func(t *testing.T) { testFqSub(t, fqSub) }) t.Run("Mul", func(t *testing.T) { testFqMul(t, fqMul) }) t.Run("Sqr", func(t *testing.T) { testFqSqr(t, fqSqr) }) } func BenchmarkFq(b *testing.B) { x, y, z := &Fq{}, &Fq{}, &Fq{} b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { fqAdd(z, x, y) } }) b.Run("Sub", func(b *testing.B) { for i := 0; i < b.N; i++ { fqSub(z, x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { fqMul(z, x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { fqSqr(z, x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { fqInv(z, x) } }) b.Run("Sqrt", func(b *testing.B) { for i := 0; i < b.N; i++ { fqSqrt(z, x, y, 1) } }) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/params.go000066400000000000000000000020361454601126700231700ustar00rootroot00000000000000package fourq // All values in little endian var ( // prime is the modulus 2^127-1 prime = [2]uint64{ 0xFFFFFFFFFFFFFFFF, 0x7FFFFFFFFFFFFFFF, } // orderGenerator is the size of the largest subgroup. orderGenerator = [4]uint64{ 0x2fb2540ec7768ce7, 0xdfbd004dfe0f7999, 0xf05397829cbc14e5, 0x0029cbc14e5e0a72, } paramD = Fq{ Fp{ 0x42, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe4, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, }, Fp{ 0x8d, 0x0c, 0xfc, 0xf1, 0x88, 0x14, 0x82, 0xb3, 0xfc, 0xe0, 0x57, 0x66, 0x84, 0x2f, 0x47, 0x5e, }, } genX = Fq{ Fp{ 0xaa, 0x33, 0x38, 0x7b, 0xad, 0x92, 0x65, 0x28, 0x05, 0xb3, 0x2f, 0x7c, 0x23, 0x72, 0x34, 0x1a, }, Fp{ 0xf6, 0x77, 0xac, 0x60, 0xb3, 0x9f, 0x86, 0x96, 0x9c, 0xaa, 0x78, 0x28, 0x3f, 0x55, 0x1f, 0x1e, }, } genY = Fq{ Fp{ 0x87, 0xb2, 0xcb, 0x2b, 0x46, 0xa2, 0x24, 0xb9, 0x5a, 0x78, 0x20, 0xa1, 0x9b, 0xee, 0x3f, 0x0e, }, Fp{ 0x5c, 0x8b, 0x4c, 0x84, 0x44, 0xc3, 0xa7, 0x49, 0x42, 0x02, 0x0e, 0x63, 0xf8, 0x4a, 0x1c, 0x6e, }, } ) golang-github-cloudflare-circl-1.3.7/ecc/fourq/point.go000066400000000000000000000172221454601126700230410ustar00rootroot00000000000000package fourq import ( "crypto/subtle" "encoding/binary" "math/bits" ) type pointR1 struct { X, Y, Z, Ta, Tb Fq // (x,y,z,t=ta*tb) } type pointR3 struct { addYX Fq // y + x subYX Fq // y - x dt2 Fq // 2*d*t } type pointR2 struct { pointR3 z2 Fq // 2 * z } // subYDiv16 update x = (x - y) / 16. func subYDiv16(x *[5]uint64, y int64) { s := uint64(y >> 63) x0, b0 := bits.Sub64((*x)[0], uint64(y), 0) x1, b1 := bits.Sub64((*x)[1], s, b0) x2, b2 := bits.Sub64((*x)[2], s, b1) x3, b3 := bits.Sub64((*x)[3], s, b2) x4, _ := bits.Sub64((*x)[4], s, b3) (*x)[0] = (x0 >> 4) | (x1 << 60) (*x)[1] = (x1 >> 4) | (x2 << 60) (*x)[2] = (x2 >> 4) | (x3 << 60) (*x)[3] = (x3 >> 4) | (x4 << 60) (*x)[4] = (x4 >> 4) } // condAddOrderN updates x = x+order if x is even, otherwise x remains unchanged. func condAddOrderN(x *[5]uint64) { var o [4]uint64 isOdd := (x[0] & 0x1) - 1 for i := range orderGenerator { o[i] = isOdd & orderGenerator[i] } x0, c0 := bits.Add64((*x)[0], o[0], 0) x1, c1 := bits.Add64((*x)[1], o[1], c0) x2, c2 := bits.Add64((*x)[2], o[2], c1) x3, c3 := bits.Add64((*x)[3], o[3], c2) x4, _ := bits.Add64((*x)[4], 0, c3) (*x)[0] = x0 (*x)[1] = x1 (*x)[2] = x2 (*x)[3] = x3 (*x)[4] = x4 } func recodeScalar(d *[65]int8, k *[32]byte) { var m [5]uint64 m[0] = binary.LittleEndian.Uint64(k[0:8]) m[1] = binary.LittleEndian.Uint64(k[8:16]) m[2] = binary.LittleEndian.Uint64(k[16:24]) m[3] = binary.LittleEndian.Uint64(k[24:32]) condAddOrderN(&m) for i := 0; i < 64; i++ { d[i] = int8((m[0] & 0x1f) - 16) subYDiv16(&m, int64(d[i])) } d[64] = int8(m[0]) } func (P *pointR1) oddMultiples(T *[8]pointR2) { var _2P, R pointR1 var _p2P pointR2 _2P.copy(P) _2P.double() _p2P.FromR1(&_2P) R.copy(P) T[0].FromR1(P) for i := 1; i < 8; i++ { R.add(&_p2P) T[i].FromR1(&R) } } // scalarMult calculates P = k*Q. func (P *pointR1) ScalarMult(k *[32]byte, Q *pointR1) { var TabQ [8]pointR2 var S pointR2 var d [65]int8 Q.oddMultiples(&TabQ) recodeScalar(&d, k) P.SetIdentity() for i := 64; i >= 0; i-- { P.double() P.double() P.double() P.double() mask := d[i] >> 7 absDi := (d[i] + mask) ^ mask inx := int((absDi - 1) >> 1) sig := int((d[i] >> 7) & 0x1) for j := range TabQ { S.cmov(&TabQ[j], int((uint64(uint32(inx^j))-1)>>63)) } S.cneg(sig) P.add(&S) } } // absolute returns always a positive value. func absolute(x int32) int32 { mask := x >> 31 return (x + mask) ^ mask } // div2subY update x = (x/2) - y. func div2subY(x *[5]uint64, y int64) { s := uint64(y >> 63) x0 := (*x)[0] x1 := (*x)[1] x2 := (*x)[2] x3 := (*x)[3] x0 = (x0 >> 1) | (x1 << 63) x1 = (x1 >> 1) | (x2 << 63) x2 = (x2 >> 1) | (x3 << 63) x3 = (x3 >> 1) x0, b0 := bits.Sub64(x0, uint64(y), 0) x1, b1 := bits.Sub64(x1, s, b0) x2, b2 := bits.Sub64(x2, s, b1) x3, _ = bits.Sub64(x3, s, b2) (*x)[0] = x0 (*x)[1] = x1 (*x)[2] = x2 (*x)[3] = x3 } // mLSBRecoding is the odd-only modified LSB-set. // // Reference: // // "Efficient and secure algorithms for GLV-based scalar multiplication and // their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) // http://doi.org/10.1007/s13389-014-0085-7. func mLSBRecoding(L []int8, k []byte) { const e = (fxT + fxW*fxV - 1) / (fxW * fxV) const d = e * fxV const l = d * fxW if len(L) == (l + 1) { var m [5]uint64 m[0] = binary.LittleEndian.Uint64(k[0:8]) m[1] = binary.LittleEndian.Uint64(k[8:16]) m[2] = binary.LittleEndian.Uint64(k[16:24]) m[3] = binary.LittleEndian.Uint64(k[24:32]) condAddOrderN(&m) L[d-1] = 1 for i := 0; i < d-1; i++ { kip1 := (m[(i+1)/64] >> (uint(i+1) % 64)) & 0x1 L[i] = int8(kip1<<1) - 1 } { // right-shift by d const right = (d % 64) const left = 64 - (d % 64) const lim = (5*64 - d) / 64 const j = d / 64 for i := 0; i < lim; i++ { m[i] = (m[i+j] >> right) | (m[i+j+1] << left) } m[lim] = m[lim+j] >> right } for i := d; i < l; i++ { L[i] = L[i%d] * int8(m[0]&0x1) div2subY(&m, int64(L[i]>>1)) } L[l] = int8(m[0]) } } func (P *pointR1) ScalarBaseMult(scalar *[Size]byte) { var S pointR3 const e = (fxT + fxW*fxV - 1) / (fxW * fxV) const d = e * fxV const l = d * fxW var L [l + 1]int8 mLSBRecoding(L[:], scalar[:]) P.SetIdentity() for ii := e - 1; ii >= 0; ii-- { P.double() for j := 0; j < fxV; j++ { dig := L[fxW*d-j*e+ii-e] for i := (fxW-1)*d - j*e + ii - e; i >= (2*d - j*e + ii - e); i = i - d { dig = 2*dig + L[i] } idx := absolute(int32(dig)) sig := L[d-j*e+ii-e] Tabj := &tableBaseFixed[fxV-j-1] for k := 0; k < fx2w1; k++ { S.cmov(&Tabj[k], subtle.ConstantTimeEq(int32(k), idx)) } S.cneg(subtle.ConstantTimeEq(int32(sig), -1)) P.mixAdd(&S) } } } func (P *pointR1) copy(Q *pointR1) { fqCopy(&P.X, &Q.X) fqCopy(&P.Y, &Q.Y) fqCopy(&P.Ta, &Q.Ta) fqCopy(&P.Tb, &Q.Tb) fqCopy(&P.Z, &Q.Z) } func (P *pointR1) SetIdentity() { P.X.setZero() P.Y.setOne() P.Ta.setZero() P.Tb.setZero() P.Z.setOne() } func (P *pointR1) IsIdentity() bool { t0, t1 := &Fq{}, &Fq{} fqMul(t0, &P.Ta, &P.Tb) fqSub(t1, &P.Y, &P.Z) return P.X.isZero() && t0.isZero() && t1.isZero() } func (P *pointR1) ToAffine() { fqInv(&P.Z, &P.Z) fqMul(&P.X, &P.X, &P.Z) fqMul(&P.Y, &P.Y, &P.Z) fqMul(&P.Ta, &P.X, &P.Y) P.Tb.setOne() P.Z.setOne() } // Marshal encodes a point P into out buffer. func (P *Point) Marshal(out *[Size]byte) { P.Y.toBytes(out[:]) // b=0 if x is positive or zero // b=1 if x is negative b := (1 - fqSgn(&P.X)) >> 1 out[Size-1] |= byte(b) << 7 } // Unmarshal retrieves a point P from the input buffer. On success, returns true. func (P *Point) Unmarshal(in *[Size]byte) bool { s := in[Size-1] >> 7 in[Size-1] &= 0x7F if ok := P.Y.fromBytes(in[:]); !ok { return ok } in[Size-1] |= s << 7 t0, t1, one := &Fq{}, &Fq{}, &Fq{} one.setOne() fqSqr(t0, &P.Y) // t0 = y^2 fqMul(t1, t0, ¶mD) // t1 = d*y^2 fqSub(t0, t0, one) // t0 = y^2 - 1 fqAdd(t1, t1, one) // t1 = d*y^2 + 1 fqSqrt(&P.X, t0, t1, 1-2*int(s)) // x = sqrt(t0/t1) if !P.IsOnCurve() { fpNeg(&P.X[1], &P.X[1]) } return true } func (P *pointR1) IsOnCurve() bool { t0, lhs, rhs := &Fq{}, &Fq{}, &Fq{} fqAdd(t0, &P.Y, &P.X) // t0 = y + x fqSub(lhs, &P.Y, &P.X) // lhs = y - x fqMul(lhs, lhs, t0) // lhs = y^2 - x^2 fqMul(rhs, &P.X, &P.Y) // rhs = xy fqSqr(rhs, rhs) // rhs = x^2y^2 fqMul(rhs, rhs, ¶mD) // rhs = dx^2y^2 t0.setOne() // t0 = 1 fqAdd(rhs, rhs, t0) // rhs = 1 + dx^2y^2 fqSub(t0, lhs, rhs) // t0 = -x^2 + y^2 - (1 + dx^2y^2) return t0.isZero() } func (P *pointR1) isEqual(Q *pointR1) bool { l, r := &Fq{}, &Fq{} fqMul(l, &P.X, &Q.Z) fqMul(r, &Q.X, &P.Z) fqSub(l, l, r) b := l.isZero() fqMul(l, &P.Y, &Q.Z) fqMul(r, &Q.Y, &P.Z) fqSub(l, l, r) b = b && l.isZero() fqMul(l, &P.Ta, &P.Tb) fqMul(l, l, &Q.Z) fqMul(r, &Q.Ta, &Q.Tb) fqMul(r, r, &P.Z) fqSub(l, l, r) b = b && l.isZero() return b } func (P *pointR1) ClearCofactor() { var Q pointR2 Q.FromR1(P) P.double() P.add(&Q) P.double() P.double() P.double() P.double() P.add(&Q) P.double() P.double() P.double() } func (P *pointR2) FromR1(Q *pointR1) { fqAdd(&P.addYX, &Q.Y, &Q.X) fqSub(&P.subYX, &Q.Y, &Q.X) fqAdd(&P.z2, &Q.Z, &Q.Z) fqMul(&P.dt2, &Q.Ta, &Q.Tb) fqMul(&P.dt2, &P.dt2, ¶mD) fqAdd(&P.dt2, &P.dt2, &P.dt2) } func (P *pointR2) cmov(Q *pointR2, b int) { P.pointR3.cmov(&Q.pointR3, b) fqCmov(&P.z2, &Q.z2, b) } func (P *pointR3) cneg(b int) { var t Fq fqCopy(&t, &P.addYX) fqCmov(&P.addYX, &P.subYX, b) fqCmov(&P.subYX, &t, b) fqNeg(&t, &P.dt2) fqCmov(&P.dt2, &t, b) } func (P *pointR3) cmov(Q *pointR3, b int) { fqCmov(&P.addYX, &Q.addYX, b) fqCmov(&P.subYX, &Q.subYX, b) fqCmov(&P.dt2, &Q.dt2, b) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/point_amd64.go000066400000000000000000000021011454601126700240220ustar00rootroot00000000000000//go:build amd64 && !purego // +build amd64,!purego package fourq import "unsafe" const ( // constants used in assembly implementation _x = unsafe.Offsetof(pointR1{}.X) _y = unsafe.Offsetof(pointR1{}.Y) _z = unsafe.Offsetof(pointR1{}.Z) _ta = unsafe.Offsetof(pointR1{}.Ta) _tb = unsafe.Offsetof(pointR1{}.Tb) _addYXR2 = unsafe.Offsetof(pointR2{}.addYX) _subYXR2 = unsafe.Offsetof(pointR2{}.subYX) _z2R2 = unsafe.Offsetof(pointR2{}.z2) _dt2R2 = unsafe.Offsetof(pointR2{}.dt2) _addYXR3 = unsafe.Offsetof(pointR3{}.addYX) _subYXR3 = unsafe.Offsetof(pointR3{}.subYX) _dt2R3 = unsafe.Offsetof(pointR3{}.dt2) _ = _x + _y + _z + _ta + _tb + _addYXR2 + _subYXR2 + _z2R2 + _dt2R2 + _addYXR3 + _subYXR3 + _dt2R3 ) func (P *pointR1) double() { doubleAmd64(P) } func (P *pointR1) add(Q *pointR2) { addAmd64(P, Q) } func (P *pointR1) mixAdd(Q *pointR3) { mixAddAmd64(P, Q) } //go:noescape func doubleAmd64(P *pointR1) //go:noescape func addAmd64(P *pointR1, Q *pointR2) //go:noescape func mixAddAmd64(P *pointR1, Q *pointR3) golang-github-cloudflare-circl-1.3.7/ecc/fourq/point_amd64.h000066400000000000000000000046051454601126700236570ustar00rootroot00000000000000#define doubleLeg \ _fqAdd(e,Px,Py) \ _fqSqrLeg(a,Px) \ _fqSqrLeg(b,Py) \ _fqSqrLeg(c,Pz) \ _fqAdd(c,c,c) \ _fqAdd(d,a,b) \ _fqSqrLeg(e,e) \ _fqSub(e,e,d) \ _fqSub(f,b,a) \ _fqSub(g,c,f) \ _fqMulLeg(Pz,f,g) \ _fqMulLeg(Px,e,g) \ _fqMulLeg(Py,d,f) #define doubleBmi2 \ _fqAdd(e,Px,Py) \ _fqSqrBmi2(a,Px) \ _fqSqrBmi2(b,Py) \ _fqSqrBmi2(c,Pz) \ _fqAdd(c,c,c) \ _fqAdd(d,a,b) \ _fqSqrBmi2(e,e) \ _fqSub(e,e,d) \ _fqSub(f,b,a) \ _fqSub(g,c,f) \ _fqMulBmi2(Pz,f,g) \ _fqMulBmi2(Px,e,g) \ _fqMulBmi2(Py,d,f) #define addLeg \ _fqMulLeg(c, Pta, Ptb) \ _fqSub(h, b, a) \ _fqAdd(b, b, a) \ _fqMulLeg(a, h, subYX) \ _fqMulLeg(b, b, addYX) \ _fqSub(e, b, a) \ _fqAdd(h, b, a) \ _fqMulLeg(d, Pz, z2) \ _fqMulLeg(c, c, dt2) \ _fqSub(f, d, c) \ _fqAdd(g, d, c) \ _fqMulLeg(Pz, f, g) \ _fqMulLeg(Px, e, f) \ _fqMulLeg(Py, g, h) #define addBmi2 \ _fqMulBmi2(c, Pta, Ptb) \ _fqSub(h, b, a) \ _fqAdd(b, b, a) \ _fqMulBmi2(a, h, subYX) \ _fqMulBmi2(b, b, addYX) \ _fqSub(e, b, a) \ _fqAdd(h, b, a) \ _fqMulBmi2(d, Pz, z2) \ _fqMulBmi2(c, c, dt2) \ _fqSub(f, d, c) \ _fqAdd(g, d, c) \ _fqMulBmi2(Pz, f, g) \ _fqMulBmi2(Px, e, f) \ _fqMulBmi2(Py, g, h) #define mixAddLeg \ _fqMulLeg(c, Pta, Ptb) \ _fqSub(h, b, a) \ _fqAdd(b, b, a) \ _fqMulLeg(a, h, subYX) \ _fqMulLeg(b, b, addYX) \ _fqSub(e, b, a) \ _fqAdd(h, b, a) \ _fqAdd(d, Pz, Pz) \ _fqMulLeg(c, c, dt2) \ _fqSub(f, d, c) \ _fqAdd(g, d, c) \ _fqMulLeg(Pz, f, g) \ _fqMulLeg(Px, e, f) \ _fqMulLeg(Py, g, h) #define mixAddBmi2 \ _fqMulBmi2(c, Pta, Ptb) \ _fqSub(h, b, a) \ _fqAdd(b, b, a) \ _fqMulBmi2(a, h, subYX) \ _fqMulBmi2(b, b, addYX) \ _fqSub(e, b, a) \ _fqAdd(h, b, a) \ _fqAdd(d, Pz, Pz) \ _fqMulBmi2(c, c, dt2) \ _fqSub(f, d, c) \ _fqAdd(g, d, c) \ _fqMulBmi2(Pz, f, g) \ _fqMulBmi2(Px, e, f) \ _fqMulBmi2(Py, g, h) golang-github-cloudflare-circl-1.3.7/ecc/fourq/point_amd64.s000066400000000000000000000044411454601126700236700ustar00rootroot00000000000000// +build amd64,!purego #include "go_asm.h" #include "fq_amd64.h" #include "point_amd64.h" // func doubleAmd64(P *pointR1) TEXT ·doubleAmd64(SB),0,$0-8 MOVQ P+0(FP), DI #define Px const__x +0(DI) #define Py const__y +0(DI) #define Pz const__z +0(DI) #define Pta const__ta+0(DI) #define Ptb const__tb+0(DI) #define a Px #define b Py #define c Pz #define d Pta #define e Ptb #define f b #define g a CHECK_BMI2(LDOUBLE, doubleLeg, doubleBmi2) #undef Px #undef Py #undef Pz #undef Pta #undef Ptb #undef a #undef b #undef c #undef d #undef e #undef f #undef g // func addAmd64(P *pointR1, R *pointR2) TEXT ·addAmd64(SB),0,$32-16 MOVQ P+0(FP), DI MOVQ Q+8(FP), SI #define addYX const__addYXR2+0(SI) #define subYX const__subYXR2+0(SI) #define z2 const__z2R2 +0(SI) #define dt2 const__dt2R2 +0(SI) #define Px const__x +0(DI) #define Py const__y +0(DI) #define Pz const__z +0(DI) #define Pta const__ta+0(DI) #define Ptb const__tb+0(DI) #define a Px #define b Py #define c 0(SP) #define d b #define e Pta #define f a #define g b #define h Ptb CHECK_BMI2(LDADD, addLeg, addBmi2) #undef addYX #undef subYX #undef z2 #undef dt2 #undef Px #undef Py #undef Pz #undef Pta #undef Ptb #undef a #undef b #undef c #undef d #undef e #undef f #undef g #undef h // func mixAddAmd64(P *pointR1, Q *pointR3) TEXT ·mixAddAmd64(SB),0,$32-16 MOVQ P+0(FP), DI MOVQ Q+8(FP), SI #define addYX const__addYXR3+0(SI) #define subYX const__subYXR3+0(SI) #define dt2 const__dt2R3 +0(SI) #define Px const__x +0(DI) #define Py const__y +0(DI) #define Pz const__z +0(DI) #define Pta const__ta+0(DI) #define Ptb const__tb+0(DI) #define a Px #define b Py #define c 0(SP) #define d b #define e Pta #define f a #define g b #define h Ptb CHECK_BMI2(LDMIXADD, mixAddLeg, mixAddBmi2) #undef addYX #undef subYX #undef dt2 #undef Px #undef Py #undef Pz #undef Pta #undef Ptb #undef a #undef b #undef c #undef d #undef e #undef f #undef g #undef h golang-github-cloudflare-circl-1.3.7/ecc/fourq/point_generic.go000066400000000000000000000026001454601126700245270ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package fourq func doubleGeneric(P *pointR1) { Px := &P.X Py := &P.Y Pz := &P.Z Pta := &P.Ta Ptb := &P.Tb a := Px b := Py c := Pz d := Pta e := Ptb f := b g := a fqAdd(e, Px, Py) fqSqr(a, Px) fqSqr(b, Py) fqSqr(c, Pz) fqAdd(c, c, c) fqAdd(d, a, b) fqSqr(e, e) fqSub(e, e, d) fqSub(f, b, a) fqSub(g, c, f) fqMul(Pz, f, g) fqMul(Px, e, g) fqMul(Py, d, f) } func addGeneric(P *pointR1, Q *pointR2) { addYX := &Q.addYX subYX := &Q.subYX z2 := &Q.z2 dt2 := &Q.dt2 Px := &P.X Py := &P.Y Pz := &P.Z Pta := &P.Ta Ptb := &P.Tb a := Px b := Py c := &Fq{} d := b e := Pta f := a g := b h := Ptb fqMul(c, Pta, Ptb) fqSub(h, b, a) fqAdd(b, b, a) fqMul(a, h, subYX) fqMul(b, b, addYX) fqSub(e, b, a) fqAdd(h, b, a) fqMul(d, Pz, z2) fqMul(c, c, dt2) fqSub(f, d, c) fqAdd(g, d, c) fqMul(Pz, f, g) fqMul(Px, e, f) fqMul(Py, g, h) } func mixAddGeneric(P *pointR1, Q *pointR3) { addYX := &Q.addYX subYX := &Q.subYX dt2 := &Q.dt2 Px := &P.X Py := &P.Y Pz := &P.Z Pta := &P.Ta Ptb := &P.Tb a := Px b := Py c := &Fq{} d := b e := Pta f := a g := b h := Ptb fqMul(c, Pta, Ptb) fqSub(h, b, a) fqAdd(b, b, a) fqMul(a, h, subYX) fqMul(b, b, addYX) fqSub(e, b, a) fqAdd(h, b, a) fqAdd(d, Pz, Pz) fqMul(c, c, dt2) fqSub(f, d, c) fqAdd(g, d, c) fqMul(Pz, f, g) fqMul(Px, e, f) fqMul(Py, g, h) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/point_noasm.go000066400000000000000000000003651454601126700242360ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package fourq func (P *pointR1) double() { doubleGeneric(P) } func (P *pointR1) add(Q *pointR2) { addGeneric(P, Q) } func (P *pointR1) mixAdd(Q *pointR3) { mixAddGeneric(P, Q) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/point_test.go000066400000000000000000000116451454601126700241030ustar00rootroot00000000000000package fourq import ( "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" ) func (P *pointR1) random() { var k [Size]byte _, _ = rand.Read(k[:]) P.ScalarBaseMult(&k) } func TestPointAddition(t *testing.T) { const testTimes = 1 << 10 var P, Q pointR1 _16P := &pointR1{} S := &pointR2{} for i := 0; i < testTimes; i++ { P.random() _16P.copy(&P) S.FromR1(&P) // 16P = 2^4P for j := 0; j < 4; j++ { _16P.double() } // 16P = P+P...+P Q.SetIdentity() for j := 0; j < 16; j++ { Q.add(S) } got := _16P.isEqual(&Q) want := true if got != want { test.ReportError(t, got, want, P) } } } func TestOddMultiples(t *testing.T) { const testTimes = 1 << 10 var P, Q, R pointR1 var Tab [8]pointR2 for i := 0; i < testTimes; i++ { P.random() // T = [1P, 3P, 5P, 7P, 9P, 11P, 13P, 15P] P.oddMultiples(&Tab) // Q = sum of all T[i] == 64P Q.SetIdentity() for j := range Tab { Q.add(&Tab[j]) } // R = (2^6)P == 64P for j := 0; j < 6; j++ { R.double() } got := Q.isEqual(&R) want := true if got != want { test.ReportError(t, got, want, P) } } } func TestScalarMult(t *testing.T) { const testTimes = 1 << 10 var P, Q, G pointR1 var k [Size]byte t.Run("0P=0", func(t *testing.T) { for i := 0; i < testTimes; i++ { P.random() Q.ScalarMult(&k, &P) got := Q.IsIdentity() want := true if got != want { test.ReportError(t, got, want, P) } } }) t.Run("order*P=0", func(t *testing.T) { conv.BigInt2BytesLe(k[:], conv.Uint64Le2BigInt(orderGenerator[:])) for i := 0; i < testTimes; i++ { P.random() Q.ScalarMult(&k, &P) got := Q.IsIdentity() want := true if got != want { test.ReportError(t, got, want, P) } } }) t.Run("cofactor*P=clear(P)", func(t *testing.T) { conv.BigInt2BytesLe(k[:], big.NewInt(392)) for i := 0; i < testTimes; i++ { P.random() Q.ScalarMult(&k, &P) P.ClearCofactor() got := Q.isEqual(&P) want := true if got != want { test.ReportError(t, got, want, P) } } }) t.Run("mult", func(t *testing.T) { G.X = genX G.Y = genY for i := 0; i < testTimes; i++ { _, _ = rand.Read(k[:]) P.ScalarMult(&k, &G) Q.ScalarBaseMult(&k) got := Q.isEqual(&P) want := true if got != want { test.ReportError(t, got, want, k) } } }) } func TestScalar(t *testing.T) { const testTimes = 1 << 12 var xx [5]uint64 two256 := big.NewInt(1) two256.Lsh(two256, 256) two64 := big.NewInt(1) two64.Lsh(two64, 64) bigOrder := conv.Uint64Le2BigInt(orderGenerator[:]) t.Run("subYdiv16", func(t *testing.T) { want := new(big.Int) for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, two256) conv.BigInt2Uint64Le(xx[:], bigX) x := xx bigY, _ := rand.Int(rand.Reader, two64) y := bigY.Int64() bigY.SetInt64(y) subYDiv16(&x, y) got := conv.Uint64Le2BigInt(x[:]) want.Sub(bigX, bigY).Rsh(want, 4) if got.Cmp(want) != 0 { test.ReportError(t, got, want, bigX, y) } } }) t.Run("div2subY", func(t *testing.T) { want := new(big.Int) for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, two256) conv.BigInt2Uint64Le(xx[:], bigX) x := xx bigY, _ := rand.Int(rand.Reader, two64) y := bigY.Int64() bigY.SetInt64(y) div2subY(&x, y) got := conv.Uint64Le2BigInt(x[:]) want.Rsh(bigX, 1).Sub(want, bigY) if got.Cmp(want) != 0 { test.ReportError(t, got, want, bigX, y) } } }) t.Run("condAddOrderN", func(t *testing.T) { for i := 0; i < testTimes; i++ { bigX, _ := rand.Int(rand.Reader, two256) conv.BigInt2Uint64Le(xx[:], bigX) x := xx condAddOrderN(&x) got := conv.Uint64Le2BigInt(x[:]) want := bigX if want.Bit(0) == 0 { want.Add(want, bigOrder) } if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } }) t.Run("recode", func(t *testing.T) { var k [32]byte var d [65]int8 got := new(big.Int) for i := 0; i < testTimes; i++ { _, _ = rand.Read(k[:]) recodeScalar(&d, &k) got.SetInt64(0) for j := len(d) - 1; j >= 0; j-- { got.Lsh(got, 4).Add(got, big.NewInt(int64(d[j]))) } want := conv.BytesLe2BigInt(k[:]) if want.Bit(0) == 0 { want.Add(want, bigOrder) } if got.Cmp(want) != 0 { test.ReportError(t, got, want, k) } } }) } func BenchmarkPoint(b *testing.B) { var P, R pointR1 var Q pointR2 var k [Size]byte _, _ = rand.Read(k[:]) P.random() R.random() Q.FromR1(&R) R.random() b.Run("affine", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ToAffine() } }) b.Run("double", func(b *testing.B) { for i := 0; i < b.N; i++ { P.double() } }) b.Run("add", func(b *testing.B) { for i := 0; i < b.N; i++ { P.add(&Q) } }) b.Run("scmulBase", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ScalarBaseMult(&k) } }) b.Run("scmul", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ScalarMult(&k, &R) } }) } golang-github-cloudflare-circl-1.3.7/ecc/fourq/tableBase.go000066400000000000000000000142161454601126700235720ustar00rootroot00000000000000package fourq const ( // This is the size of the largest scalar k = 2^256 - 1 + order fxT = 257 // Number of tables fxV = 2 // Window size fxW = 3 // Number of points per table fx2w1 = (1 << (uint(fxW) - 1)) ) var tableBaseFixed = [fxV][fx2w1]pointR3{ { { addYX: Fq{ [SizeFp]byte{0x31, 0xe6, 0x03, 0xa7, 0xf3, 0x34, 0x8a, 0xe1, 0x5f, 0x2b, 0x50, 0x1d, 0xbf, 0x60, 0x74, 0x28}, [SizeFp]byte{0x53, 0x03, 0xf9, 0xe4, 0xf7, 0x62, 0x2e, 0xe0, 0xde, 0xac, 0x86, 0x8b, 0x37, 0xa0, 0x3b, 0x0c}, }, subYX: Fq{ [SizeFp]byte{0xdc, 0x7e, 0x93, 0xb0, 0x98, 0x0f, 0xbf, 0x90, 0x55, 0xc5, 0xf0, 0x24, 0x78, 0x7c, 0x0b, 0x74}, [SizeFp]byte{0x66, 0x13, 0xa0, 0x23, 0x91, 0x23, 0x21, 0xb3, 0xa5, 0x57, 0x95, 0x3a, 0xb9, 0xf5, 0xfc, 0x4f}, }, dt2: Fq{ [SizeFp]byte{0xbb, 0x42, 0xda, 0xab, 0xcb, 0xfc, 0x7a, 0x29, 0xc6, 0x97, 0x6c, 0x55, 0x37, 0xd1, 0x48, 0x59}, [SizeFp]byte{0x4c, 0x68, 0x30, 0x33, 0x39, 0x9a, 0x18, 0xa8, 0x27, 0x1f, 0x34, 0x0a, 0x72, 0x2b, 0xaf, 0x0c}, }, }, { addYX: Fq{ [SizeFp]byte{0x6a, 0x23, 0x5d, 0xcf, 0x2e, 0xf2, 0x8b, 0x5f, 0x5a, 0x2a, 0x6f, 0xa0, 0xef, 0xa7, 0x76, 0x32}, [SizeFp]byte{0x57, 0xad, 0x0b, 0x1a, 0x60, 0xc4, 0x43, 0xdf, 0x6a, 0xbc, 0x31, 0xe6, 0x55, 0xd5, 0xc4, 0x4b}, }, subYX: Fq{ [SizeFp]byte{0xf7, 0xab, 0xbf, 0xd2, 0x55, 0x8c, 0x13, 0xfe, 0xca, 0x64, 0x65, 0x03, 0xa9, 0x93, 0x29, 0x64}, [SizeFp]byte{0xb5, 0x9b, 0xdd, 0x17, 0xb1, 0x5a, 0x0e, 0xbc, 0x22, 0x41, 0x77, 0x11, 0x25, 0x6f, 0xa1, 0x68}, }, dt2: Fq{ [SizeFp]byte{0xb6, 0x76, 0xfe, 0x14, 0xa1, 0x31, 0x4e, 0xc8, 0xc4, 0x5f, 0x2c, 0x8d, 0x05, 0x23, 0xa8, 0x16}, [SizeFp]byte{0x9d, 0x45, 0x6d, 0x97, 0xd7, 0x0a, 0x22, 0x5a, 0x7a, 0x71, 0x2c, 0x06, 0x6d, 0xeb, 0x9a, 0x7d}, }, }, { addYX: Fq{ [SizeFp]byte{0x46, 0x6b, 0x69, 0xeb, 0x7f, 0x13, 0x9a, 0x2b, 0x40, 0x0a, 0xc1, 0xdc, 0xfa, 0x66, 0xf0, 0x39}, [SizeFp]byte{0x77, 0x9c, 0xd9, 0x0a, 0x0e, 0x65, 0xb3, 0xc6, 0xbd, 0x1d, 0x7f, 0xe0, 0xf8, 0x5a, 0x4f, 0x55}, }, subYX: Fq{ [SizeFp]byte{0xc1, 0x88, 0xb5, 0x09, 0xd0, 0xc5, 0x63, 0x62, 0x8e, 0x0e, 0x6b, 0xeb, 0xfd, 0x49, 0x27, 0x7a}, [SizeFp]byte{0x8c, 0x38, 0x5e, 0x06, 0x05, 0x17, 0x5e, 0xe4, 0x2f, 0xda, 0x4b, 0x9f, 0x94, 0x68, 0x4d, 0x5b}, }, dt2: Fq{ [SizeFp]byte{0x6f, 0x84, 0xf3, 0x3f, 0x08, 0x26, 0x0c, 0xb4, 0xfa, 0xc7, 0x9e, 0xe6, 0x2f, 0xef, 0x3f, 0x53}, [SizeFp]byte{0x47, 0xd1, 0x71, 0x88, 0x9d, 0x2e, 0xcd, 0x4e, 0x94, 0x03, 0x49, 0xbe, 0x0b, 0x1a, 0x91, 0x6d}, }, }, { addYX: Fq{ [SizeFp]byte{0x73, 0x9b, 0x3b, 0x99, 0x69, 0x39, 0x8c, 0xda, 0xf2, 0x3d, 0xba, 0xad, 0x7c, 0x75, 0xeb, 0x26}, [SizeFp]byte{0x18, 0x56, 0xe6, 0xa9, 0xa4, 0x10, 0xf3, 0x13, 0x33, 0x25, 0x04, 0x60, 0x2a, 0x00, 0x62, 0x18}, }, subYX: Fq{ [SizeFp]byte{0x6d, 0xcd, 0x87, 0xca, 0xce, 0xd1, 0xda, 0xb4, 0x5f, 0xd9, 0x0c, 0x21, 0x45, 0x3d, 0xf4, 0x38}, [SizeFp]byte{0xc1, 0xe5, 0x03, 0xa6, 0x64, 0x57, 0x30, 0x13, 0xc7, 0xf8, 0xaa, 0xf2, 0xcd, 0x8f, 0x57, 0x6e}, }, dt2: Fq{ [SizeFp]byte{0x05, 0x02, 0xcb, 0x13, 0xd6, 0x24, 0xa0, 0x20, 0xa9, 0xe0, 0xe0, 0xdd, 0x90, 0x6f, 0xd0, 0x7c}, [SizeFp]byte{0xfc, 0x91, 0x59, 0x14, 0x5b, 0xa4, 0x8e, 0xf5, 0xe1, 0xc0, 0x4c, 0x82, 0xce, 0xe2, 0xf6, 0x41}, }, }, }, { { addYX: Fq{ [SizeFp]byte{0x60, 0x31, 0xb8, 0xc2, 0xb0, 0x7f, 0x36, 0xdb, 0x8c, 0xe8, 0xfc, 0x0a, 0x1b, 0xf3, 0x2e, 0x21}, [SizeFp]byte{0x5e, 0x89, 0xd9, 0xf0, 0xfc, 0x47, 0xe5, 0x20, 0x10, 0xe6, 0x26, 0xf2, 0x67, 0xdb, 0xcc, 0x42}, }, subYX: Fq{ [SizeFp]byte{0x0e, 0x3b, 0xad, 0x12, 0x15, 0xa3, 0x40, 0x9e, 0x73, 0x97, 0x99, 0x43, 0x28, 0x74, 0xfe, 0x6d}, [SizeFp]byte{0x92, 0x93, 0x68, 0xe8, 0xf5, 0xaf, 0x70, 0x4f, 0x1b, 0x4a, 0x36, 0x13, 0x21, 0x89, 0xee, 0x5f}, }, dt2: Fq{ [SizeFp]byte{0x41, 0xc5, 0x53, 0xc7, 0xf7, 0xa4, 0x99, 0x82, 0x00, 0x49, 0x7f, 0x5f, 0xbe, 0x40, 0xc2, 0x7f}, [SizeFp]byte{0xa6, 0x22, 0xe3, 0x40, 0x6e, 0xc7, 0xee, 0x4c, 0xff, 0x36, 0xf4, 0x01, 0x4b, 0x52, 0x54, 0x77}, }, }, { addYX: Fq{ [SizeFp]byte{0x35, 0x58, 0xef, 0x56, 0xbc, 0xbb, 0xdf, 0xf9, 0x59, 0x2e, 0xf2, 0x2f, 0x4d, 0x89, 0xd8, 0x1d}, [SizeFp]byte{0x6c, 0xde, 0xe6, 0xde, 0x89, 0x39, 0x24, 0x3a, 0xce, 0x8e, 0xf5, 0x46, 0x33, 0x2b, 0xa8, 0x12}, }, subYX: Fq{ [SizeFp]byte{0x60, 0x72, 0x41, 0xb1, 0x06, 0xaf, 0x7d, 0x08, 0x6e, 0xee, 0xb7, 0x5e, 0x23, 0x95, 0xbf, 0x79}, [SizeFp]byte{0x34, 0x42, 0xdc, 0x3a, 0x73, 0x96, 0x94, 0xbe, 0xb9, 0x5d, 0xb4, 0x4b, 0x10, 0x48, 0x5e, 0x25}, }, dt2: Fq{ [SizeFp]byte{0x44, 0xff, 0xf4, 0x38, 0x90, 0x9d, 0xf4, 0x14, 0x9f, 0x4d, 0x5c, 0xab, 0xee, 0x68, 0xba, 0x0d}, [SizeFp]byte{0x45, 0x95, 0xe5, 0x91, 0x20, 0x15, 0x7b, 0xe8, 0x1f, 0x89, 0x12, 0x51, 0xd3, 0xfa, 0x82, 0x0d}, }, }, { addYX: Fq{ [SizeFp]byte{0x0c, 0xa3, 0xf8, 0x33, 0x76, 0x28, 0x4f, 0x2d, 0x26, 0xcc, 0x29, 0x77, 0x1a, 0xb3, 0x6e, 0x41}, [SizeFp]byte{0xef, 0xc8, 0x87, 0x5d, 0x26, 0x5d, 0x2f, 0xd1, 0x5c, 0xe0, 0x04, 0x58, 0x1c, 0xa9, 0x80, 0x4d}, }, subYX: Fq{ [SizeFp]byte{0x0a, 0xff, 0x06, 0x42, 0xe4, 0x76, 0xc5, 0xfa, 0xcd, 0x2a, 0xfb, 0x4c, 0xfa, 0x22, 0x0a, 0x7d}, [SizeFp]byte{0xd9, 0x5c, 0x89, 0x6d, 0x63, 0xe8, 0x0a, 0xb3, 0x29, 0xa4, 0xb9, 0x42, 0x12, 0x1d, 0xea, 0x00}, }, dt2: Fq{ [SizeFp]byte{0xb3, 0x59, 0x9d, 0x40, 0xdb, 0x32, 0x11, 0x41, 0x10, 0xa1, 0xbf, 0xf1, 0x7a, 0xe3, 0xdd, 0x11}, [SizeFp]byte{0x2c, 0xcc, 0x5c, 0x98, 0x1c, 0xd5, 0x95, 0xd2, 0x96, 0x51, 0xb1, 0x82, 0xb2, 0x7f, 0xe7, 0x6a}, }, }, { addYX: Fq{ [SizeFp]byte{0x07, 0xe9, 0xb9, 0x83, 0xeb, 0xf2, 0x9f, 0xd7, 0x43, 0x7c, 0xc2, 0xb0, 0x32, 0x70, 0xd0, 0x52}, [SizeFp]byte{0xf9, 0x70, 0x82, 0x31, 0x7a, 0x9a, 0x9f, 0x75, 0xe9, 0x6c, 0x87, 0x73, 0x97, 0x1a, 0x5a, 0x22}, }, subYX: Fq{ [SizeFp]byte{0x0b, 0x3b, 0xe5, 0x98, 0xdc, 0xf6, 0xd1, 0xf5, 0xb7, 0x7e, 0x34, 0x22, 0x35, 0x60, 0x41, 0x53}, [SizeFp]byte{0x1f, 0xf4, 0xcc, 0x56, 0xbb, 0x76, 0x3e, 0xd9, 0x3b, 0x63, 0x82, 0x25, 0x98, 0x12, 0x80, 0x02}, }, dt2: Fq{ [SizeFp]byte{0xeb, 0xdc, 0x9a, 0x7a, 0x70, 0x61, 0x5d, 0x6e, 0x41, 0x05, 0xd4, 0x0b, 0x4a, 0x63, 0x2a, 0x3b}, [SizeFp]byte{0xab, 0x52, 0xe0, 0xb1, 0x3f, 0x8a, 0xb0, 0x2d, 0x55, 0xf8, 0x1c, 0xeb, 0xc1, 0x1b, 0xc8, 0x35}, }, }, }, } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/000077500000000000000000000000001454601126700223535ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/constants.go000066400000000000000000000054321454601126700247220ustar00rootroot00000000000000package goldilocks import fp "github.com/cloudflare/circl/math/fp448" var ( // genX is the x-coordinate of the generator of Goldilocks curve. genX = fp.Elt{ 0x5e, 0xc0, 0x0c, 0xc7, 0x2b, 0xa8, 0x26, 0x26, 0x8e, 0x93, 0x00, 0x8b, 0xe1, 0x80, 0x3b, 0x43, 0x11, 0x65, 0xb6, 0x2a, 0xf7, 0x1a, 0xae, 0x12, 0x64, 0xa4, 0xd3, 0xa3, 0x24, 0xe3, 0x6d, 0xea, 0x67, 0x17, 0x0f, 0x47, 0x70, 0x65, 0x14, 0x9e, 0xda, 0x36, 0xbf, 0x22, 0xa6, 0x15, 0x1d, 0x22, 0xed, 0x0d, 0xed, 0x6b, 0xc6, 0x70, 0x19, 0x4f, } // genY is the y-coordinate of the generator of Goldilocks curve. genY = fp.Elt{ 0x14, 0xfa, 0x30, 0xf2, 0x5b, 0x79, 0x08, 0x98, 0xad, 0xc8, 0xd7, 0x4e, 0x2c, 0x13, 0xbd, 0xfd, 0xc4, 0x39, 0x7c, 0xe6, 0x1c, 0xff, 0xd3, 0x3a, 0xd7, 0xc2, 0xa0, 0x05, 0x1e, 0x9c, 0x78, 0x87, 0x40, 0x98, 0xa3, 0x6c, 0x73, 0x73, 0xea, 0x4b, 0x62, 0xc7, 0xc9, 0x56, 0x37, 0x20, 0x76, 0x88, 0x24, 0xbc, 0xb6, 0x6e, 0x71, 0x46, 0x3f, 0x69, } // paramD is -39081 in Fp. paramD = fp.Elt{ 0x56, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, } // order is 2^446-0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d, // which is the number of points in the prime subgroup. order = Scalar{ 0xf3, 0x44, 0x58, 0xab, 0x92, 0xc2, 0x78, 0x23, 0x55, 0x8f, 0xc5, 0x8d, 0x72, 0xc2, 0x6c, 0x21, 0x90, 0x36, 0xd6, 0xae, 0x49, 0xdb, 0x4e, 0xc4, 0xe9, 0x23, 0xca, 0x7c, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, } // residue448 is 2^448 mod order. residue448 = [4]uint64{ 0x721cf5b5529eec34, 0x7a4cf635c8e9c2ab, 0xeec492d944a725bf, 0x20cd77058, } // invFour is 1/4 mod order. invFour = Scalar{ 0x3d, 0x11, 0xd6, 0xaa, 0xa4, 0x30, 0xde, 0x48, 0xd5, 0x63, 0x71, 0xa3, 0x9c, 0x30, 0x5b, 0x08, 0xa4, 0x8d, 0xb5, 0x6b, 0xd2, 0xb6, 0x13, 0x71, 0xfa, 0x88, 0x32, 0xdf, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, } // paramDTwist is -39082 in Fp. The D parameter of the twist curve. paramDTwist = fp.Elt{ 0x55, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, } ) golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/curve.go000066400000000000000000000043261454601126700240330ustar00rootroot00000000000000// Package goldilocks provides elliptic curve operations over the goldilocks curve. package goldilocks import fp "github.com/cloudflare/circl/math/fp448" // Curve is the Goldilocks curve x^2+y^2=z^2-39081x^2y^2. type Curve struct{} // Identity returns the identity point. func (Curve) Identity() *Point { return &Point{ y: fp.One(), z: fp.One(), } } // IsOnCurve returns true if the point lies on the curve. func (Curve) IsOnCurve(P *Point) bool { x2, y2, t, t2, z2 := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{} rhs, lhs := &fp.Elt{}, &fp.Elt{} fp.Mul(t, &P.ta, &P.tb) // t = ta*tb fp.Sqr(x2, &P.x) // x^2 fp.Sqr(y2, &P.y) // y^2 fp.Sqr(z2, &P.z) // z^2 fp.Sqr(t2, t) // t^2 fp.Add(lhs, x2, y2) // x^2 + y^2 fp.Mul(rhs, t2, ¶mD) // dt^2 fp.Add(rhs, rhs, z2) // z^2 + dt^2 fp.Sub(lhs, lhs, rhs) // x^2 + y^2 - (z^2 + dt^2) eq0 := fp.IsZero(lhs) fp.Mul(lhs, &P.x, &P.y) // xy fp.Mul(rhs, t, &P.z) // tz fp.Sub(lhs, lhs, rhs) // xy - tz eq1 := fp.IsZero(lhs) return eq0 && eq1 } // Generator returns the generator point. func (Curve) Generator() *Point { return &Point{ x: genX, y: genY, z: fp.One(), ta: genX, tb: genY, } } // Order returns the number of points in the prime subgroup. func (Curve) Order() Scalar { return order } // Double returns 2P. func (Curve) Double(P *Point) *Point { R := *P; R.Double(); return &R } // Add returns P+Q. func (Curve) Add(P, Q *Point) *Point { R := *P; R.Add(Q); return &R } // ScalarMult returns kP. This function runs in constant time. func (e Curve) ScalarMult(k *Scalar, P *Point) *Point { k4 := &Scalar{} k4.divBy4(k) return e.pull(twistCurve{}.ScalarMult(k4, e.push(P))) } // ScalarBaseMult returns kG where G is the generator point. This function runs in constant time. func (e Curve) ScalarBaseMult(k *Scalar) *Point { k4 := &Scalar{} k4.divBy4(k) return e.pull(twistCurve{}.ScalarBaseMult(k4)) } // CombinedMult returns mG+nP, where G is the generator point. This function is non-constant time. func (e Curve) CombinedMult(m, n *Scalar, P *Point) *Point { m4 := &Scalar{} n4 := &Scalar{} m4.divBy4(m) n4.divBy4(n) return e.pull(twistCurve{}.CombinedMult(m4, n4, twistCurve{}.pull(P))) } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/curve_test.go000066400000000000000000000047101454601126700250670ustar00rootroot00000000000000package goldilocks_test import ( "crypto/rand" "testing" "github.com/cloudflare/circl/ecc/goldilocks" "github.com/cloudflare/circl/internal/test" ) func TestScalarMult(t *testing.T) { const testTimes = 1 << 8 var e goldilocks.Curve k := &goldilocks.Scalar{} zero := &goldilocks.Scalar{} t.Run("rG=0", func(t *testing.T) { order := e.Order() for i := 0; i < testTimes; i++ { got := e.ScalarBaseMult(&order) got.ToAffine() want := e.Identity() if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { want.ToAffine() test.ReportError(t, got, want) } } }) t.Run("rP=0", func(t *testing.T) { order := e.Order() for i := 0; i < testTimes; i++ { P := randomPoint() got := e.ScalarMult(&order, P) got.ToAffine() want := e.Identity() if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { want.ToAffine() test.ReportError(t, got, want, P, order) } } }) t.Run("kG", func(t *testing.T) { I := e.Identity() for i := 0; i < testTimes; i++ { _, _ = rand.Read(k[:]) got := e.ScalarBaseMult(k) want := e.CombinedMult(k, zero, I) // k*G + 0*I if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { test.ReportError(t, got, want, k) } } }) t.Run("kP", func(t *testing.T) { for i := 0; i < testTimes; i++ { P := randomPoint() _, _ = rand.Read(k[:]) got := e.ScalarMult(k, P) want := e.CombinedMult(zero, k, P) if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { test.ReportError(t, got, want, P, k) } } }) t.Run("kG+lP", func(t *testing.T) { G := e.Generator() l := &goldilocks.Scalar{} for i := 0; i < testTimes; i++ { P := randomPoint() _, _ = rand.Read(k[:]) _, _ = rand.Read(l[:]) kG := e.ScalarMult(k, G) lP := e.ScalarMult(l, P) got := e.Add(kG, lP) want := e.CombinedMult(k, l, P) if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { test.ReportError(t, got, want, P, k, l) } } }) } func BenchmarkCurve(b *testing.B) { var e goldilocks.Curve var k, l goldilocks.Scalar _, _ = rand.Read(k[:]) _, _ = rand.Read(l[:]) P := randomPoint() b.Run("ScalarMult", func(b *testing.B) { for i := 0; i < b.N; i++ { P = e.ScalarMult(&k, P) } }) b.Run("ScalarBaseMult", func(b *testing.B) { for i := 0; i < b.N; i++ { e.ScalarBaseMult(&k) } }) b.Run("CombinedMult", func(b *testing.B) { for i := 0; i < b.N; i++ { P = e.CombinedMult(&k, &l, P) } }) } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/isogeny.go000066400000000000000000000032761454601126700243670ustar00rootroot00000000000000package goldilocks import fp "github.com/cloudflare/circl/math/fp448" func (Curve) pull(P *twistPoint) *Point { return twistCurve{}.push(P) } func (twistCurve) pull(P *Point) *twistPoint { return Curve{}.push(P) } // push sends a point on the Goldilocks curve to a point on the twist curve. func (Curve) push(P *Point) *twistPoint { Q := &twistPoint{} Px, Py, Pz := &P.x, &P.y, &P.z a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb fp.Add(e, Px, Py) // x+y fp.Sqr(a, Px) // A = x^2 fp.Sqr(b, Py) // B = y^2 fp.Sqr(c, Pz) // z^2 fp.Add(c, c, c) // C = 2*z^2 *d = *a // D = A fp.Sqr(e, e) // (x+y)^2 fp.Sub(e, e, a) // (x+y)^2-A fp.Sub(e, e, b) // E = (x+y)^2-A-B fp.Add(h, b, d) // H = B+D fp.Sub(g, b, d) // G = B-D fp.Sub(f, c, h) // F = C-H fp.Mul(&Q.z, f, g) // Z = F * G fp.Mul(&Q.x, e, f) // X = E * F fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H return Q } // push sends a point on the twist curve to a point on the Goldilocks curve. func (twistCurve) push(P *twistPoint) *Point { Q := &Point{} Px, Py, Pz := &P.x, &P.y, &P.z a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb fp.Add(e, Px, Py) // x+y fp.Sqr(a, Px) // A = x^2 fp.Sqr(b, Py) // B = y^2 fp.Sqr(c, Pz) // z^2 fp.Add(c, c, c) // C = 2*z^2 fp.Neg(d, a) // D = -A fp.Sqr(e, e) // (x+y)^2 fp.Sub(e, e, a) // (x+y)^2-A fp.Sub(e, e, b) // E = (x+y)^2-A-B fp.Add(h, b, d) // H = B+D fp.Sub(g, b, d) // G = B-D fp.Sub(f, c, h) // F = C-H fp.Mul(&Q.z, f, g) // Z = F * G fp.Mul(&Q.x, e, f) // X = E * F fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H return Q } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/isogeny_test.go000066400000000000000000000013011454601126700254110ustar00rootroot00000000000000package goldilocks import ( "crypto/rand" "testing" "github.com/cloudflare/circl/internal/test" ) func randomPoint() *Point { var k Scalar _, _ = rand.Read(k[:]) return Curve{}.ScalarBaseMult(&k) } func TestIsogeny(t *testing.T) { const testTimes = 1 << 10 var gold Curve var twist twistCurve for i := 0; i < testTimes; i++ { P := randomPoint() Q := gold.pull(gold.push(P)) // phi^-(phi^+(P)) got := Q want := gold.Double(gold.Double(P)) // 4P if !got.IsEqual(want) { test.ReportError(t, got, want, P) } got = twist.push(twist.pull(Q)) // phi^-(phi^+(Q)) want = gold.Double(gold.Double(Q)) // 4Q if !got.IsEqual(want) { test.ReportError(t, got, want, P) } } } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/point.go000066400000000000000000000107331454601126700240370ustar00rootroot00000000000000package goldilocks import ( "errors" "fmt" fp "github.com/cloudflare/circl/math/fp448" ) // Point is a point on the Goldilocks Curve. type Point struct{ x, y, z, ta, tb fp.Elt } func (P Point) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb) } // FromAffine creates a point from affine coordinates. func FromAffine(x, y *fp.Elt) (*Point, error) { P := &Point{ x: *x, y: *y, z: fp.One(), ta: *x, tb: *y, } if !(Curve{}).IsOnCurve(P) { return P, errors.New("point not on curve") } return P, nil } // isLessThan returns true if 0 <= x < y, and assumes that slices are of the // same length and are interpreted in little-endian order. func isLessThan(x, y []byte) bool { i := len(x) - 1 for i > 0 && x[i] == y[i] { i-- } return x[i] < y[i] } // FromBytes returns a point from the input buffer. func FromBytes(in []byte) (*Point, error) { if len(in) < fp.Size+1 { return nil, errors.New("wrong input length") } err := errors.New("invalid decoding") P := &Point{} signX := in[fp.Size] >> 7 copy(P.y[:], in[:fp.Size]) p := fp.P() if !isLessThan(P.y[:], p[:]) { return nil, err } u, v := &fp.Elt{}, &fp.Elt{} one := fp.One() fp.Sqr(u, &P.y) // u = y^2 fp.Mul(v, u, ¶mD) // v = dy^2 fp.Sub(u, u, &one) // u = y^2-1 fp.Sub(v, v, &one) // v = dy^2-1 isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v) if !isQR { return nil, err } fp.Modp(&P.x) // x = x mod p if fp.IsZero(&P.x) && signX == 1 { return nil, err } if signX != (P.x[0] & 1) { fp.Neg(&P.x, &P.x) } P.ta = P.x P.tb = P.y P.z = fp.One() return P, nil } // IsIdentity returns true is P is the identity Point. func (P *Point) IsIdentity() bool { return fp.IsZero(&P.x) && !fp.IsZero(&P.y) && !fp.IsZero(&P.z) && P.y == P.z } // IsEqual returns true if P is equivalent to Q. func (P *Point) IsEqual(Q *Point) bool { l, r := &fp.Elt{}, &fp.Elt{} fp.Mul(l, &P.x, &Q.z) fp.Mul(r, &Q.x, &P.z) fp.Sub(l, l, r) b := fp.IsZero(l) fp.Mul(l, &P.y, &Q.z) fp.Mul(r, &Q.y, &P.z) fp.Sub(l, l, r) b = b && fp.IsZero(l) fp.Mul(l, &P.ta, &P.tb) fp.Mul(l, l, &Q.z) fp.Mul(r, &Q.ta, &Q.tb) fp.Mul(r, r, &P.z) fp.Sub(l, l, r) b = b && fp.IsZero(l) return b } // Neg obtains the inverse of the Point. func (P *Point) Neg() { fp.Neg(&P.x, &P.x); fp.Neg(&P.ta, &P.ta) } // ToAffine returns the x,y affine coordinates of P. func (P *Point) ToAffine() (x, y fp.Elt) { fp.Inv(&P.z, &P.z) // 1/z fp.Mul(&P.x, &P.x, &P.z) // x/z fp.Mul(&P.y, &P.y, &P.z) // y/z fp.Modp(&P.x) fp.Modp(&P.y) fp.SetOne(&P.z) P.ta = P.x P.tb = P.y return P.x, P.y } // ToBytes stores P into a slice of bytes. func (P *Point) ToBytes(out []byte) error { if len(out) < fp.Size+1 { return errors.New("invalid decoding") } x, y := P.ToAffine() out[fp.Size] = (x[0] & 1) << 7 return fp.ToBytes(out[:fp.Size], &y) } // MarshalBinary encodes the receiver into a binary form and returns the result. func (P *Point) MarshalBinary() (data []byte, err error) { data = make([]byte, fp.Size+1) err = P.ToBytes(data[:fp.Size+1]) return data, err } // UnmarshalBinary must be able to decode the form generated by MarshalBinary. func (P *Point) UnmarshalBinary(data []byte) error { Q, err := FromBytes(data); *P = *Q; return err } // Double sets P = 2Q. func (P *Point) Double() { P.Add(P) } // Add sets P =P+Q.. func (P *Point) Add(Q *Point) { // This is formula (5) from "Twisted Edwards Curves Revisited" by // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) // https://doi.org/10.1007/978-3-540-89255-7_20 x1, y1, z1, ta1, tb1 := &P.x, &P.y, &P.z, &P.ta, &P.tb x2, y2, z2, ta2, tb2 := &Q.x, &Q.y, &Q.z, &Q.ta, &Q.tb x3, y3, z3, E, H := &P.x, &P.y, &P.z, &P.ta, &P.tb A, B, C, D := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{} t1, t2, F, G := C, D, &fp.Elt{}, &fp.Elt{} fp.Mul(t1, ta1, tb1) // t1 = ta1*tb1 fp.Mul(t2, ta2, tb2) // t2 = ta2*tb2 fp.Mul(A, x1, x2) // A = x1*x2 fp.Mul(B, y1, y2) // B = y1*y2 fp.Mul(C, t1, t2) // t1*t2 fp.Mul(C, C, ¶mD) // C = d*t1*t2 fp.Mul(D, z1, z2) // D = z1*z2 fp.Add(F, x1, y1) // x1+y1 fp.Add(E, x2, y2) // x2+y2 fp.Mul(E, E, F) // (x1+y1)*(x2+y2) fp.Sub(E, E, A) // (x1+y1)*(x2+y2)-A fp.Sub(E, E, B) // E = (x1+y1)*(x2+y2)-A-B fp.Sub(F, D, C) // F = D-C fp.Add(G, D, C) // G = D+C fp.Sub(H, B, A) // H = B-A fp.Mul(z3, F, G) // Z = F * G fp.Mul(x3, E, F) // X = E * F fp.Mul(y3, G, H) // Y = G * H, T = E * H } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/point_test.go000066400000000000000000000040241454601126700250720ustar00rootroot00000000000000package goldilocks_test import ( "crypto/rand" "encoding" "testing" "github.com/cloudflare/circl/ecc/goldilocks" "github.com/cloudflare/circl/internal/test" ) func randomPoint() *goldilocks.Point { var k goldilocks.Scalar _, _ = rand.Read(k[:]) return goldilocks.Curve{}.ScalarBaseMult(&k) } func TestPointAdd(t *testing.T) { const testTimes = 1 << 10 var e goldilocks.Curve for i := 0; i < testTimes; i++ { P := randomPoint() // 16P = 2^4P got := e.Double(e.Double(e.Double(e.Double(P)))) // 16P = P+P...+P Q := e.Identity() for j := 0; j < 16; j++ { Q = e.Add(Q, P) } want := Q if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { test.ReportError(t, got, want, P) } } } func TestPointNeg(t *testing.T) { const testTimes = 1 << 10 var e goldilocks.Curve for i := 0; i < testTimes; i++ { P := randomPoint() Q := *P Q.Neg() R := e.Add(P, &Q) got := R.IsIdentity() want := true if got != want { test.ReportError(t, got, want, P) } } } func TestPointAffine(t *testing.T) { const testTimes = 1 << 10 for i := 0; i < testTimes; i++ { got := randomPoint() x, y := got.ToAffine() want, err := goldilocks.FromAffine(&x, &y) if !got.IsEqual(want) || err != nil { test.ReportError(t, got, want) } } } func TestPointMarshal(t *testing.T) { const testTimes = 1 << 10 var want error for i := 0; i < testTimes; i++ { var P interface{} = randomPoint() mar, _ := P.(encoding.BinaryMarshaler) data, got := mar.MarshalBinary() if got != want { test.ReportError(t, got, want, P) } unmar, _ := P.(encoding.BinaryUnmarshaler) got = unmar.UnmarshalBinary(data) if got != want { test.ReportError(t, got, want, P) } } } func BenchmarkPoint(b *testing.B) { P := randomPoint() Q := randomPoint() b.Run("ToAffine", func(b *testing.B) { for i := 0; i < b.N; i++ { P.ToAffine() } }) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Add(Q) } }) b.Run("Double", func(b *testing.B) { for i := 0; i < b.N; i++ { P.Double() } }) } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/scalar.go000066400000000000000000000117311454601126700241520ustar00rootroot00000000000000package goldilocks import ( "encoding/binary" "math/bits" ) // ScalarSize is the size (in bytes) of scalars. const ScalarSize = 56 // 448 / 8 // _N is the number of 64-bit words to store scalars. const _N = 7 // 448 / 64 // Scalar represents a positive integer stored in little-endian order. type Scalar [ScalarSize]byte type scalar64 [_N]uint64 func (z *scalar64) fromScalar(x *Scalar) { z[0] = binary.LittleEndian.Uint64(x[0*8 : 1*8]) z[1] = binary.LittleEndian.Uint64(x[1*8 : 2*8]) z[2] = binary.LittleEndian.Uint64(x[2*8 : 3*8]) z[3] = binary.LittleEndian.Uint64(x[3*8 : 4*8]) z[4] = binary.LittleEndian.Uint64(x[4*8 : 5*8]) z[5] = binary.LittleEndian.Uint64(x[5*8 : 6*8]) z[6] = binary.LittleEndian.Uint64(x[6*8 : 7*8]) } func (z *scalar64) toScalar(x *Scalar) { binary.LittleEndian.PutUint64(x[0*8:1*8], z[0]) binary.LittleEndian.PutUint64(x[1*8:2*8], z[1]) binary.LittleEndian.PutUint64(x[2*8:3*8], z[2]) binary.LittleEndian.PutUint64(x[3*8:4*8], z[3]) binary.LittleEndian.PutUint64(x[4*8:5*8], z[4]) binary.LittleEndian.PutUint64(x[5*8:6*8], z[5]) binary.LittleEndian.PutUint64(x[6*8:7*8], z[6]) } // add calculates z = x + y. Assumes len(z) > max(len(x),len(y)). func add(z, x, y []uint64) uint64 { l, L, zz := len(x), len(y), y if l > L { l, L, zz = L, l, x } c := uint64(0) for i := 0; i < l; i++ { z[i], c = bits.Add64(x[i], y[i], c) } for i := l; i < L; i++ { z[i], c = bits.Add64(zz[i], 0, c) } return c } // sub calculates z = x - y. Assumes len(z) > max(len(x),len(y)). func sub(z, x, y []uint64) uint64 { l, L, zz := len(x), len(y), y if l > L { l, L, zz = L, l, x } c := uint64(0) for i := 0; i < l; i++ { z[i], c = bits.Sub64(x[i], y[i], c) } for i := l; i < L; i++ { z[i], c = bits.Sub64(zz[i], 0, c) } return c } // mulWord calculates z = x * y. Assumes len(z) >= len(x)+1. func mulWord(z, x []uint64, y uint64) { for i := range z { z[i] = 0 } carry := uint64(0) for i := range x { hi, lo := bits.Mul64(x[i], y) lo, cc := bits.Add64(lo, z[i], 0) hi, _ = bits.Add64(hi, 0, cc) z[i], cc = bits.Add64(lo, carry, 0) carry, _ = bits.Add64(hi, 0, cc) } z[len(x)] = carry } // Cmov moves x into z if b=1. func (z *scalar64) Cmov(b uint64, x *scalar64) { m := uint64(0) - b for i := range z { z[i] = (z[i] &^ m) | (x[i] & m) } } // leftShift shifts to the left the words of z returning the more significant word. func (z *scalar64) leftShift(low uint64) uint64 { high := z[_N-1] for i := _N - 1; i > 0; i-- { z[i] = z[i-1] } z[0] = low return high } // reduceOneWord calculates z = z + 2^448*x such that the result fits in a Scalar. func (z *scalar64) reduceOneWord(x uint64) { prod := (&scalar64{})[:] mulWord(prod, residue448[:], x) cc := add(z[:], z[:], prod) mulWord(prod, residue448[:], cc) add(z[:], z[:], prod) } // modOrder reduces z mod order. func (z *scalar64) modOrder() { var o64, x scalar64 o64.fromScalar(&order) // Performs: while (z >= order) { z = z-order } // At most 8 (eight) iterations reduce 3 bits by subtracting. for i := 0; i < 8; i++ { c := sub(x[:], z[:], o64[:]) // (c || x) = z-order z.Cmov(1-c, &x) // if c != 0 { z = x } } } // FromBytes stores z = x mod order, where x is a number stored in little-endian order. func (z *Scalar) FromBytes(x []byte) { n := len(x) nCeil := (n + 7) >> 3 for i := range z { z[i] = 0 } if nCeil < _N { copy(z[:], x) return } copy(z[:], x[8*(nCeil-_N):]) var z64 scalar64 z64.fromScalar(z) for i := nCeil - _N - 1; i >= 0; i-- { low := binary.LittleEndian.Uint64(x[8*i:]) high := z64.leftShift(low) z64.reduceOneWord(high) } z64.modOrder() z64.toScalar(z) } // divBy4 calculates z = x/4 mod order. func (z *Scalar) divBy4(x *Scalar) { z.Mul(x, &invFour) } // Red reduces z mod order. func (z *Scalar) Red() { var t scalar64; t.fromScalar(z); t.modOrder(); t.toScalar(z) } // Neg calculates z = -z mod order. func (z *Scalar) Neg() { z.Sub(&order, z) } // Add calculates z = x+y mod order. func (z *Scalar) Add(x, y *Scalar) { var z64, x64, y64, t scalar64 x64.fromScalar(x) y64.fromScalar(y) c := add(z64[:], x64[:], y64[:]) add(t[:], z64[:], residue448[:]) z64.Cmov(c, &t) z64.modOrder() z64.toScalar(z) } // Sub calculates z = x-y mod order. func (z *Scalar) Sub(x, y *Scalar) { var z64, x64, y64, t scalar64 x64.fromScalar(x) y64.fromScalar(y) c := sub(z64[:], x64[:], y64[:]) sub(t[:], z64[:], residue448[:]) z64.Cmov(c, &t) z64.modOrder() z64.toScalar(z) } // Mul calculates z = x*y mod order. func (z *Scalar) Mul(x, y *Scalar) { var z64, x64, y64 scalar64 prod := (&[_N + 1]uint64{})[:] x64.fromScalar(x) y64.fromScalar(y) mulWord(prod, x64[:], y64[_N-1]) copy(z64[:], prod[:_N]) z64.reduceOneWord(prod[_N]) for i := _N - 2; i >= 0; i-- { h := z64.leftShift(0) z64.reduceOneWord(h) mulWord(prod, x64[:], y64[i]) c := add(z64[:], z64[:], prod[:_N]) z64.reduceOneWord(prod[_N] + c) } z64.modOrder() z64.toScalar(z) } // IsZero returns true if z=0. func (z *Scalar) IsZero() bool { z.Red(); return *z == Scalar{} } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/scalar_test.go000066400000000000000000000045161454601126700252140ustar00rootroot00000000000000package goldilocks_test import ( "crypto/rand" "encoding/binary" "math/big" "testing" "github.com/cloudflare/circl/ecc/goldilocks" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" ) func TestReduceModOrder(t *testing.T) { order := goldilocks.Curve{}.Order() bigOrder := conv.BytesLe2BigInt(order[:]) const max = 3*goldilocks.ScalarSize - 1 var b [max]byte _, _ = rand.Read(b[:]) var z goldilocks.Scalar for i := 0; i < max; i++ { x := b[0:i] bigX := conv.BytesLe2BigInt(x) z.FromBytes(x) got := conv.BytesLe2BigInt(z[:]) got.Mod(got, bigOrder) want := bigX.Mod(bigX, bigOrder) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, i) } } } func testOp(t *testing.T, f func(z, x, y *goldilocks.Scalar), g func(z, x, y *big.Int), ) { const testTimes = 1 << 8 var x, y, z goldilocks.Scalar order := goldilocks.Curve{}.Order() want := new(big.Int) bigOrder := conv.BytesLe2BigInt(order[:]) for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) bigX := conv.BytesLe2BigInt(x[:]) bigY := conv.BytesLe2BigInt(y[:]) f(&z, &x, &y) got := conv.BytesLe2BigInt(z[:]) g(want, bigX, bigY) want.Mod(want, bigOrder) if got.Cmp(want) != 0 { test.ReportError(t, got.Text(16), want.Text(16), conv.BytesLe2Hex(x[:]), conv.BytesLe2Hex(y[:])) } } } func TestScalar(t *testing.T) { t.Run("Add", func(t *testing.T) { testOp(t, func(z, x, y *goldilocks.Scalar) { z.Add(x, y) }, func(z, x, y *big.Int) { z.Add(x, y) }) }) t.Run("Sub", func(t *testing.T) { testOp(t, func(z, x, y *goldilocks.Scalar) { z.Sub(x, y) }, func(z, x, y *big.Int) { z.Sub(x, y) }) }) t.Run("Mul", func(t *testing.T) { testOp(t, func(z, x, y *goldilocks.Scalar) { z.Mul(x, y) }, func(z, x, y *big.Int) { z.Mul(x, y) }) }) } func BenchmarkScalar(b *testing.B) { var k [2 * goldilocks.ScalarSize]byte var x, y, z goldilocks.Scalar _ = binary.Read(rand.Reader, binary.LittleEndian, x[:]) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Add(&x, &y) } }) b.Run("Sub", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Sub(&x, &y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { z.Mul(&x, &y) } }) b.Run("Red", func(b *testing.B) { for i := 0; i < b.N; i++ { z.FromBytes(k[:]) } }) } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/twist.go000066400000000000000000000060421454601126700240560ustar00rootroot00000000000000package goldilocks import ( "crypto/subtle" "math/bits" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/math" fp "github.com/cloudflare/circl/math/fp448" ) // twistCurve is -x^2+y^2=1-39082x^2y^2 and is 4-isogenous to Goldilocks. type twistCurve struct{} // Identity returns the identity point. func (twistCurve) Identity() *twistPoint { return &twistPoint{ y: fp.One(), z: fp.One(), } } // subYDiv16 update x = (x - y) / 16. func subYDiv16(x *scalar64, y int64) { s := uint64(y >> 63) x0, b0 := bits.Sub64((*x)[0], uint64(y), 0) x1, b1 := bits.Sub64((*x)[1], s, b0) x2, b2 := bits.Sub64((*x)[2], s, b1) x3, b3 := bits.Sub64((*x)[3], s, b2) x4, b4 := bits.Sub64((*x)[4], s, b3) x5, b5 := bits.Sub64((*x)[5], s, b4) x6, _ := bits.Sub64((*x)[6], s, b5) x[0] = (x0 >> 4) | (x1 << 60) x[1] = (x1 >> 4) | (x2 << 60) x[2] = (x2 >> 4) | (x3 << 60) x[3] = (x3 >> 4) | (x4 << 60) x[4] = (x4 >> 4) | (x5 << 60) x[5] = (x5 >> 4) | (x6 << 60) x[6] = (x6 >> 4) } func recodeScalar(d *[113]int8, k *Scalar) { var k64 scalar64 k64.fromScalar(k) for i := 0; i < 112; i++ { d[i] = int8((k64[0] & 0x1f) - 16) subYDiv16(&k64, int64(d[i])) } d[112] = int8(k64[0]) } // ScalarMult returns kP. func (e twistCurve) ScalarMult(k *Scalar, P *twistPoint) *twistPoint { var TabP [8]preTwistPointProy var S preTwistPointProy var d [113]int8 var isZero int if k.IsZero() { isZero = 1 } subtle.ConstantTimeCopy(isZero, k[:], order[:]) minusK := *k isEven := 1 - int(k[0]&0x1) minusK.Neg() subtle.ConstantTimeCopy(isEven, k[:], minusK[:]) recodeScalar(&d, k) P.oddMultiples(TabP[:]) Q := e.Identity() for i := 112; i >= 0; i-- { Q.Double() Q.Double() Q.Double() Q.Double() mask := d[i] >> 7 absDi := (d[i] + mask) ^ mask inx := int32((absDi - 1) >> 1) sig := int((d[i] >> 7) & 0x1) for j := range TabP { S.cmov(&TabP[j], uint(subtle.ConstantTimeEq(inx, int32(j)))) } S.cneg(sig) Q.mixAdd(&S) } Q.cneg(uint(isEven)) return Q } const ( omegaFix = 7 omegaVar = 5 ) // CombinedMult returns mG+nP. func (e twistCurve) CombinedMult(m, n *Scalar, P *twistPoint) *twistPoint { nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m[:]), omegaFix) nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n[:]), omegaVar) if len(nafFix) > len(nafVar) { nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...) } else if len(nafFix) < len(nafVar) { nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...) } var TabQ [1 << (omegaVar - 2)]preTwistPointProy P.oddMultiples(TabQ[:]) Q := e.Identity() for i := len(nafFix) - 1; i >= 0; i-- { Q.Double() // Generator point if nafFix[i] != 0 { idxM := absolute(nafFix[i]) >> 1 R := tabVerif[idxM] if nafFix[i] < 0 { R.neg() } Q.mixAddZ1(&R) } // Variable input point if nafVar[i] != 0 { idxN := absolute(nafVar[i]) >> 1 S := TabQ[idxN] if nafVar[i] < 0 { S.neg() } Q.mixAdd(&S) } } return Q } // absolute returns always a positive value. func absolute(x int32) int32 { mask := x >> 31 return (x + mask) ^ mask } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/twistPoint.go000066400000000000000000000077441454601126700251020ustar00rootroot00000000000000package goldilocks import ( "fmt" fp "github.com/cloudflare/circl/math/fp448" ) type twistPoint struct{ x, y, z, ta, tb fp.Elt } type preTwistPointAffine struct{ addYX, subYX, dt2 fp.Elt } type preTwistPointProy struct { preTwistPointAffine z2 fp.Elt } func (P *twistPoint) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb) } // cneg conditionally negates the point if b=1. func (P *twistPoint) cneg(b uint) { t := &fp.Elt{} fp.Neg(t, &P.x) fp.Cmov(&P.x, t, b) fp.Neg(t, &P.ta) fp.Cmov(&P.ta, t, b) } // Double updates P with 2P. func (P *twistPoint) Double() { // This is formula (7) from "Twisted Edwards Curves Revisited" by // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) // https://doi.org/10.1007/978-3-540-89255-7_20 Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb fp.Add(e, Px, Py) // x+y fp.Sqr(a, Px) // A = x^2 fp.Sqr(b, Py) // B = y^2 fp.Sqr(c, Pz) // z^2 fp.Add(c, c, c) // C = 2*z^2 fp.Add(h, a, b) // H = A+B fp.Sqr(e, e) // (x+y)^2 fp.Sub(e, e, h) // E = (x+y)^2-A-B fp.Sub(g, b, a) // G = B-A fp.Sub(f, c, g) // F = C-G fp.Mul(Pz, f, g) // Z = F * G fp.Mul(Px, e, f) // X = E * F fp.Mul(Py, g, h) // Y = G * H, T = E * H } // mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q = 1. func (P *twistPoint) mixAddZ1(Q *preTwistPointAffine) { fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 (z2=1) P.coreAddition(Q) } // coreAddition calculates P=P+Q for curves with A=-1. func (P *twistPoint) coreAddition(Q *preTwistPointAffine) { // This is the formula following (5) from "Twisted Edwards Curves Revisited" by // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) // https://doi.org/10.1007/978-3-540-89255-7_20 Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2 a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb fp.Mul(c, Pta, Ptb) // t1 = ta*tb fp.Sub(h, Py, Px) // y1-x1 fp.Add(b, Py, Px) // y1+x1 fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2) fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2) fp.Mul(c, c, dt2) // C = 2*D*t1*t2 fp.Sub(e, b, a) // E = B-A fp.Add(h, b, a) // H = B+A fp.Sub(f, d, c) // F = D-C fp.Add(g, d, c) // G = D+C fp.Mul(Pz, f, g) // Z = F * G fp.Mul(Px, e, f) // X = E * F fp.Mul(Py, g, h) // Y = G * H, T = E * H } func (P *preTwistPointAffine) neg() { P.addYX, P.subYX = P.subYX, P.addYX fp.Neg(&P.dt2, &P.dt2) } func (P *preTwistPointAffine) cneg(b int) { t := &fp.Elt{} fp.Cswap(&P.addYX, &P.subYX, uint(b)) fp.Neg(t, &P.dt2) fp.Cmov(&P.dt2, t, uint(b)) } func (P *preTwistPointAffine) cmov(Q *preTwistPointAffine, b uint) { fp.Cmov(&P.addYX, &Q.addYX, b) fp.Cmov(&P.subYX, &Q.subYX, b) fp.Cmov(&P.dt2, &Q.dt2, b) } // mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q != 1. func (P *twistPoint) mixAdd(Q *preTwistPointProy) { fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2 P.coreAddition(&Q.preTwistPointAffine) } // oddMultiples calculates T[i] = (2*i-1)P for 0 < i < len(T). func (P *twistPoint) oddMultiples(T []preTwistPointProy) { if n := len(T); n > 0 { T[0].FromTwistPoint(P) _2P := *P _2P.Double() R := &preTwistPointProy{} R.FromTwistPoint(&_2P) for i := 1; i < n; i++ { P.mixAdd(R) T[i].FromTwistPoint(P) } } } // cmov conditionally moves Q into P if b=1. func (P *preTwistPointProy) cmov(Q *preTwistPointProy, b uint) { P.preTwistPointAffine.cmov(&Q.preTwistPointAffine, b) fp.Cmov(&P.z2, &Q.z2, b) } // FromTwistPoint precomputes some coordinates of Q for missed addition. func (P *preTwistPointProy) FromTwistPoint(Q *twistPoint) { fp.Add(&P.addYX, &Q.y, &Q.x) // addYX = X + Y fp.Sub(&P.subYX, &Q.y, &Q.x) // subYX = Y - X fp.Mul(&P.dt2, &Q.ta, &Q.tb) // T = ta*tb fp.Mul(&P.dt2, &P.dt2, ¶mDTwist) // D*T fp.Add(&P.dt2, &P.dt2, &P.dt2) // dt2 = 2*D*T fp.Add(&P.z2, &Q.z, &Q.z) // z2 = 2*Z } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/twistTables.go000066400000000000000000001245061454601126700252170ustar00rootroot00000000000000package goldilocks import fp "github.com/cloudflare/circl/math/fp448" var tabFixMult = [fxV][fx2w1]preTwistPointAffine{ { { addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55}, }, { addYX: fp.Elt{0xca, 0xd8, 0x7d, 0x86, 0x1a, 0xef, 0xad, 0x11, 0xe3, 0x27, 0x41, 0x7e, 0x7f, 0x3e, 0xa9, 0xd2, 0xb5, 0x4e, 0x50, 0xe0, 0x77, 0x91, 0xc2, 0x13, 0x52, 0x73, 0x41, 0x09, 0xa6, 0x57, 0x9a, 0xc8, 0xa8, 0x90, 0x9d, 0x26, 0x14, 0xbb, 0xa1, 0x2a, 0xf7, 0x45, 0x43, 0x4e, 0xea, 0x35, 0x62, 0xe1, 0x08, 0x85, 0x46, 0xb8, 0x24, 0x05, 0x2d, 0xab}, subYX: fp.Elt{0x9b, 0xe6, 0xd3, 0xe5, 0xfe, 0x50, 0x36, 0x3c, 0x3c, 0x6d, 0x74, 0x1d, 0x74, 0xc0, 0xde, 0x5b, 0x45, 0x27, 0xe5, 0x12, 0xee, 0x63, 0x35, 0x6b, 0x13, 0xe2, 0x41, 0x6b, 0x3a, 0x05, 0x2b, 0xb1, 0x89, 0x26, 0xb6, 0xc6, 0xd1, 0x84, 0xff, 0x0e, 0x9b, 0xa3, 0xfb, 0x21, 0x36, 0x6b, 0x01, 0xf7, 0x9f, 0x7c, 0xeb, 0xf5, 0x18, 0x7a, 0x2a, 0x70}, dt2: fp.Elt{0x09, 0xad, 0x99, 0x1a, 0x38, 0xd3, 0xdf, 0x22, 0x37, 0x32, 0x61, 0x8b, 0xf3, 0x19, 0x48, 0x08, 0xe8, 0x49, 0xb6, 0x4a, 0xa7, 0xed, 0xa4, 0xa2, 0xee, 0x86, 0xd7, 0x31, 0x5e, 0xce, 0x95, 0x76, 0x86, 0x42, 0x1c, 0x9d, 0x07, 0x14, 0x8c, 0x34, 0x18, 0x9c, 0x6d, 0x3a, 0xdf, 0xa9, 0xe8, 0x36, 0x7e, 0xe4, 0x95, 0xbe, 0xb5, 0x09, 0xf8, 0x9c}, }, { addYX: fp.Elt{0x51, 0xdb, 0x49, 0xa8, 0x9f, 0xe3, 0xd7, 0xec, 0x0d, 0x0f, 0x49, 0xe8, 0xb6, 0xc5, 0x0f, 0x5a, 0x1c, 0xce, 0x54, 0x0d, 0xb1, 0x8d, 0x5b, 0xbf, 0xf4, 0xaa, 0x34, 0x77, 0xc4, 0x5d, 0x59, 0xb6, 0xc5, 0x0e, 0x5a, 0xd8, 0x5b, 0x30, 0xc2, 0x1d, 0xec, 0x85, 0x1c, 0x42, 0xbe, 0x24, 0x2e, 0x50, 0x55, 0x44, 0xb2, 0x3a, 0x01, 0xaa, 0x98, 0xfb}, subYX: fp.Elt{0xe7, 0x29, 0xb7, 0xd0, 0xaa, 0x4f, 0x32, 0x53, 0x56, 0xde, 0xbc, 0xd1, 0x92, 0x5d, 0x19, 0xbe, 0xa3, 0xe3, 0x75, 0x48, 0xe0, 0x7a, 0x1b, 0x54, 0x7a, 0xb7, 0x41, 0x77, 0x84, 0x38, 0xdd, 0x14, 0x9f, 0xca, 0x3f, 0xa3, 0xc8, 0xa7, 0x04, 0x70, 0xf1, 0x4d, 0x3d, 0xb3, 0x84, 0x79, 0xcb, 0xdb, 0xe4, 0xc5, 0x42, 0x9b, 0x57, 0x19, 0xf1, 0x2d}, dt2: fp.Elt{0x20, 0xb4, 0x94, 0x9e, 0xdf, 0x31, 0x44, 0x0b, 0xc9, 0x7b, 0x75, 0x40, 0x9d, 0xd1, 0x96, 0x39, 0x70, 0x71, 0x15, 0xc8, 0x93, 0xd5, 0xc5, 0xe5, 0xba, 0xfe, 0xee, 0x08, 0x6a, 0x98, 0x0a, 0x1b, 0xb2, 0xaa, 0x3a, 0xf4, 0xa4, 0x79, 0xf9, 0x8e, 0x4d, 0x65, 0x10, 0x9b, 0x3a, 0x6e, 0x7c, 0x87, 0x94, 0x92, 0x11, 0x65, 0xbf, 0x1a, 0x09, 0xde}, }, { addYX: fp.Elt{0xf3, 0x84, 0x76, 0x77, 0xa5, 0x6b, 0x27, 0x3b, 0x83, 0x3d, 0xdf, 0xa0, 0xeb, 0x32, 0x6d, 0x58, 0x81, 0x57, 0x64, 0xc2, 0x21, 0x7c, 0x9b, 0xea, 0xe6, 0xb0, 0x93, 0xf9, 0xe7, 0xc3, 0xed, 0x5a, 0x8e, 0xe2, 0xb4, 0x72, 0x76, 0x66, 0x0f, 0x22, 0x29, 0x94, 0x3e, 0x63, 0x48, 0x5e, 0x80, 0xcb, 0xac, 0xfa, 0x95, 0xb6, 0x4b, 0xc4, 0x95, 0x33}, subYX: fp.Elt{0x0c, 0x55, 0xd1, 0x5e, 0x5f, 0xbf, 0xbf, 0xe2, 0x4c, 0xfc, 0x37, 0x4a, 0xc4, 0xb1, 0xf4, 0x83, 0x61, 0x93, 0x60, 0x8e, 0x9f, 0x31, 0xf0, 0xa0, 0x41, 0xff, 0x1d, 0xe2, 0x7f, 0xca, 0x40, 0xd6, 0x88, 0xe8, 0x91, 0x61, 0xe2, 0x11, 0x18, 0x83, 0xf3, 0x25, 0x2f, 0x3f, 0x49, 0x40, 0xd4, 0x83, 0xe2, 0xd7, 0x74, 0x6a, 0x16, 0x86, 0x4e, 0xab}, dt2: fp.Elt{0xdd, 0x58, 0x65, 0xd8, 0x9f, 0xdd, 0x70, 0x7f, 0x0f, 0xec, 0xbd, 0x5c, 0x5c, 0x9b, 0x7e, 0x1b, 0x9f, 0x79, 0x36, 0x1f, 0xfd, 0x79, 0x10, 0x1c, 0x52, 0xf3, 0x22, 0xa4, 0x1f, 0x71, 0x6e, 0x63, 0x14, 0xf4, 0xa7, 0x3e, 0xbe, 0xad, 0x43, 0x30, 0x38, 0x8c, 0x29, 0xc6, 0xcf, 0x50, 0x75, 0x21, 0xe5, 0x78, 0xfd, 0xb0, 0x9a, 0xc4, 0x6d, 0xd4}, }, }, { { addYX: fp.Elt{0x7a, 0xa1, 0x38, 0xa6, 0xfd, 0x0e, 0x96, 0xd5, 0x26, 0x76, 0x86, 0x70, 0x80, 0x30, 0xa6, 0x67, 0xeb, 0xf4, 0x39, 0xdb, 0x22, 0xf5, 0x9f, 0x98, 0xe4, 0xb5, 0x3a, 0x0c, 0x59, 0xbf, 0x85, 0xc6, 0xf0, 0x0b, 0x1c, 0x41, 0x38, 0x09, 0x01, 0xdb, 0xd6, 0x3c, 0xb7, 0xf1, 0x08, 0x6b, 0x4b, 0x9e, 0x63, 0x53, 0x83, 0xd3, 0xab, 0xa3, 0x72, 0x0d}, subYX: fp.Elt{0x84, 0x68, 0x25, 0xe8, 0xe9, 0x8f, 0x91, 0xbf, 0xf7, 0xa4, 0x30, 0xae, 0xea, 0x9f, 0xdd, 0x56, 0x64, 0x09, 0xc9, 0x54, 0x68, 0x4e, 0x33, 0xc5, 0x6f, 0x7b, 0x2d, 0x52, 0x2e, 0x42, 0xbe, 0xbe, 0xf5, 0x64, 0xbf, 0x77, 0x54, 0xdf, 0xb0, 0x10, 0xd2, 0x16, 0x5d, 0xce, 0xaf, 0x9f, 0xfb, 0xa3, 0x63, 0x50, 0xcb, 0xc0, 0xd0, 0x88, 0x44, 0xa3}, dt2: fp.Elt{0xc3, 0x8b, 0xa5, 0xf1, 0x44, 0xe4, 0x41, 0xcd, 0x75, 0xe3, 0x17, 0x69, 0x5b, 0xb9, 0xbb, 0xee, 0x82, 0xbb, 0xce, 0x57, 0xdf, 0x2a, 0x9c, 0x12, 0xab, 0x66, 0x08, 0x68, 0x05, 0x1b, 0x87, 0xee, 0x5d, 0x1e, 0x18, 0x14, 0x22, 0x4b, 0x99, 0x61, 0x75, 0x28, 0xe7, 0x65, 0x1c, 0x36, 0xb6, 0x18, 0x09, 0xa8, 0xdf, 0xef, 0x30, 0x35, 0xbc, 0x58}, }, { addYX: fp.Elt{0xc5, 0xd3, 0x0e, 0x6f, 0xaf, 0x06, 0x69, 0xc4, 0x07, 0x9e, 0x58, 0x6e, 0x3f, 0x49, 0xd9, 0x0a, 0x3c, 0x2c, 0x37, 0xcd, 0x27, 0x4d, 0x87, 0x91, 0x7a, 0xb0, 0x28, 0xad, 0x2f, 0x68, 0x92, 0x05, 0x97, 0xf1, 0x30, 0x5f, 0x4c, 0x10, 0x20, 0x30, 0xd3, 0x08, 0x3f, 0xc1, 0xc6, 0xb7, 0xb5, 0xd1, 0x71, 0x7b, 0xa8, 0x0a, 0xd8, 0xf5, 0x17, 0xcf}, subYX: fp.Elt{0x64, 0xd4, 0x8f, 0x91, 0x40, 0xab, 0x6e, 0x1a, 0x62, 0x83, 0xdc, 0xd7, 0x30, 0x1a, 0x4a, 0x2a, 0x4c, 0x54, 0x86, 0x19, 0x81, 0x5d, 0x04, 0x52, 0xa3, 0xca, 0x82, 0x38, 0xdc, 0x1e, 0xf0, 0x7a, 0x78, 0x76, 0x49, 0x4f, 0x71, 0xc4, 0x74, 0x2f, 0xf0, 0x5b, 0x2e, 0x5e, 0xac, 0xef, 0x17, 0xe4, 0x8e, 0x6e, 0xed, 0x43, 0x23, 0x61, 0x99, 0x49}, dt2: fp.Elt{0x64, 0x90, 0x72, 0x76, 0xf8, 0x2c, 0x7d, 0x57, 0xf9, 0x30, 0x5e, 0x7a, 0x10, 0x74, 0x19, 0x39, 0xd9, 0xaf, 0x0a, 0xf1, 0x43, 0xed, 0x88, 0x9c, 0x8b, 0xdc, 0x9b, 0x1c, 0x90, 0xe7, 0xf7, 0xa3, 0xa5, 0x0d, 0xc6, 0xbc, 0x30, 0xfb, 0x91, 0x1a, 0x51, 0xba, 0x2d, 0xbe, 0x89, 0xdf, 0x1d, 0xdc, 0x53, 0xa8, 0x82, 0x8a, 0xd3, 0x8d, 0x16, 0x68}, }, { addYX: fp.Elt{0xef, 0x5c, 0xe3, 0x74, 0xbf, 0x13, 0x4a, 0xbf, 0x66, 0x73, 0x64, 0xb7, 0xd4, 0xce, 0x98, 0x82, 0x05, 0xfa, 0x98, 0x0c, 0x0a, 0xae, 0xe5, 0x6b, 0x9f, 0xac, 0xbb, 0x6e, 0x1f, 0xcf, 0xff, 0xa6, 0x71, 0x9a, 0xa8, 0x7a, 0x9e, 0x64, 0x1f, 0x20, 0x4a, 0x61, 0xa2, 0xd6, 0x50, 0xe3, 0xba, 0x81, 0x0c, 0x50, 0x59, 0x69, 0x59, 0x15, 0x55, 0xdb}, subYX: fp.Elt{0xe8, 0x77, 0x4d, 0xe8, 0x66, 0x3d, 0xc1, 0x00, 0x3c, 0xf2, 0x25, 0x00, 0xdc, 0xb2, 0xe5, 0x9b, 0x12, 0x89, 0xf3, 0xd6, 0xea, 0x85, 0x60, 0xfe, 0x67, 0x91, 0xfd, 0x04, 0x7c, 0xe0, 0xf1, 0x86, 0x06, 0x11, 0x66, 0xee, 0xd4, 0xd5, 0xbe, 0x3b, 0x0f, 0xe3, 0x59, 0xb3, 0x4f, 0x00, 0xb6, 0xce, 0x80, 0xc1, 0x61, 0xf7, 0xaf, 0x04, 0x6a, 0x3c}, dt2: fp.Elt{0x00, 0xd7, 0x32, 0x93, 0x67, 0x70, 0x6f, 0xd7, 0x69, 0xab, 0xb1, 0xd3, 0xdc, 0xd6, 0xa8, 0xdd, 0x35, 0x25, 0xca, 0xd3, 0x8a, 0x6d, 0xce, 0xfb, 0xfd, 0x2b, 0x83, 0xf0, 0xd4, 0xac, 0x66, 0xfb, 0x72, 0x87, 0x7e, 0x55, 0xb7, 0x91, 0x58, 0x10, 0xc3, 0x11, 0x7e, 0x15, 0xfe, 0x7c, 0x55, 0x90, 0xa3, 0x9e, 0xed, 0x9a, 0x7f, 0xa7, 0xb7, 0xeb}, }, { addYX: fp.Elt{0x25, 0x0f, 0xc2, 0x09, 0x9c, 0x10, 0xc8, 0x7c, 0x93, 0xa7, 0xbe, 0xe9, 0x26, 0x25, 0x7c, 0x21, 0xfe, 0xe7, 0x5f, 0x3c, 0x02, 0x83, 0xa7, 0x9e, 0xdf, 0xc0, 0x94, 0x2b, 0x7d, 0x1a, 0xd0, 0x1d, 0xcc, 0x2e, 0x7d, 0xd4, 0x85, 0xe7, 0xc1, 0x15, 0x66, 0xd6, 0xd6, 0x32, 0xb8, 0xf7, 0x63, 0xaa, 0x3b, 0xa5, 0xea, 0x49, 0xad, 0x88, 0x9b, 0x66}, subYX: fp.Elt{0x09, 0x97, 0x79, 0x36, 0x41, 0x56, 0x9b, 0xdf, 0x15, 0xd8, 0x43, 0x28, 0x17, 0x5b, 0x96, 0xc9, 0xcf, 0x39, 0x1f, 0x13, 0xf7, 0x4d, 0x1d, 0x1f, 0xda, 0x51, 0x56, 0xe7, 0x0a, 0x5a, 0x65, 0xb6, 0x2a, 0x87, 0x49, 0x86, 0xc2, 0x2b, 0xcd, 0xfe, 0x07, 0xf6, 0x4c, 0xe2, 0x1d, 0x9b, 0xd8, 0x82, 0x09, 0x5b, 0x11, 0x10, 0x62, 0x56, 0x89, 0xbd}, dt2: fp.Elt{0xd9, 0x15, 0x73, 0xf2, 0x96, 0x35, 0x53, 0xb0, 0xe7, 0xa8, 0x0b, 0x93, 0x35, 0x0b, 0x3a, 0x00, 0xf5, 0x18, 0xb1, 0xc3, 0x12, 0x3f, 0x91, 0x17, 0xc1, 0x4c, 0x15, 0x5a, 0x86, 0x92, 0x11, 0xbd, 0x44, 0x40, 0x5a, 0x7b, 0x15, 0x89, 0xba, 0xc1, 0xc1, 0xbc, 0x43, 0x45, 0xe6, 0x52, 0x02, 0x73, 0x0a, 0xd0, 0x2a, 0x19, 0xda, 0x47, 0xa8, 0xff}, }, }, } // tabVerif contains the odd multiples of P. The entry T[i] = (2i+1)P, where // P = phi(G) and G is the generator of the Goldilocks curve, and phi is a // 4-degree isogeny. var tabVerif = [1 << (omegaFix - 2)]preTwistPointAffine{ { /* 1P*/ addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55}, }, { /* 3P*/ addYX: fp.Elt{0xd1, 0xe9, 0xa8, 0x33, 0x20, 0x76, 0x18, 0x08, 0x45, 0x2a, 0xc9, 0x67, 0x2a, 0xc3, 0x15, 0x24, 0xf9, 0x74, 0x21, 0x30, 0x99, 0x59, 0x8b, 0xb2, 0xf0, 0xa4, 0x07, 0xe2, 0x6a, 0x36, 0x8d, 0xd9, 0xd2, 0x4a, 0x7f, 0x73, 0x50, 0x39, 0x3d, 0xaa, 0xa7, 0x51, 0x73, 0x0d, 0x2b, 0x8b, 0x96, 0x47, 0xac, 0x3c, 0x5d, 0xaa, 0x39, 0x9c, 0xcf, 0xd5}, subYX: fp.Elt{0x6b, 0x11, 0x5d, 0x1a, 0xf9, 0x41, 0x9d, 0xc5, 0x30, 0x3e, 0xad, 0x25, 0x2c, 0x04, 0x45, 0xea, 0xcc, 0x67, 0x07, 0x85, 0xe9, 0xda, 0x0e, 0xb5, 0x40, 0xb7, 0x32, 0xb4, 0x49, 0xdd, 0xff, 0xaa, 0xfc, 0xbb, 0x19, 0xca, 0x8b, 0x79, 0x2b, 0x8f, 0x8d, 0x00, 0x33, 0xc2, 0xad, 0xe9, 0xd3, 0x12, 0xa8, 0xaa, 0x87, 0x62, 0xad, 0x2d, 0xff, 0xa4}, dt2: fp.Elt{0xb0, 0xaf, 0x3b, 0xea, 0xf0, 0x42, 0x0b, 0x5e, 0x88, 0xd3, 0x98, 0x08, 0x87, 0x59, 0x72, 0x0a, 0xc2, 0xdf, 0xcb, 0x7f, 0x59, 0xb5, 0x4c, 0x63, 0x68, 0xe8, 0x41, 0x38, 0x67, 0x4f, 0xe9, 0xc6, 0xb2, 0x6b, 0x08, 0xa7, 0xf7, 0x0e, 0xcd, 0xea, 0xca, 0x3d, 0xaf, 0x8e, 0xda, 0x4b, 0x2e, 0xd2, 0x88, 0x64, 0x8d, 0xc5, 0x5f, 0x76, 0x0f, 0x3d}, }, { /* 5P*/ addYX: fp.Elt{0xe5, 0x65, 0xc9, 0xe2, 0x75, 0xf0, 0x7d, 0x1a, 0xba, 0xa4, 0x40, 0x4b, 0x93, 0x12, 0xa2, 0x80, 0x95, 0x0d, 0x03, 0x93, 0xe8, 0xa5, 0x4d, 0xe2, 0x3d, 0x81, 0xf5, 0xce, 0xd4, 0x2d, 0x25, 0x59, 0x16, 0x5c, 0xe7, 0xda, 0xc7, 0x45, 0xd2, 0x7e, 0x2c, 0x38, 0xd4, 0x37, 0x64, 0xb2, 0xc2, 0x28, 0xc5, 0x72, 0x16, 0x32, 0x45, 0x36, 0x6f, 0x9f}, subYX: fp.Elt{0x09, 0xf4, 0x7e, 0xbd, 0x89, 0xdb, 0x19, 0x58, 0xe1, 0x08, 0x00, 0x8a, 0xf4, 0x5f, 0x2a, 0x32, 0x40, 0xf0, 0x2c, 0x3f, 0x5d, 0xe4, 0xfc, 0x89, 0x11, 0x24, 0xb4, 0x2f, 0x97, 0xad, 0xac, 0x8f, 0x19, 0xab, 0xfa, 0x12, 0xe5, 0xf9, 0x50, 0x4e, 0x50, 0x6f, 0x32, 0x30, 0x88, 0xa6, 0xe5, 0x48, 0x28, 0xa2, 0x1b, 0x9f, 0xcd, 0xe2, 0x43, 0x38}, dt2: fp.Elt{0xa9, 0xcc, 0x53, 0x39, 0x86, 0x02, 0x60, 0x75, 0x34, 0x99, 0x57, 0xbd, 0xfc, 0x5a, 0x8e, 0xce, 0x5e, 0x98, 0x22, 0xd0, 0xa5, 0x24, 0xff, 0x90, 0x28, 0x9f, 0x58, 0xf3, 0x39, 0xe9, 0xba, 0x36, 0x23, 0xfb, 0x7f, 0x41, 0xcc, 0x2b, 0x5a, 0x25, 0x3f, 0x4c, 0x2a, 0xf1, 0x52, 0x6f, 0x2f, 0x07, 0xe3, 0x88, 0x81, 0x77, 0xdd, 0x7c, 0x88, 0x82}, }, { /* 7P*/ addYX: fp.Elt{0xf7, 0xee, 0x88, 0xfd, 0x3a, 0xbf, 0x7e, 0x28, 0x39, 0x23, 0x79, 0xe6, 0x5c, 0x56, 0xcb, 0xb5, 0x48, 0x6a, 0x80, 0x6d, 0x37, 0x60, 0x6c, 0x10, 0x35, 0x49, 0x4b, 0x46, 0x60, 0xd4, 0x79, 0xd4, 0x53, 0xd3, 0x67, 0x88, 0xd0, 0x41, 0xd5, 0x43, 0x85, 0xc8, 0x71, 0xe3, 0x1c, 0xb6, 0xda, 0x22, 0x64, 0x8f, 0x80, 0xac, 0xad, 0x7d, 0xd5, 0x82}, subYX: fp.Elt{0x92, 0x40, 0xc1, 0x83, 0x21, 0x9b, 0xd5, 0x7d, 0x3f, 0x29, 0xb6, 0x26, 0xef, 0x12, 0xb9, 0x27, 0x39, 0x42, 0x37, 0x97, 0x09, 0x9a, 0x08, 0xe1, 0x68, 0xb6, 0x7a, 0x3f, 0x9f, 0x45, 0xf8, 0x37, 0x19, 0x83, 0x97, 0xe6, 0x73, 0x30, 0x32, 0x35, 0xcf, 0xae, 0x5c, 0x12, 0x68, 0xdf, 0x6e, 0x2b, 0xde, 0x83, 0xa0, 0x44, 0x74, 0x2e, 0x4a, 0xe9}, dt2: fp.Elt{0xcb, 0x22, 0x0a, 0xda, 0x6b, 0xc1, 0x8a, 0x29, 0xa1, 0xac, 0x8b, 0x5b, 0x8b, 0x32, 0x20, 0xf2, 0x21, 0xae, 0x0c, 0x43, 0xc4, 0xd7, 0x19, 0x37, 0x3d, 0x79, 0x25, 0x98, 0x6c, 0x9c, 0x22, 0x31, 0x2a, 0x55, 0x9f, 0xda, 0x5e, 0xa8, 0x13, 0xdb, 0x8e, 0x2e, 0x16, 0x39, 0xf4, 0x91, 0x6f, 0xec, 0x71, 0x71, 0xc9, 0x10, 0xf2, 0xa4, 0x8f, 0x11}, }, { /* 9P*/ addYX: fp.Elt{0x85, 0xdd, 0x37, 0x62, 0x74, 0x8e, 0x33, 0x5b, 0x25, 0x12, 0x1b, 0xe7, 0xdf, 0x47, 0xe5, 0x12, 0xfd, 0x3a, 0x3a, 0xf5, 0x5d, 0x4c, 0xa2, 0x29, 0x3c, 0x5c, 0x2f, 0xee, 0x18, 0x19, 0x0a, 0x2b, 0xef, 0x67, 0x50, 0x7a, 0x0d, 0x29, 0xae, 0x55, 0x82, 0xcd, 0xd6, 0x41, 0x90, 0xb4, 0x13, 0x31, 0x5d, 0x11, 0xb8, 0xaa, 0x12, 0x86, 0x08, 0xac}, subYX: fp.Elt{0xcc, 0x37, 0x8d, 0x83, 0x5f, 0xfd, 0xde, 0xd5, 0xf7, 0xf1, 0xae, 0x0a, 0xa7, 0x0b, 0xeb, 0x6d, 0x19, 0x8a, 0xb6, 0x1a, 0x59, 0xd8, 0xff, 0x3c, 0xbc, 0xbc, 0xef, 0x9c, 0xda, 0x7b, 0x75, 0x12, 0xaf, 0x80, 0x8f, 0x2c, 0x3c, 0xaa, 0x0b, 0x17, 0x86, 0x36, 0x78, 0x18, 0xc8, 0x8a, 0xf6, 0xb8, 0x2c, 0x2f, 0x57, 0x2c, 0x62, 0x57, 0xf6, 0x90}, dt2: fp.Elt{0x83, 0xbc, 0xa2, 0x07, 0xa5, 0x38, 0x96, 0xea, 0xfe, 0x11, 0x46, 0x1d, 0x3b, 0xcd, 0x42, 0xc5, 0xee, 0x67, 0x04, 0x72, 0x08, 0xd8, 0xd9, 0x96, 0x07, 0xf7, 0xac, 0xc3, 0x64, 0xf1, 0x98, 0x2c, 0x55, 0xd7, 0x7d, 0xc8, 0x6c, 0xbd, 0x2c, 0xff, 0x15, 0xd6, 0x6e, 0xb8, 0x17, 0x8e, 0xa8, 0x27, 0x66, 0xb1, 0x73, 0x79, 0x96, 0xff, 0x29, 0x10}, }, { /* 11P*/ addYX: fp.Elt{0x76, 0xcb, 0x9b, 0x0c, 0x5b, 0xfe, 0xe1, 0x2a, 0xdd, 0x6f, 0x6c, 0xdd, 0x6f, 0xb4, 0xc0, 0xc2, 0x1b, 0x4b, 0x38, 0xe8, 0x66, 0x8c, 0x1e, 0x31, 0x63, 0xb9, 0x94, 0xcd, 0xc3, 0x8c, 0x44, 0x25, 0x7b, 0xd5, 0x39, 0x80, 0xfc, 0x01, 0xaa, 0xf7, 0x2a, 0x61, 0x8a, 0x25, 0xd2, 0x5f, 0xc5, 0x66, 0x38, 0xa4, 0x17, 0xcf, 0x3e, 0x11, 0x0f, 0xa3}, subYX: fp.Elt{0xe0, 0xb6, 0xd1, 0x9c, 0x71, 0x49, 0x2e, 0x7b, 0xde, 0x00, 0xda, 0x6b, 0xf1, 0xec, 0xe6, 0x7a, 0x15, 0x38, 0x71, 0xe9, 0x7b, 0xdb, 0xf8, 0x98, 0xc0, 0x91, 0x2e, 0x53, 0xee, 0x92, 0x87, 0x25, 0xc9, 0xb0, 0xbb, 0x33, 0x15, 0x46, 0x7f, 0xfd, 0x4f, 0x8b, 0x77, 0x05, 0x96, 0xb6, 0xe2, 0x08, 0xdb, 0x0d, 0x09, 0xee, 0x5b, 0xd1, 0x2a, 0x63}, dt2: fp.Elt{0x8f, 0x7b, 0x57, 0x8c, 0xbf, 0x06, 0x0d, 0x43, 0x21, 0x92, 0x94, 0x2d, 0x6a, 0x38, 0x07, 0x0f, 0xa0, 0xf1, 0xe3, 0xd8, 0x2a, 0xbf, 0x46, 0xc6, 0x9e, 0x1f, 0x8f, 0x2b, 0x46, 0x84, 0x0b, 0x74, 0xed, 0xff, 0xf8, 0xa5, 0x94, 0xae, 0xf1, 0x67, 0xb1, 0x9b, 0xdd, 0x4a, 0xd0, 0xdb, 0xc2, 0xb5, 0x58, 0x49, 0x0c, 0xa9, 0x1d, 0x7d, 0xa9, 0xd3}, }, { /* 13P*/ addYX: fp.Elt{0x73, 0x84, 0x2e, 0x31, 0x1f, 0xdc, 0xed, 0x9f, 0x74, 0xfa, 0xe0, 0x35, 0xb1, 0x85, 0x6a, 0x8d, 0x86, 0xd0, 0xff, 0xd6, 0x08, 0x43, 0x73, 0x1a, 0xd5, 0xf8, 0x43, 0xd4, 0xb3, 0xe5, 0x3f, 0xa8, 0x84, 0x17, 0x59, 0x65, 0x4e, 0xe6, 0xee, 0x54, 0x9c, 0xda, 0x5e, 0x7e, 0x98, 0x29, 0x6d, 0x73, 0x34, 0x1f, 0x99, 0x80, 0x54, 0x54, 0x81, 0x0b}, subYX: fp.Elt{0xb1, 0xe5, 0xbb, 0x80, 0x22, 0x9c, 0x81, 0x6d, 0xaf, 0x27, 0x65, 0x6f, 0x7e, 0x9c, 0xb6, 0x8d, 0x35, 0x5c, 0x2e, 0x20, 0x48, 0x7a, 0x28, 0xf0, 0x97, 0xfe, 0xb7, 0x71, 0xce, 0xd6, 0xad, 0x3a, 0x81, 0xf6, 0x74, 0x5e, 0xf3, 0xfd, 0x1b, 0xd4, 0x1e, 0x7c, 0xc2, 0xb7, 0xc8, 0xa6, 0xc9, 0x89, 0x03, 0x47, 0xec, 0x24, 0xd6, 0x0e, 0xec, 0x9c}, dt2: fp.Elt{0x91, 0x0a, 0x43, 0x34, 0x20, 0xc2, 0x64, 0xf7, 0x4e, 0x48, 0xc8, 0xd2, 0x95, 0x83, 0xd1, 0xa4, 0xfb, 0x4e, 0x41, 0x3b, 0x0d, 0xd5, 0x07, 0xd9, 0xf1, 0x13, 0x16, 0x78, 0x54, 0x57, 0xd0, 0xf1, 0x4f, 0x20, 0xac, 0xcf, 0x9c, 0x3b, 0x33, 0x0b, 0x99, 0x54, 0xc3, 0x7f, 0x3e, 0x57, 0x26, 0x86, 0xd5, 0xa5, 0x2b, 0x8d, 0xe3, 0x19, 0x36, 0xf7}, }, { /* 15P*/ addYX: fp.Elt{0x23, 0x69, 0x47, 0x14, 0xf9, 0x9a, 0x50, 0xff, 0x64, 0xd1, 0x50, 0x35, 0xc3, 0x11, 0xd3, 0x19, 0xcf, 0x87, 0xda, 0x30, 0x0b, 0x50, 0xda, 0xc0, 0xe0, 0x25, 0x00, 0xe5, 0x68, 0x93, 0x04, 0xc2, 0xaf, 0xbd, 0x2f, 0x36, 0x5f, 0x47, 0x96, 0x10, 0xa8, 0xbd, 0xe4, 0x88, 0xac, 0x80, 0x52, 0x61, 0x73, 0xe9, 0x63, 0xdd, 0x99, 0xad, 0x20, 0x5b}, subYX: fp.Elt{0x1b, 0x5e, 0xa2, 0x2a, 0x25, 0x0f, 0x86, 0xc0, 0xb1, 0x2e, 0x0c, 0x13, 0x40, 0x8d, 0xf0, 0xe6, 0x00, 0x55, 0x08, 0xc5, 0x7d, 0xf4, 0xc9, 0x31, 0x25, 0x3a, 0x99, 0x69, 0xdd, 0x67, 0x63, 0x9a, 0xd6, 0x89, 0x2e, 0xa1, 0x19, 0xca, 0x2c, 0xd9, 0x59, 0x5f, 0x5d, 0xc3, 0x6e, 0x62, 0x36, 0x12, 0x59, 0x15, 0xe1, 0xdc, 0xa4, 0xad, 0xc9, 0xd0}, dt2: fp.Elt{0xbc, 0xea, 0xfc, 0xaf, 0x66, 0x23, 0xb7, 0x39, 0x6b, 0x2a, 0x96, 0xa8, 0x54, 0x43, 0xe9, 0xaa, 0x32, 0x40, 0x63, 0x92, 0x5e, 0xdf, 0x35, 0xc2, 0x9f, 0x24, 0x0c, 0xed, 0xfc, 0xde, 0x73, 0x8f, 0xa7, 0xd5, 0xa3, 0x2b, 0x18, 0x1f, 0xb0, 0xf8, 0xeb, 0x55, 0xd9, 0xc3, 0xfd, 0x28, 0x7c, 0x4f, 0xce, 0x0d, 0xf7, 0xae, 0xc2, 0x83, 0xc3, 0x78}, }, { /* 17P*/ addYX: fp.Elt{0x71, 0xe6, 0x60, 0x93, 0x37, 0xdb, 0x01, 0xa5, 0x4c, 0xba, 0xe8, 0x8e, 0xd5, 0xf9, 0xd3, 0x98, 0xe5, 0xeb, 0xab, 0x3a, 0x15, 0x8b, 0x35, 0x60, 0xbe, 0xe5, 0x9c, 0x2d, 0x10, 0x9b, 0x2e, 0xcf, 0x65, 0x64, 0xea, 0x8f, 0x72, 0xce, 0xf5, 0x18, 0xe5, 0xe2, 0xf0, 0x0e, 0xae, 0x04, 0xec, 0xa0, 0x20, 0x65, 0x63, 0x07, 0xb1, 0x9f, 0x03, 0x97}, subYX: fp.Elt{0x9e, 0x41, 0x64, 0x30, 0x95, 0x7f, 0x3a, 0x89, 0x7b, 0x0a, 0x79, 0x59, 0x23, 0x9a, 0x3b, 0xfe, 0xa4, 0x13, 0x08, 0xb2, 0x2e, 0x04, 0x50, 0x10, 0x30, 0xcd, 0x2e, 0xa4, 0x91, 0x71, 0x50, 0x36, 0x4a, 0x02, 0xf4, 0x8d, 0xa3, 0x36, 0x1b, 0xf4, 0x52, 0xba, 0x15, 0x04, 0x8b, 0x80, 0x25, 0xd9, 0xae, 0x67, 0x20, 0xd9, 0x88, 0x8f, 0x97, 0xa6}, dt2: fp.Elt{0xb5, 0xe7, 0x46, 0xbd, 0x55, 0x23, 0xa0, 0x68, 0xc0, 0x12, 0xd9, 0xf1, 0x0a, 0x75, 0xe2, 0xda, 0xf4, 0x6b, 0xca, 0x14, 0xe4, 0x9f, 0x0f, 0xb5, 0x3c, 0xa6, 0xa5, 0xa2, 0x63, 0x94, 0xd1, 0x1c, 0x39, 0x58, 0x57, 0x02, 0x27, 0x98, 0xb6, 0x47, 0xc6, 0x61, 0x4b, 0x5c, 0xab, 0x6f, 0x2d, 0xab, 0xe3, 0xc1, 0x69, 0xf9, 0x12, 0xb0, 0xc8, 0xd5}, }, { /* 19P*/ addYX: fp.Elt{0x19, 0x7d, 0xd5, 0xac, 0x79, 0xa2, 0x82, 0x9b, 0x28, 0x31, 0x22, 0xc0, 0x73, 0x02, 0x76, 0x17, 0x10, 0x70, 0x79, 0x57, 0xc9, 0x84, 0x62, 0x8e, 0x04, 0x04, 0x61, 0x67, 0x08, 0x48, 0xb4, 0x4b, 0xde, 0x53, 0x8c, 0xff, 0x36, 0x1b, 0x62, 0x86, 0x5d, 0xe1, 0x9b, 0xb1, 0xe5, 0xe8, 0x44, 0x64, 0xa1, 0x68, 0x3f, 0xa8, 0x45, 0x52, 0x91, 0xed}, subYX: fp.Elt{0x42, 0x1a, 0x36, 0x1f, 0x90, 0x15, 0x24, 0x8d, 0x24, 0x80, 0xe6, 0xfe, 0x1e, 0xf0, 0xad, 0xaf, 0x6a, 0x93, 0xf0, 0xa6, 0x0d, 0x5d, 0xea, 0xf6, 0x62, 0x96, 0x7a, 0x05, 0x76, 0x85, 0x74, 0x32, 0xc7, 0xc8, 0x64, 0x53, 0x62, 0xe7, 0x54, 0x84, 0xe0, 0x40, 0x66, 0x19, 0x70, 0x40, 0x95, 0x35, 0x68, 0x64, 0x43, 0xcd, 0xba, 0x29, 0x32, 0xa8}, dt2: fp.Elt{0x3e, 0xf6, 0xd6, 0xe4, 0x99, 0xeb, 0x20, 0x66, 0x08, 0x2e, 0x26, 0x64, 0xd7, 0x76, 0xf3, 0xb4, 0xc5, 0xa4, 0x35, 0x92, 0xd2, 0x99, 0x70, 0x5a, 0x1a, 0xe9, 0xe9, 0x3d, 0x3b, 0xe1, 0xcd, 0x0e, 0xee, 0x24, 0x13, 0x03, 0x22, 0xd6, 0xd6, 0x72, 0x08, 0x2b, 0xde, 0xfd, 0x93, 0xed, 0x0c, 0x7f, 0x5e, 0x31, 0x22, 0x4d, 0x80, 0x78, 0xc0, 0x48}, }, { /* 21P*/ addYX: fp.Elt{0x8f, 0x72, 0xd2, 0x9e, 0xc4, 0xcd, 0x2c, 0xbf, 0xa8, 0xd3, 0x24, 0x62, 0x28, 0xee, 0x39, 0x0a, 0x19, 0x3a, 0x58, 0xff, 0x21, 0x2e, 0x69, 0x6c, 0x6e, 0x18, 0xd0, 0xcd, 0x61, 0xc1, 0x18, 0x02, 0x5a, 0xe9, 0xe3, 0xef, 0x1f, 0x8e, 0x10, 0xe8, 0x90, 0x2b, 0x48, 0xcd, 0xee, 0x38, 0xbd, 0x3a, 0xca, 0xbc, 0x2d, 0xe2, 0x3a, 0x03, 0x71, 0x02}, subYX: fp.Elt{0xf8, 0xa4, 0x32, 0x26, 0x66, 0xaf, 0x3b, 0x53, 0xe7, 0xb0, 0x91, 0x92, 0xf5, 0x3c, 0x74, 0xce, 0xf2, 0xdd, 0x68, 0xa9, 0xf4, 0xcd, 0x5f, 0x60, 0xab, 0x71, 0xdf, 0xcd, 0x5c, 0x5d, 0x51, 0x72, 0x3a, 0x96, 0xea, 0xd6, 0xde, 0x54, 0x8e, 0x55, 0x4c, 0x08, 0x4c, 0x60, 0xdd, 0x34, 0xa9, 0x6f, 0xf3, 0x04, 0x02, 0xa8, 0xa6, 0x4e, 0x4d, 0x62}, dt2: fp.Elt{0x76, 0x4a, 0xae, 0x38, 0x62, 0x69, 0x72, 0xdc, 0xe8, 0x43, 0xbe, 0x1d, 0x61, 0xde, 0x31, 0xc3, 0x42, 0x8f, 0x33, 0x9d, 0xca, 0xc7, 0x9c, 0xec, 0x6a, 0xe2, 0xaa, 0x01, 0x49, 0x78, 0x8d, 0x72, 0x4f, 0x38, 0xea, 0x52, 0xc2, 0xd3, 0xc9, 0x39, 0x71, 0xba, 0xb9, 0x09, 0x9b, 0xa3, 0x7f, 0x45, 0x43, 0x65, 0x36, 0x29, 0xca, 0xe7, 0x5c, 0x5f}, }, { /* 23P*/ addYX: fp.Elt{0x89, 0x42, 0x35, 0x48, 0x6d, 0x74, 0xe5, 0x1f, 0xc3, 0xdd, 0x28, 0x5b, 0x84, 0x41, 0x33, 0x9f, 0x42, 0xf3, 0x1d, 0x5d, 0x15, 0x6d, 0x76, 0x33, 0x36, 0xaf, 0xe9, 0xdd, 0xfa, 0x63, 0x4f, 0x7a, 0x9c, 0xeb, 0x1c, 0x4f, 0x34, 0x65, 0x07, 0x54, 0xbb, 0x4c, 0x8b, 0x62, 0x9d, 0xd0, 0x06, 0x99, 0xb3, 0xe9, 0xda, 0x85, 0x19, 0xb0, 0x3d, 0x3c}, subYX: fp.Elt{0xbb, 0x99, 0xf6, 0xbf, 0xaf, 0x2c, 0x22, 0x0d, 0x7a, 0xaa, 0x98, 0x6f, 0x01, 0x82, 0x99, 0xcf, 0x88, 0xbd, 0x0e, 0x3a, 0x89, 0xe0, 0x9c, 0x8c, 0x17, 0x20, 0xc4, 0xe0, 0xcf, 0x43, 0x7a, 0xef, 0x0d, 0x9f, 0x87, 0xd4, 0xfb, 0xf2, 0x96, 0xb8, 0x03, 0xe8, 0xcb, 0x5c, 0xec, 0x65, 0x5f, 0x49, 0xa4, 0x7c, 0x85, 0xb4, 0xf6, 0xc7, 0xdb, 0xa3}, dt2: fp.Elt{0x11, 0xf3, 0x32, 0xa3, 0xa7, 0xb2, 0x7d, 0x51, 0x82, 0x44, 0xeb, 0xa2, 0x7d, 0x72, 0xcb, 0xc6, 0xf6, 0xc7, 0xb2, 0x38, 0x0e, 0x0f, 0x4f, 0x29, 0x00, 0xe4, 0x5b, 0x94, 0x46, 0x86, 0x66, 0xa1, 0x83, 0xb3, 0xeb, 0x15, 0xb6, 0x31, 0x50, 0x28, 0xeb, 0xed, 0x0d, 0x32, 0x39, 0xe9, 0x23, 0x81, 0x99, 0x3e, 0xff, 0x17, 0x4c, 0x11, 0x43, 0xd1}, }, { /* 25P*/ addYX: fp.Elt{0xce, 0xe7, 0xf8, 0x94, 0x8f, 0x96, 0xf8, 0x96, 0xe6, 0x72, 0x20, 0x44, 0x2c, 0xa7, 0xfc, 0xba, 0xc8, 0xe1, 0xbb, 0xc9, 0x16, 0x85, 0xcd, 0x0b, 0xe5, 0xb5, 0x5a, 0x7f, 0x51, 0x43, 0x63, 0x8b, 0x23, 0x8e, 0x1d, 0x31, 0xff, 0x46, 0x02, 0x66, 0xcc, 0x9e, 0x4d, 0xa2, 0xca, 0xe2, 0xc7, 0xfd, 0x22, 0xb1, 0xdb, 0xdf, 0x6f, 0xe6, 0xa5, 0x82}, subYX: fp.Elt{0xd0, 0xf5, 0x65, 0x40, 0xec, 0x8e, 0x65, 0x42, 0x78, 0xc1, 0x65, 0xe4, 0x10, 0xc8, 0x0b, 0x1b, 0xdd, 0x96, 0x68, 0xce, 0xee, 0x45, 0x55, 0xd8, 0x6e, 0xd3, 0xe6, 0x77, 0x19, 0xae, 0xc2, 0x8d, 0x8d, 0x3e, 0x14, 0x3f, 0x6d, 0x00, 0x2f, 0x9b, 0xd1, 0x26, 0x60, 0x28, 0x0f, 0x3a, 0x47, 0xb3, 0xe6, 0x68, 0x28, 0x24, 0x25, 0xca, 0xc8, 0x06}, dt2: fp.Elt{0x54, 0xbb, 0x60, 0x92, 0xdb, 0x8f, 0x0f, 0x38, 0xe0, 0xe6, 0xe4, 0xc9, 0xcc, 0x14, 0x62, 0x01, 0xc4, 0x2b, 0x0f, 0xcf, 0xed, 0x7d, 0x8e, 0xa4, 0xd9, 0x73, 0x0b, 0xba, 0x0c, 0xaf, 0x0c, 0xf9, 0xe2, 0xeb, 0x29, 0x2a, 0x53, 0xdf, 0x2c, 0x5a, 0xfa, 0x8f, 0xc1, 0x01, 0xd7, 0xb1, 0x45, 0x73, 0x92, 0x32, 0x83, 0x85, 0x12, 0x74, 0x89, 0x44}, }, { /* 27P*/ addYX: fp.Elt{0x0b, 0x73, 0x3c, 0xc2, 0xb1, 0x2e, 0xe1, 0xa7, 0xf5, 0xc9, 0x7a, 0xfb, 0x3d, 0x2d, 0xac, 0x59, 0xdb, 0xfa, 0x36, 0x11, 0xd1, 0x13, 0x04, 0x51, 0x1d, 0xab, 0x9b, 0x6b, 0x93, 0xfe, 0xda, 0xb0, 0x8e, 0xb4, 0x79, 0x11, 0x21, 0x0f, 0x65, 0xb9, 0xbb, 0x79, 0x96, 0x2a, 0xfd, 0x30, 0xe0, 0xb4, 0x2d, 0x9a, 0x55, 0x25, 0x5d, 0xd4, 0xad, 0x2a}, subYX: fp.Elt{0x9e, 0xc5, 0x04, 0xfe, 0xec, 0x3c, 0x64, 0x1c, 0xed, 0x95, 0xed, 0xae, 0xaf, 0x5c, 0x6e, 0x08, 0x9e, 0x02, 0x29, 0x59, 0x7e, 0x5f, 0xc4, 0x9a, 0xd5, 0x32, 0x72, 0x86, 0xe1, 0x4e, 0x3c, 0xce, 0x99, 0x69, 0x3b, 0xc4, 0xdd, 0x4d, 0xb7, 0xbb, 0xda, 0x3b, 0x1a, 0x99, 0xaa, 0x62, 0x15, 0xc1, 0xf0, 0xb6, 0x6c, 0xec, 0x56, 0xc1, 0xff, 0x0c}, dt2: fp.Elt{0x2f, 0xf1, 0x3f, 0x7a, 0x2d, 0x56, 0x19, 0x7f, 0xea, 0xbe, 0x59, 0x2e, 0x13, 0x67, 0x81, 0xfb, 0xdb, 0xc8, 0xa3, 0x1d, 0xd5, 0xe9, 0x13, 0x8b, 0x29, 0xdf, 0xcf, 0x9f, 0xe7, 0xd9, 0x0b, 0x70, 0xd3, 0x15, 0x57, 0x4a, 0xe9, 0x50, 0x12, 0x1b, 0x81, 0x4b, 0x98, 0x98, 0xa8, 0x31, 0x1d, 0x27, 0x47, 0x38, 0xed, 0x57, 0x99, 0x26, 0xb2, 0xee}, }, { /* 29P*/ addYX: fp.Elt{0x1c, 0xb2, 0xb2, 0x67, 0x3b, 0x8b, 0x3d, 0x5a, 0x30, 0x7e, 0x38, 0x7e, 0x3c, 0x3d, 0x28, 0x56, 0x59, 0xd8, 0x87, 0x53, 0x8b, 0xe6, 0x6c, 0x5d, 0xe5, 0x0a, 0x33, 0x10, 0xce, 0xa2, 0x17, 0x0d, 0xe8, 0x76, 0xee, 0x68, 0xa8, 0x72, 0x54, 0xbd, 0xa6, 0x24, 0x94, 0x6e, 0x77, 0xc7, 0x53, 0xb7, 0x89, 0x1c, 0x7a, 0xe9, 0x78, 0x9a, 0x74, 0x5f}, subYX: fp.Elt{0x76, 0x96, 0x1c, 0xcf, 0x08, 0x55, 0xd8, 0x1e, 0x0d, 0xa3, 0x59, 0x95, 0x32, 0xf4, 0xc2, 0x8e, 0x84, 0x5e, 0x4b, 0x04, 0xda, 0x71, 0xc9, 0x78, 0x52, 0xde, 0x14, 0xb4, 0x31, 0xf4, 0xd4, 0xb8, 0x58, 0xc5, 0x20, 0xe8, 0xdd, 0x15, 0xb5, 0xee, 0xea, 0x61, 0xe0, 0xf5, 0xd6, 0xae, 0x55, 0x59, 0x05, 0x3e, 0xaf, 0x74, 0xac, 0x1f, 0x17, 0x82}, dt2: fp.Elt{0x59, 0x24, 0xcd, 0xfc, 0x11, 0x7e, 0x85, 0x18, 0x3d, 0x69, 0xf7, 0x71, 0x31, 0x66, 0x98, 0x42, 0x95, 0x00, 0x8c, 0xb2, 0xae, 0x39, 0x7e, 0x85, 0xd6, 0xb0, 0x02, 0xec, 0xce, 0xfc, 0x25, 0xb2, 0xe3, 0x99, 0x8e, 0x5b, 0x61, 0x96, 0x2e, 0x6d, 0x96, 0x57, 0x71, 0xa5, 0x93, 0x41, 0x0e, 0x6f, 0xfd, 0x0a, 0xbf, 0xa9, 0xf7, 0x56, 0xa9, 0x3e}, }, { /* 31P*/ addYX: fp.Elt{0xa2, 0x2e, 0x0c, 0x17, 0x4d, 0xcc, 0x85, 0x2c, 0x18, 0xa0, 0xd2, 0x08, 0xba, 0x11, 0xfa, 0x47, 0x71, 0x86, 0xaf, 0x36, 0x6a, 0xd7, 0xfe, 0xb9, 0xb0, 0x2f, 0x89, 0x98, 0x49, 0x69, 0xf8, 0x6a, 0xad, 0x27, 0x5e, 0x0a, 0x22, 0x60, 0x5e, 0x5d, 0xca, 0x06, 0x51, 0x27, 0x99, 0x29, 0x85, 0x68, 0x98, 0xe1, 0xc4, 0x21, 0x50, 0xa0, 0xe9, 0xc1}, subYX: fp.Elt{0x4d, 0x70, 0xee, 0x91, 0x92, 0x3f, 0xb7, 0xd3, 0x1d, 0xdb, 0x8d, 0x6e, 0x16, 0xf5, 0x65, 0x7d, 0x5f, 0xb5, 0x6c, 0x59, 0x26, 0x70, 0x4b, 0xf2, 0xfc, 0xe7, 0xdf, 0x86, 0xfe, 0xa5, 0xa7, 0xa6, 0x5d, 0xfb, 0x06, 0xe9, 0xf9, 0xcc, 0xc0, 0x37, 0xcc, 0xd8, 0x09, 0x04, 0xd2, 0xa5, 0x1d, 0xd7, 0xb7, 0xce, 0x92, 0xac, 0x3c, 0xad, 0xfb, 0xae}, dt2: fp.Elt{0x17, 0xa3, 0x9a, 0xc7, 0x86, 0x2a, 0x51, 0xf7, 0x96, 0x79, 0x49, 0x22, 0x2e, 0x5a, 0x01, 0x5c, 0xb5, 0x95, 0xd4, 0xe8, 0xcb, 0x00, 0xca, 0x2d, 0x55, 0xb6, 0x34, 0x36, 0x0b, 0x65, 0x46, 0xf0, 0x49, 0xfc, 0x87, 0x86, 0xe5, 0xc3, 0x15, 0xdb, 0x32, 0xcd, 0xf2, 0xd3, 0x82, 0x4c, 0xe6, 0x61, 0x8a, 0xaf, 0xd4, 0x9e, 0x0f, 0x5a, 0xf2, 0x81}, }, { /* 33P*/ addYX: fp.Elt{0x88, 0x10, 0xc0, 0xcb, 0xf5, 0x77, 0xae, 0xa5, 0xbe, 0xf6, 0xcd, 0x2e, 0x8b, 0x7e, 0xbd, 0x79, 0x62, 0x4a, 0xeb, 0x69, 0xc3, 0x28, 0xaa, 0x72, 0x87, 0xa9, 0x25, 0x87, 0x46, 0xea, 0x0e, 0x62, 0xa3, 0x6a, 0x1a, 0xe2, 0xba, 0xdc, 0x81, 0x10, 0x33, 0x01, 0xf6, 0x16, 0x89, 0x80, 0xc6, 0xcd, 0xdb, 0xdc, 0xba, 0x0e, 0x09, 0x4a, 0x35, 0x4a}, subYX: fp.Elt{0x86, 0xb2, 0x2b, 0xd0, 0xb8, 0x4a, 0x6d, 0x66, 0x7b, 0x32, 0xdf, 0x3b, 0x1a, 0x19, 0x1f, 0x63, 0xee, 0x1f, 0x3d, 0x1c, 0x5c, 0x14, 0x60, 0x5b, 0x72, 0x49, 0x07, 0xb1, 0x0d, 0x72, 0xc6, 0x35, 0xf0, 0xbc, 0x5e, 0xda, 0x80, 0x6b, 0x64, 0x5b, 0xe5, 0x34, 0x54, 0x39, 0xdd, 0xe6, 0x3c, 0xcb, 0xe5, 0x29, 0x32, 0x06, 0xc6, 0xb1, 0x96, 0x34}, dt2: fp.Elt{0x85, 0x86, 0xf5, 0x84, 0x86, 0xe6, 0x77, 0x8a, 0x71, 0x85, 0x0c, 0x4f, 0x81, 0x5b, 0x29, 0x06, 0xb5, 0x2e, 0x26, 0x71, 0x07, 0x78, 0x07, 0xae, 0xbc, 0x95, 0x46, 0xc3, 0x65, 0xac, 0xe3, 0x76, 0x51, 0x7d, 0xd4, 0x85, 0x31, 0xe3, 0x43, 0xf3, 0x1b, 0x7c, 0xf7, 0x6b, 0x2c, 0xf8, 0x1c, 0xbb, 0x8d, 0xca, 0xab, 0x4b, 0xba, 0x7f, 0xa4, 0xe2}, }, { /* 35P*/ addYX: fp.Elt{0x1a, 0xee, 0xe7, 0xa4, 0x8a, 0x9d, 0x53, 0x80, 0xc6, 0xb8, 0x4e, 0xdc, 0x89, 0xe0, 0xc4, 0x2b, 0x60, 0x52, 0x6f, 0xec, 0x81, 0xd2, 0x55, 0x6b, 0x1b, 0x6f, 0x17, 0x67, 0x8e, 0x42, 0x26, 0x4c, 0x65, 0x23, 0x29, 0xc6, 0x7b, 0xcd, 0x9f, 0xad, 0x4b, 0x42, 0xd3, 0x0c, 0x75, 0xc3, 0x8a, 0xf5, 0xbe, 0x9e, 0x55, 0xf7, 0x47, 0x5d, 0xbd, 0x3a}, subYX: fp.Elt{0x0d, 0xa8, 0x3b, 0xf9, 0xc7, 0x7e, 0xc6, 0x86, 0x94, 0xc0, 0x01, 0xff, 0x27, 0xce, 0x43, 0xac, 0xe5, 0xe1, 0xd2, 0x8d, 0xc1, 0x22, 0x31, 0xbe, 0xe1, 0xaf, 0xf9, 0x4a, 0x78, 0xa1, 0x0c, 0xaa, 0xd4, 0x80, 0xe4, 0x09, 0x8d, 0xfb, 0x1d, 0x52, 0xc8, 0x60, 0x2d, 0xf2, 0xa2, 0x89, 0x02, 0x56, 0x3d, 0x56, 0x27, 0x85, 0xc7, 0xf0, 0x2b, 0x9a}, dt2: fp.Elt{0x62, 0x7c, 0xc7, 0x6b, 0x2c, 0x9d, 0x0a, 0x7c, 0xe5, 0x50, 0x3c, 0xe6, 0x87, 0x1c, 0x82, 0x30, 0x67, 0x3c, 0x39, 0xb6, 0xa0, 0x31, 0xfb, 0x03, 0x7b, 0xa1, 0x58, 0xdf, 0x12, 0x76, 0x5d, 0x5d, 0x0a, 0x8f, 0x9b, 0x37, 0x32, 0xc3, 0x60, 0x33, 0xea, 0x9f, 0x0a, 0x99, 0xfa, 0x20, 0xd0, 0x33, 0x21, 0xc3, 0x94, 0xd4, 0x86, 0x49, 0x7c, 0x4e}, }, { /* 37P*/ addYX: fp.Elt{0xc7, 0x0c, 0x71, 0xfe, 0x55, 0xd1, 0x95, 0x8f, 0x43, 0xbb, 0x6b, 0x74, 0x30, 0xbd, 0xe8, 0x6f, 0x1c, 0x1b, 0x06, 0x62, 0xf5, 0xfc, 0x65, 0xa0, 0xeb, 0x81, 0x12, 0xc9, 0x64, 0x66, 0x61, 0xde, 0xf3, 0x6d, 0xd4, 0xae, 0x8e, 0xb1, 0x72, 0xe0, 0xcd, 0x37, 0x01, 0x28, 0x52, 0xd7, 0x39, 0x46, 0x0c, 0x55, 0xcf, 0x47, 0x70, 0xef, 0xa1, 0x17}, subYX: fp.Elt{0x8d, 0x58, 0xde, 0x83, 0x88, 0x16, 0x0e, 0x12, 0x42, 0x03, 0x50, 0x60, 0x4b, 0xdf, 0xbf, 0x95, 0xcc, 0x7d, 0x18, 0x17, 0x7e, 0x31, 0x5d, 0x8a, 0x66, 0xc1, 0xcf, 0x14, 0xea, 0xf4, 0xf4, 0xe5, 0x63, 0x2d, 0x32, 0x86, 0x9b, 0xed, 0x1f, 0x4f, 0x03, 0xaf, 0x33, 0x92, 0xcb, 0xaf, 0x9c, 0x05, 0x0d, 0x47, 0x1b, 0x42, 0xba, 0x13, 0x22, 0x98}, dt2: fp.Elt{0xb5, 0x48, 0xeb, 0x7d, 0x3d, 0x10, 0x9f, 0x59, 0xde, 0xf8, 0x1c, 0x4f, 0x7d, 0x9d, 0x40, 0x4d, 0x9e, 0x13, 0x24, 0xb5, 0x21, 0x09, 0xb7, 0xee, 0x98, 0x5c, 0x56, 0xbc, 0x5e, 0x2b, 0x78, 0x38, 0x06, 0xac, 0xe3, 0xe0, 0xfa, 0x2e, 0xde, 0x4f, 0xd2, 0xb3, 0xfb, 0x2d, 0x71, 0x84, 0xd1, 0x9d, 0x12, 0x5b, 0x35, 0xc8, 0x03, 0x68, 0x67, 0xc7}, }, { /* 39P*/ addYX: fp.Elt{0xb6, 0x65, 0xfb, 0xa7, 0x06, 0x35, 0xbb, 0xe0, 0x31, 0x8d, 0x91, 0x40, 0x98, 0xab, 0x30, 0xe4, 0xca, 0x12, 0x59, 0x89, 0xed, 0x65, 0x5d, 0x7f, 0xae, 0x69, 0xa0, 0xa4, 0xfa, 0x78, 0xb4, 0xf7, 0xed, 0xae, 0x86, 0x78, 0x79, 0x64, 0x24, 0xa6, 0xd4, 0xe1, 0xf6, 0xd3, 0xa0, 0x89, 0xba, 0x20, 0xf4, 0x54, 0x0d, 0x8f, 0xdb, 0x1a, 0x79, 0xdb}, subYX: fp.Elt{0xe1, 0x82, 0x0c, 0x4d, 0xde, 0x9f, 0x40, 0xf0, 0xc1, 0xbd, 0x8b, 0xd3, 0x24, 0x03, 0xcd, 0xf2, 0x92, 0x7d, 0xe2, 0x68, 0x7f, 0xf1, 0xbe, 0x69, 0xde, 0x34, 0x67, 0x4c, 0x85, 0x3b, 0xec, 0x98, 0xcc, 0x4d, 0x3e, 0xc0, 0x96, 0x27, 0xe6, 0x75, 0xfc, 0xdf, 0x37, 0xc0, 0x1e, 0x27, 0xe0, 0xf6, 0xc2, 0xbd, 0xbc, 0x3d, 0x9b, 0x39, 0xdc, 0xe2}, dt2: fp.Elt{0xd8, 0x29, 0xa7, 0x39, 0xe3, 0x9f, 0x2f, 0x0e, 0x4b, 0x24, 0x21, 0x70, 0xef, 0xfd, 0x91, 0xea, 0xbf, 0xe1, 0x72, 0x90, 0xcc, 0xc9, 0x84, 0x0e, 0xad, 0xd5, 0xe6, 0xbb, 0xc5, 0x99, 0x7f, 0xa4, 0xf0, 0x2e, 0xcc, 0x95, 0x64, 0x27, 0x19, 0xd8, 0x4c, 0x27, 0x0d, 0xff, 0xb6, 0x29, 0xe2, 0x6c, 0xfa, 0xbb, 0x4d, 0x9c, 0xbb, 0xaf, 0xa5, 0xec}, }, { /* 41P*/ addYX: fp.Elt{0xd6, 0x33, 0x3f, 0x9f, 0xcf, 0xfd, 0x4c, 0xd1, 0xfe, 0xe5, 0xeb, 0x64, 0x27, 0xae, 0x7a, 0xa2, 0x82, 0x50, 0x6d, 0xaa, 0xe3, 0x5d, 0xe2, 0x48, 0x60, 0xb3, 0x76, 0x04, 0xd9, 0x19, 0xa7, 0xa1, 0x73, 0x8d, 0x38, 0xa9, 0xaf, 0x45, 0xb5, 0xb2, 0x62, 0x9b, 0xf1, 0x35, 0x7b, 0x84, 0x66, 0xeb, 0x06, 0xef, 0xf1, 0xb2, 0x2d, 0x6a, 0x61, 0x15}, subYX: fp.Elt{0x86, 0x50, 0x42, 0xf7, 0xda, 0x59, 0xb2, 0xcf, 0x0d, 0x3d, 0xee, 0x8e, 0x53, 0x5d, 0xf7, 0x9e, 0x6a, 0x26, 0x2d, 0xc7, 0x8c, 0x8e, 0x18, 0x50, 0x6d, 0xb7, 0x51, 0x4c, 0xa7, 0x52, 0x6e, 0x0e, 0x0a, 0x16, 0x74, 0xb2, 0x81, 0x8b, 0x56, 0x27, 0x22, 0x84, 0xf4, 0x56, 0xc5, 0x06, 0xe1, 0x8b, 0xca, 0x2d, 0xdb, 0x9a, 0xf6, 0x10, 0x9c, 0x51}, dt2: fp.Elt{0x1f, 0x16, 0xa2, 0x78, 0x96, 0x1b, 0x85, 0x9c, 0x76, 0x49, 0xd4, 0x0f, 0xac, 0xb0, 0xf4, 0xd0, 0x06, 0x2c, 0x7e, 0x6d, 0x6e, 0x8e, 0xc7, 0x9f, 0x18, 0xad, 0xfc, 0x88, 0x0c, 0x0c, 0x09, 0x05, 0x05, 0xa0, 0x79, 0x72, 0x32, 0x72, 0x87, 0x0f, 0x49, 0x87, 0x0c, 0xb4, 0x12, 0xc2, 0x09, 0xf8, 0x9f, 0x30, 0x72, 0xa9, 0x47, 0x13, 0x93, 0x49}, }, { /* 43P*/ addYX: fp.Elt{0xcc, 0xb1, 0x4c, 0xd3, 0xc0, 0x9e, 0x9e, 0x4d, 0x6d, 0x28, 0x0b, 0xa5, 0x94, 0xa7, 0x2e, 0xc2, 0xc7, 0xaf, 0x29, 0x73, 0xc9, 0x68, 0xea, 0x0f, 0x34, 0x37, 0x8d, 0x96, 0x8f, 0x3a, 0x3d, 0x73, 0x1e, 0x6d, 0x9f, 0xcf, 0x8d, 0x83, 0xb5, 0x71, 0xb9, 0xe1, 0x4b, 0x67, 0x71, 0xea, 0xcf, 0x56, 0xe5, 0xeb, 0x72, 0x15, 0x2f, 0x9e, 0xa8, 0xaa}, subYX: fp.Elt{0xf4, 0x3e, 0x85, 0x1c, 0x1a, 0xef, 0x50, 0xd1, 0xb4, 0x20, 0xb2, 0x60, 0x05, 0x98, 0xfe, 0x47, 0x3b, 0xc1, 0x76, 0xca, 0x2c, 0x4e, 0x5a, 0x42, 0xa3, 0xf7, 0x20, 0xaa, 0x57, 0x39, 0xee, 0x34, 0x1f, 0xe1, 0x68, 0xd3, 0x7e, 0x06, 0xc4, 0x6c, 0xc7, 0x76, 0x2b, 0xe4, 0x1c, 0x48, 0x44, 0xe6, 0xe5, 0x44, 0x24, 0x8d, 0xb3, 0xb6, 0x88, 0x32}, dt2: fp.Elt{0x18, 0xa7, 0xba, 0xd0, 0x44, 0x6f, 0x33, 0x31, 0x00, 0xf8, 0xf6, 0x12, 0xe3, 0xc5, 0xc7, 0xb5, 0x91, 0x9c, 0x91, 0xb5, 0x75, 0x18, 0x18, 0x8a, 0xab, 0xed, 0x24, 0x11, 0x2e, 0xce, 0x5a, 0x0f, 0x94, 0x5f, 0x2e, 0xca, 0xd3, 0x80, 0xea, 0xe5, 0x34, 0x96, 0x67, 0x8b, 0x6a, 0x26, 0x5e, 0xc8, 0x9d, 0x2c, 0x5e, 0x6c, 0xa2, 0x0c, 0xbf, 0xf0}, }, { /* 45P*/ addYX: fp.Elt{0xb3, 0xbf, 0xa3, 0x85, 0xee, 0xf6, 0x58, 0x02, 0x78, 0xc4, 0x30, 0xd6, 0x57, 0x59, 0x8c, 0x88, 0x08, 0x7c, 0xbc, 0xbe, 0x0a, 0x74, 0xa9, 0xde, 0x69, 0xe7, 0x41, 0xd8, 0xbf, 0x66, 0x8d, 0x3d, 0x28, 0x00, 0x8c, 0x47, 0x65, 0x34, 0xfe, 0x86, 0x9e, 0x6a, 0xf2, 0x41, 0x6a, 0x94, 0xc4, 0x88, 0x75, 0x23, 0x0d, 0x52, 0x69, 0xee, 0x07, 0x89}, subYX: fp.Elt{0x22, 0x3c, 0xa1, 0x70, 0x58, 0x97, 0x93, 0xbe, 0x59, 0xa8, 0x0b, 0x8a, 0x46, 0x2a, 0x38, 0x1e, 0x08, 0x6b, 0x61, 0x9f, 0xf2, 0x4a, 0x8b, 0x80, 0x68, 0x6e, 0xc8, 0x92, 0x60, 0xf3, 0xc9, 0x89, 0xb2, 0x6d, 0x63, 0xb0, 0xeb, 0x83, 0x15, 0x63, 0x0e, 0x64, 0xbb, 0xb8, 0xfe, 0xb4, 0x81, 0x90, 0x01, 0x28, 0x10, 0xb9, 0x74, 0x6e, 0xde, 0xa4}, dt2: fp.Elt{0x1a, 0x23, 0x45, 0xa8, 0x6f, 0x4e, 0xa7, 0x4a, 0x0c, 0xeb, 0xb0, 0x43, 0xf9, 0xef, 0x99, 0x60, 0x5b, 0xdb, 0x66, 0xc0, 0x86, 0x71, 0x43, 0xb1, 0x22, 0x7b, 0x1c, 0xe7, 0x8d, 0x09, 0x1d, 0x83, 0x76, 0x9c, 0xd3, 0x5a, 0xdd, 0x42, 0xd9, 0x2f, 0x2d, 0xba, 0x7a, 0xc2, 0xd9, 0x6b, 0xd4, 0x7a, 0xf1, 0xd5, 0x5f, 0x6b, 0x85, 0xbf, 0x0b, 0xf1}, }, { /* 47P*/ addYX: fp.Elt{0xb2, 0x83, 0xfa, 0x1f, 0xd2, 0xce, 0xb6, 0xf2, 0x2d, 0xea, 0x1b, 0xe5, 0x29, 0xa5, 0x72, 0xf9, 0x25, 0x48, 0x4e, 0xf2, 0x50, 0x1b, 0x39, 0xda, 0x34, 0xc5, 0x16, 0x13, 0xb4, 0x0c, 0xa1, 0x00, 0x79, 0x7a, 0xf5, 0x8b, 0xf3, 0x70, 0x14, 0xb6, 0xfc, 0x9a, 0x47, 0x68, 0x1e, 0x42, 0x70, 0x64, 0x2a, 0x84, 0x3e, 0x3d, 0x20, 0x58, 0xf9, 0x6a}, subYX: fp.Elt{0xd9, 0xee, 0xc0, 0xc4, 0xf5, 0xc2, 0x86, 0xaf, 0x45, 0xd2, 0xd2, 0x87, 0x1b, 0x64, 0xd5, 0xe0, 0x8c, 0x44, 0x00, 0x4f, 0x43, 0x89, 0x04, 0x48, 0x4a, 0x0b, 0xca, 0x94, 0x06, 0x2f, 0x23, 0x5b, 0x6c, 0x8d, 0x44, 0x66, 0x53, 0xf5, 0x5a, 0x20, 0x72, 0x28, 0x58, 0x84, 0xcc, 0x73, 0x22, 0x5e, 0xd1, 0x0b, 0x56, 0x5e, 0x6a, 0xa3, 0x11, 0x91}, dt2: fp.Elt{0x6e, 0x9f, 0x88, 0xa8, 0x68, 0x2f, 0x12, 0x37, 0x88, 0xfc, 0x92, 0x8f, 0x24, 0xeb, 0x5b, 0x2a, 0x2a, 0xd0, 0x14, 0x40, 0x4c, 0xa9, 0xa4, 0x03, 0x0c, 0x45, 0x48, 0x13, 0xe8, 0xa6, 0x37, 0xab, 0xc0, 0x06, 0x38, 0x6c, 0x96, 0x73, 0x40, 0x6c, 0xc6, 0xea, 0x56, 0xc6, 0xe9, 0x1a, 0x69, 0xeb, 0x7a, 0xd1, 0x33, 0x69, 0x58, 0x2b, 0xea, 0x2f}, }, { /* 49P*/ addYX: fp.Elt{0x58, 0xa8, 0x05, 0x41, 0x00, 0x9d, 0xaa, 0xd9, 0x98, 0xcf, 0xb9, 0x41, 0xb5, 0x4a, 0x8d, 0xe2, 0xe7, 0xc0, 0x72, 0xef, 0xc8, 0x28, 0x6b, 0x68, 0x9d, 0xc9, 0xdf, 0x05, 0x8b, 0xd0, 0x04, 0x74, 0x79, 0x45, 0x52, 0x05, 0xa3, 0x6e, 0x35, 0x3a, 0xe3, 0xef, 0xb2, 0xdc, 0x08, 0x6f, 0x4e, 0x76, 0x85, 0x67, 0xba, 0x23, 0x8f, 0xdd, 0xaf, 0x09}, subYX: fp.Elt{0xb4, 0x38, 0xc8, 0xff, 0x4f, 0x65, 0x2a, 0x7e, 0xad, 0xb1, 0xc6, 0xb9, 0x3d, 0xd6, 0xf7, 0x14, 0xcf, 0xf6, 0x98, 0x75, 0xbb, 0x47, 0x83, 0x90, 0xe7, 0xe1, 0xf6, 0x14, 0x99, 0x7e, 0xfa, 0xe4, 0x77, 0x24, 0xe3, 0xe7, 0xf0, 0x1e, 0xdb, 0x27, 0x4e, 0x16, 0x04, 0xf2, 0x08, 0x52, 0xfc, 0xec, 0x55, 0xdb, 0x2e, 0x67, 0xe1, 0x94, 0x32, 0x89}, dt2: fp.Elt{0x00, 0xad, 0x03, 0x35, 0x1a, 0xb1, 0x88, 0xf0, 0xc9, 0x11, 0xe4, 0x12, 0x52, 0x61, 0xfd, 0x8a, 0x1b, 0x6a, 0x0a, 0x4c, 0x42, 0x46, 0x22, 0x0e, 0xa5, 0xf9, 0xe2, 0x50, 0xf2, 0xb2, 0x1f, 0x20, 0x78, 0x10, 0xf6, 0xbf, 0x7f, 0x0c, 0x9c, 0xad, 0x40, 0x8b, 0x82, 0xd4, 0xba, 0x69, 0x09, 0xac, 0x4b, 0x6d, 0xc4, 0x49, 0x17, 0x81, 0x57, 0x3b}, }, { /* 51P*/ addYX: fp.Elt{0x0d, 0xfe, 0xb4, 0x35, 0x11, 0xbd, 0x1d, 0x6b, 0xc2, 0xc5, 0x3b, 0xd2, 0x23, 0x2c, 0x72, 0xe3, 0x48, 0xb1, 0x48, 0x73, 0xfb, 0xa3, 0x21, 0x6e, 0xc0, 0x09, 0x69, 0xac, 0xe1, 0x60, 0xbc, 0x24, 0x03, 0x99, 0x63, 0x0a, 0x00, 0xf0, 0x75, 0xf6, 0x92, 0xc5, 0xd6, 0xdb, 0x51, 0xd4, 0x7d, 0xe6, 0xf4, 0x11, 0x79, 0xd7, 0xc3, 0xaf, 0x48, 0xd0}, subYX: fp.Elt{0xf4, 0x4f, 0xaf, 0x31, 0xe3, 0x10, 0x89, 0x95, 0xf0, 0x8a, 0xf6, 0x31, 0x9f, 0x48, 0x02, 0xba, 0x42, 0x2b, 0x3c, 0x22, 0x8b, 0xcc, 0x12, 0x98, 0x6e, 0x7a, 0x64, 0x3a, 0xc4, 0xca, 0x32, 0x2a, 0x72, 0xf8, 0x2c, 0xcf, 0x78, 0x5e, 0x7a, 0x75, 0x6e, 0x72, 0x46, 0x48, 0x62, 0x28, 0xac, 0x58, 0x1a, 0xc6, 0x59, 0x88, 0x2a, 0x44, 0x9e, 0x83}, dt2: fp.Elt{0xb3, 0xde, 0x36, 0xfd, 0xeb, 0x1b, 0xd4, 0x24, 0x1b, 0x08, 0x8c, 0xfe, 0xa9, 0x41, 0xa1, 0x64, 0xf2, 0x6d, 0xdb, 0xf9, 0x94, 0xae, 0x86, 0x71, 0xab, 0x10, 0xbf, 0xa3, 0xb2, 0xa0, 0xdf, 0x10, 0x8c, 0x74, 0xce, 0xb3, 0xfc, 0xdb, 0xba, 0x15, 0xf6, 0x91, 0x7a, 0x9c, 0x36, 0x1e, 0x45, 0x07, 0x3c, 0xec, 0x1a, 0x61, 0x26, 0x93, 0xe3, 0x50}, }, { /* 53P*/ addYX: fp.Elt{0xc5, 0x50, 0xc5, 0x83, 0xb0, 0xbd, 0xd9, 0xf6, 0x6d, 0x15, 0x5e, 0xc1, 0x1a, 0x33, 0xa0, 0xce, 0x13, 0x70, 0x3b, 0xe1, 0x31, 0xc6, 0xc4, 0x02, 0xec, 0x8c, 0xd5, 0x9c, 0x97, 0xd3, 0x12, 0xc4, 0xa2, 0xf9, 0xd5, 0xfb, 0x22, 0x69, 0x94, 0x09, 0x2f, 0x59, 0xce, 0xdb, 0xf2, 0xf2, 0x00, 0xe0, 0xa9, 0x08, 0x44, 0x2e, 0x8b, 0x6b, 0xf5, 0xb3}, subYX: fp.Elt{0x90, 0xdd, 0xec, 0xa2, 0x65, 0xb7, 0x61, 0xbc, 0xaa, 0x70, 0xa2, 0x15, 0xd8, 0xb0, 0xf8, 0x8e, 0x23, 0x3d, 0x9f, 0x46, 0xa3, 0x29, 0x20, 0xd1, 0xa1, 0x15, 0x81, 0xc6, 0xb6, 0xde, 0xbe, 0x60, 0x63, 0x24, 0xac, 0x15, 0xfb, 0xeb, 0xd3, 0xea, 0x57, 0x13, 0x86, 0x38, 0x1e, 0x22, 0xf4, 0x8c, 0x5d, 0xaf, 0x1b, 0x27, 0x21, 0x4f, 0xa3, 0x63}, dt2: fp.Elt{0x07, 0x15, 0x87, 0xc4, 0xfd, 0xa1, 0x97, 0x7a, 0x07, 0x1f, 0x56, 0xcc, 0xe3, 0x6a, 0x01, 0x90, 0xce, 0xf9, 0xfa, 0x50, 0xb2, 0xe0, 0x87, 0x8b, 0x6c, 0x63, 0x6c, 0xf6, 0x2a, 0x09, 0xef, 0xef, 0xd2, 0x31, 0x40, 0x25, 0xf6, 0x84, 0xcb, 0xe0, 0xc4, 0x23, 0xc1, 0xcb, 0xe2, 0x02, 0x83, 0x2d, 0xed, 0x74, 0x74, 0x8b, 0xf8, 0x7c, 0x81, 0x18}, }, { /* 55P*/ addYX: fp.Elt{0x9e, 0xe5, 0x59, 0x95, 0x63, 0x2e, 0xac, 0x8b, 0x03, 0x3c, 0xc1, 0x8e, 0xe1, 0x5b, 0x56, 0x3c, 0x16, 0x41, 0xe4, 0xc2, 0x60, 0x0c, 0x6d, 0x65, 0x9f, 0xfc, 0x27, 0x68, 0x43, 0x44, 0x05, 0x12, 0x6c, 0xda, 0x04, 0xef, 0xcf, 0xcf, 0xdc, 0x0a, 0x1a, 0x7f, 0x12, 0xd3, 0xeb, 0x02, 0xb6, 0x04, 0xca, 0xd6, 0xcb, 0xf0, 0x22, 0xba, 0x35, 0x6d}, subYX: fp.Elt{0x09, 0x6d, 0xf9, 0x64, 0x4c, 0xe6, 0x41, 0xff, 0x01, 0x4d, 0xce, 0x1e, 0xfa, 0x38, 0xa2, 0x25, 0x62, 0xff, 0x03, 0x39, 0x18, 0x91, 0xbb, 0x9d, 0xce, 0x02, 0xf0, 0xf1, 0x3c, 0x55, 0x18, 0xa9, 0xab, 0x4d, 0xd2, 0x35, 0xfd, 0x8d, 0xa9, 0xb2, 0xad, 0xb7, 0x06, 0x6e, 0xc6, 0x69, 0x49, 0xd6, 0x98, 0x98, 0x0b, 0x22, 0x81, 0x6b, 0xbd, 0xa0}, dt2: fp.Elt{0x22, 0xf4, 0x85, 0x5d, 0x2b, 0xf1, 0x55, 0xa5, 0xd6, 0x27, 0x86, 0x57, 0x12, 0x1f, 0x16, 0x0a, 0x5a, 0x9b, 0xf2, 0x38, 0xb6, 0x28, 0xd8, 0x99, 0x0c, 0x89, 0x1d, 0x7f, 0xca, 0x21, 0x17, 0x1a, 0x0b, 0x02, 0x5f, 0x77, 0x2f, 0x73, 0x30, 0x7c, 0xc8, 0xd7, 0x2b, 0xcc, 0xe7, 0xf3, 0x21, 0xac, 0x53, 0xa7, 0x11, 0x5d, 0xd8, 0x1d, 0x9b, 0xf5}, }, { /* 57P*/ addYX: fp.Elt{0x94, 0x63, 0x5d, 0xef, 0xfd, 0x6d, 0x25, 0x4e, 0x6d, 0x29, 0x03, 0xed, 0x24, 0x28, 0x27, 0x57, 0x47, 0x3e, 0x6a, 0x1a, 0xfe, 0x37, 0xee, 0x5f, 0x83, 0x29, 0x14, 0xfd, 0x78, 0x25, 0x8a, 0xe1, 0x02, 0x38, 0xd8, 0xca, 0x65, 0x55, 0x40, 0x7d, 0x48, 0x2c, 0x7c, 0x7e, 0x60, 0xb6, 0x0c, 0x6d, 0xf7, 0xe8, 0xb3, 0x62, 0x53, 0xd6, 0x9c, 0x2b}, subYX: fp.Elt{0x47, 0x25, 0x70, 0x62, 0xf5, 0x65, 0x93, 0x62, 0x08, 0xac, 0x59, 0x66, 0xdb, 0x08, 0xd9, 0x1a, 0x19, 0xaf, 0xf4, 0xef, 0x02, 0xa2, 0x78, 0xa9, 0x55, 0x1c, 0xfa, 0x08, 0x11, 0xcb, 0xa3, 0x71, 0x74, 0xb1, 0x62, 0xe7, 0xc7, 0xf3, 0x5a, 0xb5, 0x8b, 0xd4, 0xf6, 0x10, 0x57, 0x79, 0x72, 0x2f, 0x13, 0x86, 0x7b, 0x44, 0x5f, 0x48, 0xfd, 0x88}, dt2: fp.Elt{0x10, 0x02, 0xcd, 0x05, 0x9a, 0xc3, 0x32, 0x6d, 0x10, 0x3a, 0x74, 0xba, 0x06, 0xc4, 0x3b, 0x34, 0xbc, 0x36, 0xed, 0xa3, 0xba, 0x9a, 0xdb, 0x6d, 0xd4, 0x69, 0x99, 0x97, 0xd0, 0xe4, 0xdd, 0xf5, 0xd4, 0x7c, 0xd3, 0x4e, 0xab, 0xd1, 0x3b, 0xbb, 0xe9, 0xc7, 0x6a, 0x94, 0x25, 0x61, 0xf0, 0x06, 0xc5, 0x12, 0xa8, 0x86, 0xe5, 0x35, 0x46, 0xeb}, }, { /* 59P*/ addYX: fp.Elt{0x9e, 0x95, 0x11, 0xc6, 0xc7, 0xe8, 0xee, 0x5a, 0x26, 0xa0, 0x72, 0x72, 0x59, 0x91, 0x59, 0x16, 0x49, 0x99, 0x7e, 0xbb, 0xd7, 0x15, 0xb4, 0xf2, 0x40, 0xf9, 0x5a, 0x4d, 0xc8, 0xa0, 0xe2, 0x34, 0x7b, 0x34, 0xf3, 0x99, 0xbf, 0xa9, 0xf3, 0x79, 0xc1, 0x1a, 0x0c, 0xf4, 0x86, 0x74, 0x4e, 0xcb, 0xbc, 0x90, 0xad, 0xb6, 0x51, 0x6d, 0xaa, 0x33}, subYX: fp.Elt{0x9f, 0xd1, 0xc5, 0xa2, 0x6c, 0x24, 0x88, 0x15, 0x71, 0x68, 0xf6, 0x07, 0x45, 0x02, 0xc4, 0x73, 0x7e, 0x75, 0x87, 0xca, 0x7c, 0xf0, 0x92, 0x00, 0x75, 0xd6, 0x5a, 0xdd, 0xe0, 0x64, 0x16, 0x9d, 0x62, 0x80, 0x33, 0x9f, 0xf4, 0x8e, 0x1a, 0x15, 0x1c, 0xd3, 0x0f, 0x4d, 0x4f, 0x62, 0x2d, 0xd7, 0xa5, 0x77, 0xe3, 0xea, 0xf0, 0xfb, 0x1a, 0xdb}, dt2: fp.Elt{0x6a, 0xa2, 0xb1, 0xaa, 0xfb, 0x5a, 0x32, 0x4e, 0xff, 0x47, 0x06, 0xd5, 0x9a, 0x4f, 0xce, 0x83, 0x5b, 0x82, 0x34, 0x3e, 0x47, 0xb8, 0xf8, 0xe9, 0x7c, 0x67, 0x69, 0x8d, 0x9c, 0xb7, 0xde, 0x57, 0xf4, 0x88, 0x41, 0x56, 0x0c, 0x87, 0x1e, 0xc9, 0x2f, 0x54, 0xbf, 0x5c, 0x68, 0x2c, 0xd9, 0xc4, 0xef, 0x53, 0x73, 0x1e, 0xa6, 0x38, 0x02, 0x10}, }, { /* 61P*/ addYX: fp.Elt{0x08, 0x80, 0x4a, 0xc9, 0xb7, 0xa8, 0x88, 0xd9, 0xfc, 0x6a, 0xc0, 0x3e, 0xc2, 0x33, 0x4d, 0x2b, 0x2a, 0xa3, 0x6d, 0x72, 0x3e, 0xdc, 0x34, 0x68, 0x08, 0xbf, 0x27, 0xef, 0xf4, 0xff, 0xe2, 0x0c, 0x31, 0x0c, 0xa2, 0x0a, 0x1f, 0x65, 0xc1, 0x4c, 0x61, 0xd3, 0x1b, 0xbc, 0x25, 0xb1, 0xd0, 0xd4, 0x89, 0xb2, 0x53, 0xfb, 0x43, 0xa5, 0xaf, 0x04}, subYX: fp.Elt{0xe3, 0xe1, 0x37, 0xad, 0x58, 0xa9, 0x55, 0x81, 0xee, 0x64, 0x21, 0xb9, 0xf5, 0x4c, 0x35, 0xea, 0x4a, 0xd3, 0x26, 0xaa, 0x90, 0xd4, 0x60, 0x46, 0x09, 0x4b, 0x4a, 0x62, 0xf9, 0xcd, 0xe1, 0xee, 0xbb, 0xc2, 0x09, 0x0b, 0xb0, 0x96, 0x8e, 0x43, 0x77, 0xaf, 0x25, 0x20, 0x5e, 0x47, 0xe4, 0x1d, 0x50, 0x69, 0x74, 0x08, 0xd7, 0xb9, 0x90, 0x13}, dt2: fp.Elt{0x51, 0x91, 0x95, 0x64, 0x03, 0x16, 0xfd, 0x6e, 0x26, 0x94, 0x6b, 0x61, 0xe7, 0xd9, 0xe0, 0x4a, 0x6d, 0x7c, 0xfa, 0xc0, 0xe2, 0x43, 0x23, 0x53, 0x70, 0xf5, 0x6f, 0x73, 0x8b, 0x81, 0xb0, 0x0c, 0xee, 0x2e, 0x46, 0xf2, 0x8d, 0xa6, 0xfb, 0xb5, 0x1c, 0x33, 0xbf, 0x90, 0x59, 0xc9, 0x7c, 0xb8, 0x6f, 0xad, 0x75, 0x02, 0x90, 0x8e, 0x59, 0x75}, }, { /* 63P*/ addYX: fp.Elt{0x36, 0x4d, 0x77, 0x04, 0xb8, 0x7d, 0x4a, 0xd1, 0xc5, 0xbb, 0x7b, 0x50, 0x5f, 0x8d, 0x9d, 0x62, 0x0f, 0x66, 0x71, 0xec, 0x87, 0xc5, 0x80, 0x82, 0xc8, 0xf4, 0x6a, 0x94, 0x92, 0x5b, 0xb0, 0x16, 0x9b, 0xb2, 0xc9, 0x6f, 0x2b, 0x2d, 0xee, 0x95, 0x73, 0x2e, 0xc2, 0x1b, 0xc5, 0x55, 0x36, 0x86, 0x24, 0xf8, 0x20, 0x05, 0x0d, 0x93, 0xd7, 0x76}, subYX: fp.Elt{0x7f, 0x01, 0xeb, 0x2e, 0x48, 0x4d, 0x1d, 0xf1, 0x06, 0x7e, 0x7c, 0x2a, 0x43, 0xbf, 0x28, 0xac, 0xe9, 0x58, 0x13, 0xc8, 0xbf, 0x8e, 0xc0, 0xef, 0xe8, 0x4f, 0x46, 0x8a, 0xe7, 0xc0, 0xf6, 0x0f, 0x0a, 0x03, 0x48, 0x91, 0x55, 0x39, 0x2a, 0xe3, 0xdc, 0xf6, 0x22, 0x9d, 0x4d, 0x71, 0x55, 0x68, 0x25, 0x6e, 0x95, 0x52, 0xee, 0x4c, 0xd9, 0x01}, dt2: fp.Elt{0xac, 0x33, 0x3f, 0x7c, 0x27, 0x35, 0x15, 0x91, 0x33, 0x8d, 0xf9, 0xc4, 0xf4, 0xf3, 0x90, 0x09, 0x75, 0x69, 0x62, 0x9f, 0x61, 0x35, 0x83, 0x92, 0x04, 0xef, 0x96, 0x38, 0x80, 0x9e, 0x88, 0xb3, 0x67, 0x95, 0xbe, 0x79, 0x3c, 0x35, 0xd8, 0xdc, 0xb2, 0x3e, 0x2d, 0xe6, 0x46, 0xbe, 0x81, 0xf3, 0x32, 0x0e, 0x37, 0x23, 0x75, 0x2a, 0x3d, 0xa0}, }, } golang-github-cloudflare-circl-1.3.7/ecc/goldilocks/twist_basemult.go000066400000000000000000000026601454601126700257540ustar00rootroot00000000000000package goldilocks import ( "crypto/subtle" mlsb "github.com/cloudflare/circl/math/mlsbset" ) const ( // MLSBRecoding parameters fxT = 448 fxV = 2 fxW = 3 fx2w1 = 1 << (uint(fxW) - 1) ) // ScalarBaseMult returns kG where G is the generator point. func (e twistCurve) ScalarBaseMult(k *Scalar) *twistPoint { m, err := mlsb.New(fxT, fxV, fxW) if err != nil { panic(err) } if m.IsExtended() { panic("not extended") } var isZero int if k.IsZero() { isZero = 1 } subtle.ConstantTimeCopy(isZero, k[:], order[:]) minusK := *k isEven := 1 - int(k[0]&0x1) minusK.Neg() subtle.ConstantTimeCopy(isEven, k[:], minusK[:]) c, err := m.Encode(k[:]) if err != nil { panic(err) } gP := c.Exp(groupMLSB{}) P := gP.(*twistPoint) P.cneg(uint(isEven)) return P } type groupMLSB struct{} func (e groupMLSB) ExtendedEltP() mlsb.EltP { return nil } func (e groupMLSB) Sqr(x mlsb.EltG) { x.(*twistPoint).Double() } func (e groupMLSB) Mul(x mlsb.EltG, y mlsb.EltP) { x.(*twistPoint).mixAddZ1(y.(*preTwistPointAffine)) } func (e groupMLSB) Identity() mlsb.EltG { return twistCurve{}.Identity() } func (e groupMLSB) NewEltP() mlsb.EltP { return &preTwistPointAffine{} } func (e groupMLSB) Lookup(a mlsb.EltP, v uint, s, u int32) { Tabj := &tabFixMult[v] P := a.(*preTwistPointAffine) for k := range Tabj { P.cmov(&Tabj[k], uint(subtle.ConstantTimeEq(int32(k), u))) } P.cneg(int(s >> 31)) } golang-github-cloudflare-circl-1.3.7/ecc/p384/000077500000000000000000000000001454601126700207175ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ecc/p384/LICENSE000066400000000000000000000027211454601126700217260ustar00rootroot00000000000000Copyright (c) 2018, Brendan McMillion. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. golang-github-cloudflare-circl-1.3.7/ecc/p384/arith.go000066400000000000000000000074611454601126700223650ustar00rootroot00000000000000//go:build (!noasm && arm64) || (!noasm && amd64) // +build !noasm,arm64 !noasm,amd64 package p384 import ( "math/big" "github.com/cloudflare/circl/internal/conv" ) const sizeFp = 48 type fp384 [sizeFp]byte func (e fp384) BigInt() *big.Int { return conv.BytesLe2BigInt(e[:]) } func (e fp384) String() string { return conv.BytesLe2Hex(e[:]) } func (e *fp384) SetBigInt(b *big.Int) { if b.BitLen() > 384 || b.Sign() < 0 { b = new(big.Int).Mod(b, p.BigInt()) } conv.BigInt2BytesLe(e[:], b) } func montEncode(c, a *fp384) { fp384Mul(c, a, &r2) } func montDecode(c, a *fp384) { fp384Mul(c, a, &fp384{1}) } func fp384Sqr(c, a *fp384) { fp384Mul(c, a, a) } func fp384Inv(z, x *fp384) { t0, t1, t2, t3, t4 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} /* alpha_1 */ fp384Sqr(t4, x) /* alpha_2 */ fp384Mul(t4, t4, x) /* alpha_3 */ fp384Sqr(t0, t4) fp384Mul(t0, t0, x) /* alpha_6 */ fp384Sqr(t1, t0) fp384Sqr(t1, t1) fp384Sqr(t1, t1) fp384Mul(t1, t1, t0) /* alpha_12 */ fp384Sqr(t2, t1) for i := 0; i < 5; i++ { fp384Sqr(t2, t2) } fp384Mul(t2, t2, t1) /* alpha_15 */ for i := 0; i < 3; i++ { fp384Sqr(t2, t2) } fp384Mul(t2, t2, t0) /* alpha_30 */ fp384Sqr(t1, t2) for i := 0; i < 14; i++ { fp384Sqr(t1, t1) } fp384Mul(t1, t1, t2) /* alpha_60 */ fp384Sqr(t3, t1) for i := 0; i < 29; i++ { fp384Sqr(t3, t3) } fp384Mul(t3, t3, t1) /* T_3 = alpha_30^(2^2) */ fp384Sqr(t1, t1) fp384Sqr(t1, t1) /* alpha_32 */ *t0 = *t1 fp384Mul(t0, t0, t4) /* T_3 = a^(2^32-3) = (alpha_30)^(2^2)*alpha_1 */ fp384Mul(t1, t1, x) /* alpha_120 */ fp384Sqr(t4, t3) for i := 0; i < 59; i++ { fp384Sqr(t4, t4) } fp384Mul(t4, t4, t3) /* alpha_240 */ fp384Sqr(t3, t4) for i := 0; i < 119; i++ { fp384Sqr(t3, t3) } fp384Mul(t3, t3, t4) /* alpha_255 */ for i := 0; i < 15; i++ { fp384Sqr(t3, t3) } fp384Mul(t3, t3, t2) /* T_5 = a^(2^288-2^32-1) = (alpha_255)^(2^33)*alpha_32 */ for i := 0; i < 33; i++ { fp384Sqr(t3, t3) } fp384Mul(t3, t3, t0) /* T_1 = a^(2^384-2^128-2^96+2^32-3) = (T_1)^(2^96)*T_3 */ fp384Sqr(t4, t3) for i := 0; i < 95; i++ { fp384Sqr(t4, t4) } fp384Mul(z, t4, t1) } //go:noescape func fp384Cmov(x, y *fp384, b int) //go:noescape func fp384Neg(c, a *fp384) //go:noescape func fp384Add(c, a, b *fp384) //go:noescape func fp384Sub(c, a, b *fp384) //go:noescape func fp384Mul(c, a, b *fp384) var ( // p is the order of the base field, represented as little-endian 64-bit words. p = fp384{ 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, } // pp satisfies r*rp - p*pp = 1 where rp and pp are both integers. pp = fp384{ //nolint 0x01, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xfb, 0xff, 0xff, 0xff, 0xfa, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, 0x02, 0x00, 0x00, 0x00, 0x0c, 0x00, 0x00, 0x00, 0x14, 0x00, 0x00, 0x00, 0x14, 0x00, 0x00, 0x00, } // r2 is R^2 where R = 2^384 mod p. r2 = fp384{ 0x01, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x02, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, } // bb is the Montgomery encoding of the curve parameter B. bb = fp384{ 0xcc, 0x2d, 0x41, 0x9d, 0x71, 0x88, 0x11, 0x08, 0xec, 0x32, 0x4c, 0x7a, 0xd8, 0xad, 0x29, 0xf7, 0x2e, 0x02, 0x20, 0x19, 0x9b, 0x20, 0xf2, 0x77, 0xe2, 0x8a, 0x93, 0x94, 0xee, 0x4b, 0x37, 0xe3, 0x94, 0x20, 0x02, 0x1f, 0xf4, 0x21, 0x2b, 0xb6, 0xf9, 0xbf, 0x4f, 0x60, 0x4b, 0x11, 0x08, 0xcd, } ) golang-github-cloudflare-circl-1.3.7/ecc/p384/arith_amd64.go000066400000000000000000000002071454601126700233470ustar00rootroot00000000000000//go:build amd64 && !noasm // +build amd64,!noasm package p384 import "golang.org/x/sys/cpu" var hasBMI2 = cpu.X86.HasBMI2 //nolint golang-github-cloudflare-circl-1.3.7/ecc/p384/arith_amd64.s000066400000000000000000000323251454601126700232120ustar00rootroot00000000000000// +build amd64,!noasm #include "textflag.h" #define storeBlock(a0,a1,a2,a3,a4,a5, r) \ MOVQ a0, 0+r \ MOVQ a1, 8+r \ MOVQ a2, 16+r \ MOVQ a3, 24+r \ MOVQ a4, 32+r \ MOVQ a5, 40+r #define loadBlock(r, a0,a1,a2,a3,a4,a5) \ MOVQ 0+r, a0 \ MOVQ 8+r, a1 \ MOVQ 16+r, a2 \ MOVQ 24+r, a3 \ MOVQ 32+r, a4 \ MOVQ 40+r, a5 #define fp384Carry(a0,a1,a2,a3,a4,a5,a6, b0,b1,b2,b3,b4,b5,b6) \ \ // b = a-p MOVQ a0, b0 \ MOVQ a1, b1 \ MOVQ a2, b2 \ MOVQ a3, b3 \ MOVQ a4, b4 \ MOVQ a5, b5 \ MOVQ a6, b6 \ \ SUBQ ·p+0(SB), b0 \ SBBQ ·p+8(SB), b1 \ SBBQ ·p+16(SB), b2 \ SBBQ ·p+24(SB), b3 \ SBBQ ·p+32(SB), b4 \ SBBQ ·p+40(SB), b5 \ SBBQ $0, b6 \ \ \ // if b is negative then return a \ // else return b CMOVQCC b0, a0 \ CMOVQCC b1, a1 \ CMOVQCC b2, a2 \ CMOVQCC b3, a3 \ CMOVQCC b4, a4 \ CMOVQCC b5, a5 #define mul(a0,a1,a2,a3,a4,a5, rb, stack) \ \ // a0 MOVQ a0, AX \ MULQ 0+rb \ MOVQ AX, R8 \ MOVQ DX, R9 \ MOVQ a0, AX \ MULQ 8+rb \ ADDQ AX, R9 \ ADCQ $0, DX \ MOVQ DX, R10 \ MOVQ a0, AX \ MULQ 16+rb \ ADDQ AX, R10 \ ADCQ $0, DX \ MOVQ DX, R11 \ MOVQ a0, AX \ MULQ 24+rb \ ADDQ AX, R11 \ ADCQ $0, DX \ MOVQ DX, R12 \ MOVQ a0, AX \ MULQ 32+rb \ ADDQ AX, R12 \ ADCQ $0, DX \ MOVQ DX, R13 \ MOVQ a0, AX \ MULQ 40+rb \ ADDQ AX, R13 \ ADCQ $0, DX \ MOVQ DX, R14 \ \ storeBlock(R8,R9,R10,R11,R12,R13, 0+stack) \ MOVQ R14, 48+stack \ \ \ // a1 MOVQ a1, AX \ MULQ 0+rb \ MOVQ AX, R8 \ MOVQ DX, R9 \ MOVQ a1, AX \ MULQ 8+rb \ ADDQ AX, R9 \ ADCQ $0, DX \ MOVQ DX, R10 \ MOVQ a1, AX \ MULQ 16+rb \ ADDQ AX, R10 \ ADCQ $0, DX \ MOVQ DX, R11 \ MOVQ a1, AX \ MULQ 24+rb \ ADDQ AX, R11 \ ADCQ $0, DX \ MOVQ DX, R12 \ MOVQ a1, AX \ MULQ 32+rb \ ADDQ AX, R12 \ ADCQ $0, DX \ MOVQ DX, R13 \ MOVQ a1, AX \ MULQ 40+rb \ ADDQ AX, R13 \ ADCQ $0, DX \ MOVQ DX, R14 \ \ ADDQ 8+stack, R8 \ ADCQ 16+stack, R9 \ ADCQ 24+stack, R10 \ ADCQ 32+stack, R11 \ ADCQ 40+stack, R12 \ ADCQ 48+stack, R13 \ ADCQ $0, R14 \ storeBlock(R8,R9,R10,R11,R12,R13, 8+stack) \ MOVQ R14, 56+stack \ \ \ // a2 MOVQ a2, AX \ MULQ 0+rb \ MOVQ AX, R8 \ MOVQ DX, R9 \ MOVQ a2, AX \ MULQ 8+rb \ ADDQ AX, R9 \ ADCQ $0, DX \ MOVQ DX, R10 \ MOVQ a2, AX \ MULQ 16+rb \ ADDQ AX, R10 \ ADCQ $0, DX \ MOVQ DX, R11 \ MOVQ a2, AX \ MULQ 24+rb \ ADDQ AX, R11 \ ADCQ $0, DX \ MOVQ DX, R12 \ MOVQ a2, AX \ MULQ 32+rb \ ADDQ AX, R12 \ ADCQ $0, DX \ MOVQ DX, R13 \ MOVQ a2, AX \ MULQ 40+rb \ ADDQ AX, R13 \ ADCQ $0, DX \ MOVQ DX, R14 \ \ ADDQ 16+stack, R8 \ ADCQ 24+stack, R9 \ ADCQ 32+stack, R10 \ ADCQ 40+stack, R11 \ ADCQ 48+stack, R12 \ ADCQ 56+stack, R13 \ ADCQ $0, R14 \ storeBlock(R8,R9,R10,R11,R12,R13, 16+stack) \ MOVQ R14, 64+stack \ \ \ // a3 MOVQ a3, AX \ MULQ 0+rb \ MOVQ AX, R8 \ MOVQ DX, R9 \ MOVQ a3, AX \ MULQ 8+rb \ ADDQ AX, R9 \ ADCQ $0, DX \ MOVQ DX, R10 \ MOVQ a3, AX \ MULQ 16+rb \ ADDQ AX, R10 \ ADCQ $0, DX \ MOVQ DX, R11 \ MOVQ a3, AX \ MULQ 24+rb \ ADDQ AX, R11 \ ADCQ $0, DX \ MOVQ DX, R12 \ MOVQ a3, AX \ MULQ 32+rb \ ADDQ AX, R12 \ ADCQ $0, DX \ MOVQ DX, R13 \ MOVQ a3, AX \ MULQ 40+rb \ ADDQ AX, R13 \ ADCQ $0, DX \ MOVQ DX, R14 \ \ ADDQ 24+stack, R8 \ ADCQ 32+stack, R9 \ ADCQ 40+stack, R10 \ ADCQ 48+stack, R11 \ ADCQ 56+stack, R12 \ ADCQ 64+stack, R13 \ ADCQ $0, R14 \ storeBlock(R8,R9,R10,R11,R12,R13, 24+stack) \ MOVQ R14, 72+stack \ \ \ // a4 MOVQ a4, AX \ MULQ 0+rb \ MOVQ AX, R8 \ MOVQ DX, R9 \ MOVQ a4, AX \ MULQ 8+rb \ ADDQ AX, R9 \ ADCQ $0, DX \ MOVQ DX, R10 \ MOVQ a4, AX \ MULQ 16+rb \ ADDQ AX, R10 \ ADCQ $0, DX \ MOVQ DX, R11 \ MOVQ a4, AX \ MULQ 24+rb \ ADDQ AX, R11 \ ADCQ $0, DX \ MOVQ DX, R12 \ MOVQ a4, AX \ MULQ 32+rb \ ADDQ AX, R12 \ ADCQ $0, DX \ MOVQ DX, R13 \ MOVQ a4, AX \ MULQ 40+rb \ ADDQ AX, R13 \ ADCQ $0, DX \ MOVQ DX, R14 \ \ ADDQ 32+stack, R8 \ ADCQ 40+stack, R9 \ ADCQ 48+stack, R10 \ ADCQ 56+stack, R11 \ ADCQ 64+stack, R12 \ ADCQ 72+stack, R13 \ ADCQ $0, R14 \ storeBlock(R8,R9,R10,R11,R12,R13, 32+stack) \ MOVQ R14, 80+stack \ \ \ // a5 MOVQ a5, AX \ MULQ 0+rb \ MOVQ AX, R8 \ MOVQ DX, R9 \ MOVQ a5, AX \ MULQ 8+rb \ ADDQ AX, R9 \ ADCQ $0, DX \ MOVQ DX, R10 \ MOVQ a5, AX \ MULQ 16+rb \ ADDQ AX, R10 \ ADCQ $0, DX \ MOVQ DX, R11 \ MOVQ a5, AX \ MULQ 24+rb \ ADDQ AX, R11 \ ADCQ $0, DX \ MOVQ DX, R12 \ MOVQ a5, AX \ MULQ 32+rb \ ADDQ AX, R12 \ ADCQ $0, DX \ MOVQ DX, R13 \ MOVQ a5, AX \ MULQ 40+rb \ ADDQ AX, R13 \ ADCQ $0, DX \ MOVQ DX, R14 \ \ ADDQ 40+stack, R8 \ ADCQ 48+stack, R9 \ ADCQ 56+stack, R10 \ ADCQ 64+stack, R11 \ ADCQ 72+stack, R12 \ ADCQ 80+stack, R13 \ ADCQ $0, R14 \ storeBlock(R8,R9,R10,R11,R12,R13, 40+stack) \ MOVQ R14, 88+stack #define fp384Reduce(stack) \ \ // m = (T * P') mod R, store m in R8:R9:R10:R11:R12:R13 MOVQ ·pp+0(SB), AX \ MULQ 0+stack \ MOVQ AX, R8 ; MOVQ R8, 96+stack\ MOVQ DX, R9 \ MOVQ ·pp+0(SB), AX \ MULQ 8+stack \ ADDQ AX, R9 \ ADCQ $0, DX \ MOVQ DX, R10 \ MOVQ ·pp+0(SB), AX \ MULQ 16+stack \ ADDQ AX, R10 \ ADCQ $0, DX \ MOVQ DX, R11 \ MOVQ ·pp+0(SB), AX \ MULQ 24+stack \ ADDQ AX, R11 \ ADCQ $0, DX \ MOVQ DX, R12 \ MOVQ ·pp+0(SB), AX \ MULQ 32+stack \ ADDQ AX, R12 \ ADCQ $0, DX \ MOVQ DX, R13 \ MOVQ ·pp+0(SB), AX \ MULQ 40+stack \ ADDQ AX, R13 \ \ ADDQ 0+stack, R9 \ ADCQ 8+stack, R10 \ ADCQ 16+stack, R11 \ ADCQ 24+stack, R12 \ ADCQ 32+stack, R13 \ \ MOVQ ·pp+16(SB), AX \ MULQ 0+stack \ MOVQ AX, R14 \ MOVQ DX, R8 \ MOVQ ·pp+16(SB), AX \ MULQ 8+stack \ ADDQ AX, R8 \ ADCQ $0, DX \ MOVQ DX, BX \ MOVQ ·pp+16(SB), AX \ MULQ 16+stack \ ADDQ AX, BX \ ADCQ $0, DX \ MOVQ DX, CX \ MOVQ ·pp+16(SB), AX \ MULQ 24+stack \ ADDQ AX, CX \ \ ADDQ R14, R10 \ ADCQ R8, R11 \ ADCQ BX, R12 \ ADCQ CX, R13 \ \ MOVQ ·pp+24(SB), AX \ MULQ 0+stack \ MOVQ AX, R14 \ MOVQ DX, R8 \ MOVQ ·pp+24(SB), AX \ MULQ 8+stack \ ADDQ AX, R8 \ ADCQ $0, DX \ MOVQ DX, BX \ MOVQ ·pp+24(SB), AX \ MULQ 16+stack \ ADDQ AX, BX \ \ ADDQ R14, R11 \ ADCQ R8, R12 \ ADCQ BX, R13 \ \ MOVQ ·pp+32(SB), AX \ MULQ 0+stack \ MOVQ AX, R14 \ MOVQ DX, R8 \ MOVQ ·pp+32(SB), AX \ MULQ 8+stack \ ADDQ AX, R8 \ \ ADDQ R14, R12 \ ADCQ R8, R13 \ \ MOVQ ·pp+40(SB), AX \ MULQ 0+stack \ ADDQ AX, R13 \ \ MOVQ 96+stack, R8 \ \ storeBlock(R8,R9,R10,R11,R12,R13, 96+stack) \ \ \ // m * P mul(·p+0(SB),·p+8(SB),·p+16(SB),·p+24(SB),·p+32(SB),·p+40(SB), 96+stack, 144+stack) \ \ \ // Add the 768-bit intermediate to m*N MOVQ $0, R15 \ loadBlock(144+stack, R8,R9,R10,R11,R12,R13) \ loadBlock(192+stack, R14,SI,AX,BX,CX,DX) \ \ ADDQ 0+stack, R8 \ ADCQ 8+stack, R9 \ ADCQ 16+stack, R10 \ ADCQ 24+stack, R11 \ ADCQ 32+stack, R12 \ ADCQ 40+stack, R13 \ ADCQ 48+stack, R14 \ ADCQ 56+stack, SI \ ADCQ 64+stack, AX \ ADCQ 72+stack, BX \ ADCQ 80+stack, CX \ ADCQ 88+stack, DX \ ADCQ $0, R15 \ \ fp384Carry(R14,SI,AX,BX,CX,DX,R15, R8,R9,R10,R11,R12,R13,DI) #define mulBMI2(a0,a1,a2,a3,a4,a5, rb, stack) \ MOVQ a0, DX \ MULXQ 0+rb, R8, R9; MOVQ R8, 0+stack; MOVQ $0, R8 \ MULXQ 8+rb, AX, R10 \ ADDQ AX, R9 \ MULXQ 16+rb, AX, R11 \ ADCQ AX, R10 \ MULXQ 24+rb, AX, R12 \ ADCQ AX, R11 \ MULXQ 32+rb, AX, R13 \ ADCQ AX, R12 \ MULXQ 40+rb, AX, R14 \ ADCQ AX, R13 \ ADCQ $0, R14 \ \ MOVQ a1, DX \ MULXQ 0+rb, AX, BX \ ADDQ AX, R9; MOVQ R9, 8+stack; MOVL $0, R9 \ ADCQ BX, R10 \ MULXQ 16+rb, AX, BX \ ADCQ AX, R11 \ ADCQ BX, R12 \ MULXQ 32+rb, AX, BX \ ADCQ AX, R13 \ ADCQ BX, R14 \ ADCQ $0, R8 \ MULXQ 8+rb, AX, BX \ ADDQ AX, R10 \ ADCQ BX, R11 \ MULXQ 24+rb, AX, BX \ ADCQ AX, R12 \ ADCQ BX, R13 \ MULXQ 40+rb, AX, BX \ ADCQ AX, R14 \ ADCQ BX, R8 \ ADCQ $0, R9 \ \ MOVQ a2, DX \ MULXQ 0+rb, AX, BX \ ADDQ AX, R10; MOVQ R10, 16+stack; MOVL $0, R10 \ ADCQ BX, R11 \ MULXQ 16+rb, AX, BX \ ADCQ AX, R12 \ ADCQ BX, R13 \ MULXQ 32+rb, AX, BX \ ADCQ AX, R14 \ ADCQ BX, R8 \ ADCQ $0, R9 \ MULXQ 8+rb, AX, BX \ ADDQ AX, R11 \ ADCQ BX, R12 \ MULXQ 24+rb, AX, BX \ ADCQ AX, R13 \ ADCQ BX, R14 \ MULXQ 40+rb, AX, BX \ ADCQ AX, R8 \ ADCQ BX, R9 \ ADCQ $0, R10 \ \ MOVQ a3, DX \ MULXQ 0+rb, AX, BX \ ADDQ AX, R11; MOVQ R11, 24+stack; MOVL $0, R11 \ ADCQ BX, R12 \ MULXQ 16+rb, AX, BX \ ADCQ AX, R13 \ ADCQ BX, R14 \ MULXQ 32+rb, AX, BX \ ADCQ AX, R8 \ ADCQ BX, R9 \ ADCQ $0, R10 \ MULXQ 8+rb, AX, BX \ ADDQ AX, R12 \ ADCQ BX, R13 \ MULXQ 24+rb, AX, BX \ ADCQ AX, R14 \ ADCQ BX, R8 \ MULXQ 40+rb, AX, BX \ ADCQ AX, R9 \ ADCQ BX, R10 \ ADCQ $0, R11 \ \ MOVQ a4, DX \ MULXQ 0+rb, AX, BX \ ADDQ AX, R12; MOVQ R12, 32+stack; MOVL $0, R12 \ ADCQ BX, R13 \ MULXQ 16+rb, AX, BX \ ADCQ AX, R14 \ ADCQ BX, R8 \ MULXQ 32+rb, AX, BX \ ADCQ AX, R9 \ ADCQ BX, R10 \ ADCQ $0, R11 \ MULXQ 8+rb, AX, BX \ ADDQ AX, R13 \ ADCQ BX, R14 \ MULXQ 24+rb, AX, BX \ ADCQ AX, R8 \ ADCQ BX, R9 \ MULXQ 40+rb, AX, BX \ ADCQ AX, R10 \ ADCQ BX, R11 \ ADCQ $0, R12 \ \ MOVQ a5, DX \ MULXQ 0+rb, AX, BX \ ADDQ AX, R13; MOVQ R13, 40+stack \ ADCQ BX, R14 \ MULXQ 16+rb, AX, BX \ ADCQ AX, R8 \ ADCQ BX, R9 \ MULXQ 32+rb, AX, BX \ ADCQ AX, R10 \ ADCQ BX, R11 \ ADCQ $0, R12 \ MULXQ 8+rb, AX, BX \ ADDQ AX, R14 \ ADCQ BX, R8 \ MULXQ 24+rb, AX, BX \ ADCQ AX, R9 \ ADCQ BX, R10 \ MULXQ 40+rb, AX, BX \ ADCQ AX, R11 \ ADCQ BX, R12 #define fp384ReduceBMI2(stack) \ \ // m = (T * P') mod R, store m in R8:R9:R10:R11:R12:R13 MOVQ ·pp+0(SB), DX \ MULXQ 0+stack, R8, R9 \ MULXQ 8+stack, AX, R10 \ ADDQ AX, R9 \ MULXQ 16+stack, AX, R11 \ ADCQ AX, R10 \ MULXQ 24+stack, AX, R12 \ ADCQ AX, R11 \ MULXQ 32+stack, AX, R13 \ ADCQ AX, R12 \ MULXQ 40+stack, AX, BX \ ADCQ AX, R13 \ \ ADDQ 0+stack, R9 \ ADCQ 8+stack, R10 \ ADCQ 16+stack, R11 \ ADCQ 24+stack, R12 \ ADCQ 32+stack, R13 \ \ MOVQ ·pp+16(SB), DX \ MULXQ 0+stack, AX, BX \ ADDQ AX, R10 \ ADCQ BX, R11 \ MULXQ 16+stack, AX, BX \ ADCQ AX, R12 \ ADCQ BX, R13 \ MULXQ 8+stack, AX, BX \ ADDQ AX, R11 \ ADCQ BX, R12 \ MULXQ 24+stack, AX, BX \ ADCQ AX, R13 \ \ MOVQ ·pp+24(SB), DX \ MULXQ 0+stack, AX, BX \ ADDQ AX, R11 \ ADCQ BX, R12 \ MULXQ 16+stack, AX, BX \ ADCQ AX, R13 \ MULXQ 8+stack, AX, BX \ ADDQ AX, R12 \ ADCQ BX, R13 \ \ MOVQ ·pp+32(SB), DX \ MULXQ 0+stack, AX, BX \ ADDQ AX, R12 \ ADCQ BX, R13 \ MULXQ 8+stack, AX, BX \ ADDQ AX, R13 \ \ MOVQ ·pp+40(SB), DX \ MULXQ 0+stack, AX, BX \ ADDQ AX, R13 \ \ storeBlock(R8,R9,R10,R11,R12,R13, 96+stack) \ \ \ // m * P mulBMI2(·p+0(SB),·p+8(SB),·p+16(SB),·p+24(SB),·p+32(SB),·p+40(SB), 96+stack, 144+stack) \ \ \ // Add the 768-bit intermediate to m*N loadBlock(144+stack, AX,R13,BX,CX,DX,DI) \ \ ADDQ 0+stack, AX \ ADCQ 8+stack, R13 \ ADCQ 16+stack, BX \ ADCQ 24+stack, CX \ ADCQ 32+stack, DX \ ADCQ 40+stack, DI \ ADCQ 48+stack, R14 \ ADCQ 56+stack, R8 \ ADCQ 64+stack, R9 \ ADCQ 72+stack, R10 \ ADCQ 80+stack, R11 \ ADCQ 88+stack, R12 \ MOVQ $0, 0+stack \ ADCQ $0, 0+stack \ \ fp384Carry(R14,R8,R9,R10,R11,R12, 0+stack, AX,R13,BX,CX,DX,DI,SI) TEXT ·fp384Neg(SB), NOSPLIT, $0-16 MOVQ ·p+0(SB), R8 MOVQ ·p+8(SB), R9 MOVQ ·p+16(SB), R10 MOVQ ·p+24(SB), R11 MOVQ ·p+32(SB), R12 MOVQ ·p+40(SB), R13 MOVQ a+8(FP), DI SUBQ 0(DI), R8 SBBQ 8(DI), R9 SBBQ 16(DI), R10 SBBQ 24(DI), R11 SBBQ 32(DI), R12 SBBQ 40(DI), R13 MOVQ $0, R15 fp384Carry(R8,R9,R10,R11,R12,R13,R15, R14,AX,BX,CX,DX,DI,SI) MOVQ c+0(FP), DI storeBlock(R8,R9,R10,R11,R12,R13, 0(DI)) RET TEXT ·fp384Add(SB), NOSPLIT, $0-24 MOVQ a+8(FP), DI MOVQ b+16(FP), SI loadBlock(0(DI), R8,R9,R10,R11,R12,R13) MOVQ $0, R15 ADDQ 0(SI), R8 ADCQ 8(SI), R9 ADCQ 16(SI), R10 ADCQ 24(SI), R11 ADCQ 32(SI), R12 ADCQ 40(SI), R13 ADCQ $0, R15 fp384Carry(R8,R9,R10,R11,R12,R13,R15, R14,AX,BX,CX,DX,DI,SI) MOVQ c+0(FP), DI storeBlock(R8,R9,R10,R11,R12,R13, 0(DI)) RET TEXT ·fp384Sub(SB), NOSPLIT, $0-24 MOVQ ·p+0(SB), R8 MOVQ ·p+8(SB), R9 MOVQ ·p+16(SB), R10 MOVQ ·p+24(SB), R11 MOVQ ·p+32(SB), R12 MOVQ ·p+40(SB), R13 MOVQ b+16(FP), DI SUBQ 0(DI), R8 SBBQ 8(DI), R9 SBBQ 16(DI), R10 SBBQ 24(DI), R11 SBBQ 32(DI), R12 SBBQ 40(DI), R13 MOVQ $0, R15 MOVQ a+8(FP), DI ADDQ 0(DI), R8 ADCQ 8(DI), R9 ADCQ 16(DI), R10 ADCQ 24(DI), R11 ADCQ 32(DI), R12 ADCQ 40(DI), R13 ADCQ $0, R15 fp384Carry(R8,R9,R10,R11,R12,R13,R15, R14,AX,BX,CX,DX,DI,SI) MOVQ c+0(FP), DI storeBlock(R8,R9,R10,R11,R12,R13, 0(DI)) RET TEXT ·fp384Mul(SB), NOSPLIT, $240-24 MOVQ a+8(FP), DI MOVQ b+16(FP), SI // Jump to a slightly different implementation if MULX isn't supported. CMPB ·hasBMI2(SB), $0 JE nobmi2Mul // T = a * b mulBMI2(0(DI),8(DI),16(DI),24(DI),32(DI),40(DI), 0(SI), 0(SP)) storeBlock(R14,R8,R9,R10,R11,R12, 48(SP)) // Reduce T. fp384ReduceBMI2(0(SP)) MOVQ c+0(FP), DI storeBlock(R14,R8,R9,R10,R11,R12, 0(DI)) JMP end nobmi2Mul: // T = a * b mul(0(DI),8(DI),16(DI),24(DI),32(DI),40(DI), 0(SI), 0(SP)) // Reduce T. fp384Reduce(0(SP)) MOVQ c+0(FP), DI storeBlock(R14,SI,AX,BX,CX,DX, 0(DI)) end: RET TEXT ·fp384Cmov(SB), NOSPLIT, $0 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVQ b+16(FP), BX TESTQ BX, BX MOVQ 0(DI), AX; MOVQ 0(SI), DX; CMOVQNE DX, AX; MOVQ AX, 0(DI); MOVQ 8(DI), AX; MOVQ 8(SI), DX; CMOVQNE DX, AX; MOVQ AX, 8(DI); MOVQ 16(DI), AX; MOVQ 16(SI), DX; CMOVQNE DX, AX; MOVQ AX, 16(DI); MOVQ 24(DI), AX; MOVQ 24(SI), DX; CMOVQNE DX, AX; MOVQ AX, 24(DI); MOVQ 32(DI), AX; MOVQ 32(SI), DX; CMOVQNE DX, AX; MOVQ AX, 32(DI); MOVQ 40(DI), AX; MOVQ 40(SI), DX; CMOVQNE DX, AX; MOVQ AX, 40(DI); RET golang-github-cloudflare-circl-1.3.7/ecc/p384/arith_arm64.s000066400000000000000000000235711454601126700232330ustar00rootroot00000000000000// +build arm64,!noasm #include "textflag.h" TEXT ·fp384Cmov(SB), NOSPLIT, $0 MOVD x+0(FP), R0 MOVD y+8(FP), R1 MOVW b+16(FP), R2 CMP $0, R2 LDP 0(R0), (R3, R5) LDP 0(R1), (R4, R6) CSEL NE,R4,R3,R7 CSEL NE,R6,R5,R8 STP (R7, R8), 0(R0) LDP 16(R0), (R3, R5) LDP 16(R1), (R4, R6) CSEL NE,R4,R3,R7 CSEL NE,R6,R5,R8 STP (R7, R8), 16(R0) LDP 32(R0), (R3, R5) LDP 32(R1), (R4, R6) CSEL NE,R4,R3,R7 CSEL NE,R6,R5,R8 STP (R7, R8), 32(R0) RET // Compute c = -a mod p TEXT ·fp384Neg(SB), NOSPLIT, $0-16 MOVD c+0(FP), R0 MOVD a+8(FP), R1 // Load p in R2-R7, a in R8-R13 // Compute p-a in R8-R13 LDP ·p+0(SB), (R2, R3) LDP 0(R1), (R8, R9) SUBS R8, R2, R8 SBCS R9, R3, R9 LDP ·p+16(SB), (R4, R5) LDP 16(R1), (R10, R11) SBCS R10, R4, R10 SBCS R11, R5, R11 LDP ·p+32(SB), (R6, R7) LDP 32(R1), (R12, R13) SBCS R12, R6, R12 SBC R13, R7, R13 // Compute (p-a)-p in R2-R7 SUBS R2, R8, R2 SBCS R3, R9, R3 SBCS R4, R10, R4 SBCS R5, R11, R5 SBCS R6, R12, R6 SBCS R7, R13, R7 // If (p-a)-p < 0 (nearly always), return p-a // Only return (p-a)-p for a = 0 // Store result in c CSEL CC, R8, R2, R2 CSEL CC, R9, R3, R3 STP (R2, R3), 0(R0) CSEL CC, R10, R4, R4 CSEL CC, R11, R5, R5 STP (R4, R5), 16(R0) CSEL CC, R12, R6, R6 CSEL CC, R13, R7, R7 STP (R6, R7), 32(R0) RET // Compute c = a+b mod p TEXT ·fp384Add(SB), NOSPLIT, $0-24 MOVD c+0(FP), R0 MOVD a+8(FP), R1 MOVD b+16(FP), R2 // Load a in R3-R8, b in R9-R14 // Compute a+b in R3-R9 LDP 0(R1), (R3, R4) LDP 0(R2), (R9, R10) ADDS R9, R3 ADCS R10, R4 LDP 16(R1), (R5, R6) LDP 16(R2), (R11, R12) ADCS R11, R5 ADCS R12, R6 LDP 32(R1), (R7, R8) LDP 32(R2), (R13, R14) ADCS R13, R7 ADCS R14, R8 ADC ZR, ZR, R9 // Load p in R10-R15 LDP ·p+ 0(SB), (R10, R11) LDP ·p+16(SB), (R12, R13) LDP ·p+32(SB), (R14, R15) // Compute a+b-p in R10-R16 SUBS R10, R3, R10 SBCS R11, R4, R11 SBCS R12, R5, R12 SBCS R13, R6, R13 SBCS R14, R7, R14 SBCS R15, R8, R15 SBCS ZR, R9, R16 // If a+b-p is negative, return a+b // Store result in c CSEL CC, R3, R10, R3 CSEL CC, R4, R11, R4 STP (R3, R4), 0(R0) CSEL CC, R5, R12, R5 CSEL CC, R6, R13, R6 STP (R5, R6), 16(R0) CSEL CC, R7, R14, R7 CSEL CC, R8, R15, R8 STP (R7, R8), 32(R0) RET // Compute c = a-b mod p TEXT ·fp384Sub(SB), NOSPLIT, $0-24 MOVD c+0(FP), R0 MOVD a+8(FP), R1 MOVD b+16(FP), R2 // Load a in R3-R8, b in R9-R14 // Compute a-b in R3-R9 LDP 0(R1), (R3, R4) LDP 0(R2), (R9, R10) SUBS R9, R3 SBCS R10, R4 LDP 16(R1), (R5, R6) LDP 16(R2), (R11, R12) SBCS R11, R5 SBCS R12, R6 LDP 32(R1), (R7, R8) LDP 32(R2), (R13, R14) SBCS R13, R7 SBCS R14, R8 SBC ZR, ZR, R9 // Load p in R10-R15 // If a-b < 0, (a-b)+p to R3-R8 // Store result in c LDP ·p+ 0(SB), (R10, R11) AND R9, R10 LDP ·p+16(SB), (R12, R13) AND R9, R11 AND R9, R12 LDP ·p+32(SB), (R14, R15) AND R9, R13 AND R9, R14 AND R9, R15 ADDS R10, R3 ADCS R11, R4 STP (R3, R4), 0(R0) ADCS R12, R5 ADCS R13, R6 STP (R5, R6), 16(R0) ADCS R14, R7 ADC R15, R8 STP (R7, R8), 32(R0) RET // Expects that A0*B0 is already in C0(low),C3(high) and A0*B1 in C1(low),C2(high) // C0 is not actually touched // Result of (A0-A2) * (B0-B2) will be in C0-C5 // Inputs remain intact #define mul192x192comba(A0,A1,A2, B0,B1,B2, C0,C1,C2,C3,C4,C5, S0,S1,S2,S3) \ MUL A1, B0, S2 \ UMULH A1, B0, S3 \ \ ADDS C3, C1 \ ADCS ZR, C2 \ ADC ZR, ZR, C3 \ \ MUL A0, B2, S0 \ UMULH A0, B2, S1 \ \ ADDS S2, C1 \ ADCS S3, C2 \ ADC ZR, C3 \ \ MUL A1, B1, S2 \ UMULH A1, B1, S3 \ \ ADDS S0, C2 \ ADCS S1, C3 \ ADC ZR, ZR, C4 \ \ MUL A2, B0, S0 \ UMULH A2, B0, S1 \ \ ADDS S2, C2 \ ADCS S3, C3 \ ADC ZR, C4 \ \ MUL A1, B2, S2 \ UMULH A1, B2, S3 \ \ ADDS S0, C2 \ ADCS S1, C3 \ ADC ZR, C4 \ \ MUL A2, B1, S0 \ UMULH A2, B1, S1 \ \ ADDS S2, C3 \ ADCS S3, C4 \ ADC ZR, ZR, C5 \ \ MUL A2, B2, S2 \ UMULH A2, B2, S3 \ \ ADDS S0, C3 \ ADCS S1, C4 \ ADC ZR, C5 \ \ ADDS S2, C4 \ ADC S3, C5 // Assumes that there are at least 96 bytes left on the stack // Expects that X and Y point to input // X and Y get overwritten, Z0 will be in Y #define mul384x384karatsuba(X,Y, Z1,Z2,Z3,Z4,Z5,Z6,Z7,Z8,Z9,Z10,Z11, T0,T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12) \ /* Load a in Z1-Z6, b in T12,Z7-Z11 */ \ LDP 0(X), ( Z1, Z2) \ LDP 0(Y), (T12, Z7) \ MUL Z1, Z7, T1 \ UMULH Z1, T12, T3 \ LDP 16(X), ( Z3, Z4) \ LDP 16(Y), ( Z8, Z9) \ MUL Z1, T12, T0 \ UMULH Z1, Z7, T2 \ LDP 32(X), ( Z5, Z6) \ LDP 32(Y), (Z10, Z11) \ \ /* Compute aL*bL in T0-T5 */ \ mul192x192comba(Z1,Z2,Z3, T12,Z7,Z8, T0,T1,T2,T3,T4,T5, T6,T7,T8,T9) \ \ /* Compute aH*bH in T6-T11, destroys aL and bL */ \ MUL Z4, Z10, T7 \ MUL Z4, Z9, T6 \ UMULH Z4, Z9, T9 \ UMULH Z4, Z10, T8 \ mul192x192comba(Z4,Z5,Z6, Z9,Z10,Z11, T6,T7,T8,T9,T10,T11, Z1,Z2,T12,Z7) \ \ /* Compute aL*bL + aH*bH in Z1-Z6,T12, destroys aH */ \ ADDS T0, T6, Z1 \ ADCS T1, T7, Z2 \ ADCS T2, T8, Z3 \ ADCS T3, T9, Z4 \ ADCS T4, T10, Z5 \ ADCS T5, T11, Z6 \ ADC ZR, ZR, T12 \ \ /* Add to T0-T11 and store on stack */ \ STP ( T0, T1), -16(RSP) \ ADDS Z1, T3 \ STP ( T2, T3), -32(RSP) \ ADCS Z2, T4 \ ADCS Z3, T5 \ STP ( T4, T5), -48(RSP) \ ADCS Z4, T6 \ ADCS Z5, T7 \ STP ( T6, T7), -64(RSP) \ ADCS Z6, T8 \ ADC ZR, T12 \ STP ( T8, T9), -80(RSP) \ STP (T10, T11), -96(RSP) \ \ /* Load a to Z1-Z6 */ \ LDP 0(X), (Z1, Z2) \ LDP 16(X), (Z3, Z4) \ LDP 32(X), (Z5, Z6) \ \ /* Compute |aL-aH| to Z1-Z3, keep borrow in X */ \ SUBS Z4, Z1 \ SBCS Z5, Z2 \ SBCS Z6, Z3 \ SBC ZR, ZR, X \ NEGS Z1, Z4 \ NGCS Z2, Z5 \ NGC Z3, Z6 \ ADDS $1, X \ \ /* Load b to Z7-Z11,T0 */ \ LDP 0(Y), ( Z7, Z8) \ LDP 16(Y), ( Z9, Z10) \ LDP 32(Y), (Z11, T0) \ \ CSEL EQ, Z4, Z1, Z1 \ CSEL EQ, Z5, Z2 ,Z2 \ CSEL EQ, Z6, Z3, Z3 \ \ /* Compute |bH-bL| to Z7-Z9, keep borrow in Y */ \ SUBS Z7, Z10 \ SBCS Z8, Z11 \ SBCS Z9, T0 \ SBC ZR, ZR, Y \ NEGS Z10, Z7 \ NGCS Z11, Z8 \ NGC T0, Z9 \ ADDS $1, Y \ CSEL EQ, Z7, Z10, Z7 \ CSEL EQ, Z8, Z11, Z8 \ CSEL EQ, Z9, T0, Z9 \ \ /* Combine borrows */ \ EOR Y, X \ \ /* Compute |aL-aH|*|bH-bL| to Z10,Z11,T0-T3 */ \ MUL Z1, Z8, Z11 \ MUL Z1, Z7, Z10 \ UMULH Z1, Z8, T0 \ UMULH Z1, Z7, T1 \ mul192x192comba(Z1,Z2,Z3, Z7,Z8,Z9, Z10,Z11,T0,T1,T2,T3, T4,T5,T6,T7) \ \ /* The result has to be negated if exactly one of the operands was negative */ \ NEGS Z10, Y \ NGCS Z11, Z1 \ NGCS T0, Z2 \ NGCS T1, Z3 \ NGCS T2, Z4 \ NGCS T3, Z5 \ NGC ZR, T4 \ \ AND T4, X \ CMP $1, X \ CSEL EQ, Y, Z10, Z10 \ CSEL EQ, Z1, Z11, Z11 \ CSEL EQ, Z2, T0, T0 \ CSEL EQ, Z3, T1, T1 \ CSEL EQ, Z4, T2, T2 \ CSEL EQ, Z5, T3, T3 \ \ /* Add that to the middle part */ \ LDP -16(RSP), ( Y, Z1) \ LDP -32(RSP), ( Z2, Z3) \ LDP -48(RSP), ( Z4, Z5) \ ADDS Z10, Z3 \ ADCS Z11, Z4 \ LDP -64(RSP), ( Z6, Z7) \ ADCS T0, Z5 \ ADCS T1, Z6 \ LDP -80(RSP), ( Z8, Z9) \ ADCS T2, Z7 \ ADCS T3, Z8 \ LDP -96(RSP), (Z10, Z11) \ ADCS T12, Z9 \ ADCS ZR, Z10 \ ADC ZR, Z11 \ SUBS X, Z9 \ SBCS ZR, Z10 \ SBC ZR, Z11 // Compute c = a*b*R^-1 mod p TEXT ·fp384Mul(SB), NOSPLIT, $200-24 MOVD c+0(FP), R0 MOVD a+8(FP), R1 MOVD b+16(FP), R2 // Compute a*b in R2-R13 mul384x384karatsuba(R1, R2, R3,R4,R5,R6,R7,R8,R9,R10,R11,R12,R13, R14,R15,R16,R17,R19,R20,R21,R22,R23,R24,R25,R26,R27) // Store a*b on the stack STP ( R2, R3), -112(RSP) STP ( R4, R5), -128(RSP) STP ( R6, R7), -144(RSP) STP ( R8, R9), -160(RSP) STP (R10, R11), -176(RSP) STP (R12, R13), -192(RSP) // Compute m = a*b*pp mod 2^384 in R19-R24 // Store it temporarily in c MOVD ·pp+0(SB), R14 MUL R14, R2, R19 UMULH R14, R2, R20 MUL R14, R3, R16 UMULH R14, R3, R21 ADDS R16, R20 ADC ZR, R21 MUL R14, R4, R16 UMULH R14, R4, R22 ADDS R16, R21 ADC ZR, R22 MUL R14, R5, R16 UMULH R14, R5, R23 ADDS R16, R22 ADC ZR, R23 MUL R14, R6, R16 UMULH R14, R6, R24 ADDS R16, R23 ADC ZR, R24 MADD R14, R24, R7, R24 // ·pp+8(SB) = 1, so we can just add ADDS R2, R20 STP (R19, R20), 0(R0) ADCS R3, R21 ADCS R4, R22 ADCS R5, R23 ADC R6, R24 LDP ·pp+16(SB), (R14, R15) MUL R14, R2, R8 UMULH R14, R2, R9 MUL R14, R3, R16 UMULH R14, R3, R10 ADDS R16, R9 ADC ZR, R10 MUL R14, R4, R16 UMULH R14, R4, R11 ADDS R16, R10 ADC ZR, R11 MUL R14, R5, R16 ADD R16, R11 ADDS R8, R21 ADCS R9, R22 ADCS R10, R23 ADC R11, R24 MUL R15, R2, R8 UMULH R15, R2, R9 MUL R15, R3, R16 UMULH R15, R3, R10 ADDS R16, R9 ADC ZR, R10 MADD R15, R10, R4, R10 ADDS R8, R22 STP (R21, R22), 16(R0) ADCS R9, R23 ADC R10, R24 LDP ·pp+32(SB), (R14, R15) MUL R14, R2, R8 UMULH R14, R2, R9 MADD R14, R9, R3, R9 ADDS R8, R23 ADC R9, R24 MADD R15, R24, R2, R24 STP (R23, R24), 32(R0) // Compute m*p in R1-R12 MOVD $·p(SB), R1 mul384x384karatsuba(R0, R1, R2,R3,R4,R5,R6,R7,R8,R9,R10,R11,R12, R13,R14,R15,R16,R17,R19,R20,R21,R22,R23,R24,R25,R26) // Add a*b to m*p in R1-R12,R26 LDP -112(RSP), (R13, R14) ADDS R13, R1 LDP -128(RSP), (R15, R16) ADCS R14, R2 ADCS R15, R3 LDP -144(RSP), (R17, R19) ADCS R16, R4 ADCS R17, R5 LDP -160(RSP), (R20, R21) ADCS R19, R6 ADCS R20, R7 LDP -176(RSP), (R22, R23) ADCS R21, R8 ADCS R22, R9 LDP -192(RSP), (R24, R25) ADCS R23, R10 ADCS R24, R11 ADCS R25, R12 ADC ZR, ZR, R26 // Reduce the top half mod p LDP ·p+ 0(SB), (R13, R14) SUBS R13, R7, R13 LDP ·p+16(SB), (R15, R16) SBCS R14, R8, R14 SBCS R15, R9, R15 LDP ·p+32(SB), (R17, R19) SBCS R16, R10, R16 SBCS R17, R11, R17 SBCS R19, R12, R19 SBCS ZR, R26 // Store result in c MOVD c+0(FP), R0 CSEL CC, R7, R13, R7 CSEL CC, R8, R14, R8 STP ( R7, R8), 0(R0) CSEL CC, R9, R15, R9 CSEL CC, R10, R16, R10 STP ( R9, R10), 16(R0) CSEL CC, R11, R17, R11 CSEL CC, R12, R19, R12 STP (R11, R12), 32(R0) RET golang-github-cloudflare-circl-1.3.7/ecc/p384/arith_test.go000066400000000000000000000117021454601126700234150ustar00rootroot00000000000000//go:build (!noasm && arm64) || (!noasm && amd64) // +build !noasm,arm64 !noasm,amd64 package p384 import ( "crypto/elliptic" "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) func TestFpCmov(t *testing.T) { var x, y, z fp384 for _, b := range []int{-2, -1, 1, 2} { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) z = x fp384Cmov(&z, &y, b) got := z want := y if got != want { test.ReportError(t, got, want, b, x, y) } } _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) z = x fp384Cmov(&z, &y, 0) got := z want := x if got != want { test.ReportError(t, got, want, 0, x, y) } } func TestFpNegZero(t *testing.T) { zero, x := &fp384{}, &fp384{} fp384Neg(x, zero) got := x.BigInt() want := zero.BigInt() if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } func TestFpSetBigInt(t *testing.T) { P := elliptic.P384().Params().P neg := big.NewInt(-0xFF) // negative zero := big.NewInt(0) // zero one := big.NewInt(1) // one two96 := new(big.Int).Lsh(one, 96) // 2^96 two384 := new(big.Int).Lsh(one, 384) // 2^384 two384two96 := new(big.Int).Sub(two384, two96) // 2^384-2^96 two768 := new(big.Int).Lsh(one, 768) // 2^768 for id, b := range []*big.Int{ neg, zero, one, two96, two384, two384two96, two768, } { var x fp384 x.SetBigInt(b) got := x.BigInt() if b.BitLen() > 384 || b.Sign() < 0 { b.Mod(b, P) } want := b if got.Cmp(want) != 0 { test.ReportError(t, got, want, id) } } } func TestMulZero(t *testing.T) { x, zero := &fp384{}, &fp384{} _, _ = rand.Read(x[:]) fp384Mul(x, x, zero) got := x.BigInt() want := zero.BigInt() if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } func TestFp(t *testing.T) { P := elliptic.P384().Params().P x, y, z := &fp384{}, &fp384{}, &fp384{} testTimes := 1 << 12 var bigR, bigR2, bigRinv big.Int one := big.NewInt(1) bigR.Lsh(one, 384).Mod(&bigR, P) bigR2.Lsh(one, 2*384).Mod(&bigR2, P) bigRinv.ModInverse(&bigR, P) t.Run("Encode", func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) bigX := x.BigInt() // fp384 montEncode(z, x) got := z.BigInt() // big.Int want := bigX.Mul(bigX, &bigR).Mod(bigX, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } }) t.Run("Decode", func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) bigX := x.BigInt() // fp384 montDecode(z, x) got := z.BigInt() // big.Int want := bigX.Mul(bigX, new(big.Int).ModInverse(&bigR, P)).Mod(bigX, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } }) t.Run("Neg", func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) bigX := x.BigInt() // fp384 fp384Neg(z, x) got := z.BigInt() // big.Int want := bigX.Neg(bigX).Mod(bigX, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } }) t.Run("Add", func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) bigX := x.BigInt() bigY := y.BigInt() // fp384 fp384Add(z, x, y) got := z.BigInt() // big.Int want := bigX.Add(bigX, bigY) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("Sub", func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) bigX := x.BigInt() bigY := y.BigInt() // fp384 fp384Sub(z, x, y) got := z.BigInt() // big.Int want := bigX.Sub(bigX, bigY) want = want.Mod(want, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("Mul", func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) bigX := x.BigInt() bigY := y.BigInt() // fp384 fp384Mul(z, x, y) got := z.BigInt() // big.Int want := bigX.Mul(bigX, bigY).Mul(bigX, &bigRinv).Mod(bigX, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } }) t.Run("Inv", func(t *testing.T) { for i := 0; i < testTimes; i++ { _, _ = rand.Read(x[:]) bigX := x.BigInt() // fp384 fp384Inv(z, x) got := z.BigInt() // big.Int want := bigX.ModInverse(bigX, P).Mul(bigX, &bigR2).Mod(bigX, P) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } }) } func BenchmarkFp(b *testing.B) { x, y, z := &fp384{}, &fp384{}, &fp384{} b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { fp384Add(z, x, y) } }) b.Run("Sub", func(b *testing.B) { for i := 0; i < b.N; i++ { fp384Sub(z, x, y) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { fp384Mul(z, x, y) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { fp384Sqr(z, x) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { fp384Inv(z, x) } }) } golang-github-cloudflare-circl-1.3.7/ecc/p384/doc.go000066400000000000000000000007301454601126700220130ustar00rootroot00000000000000// Package p384 provides optimized elliptic curve operations on the P-384 curve. // // These are some improvements over crypto/elliptic package: // - Around 10x faster in amd64 architecture. // - Reduced number of memory allocations. // - Native support for arm64 architecture. // - ScalarMult is performed using a constant-time algorithm. // - ScalarBaseMult fallbacks into ScalarMult. // - A new method included for double-point multiplication. package p384 golang-github-cloudflare-circl-1.3.7/ecc/p384/opt_test.go000066400000000000000000000041511454601126700231100ustar00rootroot00000000000000//go:build (!noasm && arm64) || (!noasm && amd64) // +build !noasm,arm64 !noasm,amd64 package p384 import ( "bytes" "crypto/elliptic" "crypto/rand" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) func TestInternals(t *testing.T) { t.Run("reduceScalar", func(t *testing.T) { var c curve order := c.Params().N var buffer [3 * sizeFp]byte for i := 0; i < sizeFp; i++ { buffer[i] = 0xFF } _, err := rand.Read(buffer[sizeFp:]) if err != nil { t.Fatal(err) } for i := 0; i < 3*sizeFp; i++ { k := buffer[:i] got := c.reduceScalar(k) bigK := new(big.Int).SetBytes(k) bigK.Mod(bigK, order) want := bigK.FillBytes(make([]byte, sizeFp)) if !bytes.Equal(got, want) { test.ReportError(t, got, want, k) } } }) t.Run("absolute", func(t *testing.T) { cases := []int32{-2, -1, 0, 1, 2} expected := []int32{2, 1, 0, 1, 2} for i := range cases { got := absolute(cases[i]) want := expected[i] if got != want { test.ReportError(t, got, want, cases[i]) } } }) t.Run("toOdd", func(t *testing.T) { var c curve k := []byte{0xF0} oddK, _ := c.toOdd(k) got := len(oddK) want := 48 if got != want { test.ReportError(t, got, want) } oddK[sizeFp-1] = 0x0 smallOddK, _ := c.toOdd(oddK) got = len(smallOddK) want = 48 if got != want { test.ReportError(t, got, want) } }) t.Run("special k", func(t *testing.T) { cases := []struct { // known cases that require complete addition w uint k int }{ {w: 2, k: 2}, {w: 5, k: 6}, {w: 6, k: 38}, {w: 7, k: 102}, {w: 9, k: 230}, {w: 12, k: 742}, {w: 14, k: 4838}, {w: 17, k: 21222}, {w: 19, k: 152294}, } var c curve StdCurve := elliptic.P384() params := StdCurve.Params() for _, caseI := range cases { k := big.NewInt(int64(caseI.k)).Bytes() gotX, gotY := c.scalarMultOmega(params.Gx, params.Gy, k, caseI.w) wantX, wantY := StdCurve.ScalarMult(params.Gx, params.Gy, k) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, caseI) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, caseI) } } }) } golang-github-cloudflare-circl-1.3.7/ecc/p384/p384.go000066400000000000000000000020161454601126700217430ustar00rootroot00000000000000package p384 import ( "crypto/elliptic" "math/big" ) // Curve is used to provide the extended functionality and performance of // elliptic.Curve interface. type Curve interface { elliptic.Curve // IsAtInfinity returns True is the point is the identity point. IsAtInfinity(X, Y *big.Int) bool // CombinedMult calculates P=mG+nQ, where G is the generator and // Q=(Qx,Qy). The scalars m and n are positive integers in big-endian form. // Runs in non-constant time to be used in signature verification. CombinedMult(Qx, Qy *big.Int, m, n []byte) (Px, Py *big.Int) } // Params returns the parameters for the curve. Note: The value returned by // this function fallbacks to the stdlib implementation of elliptic curve // operations. Use this method to only recover elliptic curve parameters. func (c curve) Params() *elliptic.CurveParams { return elliptic.P384().Params() } // IsAtInfinity returns True is the point is the identity point. func (c curve) IsAtInfinity(x, y *big.Int) bool { return x.Sign() == 0 && y.Sign() == 0 } golang-github-cloudflare-circl-1.3.7/ecc/p384/p384_generic.go000066400000000000000000000010401454601126700234330ustar00rootroot00000000000000//go:build noasm || (!amd64 && !arm64) // +build noasm !amd64,!arm64 package p384 import ( "crypto/elliptic" "math/big" ) type curve struct{ elliptic.Curve } func P384() Curve { return curve{elliptic.P384()} } // CombinedMult calculates P=mG+nQ, where G is the generator and Q=(x,y,z). // The scalars m and n are integers in big-endian form. Non-constant time. func (c curve) CombinedMult(xQ, yQ *big.Int, m, n []byte) (xP, yP *big.Int) { x1, y1 := c.ScalarBaseMult(m) x2, y2 := c.ScalarMult(xQ, yQ, n) return c.Add(x1, y1, x2, y2) } golang-github-cloudflare-circl-1.3.7/ecc/p384/p384_test.go000066400000000000000000000141451454601126700230100ustar00rootroot00000000000000package p384_test import ( "crypto/elliptic" "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/ecc/p384" "github.com/cloudflare/circl/internal/test" ) func TestIsOnCurveTrue(t *testing.T) { CirclCurve := p384.P384() k := make([]byte, 384/8) for i := 0; i < 128; i++ { _, _ = rand.Read(k) x, y := elliptic.P384().ScalarBaseMult(k) got := CirclCurve.IsOnCurve(x, y) want := true if got != want { test.ReportError(t, got, want, k) } x = x.Neg(x) got = CirclCurve.IsOnCurve(x, y) want = false if got != want { test.ReportError(t, got, want, k) } } } func TestAffine(t *testing.T) { const testTimes = 1 << 7 CirclCurve := p384.P384() StdCurve := elliptic.P384() params := StdCurve.Params() t.Run("Addition", func(t *testing.T) { for i := 0; i < testTimes; i++ { K1, _ := rand.Int(rand.Reader, params.N) K2, _ := rand.Int(rand.Reader, params.N) X1, Y1 := StdCurve.ScalarBaseMult(K1.Bytes()) X2, Y2 := StdCurve.ScalarBaseMult(K2.Bytes()) wantX, wantY := StdCurve.Add(X1, Y1, X2, Y2) gotX, gotY := CirclCurve.Add(X1, Y1, X2, Y2) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, K1, K2) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) t.Run("Double", func(t *testing.T) { for i := 0; i < testTimes; i++ { k, _ := rand.Int(rand.Reader, params.N) x, y := StdCurve.ScalarBaseMult(k.Bytes()) wantX, wantY := StdCurve.Double(x, y) gotX, gotY := CirclCurve.Double(x, y) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, k) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) } func TestScalarBaseMult(t *testing.T) { const testTimes = 1 << 6 CirclCurve := p384.P384() StdCurve := elliptic.P384() t.Run("0P", func(t *testing.T) { k := make([]byte, 500) for i := 0; i < len(k); i += 20 { gotX, gotY := CirclCurve.ScalarBaseMult(k[:i]) wantX, wantY := StdCurve.ScalarBaseMult(k[:i]) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, k[:i]) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) t.Run("kP", func(t *testing.T) { k := make([]byte, 48) for i := 0; i < testTimes; i++ { _, _ = rand.Read(k) gotX, gotY := CirclCurve.ScalarBaseMult(k) wantX, wantY := StdCurve.ScalarBaseMult(k) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, k) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) t.Run("kSmall", func(t *testing.T) { k := make([]byte, 16) for i := 0; i < testTimes; i++ { _, _ = rand.Read(k) gotX, gotY := CirclCurve.ScalarBaseMult(k) wantX, wantY := StdCurve.ScalarBaseMult(k) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, k) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) t.Run("kLarge", func(t *testing.T) { k := make([]byte, 384) for i := 0; i < testTimes; i++ { _, _ = rand.Read(k) gotX, gotY := CirclCurve.ScalarBaseMult(k) wantX, wantY := StdCurve.ScalarBaseMult(k) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, k) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) } func TestScalarMult(t *testing.T) { const testTimes = 1 << 6 CirclCurve := p384.P384() StdCurve := elliptic.P384() params := StdCurve.Params() t.Run("k=0", func(t *testing.T) { k := []byte{0x0} gotX, gotY := CirclCurve.ScalarMult(params.Gx, params.Gy, k) got := CirclCurve.IsAtInfinity(gotX, gotY) want := true if got != want { test.ReportError(t, got, want) } }) t.Run("random k", func(t *testing.T) { for i := 0; i < testTimes; i++ { k, _ := rand.Int(rand.Reader, params.N) gotX, gotY := CirclCurve.ScalarMult(params.Gx, params.Gy, k.Bytes()) wantX, wantY := StdCurve.ScalarMult(params.Gx, params.Gy, k.Bytes()) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, k) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) t.Run("wrong P", func(t *testing.T) { for i := 0; i < testTimes; i++ { k, _ := rand.Int(rand.Reader, params.N) x, _ := rand.Int(rand.Reader, params.P) y, _ := rand.Int(rand.Reader, params.P) got := CirclCurve.IsOnCurve(x, y) && CirclCurve.IsOnCurve(CirclCurve.ScalarMult(x, y, k.Bytes())) want := StdCurve.IsOnCurve(x, y) && StdCurve.IsOnCurve(StdCurve.ScalarMult(x, y, k.Bytes())) if got != want { test.ReportError(t, got, want, k, x, y) } } }) } func TestCombinedMult(t *testing.T) { const testTimes = 1 << 7 CirclCurve := p384.P384() StdCurve := elliptic.P384() params := StdCurve.Params() for i := 0; i < testTimes; i++ { K, _ := rand.Int(rand.Reader, params.N) X, Y := StdCurve.ScalarBaseMult(K.Bytes()) K1, _ := rand.Int(rand.Reader, params.N) K2, _ := rand.Int(rand.Reader, params.N) x1, y1 := StdCurve.ScalarBaseMult(K1.Bytes()) x2, y2 := StdCurve.ScalarMult(X, Y, K2.Bytes()) wantX, wantY := StdCurve.Add(x1, y1, x2, y2) gotX, gotY := CirclCurve.CombinedMult(X, Y, K1.Bytes(), K2.Bytes()) if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, K, K1, K2) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } } func BenchmarkScalarMult(b *testing.B) { curve := p384.P384() params := curve.Params() K, _ := rand.Int(rand.Reader, params.N) M, _ := rand.Int(rand.Reader, params.N) N, _ := rand.Int(rand.Reader, params.N) k := K.Bytes() m := M.Bytes() n := N.Bytes() b.Run("kG", func(b *testing.B) { for i := 0; i < b.N; i++ { curve.ScalarBaseMult(k) } }) b.Run("kP", func(b *testing.B) { for i := 0; i < b.N; i++ { curve.ScalarMult(params.Gx, params.Gy, k) } }) b.Run("kG+lP", func(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = curve.CombinedMult(params.Gx, params.Gy, m, n) } }) } func Example_p384() { // import "github.com/cloudflare/circl/ecc/p384" // import "crypto/elliptic" circl := p384.P384() stdlib := elliptic.P384() params := circl.Params() K, _ := rand.Int(rand.Reader, params.N) k := K.Bytes() x1, y1 := circl.ScalarBaseMult(k) x2, y2 := stdlib.ScalarBaseMult(k) fmt.Printf("%v, %v", x1.Cmp(x2) == 0, y1.Cmp(y2) == 0) // Output: true, true } golang-github-cloudflare-circl-1.3.7/ecc/p384/p384opt.go000066400000000000000000000106411454601126700224710ustar00rootroot00000000000000//go:build (!noasm && arm64) || (!noasm && amd64) // +build !noasm,arm64 !noasm,amd64 package p384 import ( "crypto/subtle" "math/big" "github.com/cloudflare/circl/math" ) type curve struct{} // P384 returns a Curve which implements P-384 (see FIPS 186-3, section D.2.4). func P384() Curve { return curve{} } // IsOnCurve reports whether the given (x,y) lies on the curve. func (c curve) IsOnCurve(x, y *big.Int) bool { x1, y1 := &fp384{}, &fp384{} x1.SetBigInt(x) y1.SetBigInt(y) montEncode(x1, x1) montEncode(y1, y1) y2, x3 := &fp384{}, &fp384{} fp384Sqr(y2, y1) fp384Sqr(x3, x1) fp384Mul(x3, x3, x1) threeX := &fp384{} fp384Add(threeX, x1, x1) fp384Add(threeX, threeX, x1) fp384Sub(x3, x3, threeX) fp384Add(x3, x3, &bb) return *y2 == *x3 } // Add returns the sum of (x1,y1) and (x2,y2). func (c curve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) { P := newAffinePoint(x1, y1).toJacobian() P.mixadd(P, newAffinePoint(x2, y2)) return P.toAffine().toInt() } // Double returns 2*(x,y). func (c curve) Double(x1, y1 *big.Int) (x, y *big.Int) { P := newAffinePoint(x1, y1).toJacobian() P.double() return P.toAffine().toInt() } // reduceScalar shorten a scalar modulo the order of the curve. func (c curve) reduceScalar(k []byte) []byte { bigK := new(big.Int).SetBytes(k) bigK.Mod(bigK, c.Params().N) return bigK.FillBytes(make([]byte, sizeFp)) } // toOdd performs k = (-k mod N) if k is even. func (c curve) toOdd(k []byte) ([]byte, int) { var X, Y big.Int X.SetBytes(k) Y.Neg(&X).Mod(&Y, c.Params().N) isEven := 1 - int(X.Bit(0)) x := X.Bytes() y := Y.Bytes() if len(x) < len(y) { x = append(make([]byte, len(y)-len(x)), x...) } else if len(x) > len(y) { y = append(make([]byte, len(x)-len(y)), y...) } subtle.ConstantTimeCopy(isEven, x, y) return x, isEven } // ScalarMult returns (Qx,Qy)=k*(Px,Py) where k is a number in big-endian form. func (c curve) ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int) { return c.scalarMultOmega(x1, y1, k, 5) } func (c curve) scalarMultOmega(x1, y1 *big.Int, k []byte, omega uint) (x, y *big.Int) { k = c.reduceScalar(k) oddK, isEvenK := c.toOdd(k) var scalar big.Int scalar.SetBytes(oddK) if scalar.Sign() == 0 { return new(big.Int), new(big.Int) } const bitsN = uint(384) L := math.SignedDigit(&scalar, omega, bitsN) var R jacobianPoint Q := zeroPoint().toJacobian() TabP := newAffinePoint(x1, y1).oddMultiples(omega) for i := len(L) - 1; i > 0; i-- { for j := uint(0); j < omega-1; j++ { Q.double() } idx := absolute(L[i]) >> 1 for j := range TabP { R.cmov(&TabP[j], subtle.ConstantTimeEq(int32(j), idx)) } R.cneg(int(L[i]>>31) & 1) Q.add(Q, &R) } // Calculate the last iteration using complete addition formula. for j := uint(0); j < omega-1; j++ { Q.double() } idx := absolute(L[0]) >> 1 for j := range TabP { R.cmov(&TabP[j], subtle.ConstantTimeEq(int32(j), idx)) } R.cneg(int(L[0]>>31) & 1) QQ := Q.toProjective() QQ.completeAdd(QQ, R.toProjective()) QQ.cneg(isEvenK) return QQ.toAffine().toInt() } // ScalarBaseMult returns k*G, where G is the base point of the group // and k is an integer in big-endian form. func (c curve) ScalarBaseMult(k []byte) (x, y *big.Int) { params := c.Params() return c.ScalarMult(params.Gx, params.Gy, k) } // CombinedMult calculates P=mG+nQ, where G is the generator and Q=(x,y,z). // The scalars m and n are integers in big-endian form. Non-constant time. func (c curve) CombinedMult(xQ, yQ *big.Int, m, n []byte) (xP, yP *big.Int) { const nOmega = uint(5) var k big.Int k.SetBytes(m) nafM := math.OmegaNAF(&k, baseOmega) k.SetBytes(n) nafN := math.OmegaNAF(&k, nOmega) if len(nafM) > len(nafN) { nafN = append(nafN, make([]int32, len(nafM)-len(nafN))...) } else if len(nafM) < len(nafN) { nafM = append(nafM, make([]int32, len(nafN)-len(nafM))...) } TabQ := newAffinePoint(xQ, yQ).oddMultiples(nOmega) var jR jacobianPoint var aR affinePoint P := zeroPoint().toJacobian() for i := len(nafN) - 1; i >= 0; i-- { P.double() // Generator point if nafM[i] != 0 { idxM := absolute(nafM[i]) >> 1 aR = baseOddMultiples[idxM] if nafM[i] < 0 { aR.neg() } P.mixadd(P, &aR) } // Input point if nafN[i] != 0 { idxN := absolute(nafN[i]) >> 1 jR = TabQ[idxN] if nafN[i] < 0 { jR.neg() } P.add(P, &jR) } } return P.toAffine().toInt() } // absolute returns always a positive value. func absolute(x int32) int32 { mask := x >> 31 return (x + mask) ^ mask } golang-github-cloudflare-circl-1.3.7/ecc/p384/point.go000066400000000000000000000231571454601126700224070ustar00rootroot00000000000000//go:build (!noasm && arm64) || (!noasm && amd64) // +build !noasm,arm64 !noasm,amd64 package p384 import ( "fmt" "math/big" ) // affinePoint represents an affine point of the curve. The point at // infinity is (0,0) leveraging that it is not an affine point. type affinePoint struct{ x, y fp384 } func newAffinePoint(x, y *big.Int) *affinePoint { var P affinePoint P.x.SetBigInt(x) P.y.SetBigInt(y) montEncode(&P.x, &P.x) montEncode(&P.y, &P.y) return &P } func zeroPoint() *affinePoint { return &affinePoint{} } func (ap affinePoint) String() string { if ap.isZero() { return "inf" } return fmt.Sprintf("x: %v\ny: %v", ap.x, ap.y) } func (ap *affinePoint) isZero() bool { zero := fp384{} return ap.x == zero && ap.y == zero } func (ap *affinePoint) neg() { fp384Neg(&ap.y, &ap.y) } func (ap *affinePoint) toInt() (x, y *big.Int) { var x1, y1 fp384 montDecode(&x1, &ap.x) montDecode(&y1, &ap.y) return x1.BigInt(), y1.BigInt() } func (ap *affinePoint) toJacobian() *jacobianPoint { var P jacobianPoint if ap.isZero() { montEncode(&P.x, &fp384{1}) montEncode(&P.y, &fp384{1}) } else { P.x = ap.x P.y = ap.y montEncode(&P.z, &fp384{1}) } return &P } func (ap *affinePoint) toProjective() *projectivePoint { var P projectivePoint if ap.isZero() { montEncode(&P.y, &fp384{1}) } else { P.x = ap.x P.y = ap.y montEncode(&P.z, &fp384{1}) } return &P } // OddMultiples calculates the points iP for i={1,3,5,7,..., 2^(n-1)-1} // Ensure that 1 < n < 31, otherwise it returns an empty slice. func (ap affinePoint) oddMultiples(n uint) []jacobianPoint { var t []jacobianPoint if n > 1 && n < 31 { P := ap.toJacobian() s := int32(1) << (n - 1) t = make([]jacobianPoint, s) t[0] = *P _2P := *P _2P.double() for i := int32(1); i < s; i++ { t[i].add(&t[i-1], &_2P) } } return t } // p2Point is a point in P^2 type p2Point struct{ x, y, z fp384 } func (P *p2Point) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v", P.x, P.y, P.z) } func (P *p2Point) neg() { fp384Neg(&P.y, &P.y) } // condNeg if P is negated if b=1. func (P *p2Point) cneg(b int) { var mY fp384 fp384Neg(&mY, &P.y) fp384Cmov(&P.y, &mY, b) } // cmov sets P to Q if b=1. func (P *p2Point) cmov(Q *p2Point, b int) { fp384Cmov(&P.x, &Q.x, b) fp384Cmov(&P.y, &Q.y, b) fp384Cmov(&P.z, &Q.z, b) } func (P *p2Point) toInt() (x, y, z *big.Int) { var x1, y1, z1 fp384 montDecode(&x1, &P.x) montDecode(&y1, &P.y) montDecode(&z1, &P.z) return x1.BigInt(), y1.BigInt(), z1.BigInt() } // jacobianPoint represents a point in Jacobian coordinates. The point at // infinity is any point (x,y,0) such that x and y are different from 0. type jacobianPoint struct{ p2Point } func (P *jacobianPoint) isZero() bool { zero := fp384{} return P.x != zero && P.y != zero && P.z == zero } func (P *jacobianPoint) toAffine() *affinePoint { var aP affinePoint z, z2 := &fp384{}, &fp384{} fp384Inv(z, &P.z) fp384Sqr(z2, z) fp384Mul(&aP.x, &P.x, z2) fp384Mul(&aP.y, &P.y, z) fp384Mul(&aP.y, &aP.y, z2) return &aP } func (P *jacobianPoint) cmov(Q *jacobianPoint, b int) { P.p2Point.cmov(&Q.p2Point, b) } // add calculates P=Q+R such that Q and R are different than the identity point, // and Q!==R. This function cannot be used for doublings. func (P *jacobianPoint) add(Q, R *jacobianPoint) { if Q.isZero() { *P = *R return } else if R.isZero() { *P = *Q return } // Cohen-Miyagi-Ono (1998) // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2 X1, Y1, Z1 := &Q.x, &Q.y, &Q.z X2, Y2, Z2 := &R.x, &R.y, &R.z Z1Z1, Z2Z2, U1, U2 := &fp384{}, &fp384{}, &fp384{}, &fp384{} H, HH, HHH, RR := &fp384{}, &fp384{}, &fp384{}, &fp384{} V, t4, t5, t6, t7, t8 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} t0, t1, t2, t3, S1, S2 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} fp384Sqr(Z1Z1, Z1) // Z1Z1 = Z1 ^ 2 fp384Sqr(Z2Z2, Z2) // Z2Z2 = Z2 ^ 2 fp384Mul(U1, X1, Z2Z2) // U1 = X1 * Z2Z2 fp384Mul(U2, X2, Z1Z1) // U2 = X2 * Z1Z1 fp384Mul(t0, Z2, Z2Z2) // t0 = Z2 * Z2Z2 fp384Mul(S1, Y1, t0) // S1 = Y1 * t0 fp384Mul(t1, Z1, Z1Z1) // t1 = Z1 * Z1Z1 fp384Mul(S2, Y2, t1) // S2 = Y2 * t1 fp384Sub(H, U2, U1) // H = U2 - U1 fp384Sqr(HH, H) // HH = H ^ 2 fp384Mul(HHH, H, HH) // HHH = H * HH fp384Sub(RR, S2, S1) // r = S2 - S1 fp384Mul(V, U1, HH) // V = U1 * HH fp384Sqr(t2, RR) // t2 = r ^ 2 fp384Add(t3, V, V) // t3 = V + V fp384Sub(t4, t2, HHH) // t4 = t2 - HHH fp384Sub(&P.x, t4, t3) // X3 = t4 - t3 fp384Sub(t5, V, &P.x) // t5 = V - X3 fp384Mul(t6, S1, HHH) // t6 = S1 * HHH fp384Mul(t7, RR, t5) // t7 = r * t5 fp384Sub(&P.y, t7, t6) // Y3 = t7 - t6 fp384Mul(t8, Z2, H) // t8 = Z2 * H fp384Mul(&P.z, Z1, t8) // Z3 = Z1 * t8 } // mixadd calculates P=Q+R such that P and Q different than the identity point, // and Q not in {P,-P, O}. func (P *jacobianPoint) mixadd(Q *jacobianPoint, R *affinePoint) { if Q.isZero() { *P = *R.toJacobian() return } else if R.isZero() { *P = *Q return } z1z1, u2 := &fp384{}, &fp384{} fp384Sqr(z1z1, &Q.z) fp384Mul(u2, &R.x, z1z1) s2 := &fp384{} fp384Mul(s2, &R.y, &Q.z) fp384Mul(s2, s2, z1z1) if Q.x == *u2 { if Q.y != *s2 { *P = *(zeroPoint().toJacobian()) return } *P = *Q P.double() return } h, r := &fp384{}, &fp384{} fp384Sub(h, u2, &Q.x) fp384Mul(&P.z, h, &Q.z) fp384Sub(r, s2, &Q.y) h2, h3 := &fp384{}, &fp384{} fp384Sqr(h2, h) fp384Mul(h3, h2, h) h3y1 := &fp384{} fp384Mul(h3y1, h3, &Q.y) h2x1 := &fp384{} fp384Mul(h2x1, h2, &Q.x) fp384Sqr(&P.x, r) fp384Sub(&P.x, &P.x, h3) fp384Sub(&P.x, &P.x, h2x1) fp384Sub(&P.x, &P.x, h2x1) fp384Sub(&P.y, h2x1, &P.x) fp384Mul(&P.y, &P.y, r) fp384Sub(&P.y, &P.y, h3y1) } func (P *jacobianPoint) double() { delta, gamma, alpha, alpha2 := &fp384{}, &fp384{}, &fp384{}, &fp384{} fp384Sqr(delta, &P.z) fp384Sqr(gamma, &P.y) fp384Sub(alpha, &P.x, delta) fp384Add(alpha2, &P.x, delta) fp384Mul(alpha, alpha, alpha2) *alpha2 = *alpha fp384Add(alpha, alpha, alpha) fp384Add(alpha, alpha, alpha2) beta := &fp384{} fp384Mul(beta, &P.x, gamma) beta8 := &fp384{} fp384Sqr(&P.x, alpha) fp384Add(beta8, beta, beta) fp384Add(beta8, beta8, beta8) fp384Add(beta8, beta8, beta8) fp384Sub(&P.x, &P.x, beta8) fp384Add(&P.z, &P.y, &P.z) fp384Sqr(&P.z, &P.z) fp384Sub(&P.z, &P.z, gamma) fp384Sub(&P.z, &P.z, delta) fp384Add(beta, beta, beta) fp384Add(beta, beta, beta) fp384Sub(beta, beta, &P.x) fp384Mul(&P.y, alpha, beta) fp384Sqr(gamma, gamma) fp384Add(gamma, gamma, gamma) fp384Add(gamma, gamma, gamma) fp384Add(gamma, gamma, gamma) fp384Sub(&P.y, &P.y, gamma) } func (P *jacobianPoint) toProjective() *projectivePoint { var hP projectivePoint hP.y = P.y fp384Mul(&hP.x, &P.x, &P.z) fp384Sqr(&hP.z, &P.z) fp384Mul(&hP.z, &hP.z, &P.z) return &hP } // projectivePoint represents a point in projective homogeneous coordinates. // The point at infinity is (0,y,0) such that y is different from 0. type projectivePoint struct{ p2Point } func (P *projectivePoint) isZero() bool { zero := fp384{} return P.x == zero && P.y != zero && P.z == zero } func (P *projectivePoint) toAffine() *affinePoint { var aP affinePoint z := &fp384{} fp384Inv(z, &P.z) fp384Mul(&aP.x, &P.x, z) fp384Mul(&aP.y, &P.y, z) return &aP } // add calculates P=Q+R using complete addition formula for prime groups. func (P *projectivePoint) completeAdd(Q, R *projectivePoint) { // Reference: // "Complete addition formulas for prime order elliptic curves" by // Costello-Renes-Batina. [Alg.4] (eprint.iacr.org/2015/1060). X1, Y1, Z1 := &Q.x, &Q.y, &Q.z X2, Y2, Z2 := &R.x, &R.y, &R.z X3, Y3, Z3 := &fp384{}, &fp384{}, &fp384{} t0, t1, t2, t3, t4 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} fp384Mul(t0, X1, X2) // 1. t0 ← X1 · X2 fp384Mul(t1, Y1, Y2) // 2. t1 ← Y1 · Y2 fp384Mul(t2, Z1, Z2) // 3. t2 ← Z1 · Z2 fp384Add(t3, X1, Y1) // 4. t3 ← X1 + Y1 fp384Add(t4, X2, Y2) // 5. t4 ← X2 + Y2 fp384Mul(t3, t3, t4) // 6. t3 ← t3 · t4 fp384Add(t4, t0, t1) // 7. t4 ← t0 + t1 fp384Sub(t3, t3, t4) // 8. t3 ← t3 − t4 fp384Add(t4, Y1, Z1) // 9. t4 ← Y1 + Z1 fp384Add(X3, Y2, Z2) // 10. X3 ← Y2 + Z2 fp384Mul(t4, t4, X3) // 11. t4 ← t4 · X3 fp384Add(X3, t1, t2) // 12. X3 ← t1 + t2 fp384Sub(t4, t4, X3) // 13. t4 ← t4 − X3 fp384Add(X3, X1, Z1) // 14. X3 ← X1 + Z1 fp384Add(Y3, X2, Z2) // 15. Y3 ← X2 + Z2 fp384Mul(X3, X3, Y3) // 16. X3 ← X3 · Y3 fp384Add(Y3, t0, t2) // 17. Y3 ← t0 + t2 fp384Sub(Y3, X3, Y3) // 18. Y3 ← X3 − Y3 fp384Mul(Z3, &bb, t2) // 19. Z3 ← b · t2 fp384Sub(X3, Y3, Z3) // 20. X3 ← Y3 − Z3 fp384Add(Z3, X3, X3) // 21. Z3 ← X3 + X3 fp384Add(X3, X3, Z3) // 22. X3 ← X3 + Z3 fp384Sub(Z3, t1, X3) // 23. Z3 ← t1 − X3 fp384Add(X3, t1, X3) // 24. X3 ← t1 + X3 fp384Mul(Y3, &bb, Y3) // 25. Y3 ← b · Y3 fp384Add(t1, t2, t2) // 26. t1 ← t2 + t2 fp384Add(t2, t1, t2) // 27. t2 ← t1 + t2 fp384Sub(Y3, Y3, t2) // 28. Y3 ← Y3 − t2 fp384Sub(Y3, Y3, t0) // 29. Y3 ← Y3 − t0 fp384Add(t1, Y3, Y3) // 30. t1 ← Y3 + Y3 fp384Add(Y3, t1, Y3) // 31. Y3 ← t1 + Y3 fp384Add(t1, t0, t0) // 32. t1 ← t0 + t0 fp384Add(t0, t1, t0) // 33. t0 ← t1 + t0 fp384Sub(t0, t0, t2) // 34. t0 ← t0 − t2 fp384Mul(t1, t4, Y3) // 35. t1 ← t4 · Y3 fp384Mul(t2, t0, Y3) // 36. t2 ← t0 · Y3 fp384Mul(Y3, X3, Z3) // 37. Y3 ← X3 · Z3 fp384Add(Y3, Y3, t2) // 38. Y3 ← Y3 + t2 fp384Mul(X3, t3, X3) // 39. X3 ← t3 · X3 fp384Sub(X3, X3, t1) // 40. X3 ← X3 − t1 fp384Mul(Z3, t4, Z3) // 41. Z3 ← t4 · Z3 fp384Mul(t1, t3, t0) // 42. t1 ← t3 · t0 fp384Add(Z3, Z3, t1) // 43. Z3 ← Z3 + t1 P.x, P.y, P.z = *X3, *Y3, *Z3 } golang-github-cloudflare-circl-1.3.7/ecc/p384/point_test.go000066400000000000000000000211621454601126700234400ustar00rootroot00000000000000//go:build (!noasm && arm64) || (!noasm && amd64) // +build !noasm,arm64 !noasm,amd64 package p384 import ( "crypto/elliptic" "crypto/rand" "encoding/binary" "testing" "github.com/cloudflare/circl/internal/test" ) func randomAffine() *affinePoint { params := elliptic.P384().Params() k, _ := rand.Int(rand.Reader, params.N) return newAffinePoint(params.ScalarBaseMult(k.Bytes())) } func randomJacobian() *jacobianPoint { params := elliptic.P384().Params() P := randomAffine().toJacobian() z, _ := rand.Int(rand.Reader, params.P) var l fp384 l.SetBigInt(z) fp384Mul(&P.z, &P.z, &l) // z = z * l^1 fp384Mul(&P.y, &P.y, &l) fp384Sqr(&l, &l) fp384Mul(&P.x, &P.x, &l) // x = x * l^2 fp384Mul(&P.y, &P.y, &l) // y = y * l^3 return P } func randomProjective() *projectivePoint { return randomJacobian().toProjective() } func TestPointDouble(t *testing.T) { t.Run("2∞=∞", func(t *testing.T) { Z := zeroPoint().toJacobian() Z.double() got := Z.isZero() want := true if got != want { test.ReportError(t, got, want) } }) t.Run("2P=P+P", func(t *testing.T) { StdCurve := elliptic.P384() for i := 0; i < 128; i++ { P := randomJacobian() x1, y1 := P.toAffine().toInt() wantX, wantY := StdCurve.Double(x1, y1) P.double() gotX, gotY := P.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) } func TestPointAdd(t *testing.T) { StdCurve := elliptic.P384() Q, R := &jacobianPoint{}, &jacobianPoint{} Z := zeroPoint().toJacobian() P := randomJacobian() t.Run("∞+∞=∞", func(t *testing.T) { R.add(Z, Z) got := R.isZero() want := true if got != want { test.ReportError(t, got, want) } }) t.Run("∞+P=P", func(t *testing.T) { R.add(Z, P) gotX, gotY := R.toAffine().toInt() wantX, wantY := P.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P) } }) t.Run("P+∞=P", func(t *testing.T) { R.add(P, Z) gotX, gotY := R.toAffine().toInt() wantX, wantY := P.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P) } }) t.Run("P+(-P)=∞", func(t *testing.T) { *Q = *P Q.neg() R.add(P, Q) got := R.isZero() want := true if got != want { test.ReportError(t, got, want, P) } }) t.Run("P+P=2P", func(t *testing.T) { // This verifies that add function cannot be used for doublings. for i := 0; i < 128; i++ { P = randomJacobian() R.add(P, P) gotX, gotY := R.toAffine().toInt() wantX, wantY := zeroPoint().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P) } } }) t.Run("P+Q=R", func(t *testing.T) { for i := 0; i < 128; i++ { P = randomJacobian() Q = randomJacobian() x1, y1 := P.toAffine().toInt() x2, y2 := Q.toAffine().toInt() wantX, wantY := StdCurve.Add(x1, y1, x2, y2) R.add(P, Q) gotX, gotY := R.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P, Q) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P, Q) } } }) } func TestPointCompleteAdd(t *testing.T) { StdCurve := elliptic.P384() Q, R := &projectivePoint{}, &projectivePoint{} Z := zeroPoint().toProjective() P := randomProjective() t.Run("∞+∞=∞", func(t *testing.T) { R.completeAdd(Z, Z) got := R.isZero() want := true if got != want { test.ReportError(t, got, want) } }) t.Run("∞+P=P", func(t *testing.T) { R.completeAdd(Z, P) gotX, gotY := R.toAffine().toInt() wantX, wantY := P.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P) } }) t.Run("P+∞=P", func(t *testing.T) { R.completeAdd(P, Z) gotX, gotY := R.toAffine().toInt() wantX, wantY := P.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P) } }) t.Run("P+(-P)=∞", func(t *testing.T) { *Q = *P Q.cneg(1) R.completeAdd(P, Q) got := R.isZero() want := true if got != want { test.ReportError(t, got, want, P) } }) t.Run("P+P=2P", func(t *testing.T) { // This verifies that completeAdd can be used for doublings. for i := 0; i < 128; i++ { P := randomJacobian() PP := P.toProjective() R.completeAdd(PP, PP) P.double() gotX, gotY := R.toAffine().toInt() wantX, wantY := P.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P) } } }) t.Run("P+Q=R", func(t *testing.T) { for i := 0; i < 128; i++ { P := randomProjective() Q := randomProjective() x1, y1 := P.toAffine().toInt() x2, y2 := Q.toAffine().toInt() wantX, wantY := StdCurve.Add(x1, y1, x2, y2) R.completeAdd(P, Q) gotX, gotY := R.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, P, Q) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY, P, Q) } } }) } func TestPointMixAdd(t *testing.T) { StdCurve := elliptic.P384() aZ := zeroPoint() jZ := zeroPoint().toJacobian() R := &jacobianPoint{} aQ := &affinePoint{} aP := randomAffine() jP := randomJacobian() t.Run("∞+∞=∞", func(t *testing.T) { R.mixadd(jZ, aZ) got := R.isZero() want := true if got != want { test.ReportError(t, got, want) } }) t.Run("∞+P=P", func(t *testing.T) { R.mixadd(jZ, aP) gotX, gotY := R.toAffine().toInt() wantX, wantY := aP.toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, aP) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } }) t.Run("P+∞=P", func(t *testing.T) { R.mixadd(jP, aZ) gotX, gotY, gotZ := R.toInt() wantX, wantY, wantZ := jP.toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, jP) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } if gotZ.Cmp(wantZ) != 0 { test.ReportError(t, gotZ, wantZ) } }) t.Run("P+(-P)=∞", func(t *testing.T) { aQ = jP.toAffine() aQ.neg() R.mixadd(jP, aQ) got := R.isZero() want := true if got != want { test.ReportError(t, got, want, jP) } }) t.Run("P+P=2P", func(t *testing.T) { for i := 0; i < 128; i++ { aQ := randomAffine() jQ := aQ.toJacobian() x, y := aQ.toInt() wantX, wantY := StdCurve.Double(x, y) R.mixadd(jQ, aQ) gotX, gotY := R.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, aQ) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) t.Run("P+Q=R", func(t *testing.T) { for i := 0; i < 128; i++ { aP = randomAffine() jP = randomJacobian() x1, y1 := jP.toAffine().toInt() x2, y2 := aP.toInt() wantX, wantY := StdCurve.Add(x1, y1, x2, y2) R.mixadd(jP, aP) gotX, gotY := R.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, jP, aP) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } }) } func TestOddMultiples(t *testing.T) { t.Run("invalidOmega", func(t *testing.T) { for w := uint(0); w < 2; w++ { P := randomAffine() PP := P.oddMultiples(w) got := len(PP) want := 0 if got != want { test.ReportError(t, got, want, w) } } }) t.Run("validOmega", func(t *testing.T) { StdCurve := elliptic.P384() var jOdd [4]byte for i := 0; i < 32; i++ { P := randomAffine() X, Y := P.toInt() for w := uint(2); w < 10; w++ { PP := P.oddMultiples(w) for j, jP := range PP { binary.BigEndian.PutUint32(jOdd[:], uint32(2*j+1)) wantX, wantY := StdCurve.ScalarMult(X, Y, jOdd[:]) gotX, gotY := jP.toAffine().toInt() if gotX.Cmp(wantX) != 0 { test.ReportError(t, gotX, wantX, w, j) } if gotY.Cmp(wantY) != 0 { test.ReportError(t, gotY, wantY) } } } } }) } func BenchmarkPoint(b *testing.B) { P := randomJacobian() Q := randomJacobian() R := randomJacobian() QQ := randomProjective() RR := randomProjective() aR := randomAffine() b.Run("addition", func(b *testing.B) { for i := 0; i < b.N; i++ { R.add(P, Q) } }) b.Run("fullAddition", func(b *testing.B) { for i := 0; i < b.N; i++ { RR.completeAdd(RR, QQ) } }) b.Run("mixadd", func(b *testing.B) { for i := 0; i < b.N; i++ { P.mixadd(P, aR) } }) b.Run("double", func(b *testing.B) { for i := 0; i < b.N; i++ { P.double() } }) } golang-github-cloudflare-circl-1.3.7/ecc/p384/tableBase.go000066400000000000000000001145551454601126700231430ustar00rootroot00000000000000//go:build (!noasm && arm64) || (!noasm && amd64) // +build !noasm,arm64 !noasm,amd64 package p384 const baseOmega = uint(7) // baseOddMultiples has [2*i+1] * G at position i. // Each coordinate has been multiplied by R=2^384 var baseOddMultiples = [1 << (baseOmega - 1)]affinePoint{ // 1P { x: fp384{0x28, 0xb5, 0xc0, 0x49, 0x66, 0x75, 0xd0, 0x3d, 0x38, 0xce, 0xd6, 0xa0, 0xe2, 0x78, 0xe3, 0x20, 0x6e, 0x4d, 0x1b, 0x54, 0xfc, 0x3a, 0x9c, 0x87, 0xff, 0xe, 0xa3, 0x59, 0x84, 0x86, 0x54, 0x64, 0x2b, 0xde, 0x4e, 0x61, 0x23, 0xf7, 0x2f, 0x81, 0x13, 0x15, 0x9e, 0x29, 0xc2, 0xad, 0x3a, 0x4d}, y: fp384{0xfe, 0xa4, 0x3, 0x4b, 0xad, 0x3d, 0x4, 0x23, 0xac, 0xa9, 0xb4, 0x7b, 0xbf, 0xa8, 0xbf, 0xa1, 0x50, 0xb0, 0x83, 0x2e, 0x56, 0xe7, 0xad, 0x8b, 0xd9, 0xff, 0xf4, 0x68, 0x19, 0x52, 0xc3, 0xc6, 0x40, 0xa8, 0x69, 0x39, 0x26, 0x2, 0x80, 0xdd, 0xe9, 0xc5, 0x15, 0x5a, 0xc2, 0xab, 0x78, 0x2b}, }, // 3P { x: fp384{0x73, 0x40, 0xdc, 0xc1, 0xe6, 0xdb, 0xe4, 0x5, 0x9c, 0x77, 0x4f, 0xf0, 0xff, 0xa9, 0x4e, 0xc5, 0xf0, 0xcc, 0x70, 0xa1, 0xe9, 0x34, 0x20, 0x6b, 0x3e, 0x6c, 0x1c, 0xd5, 0x32, 0xd7, 0x48, 0x3a, 0x70, 0xa4, 0x3a, 0x26, 0x2d, 0x7e, 0x6f, 0xe3, 0xac, 0xc3, 0xc1, 0xe7, 0x68, 0xfe, 0x83, 0xd2}, y: fp384{0x57, 0xe1, 0x4e, 0xc0, 0x21, 0x48, 0x28, 0x7e, 0x6d, 0xe3, 0xe0, 0x7a, 0xa7, 0x89, 0xd7, 0x92, 0x46, 0x74, 0xf6, 0x4e, 0xc0, 0x63, 0x26, 0x13, 0xb4, 0xd0, 0xe1, 0xd2, 0x5a, 0x2d, 0x1, 0x68, 0x39, 0xb3, 0x2, 0x51, 0xb1, 0x68, 0xdb, 0xf6, 0xaf, 0x92, 0x32, 0x98, 0xfc, 0x65, 0x54, 0x46}, }, // 5P { x: fp384{0xdf, 0xf0, 0xf1, 0x68, 0xba, 0x5e, 0x59, 0xbb, 0x66, 0x34, 0x87, 0xcc, 0xcb, 0xc0, 0x85, 0xc1, 0x3b, 0x70, 0x3c, 0x29, 0xb5, 0xb1, 0x1e, 0x7f, 0xe6, 0x5, 0xcc, 0xaa, 0xf5, 0x2c, 0xdb, 0x60, 0xc6, 0xe4, 0xe8, 0xe2, 0x87, 0xb9, 0x76, 0xc6, 0xfb, 0x8f, 0x17, 0x1d, 0xb1, 0x26, 0xbb, 0xe1}, y: fp384{0x21, 0xfa, 0x73, 0x70, 0xa0, 0x4b, 0x69, 0x2b, 0x66, 0x45, 0xf3, 0x72, 0x2e, 0x6e, 0xc1, 0x22, 0x99, 0x5b, 0xc3, 0x1, 0x31, 0x1b, 0xb6, 0x80, 0x11, 0x4, 0x2c, 0x98, 0xaf, 0x7f, 0x23, 0x4b, 0x6d, 0x23, 0xde, 0x24, 0x40, 0x94, 0xc5, 0xe6, 0xa3, 0xe4, 0x9, 0xe2, 0xd6, 0xc9, 0xb1, 0x4d}, }, // 7P { x: fp384{0x2b, 0x22, 0x69, 0x7d, 0xd1, 0xb9, 0x13, 0xdf, 0xb1, 0x74, 0x47, 0x87, 0x5f, 0x41, 0xe6, 0x4c, 0x95, 0xaa, 0x1f, 0x21, 0xf8, 0xdc, 0x1e, 0x73, 0xed, 0x53, 0x97, 0x65, 0xd1, 0x15, 0x42, 0x5f, 0x55, 0xdf, 0xb2, 0x9d, 0x58, 0xdb, 0x93, 0xf8, 0x5b, 0x2, 0x89, 0x1c, 0x81, 0x9f, 0x2c, 0x93}, y: fp384{0x1e, 0xa6, 0x6, 0x77, 0x20, 0xb2, 0x96, 0x9, 0x79, 0x1c, 0x64, 0xa8, 0xd5, 0x49, 0x53, 0x13, 0x44, 0x8, 0x13, 0x50, 0x6f, 0xd7, 0xaa, 0x65, 0x80, 0xf7, 0xff, 0x1, 0x4, 0x7c, 0xf3, 0xf, 0x6, 0x7, 0x3b, 0x69, 0x8e, 0x23, 0x7f, 0xf5, 0x3e, 0x9b, 0x6c, 0xaf, 0xb6, 0x16, 0xa, 0xd9}, }, // 9P { x: fp384{0x2f, 0xb9, 0x53, 0x23, 0xe, 0x20, 0x5d, 0x2f, 0xf9, 0xe4, 0xd7, 0x3f, 0x29, 0x87, 0x5d, 0xe3, 0x5d, 0x74, 0x6d, 0xa9, 0x33, 0x48, 0x9, 0x26, 0x3f, 0xff, 0xbf, 0x3c, 0xc1, 0x1d, 0x35, 0xdc, 0x6a, 0x4d, 0xd5, 0xda, 0xc6, 0x64, 0xd4, 0x26, 0x6a, 0x6c, 0x63, 0x53, 0x1d, 0x1d, 0xab, 0x5c}, y: fp384{0xb0, 0xc0, 0x8e, 0xb1, 0x72, 0x30, 0x81, 0xf2, 0x2f, 0xaa, 0x42, 0xd7, 0x70, 0xe2, 0x77, 0x37, 0xc2, 0xa7, 0x3c, 0x3, 0xc7, 0x61, 0xf0, 0x27, 0xd8, 0xd0, 0xea, 0x68, 0xcc, 0xac, 0xec, 0xa6, 0x54, 0xa7, 0x69, 0xee, 0xf4, 0x29, 0x94, 0x7d, 0xc6, 0xf5, 0xe8, 0x31, 0x34, 0x63, 0x70, 0xe7}, }, // 11P { x: fp384{0x7d, 0x8c, 0x8b, 0xb6, 0x19, 0x8b, 0x70, 0xc7, 0xba, 0x7a, 0x37, 0x44, 0x7c, 0x7, 0x32, 0x45, 0x4f, 0xd6, 0xda, 0x6c, 0x70, 0x67, 0xcc, 0xd, 0x2, 0x66, 0x7b, 0x14, 0x56, 0xbf, 0xb8, 0x1, 0x79, 0x1d, 0x56, 0xf0, 0x85, 0x98, 0xd8, 0xf8, 0x37, 0xc4, 0xa9, 0x7b, 0xfc, 0xe9, 0x19, 0x9c}, y: fp384{0x25, 0xba, 0xc4, 0xbd, 0x46, 0xb1, 0x4e, 0x76, 0x83, 0x4b, 0x14, 0xac, 0x6b, 0xe4, 0x4f, 0x60, 0x80, 0xe7, 0x77, 0x8a, 0x29, 0x13, 0xe8, 0x3c, 0x2e, 0x68, 0x9e, 0xfe, 0x36, 0xf, 0x7, 0x2e, 0x7a, 0x28, 0x53, 0x3a, 0xc, 0x1d, 0x82, 0x41, 0x18, 0xf9, 0x33, 0x35, 0x9f, 0x2f, 0xa6, 0x9a}, }, // 13P { x: fp384{0xfb, 0xbd, 0xcc, 0x75, 0x7e, 0xeb, 0x7a, 0x9b, 0x95, 0x9a, 0x74, 0xf6, 0xc5, 0x28, 0x5e, 0xb2, 0xae, 0xd4, 0xb7, 0x33, 0x46, 0x8e, 0x7a, 0x8a, 0x56, 0xbd, 0xc1, 0xd9, 0xa8, 0x3, 0x52, 0xdb, 0x97, 0xdf, 0x22, 0xed, 0x65, 0x72, 0x65, 0xd2, 0x94, 0x3c, 0xf2, 0x8c, 0xe1, 0x56, 0x1c, 0xb5}, y: fp384{0x2d, 0x81, 0x3d, 0x6c, 0x59, 0x94, 0xd3, 0xf4, 0xc2, 0xe0, 0xca, 0x87, 0x1a, 0x8f, 0xe8, 0xd8, 0xe3, 0xf, 0x4d, 0xcf, 0x48, 0x2a, 0x9a, 0x78, 0x60, 0x8d, 0xc3, 0xfe, 0x2d, 0xac, 0xfe, 0xb7, 0xc3, 0xe, 0x49, 0x3b, 0x1c, 0xbd, 0xfd, 0x81, 0xe1, 0x79, 0x69, 0xcc, 0xb7, 0xad, 0x17, 0x46}, }, // 15P { x: fp384{0xa9, 0xf4, 0x9, 0x47, 0x88, 0xd8, 0x6a, 0x44, 0xd8, 0xab, 0x3d, 0xec, 0xe2, 0x10, 0x72, 0x2b, 0x34, 0x7b, 0xe0, 0x50, 0x95, 0xf1, 0xcc, 0x83, 0x75, 0x30, 0x9b, 0x78, 0x17, 0x9, 0x50, 0x59, 0x93, 0x59, 0x8, 0xeb, 0xd4, 0x1f, 0xc0, 0xf, 0x6b, 0x2, 0x3, 0x49, 0x6f, 0xd2, 0x62, 0xfb}, y: fp384{0xbb, 0x89, 0xe9, 0x6f, 0x9d, 0xcc, 0x9, 0x23, 0x86, 0xd5, 0x4b, 0x14, 0xbd, 0x9c, 0x60, 0x61, 0xc, 0x61, 0x6, 0xde, 0xa0, 0xd3, 0x23, 0x4b, 0x70, 0xf4, 0x98, 0xd8, 0x66, 0x28, 0xdc, 0xdd, 0x97, 0x57, 0xc, 0x40, 0x41, 0xfc, 0x33, 0x87, 0x16, 0x27, 0xbc, 0xd0, 0xfe, 0xc6, 0x68, 0x5a}, }, // 17P { x: fp384{0xd0, 0x3c, 0x4a, 0x4b, 0x30, 0xe1, 0x3, 0x89, 0x3e, 0xf4, 0xf1, 0x8f, 0x4c, 0xea, 0xa4, 0x3e, 0xd, 0xa1, 0x55, 0xf6, 0x2a, 0x3f, 0xfc, 0xe6, 0xfc, 0xfe, 0x4f, 0x52, 0x7d, 0x73, 0xe3, 0x7b, 0x5e, 0x45, 0x30, 0x53, 0x55, 0x28, 0x69, 0x9f, 0x70, 0xce, 0x75, 0xe4, 0x6e, 0x16, 0x4f, 0x52}, y: fp384{0x55, 0xf0, 0x12, 0x6c, 0xcd, 0x69, 0xcc, 0x3f, 0xda, 0xc0, 0xb9, 0xd5, 0xff, 0xb6, 0x23, 0x4e, 0x83, 0xf1, 0x6b, 0x33, 0x93, 0x69, 0xce, 0x49, 0x4a, 0x50, 0x54, 0x4a, 0x85, 0x6d, 0x7d, 0xf8, 0x7a, 0x67, 0xc2, 0xb3, 0xf1, 0x5d, 0xeb, 0x25, 0xc9, 0x64, 0xb1, 0x55, 0x6f, 0x98, 0x37, 0xac}, }, // 19P { x: fp384{0x8, 0x4c, 0xa8, 0xba, 0x4a, 0xed, 0xa2, 0x82, 0x12, 0xc9, 0xa8, 0x41, 0x5f, 0xcc, 0xc4, 0x22, 0x5e, 0xad, 0x4a, 0x15, 0x3b, 0x9c, 0x10, 0xca, 0x8e, 0x53, 0x38, 0xfc, 0x98, 0x12, 0x89, 0x23, 0xae, 0x2, 0x98, 0x53, 0x9c, 0x63, 0xb6, 0xb3, 0x6, 0xd7, 0x90, 0x3, 0x45, 0x1f, 0xf, 0xfa}, y: fp384{0xd0, 0x21, 0xdc, 0xb0, 0x5d, 0x8e, 0xb7, 0x46, 0xac, 0x2e, 0xda, 0xc3, 0x3c, 0x2d, 0xc7, 0xa8, 0x43, 0xf6, 0xf2, 0x6f, 0x78, 0xb3, 0x70, 0x91, 0xc3, 0x30, 0x7f, 0xb6, 0x9b, 0x79, 0x5a, 0x3f, 0x72, 0xb6, 0x64, 0x82, 0x77, 0xdc, 0xd1, 0x15, 0x64, 0x77, 0x57, 0xe9, 0x23, 0x7b, 0xd4, 0xa1}, }, // 21P { x: fp384{0x2f, 0xce, 0x22, 0x4, 0x51, 0x5e, 0x26, 0x8, 0x21, 0x9e, 0x2f, 0xdd, 0x96, 0xd4, 0xe0, 0x88, 0x5d, 0xf7, 0x77, 0x61, 0xa0, 0x8a, 0x12, 0x30, 0x69, 0xbe, 0x9e, 0xbd, 0x62, 0xab, 0x59, 0x2e, 0x37, 0xe5, 0xf0, 0x5d, 0x6c, 0xf, 0x1a, 0x1b, 0xb5, 0x12, 0xc0, 0xda, 0x26, 0xc6, 0x16, 0xab}, y: fp384{0xe7, 0x5d, 0x8c, 0x0, 0x4b, 0x21, 0x14, 0x80, 0xea, 0x7b, 0xf1, 0x38, 0x9e, 0xa, 0x74, 0xaa, 0x98, 0x90, 0x14, 0x8a, 0x49, 0xbb, 0x2e, 0x26, 0x59, 0xcd, 0x27, 0x85, 0x1e, 0x11, 0x54, 0xb4, 0x17, 0x58, 0xea, 0xac, 0x5a, 0xd1, 0x6a, 0x26, 0xba, 0xcc, 0x53, 0x13, 0x41, 0x4f, 0x82, 0x21}, }, // 23P { x: fp384{0x3b, 0x68, 0xe3, 0x12, 0x4d, 0xe7, 0xb4, 0xd1, 0xf6, 0x8e, 0x9b, 0x56, 0xb, 0xd2, 0xe, 0x99, 0x18, 0xa, 0x9c, 0x42, 0x25, 0xdd, 0xd3, 0xb9, 0x83, 0x17, 0x35, 0x2a, 0xab, 0xb8, 0x75, 0x1c, 0xf0, 0x32, 0x54, 0x90, 0x2b, 0xca, 0xe4, 0x61, 0x24, 0xf2, 0xa8, 0xee, 0x69, 0x6a, 0x82, 0x80}, y: fp384{0xad, 0xab, 0x52, 0xec, 0x6b, 0x3a, 0xc3, 0x7f, 0x13, 0x48, 0x5e, 0xa6, 0xf0, 0xa3, 0xcc, 0xb, 0xbe, 0xce, 0x27, 0xa5, 0x32, 0xa1, 0xd8, 0x7a, 0x7e, 0x2c, 0xf2, 0xea, 0x50, 0x89, 0x13, 0xf0, 0xc1, 0x18, 0x67, 0x56, 0x37, 0x24, 0x2d, 0x28, 0x59, 0x25, 0x21, 0xe2, 0xd, 0xcb, 0xfc, 0x9d}, }, // 25P { x: fp384{0x83, 0x3b, 0xce, 0x58, 0x27, 0x72, 0x93, 0x1e, 0x36, 0xfb, 0xb3, 0x3c, 0xfa, 0xd, 0x28, 0xbb, 0x4a, 0x17, 0xbe, 0xe2, 0xd2, 0xf3, 0xd0, 0x57, 0x1e, 0xbe, 0x8a, 0x20, 0x99, 0x1b, 0xd5, 0x9b, 0x24, 0x80, 0x24, 0xde, 0x50, 0xab, 0x9, 0x38, 0x31, 0x73, 0xbb, 0xa5, 0x2c, 0x6e, 0x9c, 0xc2}, y: fp384{0x5, 0x4f, 0x12, 0x61, 0x2e, 0xfd, 0x44, 0x99, 0x91, 0xe3, 0x9, 0x90, 0x4e, 0xbc, 0xcc, 0x83, 0xcc, 0xa3, 0x24, 0x94, 0x5, 0x8f, 0x62, 0x1, 0x44, 0x43, 0x8e, 0xea, 0x1d, 0xf5, 0xa2, 0xd6, 0x6e, 0xc9, 0xeb, 0x4c, 0x3d, 0x1a, 0x3e, 0xda, 0xdc, 0x9, 0x78, 0xe9, 0x42, 0xfb, 0xe6, 0x1f}, }, // 27P { x: fp384{0xe4, 0x66, 0x7d, 0x46, 0xd2, 0x82, 0x44, 0xa0, 0x1d, 0x29, 0x78, 0x4d, 0x93, 0x12, 0x19, 0xcf, 0xf9, 0x96, 0x23, 0x48, 0x68, 0x41, 0xd, 0x8e, 0xd0, 0x14, 0x8f, 0xd1, 0xd5, 0xe2, 0x28, 0x72, 0xfe, 0x58, 0x6a, 0x9c, 0x50, 0x8d, 0x7e, 0x2f, 0xec, 0x5a, 0x3e, 0x37, 0xe, 0x78, 0xca, 0xe8}, y: fp384{0xf8, 0xe9, 0x68, 0x1b, 0xd6, 0xd1, 0xaa, 0x42, 0xf4, 0xf8, 0xe2, 0x69, 0xf5, 0xd7, 0xa6, 0x58, 0xea, 0x1b, 0xda, 0x31, 0xfe, 0xad, 0x79, 0xd7, 0x85, 0x5a, 0xc8, 0x38, 0x6, 0x54, 0x26, 0x7d, 0xdf, 0x3c, 0x4d, 0xd4, 0x95, 0x71, 0xe6, 0x67, 0xd7, 0x4e, 0x13, 0xc5, 0xb, 0xa, 0x82, 0x17}, }, // 29P { x: fp384{0x70, 0x14, 0x2, 0xd3, 0xc5, 0x6a, 0x9d, 0x1, 0xd6, 0x43, 0x4, 0x78, 0x66, 0x6b, 0x84, 0x25, 0x47, 0x76, 0xc9, 0x55, 0xed, 0x15, 0x3c, 0xce, 0xf, 0xeb, 0x3f, 0xe, 0x49, 0x2d, 0xc2, 0x3d, 0xe4, 0x26, 0xdf, 0xa7, 0xcb, 0xb7, 0x65, 0x20, 0x1f, 0xea, 0x7c, 0x18, 0xe8, 0xa, 0xb0, 0xc8}, y: fp384{0xd3, 0xde, 0x5d, 0x86, 0xa0, 0x84, 0x52, 0x1a, 0xe2, 0x3d, 0xc8, 0x20, 0x49, 0x16, 0x3c, 0x29, 0xb3, 0x51, 0xe8, 0xcc, 0x26, 0x8d, 0x17, 0xab, 0xfb, 0x5, 0x45, 0x40, 0xb, 0xb1, 0x6d, 0x8e, 0x33, 0x20, 0xc8, 0x90, 0x71, 0x7e, 0xf5, 0xf6, 0x6c, 0xf1, 0x77, 0x59, 0x1, 0x1c, 0x2a, 0x1d}, }, // 31P { x: fp384{0xa4, 0x6, 0x89, 0x7c, 0x31, 0x89, 0x9c, 0xa3, 0xe6, 0x1e, 0x82, 0x9e, 0xdd, 0xec, 0xe7, 0xb6, 0xe6, 0x4f, 0xdf, 0xf0, 0x40, 0x83, 0xcf, 0x2e, 0x65, 0x49, 0xc1, 0x53, 0xc9, 0x7d, 0x2f, 0xd4, 0x85, 0x82, 0xba, 0xe3, 0xa3, 0x51, 0xfb, 0x1a, 0xd1, 0x5, 0x33, 0xa, 0x4, 0xc4, 0x7, 0x6c}, y: fp384{0xda, 0xc1, 0x7f, 0x12, 0x88, 0x32, 0xb8, 0xda, 0x8, 0x4b, 0x4c, 0x37, 0x9b, 0x69, 0xa, 0xbc, 0xdd, 0x20, 0xeb, 0x42, 0xab, 0x9b, 0x2a, 0x40, 0x1c, 0x7a, 0x5a, 0x4, 0x4f, 0x46, 0xdd, 0xd7, 0xc4, 0xec, 0xbe, 0x36, 0x6d, 0xd, 0x3d, 0x5b, 0x9d, 0xa1, 0x98, 0x63, 0x75, 0x3e, 0x5a, 0x47}, }, // 33P { x: fp384{0x63, 0xba, 0xb3, 0x2f, 0x38, 0x3a, 0x33, 0x61, 0x86, 0x3c, 0x94, 0x5b, 0x9d, 0xd, 0x33, 0xdf, 0xaf, 0xf3, 0x5e, 0x95, 0xee, 0xc7, 0xc7, 0xbb, 0xfb, 0x9e, 0xf0, 0x60, 0xc1, 0x1f, 0x63, 0xda, 0x0, 0xc4, 0xd5, 0x41, 0x26, 0x62, 0xaf, 0x68, 0x9d, 0x3e, 0x83, 0x6c, 0xa4, 0x97, 0x9e, 0xcc}, y: fp384{0x76, 0x5e, 0x62, 0x3a, 0x8e, 0x3e, 0xd7, 0x7f, 0x5e, 0xe5, 0x9, 0xc2, 0x24, 0x61, 0xbf, 0x13, 0x91, 0xb, 0xb9, 0x48, 0xea, 0x7c, 0x46, 0x8, 0xba, 0xa, 0x6f, 0xbb, 0xb9, 0x6e, 0x41, 0x8a, 0x72, 0x10, 0xc3, 0xb8, 0xa1, 0x93, 0xcc, 0x6f, 0xd7, 0xda, 0x57, 0x90, 0x61, 0x2b, 0xfd, 0xa7}, }, // 35P { x: fp384{0x9b, 0xec, 0x20, 0x37, 0x43, 0xb5, 0xa5, 0x58, 0xb4, 0x2f, 0x7c, 0x2d, 0xd5, 0x0, 0x38, 0xbb, 0xa, 0xbd, 0xe6, 0xdd, 0x20, 0x86, 0x50, 0x4a, 0xfd, 0x83, 0x25, 0xa0, 0x73, 0x62, 0xf1, 0x65, 0x23, 0x85, 0xc7, 0x4f, 0xe3, 0xd8, 0x2b, 0x83, 0xc6, 0x7b, 0x41, 0xe9, 0x75, 0x9f, 0x14, 0xd6}, y: fp384{0x2a, 0xb5, 0xee, 0x3d, 0xe9, 0x26, 0xb0, 0xfe, 0x56, 0x9, 0x5e, 0xa5, 0x88, 0x80, 0xe1, 0xc, 0xa2, 0x92, 0x80, 0x98, 0x98, 0x89, 0x1, 0x50, 0xee, 0x5e, 0xf3, 0x28, 0xab, 0x9f, 0xf1, 0x22, 0x5c, 0xd3, 0xcc, 0x52, 0x7f, 0x87, 0x8a, 0xac, 0x26, 0x3f, 0xe2, 0x30, 0xd8, 0x8a, 0x3a, 0xb1}, }, // 37P { x: fp384{0xa3, 0x61, 0x4f, 0xe4, 0x7d, 0xd5, 0x2, 0x2, 0xf2, 0xe, 0x63, 0xb5, 0x4b, 0x70, 0x27, 0x40, 0x5d, 0x4a, 0xb5, 0xf5, 0xdf, 0xe2, 0x29, 0xa1, 0x86, 0x2b, 0x48, 0x97, 0x75, 0xa, 0xb6, 0xac, 0x14, 0x71, 0xf2, 0x7e, 0xe8, 0xed, 0x61, 0x92, 0xb5, 0x58, 0xfc, 0xde, 0xf3, 0x28, 0xba, 0x1e}, y: fp384{0x9e, 0x58, 0xe5, 0x8b, 0xc9, 0xc0, 0x91, 0x6c, 0xee, 0x4b, 0x59, 0x14, 0xd5, 0x43, 0x16, 0x2f, 0x34, 0xa0, 0x2c, 0x5d, 0x43, 0x12, 0xa9, 0x2e, 0x1f, 0x7d, 0x4, 0x94, 0xa8, 0x49, 0x6, 0xb5, 0x37, 0xa3, 0x8c, 0x63, 0xb5, 0xcb, 0x4f, 0x28, 0x85, 0xbf, 0x85, 0xfe, 0xb7, 0x7, 0xe, 0xfa}, }, // 39P { x: fp384{0x42, 0xe, 0x6e, 0x50, 0x80, 0x4f, 0x89, 0x7d, 0x46, 0x2c, 0x3d, 0x8e, 0x4a, 0x24, 0x84, 0xd9, 0x6f, 0x0, 0x7f, 0x2b, 0x64, 0xdf, 0x7e, 0x6d, 0x30, 0x62, 0x9b, 0xde, 0x6d, 0xcd, 0xa1, 0x36, 0x65, 0x6, 0x6c, 0xb7, 0x40, 0x50, 0x98, 0xc9, 0xc2, 0x1f, 0x9b, 0xb8, 0xd6, 0xf4, 0x7d, 0x58}, y: fp384{0x7a, 0xae, 0x71, 0x6a, 0x47, 0x38, 0x6, 0x4c, 0x47, 0x47, 0x29, 0xe8, 0xb3, 0xa, 0x2b, 0x7b, 0xb8, 0x53, 0x31, 0xb5, 0x3a, 0x55, 0x5c, 0x34, 0xe2, 0x9f, 0x6d, 0x43, 0x53, 0xe4, 0x46, 0xb6, 0x40, 0x3, 0xd6, 0x1c, 0x5f, 0x35, 0x95, 0x1a, 0xfb, 0x68, 0x49, 0x7, 0x28, 0xc1, 0x7b, 0x2d}, }, // 41P { x: fp384{0x4c, 0xd1, 0xa6, 0xbc, 0x87, 0x8e, 0x14, 0xad, 0x1e, 0x20, 0x6a, 0x45, 0x4d, 0xd2, 0xdf, 0x41, 0xf3, 0x68, 0xd, 0xa8, 0x33, 0x29, 0xa8, 0x73, 0x35, 0xa0, 0x2c, 0x85, 0x8d, 0x6c, 0x74, 0x89, 0xae, 0x71, 0xfd, 0x95, 0x88, 0x77, 0xbc, 0xe3, 0x5d, 0x24, 0x92, 0xda, 0x2c, 0xcd, 0x64, 0x87}, y: fp384{0xe2, 0x23, 0xeb, 0x82, 0x47, 0x2c, 0xfe, 0xa2, 0x6e, 0x9d, 0x3c, 0xf, 0xe0, 0x62, 0xc7, 0x5a, 0x31, 0x6f, 0x64, 0x21, 0xe1, 0xc, 0x86, 0x57, 0x9a, 0x58, 0x9f, 0x4f, 0xc3, 0xd6, 0xc9, 0xbd, 0x2e, 0x27, 0x93, 0xd1, 0xc7, 0x52, 0x99, 0x67, 0xc5, 0xf1, 0x18, 0xeb, 0x2e, 0x70, 0xea, 0x82}, }, // 43P { x: fp384{0x44, 0x6d, 0x84, 0x0, 0x55, 0x93, 0xfa, 0x37, 0x8c, 0xbc, 0x78, 0x5, 0xc5, 0x2f, 0x11, 0x9, 0x3d, 0x94, 0xc4, 0x39, 0xb2, 0xf5, 0xd9, 0xda, 0x86, 0xbd, 0x6d, 0x41, 0xf0, 0xf5, 0x14, 0x73, 0x56, 0xfb, 0xfe, 0x1, 0xa9, 0x95, 0xf0, 0x5c, 0x93, 0xb3, 0xda, 0x22, 0xad, 0x8b, 0x17, 0x35}, y: fp384{0xa7, 0xf1, 0xba, 0x36, 0x1b, 0xfc, 0x79, 0xcf, 0x98, 0x54, 0x9e, 0x74, 0x2d, 0xe4, 0x7e, 0x1b, 0xbb, 0x14, 0xe3, 0xed, 0xa9, 0x8a, 0xe7, 0xbc, 0xdf, 0x28, 0x6, 0xbd, 0xf6, 0xe0, 0xf8, 0xaa, 0x48, 0xf9, 0xcb, 0x15, 0x94, 0xb0, 0x74, 0xa9, 0x78, 0x2b, 0x63, 0xc9, 0x63, 0x1f, 0x3f, 0x8f}, }, // 45P { x: fp384{0x5b, 0xda, 0xdd, 0x4f, 0x56, 0x11, 0xc4, 0xd4, 0x12, 0x91, 0xad, 0x73, 0xc6, 0x65, 0xaf, 0xd4, 0x59, 0x8f, 0xeb, 0x39, 0xbb, 0xe0, 0xe8, 0xff, 0x13, 0xcf, 0x6f, 0x8d, 0xe, 0xc, 0x4, 0xb0, 0x99, 0xb5, 0x2b, 0x1f, 0xc6, 0xc0, 0xe1, 0x99, 0x5, 0x34, 0xac, 0xb2, 0x58, 0xc8, 0x94, 0x9c}, y: fp384{0x5d, 0xd8, 0xee, 0x6e, 0xd7, 0x78, 0x88, 0x8f, 0x3f, 0xca, 0xfc, 0x51, 0x43, 0xf5, 0xb2, 0x62, 0x18, 0x69, 0xb5, 0xe5, 0xa9, 0x44, 0x3b, 0xeb, 0x93, 0x4e, 0x23, 0xb7, 0x76, 0x66, 0xf9, 0x16, 0x9e, 0xf1, 0x2a, 0xbd, 0x22, 0x77, 0x47, 0x17, 0x85, 0xa4, 0x83, 0xdb, 0x79, 0x29, 0xeb, 0x42}, }, // 47P { x: fp384{0xca, 0x68, 0xc6, 0xf0, 0x7d, 0x8f, 0x88, 0x6f, 0x6c, 0xc6, 0xd, 0x5f, 0x78, 0x88, 0xc7, 0x65, 0xa0, 0x7, 0x5b, 0x5f, 0x12, 0x85, 0xb1, 0xbf, 0xd0, 0xac, 0x78, 0xd8, 0xf7, 0xbf, 0xa, 0x78, 0x50, 0xf9, 0xc, 0x57, 0xb1, 0x21, 0x4f, 0x50, 0x71, 0x33, 0x23, 0xda, 0xc5, 0x37, 0x5b, 0xea}, y: fp384{0xd1, 0x7e, 0x43, 0x22, 0xbd, 0xe8, 0x7a, 0x48, 0xb7, 0xf9, 0x9c, 0x24, 0x58, 0x17, 0x70, 0x9c, 0xff, 0x34, 0xfb, 0x98, 0xa8, 0x62, 0x65, 0xf8, 0x91, 0xfc, 0xe0, 0x65, 0xa2, 0xa1, 0xee, 0xdf, 0x23, 0xfc, 0x20, 0x2e, 0x91, 0x6, 0xf0, 0xee, 0x8b, 0x2a, 0xa7, 0xdf, 0xc7, 0xfe, 0x9d, 0xac}, }, // 49P { x: fp384{0xc6, 0x36, 0x71, 0x69, 0xef, 0x3a, 0x5c, 0xfa, 0xb8, 0x6f, 0xea, 0xa5, 0x63, 0xaf, 0xa5, 0x8e, 0xa4, 0x65, 0xe3, 0x42, 0x65, 0x15, 0x69, 0xa6, 0x86, 0x33, 0x6e, 0x5b, 0x11, 0x6c, 0xc5, 0x47, 0x56, 0x3f, 0xa0, 0xce, 0x2b, 0x83, 0x97, 0x11, 0x9e, 0xea, 0xe4, 0x50, 0xb2, 0xb, 0x47, 0xb}, y: fp384{0x12, 0x57, 0xb2, 0x13, 0x43, 0xc7, 0x13, 0x31, 0x48, 0x7d, 0x49, 0xd2, 0x4e, 0x17, 0x6c, 0x8d, 0xe8, 0xeb, 0xc9, 0x49, 0xee, 0x86, 0x44, 0xfc, 0xd3, 0xbd, 0x82, 0x7f, 0xd5, 0xed, 0x87, 0x24, 0x2f, 0xbe, 0x57, 0x5b, 0x41, 0x64, 0x1e, 0x77, 0xdb, 0x2b, 0x8b, 0xe2, 0x18, 0xc5, 0x1c, 0x2d}, }, // 51P { x: fp384{0x8d, 0xac, 0x70, 0x20, 0xc7, 0xca, 0x4c, 0x2c, 0xb8, 0x22, 0x4a, 0xec, 0xca, 0xc0, 0x47, 0x19, 0xd9, 0x78, 0x5a, 0x8c, 0x59, 0xfb, 0xe0, 0xa5, 0xe7, 0x4d, 0xa8, 0x41, 0xd2, 0xe8, 0x4a, 0x46, 0x27, 0xbc, 0xaa, 0xda, 0xe9, 0x16, 0xba, 0x3d, 0x3c, 0xcb, 0x35, 0x4f, 0x50, 0x4a, 0x63, 0x16}, y: fp384{0x4f, 0xc8, 0x6e, 0xb1, 0xf9, 0x8b, 0xc1, 0xad, 0x35, 0xdd, 0x59, 0x73, 0x7e, 0x6, 0x4d, 0x32, 0xf0, 0x43, 0x5, 0x57, 0xc3, 0xc0, 0xea, 0xda, 0x36, 0x7d, 0x88, 0x3c, 0x0, 0x40, 0x22, 0xb, 0xd, 0x1a, 0x3f, 0x37, 0xe2, 0x89, 0x94, 0xc6, 0x97, 0xd, 0xaa, 0xcb, 0x7d, 0x4, 0x8b, 0x51}, }, // 53P { x: fp384{0xef, 0x49, 0xde, 0xfb, 0xc6, 0xdd, 0x1b, 0x3b, 0xcc, 0x15, 0x9, 0x8a, 0x26, 0x7c, 0xed, 0xda, 0xa2, 0x22, 0x4, 0xf, 0x61, 0x10, 0x1, 0xb, 0x16, 0x4b, 0xc5, 0xa7, 0x74, 0x5c, 0x48, 0xcf, 0xe2, 0xaa, 0xc3, 0x15, 0xe6, 0xc4, 0x2e, 0x64, 0xea, 0x83, 0xf3, 0xe0, 0x10, 0x8f, 0xba, 0xa8}, y: fp384{0x1, 0x85, 0x61, 0x95, 0xb4, 0x54, 0x20, 0x2a, 0x8b, 0xfa, 0x9e, 0x8, 0x42, 0x64, 0xec, 0xeb, 0x3e, 0xa8, 0x2f, 0x4e, 0x9a, 0xa1, 0x86, 0x57, 0x63, 0x99, 0x6, 0x39, 0xd1, 0x1a, 0xc7, 0xd2, 0xe2, 0x65, 0x17, 0x48, 0x9a, 0x3d, 0xc9, 0xad, 0x85, 0x94, 0xcc, 0x7e, 0xeb, 0xe3, 0xf2, 0xed}, }, // 55P { x: fp384{0x67, 0x33, 0x9f, 0x6, 0x60, 0x5f, 0xab, 0xbc, 0x3c, 0xec, 0x18, 0x17, 0xbc, 0x22, 0x66, 0xfd, 0xd6, 0x42, 0xa1, 0xe3, 0x67, 0x78, 0xfb, 0xa4, 0xb3, 0xae, 0x5f, 0x8, 0xbf, 0xd8, 0x78, 0x60, 0x4f, 0x55, 0xf4, 0x60, 0xda, 0xbf, 0x5c, 0xfa, 0x8, 0xd4, 0xc, 0x69, 0xd1, 0xd5, 0xfc, 0xb3}, y: fp384{0x84, 0x78, 0x1f, 0x28, 0x7d, 0xee, 0xbd, 0x4e, 0xa7, 0x63, 0xa, 0x18, 0xaa, 0x23, 0xaf, 0x82, 0x61, 0x9f, 0x7, 0x3d, 0x7c, 0x10, 0xe3, 0x8d, 0xf8, 0x34, 0x23, 0xbe, 0xcb, 0xb5, 0xc6, 0x17, 0x6, 0xfa, 0xd0, 0x97, 0x39, 0xe7, 0x91, 0x6a, 0xd4, 0xee, 0xce, 0x14, 0x73, 0x25, 0x60, 0x74}, }, // 57P { x: fp384{0x5c, 0x86, 0x7f, 0xf9, 0x1c, 0xa6, 0x4b, 0xb1, 0xd, 0x8b, 0x4b, 0x69, 0xc1, 0xe4, 0xba, 0x73, 0x62, 0xbf, 0x4b, 0xac, 0xdf, 0x67, 0x49, 0xa1, 0xe0, 0x46, 0xf4, 0x9b, 0x50, 0xd1, 0x9d, 0x1e, 0xef, 0xce, 0x99, 0x1c, 0xeb, 0xf3, 0x52, 0xc0, 0x89, 0xc1, 0x78, 0x7a, 0xa0, 0x7f, 0x4d, 0x81}, y: fp384{0x5d, 0xb0, 0x74, 0xab, 0x83, 0xa4, 0x1, 0xa1, 0x65, 0x7b, 0x73, 0xa1, 0x58, 0xc2, 0x88, 0x77, 0x3c, 0xa1, 0x9, 0xe8, 0xb7, 0xba, 0x60, 0xd, 0x5b, 0x1d, 0xc8, 0x73, 0xc4, 0x7b, 0x42, 0x8f, 0xfc, 0xc1, 0x52, 0x29, 0x55, 0x30, 0xe1, 0xd2, 0x63, 0xdf, 0x26, 0x4b, 0x9a, 0x3b, 0x82, 0xa}, }, // 59P { x: fp384{0xc9, 0x64, 0xbf, 0x27, 0xe2, 0x7c, 0x46, 0xaf, 0x4c, 0x97, 0x29, 0xf9, 0x97, 0x68, 0xca, 0xdf, 0x38, 0x27, 0x32, 0x5c, 0x59, 0x3b, 0x47, 0x64, 0x15, 0xe3, 0xd0, 0x1e, 0xcf, 0x17, 0xa9, 0x96, 0xb9, 0x4d, 0xe6, 0xd, 0x5b, 0x43, 0x3, 0x37, 0x46, 0xb6, 0x67, 0x92, 0x67, 0x39, 0xa0, 0x9b}, y: fp384{0xbe, 0x2f, 0x52, 0x3a, 0xae, 0x2a, 0xc, 0xdf, 0xf0, 0xef, 0x35, 0xb3, 0x41, 0xb7, 0xbd, 0x41, 0x3, 0x97, 0x5, 0x7b, 0xdd, 0x2e, 0xcf, 0xac, 0xce, 0x3c, 0x46, 0x28, 0x30, 0x4b, 0xb3, 0x6f, 0x19, 0xca, 0xe3, 0xd9, 0xb, 0xba, 0xd9, 0x96, 0xc1, 0x55, 0x46, 0x50, 0x12, 0x6f, 0x33, 0xff}, }, // 61P { x: fp384{0xe0, 0xa6, 0x60, 0xfc, 0xd3, 0x1f, 0xda, 0x48, 0xe8, 0x41, 0x22, 0x22, 0x34, 0x5a, 0xfb, 0x54, 0x80, 0xe0, 0x2a, 0x77, 0x4f, 0xe3, 0x35, 0x60, 0xd0, 0x82, 0x29, 0x33, 0xf2, 0x7f, 0xf7, 0x5f, 0xfd, 0x51, 0xfe, 0x0, 0x73, 0x46, 0x66, 0x23, 0x6, 0xa0, 0x6b, 0xef, 0x49, 0xa0, 0x3e, 0xc9}, y: fp384{0x66, 0x12, 0x38, 0x7d, 0x17, 0xf1, 0x40, 0x66, 0xac, 0xf4, 0xe9, 0x6a, 0xcd, 0x32, 0x4d, 0x39, 0xeb, 0x3, 0xd3, 0x70, 0x53, 0x88, 0xa7, 0xe6, 0x67, 0x57, 0x27, 0xe5, 0xff, 0x19, 0xda, 0xd, 0x23, 0x6d, 0x46, 0x1, 0x72, 0xc7, 0xa6, 0xb0, 0x29, 0x98, 0xc6, 0x1f, 0x45, 0x11, 0xcc, 0xc4}, }, // 63P { x: fp384{0xc0, 0x89, 0xed, 0xaa, 0xd7, 0xe6, 0xc0, 0xc5, 0x96, 0x18, 0x9a, 0x14, 0xd6, 0xea, 0xe8, 0x6c, 0x8f, 0x9f, 0x94, 0x8c, 0x45, 0xf7, 0x50, 0x7a, 0xaa, 0x71, 0x2b, 0x6e, 0xf7, 0x35, 0x7e, 0xcd, 0x7a, 0x9f, 0x4, 0x9a, 0x51, 0x9e, 0x15, 0xf6, 0x1e, 0x2d, 0xe5, 0xf1, 0xb0, 0xf0, 0x9b, 0x1c}, y: fp384{0x80, 0x2c, 0x20, 0x18, 0xf5, 0xc1, 0xb6, 0x3b, 0x1a, 0x7b, 0xcd, 0x1e, 0x62, 0x5f, 0x3a, 0x8d, 0x19, 0x7f, 0xd1, 0x88, 0xe8, 0x34, 0xb0, 0x3b, 0x8d, 0x4, 0xd4, 0x97, 0x49, 0xbd, 0x89, 0xdc, 0x22, 0xdf, 0x35, 0x37, 0x8e, 0x7b, 0xaf, 0xf5, 0xe8, 0x89, 0xa6, 0xa0, 0x12, 0x37, 0xbb, 0x52}, }, // 65P { x: fp384{0x79, 0x96, 0x9b, 0x83, 0x54, 0x94, 0x46, 0x8e, 0x9f, 0x27, 0x1d, 0xd, 0x3b, 0xa4, 0xcd, 0xbe, 0x80, 0x3c, 0xb6, 0xed, 0x15, 0xdc, 0x9e, 0xcf, 0x2, 0xf0, 0xd5, 0xbd, 0x8a, 0xec, 0x97, 0x45, 0x53, 0x22, 0xb, 0x65, 0xb2, 0x50, 0x3, 0x8b, 0x6f, 0x26, 0xd4, 0x5f, 0x6a, 0x3a, 0x4c, 0xb8}, y: fp384{0xf9, 0x79, 0xfc, 0x30, 0x3d, 0xd8, 0x16, 0xe, 0xd3, 0x95, 0xd9, 0x3a, 0x83, 0x87, 0xa4, 0xb6, 0x66, 0xc2, 0x2b, 0xde, 0x2c, 0x4b, 0x78, 0xab, 0xdd, 0x66, 0x9d, 0x88, 0x6d, 0x3d, 0x76, 0x19, 0x87, 0xf0, 0xf9, 0xc8, 0x24, 0x6c, 0x86, 0xa2, 0xc9, 0xb1, 0x5b, 0xa5, 0x28, 0x25, 0x6f, 0xea}, }, // 67P { x: fp384{0xca, 0x72, 0x17, 0x8b, 0xbc, 0x5c, 0xfc, 0x6e, 0x68, 0x4f, 0x63, 0xb, 0x3b, 0xdd, 0xc7, 0xea, 0x85, 0x61, 0x5d, 0xa5, 0xda, 0x5e, 0xd7, 0x65, 0xf7, 0xd8, 0xf3, 0x6e, 0x7e, 0x63, 0x6e, 0x55, 0x25, 0x9d, 0x90, 0x90, 0x4d, 0x3e, 0xaf, 0xf9, 0x5a, 0x3, 0x53, 0xe1, 0x48, 0xca, 0x62, 0xe4}, y: fp384{0xd1, 0x9e, 0x10, 0xa, 0x7b, 0x3b, 0x76, 0x52, 0x6, 0x5d, 0x78, 0x42, 0xa6, 0xb1, 0x4a, 0x10, 0xbc, 0xe4, 0x59, 0x3f, 0xed, 0x35, 0x7e, 0x1a, 0x3, 0xc0, 0xeb, 0xc6, 0x46, 0xb7, 0x90, 0x59, 0xf9, 0xc5, 0x62, 0x13, 0xf0, 0x6b, 0x6a, 0x9, 0x94, 0x49, 0x79, 0xac, 0x8a, 0xcb, 0x22, 0x83}, }, // 69P { x: fp384{0x52, 0x27, 0xc, 0x67, 0x74, 0xdf, 0xd3, 0xf8, 0x28, 0x5e, 0x11, 0xa1, 0x59, 0x28, 0xcb, 0x5c, 0x1b, 0x98, 0x19, 0xf, 0xaa, 0xc8, 0x66, 0xcc, 0x65, 0xfd, 0xab, 0x25, 0xb1, 0xc8, 0xbc, 0xd4, 0xca, 0x3c, 0xdd, 0x4f, 0x16, 0xee, 0x86, 0x2c, 0xf4, 0x35, 0xf7, 0xa3, 0x78, 0x5d, 0xd6, 0x59}, y: fp384{0xce, 0x55, 0xc, 0x7c, 0x28, 0xde, 0x5a, 0x3, 0x4d, 0x99, 0xd3, 0x45, 0x62, 0x9d, 0x76, 0x57, 0xa4, 0x23, 0xd4, 0x2b, 0x89, 0xe4, 0x3a, 0xd1, 0xbc, 0x66, 0xed, 0x82, 0x48, 0xee, 0xce, 0xa, 0x32, 0x7a, 0x16, 0x73, 0x8b, 0x9e, 0x2c, 0x6f, 0x7a, 0xbd, 0x1d, 0x27, 0x0, 0x1, 0xcd, 0xfb}, }, // 71P { x: fp384{0xb1, 0xfc, 0xfe, 0xef, 0x45, 0xce, 0x2e, 0xc4, 0x41, 0x14, 0xb1, 0xab, 0xb3, 0x31, 0x57, 0xbf, 0x92, 0xa, 0x8d, 0xe5, 0xcf, 0x15, 0xba, 0x93, 0x54, 0xac, 0x8, 0x35, 0x14, 0xde, 0xbb, 0x27, 0xda, 0x5d, 0x25, 0xfe, 0x38, 0x37, 0x12, 0x2b, 0x70, 0xcd, 0x7e, 0x53, 0x5a, 0xaa, 0x4f, 0xb}, y: fp384{0xc6, 0x83, 0xec, 0xdd, 0x84, 0xd0, 0x44, 0x6a, 0x3d, 0x52, 0x1, 0x8, 0x4d, 0x3c, 0x79, 0x86, 0x19, 0xe3, 0xb3, 0x25, 0x50, 0x28, 0x4f, 0x15, 0x3a, 0x37, 0x64, 0xce, 0xf1, 0xda, 0x44, 0x21, 0x66, 0x95, 0x13, 0x7, 0xee, 0x24, 0xb9, 0xbd, 0x1c, 0xd0, 0x2a, 0x73, 0x28, 0xea, 0xa7, 0xf9}, }, // 73P { x: fp384{0x2, 0xa7, 0x51, 0xd8, 0x32, 0x5c, 0x38, 0x43, 0x3b, 0x96, 0xe8, 0x1d, 0xb1, 0xa9, 0xc2, 0xa9, 0x24, 0x9b, 0x8b, 0xdf, 0xb, 0x23, 0x8d, 0x5b, 0xc2, 0x31, 0x37, 0x2d, 0x25, 0xa9, 0x29, 0x90, 0xd2, 0xa7, 0xca, 0xe8, 0x4d, 0xb0, 0x8d, 0xb0, 0x3c, 0x67, 0xf4, 0x2b, 0xe7, 0x83, 0x9d, 0xb8}, y: fp384{0x24, 0x44, 0xf2, 0xe1, 0xbf, 0x39, 0xfd, 0xa8, 0x16, 0xd6, 0xe8, 0xe1, 0xd6, 0xb6, 0x89, 0x9f, 0x6e, 0x21, 0x1d, 0x4f, 0x7b, 0xc8, 0x9f, 0xaf, 0x59, 0x5a, 0x26, 0x92, 0x3, 0x1e, 0xe2, 0x4, 0x73, 0x63, 0xb8, 0x87, 0x3, 0x74, 0x15, 0xb, 0x62, 0xa1, 0x98, 0x7c, 0x3b, 0xaf, 0x65, 0x6f}, }, // 75P { x: fp384{0xde, 0x3, 0x73, 0x86, 0x14, 0x40, 0x5d, 0x6b, 0xef, 0xb7, 0xa, 0x42, 0xa, 0xc4, 0xcb, 0xc8, 0x96, 0x9a, 0x54, 0x91, 0x89, 0xcf, 0x28, 0x5b, 0x66, 0x8f, 0x2f, 0x39, 0xb4, 0x31, 0x46, 0x5d, 0xc8, 0xb5, 0x67, 0xf3, 0x3d, 0xe2, 0x7e, 0x4a, 0x15, 0x7a, 0xca, 0xe6, 0xf, 0xae, 0xe0, 0xa1}, y: fp384{0x7c, 0xa2, 0x9f, 0x13, 0xe1, 0x5e, 0x65, 0x2a, 0x1, 0xb9, 0xfa, 0x50, 0xc4, 0xc2, 0x31, 0xa5, 0x71, 0xed, 0xa, 0x43, 0x69, 0xab, 0x62, 0x67, 0x1d, 0x2e, 0x40, 0xf0, 0xe3, 0x39, 0xe2, 0x64, 0x45, 0xe4, 0x7f, 0x95, 0x42, 0x0, 0x87, 0xd7, 0x62, 0x65, 0x7d, 0x41, 0x62, 0xd8, 0x42, 0xfd}, }, // 77P { x: fp384{0x3f, 0x1a, 0x50, 0x2a, 0xc1, 0x34, 0x21, 0x9f, 0xa7, 0x93, 0x47, 0x33, 0x40, 0x9b, 0x4a, 0x11, 0x25, 0x61, 0x2a, 0x21, 0xc0, 0xb6, 0xcc, 0x27, 0xa3, 0x78, 0xce, 0x98, 0xb9, 0x30, 0xa9, 0xc, 0x27, 0x26, 0xa1, 0x28, 0xb, 0x6, 0x2e, 0x74, 0x16, 0x98, 0x5c, 0xfa, 0x7, 0x36, 0xd2, 0x63}, y: fp384{0xdc, 0x91, 0x1f, 0xec, 0xa4, 0xcb, 0x4d, 0x77, 0x23, 0x1d, 0x4d, 0xf3, 0x2e, 0x7e, 0xcd, 0x34, 0x3d, 0x3c, 0xfd, 0x49, 0xe, 0x85, 0x0, 0x15, 0xb2, 0xcf, 0xc9, 0x30, 0x0, 0x95, 0x3, 0xdd, 0xa6, 0x41, 0x29, 0x57, 0xe5, 0xc3, 0x61, 0xce, 0x2e, 0xfd, 0x2c, 0x30, 0x75, 0x10, 0x4b, 0xd4}, }, // 79P { x: fp384{0x24, 0xc2, 0xa6, 0xe9, 0xd4, 0xd9, 0x11, 0xca, 0x85, 0x45, 0xb7, 0xc3, 0x48, 0xc2, 0xda, 0x2c, 0x71, 0x55, 0xca, 0x4, 0xa2, 0x1, 0x89, 0xe5, 0xf0, 0x1, 0x5d, 0xd1, 0x2d, 0x31, 0x1c, 0x49, 0x7c, 0xcb, 0x69, 0x70, 0x8a, 0x81, 0xcc, 0xb3, 0xda, 0x12, 0x39, 0xd5, 0xa5, 0x45, 0xb2, 0x23}, y: fp384{0x63, 0xb1, 0xb0, 0xa6, 0x8b, 0x83, 0xf7, 0x30, 0x52, 0x55, 0x77, 0x32, 0x3e, 0xeb, 0x52, 0xa0, 0xc1, 0x5e, 0xb9, 0xee, 0xe9, 0x43, 0x32, 0x40, 0xb3, 0x2e, 0x63, 0x8, 0x1b, 0x30, 0x7b, 0x61, 0xf9, 0x81, 0x2, 0xf3, 0xc9, 0x66, 0x1c, 0x94, 0x55, 0xb2, 0x7a, 0x1d, 0xf8, 0x28, 0x97, 0x4b}, }, // 81P { x: fp384{0x82, 0xf6, 0x6, 0xdb, 0xcb, 0xd3, 0xbd, 0x3c, 0x85, 0x87, 0xc0, 0x86, 0x3e, 0x47, 0x45, 0xde, 0xfb, 0x1b, 0x7b, 0xe0, 0x60, 0x35, 0xcb, 0xd8, 0xaf, 0x38, 0xf1, 0xea, 0x8f, 0x11, 0xc3, 0xf2, 0xaf, 0x6f, 0x43, 0x9f, 0x85, 0x8a, 0x23, 0x11, 0x4f, 0x34, 0xdf, 0x7c, 0xe3, 0xc2, 0x84, 0x9}, y: fp384{0x4f, 0x58, 0x82, 0xc3, 0x17, 0x3c, 0x8, 0xe1, 0x40, 0xa2, 0x6f, 0x73, 0xd4, 0x14, 0x9a, 0x95, 0x7d, 0x63, 0xf2, 0x18, 0xf0, 0xd2, 0xad, 0x56, 0x8d, 0x27, 0xdd, 0xe5, 0x5e, 0x7a, 0x4, 0x1, 0xa7, 0x6, 0x27, 0xae, 0x63, 0x8d, 0xe3, 0x5d, 0x7e, 0xb8, 0x45, 0x97, 0x60, 0xb7, 0xd7, 0x9d}, }, // 83P { x: fp384{0x71, 0x40, 0xe9, 0x44, 0xbf, 0xf0, 0x61, 0x8e, 0xb4, 0x5e, 0xf0, 0xd2, 0x7e, 0x84, 0xcf, 0x44, 0xeb, 0x94, 0x66, 0x4a, 0xd, 0xaa, 0x87, 0x84, 0xb5, 0xaa, 0xa4, 0xc7, 0xa1, 0x8c, 0xb8, 0xee, 0x26, 0x89, 0xa, 0x52, 0x3, 0xaa, 0x5b, 0xc2, 0x5, 0x78, 0x3d, 0xc0, 0x6a, 0xb1, 0x75, 0xa0}, y: fp384{0xc3, 0x70, 0xd9, 0x13, 0x8a, 0xa4, 0x57, 0xc3, 0x3e, 0x64, 0x9, 0x60, 0x70, 0x13, 0x3c, 0x4e, 0x29, 0x4, 0xe6, 0x49, 0x57, 0xa9, 0x21, 0xcf, 0xda, 0xbc, 0x51, 0x22, 0xba, 0x62, 0xa2, 0xa, 0xe4, 0x78, 0x3c, 0x56, 0xd0, 0x7c, 0x2a, 0xb7, 0xf9, 0x1c, 0xce, 0x69, 0xda, 0xfe, 0x3d, 0x77}, }, // 85P { x: fp384{0x2d, 0x76, 0x6, 0x9b, 0xdf, 0x2c, 0x5d, 0x93, 0x5a, 0x25, 0x7, 0x82, 0xb8, 0xbb, 0x48, 0x21, 0xd8, 0x53, 0x31, 0x5, 0xdd, 0xca, 0xbd, 0x7b, 0x57, 0x6a, 0x25, 0x73, 0xff, 0xaa, 0x53, 0xd9, 0x1, 0x6f, 0x4e, 0x11, 0xe1, 0x8f, 0xa0, 0xb0, 0x4d, 0x4d, 0xe6, 0x46, 0x54, 0x2, 0x35, 0xc8}, y: fp384{0x57, 0xc1, 0xdb, 0x0, 0xd8, 0xba, 0xcf, 0xe7, 0x69, 0xe9, 0xfb, 0x71, 0x2, 0xae, 0x2a, 0x39, 0x14, 0xe3, 0xeb, 0xb, 0x2a, 0xa7, 0x22, 0x74, 0xf2, 0x52, 0xaf, 0x2c, 0xd2, 0x55, 0xd4, 0xc3, 0x95, 0x51, 0x89, 0xe2, 0x9f, 0x83, 0x31, 0xa2, 0x13, 0xf2, 0x93, 0xc9, 0x92, 0x8d, 0x21, 0x6c}, }, // 87P { x: fp384{0x2e, 0x37, 0xa0, 0x4a, 0x2e, 0xa0, 0x11, 0x4f, 0x75, 0x77, 0x96, 0x10, 0x30, 0x47, 0x42, 0x59, 0x95, 0x91, 0x80, 0x8b, 0xba, 0xc1, 0xe, 0xdf, 0xf1, 0x3a, 0x3c, 0x9a, 0x8d, 0x92, 0xa, 0xf3, 0x2e, 0x6b, 0x7b, 0x38, 0x20, 0x3, 0x84, 0xc4, 0x22, 0xbb, 0x0, 0xa5, 0x17, 0x34, 0x1b, 0x1c}, y: fp384{0xf2, 0x66, 0x32, 0xbf, 0xc7, 0xe6, 0xe, 0x69, 0x81, 0x96, 0x90, 0xa7, 0x74, 0x6d, 0x24, 0x18, 0x8f, 0xa8, 0x84, 0xf9, 0x54, 0x24, 0xdf, 0xde, 0x9, 0x9f, 0x55, 0xe7, 0x75, 0x41, 0x94, 0x31, 0xb7, 0x4d, 0x7b, 0xe, 0x88, 0x81, 0xac, 0xbd, 0x68, 0xfe, 0x96, 0xe9, 0xae, 0x6f, 0x4, 0x9f}, }, // 89P { x: fp384{0xac, 0xd4, 0x71, 0x2d, 0x4b, 0x9, 0x62, 0xc, 0xe0, 0x63, 0xf1, 0x4b, 0xdc, 0x9f, 0xa4, 0x18, 0x1f, 0x72, 0x96, 0x0, 0xb, 0xf3, 0x3d, 0x46, 0x7b, 0x5b, 0xe5, 0xc8, 0x4a, 0x64, 0xd3, 0x67, 0xb6, 0xe2, 0xe0, 0x19, 0x9d, 0xd2, 0x3d, 0xd6, 0x61, 0x73, 0x4b, 0x16, 0xde, 0x5, 0xd1, 0xd0}, y: fp384{0x8e, 0x18, 0x17, 0x2, 0x4e, 0x5c, 0x86, 0xe5, 0x7e, 0xcf, 0x93, 0x20, 0x1b, 0xb7, 0x61, 0x78, 0x3c, 0x25, 0xaa, 0x2d, 0x51, 0xf0, 0xcc, 0x65, 0xc0, 0xe4, 0x4d, 0xb, 0x9, 0x1, 0x77, 0x14, 0xd9, 0x62, 0xb9, 0x40, 0x35, 0x24, 0x28, 0x1d, 0xf3, 0x37, 0xdf, 0xb8, 0x39, 0xe9, 0xc7, 0x1}, }, // 91P { x: fp384{0x58, 0x8, 0xba, 0x9c, 0x9c, 0x40, 0xea, 0x5d, 0x63, 0x3f, 0xae, 0x14, 0x1b, 0x42, 0xc2, 0x35, 0x8a, 0x61, 0xc2, 0xbb, 0x34, 0xe5, 0xf6, 0xa4, 0x5f, 0x4f, 0xd7, 0x42, 0x7d, 0x97, 0x4b, 0xb0, 0xb7, 0x3e, 0xdc, 0x59, 0x27, 0x38, 0xe7, 0xe7, 0xb0, 0x23, 0xf2, 0x8b, 0x34, 0x52, 0xf, 0xeb}, y: fp384{0x58, 0x51, 0xc7, 0xf, 0x67, 0x51, 0x1c, 0x99, 0x6d, 0x2c, 0xde, 0x3f, 0x1a, 0x81, 0x12, 0xd0, 0x3d, 0x34, 0x36, 0x92, 0x31, 0xb3, 0xd0, 0x9, 0xa0, 0xcb, 0xa2, 0x63, 0xc8, 0xe0, 0x78, 0xcb, 0x78, 0x84, 0xb8, 0x9a, 0xbd, 0xb3, 0x9, 0xb, 0xe2, 0xc6, 0x16, 0xf1, 0x3, 0xc7, 0xca, 0x47}, }, // 93P { x: fp384{0xaf, 0x80, 0x2d, 0xe3, 0x71, 0x4d, 0xd1, 0xeb, 0x5e, 0x67, 0x80, 0x53, 0x4f, 0xc2, 0x1c, 0x1b, 0xcd, 0x42, 0x61, 0xb1, 0x64, 0x47, 0x63, 0x1c, 0xe, 0xb0, 0xfd, 0x7c, 0xde, 0x45, 0x35, 0x7a, 0x54, 0x51, 0xd1, 0xcf, 0x89, 0x16, 0xf9, 0x2d, 0xd7, 0xa2, 0xa, 0x43, 0xb3, 0x55, 0x33, 0x81}, y: fp384{0x7e, 0xca, 0xf2, 0x85, 0xc9, 0xe2, 0xdc, 0x16, 0x79, 0xbb, 0x3a, 0xe0, 0xf7, 0x3, 0xe3, 0xd9, 0x98, 0x66, 0xb0, 0x3c, 0x10, 0xa8, 0x7c, 0xfe, 0xcb, 0xd, 0x67, 0x71, 0x5b, 0x42, 0x2a, 0x57, 0xe5, 0x68, 0xa2, 0x90, 0x54, 0x39, 0x1b, 0xc7, 0x9, 0x9d, 0xbf, 0x66, 0x8f, 0xf3, 0x71, 0xc0}, }, // 95P { x: fp384{0x91, 0x3c, 0xbc, 0xd, 0x63, 0xf2, 0xc0, 0xf, 0xb1, 0xcb, 0xc0, 0x9b, 0x16, 0xca, 0x74, 0x9f, 0x77, 0x89, 0xf9, 0xe, 0x9d, 0x7b, 0x60, 0x4a, 0x79, 0x2b, 0x7d, 0xa2, 0xef, 0xb, 0xe9, 0xb, 0xe1, 0x23, 0x7f, 0xad, 0xb5, 0xb, 0x7b, 0x25, 0xe4, 0xd1, 0xea, 0x2f, 0xe5, 0x2f, 0xf4, 0xb8}, y: fp384{0x92, 0xb5, 0x93, 0x5f, 0x31, 0xe4, 0x78, 0xde, 0x7d, 0x61, 0x79, 0xfd, 0xeb, 0xe7, 0x5f, 0x50, 0xfb, 0xf9, 0x99, 0xdd, 0x14, 0x3f, 0xcc, 0x45, 0x91, 0xb5, 0xc7, 0x3b, 0xe8, 0x64, 0xf, 0x8c, 0xf9, 0x93, 0xab, 0x55, 0xed, 0x4d, 0x36, 0x65, 0x6e, 0x28, 0xdf, 0x42, 0xa5, 0x4b, 0x6d, 0xbb}, }, // 97P { x: fp384{0xe2, 0x54, 0x5c, 0x7f, 0x5d, 0x3, 0xd2, 0x7c, 0x2c, 0x49, 0x49, 0x4a, 0x0, 0xdb, 0xf0, 0xc1, 0x98, 0x8f, 0x27, 0x65, 0x30, 0x3e, 0x27, 0x8f, 0x9d, 0x9d, 0xef, 0x6f, 0xd1, 0x1e, 0x24, 0x10, 0x16, 0x96, 0x6, 0xac, 0x1b, 0xe5, 0xb1, 0x87, 0x7f, 0x80, 0xd, 0x17, 0xcd, 0x1a, 0x8, 0x8c}, y: fp384{0x98, 0xb5, 0x73, 0x1c, 0xea, 0x51, 0x50, 0x0, 0xf4, 0x5b, 0x86, 0xd6, 0x12, 0x55, 0xeb, 0xe4, 0xd3, 0x5d, 0xe0, 0x30, 0xf4, 0x4e, 0xd2, 0xd7, 0x9e, 0xa3, 0x89, 0x78, 0xed, 0xe4, 0x47, 0xcb, 0x64, 0x69, 0xf5, 0xc4, 0x91, 0x24, 0x3e, 0x4c, 0x6, 0x30, 0xf0, 0xc4, 0x8e, 0xb7, 0xc6, 0x83}, }, // 99P { x: fp384{0xa1, 0x84, 0x5f, 0xb0, 0xa9, 0x35, 0x38, 0x6e, 0x4e, 0x17, 0xaa, 0x41, 0xf, 0x9e, 0x4f, 0xbb, 0x69, 0xa4, 0x8b, 0x70, 0x7c, 0x17, 0x41, 0x1b, 0xbd, 0xf8, 0xc8, 0x79, 0xb4, 0xe6, 0xb2, 0xb9, 0xbd, 0xd6, 0xd9, 0x82, 0x9, 0xae, 0x9c, 0xd4, 0x3a, 0x22, 0x28, 0xbb, 0x0, 0x5f, 0x8c, 0x64}, y: fp384{0xa5, 0xc4, 0x8c, 0x5d, 0x76, 0x85, 0xf4, 0x4, 0x8d, 0xa3, 0xa0, 0x81, 0xdd, 0x96, 0x30, 0xfe, 0xe1, 0x47, 0x82, 0x70, 0x8f, 0x13, 0x75, 0x66, 0x8, 0xea, 0xa0, 0xd1, 0xd8, 0x59, 0xf7, 0xd6, 0x98, 0xd, 0x19, 0x76, 0xb1, 0x93, 0x74, 0x1f, 0xbd, 0x63, 0x2d, 0x32, 0x8b, 0x69, 0xe1, 0x3}, }, // 101P { x: fp384{0xac, 0xde, 0x8a, 0x9b, 0xf6, 0xc6, 0x66, 0x8e, 0x70, 0x6d, 0xc6, 0x50, 0xfe, 0xf5, 0x39, 0xb5, 0x1a, 0xfb, 0xcc, 0x2e, 0x2c, 0xcd, 0xdd, 0x73, 0xfc, 0x5c, 0x8b, 0x8b, 0xad, 0x1f, 0x3b, 0xd7, 0x10, 0x87, 0xa1, 0x47, 0x35, 0x94, 0xdd, 0x9c, 0xdb, 0x14, 0xc8, 0x7b, 0xbf, 0x92, 0x23, 0x7e}, y: fp384{0xe8, 0x74, 0x8f, 0x6c, 0xc0, 0x93, 0x41, 0x91, 0x4d, 0xc0, 0x67, 0x1d, 0x21, 0xdc, 0xed, 0xff, 0x93, 0x86, 0xd6, 0xa, 0x85, 0x41, 0xef, 0x1f, 0x54, 0x80, 0x3e, 0xf5, 0x9a, 0x1d, 0x3e, 0xa7, 0x4, 0xc1, 0xe, 0x42, 0x6f, 0x65, 0x9b, 0x90, 0xde, 0xe1, 0x2, 0x17, 0x36, 0x2d, 0x87, 0x73}, }, // 103P { x: fp384{0x5f, 0x5d, 0x35, 0x21, 0xaa, 0xab, 0x4c, 0xd2, 0xbd, 0x2, 0xd4, 0xaf, 0xe, 0xb1, 0xcb, 0xdd, 0xe1, 0x1d, 0xc2, 0x29, 0x43, 0xd1, 0xf0, 0xd3, 0xfc, 0x84, 0x3d, 0xf2, 0x94, 0x5a, 0xd9, 0x1a, 0xd, 0x53, 0xda, 0xe3, 0x2, 0x79, 0x3a, 0x11, 0x48, 0x10, 0x67, 0x64, 0x8e, 0xa8, 0xd, 0x59}, y: fp384{0xda, 0xf0, 0x5b, 0x92, 0x82, 0x82, 0xa5, 0xf4, 0xb, 0x6e, 0x2e, 0xe6, 0xe7, 0xe4, 0x52, 0x1a, 0xfd, 0x4d, 0x6f, 0xd8, 0x4e, 0xbb, 0xeb, 0x97, 0xc3, 0xd1, 0xfa, 0x58, 0xc3, 0xd1, 0x1b, 0x60, 0x52, 0x5, 0xe4, 0x2d, 0xa6, 0xd5, 0xe2, 0xd6, 0xed, 0xdb, 0x73, 0x72, 0x37, 0x71, 0x9e, 0xc}, }, // 105P { x: fp384{0x45, 0x28, 0x80, 0xe5, 0x85, 0x19, 0xe9, 0xe6, 0xbc, 0x1, 0xe2, 0xa6, 0xae, 0xd6, 0x67, 0xc3, 0xbe, 0x23, 0x2c, 0xdd, 0xe5, 0x30, 0x7f, 0x7, 0xe3, 0x75, 0x50, 0x27, 0x9c, 0xf3, 0x2e, 0x86, 0x42, 0x65, 0x80, 0x1a, 0x44, 0x75, 0x2c, 0x2, 0x9c, 0xd0, 0xeb, 0x99, 0x3a, 0x3e, 0xab, 0xd0}, y: fp384{0xb8, 0x28, 0x90, 0xd9, 0x60, 0xef, 0x67, 0x7d, 0x6b, 0x13, 0xad, 0xa9, 0x4f, 0x36, 0xcf, 0xa5, 0x8c, 0xff, 0x1f, 0xa9, 0xa9, 0x23, 0x2c, 0x37, 0x60, 0x25, 0x20, 0x47, 0x95, 0x7a, 0xd5, 0xd3, 0x23, 0x19, 0x2f, 0x15, 0x45, 0xf1, 0xba, 0xce, 0xa5, 0x73, 0x89, 0x6d, 0x2c, 0xe7, 0x3a, 0xcc}, }, // 107P { x: fp384{0x23, 0x3f, 0x36, 0xf4, 0xe1, 0xe8, 0x18, 0xd7, 0x90, 0x14, 0x76, 0x4f, 0x20, 0x1e, 0xc2, 0x73, 0x46, 0x5d, 0x7, 0xa0, 0x25, 0xec, 0xc6, 0x27, 0xd0, 0x40, 0x3f, 0x75, 0x56, 0xf4, 0xd4, 0xcc, 0x22, 0x16, 0xa9, 0x60, 0x49, 0x4c, 0x99, 0x50, 0x48, 0xb, 0x74, 0x3f, 0x79, 0x4d, 0x96, 0x77}, y: fp384{0x2, 0xed, 0x47, 0xf6, 0xe2, 0x55, 0xc9, 0xf4, 0x79, 0x3d, 0x19, 0xe4, 0x9a, 0xc7, 0x4f, 0x84, 0x9f, 0x3f, 0x7f, 0xa2, 0xd1, 0x74, 0x83, 0x48, 0x63, 0x94, 0x65, 0xb8, 0x45, 0xad, 0xd6, 0x95, 0x39, 0x8e, 0x43, 0xc7, 0x78, 0x9f, 0xd9, 0xe1, 0xf2, 0xed, 0xfc, 0x2a, 0x17, 0xa7, 0x82, 0x51}, }, // 109P { x: fp384{0xfa, 0xb1, 0xde, 0xb2, 0x27, 0x2e, 0xfc, 0xe, 0x4b, 0x18, 0xc1, 0x3c, 0x83, 0x35, 0x7d, 0x9c, 0xc8, 0xbd, 0xdc, 0xa8, 0xf8, 0xc5, 0x41, 0x58, 0xbb, 0x3a, 0xd9, 0xf0, 0x8a, 0xa5, 0x11, 0xa9, 0x87, 0xf8, 0xcf, 0xb9, 0x33, 0x8c, 0xd1, 0x3c, 0x3, 0x24, 0x3f, 0xf1, 0xbb, 0x27, 0x3c, 0x6e}, y: fp384{0xe6, 0x3a, 0x53, 0xea, 0x12, 0x17, 0x39, 0x5b, 0x5, 0x4c, 0x29, 0x54, 0xb, 0xd9, 0xcd, 0x35, 0xf4, 0xda, 0x60, 0xf5, 0xb4, 0x7f, 0xb5, 0x2d, 0x1d, 0x41, 0xa1, 0xf5, 0xca, 0x33, 0xad, 0x75, 0x68, 0x75, 0x7c, 0x7f, 0x4e, 0x9a, 0xe1, 0x87, 0x5, 0x77, 0x8c, 0x19, 0x56, 0x6c, 0xc4, 0xf4}, }, // 111P { x: fp384{0xb8, 0x74, 0xbe, 0x5, 0x48, 0xb7, 0xb3, 0x8d, 0xab, 0x5f, 0x76, 0x0, 0x50, 0x80, 0xe0, 0x8, 0xd9, 0x7f, 0x44, 0x50, 0xb, 0x72, 0x44, 0x67, 0x3, 0xbe, 0x27, 0xc7, 0x12, 0x20, 0x55, 0x27, 0x7f, 0x66, 0x2, 0x8b, 0x51, 0x7b, 0x90, 0xc3, 0x14, 0xef, 0xbd, 0xb9, 0xbc, 0xaa, 0x58, 0xa1}, y: fp384{0x6f, 0xc5, 0x9c, 0xf4, 0x3, 0xfa, 0xdd, 0xaa, 0x96, 0xfb, 0x5, 0xe3, 0xe4, 0xbe, 0x95, 0x10, 0x19, 0x26, 0xc3, 0x93, 0xbc, 0x54, 0xff, 0xa2, 0x85, 0x26, 0xeb, 0x4a, 0xf9, 0xe1, 0xf8, 0xcc, 0xfe, 0xd9, 0x0, 0x23, 0xb8, 0x47, 0x4b, 0xc6, 0xa9, 0x9d, 0x27, 0x8, 0x68, 0x77, 0xca, 0x9}, }, // 113P { x: fp384{0x12, 0xda, 0xb, 0x9b, 0xb7, 0x86, 0x5b, 0xf8, 0x72, 0x35, 0xe3, 0xbb, 0xd1, 0x16, 0xc6, 0xd2, 0x7f, 0xd2, 0x2b, 0x85, 0xef, 0x15, 0x22, 0xe7, 0xc5, 0x7f, 0x9b, 0x13, 0x9, 0x5b, 0x81, 0xe9, 0xc2, 0xa0, 0x7f, 0x8d, 0x4, 0xdb, 0x5b, 0x4a, 0x86, 0xa9, 0x86, 0xff, 0x17, 0xcd, 0x9f, 0x86}, y: fp384{0xbe, 0xf6, 0xda, 0x91, 0x17, 0x52, 0x78, 0x32, 0x4, 0x4d, 0x66, 0xd6, 0xf1, 0x7, 0xc0, 0xb9, 0x29, 0x20, 0xb1, 0xe7, 0x2a, 0x72, 0x98, 0x69, 0x67, 0xbb, 0x31, 0xfc, 0xd9, 0xde, 0x7f, 0xbf, 0x57, 0x77, 0xb8, 0x31, 0x7c, 0xd1, 0xe, 0x3d, 0x4b, 0x94, 0xf7, 0x55, 0xf2, 0x3d, 0xb, 0xa1}, }, // 115P { x: fp384{0x56, 0x8f, 0x49, 0x34, 0x3b, 0x67, 0x4e, 0xaa, 0x6d, 0x45, 0x43, 0xa0, 0xb3, 0xf7, 0x20, 0x91, 0x26, 0x88, 0xa4, 0x26, 0xf3, 0x68, 0xe8, 0x33, 0xfd, 0x6b, 0x40, 0x32, 0xf4, 0xcc, 0x7a, 0xa9, 0x46, 0x7, 0xc5, 0x23, 0x41, 0x2a, 0x44, 0x84, 0x2d, 0x98, 0x50, 0x73, 0x65, 0x69, 0x4c, 0x27}, y: fp384{0xaa, 0x9e, 0xdc, 0x95, 0xfb, 0xb7, 0x6, 0x31, 0x41, 0xe2, 0x7a, 0xec, 0xb1, 0x1d, 0xbf, 0x3e, 0x86, 0x5b, 0x8a, 0x84, 0xb8, 0x39, 0xdc, 0x0, 0xc6, 0x2e, 0x31, 0xf6, 0x3a, 0x34, 0x9a, 0xdf, 0x3, 0x1f, 0x12, 0xcf, 0x32, 0x9e, 0x2, 0x75, 0xdb, 0x11, 0x5a, 0xcf, 0xf6, 0xbd, 0xc5, 0xc0}, }, // 117P { x: fp384{0x9a, 0x55, 0x23, 0x7, 0xa8, 0xe7, 0xcc, 0xfd, 0x70, 0xd0, 0x29, 0xa2, 0xe, 0xb3, 0x32, 0x95, 0x61, 0x79, 0x85, 0xfe, 0x94, 0x52, 0x3e, 0x61, 0x8d, 0x73, 0xea, 0x9a, 0x9a, 0x74, 0x9e, 0xad, 0x53, 0xba, 0xac, 0x23, 0xae, 0x6b, 0x7a, 0x51, 0x8b, 0x56, 0x23, 0x78, 0xcd, 0x74, 0x67, 0xf2}, y: fp384{0x4d, 0x11, 0x53, 0xae, 0xa1, 0x67, 0x7, 0x94, 0x7b, 0x5, 0x8c, 0xeb, 0x4b, 0x3a, 0xcb, 0xc6, 0x0, 0xf6, 0xae, 0x6, 0x5f, 0xc0, 0x99, 0x6d, 0x81, 0x84, 0x79, 0xb2, 0x8d, 0x9b, 0x72, 0xa6, 0x5b, 0x58, 0xf1, 0xbf, 0x82, 0x65, 0x54, 0x7a, 0x73, 0x97, 0xb0, 0x82, 0xb0, 0x9a, 0x50, 0x70}, }, // 119P { x: fp384{0xd1, 0xd8, 0x29, 0x73, 0xac, 0x95, 0x25, 0x73, 0xc4, 0xbc, 0x73, 0xab, 0x8d, 0x7, 0xf9, 0x59, 0xde, 0x9d, 0xcf, 0x21, 0xb4, 0xe7, 0x55, 0xcd, 0x27, 0xab, 0x5f, 0x87, 0xa1, 0xb, 0x63, 0xa4, 0xcd, 0xf4, 0x9c, 0xec, 0xb8, 0x7f, 0x16, 0x13, 0x77, 0x5, 0x8b, 0x99, 0x57, 0x5c, 0xfc, 0xd2}, y: fp384{0x6f, 0x1b, 0xf5, 0x5f, 0xc1, 0x60, 0x13, 0x76, 0xeb, 0x9c, 0xcf, 0x6, 0xf2, 0x96, 0xdb, 0xb2, 0x46, 0x8f, 0xdc, 0x99, 0x48, 0xa6, 0x77, 0xd6, 0xe5, 0xb7, 0x9, 0x91, 0xbc, 0xca, 0x9e, 0xeb, 0xa3, 0xb7, 0x21, 0x92, 0xac, 0xb1, 0x1b, 0x9a, 0xcd, 0xa5, 0x40, 0x8a, 0x28, 0x36, 0x65, 0xb1}, }, // 121P { x: fp384{0x8d, 0xfa, 0x9d, 0x18, 0x40, 0xba, 0x98, 0x51, 0x1e, 0xab, 0x96, 0xa8, 0xe3, 0x16, 0x9a, 0x8c, 0xe4, 0x44, 0x67, 0xba, 0xd6, 0xd5, 0x33, 0x6c, 0x8a, 0x77, 0x72, 0x77, 0xd4, 0xfb, 0x9a, 0xc2, 0xe0, 0xf7, 0x29, 0x93, 0x95, 0x3c, 0xdf, 0x65, 0x81, 0xdb, 0x91, 0x38, 0x1e, 0x3f, 0xcd, 0x79}, y: fp384{0x9b, 0x1, 0x84, 0xd7, 0xb, 0x8f, 0xaa, 0xca, 0x62, 0x8e, 0x2, 0xe9, 0x6b, 0x4f, 0x40, 0xf5, 0x85, 0x89, 0x4d, 0xae, 0x54, 0x7a, 0x50, 0x95, 0x1b, 0xf2, 0x16, 0xb7, 0xa8, 0x39, 0x1d, 0x9c, 0x7e, 0x5b, 0x26, 0xf8, 0xf9, 0xd, 0x3d, 0x47, 0x16, 0x9, 0x4d, 0xc6, 0xa1, 0xed, 0xae, 0x11}, }, // 123P { x: fp384{0x80, 0xb, 0x4c, 0xc, 0x48, 0x98, 0x11, 0x15, 0xfe, 0x18, 0x10, 0x2a, 0x4a, 0x7d, 0xb0, 0x46, 0x7b, 0x90, 0x80, 0xea, 0xeb, 0xc3, 0xa9, 0x14, 0x5, 0x44, 0x95, 0x42, 0xee, 0x5, 0x3d, 0x4b, 0xd2, 0x18, 0x4, 0x55, 0x78, 0xfd, 0xd6, 0xd4, 0xa6, 0x82, 0xdc, 0x21, 0x63, 0x4f, 0x4a, 0x8e}, y: fp384{0xd9, 0xb9, 0x78, 0xa1, 0xf7, 0xd7, 0xe4, 0x1b, 0x9f, 0x8c, 0x78, 0x70, 0x4, 0xba, 0xc6, 0x83, 0xe8, 0xf7, 0x30, 0x9f, 0x3e, 0xaf, 0x82, 0x5a, 0x7b, 0x44, 0x8f, 0x49, 0xf, 0xab, 0x86, 0x8a, 0x33, 0xcf, 0x5c, 0xc2, 0xec, 0xbc, 0xba, 0x3, 0xdd, 0x8a, 0x79, 0x1a, 0xed, 0x62, 0xc4, 0x74}, }, // 125P { x: fp384{0xbb, 0x44, 0xfb, 0x3c, 0xbc, 0xb8, 0x12, 0x96, 0xda, 0x6a, 0x9d, 0x71, 0x77, 0x56, 0xf2, 0x70, 0xe2, 0x14, 0xf6, 0x46, 0xaa, 0x65, 0xea, 0x50, 0x6d, 0x35, 0x50, 0x34, 0xcf, 0xa8, 0x36, 0x94, 0xac, 0x3, 0x67, 0x3, 0xad, 0xeb, 0xd6, 0x7a, 0xae, 0x48, 0xcf, 0x45, 0xb2, 0xda, 0xb2, 0x3}, y: fp384{0x1e, 0x6, 0x17, 0x41, 0x2a, 0x3d, 0x95, 0x21, 0xa4, 0x55, 0x4f, 0xed, 0x30, 0xb7, 0x3f, 0xdf, 0x8e, 0xab, 0x19, 0xe1, 0x41, 0x36, 0xf5, 0xec, 0xaa, 0x87, 0x91, 0x21, 0xbc, 0x41, 0x1f, 0x55, 0x2, 0x58, 0x9, 0xb0, 0x4b, 0xa7, 0xd5, 0x7c, 0xcb, 0x5c, 0xf3, 0x72, 0xf5, 0xbf, 0x33, 0x89}, }, // 127P { x: fp384{0xec, 0x1, 0xa1, 0xec, 0x46, 0x32, 0x75, 0xf7, 0xaf, 0x4, 0x96, 0x56, 0x4c, 0xfa, 0xac, 0x2a, 0x79, 0x62, 0x2c, 0x52, 0x34, 0x8f, 0xf2, 0xee, 0xf, 0x1e, 0x23, 0x74, 0x38, 0xe6, 0xfd, 0x96, 0x9d, 0xf0, 0xe0, 0xd6, 0x1b, 0xb1, 0x2b, 0xa9, 0xb4, 0x5d, 0x39, 0xf, 0x74, 0x4e, 0xe3, 0xbb}, y: fp384{0xf9, 0x3c, 0x94, 0xbf, 0xdd, 0x59, 0x6e, 0xaa, 0xaa, 0xd5, 0x8a, 0x1, 0xbe, 0xbd, 0x98, 0x56, 0x19, 0xc5, 0x67, 0xa4, 0x44, 0x2a, 0xd2, 0x88, 0xe, 0xb, 0x18, 0xad, 0x39, 0xe3, 0x29, 0x9e, 0x94, 0x2f, 0x7b, 0x36, 0x2e, 0x83, 0xd6, 0xf3, 0x69, 0x80, 0x94, 0xe3, 0x61, 0x2a, 0xe9, 0xc7}, }, } golang-github-cloudflare-circl-1.3.7/expander/000077500000000000000000000000001454601126700212755ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/expander/expander.go000066400000000000000000000065161454601126700234420ustar00rootroot00000000000000// Package expander generates arbitrary bytes from an XOF or Hash function. package expander import ( "crypto" "encoding/binary" "errors" "io" "github.com/cloudflare/circl/xof" ) type Expander interface { // Expand generates a pseudo-random byte string of a determined length by // expanding an input string. Expand(in []byte, length uint) (pseudo []byte) } type expanderMD struct { h crypto.Hash dst []byte } // NewExpanderMD returns a hash function based on a Merkle-Damgård hash function. func NewExpanderMD(h crypto.Hash, dst []byte) *expanderMD { return &expanderMD{h, dst} } func (e *expanderMD) calcDSTPrime() []byte { var dstPrime []byte if l := len(e.dst); l > maxDSTLength { H := e.h.New() mustWrite(H, longDSTPrefix[:]) mustWrite(H, e.dst) dstPrime = H.Sum(nil) } else { dstPrime = make([]byte, l, l+1) copy(dstPrime, e.dst) } return append(dstPrime, byte(len(dstPrime))) } func (e *expanderMD) Expand(in []byte, n uint) []byte { H := e.h.New() bLen := uint(H.Size()) ell := (n + (bLen - 1)) / bLen if ell > 255 { panic(errorLongOutput) } zPad := make([]byte, H.BlockSize()) libStr := []byte{0, 0} libStr[0] = byte((n >> 8) & 0xFF) libStr[1] = byte(n & 0xFF) dstPrime := e.calcDSTPrime() mustWrite(H, zPad) mustWrite(H, in) mustWrite(H, libStr) mustWrite(H, []byte{0}) mustWrite(H, dstPrime) b0 := H.Sum(nil) H.Reset() mustWrite(H, b0) mustWrite(H, []byte{1}) mustWrite(H, dstPrime) bi := H.Sum(nil) pseudo := append([]byte{}, bi...) for i := uint(2); i <= ell; i++ { H.Reset() for i := range b0 { bi[i] ^= b0[i] } mustWrite(H, bi) mustWrite(H, []byte{byte(i)}) mustWrite(H, dstPrime) bi = H.Sum(nil) pseudo = append(pseudo, bi...) } return pseudo[0:n] } // expanderXOF is based on an extendable output function. type expanderXOF struct { id xof.ID kSecLevel uint dst []byte } // NewExpanderXOF returns an Expander based on an extendable output function. // The kSecLevel parameter is the target security level in bits, and dst is // a domain separation string. func NewExpanderXOF(id xof.ID, kSecLevel uint, dst []byte) *expanderXOF { return &expanderXOF{id, kSecLevel, dst} } // Expand panics if output's length is longer than 2^16 bytes. func (e *expanderXOF) Expand(in []byte, n uint) []byte { bLen := []byte{0, 0} binary.BigEndian.PutUint16(bLen, uint16(n)) pseudo := make([]byte, n) dstPrime := e.calcDSTPrime() H := e.id.New() mustWrite(H, in) mustWrite(H, bLen) mustWrite(H, dstPrime) mustReadFull(H, pseudo) return pseudo } func (e *expanderXOF) calcDSTPrime() []byte { var dstPrime []byte if l := len(e.dst); l > maxDSTLength { H := e.id.New() mustWrite(H, longDSTPrefix[:]) mustWrite(H, e.dst) max := ((2 * e.kSecLevel) + 7) / 8 dstPrime = make([]byte, max, max+1) mustReadFull(H, dstPrime) } else { dstPrime = make([]byte, l, l+1) copy(dstPrime, e.dst) } return append(dstPrime, byte(len(dstPrime))) } func mustWrite(w io.Writer, b []byte) { if n, err := w.Write(b); err != nil || n != len(b) { panic(err) } } func mustReadFull(r io.Reader, b []byte) { if n, err := io.ReadFull(r, b); err != nil || n != len(b) { panic(err) } } const maxDSTLength = 255 var ( longDSTPrefix = [17]byte{'H', '2', 'C', '-', 'O', 'V', 'E', 'R', 'S', 'I', 'Z', 'E', '-', 'D', 'S', 'T', '-'} errorLongOutput = errors.New("requested too many bytes") ) golang-github-cloudflare-circl-1.3.7/expander/expander_test.go000066400000000000000000000046651454601126700245040ustar00rootroot00000000000000package expander_test import ( "bytes" "crypto" _ "crypto/sha256" _ "crypto/sha512" "encoding/hex" "encoding/json" "fmt" "os" "path/filepath" "strconv" "testing" "github.com/cloudflare/circl/expander" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/xof" ) func TestExpander(t *testing.T) { fileNames, err := filepath.Glob("./testdata/*.json") if err != nil { t.Fatal(err) } for _, fileName := range fileNames { f, err := os.Open(fileName) if err != nil { t.Fatal(err) } dec := json.NewDecoder(f) var v vectorExpanderSuite err = dec.Decode(&v) if err != nil { t.Fatal(err) } f.Close() t.Run(v.Name+"/"+v.Hash, func(t *testing.T) { testExpander(t, &v) }) } } func testExpander(t *testing.T, vs *vectorExpanderSuite) { var exp expander.Expander switch vs.Hash { case "SHA256": exp = expander.NewExpanderMD(crypto.SHA256, []byte(vs.DST)) case "SHA512": exp = expander.NewExpanderMD(crypto.SHA512, []byte(vs.DST)) case "SHAKE128": exp = expander.NewExpanderXOF(xof.SHAKE128, vs.K, []byte(vs.DST)) case "SHAKE256": exp = expander.NewExpanderXOF(xof.SHAKE256, vs.K, []byte(vs.DST)) default: t.Skip("hash not supported: " + vs.Hash) } for i, v := range vs.Tests { lenBytes, err := strconv.ParseUint(v.Len, 0, 64) if err != nil { t.Fatal(err) } got := exp.Expand([]byte(v.Msg), uint(lenBytes)) want, err := hex.DecodeString(v.UniformBytes) if err != nil { t.Fatal(err) } if !bytes.Equal(got, want) { test.ReportError(t, got, want, i) } } } type vectorExpanderSuite struct { DST string `json:"DST"` Hash string `json:"hash"` Name string `json:"name"` K uint `json:"k"` Tests []struct { DstPrime string `json:"DST_prime"` Len string `json:"len_in_bytes"` Msg string `json:"msg"` MsgPrime string `json:"msg_prime"` UniformBytes string `json:"uniform_bytes"` } `json:"tests"` } func BenchmarkExpander(b *testing.B) { in := []byte("input") dst := []byte("dst") for _, v := range []struct { Name string Exp expander.Expander }{ {"XMD", expander.NewExpanderMD(crypto.SHA256, dst)}, {"XOF", expander.NewExpanderXOF(xof.SHAKE128, 0, dst)}, } { exp := v.Exp for l := 8; l <= 10; l++ { max := int64(1) << uint(l) b.Run(fmt.Sprintf("%v/%v", v.Name, max), func(b *testing.B) { b.SetBytes(max) b.ResetTimer() for i := 0; i < b.N; i++ { exp.Expand(in, uint(max)) } }) } } } golang-github-cloudflare-circl-1.3.7/expander/testdata/000077500000000000000000000000001454601126700231065ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/expander/testdata/expand_message_xmd_SHA256_256.json000066400000000000000000000233331454601126700311640ustar00rootroot00000000000000{ "DST": "QUUX-V01-CS02-with-expander-SHA256-128-long-DST-1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "hash": "SHA256", "k": 128, "name": "expand_message_xmd", "tests": [ { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x20", "msg": "", "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "e8dc0c8b686b7ef2074086fbdd2f30e3f8bfbd3bdf177f73f04b97ce618a3ed3" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x20", "msg": "abc", "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "52dbf4f36cf560fca57dedec2ad924ee9c266341d8f3d6afe5171733b16bbb12" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x20", "msg": "abcdef0123456789", "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "35387dcf22618f3728e6c686490f8b431f76550b0b2c61cbc1ce7001536f4521" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x20", "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "01b637612bb18e840028be900a833a74414140dde0c4754c198532c3a0ba42bc" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x20", "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000613531325f6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "20cce7033cabc5460743180be6fa8aac5a103f56d481cf369a8accc0c374431b" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x80", "msg": "", "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "14604d85432c68b757e485c8894db3117992fc57e0e136f71ad987f789a0abc287c47876978e2388a02af86b1e8d1342e5ce4f7aaa07a87321e691f6fba7e0072eecc1218aebb89fb14a0662322d5edbd873f0eb35260145cd4e64f748c5dfe60567e126604bcab1a3ee2dc0778102ae8a5cfd1429ebc0fa6bf1a53c36f55dfc" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x80", "msg": "abc", "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "1a30a5e36fbdb87077552b9d18b9f0aee16e80181d5b951d0471d55b66684914aef87dbb3626eaabf5ded8cd0686567e503853e5c84c259ba0efc37f71c839da2129fe81afdaec7fbdc0ccd4c794727a17c0d20ff0ea55e1389d6982d1241cb8d165762dbc39fb0cee4474d2cbbd468a835ae5b2f20e4f959f56ab24cd6fe267" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x80", "msg": "abcdef0123456789", "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "uniform_bytes": "d2ecef3635d2397f34a9f86438d772db19ffe9924e28a1caf6f1c8f15603d4028f40891044e5c7e39ebb9b31339979ff33a4249206f67d4a1e7c765410bcd249ad78d407e303675918f20f26ce6d7027ed3774512ef5b00d816e51bfcc96c3539601fa48ef1c07e494bdc37054ba96ecb9dbd666417e3de289d4f424f502a982" }, { "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", "len_in_bytes": "0x80", "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620", 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"uniform_bytes": "05b0bfef265dcee87654372777b7c44177e2ae4c13a27f103340d9cd11c86cb2426ffcad5bd964080c2aee97f03be1ca18e30a1f14e27bc11ebbd650f305269cc9fb1db08bf90bfc79b42a952b46daf810359e7bc36452684784a64952c343c52e5124cd1f71d474d5197fefc571a92929c9084ffe1112cf5eea5192ebff330b" } ] } golang-github-cloudflare-circl-1.3.7/expander/testdata/expand_message_xof_SHAKE128_256.json000066400000000000000000000207111454601126700314030ustar00rootroot00000000000000{ "DST": "QUUX-V01-CS02-with-expander-SHAKE128-long-DST-111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111", "hash": "SHAKE128", "k": 128, "name": "expand_message_xof", "tests": [ { "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20", "len_in_bytes": "0x20", "msg": "", "msg_prime": "0020acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20", 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"uniform_bytes": "945373f0b3431a103333ba6a0a34f1efab2702efde41754c4cb1d5216d5b0a92a67458d968562bde7fa6310a83f53dda1383680a276a283438d58ceebfa7ab7ba72499d4a3eddc860595f63c93b1c5e823ea41fc490d938398a26db28f61857698553e93f0574eb8c5017bfed6249491f9976aaa8d23d9485339cc85ca329308" } ] } golang-github-cloudflare-circl-1.3.7/expander/testdata/expand_message_xof_SHAKE128_36.json000066400000000000000000000206151454601126700313220ustar00rootroot00000000000000{ "DST": "QUUX-V01-CS02-with-expander-SHAKE128", "hash": "SHAKE128", "k": 128, "name": "expand_message_xof", "tests": [ { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "len_in_bytes": "0x20", "msg": "", "msg_prime": "0020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "uniform_bytes": "86518c9cd86581486e9485aa74ab35ba150d1c75c88e26b7043e44e2acd735a2" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "len_in_bytes": "0x20", 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"uniform_bytes": "df3447cc5f3e9a77da10f819218ddf31342c310778e0e4ef72bbaecee786a4fe" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "len_in_bytes": "0x80", "msg": "", "msg_prime": "0080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "uniform_bytes": "7314ff1a155a2fb99a0171dc71b89ab6e3b2b7d59e38e64419b8b6294d03ffee42491f11370261f436220ef787f8f76f5b26bdcd850071920ce023f3ac46847744f4612b8714db8f5db83205b2e625d95afd7d7b4d3094d3bdde815f52850bb41ead9822e08f22cf41d615a303b0d9dde73263c049a7b9898208003a739a2e57" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "len_in_bytes": "0x80", "msg": "abc", "msg_prime": "6162630080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "uniform_bytes": "c952f0c8e529ca8824acc6a4cab0e782fc3648c563ddb00da7399f2ae35654f4860ec671db2356ba7baa55a34a9d7f79197b60ddae6e64768a37d699a78323496db3878c8d64d909d0f8a7de4927dcab0d3dbbc26cb20a49eceb0530b431cdf47bc8c0fa3e0d88f53b318b6739fbed7d7634974f1b5c386d6230c76260d5337a" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "len_in_bytes": "0x80", "msg": "abcdef0123456789", "msg_prime": "616263646566303132333435363738390080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "uniform_bytes": "19b65ee7afec6ac06a144f2d6134f08eeec185f1a890fe34e68f0e377b7d0312883c048d9b8a1d6ecc3b541cb4987c26f45e0c82691ea299b5e6889bbfe589153016d8131717ba26f07c3c14ffbef1f3eff9752e5b6183f43871a78219a75e7000fbac6a7072e2b83c790a3a5aecd9d14be79f9fd4fb180960a3772e08680495" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "len_in_bytes": "0x80", "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "uniform_bytes": "ca1b56861482b16eae0f4a26212112362fcc2d76dcc80c93c4182ed66c5113fe41733ed68be2942a3487394317f3379856f4822a611735e50528a60e7ade8ec8c71670fec6661e2c59a09ed36386513221688b35dc47e3c3111ee8c67ff49579089d661caa29db1ef10eb6eace575bf3dc9806e7c4016bd50f3c0e2a6481ee6d" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "len_in_bytes": "0x80", "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824", "uniform_bytes": "9d763a5ce58f65c91531b4100c7266d479a5d9777ba761693d052acd37d149e7ac91c796a10b919cd74a591a1e38719fb91b7203e2af31eac3bff7ead2c195af7d88b8bc0a8adf3d1e90ab9bed6ddc2b7f655dd86c730bdeaea884e73741097142c92f0e3fc1811b699ba593c7fbd81da288a29d423df831652e3a01a9374999" } ] } golang-github-cloudflare-circl-1.3.7/expander/testdata/expand_message_xof_SHAKE256_36.json000066400000000000000000000206151454601126700313240ustar00rootroot00000000000000{ "DST": "QUUX-V01-CS02-with-expander-SHAKE256", "hash": "SHAKE256", "k": 256, "name": "expand_message_xof", "tests": [ { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x20", "msg": "", "msg_prime": "0020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "2ffc05c48ed32b95d72e807f6eab9f7530dd1c2f013914c8fed38c5ccc15ad76" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x20", "msg": "abc", "msg_prime": "6162630020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "b39e493867e2767216792abce1f2676c197c0692aed061560ead251821808e07" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x20", "msg": "abcdef0123456789", "msg_prime": "616263646566303132333435363738390020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "245389cf44a13f0e70af8665fe5337ec2dcd138890bb7901c4ad9cfceb054b65" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x20", "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "719b3911821e6428a5ed9b8e600f2866bcf23c8f0515e52d6c6c019a03f16f0e" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x20", "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "9181ead5220b1963f1b5951f35547a5ea86a820562287d6ca4723633d17ccbbc" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x80", "msg": "", "msg_prime": "0080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "7a1361d2d7d82d79e035b8880c5a3c86c5afa719478c007d96e6c88737a3f631dd74a2c88df79a4cb5e5d9f7504957c70d669ec6bfedc31e01e2bacc4ff3fdf9b6a00b17cc18d9d72ace7d6b81c2e481b4f73f34f9a7505dccbe8f5485f3d20c5409b0310093d5d6492dea4e18aa6979c23c8ea5de01582e9689612afbb353df" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x80", "msg": "abc", "msg_prime": "6162630080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "a54303e6b172909783353ab05ef08dd435a558c3197db0c132134649708e0b9b4e34fb99b92a9e9e28fc1f1d8860d85897a8e021e6382f3eea10577f968ff6df6c45fe624ce65ca25932f679a42a404bc3681efe03fcd45ef73bb3a8f79ba784f80f55ea8a3c367408f30381299617f50c8cf8fbb21d0f1e1d70b0131a7b6fbe" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x80", "msg": "abcdef0123456789", "msg_prime": "616263646566303132333435363738390080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "e42e4d9538a189316e3154b821c1bafb390f78b2f010ea404e6ac063deb8c0852fcd412e098e231e43427bd2be1330bb47b4039ad57b30ae1fc94e34993b162ff4d695e42d59d9777ea18d3848d9d336c25d2acb93adcad009bcfb9cde12286df267ada283063de0bb1505565b2eb6c90e31c48798ecdc71a71756a9110ff373" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x80", "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "4ac054dda0a38a65d0ecf7afd3c2812300027c8789655e47aecf1ecc1a2426b17444c7482c99e5907afd9c25b991990490bb9c686f43e79b4471a23a703d4b02f23c669737a886a7ec28bddb92c3a98de63ebf878aa363a501a60055c048bea11840c4717beae7eee28c3cfa42857b3d130188571943a7bd747de831bd6444e0" }, { "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "len_in_bytes": "0x80", "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624", "uniform_bytes": "09afc76d51c2cccbc129c2315df66c2be7295a231203b8ab2dd7f95c2772c68e500bc72e20c602abc9964663b7a03a389be128c56971ce81001a0b875e7fd17822db9d69792ddf6a23a151bf470079c518279aef3e75611f8f828994a9988f4a8a256ddb8bae161e658d5a2a09bcfe839c6396dc06ee5c8ff3c22d3b1f9deb7e" } ] } golang-github-cloudflare-circl-1.3.7/go.mod000066400000000000000000000002311454601126700205710ustar00rootroot00000000000000module github.com/cloudflare/circl go 1.19 require ( github.com/bwesterb/go-ristretto v1.2.3 golang.org/x/crypto v0.17.0 golang.org/x/sys v0.15.0 ) golang-github-cloudflare-circl-1.3.7/go.sum000066400000000000000000000007571454601126700206330ustar00rootroot00000000000000github.com/bwesterb/go-ristretto v1.2.3 h1:1w53tCkGhCQ5djbat3+MH0BAQ5Kfgbt56UZQ/JMzngw= github.com/bwesterb/go-ristretto v1.2.3/go.mod h1:fUIoIZaG73pV5biE2Blr2xEzDoMj7NFEuV9ekS419A0= golang.org/x/crypto v0.17.0 h1:r8bRNjWL3GshPW3gkd+RpvzWrZAwPS49OmTGZ/uhM4k= golang.org/x/crypto v0.17.0/go.mod h1:gCAAfMLgwOJRpTjQ2zCCt2OcSfYMTeZVSRtQlPC7Nq4= golang.org/x/sys v0.15.0 h1:h48lPFYpsTvQJZF4EKyI4aLHaev3CxivZmv7yZig9pc= golang.org/x/sys v0.15.0/go.mod h1:/VUhepiaJMQUp4+oa/7Zr1D23ma6VTLIYjOOTFZPUcA= golang-github-cloudflare-circl-1.3.7/group/000077500000000000000000000000001454601126700206235ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/group/group.go000066400000000000000000000137651454601126700223220ustar00rootroot00000000000000// Package group provides prime-order groups based on elliptic curves. package group import ( "encoding" "errors" "io" "math/big" ) // Params stores the size in bytes of elements and scalars. type Params struct { ElementLength uint // Length in bytes of an element. CompressedElementLength uint // Length in bytes of a compressed element. ScalarLength uint // Length in bytes of a scalar. } // Group represents an additive prime-order group based on elliptic curves. type Group interface { Params() *Params // Params returns parameters for the group // Creates an element of the group set to the identity of the group. NewElement() Element // Creates a scalar of the group set to zero. NewScalar() Scalar // Creates an element of the group set to the identity of the group. Identity() Element // Creates an element of the group set to the generator of the group. Generator() Element // Returns a scalar set to the group order. Order() Scalar // RandomElement creates an element chosen at random (using randomness // from rnd) from the set of group elements. Use crypto/rand.Reader as // a cryptographically secure random number generator RandomElement(rnd io.Reader) Element // RandomScalar creates a scalar chosen at random (using randomness // from rnd) from the set of group scalars. Use crypto/rand.Reader as // a cryptographically secure random number generator RandomScalar(rnd io.Reader) Scalar // RandomNonZeroScalar creates a scalar chosen at random (using randomness // from rnd) from the set of group scalars. Use crypto/rand.Reader as // a cryptographically secure random number generator. It is guaranteed // the scalar is not zero. RandomNonZeroScalar(io.Reader) Scalar // HashToElement hashes a message (msg) using a domain separation string // (dst) producing a group element with uniform distribution. HashToElement(msg, dst []byte) Element // HashToElementNonUniform hashes a message (msg) using a domain separation // string (dst) producing a group element with nonuniform distribution. HashToElementNonUniform(msg, dst []byte) Element // HashToScalar hashes a message (msg) using a domain separation string // (dst) producing a group scalar with uniform distribution. HashToScalar(msg, dst []byte) Scalar } // Element represents an element of a prime-order group. type Element interface { // Returns the group that the element belongs to. Group() Group // Set the receiver to x, and returns the receiver. Set(x Element) Element // Copy returns a new element equal to the receiver. Copy() Element // IsIdentity returns true if the receiver is the identity element of the // group. IsIdentity() bool // IsEqual returns true if the receiver is equal to x. IsEqual(x Element) bool // CMov sets the receiver to x if b=1; the receiver is unmodified if b=0; // otherwise panics if b is not 0 or 1. In all the cases, it returns the // receiver. CMov(b int, x Element) Element // CSelect sets the receiver to x if b=1; sets the receiver to y if b=0; // otherwise panics if b is not 0 or 1. In all the cases, it returns the // receiver. CSelect(b int, x, y Element) Element // Add sets the receiver to x + y, and returns the receiver. Add(x, y Element) Element // Dbl sets the receiver to 2 * x, and returns the receiver. Dbl(x Element) Element // Neg sets the receiver to -x, and returns the receiver. Neg(x Element) Element // Mul sets the receiver to s * x, and returns the receiver. Mul(x Element, s Scalar) Element // MulGen sets the receiver to s * Generator(), and returns the receiver. MulGen(s Scalar) Element // BinaryMarshaler returns a byte representation of the element. encoding.BinaryMarshaler // BinaryUnmarshaler recovers an element from a byte representation // produced either by encoding.BinaryMarshaler or MarshalBinaryCompress. encoding.BinaryUnmarshaler // MarshalBinaryCompress returns a byte representation of an element in a // compact form whenever the group supports it; otherwise, returns the // same byte representation produced by encoding.BinaryMarshaler. MarshalBinaryCompress() ([]byte, error) } // Scalar represents a scalar of a prime-order group. type Scalar interface { // Returns the group that the scalar belongs to. Group() Group // Set the receiver to x, and returns the receiver. Set(x Scalar) Scalar // Copy returns a new scalar equal to the receiver. Copy() Scalar // IsZero returns true if the receiver is equal to zero. IsZero() bool // IsEqual returns true if the receiver is equal to x. IsEqual(x Scalar) bool // SetUint64 sets the receiver to x, and returns the receiver. SetUint64(x uint64) Scalar // SetBigInt sets the receiver to x, and returns the receiver. // Warning: operations on big.Int are not constant time. Do not use them // for cryptography unless you're sure it's safe in your use-case. SetBigInt(b *big.Int) Scalar // CMov sets the receiver to x if b=1; the receiver is unmodified if b=0; // otherwise panics if b is not 0 or 1. In all the cases, it returns the // receiver. CMov(b int, x Scalar) Scalar // CSelect sets the receiver to x if b=1; sets the receiver to y if b=0; // otherwise panics if b is not 0 or 1. In all the cases, it returns the // receiver. CSelect(b int, x, y Scalar) Scalar // Add sets the receiver to x + y, and returns the receiver. Add(x, y Scalar) Scalar // Sub sets the receiver to x - y, and returns the receiver. Sub(x, y Scalar) Scalar // Mul sets the receiver to x * y, and returns the receiver. Mul(x, y Scalar) Scalar // Neg sets the receiver to -x, and returns the receiver. Neg(x Scalar) Scalar // Inv sets the receiver to 1/x, and returns the receiver. Inv(x Scalar) Scalar // BinaryMarshaler returns a byte representation of the scalar. encoding.BinaryMarshaler // BinaryUnmarshaler recovers a scalar from a byte representation produced // by encoding.BinaryMarshaler. encoding.BinaryUnmarshaler } var ( ErrType = errors.New("group: type mismatch") ErrUnmarshal = errors.New("group: error unmarshaling") ErrSelector = errors.New("group: selector must be 0 or 1") ) golang-github-cloudflare-circl-1.3.7/group/group_test.go000066400000000000000000000215301454601126700233460ustar00rootroot00000000000000package group_test import ( "bytes" "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/internal/test" ) var allGroups = []group.Group{ group.P256, group.P384, group.P521, group.Ristretto255, } func TestGroup(t *testing.T) { const testTimes = 1 << 7 for _, g := range allGroups { g := g n := g.(fmt.Stringer).String() t.Run(n+"/Add", func(tt *testing.T) { testAdd(tt, testTimes, g) }) t.Run(n+"/Neg", func(tt *testing.T) { testNeg(tt, testTimes, g) }) t.Run(n+"/Mul", func(tt *testing.T) { testMul(tt, testTimes, g) }) t.Run(n+"/MulGen", func(tt *testing.T) { testMulGen(tt, testTimes, g) }) t.Run(n+"/CMov", func(tt *testing.T) { testCMov(tt, testTimes, g) }) t.Run(n+"/CSelect", func(tt *testing.T) { testCSelect(tt, testTimes, g) }) t.Run(n+"/Order", func(tt *testing.T) { testOrder(tt, testTimes, g) }) t.Run(n+"/Marshal", func(tt *testing.T) { testMarshal(tt, testTimes, g) }) t.Run(n+"/Scalar", func(tt *testing.T) { testScalar(tt, testTimes, g) }) } } func testAdd(t *testing.T, testTimes int, g group.Group) { Q := g.NewElement() for i := 0; i < testTimes; i++ { P := g.RandomElement(rand.Reader) got := Q.Dbl(P).Dbl(Q).Dbl(Q).Dbl(Q) // Q = 16P R := g.Identity() for j := 0; j < 16; j++ { R.Add(R, P) } want := R // R = 16P = P+P...+P if !got.IsEqual(want) { test.ReportError(t, got, want, P) } } } func testNeg(t *testing.T, testTimes int, g group.Group) { Q := g.NewElement() for i := 0; i < testTimes; i++ { P := g.RandomElement(rand.Reader) Q.Neg(P) Q.Add(Q, P) got := Q.IsIdentity() want := true if got != want { test.ReportError(t, got, want, P) } } } func testMul(t *testing.T, testTimes int, g group.Group) { Q := g.NewElement() kInv := g.NewScalar() for i := 0; i < testTimes; i++ { P := g.RandomElement(rand.Reader) k := g.RandomScalar(rand.Reader) kInv.Inv(k) Q.Mul(P, k) Q.Mul(Q, kInv) got := P want := Q if !got.IsEqual(want) { test.ReportError(t, got, want, P, k) } } } func testMulGen(t *testing.T, testTimes int, g group.Group) { G := g.Generator() P := g.NewElement() Q := g.NewElement() for i := 0; i < testTimes; i++ { k := g.RandomScalar(rand.Reader) P.Mul(G, k) Q.MulGen(k) got := P want := Q if !got.IsEqual(want) { test.ReportError(t, got, want, P, k) } } } func testCMov(t *testing.T, testTimes int, g group.Group) { P := g.RandomElement(rand.Reader) Q := g.RandomElement(rand.Reader) err := test.CheckPanic(func() { P.CMov(0, Q) }) test.CheckIsErr(t, err, "shouldn't fail with 0") err = test.CheckPanic(func() { P.CMov(1, Q) }) test.CheckIsErr(t, err, "shouldn't fail with 1") err = test.CheckPanic(func() { P.CMov(2, Q) }) test.CheckNoErr(t, err, "should fail with dif 0,1") for i := 0; i < testTimes; i++ { P = g.RandomElement(rand.Reader) Q = g.RandomElement(rand.Reader) want := P.Copy() got := P.CMov(0, Q) if !got.IsEqual(want) { test.ReportError(t, got, want) } want = Q.Copy() got = P.CMov(1, Q) if !got.IsEqual(want) { test.ReportError(t, got, want) } } } func testCSelect(t *testing.T, testTimes int, g group.Group) { P := g.RandomElement(rand.Reader) Q := g.RandomElement(rand.Reader) R := g.RandomElement(rand.Reader) err := test.CheckPanic(func() { P.CSelect(0, Q, R) }) test.CheckIsErr(t, err, "shouldn't fail with 0") err = test.CheckPanic(func() { P.CSelect(1, Q, R) }) test.CheckIsErr(t, err, "shouldn't fail with 1") err = test.CheckPanic(func() { P.CSelect(2, Q, R) }) test.CheckNoErr(t, err, "should fail with dif 0,1") for i := 0; i < testTimes; i++ { P = g.RandomElement(rand.Reader) Q = g.RandomElement(rand.Reader) R = g.RandomElement(rand.Reader) want := R.Copy() got := P.CSelect(0, Q, R) if !got.IsEqual(want) { test.ReportError(t, got, want) } want = Q.Copy() got = P.CSelect(1, Q, R) if !got.IsEqual(want) { test.ReportError(t, got, want) } } } func testOrder(t *testing.T, testTimes int, g group.Group) { Q := g.NewElement() order := g.Order() for i := 0; i < testTimes; i++ { P := g.RandomElement(rand.Reader) Q.Mul(P, order) got := Q.IsIdentity() want := true if got != want { test.ReportError(t, got, want, P) } } } func isZero(b []byte) bool { for i := 0; i < len(b); i++ { if b[i] != 0x00 { return false } } return true } func testMarshal(t *testing.T, testTimes int, g group.Group) { params := g.Params() I := g.Identity() got, err := I.MarshalBinary() test.CheckNoErr(t, err, "error on MarshalBinary") if !isZero(got) { test.ReportError(t, got, "Non-zero identity") } if l := uint(len(got)); !(l == 1 || l == params.ElementLength) { test.ReportError(t, l, params.ElementLength) } got, err = I.MarshalBinaryCompress() test.CheckNoErr(t, err, "error on MarshalBinaryCompress") if !isZero(got) { test.ReportError(t, got, "Non-zero identity") } if l := uint(len(got)); !(l == 1 || l == params.CompressedElementLength) { test.ReportError(t, l, params.CompressedElementLength) } II := g.NewElement() err = II.UnmarshalBinary(got) if err != nil || !I.IsEqual(II) { test.ReportError(t, I, II) } got1 := g.NewElement() got2 := g.NewElement() for i := 0; i < testTimes; i++ { x := g.RandomElement(rand.Reader) enc1, err1 := x.MarshalBinary() enc2, err2 := x.MarshalBinaryCompress() test.CheckNoErr(t, err1, "error on marshalling") test.CheckNoErr(t, err2, "error on marshalling compress") err1 = got1.UnmarshalBinary(enc1) err2 = got2.UnmarshalBinary(enc2) test.CheckNoErr(t, err1, "error on unmarshalling") test.CheckNoErr(t, err2, "error on unmarshalling compress") if !x.IsEqual(got1) { test.ReportError(t, got1, x) } if !x.IsEqual(got2) { test.ReportError(t, got2, x) } if l := uint(len(enc1)); l != params.ElementLength { test.ReportError(t, l, params.ElementLength) } if l := uint(len(enc2)); l != params.CompressedElementLength { test.ReportError(t, l, params.CompressedElementLength) } } } func testScalar(t *testing.T, testTimes int, g group.Group) { a := g.RandomScalar(rand.Reader) b := g.RandomScalar(rand.Reader) c := g.NewScalar() d := g.NewScalar() e := g.NewScalar() f := g.NewScalar() one := g.NewScalar() one.SetUint64(1) params := g.Params() err := test.CheckPanic(func() { a.CMov(0, b) }) test.CheckIsErr(t, err, "shouldn't fail with 0") err = test.CheckPanic(func() { a.CMov(1, b) }) test.CheckIsErr(t, err, "shouldn't fail with 1") err = test.CheckPanic(func() { a.CMov(2, b) }) test.CheckNoErr(t, err, "should fail with dif 0,1") err = test.CheckPanic(func() { a.CSelect(0, b, c) }) test.CheckIsErr(t, err, "shouldn't fail with 0") err = test.CheckPanic(func() { a.CSelect(1, b, c) }) test.CheckIsErr(t, err, "shouldn't fail with 1") err = test.CheckPanic(func() { a.CSelect(2, b, c) }) test.CheckNoErr(t, err, "should fail with dif 0,1") for i := 0; i < testTimes; i++ { a = g.RandomScalar(rand.Reader) b = g.RandomScalar(rand.Reader) c.Add(a, b) d.Sub(a, b) e.Mul(c, d) e.Add(e, one) c.Mul(a, a) d.Mul(b, b) d.Neg(d) f.Add(c, d) f.Add(f, one) enc1, err1 := e.MarshalBinary() enc2, err2 := f.MarshalBinary() if err1 != nil || err2 != nil || !bytes.Equal(enc1, enc2) { test.ReportError(t, enc1, enc2, a, b) } if l := uint(len(enc1)); l != params.ScalarLength { test.ReportError(t, l, params.ScalarLength) } want := c.Copy() got := c.CMov(0, a) if !got.IsEqual(want) { test.ReportError(t, got, want) } want = b.Copy() got = d.CMov(1, b) if !got.IsEqual(want) { test.ReportError(t, got, want) } want = b.Copy() got = e.CSelect(0, a, b) if !got.IsEqual(want) { test.ReportError(t, got, want) } want = a.Copy() got = f.CSelect(1, a, b) if !got.IsEqual(want) { test.ReportError(t, got, want) } } c.Inv(a) c.Mul(c, a) c.Sub(c, one) if !c.IsZero() { test.ReportError(t, c, one, a) } } func BenchmarkElement(b *testing.B) { for _, g := range allGroups { x := g.RandomElement(rand.Reader) y := g.RandomElement(rand.Reader) n := g.RandomScalar(rand.Reader) name := g.(fmt.Stringer).String() b.Run(name+"/Add", func(b *testing.B) { for i := 0; i < b.N; i++ { x.Add(x, y) } }) b.Run(name+"/Dbl", func(b *testing.B) { for i := 0; i < b.N; i++ { x.Dbl(x) } }) b.Run(name+"/Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { y.Mul(x, n) } }) b.Run(name+"/MulGen", func(b *testing.B) { for i := 0; i < b.N; i++ { x.MulGen(n) } }) } } func BenchmarkScalar(b *testing.B) { for _, g := range allGroups { x := g.RandomScalar(rand.Reader) y := g.RandomScalar(rand.Reader) name := g.(fmt.Stringer).String() b.Run(name+"/Add", func(b *testing.B) { for i := 0; i < b.N; i++ { x.Add(x, y) } }) b.Run(name+"/Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { x.Mul(x, y) } }) b.Run(name+"/Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { y.Inv(x) } }) } } golang-github-cloudflare-circl-1.3.7/group/hash.go000066400000000000000000000006541454601126700221020ustar00rootroot00000000000000package group import ( "math/big" "github.com/cloudflare/circl/expander" ) // HashToField generates a set of elements {u1,..., uN} = Hash(b) where each // u in GF(p) and L is the security parameter. func HashToField(u []big.Int, b []byte, e expander.Expander, p *big.Int, L uint) { count := uint(len(u)) bytes := e.Expand(b, count*L) for i := range u { j := uint(i) * L u[i].Mod(u[i].SetBytes(bytes[j:j+L]), p) } } golang-github-cloudflare-circl-1.3.7/group/hash_test.go000066400000000000000000000052511454601126700231370ustar00rootroot00000000000000package group_test import ( "encoding/hex" "encoding/json" "fmt" "os" "path/filepath" "testing" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/internal/test" ) func TestHashToElement(t *testing.T) { fileNames, err := filepath.Glob("./testdata/P*.json") if err != nil { t.Fatal(err) } for _, fileName := range fileNames { f, err := os.Open(fileName) if err != nil { t.Fatal(err) } dec := json.NewDecoder(f) var v vectorSuite err = dec.Decode(&v) if err != nil { t.Fatal(err) } f.Close() t.Run(v.Ciphersuite, func(t *testing.T) { testHashing(t, &v) }) } } func testHashing(t *testing.T, vs *vectorSuite) { var G group.Group switch vs.Ciphersuite[0:4] { case "P256": G = group.P256 case "P384": G = group.P384 case "P521": G = group.P521 default: t.Fatal("non supported suite") } hashFunc := G.HashToElement if !vs.RandomOracle { hashFunc = G.HashToElementNonUniform } want := G.NewElement() for i, v := range vs.Vectors { got := hashFunc([]byte(v.Msg), []byte(vs.Dst)) err := want.UnmarshalBinary(v.P.toBytes()) if err != nil { t.Fatal(err) } if !got.IsEqual(want) { test.ReportError(t, got, want, i) } } } type vectorSuite struct { L string `json:"L"` Z string `json:"Z"` Ciphersuite string `json:"ciphersuite"` Curve string `json:"curve"` Dst string `json:"dst"` Expand string `json:"expand"` Field struct { M string `json:"m"` P string `json:"p"` } `json:"field"` Hash string `json:"hash"` K string `json:"k"` Map struct { Name string `json:"name"` } `json:"map"` RandomOracle bool `json:"randomOracle"` Vectors []vector `json:"vectors"` } type point struct { X string `json:"x"` Y string `json:"y"` } func (p point) toBytes() []byte { x, err := hex.DecodeString(p.X[2:]) if err != nil { panic(err) } y, err := hex.DecodeString(p.Y[2:]) if err != nil { panic(err) } return append(append([]byte{0x04}, x...), y...) } type vector struct { P point `json:"P"` Q0 point `json:"Q0,omitempty"` Q1 point `json:"Q1,omitempty"` Q point `json:"Q,omitempty"` Msg string `json:"msg"` U []string `json:"u"` } func BenchmarkHash(b *testing.B) { for _, g := range allGroups { g := g name := g.(fmt.Stringer).String() b.Run(name+"/HashToElement", func(b *testing.B) { for i := 0; i < b.N; i++ { g.HashToElement(nil, nil) } }) b.Run(name+"/HashToElementNonUniform", func(b *testing.B) { for i := 0; i < b.N; i++ { g.HashToElementNonUniform(nil, nil) } }) b.Run(name+"/HashToScalar", func(b *testing.B) { for i := 0; i < b.N; i++ { g.HashToScalar(nil, nil) } }) } } golang-github-cloudflare-circl-1.3.7/group/ristretto255.go000066400000000000000000000146701454601126700234550ustar00rootroot00000000000000package group import ( "crypto" _ "crypto/sha512" "fmt" "io" "math/big" r255 "github.com/bwesterb/go-ristretto" "github.com/cloudflare/circl/expander" "github.com/cloudflare/circl/internal/conv" ) // Ristretto255 is a quotient group generated from the edwards25519 curve. var Ristretto255 Group = ristrettoGroup{} type ristrettoGroup struct{} func (g ristrettoGroup) String() string { return "ristretto255" } func (g ristrettoGroup) Params() *Params { return &Params{32, 32, 32} } type ristrettoElement struct { p r255.Point } type ristrettoScalar struct { s r255.Scalar } func (g ristrettoGroup) NewElement() Element { return g.Identity() } func (g ristrettoGroup) NewScalar() Scalar { return &ristrettoScalar{ s: r255.Scalar{}, } } func (g ristrettoGroup) Identity() Element { var zero r255.Point zero.SetZero() return &ristrettoElement{ p: zero, } } func (g ristrettoGroup) Generator() Element { var base r255.Point base.SetBase() return &ristrettoElement{ p: base, } } func (g ristrettoGroup) Order() Scalar { q := r255.Scalar{ 0x5cf5d3ed, 0x5812631a, 0xa2f79cd6, 0x14def9de, 0x00000000, 0x00000000, 0x00000000, 0x10000000, } return &ristrettoScalar{ s: q, } } func (g ristrettoGroup) RandomElement(r io.Reader) Element { var x r255.Point x.Rand() return &ristrettoElement{ p: x, } } func (g ristrettoGroup) RandomScalar(io.Reader) Scalar { var x r255.Scalar x.Rand() return &ristrettoScalar{ s: x, } } func (g ristrettoGroup) RandomNonZeroScalar(io.Reader) Scalar { var s r255.Scalar for { s.Rand() if s.IsNonZeroI() == 1 { return &ristrettoScalar{s} } } } func (g ristrettoGroup) HashToElementNonUniform(b, dst []byte) Element { return g.HashToElement(b, dst) } func (g ristrettoGroup) HashToElement(msg, dst []byte) Element { // Compliant with draft-irtf-cfrg-hash-to-curve. // Appendix B - Hashing to ristretto255 // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-14#appendix-B // SuiteID: ristretto255_XMD:SHA-512_R255MAP_RO_ var buf [32]byte xmd := expander.NewExpanderMD(crypto.SHA512, dst) uniformBytes := xmd.Expand(msg, 64) copy(buf[:], uniformBytes[:32]) p0 := new(r255.Point).SetElligator(&buf) copy(buf[:], uniformBytes[32:]) p1 := new(r255.Point).SetElligator(&buf) p0.Add(p0, p1) return &ristrettoElement{*p0} } func (g ristrettoGroup) HashToScalar(msg, dst []byte) Scalar { // Adapted to be compliant with draft-irtf-cfrg-voprf // Section 4.1.1 - OPRF(ristretto255, SHA-512) // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-voprf-09#section-4.1.1 var uniformBytes [64]byte xmd := expander.NewExpanderMD(crypto.SHA512, dst) copy(uniformBytes[:], xmd.Expand(msg, 64)) s := g.NewScalar() s.(*ristrettoScalar).s.SetReduced(&uniformBytes) return s } func (e *ristrettoElement) Group() Group { return Ristretto255 } func (e *ristrettoElement) String() string { return fmt.Sprintf("%x", e.p.Bytes()) } func (e *ristrettoElement) IsIdentity() bool { var zero r255.Point zero.SetZero() return e.p.Equals(&zero) } func (e *ristrettoElement) IsEqual(x Element) bool { return e.p.Equals(&x.(*ristrettoElement).p) } func (e *ristrettoElement) Set(x Element) Element { e.p.Set(&x.(*ristrettoElement).p) return e } func (e *ristrettoElement) Copy() Element { return &ristrettoElement{*new(r255.Point).Set(&e.p)} } func (e *ristrettoElement) CMov(v int, x Element) Element { if !(v == 0 || v == 1) { panic(ErrSelector) } e.p.ConditionalSet(&x.(*ristrettoElement).p, int32(v)) return e } func (e *ristrettoElement) CSelect(v int, x Element, y Element) Element { if !(v == 0 || v == 1) { panic(ErrSelector) } e.p.ConditionalSet(&x.(*ristrettoElement).p, int32(v)) e.p.ConditionalSet(&y.(*ristrettoElement).p, int32(1-v)) return e } func (e *ristrettoElement) Add(x Element, y Element) Element { e.p.Add(&x.(*ristrettoElement).p, &y.(*ristrettoElement).p) return e } func (e *ristrettoElement) Dbl(x Element) Element { return e.Add(x, x) } func (e *ristrettoElement) Neg(x Element) Element { e.p.Neg(&x.(*ristrettoElement).p) return e } func (e *ristrettoElement) Mul(x Element, y Scalar) Element { e.p.ScalarMult(&x.(*ristrettoElement).p, &y.(*ristrettoScalar).s) return e } func (e *ristrettoElement) MulGen(x Scalar) Element { e.p.ScalarMultBase(&x.(*ristrettoScalar).s) return e } func (e *ristrettoElement) MarshalBinaryCompress() ([]byte, error) { return e.p.MarshalBinary() } func (e *ristrettoElement) MarshalBinary() ([]byte, error) { return e.p.MarshalBinary() } func (e *ristrettoElement) UnmarshalBinary(data []byte) error { return e.p.UnmarshalBinary(data) } func (s *ristrettoScalar) Group() Group { return Ristretto255 } func (s *ristrettoScalar) String() string { return conv.BytesLe2Hex(s.s.Bytes()) } func (s *ristrettoScalar) SetUint64(n uint64) Scalar { s.s.SetUint64(n); return s } func (s *ristrettoScalar) SetBigInt(x *big.Int) Scalar { s.s.SetBigInt(x); return s } func (s *ristrettoScalar) IsZero() bool { return s.s.IsNonZeroI() == 0 } func (s *ristrettoScalar) IsEqual(x Scalar) bool { return s.s.Equals(&x.(*ristrettoScalar).s) } func (s *ristrettoScalar) Set(x Scalar) Scalar { s.s.Set(&x.(*ristrettoScalar).s) return s } func (s *ristrettoScalar) Copy() Scalar { return &ristrettoScalar{*new(r255.Scalar).Set(&s.s)} } func (s *ristrettoScalar) CMov(v int, x Scalar) Scalar { if !(v == 0 || v == 1) { panic(ErrSelector) } s.s.ConditionalSet(&x.(*ristrettoScalar).s, int32(v)) return s } func (s *ristrettoScalar) CSelect(v int, x Scalar, y Scalar) Scalar { if !(v == 0 || v == 1) { panic(ErrSelector) } s.s.ConditionalSet(&x.(*ristrettoScalar).s, int32(v)) s.s.ConditionalSet(&y.(*ristrettoScalar).s, int32(1-v)) return s } func (s *ristrettoScalar) Add(x Scalar, y Scalar) Scalar { s.s.Add(&x.(*ristrettoScalar).s, &y.(*ristrettoScalar).s) return s } func (s *ristrettoScalar) Sub(x Scalar, y Scalar) Scalar { s.s.Sub(&x.(*ristrettoScalar).s, &y.(*ristrettoScalar).s) return s } func (s *ristrettoScalar) Mul(x Scalar, y Scalar) Scalar { s.s.Mul(&x.(*ristrettoScalar).s, &y.(*ristrettoScalar).s) return s } func (s *ristrettoScalar) Neg(x Scalar) Scalar { s.s.Neg(&x.(*ristrettoScalar).s) return s } func (s *ristrettoScalar) Inv(x Scalar) Scalar { s.s.Inverse(&x.(*ristrettoScalar).s) return s } func (s *ristrettoScalar) MarshalBinary() ([]byte, error) { return s.s.MarshalBinary() } func (s *ristrettoScalar) UnmarshalBinary(data []byte) error { return s.s.UnmarshalBinary(data) } golang-github-cloudflare-circl-1.3.7/group/ristretto255_test.go000066400000000000000000000123611454601126700245070ustar00rootroot00000000000000package group import ( "bytes" "crypto/rand" "encoding/hex" "testing" ) // https://tools.ietf.org/html/draft-irtf-cfrg-ristretto255-decaf448-00#appendix-A.1 func TestGeneratorMultiples(t *testing.T) { encVec := []string{ "0000000000000000000000000000000000000000000000000000000000000000", "e2f2ae0a6abc4e71a884a961c500515f58e30b6aa582dd8db6a65945e08d2d76", "6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919", "94741f5d5d52755ece4f23f044ee27d5d1ea1e2bd196b462166b16152a9d0259", "da80862773358b466ffadfe0b3293ab3d9fd53c5ea6c955358f568322daf6a57", "e882b131016b52c1d3337080187cf768423efccbb517bb495ab812c4160ff44e", "f64746d3c92b13050ed8d80236a7f0007c3b3f962f5ba793d19a601ebb1df403", "44f53520926ec81fbd5a387845beb7df85a96a24ece18738bdcfa6a7822a176d", "903293d8f2287ebe10e2374dc1a53e0bc887e592699f02d077d5263cdd55601c", "02622ace8f7303a31cafc63f8fc48fdc16e1c8c8d234b2f0d6685282a9076031", "20706fd788b2720a1ed2a5dad4952b01f413bcf0e7564de8cdc816689e2db95f", "bce83f8ba5dd2fa572864c24ba1810f9522bc6004afe95877ac73241cafdab42", "e4549ee16b9aa03099ca208c67adafcafa4c3f3e4e5303de6026e3ca8ff84460", "aa52e000df2e16f55fb1032fc33bc42742dad6bd5a8fc0be0167436c5948501f", "46376b80f409b29dc2b5f6f0c52591990896e5716f41477cd30085ab7f10301e", "e0c418f7c8d9c4cdd7395b93ea124f3ad99021bb681dfc3302a9d99a2e53e64e", } g := Ristretto255 base := g.NewElement() encBase, err := hex.DecodeString(encVec[0]) if err != nil { t.Fatal("DecodeString") } err = base.UnmarshalBinary(encBase) if err != nil { t.Fatal("UnmarshalBinary") } if !base.IsIdentity() { t.Fatal("Base element is not identity") } for i := 1; i < len(encVec); i++ { base.Add(base, g.Generator()) baseEnc, err := base.MarshalBinary() if err != nil { t.Fatalf("MarshalBinary %d", i) } if hex.EncodeToString(baseEnc) != encVec[i] { t.Fatalf("Multiple %d mismatch", i) } } } // https://tools.ietf.org/html/draft-irtf-cfrg-ristretto255-decaf448-00#appendix-A.2 func TestInvalidEncodings(t *testing.T) { encVec := []string{ // Non-canonical field encodings. "00ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", // The internal ristretto255 implementation ignores the MSB, so the following two encodings fail. // "f3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", // "edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", // Negative field elements. "0100000000000000000000000000000000000000000000000000000000000000", "01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", "ed57ffd8c914fb201471d1c3d245ce3c746fcbe63a3679d51b6a516ebebe0e20", "c34c4e1826e5d403b78e246e88aa051c36ccf0aafebffe137d148a2bf9104562", "c940e5a4404157cfb1628b108db051a8d439e1a421394ec4ebccb9ec92a8ac78", "47cfc5497c53dc8e61c91d17fd626ffb1c49e2bca94eed052281b510b1117a24", "f1c6165d33367351b0da8f6e4511010c68174a03b6581212c71c0e1d026c3c72", "87260f7a2f12495118360f02c26a470f450dadf34a413d21042b43b9d93e1309", // Non-square x^2. "26948d35ca62e643e26a83177332e6b6afeb9d08e4268b650f1f5bbd8d81d371", "4eac077a713c57b4f4397629a4145982c661f48044dd3f96427d40b147d9742f", "de6a7b00deadc788eb6b6c8d20c0ae96c2f2019078fa604fee5b87d6e989ad7b", "bcab477be20861e01e4a0e295284146a510150d9817763caf1a6f4b422d67042", "2a292df7e32cababbd9de088d1d1abec9fc0440f637ed2fba145094dc14bea08", "f4a9e534fc0d216c44b218fa0c42d99635a0127ee2e53c712f70609649fdff22", "8268436f8c4126196cf64b3c7ddbda90746a378625f9813dd9b8457077256731", "2810e5cbc2cc4d4eece54f61c6f69758e289aa7ab440b3cbeaa21995c2f4232b", // Negative xy value. "3eb858e78f5a7254d8c9731174a94f76755fd3941c0ac93735c07ba14579630e", "a45fdc55c76448c049a1ab33f17023edfb2be3581e9c7aade8a6125215e04220", "d483fe813c6ba647ebbfd3ec41adca1c6130c2beeee9d9bf065c8d151c5f396e", "8a2e1d30050198c65a54483123960ccc38aef6848e1ec8f5f780e8523769ba32", "32888462f8b486c68ad7dd9610be5192bbeaf3b443951ac1a8118419d9fa097b", "227142501b9d4355ccba290404bde41575b037693cef1f438c47f8fbf35d1165", "5c37cc491da847cfeb9281d407efc41e15144c876e0170b499a96a22ed31e01e", "445425117cb8c90edcbc7c1cc0e74f747f2c1efa5630a967c64f287792a48a4b", // s = -1, which causes y = 0. "ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", } for i, enc := range encVec { raw, err := hex.DecodeString(enc) if err != nil { t.Fatal("DecodeString") } err = Ristretto255.NewElement().UnmarshalBinary(raw) if err == nil { t.Fatalf("Decode succeeded for vector %d: %v", i, enc) } } } func TestRistrettoElGamal(t *testing.T) { g := Ristretto255 pk := g.NewElement() sk := g.RandomScalar(rand.Reader) pk.MulGen(sk) // El'Gamal encrypt a random element p into a ciphertext-pair (c1,c2) p := g.RandomElement(rand.Reader) r := g.RandomScalar(rand.Reader) c2 := g.NewElement() c1 := g.NewElement() c2.MulGen(r) c1.Mul(pk, r) c1.Add(c1, p) // Decrypt (c1,c2) back to p b := g.NewElement() p2 := g.NewElement() b.Mul(c2, sk) p2.Add(c1, b.Neg(b)) if !p.IsEqual(p2) { t.Fatal("Encryption/decryption failed") } pEnc, err := p.MarshalBinary() if err != nil { t.Fatal("MarshalBinary") } p2Enc, err := p2.MarshalBinary() if err != nil { t.Fatal("MarshalBinary") } if !bytes.Equal(pEnc, p2Enc) { t.Fatal("Unequal encodings") } } golang-github-cloudflare-circl-1.3.7/group/short.go000066400000000000000000000277371454601126700223310ustar00rootroot00000000000000package group import ( "crypto" "crypto/elliptic" _ "crypto/sha256" _ "crypto/sha512" "crypto/subtle" "fmt" "io" "math/big" "github.com/cloudflare/circl/ecc/p384" "github.com/cloudflare/circl/expander" ) var ( // P256 is the group generated by P-256 elliptic curve. P256 Group = wG{elliptic.P256()} // P384 is the group generated by P-384 elliptic curve. P384 Group = wG{p384.P384()} // P521 is the group generated by P-521 elliptic curve. P521 Group = wG{elliptic.P521()} ) type wG struct { c elliptic.Curve } func (g wG) String() string { return g.c.Params().Name } func (g wG) NewElement() Element { return g.zeroElement() } func (g wG) NewScalar() Scalar { return g.zeroScalar() } func (g wG) Identity() Element { return g.zeroElement() } func (g wG) zeroScalar() *wScl { return &wScl{g, make([]byte, (g.c.Params().BitSize+7)/8)} } func (g wG) zeroElement() *wElt { return &wElt{g, new(big.Int), new(big.Int)} } func (g wG) Generator() Element { return &wElt{g, g.c.Params().Gx, g.c.Params().Gy} } func (g wG) Order() Scalar { s := &wScl{g, nil}; s.fromBig(g.c.Params().N); return s } func (g wG) RandomElement(rd io.Reader) Element { b := make([]byte, (g.c.Params().BitSize+7)/8) if n, err := io.ReadFull(rd, b); err != nil || n != len(b) { panic(err) } return g.HashToElement(b, nil) } func (g wG) RandomScalar(rd io.Reader) Scalar { b := make([]byte, (g.c.Params().BitSize+7)/8) if n, err := io.ReadFull(rd, b); err != nil || n != len(b) { panic(err) } return g.HashToScalar(b, nil) } func (g wG) RandomNonZeroScalar(rd io.Reader) Scalar { zero := g.zeroScalar() for { s := g.RandomScalar(rd) if !s.IsEqual(zero) { return s } } } func (g wG) cvtElt(e Element) *wElt { if e == nil { return g.zeroElement() } ee, ok := e.(*wElt) if !ok || g.c.Params().BitSize != ee.c.Params().BitSize { panic(ErrType) } return ee } func (g wG) cvtScl(s Scalar) *wScl { if s == nil { return g.zeroScalar() } ss, ok := s.(*wScl) if !ok || g.c.Params().BitSize != ss.c.Params().BitSize { panic(ErrType) } return ss } func (g wG) Params() *Params { fieldLen := uint((g.c.Params().BitSize + 7) / 8) return &Params{ ElementLength: 1 + 2*fieldLen, CompressedElementLength: 1 + fieldLen, ScalarLength: fieldLen, } } func (g wG) HashToElementNonUniform(b, dst []byte) Element { var u [1]big.Int mapping, h, L := g.mapToCurveParams() xmd := expander.NewExpanderMD(h, dst) HashToField(u[:], b, xmd, g.c.Params().P, L) return mapping(&u[0]) } func (g wG) HashToElement(b, dst []byte) Element { var u [2]big.Int mapping, h, L := g.mapToCurveParams() xmd := expander.NewExpanderMD(h, dst) HashToField(u[:], b, xmd, g.c.Params().P, L) Q0 := mapping(&u[0]) Q1 := mapping(&u[1]) return Q0.Add(Q0, Q1) } func (g wG) HashToScalar(b, dst []byte) Scalar { var u [1]big.Int _, h, L := g.mapToCurveParams() xmd := expander.NewExpanderMD(h, dst) HashToField(u[:], b, xmd, g.c.Params().N, L) s := g.NewScalar().(*wScl) s.fromBig(&u[0]) return s } type wElt struct { wG x, y *big.Int } func (e *wElt) Group() Group { return e.wG } func (e *wElt) String() string { return fmt.Sprintf("x: 0x%v\ny: 0x%v", e.x.Text(16), e.y.Text(16)) } func (e *wElt) IsIdentity() bool { return e.x.Sign() == 0 && e.y.Sign() == 0 } func (e *wElt) IsEqual(o Element) bool { oo := e.cvtElt(o) return e.x.Cmp(oo.x) == 0 && e.y.Cmp(oo.y) == 0 } func (e *wElt) Set(a Element) Element { aa := e.cvtElt(a) e.x.Set(aa.x) e.y.Set(aa.y) return e } func (e *wElt) Copy() Element { return e.wG.zeroElement().Set(e) } func (e *wElt) CMov(v int, a Element) Element { if !(v == 0 || v == 1) { panic(ErrSelector) } aa := e.cvtElt(a) l := (e.wG.c.Params().BitSize + 7) / 8 bufE := make([]byte, l) bufA := make([]byte, l) e.x.FillBytes(bufE) aa.x.FillBytes(bufA) subtle.ConstantTimeCopy(v, bufE, bufA) e.x.SetBytes(bufE) e.y.FillBytes(bufE) aa.y.FillBytes(bufA) subtle.ConstantTimeCopy(v, bufE, bufA) e.y.SetBytes(bufE) return e } func (e *wElt) CSelect(v int, a Element, b Element) Element { if !(v == 0 || v == 1) { panic(ErrSelector) } aa, bb := e.cvtElt(a), e.cvtElt(b) l := (e.wG.c.Params().BitSize + 7) / 8 bufE := make([]byte, l) bufA := make([]byte, l) bufB := make([]byte, l) e.x.FillBytes(bufE) aa.x.FillBytes(bufA) bb.x.FillBytes(bufB) for i := range bufE { bufE[i] = byte(subtle.ConstantTimeSelect(v, int(bufA[i]), int(bufB[i]))) } e.x.SetBytes(bufE) e.y.FillBytes(bufE) aa.y.FillBytes(bufA) bb.y.FillBytes(bufB) for i := range bufE { bufE[i] = byte(subtle.ConstantTimeSelect(v, int(bufA[i]), int(bufB[i]))) } e.y.SetBytes(bufE) return e } func (e *wElt) Add(a, b Element) Element { aa, bb := e.cvtElt(a), e.cvtElt(b) e.x, e.y = e.c.Add(aa.x, aa.y, bb.x, bb.y) return e } func (e *wElt) Dbl(a Element) Element { aa := e.cvtElt(a) e.x, e.y = e.c.Double(aa.x, aa.y) return e } func (e *wElt) Neg(a Element) Element { aa := e.cvtElt(a) e.x.Set(aa.x) e.y.Neg(aa.y).Mod(e.y, e.c.Params().P) return e } func (e *wElt) Mul(a Element, s Scalar) Element { aa, ss := e.cvtElt(a), e.cvtScl(s) e.x, e.y = e.c.ScalarMult(aa.x, aa.y, ss.k) return e } func (e *wElt) MulGen(s Scalar) Element { ss := e.cvtScl(s) e.x, e.y = e.c.ScalarBaseMult(ss.k) return e } func (e *wElt) MarshalBinary() ([]byte, error) { if e.IsIdentity() { return []byte{0x0}, nil } e.x.Mod(e.x, e.c.Params().P) e.y.Mod(e.y, e.c.Params().P) return elliptic.Marshal(e.wG.c, e.x, e.y), nil } func (e *wElt) MarshalBinaryCompress() ([]byte, error) { if e.IsIdentity() { return []byte{0x0}, nil } e.x.Mod(e.x, e.c.Params().P) e.y.Mod(e.y, e.c.Params().P) return elliptic.MarshalCompressed(e.wG.c, e.x, e.y), nil } func (e *wElt) UnmarshalBinary(b []byte) error { byteLen := (e.c.Params().BitSize + 7) / 8 l := len(b) switch { case l == 1 && b[0] == 0x00: // point at infinity e.x.SetInt64(0) e.y.SetInt64(0) case l == 1+byteLen && (b[0] == 0x02 || b[0] == 0x03): // compressed x, y := elliptic.UnmarshalCompressed(e.wG.c, b) if x == nil { return ErrUnmarshal } e.x, e.y = x, y case l == 1+2*byteLen && b[0] == 0x04: // uncompressed x, y := elliptic.Unmarshal(e.wG.c, b) if x == nil { return ErrUnmarshal } e.x, e.y = x, y default: return ErrUnmarshal } return nil } type wScl struct { wG k []byte } func (s *wScl) Group() Group { return s.wG } func (s *wScl) String() string { return fmt.Sprintf("0x%x", s.k) } func (s *wScl) SetUint64(n uint64) Scalar { s.fromBig(new(big.Int).SetUint64(n)); return s } func (s *wScl) SetBigInt(x *big.Int) Scalar { s.fromBig(x); return s } func (s *wScl) IsZero() bool { return subtle.ConstantTimeCompare(s.k, make([]byte, (s.wG.c.Params().BitSize+7)/8)) == 1 } func (s *wScl) IsEqual(a Scalar) bool { aa := s.cvtScl(a) return subtle.ConstantTimeCompare(s.k, aa.k) == 1 } func (s *wScl) fromBig(b *big.Int) { k := new(big.Int).Mod(b, s.c.Params().N) if err := s.UnmarshalBinary(k.Bytes()); err != nil { panic(err) } } func (s *wScl) Set(a Scalar) Scalar { aa := s.cvtScl(a) if err := s.UnmarshalBinary(aa.k); err != nil { panic(err) } return s } func (s *wScl) Copy() Scalar { return s.wG.zeroScalar().Set(s) } func (s *wScl) CMov(v int, a Scalar) Scalar { if !(v == 0 || v == 1) { panic(ErrSelector) } aa := s.cvtScl(a) subtle.ConstantTimeCopy(v, s.k, aa.k) return s } func (s *wScl) CSelect(v int, a Scalar, b Scalar) Scalar { if !(v == 0 || v == 1) { panic(ErrSelector) } aa, bb := s.cvtScl(a), s.cvtScl(b) for i := range s.k { s.k[i] = byte(subtle.ConstantTimeSelect(v, int(aa.k[i]), int(bb.k[i]))) } return s } func (s *wScl) Add(a, b Scalar) Scalar { aa, bb := s.cvtScl(a), s.cvtScl(b) r := new(big.Int) r.SetBytes(aa.k).Add(r, new(big.Int).SetBytes(bb.k)) s.fromBig(r) return s } func (s *wScl) Sub(a, b Scalar) Scalar { aa, bb := s.cvtScl(a), s.cvtScl(b) r := new(big.Int) r.SetBytes(aa.k).Sub(r, new(big.Int).SetBytes(bb.k)) s.fromBig(r) return s } func (s *wScl) Mul(a, b Scalar) Scalar { aa, bb := s.cvtScl(a), s.cvtScl(b) r := new(big.Int) r.SetBytes(aa.k).Mul(r, new(big.Int).SetBytes(bb.k)) s.fromBig(r) return s } func (s *wScl) Neg(a Scalar) Scalar { aa := s.cvtScl(a) r := new(big.Int) r.SetBytes(aa.k).Neg(r) s.fromBig(r) return s } func (s *wScl) Inv(a Scalar) Scalar { aa := s.cvtScl(a) r := new(big.Int) r.SetBytes(aa.k).ModInverse(r, s.c.Params().N) s.fromBig(r) return s } func (s *wScl) MarshalBinary() (data []byte, err error) { data = make([]byte, (s.c.Params().BitSize+7)/8) copy(data, s.k) return data, nil } func (s *wScl) UnmarshalBinary(b []byte) error { l := (s.c.Params().BitSize + 7) / 8 s.k = make([]byte, l) copy(s.k[l-len(b):l], b) return nil } func (g wG) mapToCurveParams() (mapping func(u *big.Int) *wElt, h crypto.Hash, L uint) { var Z, C2 big.Int switch g.c.Params().BitSize { case 256: Z.SetInt64(-10) C2.SetString("0x78bc71a02d89ec07214623f6d0f955072c7cc05604a5a6e23ffbf67115fa5301", 0) h = crypto.SHA256 L = 48 case 384: Z.SetInt64(-12) C2.SetString("0x19877cc1041b7555743c0ae2e3a3e61fb2aaa2e0e87ea557a563d8b598a0940d0a697a9e0b9e92cfaa314f583c9d066", 0) h = crypto.SHA384 L = 72 case 521: Z.SetInt64(-4) C2.SetInt64(8) h = crypto.SHA512 L = 98 default: panic("curve not supported") } return func(u *big.Int) *wElt { return g.sswu3mod4Map(u, &Z, &C2) }, h, L } func (g wG) sswu3mod4Map(u *big.Int, Z, C2 *big.Int) *wElt { tv1 := new(big.Int) tv2 := new(big.Int) tv3 := new(big.Int) tv4 := new(big.Int) xn := new(big.Int) xd := new(big.Int) x1n := new(big.Int) x2n := new(big.Int) gx1 := new(big.Int) gxd := new(big.Int) y1 := new(big.Int) y2 := new(big.Int) x := new(big.Int) y := new(big.Int) A := big.NewInt(-3) B := g.c.Params().B p := g.c.Params().P c1 := new(big.Int) c1.Sub(p, big.NewInt(3)).Rsh(c1, 2) // 1. c1 = (q - 3) / 4 add := func(c, a, b *big.Int) { c.Add(a, b).Mod(c, p) } mul := func(c, a, b *big.Int) { c.Mul(a, b).Mod(c, p) } sqr := func(c, a *big.Int) { c.Mul(a, a).Mod(c, p) } exp := func(c, a, b *big.Int) { c.Exp(a, b, p) } sgn := func(a *big.Int) uint { a.Mod(a, p); return a.Bit(0) } cmv := func(c, a, b *big.Int, k bool) { if k { c.Set(b) } else { c.Set(a) } } sqr(tv1, u) // 1. tv1 = u^2 mul(tv3, Z, tv1) // 2. tv3 = Z * tv1 sqr(tv2, tv3) // 3. tv2 = tv3^2 add(xd, tv2, tv3) // 4. xd = tv2 + tv3 add(x1n, xd, big.NewInt(1)) // 5. x1n = xd + 1 mul(x1n, x1n, B) // 6. x1n = x1n * B tv4.Neg(A) // mul(xd, tv4, xd) // 7. xd = -A * xd e1 := xd.Sign() == 0 // 8. e1 = xd == 0 mul(tv4, Z, A) // cmv(xd, xd, tv4, e1) // 9. xd = CMOV(xd, Z * A, e1) sqr(tv2, xd) // 10. tv2 = xd^2 mul(gxd, tv2, xd) // 11. gxd = tv2 * xd mul(tv2, A, tv2) // 12. tv2 = A * tv2 sqr(gx1, x1n) // 13. gx1 = x1n^2 add(gx1, gx1, tv2) // 14. gx1 = gx1 + tv2 mul(gx1, gx1, x1n) // 15. gx1 = gx1 * x1n mul(tv2, B, gxd) // 16. tv2 = B * gxd add(gx1, gx1, tv2) // 17. gx1 = gx1 + tv2 sqr(tv4, gxd) // 18. tv4 = gxd^2 mul(tv2, gx1, gxd) // 19. tv2 = gx1 * gxd mul(tv4, tv4, tv2) // 20. tv4 = tv4 * tv2 exp(y1, tv4, c1) // 21. y1 = tv4^c1 mul(y1, y1, tv2) // 22. y1 = y1 * tv2 mul(x2n, tv3, x1n) // 23. x2n = tv3 * x1n mul(y2, y1, C2) // 24. y2 = y1 * c2 mul(y2, y2, tv1) // 25. y2 = y2 * tv1 mul(y2, y2, u) // 26. y2 = y2 * u sqr(tv2, y1) // 27. tv2 = y1^2 mul(tv2, tv2, gxd) // 28. tv2 = tv2 * gxd e2 := tv2.Cmp(gx1) == 0 // 29. e2 = tv2 == gx1 cmv(xn, x2n, x1n, e2) // 30. xn = CMOV(x2n, x1n, e2) cmv(y, y2, y1, e2) // 31. y = CMOV(y2, y1, e2) e3 := sgn(u) == sgn(y) // 32. e3 = sgn0(u) == sgn0(y) tv1.Neg(y) // cmv(y, tv1, y, e3) // 33. y = CMOV(-y, y, e3) tv1.ModInverse(xd, p) // mul(x, xn, tv1) // 34. return (xn, xd, y, 1) y.Mod(y, p) return &wElt{g, x, y} } golang-github-cloudflare-circl-1.3.7/group/testdata/000077500000000000000000000000001454601126700224345ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/group/testdata/P256_XMD-SHA-256_SSWU_NU_.json000066400000000000000000000070771454601126700270530ustar00rootroot00000000000000{ "L": "0x30", "Z": "0xffffffff00000001000000000000000000000000fffffffffffffffffffffff5", "ciphersuite": "P256_XMD:SHA-256_SSWU_NU_", "curve": "NIST P-256", "dst": "QUUX-V01-CS02-with-P256_XMD:SHA-256_SSWU_NU_", "expand": "XMD", "field": { "m": "0x1", "p": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff" }, "hash": "sha256", "k": "0x80", "map": { "name": "SSWU" }, "randomOracle": false, "vectors": [ { "P": { "x": "0xf871caad25ea3b59c16cf87c1894902f7e7b2c822c3d3f73596c5ace8ddd14d1", "y": "0x87b9ae23335bee057b99bac1e68588b18b5691af476234b8971bc4f011ddc99b" }, "Q": { "x": "0xf871caad25ea3b59c16cf87c1894902f7e7b2c822c3d3f73596c5ace8ddd14d1", "y": "0x87b9ae23335bee057b99bac1e68588b18b5691af476234b8971bc4f011ddc99b" }, "msg": "", "u": [ "0xb22d487045f80e9edcb0ecc8d4bf77833e2bf1f3a54004d7df1d57f4802d311f" ] }, { "P": { "x": "0xfc3f5d734e8dce41ddac49f47dd2b8a57257522a865c124ed02b92b5237befa4", "y": "0xfe4d197ecf5a62645b9690599e1d80e82c500b22ac705a0b421fac7b47157866" }, "Q": { "x": "0xfc3f5d734e8dce41ddac49f47dd2b8a57257522a865c124ed02b92b5237befa4", "y": "0xfe4d197ecf5a62645b9690599e1d80e82c500b22ac705a0b421fac7b47157866" }, "msg": "abc", "u": [ "0xc7f96eadac763e176629b09ed0c11992225b3a5ae99479760601cbd69c221e58" ] }, { "P": { "x": "0xf164c6674a02207e414c257ce759d35eddc7f55be6d7f415e2cc177e5d8faa84", "y": "0x3aa274881d30db70485368c0467e97da0e73c18c1d00f34775d012b6fcee7f97" }, "Q": { "x": "0xf164c6674a02207e414c257ce759d35eddc7f55be6d7f415e2cc177e5d8faa84", "y": "0x3aa274881d30db70485368c0467e97da0e73c18c1d00f34775d012b6fcee7f97" }, "msg": "abcdef0123456789", "u": [ "0x314e8585fa92068b3ea2c3bab452d4257b38be1c097d58a21890456c2929614d" ] }, { "P": { "x": "0x324532006312be4f162614076460315f7a54a6f85544da773dc659aca0311853", "y": "0x8d8197374bcd52de2acfefc8a54fe2c8d8bebd2a39f16be9b710e4b1af6ef883" }, "Q": { "x": "0x324532006312be4f162614076460315f7a54a6f85544da773dc659aca0311853", "y": "0x8d8197374bcd52de2acfefc8a54fe2c8d8bebd2a39f16be9b710e4b1af6ef883" }, "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", "u": [ "0x752d8eaa38cd785a799a31d63d99c2ae4261823b4a367b133b2c6627f48858ab" ] }, { "P": { "x": "0x5c4bad52f81f39c8e8de1260e9a06d72b8b00a0829a8ea004a610b0691bea5d9", "y": "0xc801e7c0782af1f74f24fc385a8555da0582032a3ce038de637ccdcb16f7ef7b" }, "Q": { "x": "0x5c4bad52f81f39c8e8de1260e9a06d72b8b00a0829a8ea004a610b0691bea5d9", "y": "0xc801e7c0782af1f74f24fc385a8555da0582032a3ce038de637ccdcb16f7ef7b" }, "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "u": [ "0x0e1527840b9df2dfbef966678ff167140f2b27c4dccd884c25014dce0e41dfa3" ] } ] } golang-github-cloudflare-circl-1.3.7/group/testdata/P256_XMD-SHA-256_SSWU_RO_.json000066400000000000000000000115651454601126700270460ustar00rootroot00000000000000{ "L": "0x30", "Z": "0xffffffff00000001000000000000000000000000fffffffffffffffffffffff5", "ciphersuite": "P256_XMD:SHA-256_SSWU_RO_", "curve": "NIST P-256", "dst": "QUUX-V01-CS02-with-P256_XMD:SHA-256_SSWU_RO_", "expand": "XMD", "field": { "m": "0x1", "p": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff" }, "hash": "sha256", "k": "0x80", "map": { "name": "SSWU" }, "randomOracle": true, "vectors": [ { "P": { "x": "0x2c15230b26dbc6fc9a37051158c95b79656e17a1a920b11394ca91c44247d3e4", "y": "0x8a7a74985cc5c776cdfe4b1f19884970453912e9d31528c060be9ab5c43e8415" }, "Q0": { "x": "0xab640a12220d3ff283510ff3f4b1953d09fad35795140b1c5d64f313967934d5", "y": "0xdccb558863804a881d4fff3455716c836cef230e5209594ddd33d85c565b19b1" }, "Q1": { "x": "0x51cce63c50d972a6e51c61334f0f4875c9ac1cd2d3238412f84e31da7d980ef5", "y": "0xb45d1a36d00ad90e5ec7840a60a4de411917fbe7c82c3949a6e699e5a1b66aac" }, "msg": "", "u": [ "0xad5342c66a6dd0ff080df1da0ea1c04b96e0330dd89406465eeba11582515009", "0x8c0f1d43204bd6f6ea70ae8013070a1518b43873bcd850aafa0a9e220e2eea5a" ] }, { "P": { "x": "0x0bb8b87485551aa43ed54f009230450b492fead5f1cc91658775dac4a3388a0f", "y": "0x5c41b3d0731a27a7b14bc0bf0ccded2d8751f83493404c84a88e71ffd424212e" }, "Q0": { "x": "0x5219ad0ddef3cc49b714145e91b2f7de6ce0a7a7dc7406c7726c7e373c58cb48", "y": "0x7950144e52d30acbec7b624c203b1996c99617d0b61c2442354301b191d93ecf" }, "Q1": { "x": "0x019b7cb4efcfeaf39f738fe638e31d375ad6837f58a852d032ff60c69ee3875f", "y": "0x589a62d2b22357fed5449bc38065b760095ebe6aeac84b01156ee4252715446e" }, "msg": "abc", "u": [ "0xafe47f2ea2b10465cc26ac403194dfb68b7f5ee865cda61e9f3e07a537220af1", "0x379a27833b0bfe6f7bdca08e1e83c760bf9a338ab335542704edcd69ce9e46e0" ] }, { "P": { "x": "0x65038ac8f2b1def042a5df0b33b1f4eca6bff7cb0f9c6c1526811864e544ed80", "y": "0xcad44d40a656e7aff4002a8de287abc8ae0482b5ae825822bb870d6df9b56ca3" }, "Q0": { "x": "0xa17bdf2965eb88074bc01157e644ed409dac97cfcf0c61c998ed0fa45e79e4a2", "y": "0x4f1bc80c70d411a3cc1d67aeae6e726f0f311639fee560c7f5a664554e3c9c2e" }, "Q1": { "x": "0x7da48bb67225c1a17d452c983798113f47e438e4202219dd0715f8419b274d66", "y": "0xb765696b2913e36db3016c47edb99e24b1da30e761a8a3215dc0ec4d8f96e6f9" }, "msg": "abcdef0123456789", "u": [ "0x0fad9d125a9477d55cf9357105b0eb3a5c4259809bf87180aa01d651f53d312c", "0xb68597377392cd3419d8fcc7d7660948c8403b19ea78bbca4b133c9d2196c0fb" ] }, { "P": { "x": "0x4be61ee205094282ba8a2042bcb48d88dfbb609301c49aa8b078533dc65a0b5d", "y": "0x98f8df449a072c4721d241a3b1236d3caccba603f916ca680f4539d2bfb3c29e" }, "Q0": { "x": "0xc76aaa823aeadeb3f356909cb08f97eee46ecb157c1f56699b5efebddf0e6398", "y": "0x776a6f45f528a0e8d289a4be12c4fab80762386ec644abf2bffb9b627e4352b1" }, "Q1": { "x": "0x418ac3d85a5ccc4ea8dec14f750a3a9ec8b85176c95a7022f391826794eb5a75", "y": "0xfd6604f69e9d9d2b74b072d14ea13050db72c932815523305cb9e807cc900aff" }, "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", "u": [ "0x3bbc30446f39a7befad080f4d5f32ed116b9534626993d2cc5033f6f8d805919", "0x76bb02db019ca9d3c1e02f0c17f8baf617bbdae5c393a81d9ce11e3be1bf1d33" ] }, { "P": { "x": "0x457ae2981f70ca85d8e24c308b14db22f3e3862c5ea0f652ca38b5e49cd64bc5", "y": "0xecb9f0eadc9aeed232dabc53235368c1394c78de05dd96893eefa62b0f4757dc" }, "Q0": { "x": "0xd88b989ee9d1295df413d4456c5c850b8b2fb0f5402cc5c4c7e815412e926db8", "y": "0xbb4a1edeff506cf16def96afff41b16fc74f6dbd55c2210e5b8f011ba32f4f40" }, "Q1": { "x": "0xa281e34e628f3a4d2a53fa87ff973537d68ad4fbc28d3be5e8d9f6a2571c5a4b", "y": "0xf6ed88a7aab56a488100e6f1174fa9810b47db13e86be999644922961206e184" }, "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "u": [ "0x4ebc95a6e839b1ae3c63b847798e85cb3c12d3817ec6ebc10af6ee51adb29fec", "0x4e21af88e22ea80156aff790750121035b3eefaa96b425a8716e0d20b4e269ee" ] } ] } golang-github-cloudflare-circl-1.3.7/group/testdata/P384_XMD-SHA-384_SSWU_NU_.json000066400000000000000000000106371454601126700270530ustar00rootroot00000000000000{ "L": "0x48", "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffff3", "ciphersuite": "P384_XMD:SHA-384_SSWU_NU_", "curve": "NIST P-384", "dst": "QUUX-V01-CS02-with-P384_XMD:SHA-384_SSWU_NU_", "expand": "XMD", "field": { "m": "0x1", "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff" }, "hash": "sha384", "k": "0xc0", "map": { "name": "SSWU" }, "randomOracle": false, "vectors": [ { "P": { "x": "0xde5a893c83061b2d7ce6a0d8b049f0326f2ada4b966dc7e72927256b033ef61058029a3bfb13c1c7ececd6641881ae20", "y": "0x63f46da6139785674da315c1947e06e9a0867f5608cf24724eb3793a1f5b3809ee28eb21a0c64be3be169afc6cdb38ca" }, "Q": { "x": "0xde5a893c83061b2d7ce6a0d8b049f0326f2ada4b966dc7e72927256b033ef61058029a3bfb13c1c7ececd6641881ae20", "y": "0x63f46da6139785674da315c1947e06e9a0867f5608cf24724eb3793a1f5b3809ee28eb21a0c64be3be169afc6cdb38ca" }, "msg": "", "u": [ "0xbc7dc1b2cdc5d588a66de3276b0f24310d4aca4977efda7d6272e1be25187b001493d267dc53b56183c9e28282368e60" ] }, { "P": { "x": "0x1f08108b87e703c86c872ab3eb198a19f2b708237ac4be53d7929fb4bd5194583f40d052f32df66afe5249c9915d139b", "y": "0x1369dc8d5bf038032336b989994874a2270adadb67a7fcc32f0f8824bc5118613f0ac8de04a1041d90ff8a5ad555f96c" }, "Q": { "x": "0x1f08108b87e703c86c872ab3eb198a19f2b708237ac4be53d7929fb4bd5194583f40d052f32df66afe5249c9915d139b", "y": "0x1369dc8d5bf038032336b989994874a2270adadb67a7fcc32f0f8824bc5118613f0ac8de04a1041d90ff8a5ad555f96c" }, "msg": "abc", "u": [ "0x9de6cf41e6e41c03e4a7784ac5c885b4d1e49d6de390b3cdd5a1ac5dd8c40afb3dfd7bb2686923bab644134483fc1926" ] }, { "P": { "x": "0x4dac31ec8a82ee3c02ba2d7c9fa431f1e59ffe65bf977b948c59e1d813c2d7963c7be81aa6db39e78ff315a10115c0d0", "y": "0x845333cdb5702ad5c525e603f302904d6fc84879f0ef2ee2014a6b13edd39131bfd66f7bd7cdc2d9ccf778f0c8892c3f" }, "Q": { "x": "0x4dac31ec8a82ee3c02ba2d7c9fa431f1e59ffe65bf977b948c59e1d813c2d7963c7be81aa6db39e78ff315a10115c0d0", "y": "0x845333cdb5702ad5c525e603f302904d6fc84879f0ef2ee2014a6b13edd39131bfd66f7bd7cdc2d9ccf778f0c8892c3f" }, "msg": "abcdef0123456789", "u": [ "0x84e2d430a5e2543573e58e368af41821ca3ccc97baba7e9aab51a84543d5a0298638a22ceee6090d9d642921112af5b7" ] }, { "P": { "x": "0x13c1f8c52a492183f7c28e379b0475486718a7e3ac1dfef39283b9ce5fb02b73f70c6c1f3dfe0c286b03e2af1af12d1d", "y": "0x57e101887e73e40eab8963324ed16c177d55eb89f804ec9df06801579820420b5546b579008df2145fd770f584a1a54c" }, "Q": { "x": 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golang-github-cloudflare-circl-1.3.7/hpke/000077500000000000000000000000001454601126700204165ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/hpke/aead.go000066400000000000000000000045701454601126700216450ustar00rootroot00000000000000package hpke import ( "crypto/cipher" "fmt" ) type encdecContext struct { // Serialized parameters suite Suite sharedSecret []byte secret []byte keyScheduleContext []byte exporterSecret []byte key []byte baseNonce []byte sequenceNumber []byte // Operational parameters cipher.AEAD nonce []byte } type ( sealContext struct{ *encdecContext } openContext struct{ *encdecContext } ) // Export takes a context string exporterContext and a desired length (in // bytes), and produces a secret derived from the internal exporter secret // using the corresponding KDF Expand function. It panics if length is // greater than 255*N bytes, where N is the size (in bytes) of the KDF's // output. func (c *encdecContext) Export(exporterContext []byte, length uint) []byte { maxLength := uint(255 * c.suite.kdfID.ExtractSize()) if length > maxLength { panic(fmt.Errorf("output length must be lesser than %v bytes", maxLength)) } return c.suite.labeledExpand(c.exporterSecret, []byte("sec"), exporterContext, uint16(length)) } func (c *encdecContext) Suite() Suite { return c.suite } func (c *encdecContext) calcNonce() []byte { for i := range c.baseNonce { c.nonce[i] = c.baseNonce[i] ^ c.sequenceNumber[i] } return c.nonce } func (c *encdecContext) increment() error { // tests whether the sequence number is all-ones, which prevents an // overflow after the increment. allOnes := byte(0xFF) for i := range c.sequenceNumber { allOnes &= c.sequenceNumber[i] } if allOnes == byte(0xFF) { return ErrAEADSeqOverflows } // performs an increment by 1 and verifies whether the sequence overflows. carry := uint(1) for i := len(c.sequenceNumber) - 1; i >= 0; i-- { sum := uint(c.sequenceNumber[i]) + carry carry = sum >> 8 c.sequenceNumber[i] = byte(sum & 0xFF) } if carry != 0 { return ErrAEADSeqOverflows } return nil } func (c *sealContext) Seal(pt, aad []byte) ([]byte, error) { ct := c.AEAD.Seal(nil, c.calcNonce(), pt, aad) err := c.increment() if err != nil { for i := range ct { ct[i] = 0 } return nil, err } return ct, nil } func (c *openContext) Open(ct, aad []byte) ([]byte, error) { pt, err := c.AEAD.Open(nil, c.calcNonce(), ct, aad) if err != nil { return nil, err } err = c.increment() if err != nil { for i := range pt { pt[i] = 0 } return nil, err } return pt, nil } golang-github-cloudflare-circl-1.3.7/hpke/aead_test.go000066400000000000000000000101171454601126700226760ustar00rootroot00000000000000package hpke import ( "bytes" "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/internal/test" ) func TestAeadExporter(t *testing.T) { suite := Suite{kdfID: KDF_HKDF_SHA256, aeadID: AEAD_AES128GCM} exporter := &encdecContext{suite: suite} maxLength := uint(255 * suite.kdfID.ExtractSize()) err := test.CheckPanic(func() { exporter.Export([]byte("exporter"), maxLength+1) }) test.CheckNoErr(t, err, "exporter max size") } func setupAeadTest() (*sealContext, *openContext, error) { suite := Suite{aeadID: AEAD_AES128GCM} key := make([]byte, suite.aeadID.KeySize()) if n, err := rand.Read(key); err != nil { return nil, nil, err } else if n != len(key) { return nil, nil, fmt.Errorf("unexpected key size: got %d; want %d", n, len(key)) } aead, err := suite.aeadID.New(key) if err != nil { return nil, nil, err } Nn := suite.aeadID.NonceSize() baseNonce := make([]byte, Nn) if n, err := rand.Read(baseNonce); err != nil { return nil, nil, err } else if n != len(baseNonce) { return nil, nil, fmt.Errorf("unexpected base nonce size: got %d; want %d", n, len(baseNonce)) } sealer := &sealContext{ &encdecContext{ suite, nil, nil, nil, nil, nil, baseNonce, make([]byte, Nn), aead, make([]byte, Nn), }, } opener := &openContext{ &encdecContext{ suite, nil, nil, nil, nil, nil, baseNonce, make([]byte, Nn), aead, make([]byte, Nn), }, } return sealer, opener, nil } func TestAeadNonceUpdate(t *testing.T) { sealer, opener, err := setupAeadTest() test.CheckNoErr(t, err, "setup failed") pt := []byte("plaintext") aad := []byte("aad") numAttempts := 2 var prevCt []byte for i := 0; i < numAttempts; i++ { ct, err := sealer.Seal(pt, aad) if err != nil { t.Fatalf("encryption failed: %s", err) } if prevCt != nil && bytes.Equal(ct, prevCt) { t.Error("ciphertext matches the previous (nonce not updated)") } _, err = opener.Open(ct, aad) if err != nil { t.Errorf("decryption failed: %s", err) } prevCt = ct } } func TestOpenPhaseMismatch(t *testing.T) { sealer, opener, err := setupAeadTest() test.CheckNoErr(t, err, "setup failed") pt := []byte("plaintext") aad := []byte("aad") ct, err := sealer.Seal(pt, aad) if err != nil { t.Fatalf("encryption failed: %s", err) } recovered, err := opener.Open(ct, aad) if err != nil { t.Fatalf("decryption failed: %s", err) } if !bytes.Equal(pt, recovered) { t.Fatal("Plaintext mismatch") } _, err = opener.Open(ct, aad) if err == nil { t.Fatal("decryption succeeded when it should have failed") } } func TestSealPhaseMismatch(t *testing.T) { sealer, opener, err := setupAeadTest() test.CheckNoErr(t, err, "setup failed") pt := []byte("plaintext") aad := []byte("aad") _, err = sealer.Seal(pt, aad) if err != nil { t.Fatalf("encryption failed: %s", err) } ct, err := sealer.Seal(pt, aad) if err != nil { t.Fatalf("encryption failed: %s", err) } _, err = opener.Open(ct, aad) if err == nil { t.Fatal("decryption succeeded when it should have failed") } } func TestAeadSeqOverflow(t *testing.T) { sealer, opener, err := setupAeadTest() test.CheckNoErr(t, err, "setup failed") Nn := len(sealer.baseNonce) pt := []byte("plaintext") aad := []byte("aad") // Sets sequence number to 256 before its max value = 0xFF...FF. for i := 0; i < Nn; i++ { sealer.sequenceNumber[i] = 0xFF opener.sequenceNumber[i] = 0xFF } sealer.sequenceNumber[Nn-1] = 0x00 opener.sequenceNumber[Nn-1] = 0x00 numAttempts := 260 wantCorrect := 2 * 255 wantIncorrect := 2*numAttempts - wantCorrect gotCorrect := 0 gotIncorrect := 0 for i := 0; i < numAttempts; i++ { ct, err := sealer.Seal(pt, aad) switch { case ct != nil && err == nil: gotCorrect++ case ct == nil && err != nil: gotIncorrect++ default: t.FailNow() } pt2, err := opener.Open(ct, aad) switch { case pt2 != nil && err == nil: gotCorrect++ case pt2 == nil && err != nil: gotIncorrect++ default: t.FailNow() } } if gotCorrect != wantCorrect { test.ReportError(t, gotCorrect, wantCorrect) } if gotIncorrect != wantIncorrect { test.ReportError(t, gotIncorrect, wantIncorrect) } } golang-github-cloudflare-circl-1.3.7/hpke/algs.go000066400000000000000000000173561454601126700217070ustar00rootroot00000000000000package hpke import ( "crypto" "crypto/aes" "crypto/cipher" "crypto/elliptic" _ "crypto/sha256" // Linking sha256. _ "crypto/sha512" // Linking sha512. "fmt" "hash" "io" "github.com/cloudflare/circl/dh/x25519" "github.com/cloudflare/circl/dh/x448" "github.com/cloudflare/circl/ecc/p384" "github.com/cloudflare/circl/kem" "github.com/cloudflare/circl/kem/kyber/kyber768" "golang.org/x/crypto/chacha20poly1305" "golang.org/x/crypto/hkdf" ) type KEM uint16 //nolint:golint,stylecheck const ( // KEM_P256_HKDF_SHA256 is a KEM using P256 curve and HKDF with SHA-256. KEM_P256_HKDF_SHA256 KEM = 0x10 // KEM_P384_HKDF_SHA384 is a KEM using P384 curve and HKDF with SHA-384. KEM_P384_HKDF_SHA384 KEM = 0x11 // KEM_P521_HKDF_SHA512 is a KEM using P521 curve and HKDF with SHA-512. KEM_P521_HKDF_SHA512 KEM = 0x12 // KEM_X25519_HKDF_SHA256 is a KEM using X25519 Diffie-Hellman function // and HKDF with SHA-256. KEM_X25519_HKDF_SHA256 KEM = 0x20 // KEM_X448_HKDF_SHA512 is a KEM using X448 Diffie-Hellman function and // HKDF with SHA-512. KEM_X448_HKDF_SHA512 KEM = 0x21 // KEM_X25519_KYBER768_DRAFT00 is a hybrid KEM built on DHKEM(X25519, HKDF-SHA256) // and Kyber768Draft00 KEM_X25519_KYBER768_DRAFT00 KEM = 0x30 ) // IsValid returns true if the KEM identifier is supported by the HPKE package. func (k KEM) IsValid() bool { switch k { case KEM_P256_HKDF_SHA256, KEM_P384_HKDF_SHA384, KEM_P521_HKDF_SHA512, KEM_X25519_HKDF_SHA256, KEM_X448_HKDF_SHA512, KEM_X25519_KYBER768_DRAFT00: return true default: return false } } // Scheme returns an instance of a KEM that supports authentication. Panics if // the KEM identifier is invalid. func (k KEM) Scheme() kem.AuthScheme { switch k { case KEM_P256_HKDF_SHA256: return dhkemp256hkdfsha256 case KEM_P384_HKDF_SHA384: return dhkemp384hkdfsha384 case KEM_P521_HKDF_SHA512: return dhkemp521hkdfsha512 case KEM_X25519_HKDF_SHA256: return dhkemx25519hkdfsha256 case KEM_X448_HKDF_SHA512: return dhkemx448hkdfsha512 case KEM_X25519_KYBER768_DRAFT00: return hybridkemX25519Kyber768 default: panic(ErrInvalidKEM) } } type KDF uint16 //nolint:golint,stylecheck const ( // KDF_HKDF_SHA256 is a KDF using HKDF with SHA-256. KDF_HKDF_SHA256 KDF = 0x01 // KDF_HKDF_SHA384 is a KDF using HKDF with SHA-384. KDF_HKDF_SHA384 KDF = 0x02 // KDF_HKDF_SHA512 is a KDF using HKDF with SHA-512. KDF_HKDF_SHA512 KDF = 0x03 ) func (k KDF) IsValid() bool { switch k { case KDF_HKDF_SHA256, KDF_HKDF_SHA384, KDF_HKDF_SHA512: return true default: return false } } // ExtractSize returns the size (in bytes) of the pseudorandom key produced // by KDF.Extract. func (k KDF) ExtractSize() int { switch k { case KDF_HKDF_SHA256: return crypto.SHA256.Size() case KDF_HKDF_SHA384: return crypto.SHA384.Size() case KDF_HKDF_SHA512: return crypto.SHA512.Size() default: panic(ErrInvalidKDF) } } // Extract derives a pseudorandom key from a high-entropy, secret input and a // salt. The size of the output is determined by KDF.ExtractSize. func (k KDF) Extract(secret, salt []byte) (pseudorandomKey []byte) { return hkdf.Extract(k.hash(), secret, salt) } // Expand derives a variable length pseudorandom string from a pseudorandom key // and an information string. Panics if the pseudorandom key is less // than N bytes, or if the output length is greater than 255*N bytes, // where N is the size returned by KDF.Extract function. func (k KDF) Expand(pseudorandomKey, info []byte, outputLen uint) []byte { extractSize := k.ExtractSize() if len(pseudorandomKey) < extractSize { panic(fmt.Errorf("pseudorandom key must be %v bytes", extractSize)) } maxLength := uint(255 * extractSize) if outputLen > maxLength { panic(fmt.Errorf("output length must be less than %v bytes", maxLength)) } output := make([]byte, outputLen) rd := hkdf.Expand(k.hash(), pseudorandomKey[:extractSize], info) _, err := io.ReadFull(rd, output) if err != nil { panic(err) } return output } func (k KDF) hash() func() hash.Hash { switch k { case KDF_HKDF_SHA256: return crypto.SHA256.New case KDF_HKDF_SHA384: return crypto.SHA384.New case KDF_HKDF_SHA512: return crypto.SHA512.New default: panic(ErrInvalidKDF) } } type AEAD uint16 //nolint:golint,stylecheck const ( // AEAD_AES128GCM is AES-128 block cipher in Galois Counter Mode (GCM). AEAD_AES128GCM AEAD = 0x01 // AEAD_AES256GCM is AES-256 block cipher in Galois Counter Mode (GCM). AEAD_AES256GCM AEAD = 0x02 // AEAD_ChaCha20Poly1305 is ChaCha20 stream cipher and Poly1305 MAC. AEAD_ChaCha20Poly1305 AEAD = 0x03 ) // New instantiates an AEAD cipher from the identifier, returns an error if the // identifier is not known. func (a AEAD) New(key []byte) (cipher.AEAD, error) { switch a { case AEAD_AES128GCM, AEAD_AES256GCM: block, err := aes.NewCipher(key) if err != nil { return nil, err } return cipher.NewGCM(block) case AEAD_ChaCha20Poly1305: return chacha20poly1305.New(key) default: panic(ErrInvalidAEAD) } } func (a AEAD) IsValid() bool { switch a { case AEAD_AES128GCM, AEAD_AES256GCM, AEAD_ChaCha20Poly1305: return true default: return false } } // KeySize returns the size in bytes of the keys used by the AEAD cipher. func (a AEAD) KeySize() uint { switch a { case AEAD_AES128GCM: return 16 case AEAD_AES256GCM: return 32 case AEAD_ChaCha20Poly1305: return chacha20poly1305.KeySize default: panic(ErrInvalidAEAD) } } // NonceSize returns the size in bytes of the nonce used by the AEAD cipher. func (a AEAD) NonceSize() uint { switch a { case AEAD_AES128GCM, AEAD_AES256GCM, AEAD_ChaCha20Poly1305: return 12 default: panic(ErrInvalidAEAD) } } // CipherLen returns the length of a ciphertext corresponding to a message of // length mLen. func (a AEAD) CipherLen(mLen uint) uint { switch a { case AEAD_AES128GCM, AEAD_AES256GCM, AEAD_ChaCha20Poly1305: return mLen + 16 default: panic(ErrInvalidAEAD) } } var ( dhkemp256hkdfsha256, dhkemp384hkdfsha384, dhkemp521hkdfsha512 shortKEM dhkemx25519hkdfsha256, dhkemx448hkdfsha512 xKEM hybridkemX25519Kyber768 hybridKEM ) func init() { dhkemp256hkdfsha256.Curve = elliptic.P256() dhkemp256hkdfsha256.dhKemBase.id = KEM_P256_HKDF_SHA256 dhkemp256hkdfsha256.dhKemBase.name = "HPKE_KEM_P256_HKDF_SHA256" dhkemp256hkdfsha256.dhKemBase.Hash = crypto.SHA256 dhkemp256hkdfsha256.dhKemBase.dhKEM = dhkemp256hkdfsha256 dhkemp384hkdfsha384.Curve = p384.P384() dhkemp384hkdfsha384.dhKemBase.id = KEM_P384_HKDF_SHA384 dhkemp384hkdfsha384.dhKemBase.name = "HPKE_KEM_P384_HKDF_SHA384" dhkemp384hkdfsha384.dhKemBase.Hash = crypto.SHA384 dhkemp384hkdfsha384.dhKemBase.dhKEM = dhkemp384hkdfsha384 dhkemp521hkdfsha512.Curve = elliptic.P521() dhkemp521hkdfsha512.dhKemBase.id = KEM_P521_HKDF_SHA512 dhkemp521hkdfsha512.dhKemBase.name = "HPKE_KEM_P521_HKDF_SHA512" dhkemp521hkdfsha512.dhKemBase.Hash = crypto.SHA512 dhkemp521hkdfsha512.dhKemBase.dhKEM = dhkemp521hkdfsha512 dhkemx25519hkdfsha256.size = x25519.Size dhkemx25519hkdfsha256.dhKemBase.id = KEM_X25519_HKDF_SHA256 dhkemx25519hkdfsha256.dhKemBase.name = "HPKE_KEM_X25519_HKDF_SHA256" dhkemx25519hkdfsha256.dhKemBase.Hash = crypto.SHA256 dhkemx25519hkdfsha256.dhKemBase.dhKEM = dhkemx25519hkdfsha256 dhkemx448hkdfsha512.size = x448.Size dhkemx448hkdfsha512.dhKemBase.id = KEM_X448_HKDF_SHA512 dhkemx448hkdfsha512.dhKemBase.name = "HPKE_KEM_X448_HKDF_SHA512" dhkemx448hkdfsha512.dhKemBase.Hash = crypto.SHA512 dhkemx448hkdfsha512.dhKemBase.dhKEM = dhkemx448hkdfsha512 hybridkemX25519Kyber768.kemBase.id = KEM_X25519_KYBER768_DRAFT00 hybridkemX25519Kyber768.kemBase.name = "HPKE_KEM_X25519_KYBER768_HKDF_SHA256" hybridkemX25519Kyber768.kemBase.Hash = crypto.SHA256 hybridkemX25519Kyber768.kemA = dhkemx25519hkdfsha256 hybridkemX25519Kyber768.kemB = kyber768.Scheme() } golang-github-cloudflare-circl-1.3.7/hpke/hpke.go000066400000000000000000000173671454601126700217120ustar00rootroot00000000000000// Package hpke implements the Hybrid Public Key Encryption (HPKE) standard // specified by draft-irtf-cfrg-hpke-07. // // HPKE works for any combination of a public-key encapsulation mechanism // (KEM), a key derivation function (KDF), and an authenticated encryption // scheme with additional data (AEAD). // // Specification in // https://datatracker.ietf.org/doc/draft-irtf-cfrg-hpke // // BUG(cjpatton): This package does not implement the "Export-Only" mode of the // HPKE context. In particular, it does not recognize the AEAD codepoint // reserved for this purpose (0xFFFF). package hpke import ( "crypto/rand" "encoding" "errors" "io" "github.com/cloudflare/circl/kem" ) const versionLabel = "HPKE-v1" // Context defines the capabilities of an HPKE context. type Context interface { encoding.BinaryMarshaler // Export takes a context string exporterContext and a desired length (in // bytes), and produces a secret derived from the internal exporter secret // using the corresponding KDF Expand function. It panics if length is // greater than 255*N bytes, where N is the size (in bytes) of the KDF's // output. Export(exporterContext []byte, length uint) []byte // Suite returns the cipher suite corresponding to this context. Suite() Suite } // Sealer encrypts a plaintext using an AEAD encryption. type Sealer interface { Context // Seal takes a plaintext and associated data to produce a ciphertext. // The nonce is handled by the Sealer and incremented after each call. Seal(pt, aad []byte) (ct []byte, err error) } // Opener decrypts a ciphertext using an AEAD encryption. type Opener interface { Context // Open takes a ciphertext and associated data to recover, if successful, // the plaintext. The nonce is handled by the Opener and incremented after // each call. Open(ct, aad []byte) (pt []byte, err error) } // modeID represents an HPKE variant. type modeID = uint8 const ( // modeBase to enable encryption to the holder of a given KEM private key. modeBase modeID = 0x00 // modePSK extends the base mode by allowing the Receiver to authenticate // that the sender possessed a given pre-shared key (PSK). modePSK modeID = 0x01 // modeAuth extends the base mode by allowing the Receiver to authenticate // that the sender possessed a given KEM private key. modeAuth modeID = 0x02 // modeAuthPSK provides a combination of the PSK and Auth modes. modeAuthPSK modeID = 0x03 ) // Suite is an HPKE cipher suite consisting of a KEM, KDF, and AEAD algorithm. type Suite struct { kemID KEM kdfID KDF aeadID AEAD } // NewSuite builds a Suite from a specified set of algorithms. Panics // if an algorithm identifier is not valid. func NewSuite(kemID KEM, kdfID KDF, aeadID AEAD) Suite { s := Suite{kemID, kdfID, aeadID} if !s.isValid() { panic(ErrInvalidHPKESuite) } return s } type state struct { Suite modeID modeID skS kem.PrivateKey pkS kem.PublicKey psk []byte pskID []byte info []byte } // Sender performs hybrid public-key encryption. type Sender struct { state pkR kem.PublicKey } // NewSender creates a Sender with knowledge of the receiver's public-key. func (suite Suite) NewSender(pkR kem.PublicKey, info []byte) (*Sender, error) { return &Sender{ state: state{Suite: suite, info: info}, pkR: pkR, }, nil } // Setup generates a new HPKE context used for Base Mode encryption. // Returns the Sealer and corresponding encapsulated key. func (s *Sender) Setup(rnd io.Reader) (enc []byte, seal Sealer, err error) { s.modeID = modeBase return s.allSetup(rnd) } // SetupAuth generates a new HPKE context used for Auth Mode encryption. // Returns the Sealer and corresponding encapsulated key. func (s *Sender) SetupAuth(rnd io.Reader, skS kem.PrivateKey) ( enc []byte, seal Sealer, err error, ) { s.modeID = modeAuth s.state.skS = skS return s.allSetup(rnd) } // SetupPSK generates a new HPKE context used for PSK Mode encryption. // Returns the Sealer and corresponding encapsulated key. func (s *Sender) SetupPSK(rnd io.Reader, psk, pskID []byte) ( enc []byte, seal Sealer, err error, ) { s.modeID = modePSK s.state.psk = psk s.state.pskID = pskID return s.allSetup(rnd) } // SetupAuthPSK generates a new HPKE context used for Auth-PSK Mode encryption. // Returns the Sealer and corresponding encapsulated key. func (s *Sender) SetupAuthPSK(rnd io.Reader, skS kem.PrivateKey, psk, pskID []byte) ( enc []byte, seal Sealer, err error, ) { s.modeID = modeAuthPSK s.state.skS = skS s.state.psk = psk s.state.pskID = pskID return s.allSetup(rnd) } // Receiver performs hybrid public-key decryption. type Receiver struct { state skR kem.PrivateKey enc []byte } // NewReceiver creates a Receiver with knowledge of a private key. func (suite Suite) NewReceiver(skR kem.PrivateKey, info []byte) ( *Receiver, error, ) { return &Receiver{state: state{Suite: suite, info: info}, skR: skR}, nil } // Setup generates a new HPKE context used for Base Mode encryption. // Setup takes an encapsulated key and returns an Opener. func (r *Receiver) Setup(enc []byte) (Opener, error) { r.modeID = modeBase r.enc = enc return r.allSetup() } // SetupAuth generates a new HPKE context used for Auth Mode encryption. // SetupAuth takes an encapsulated key and a public key, and returns an Opener. func (r *Receiver) SetupAuth(enc []byte, pkS kem.PublicKey) (Opener, error) { r.modeID = modeAuth r.enc = enc r.state.pkS = pkS return r.allSetup() } // SetupPSK generates a new HPKE context used for PSK Mode encryption. // SetupPSK takes an encapsulated key, and a pre-shared key; and returns an // Opener. func (r *Receiver) SetupPSK(enc, psk, pskID []byte) (Opener, error) { r.modeID = modePSK r.enc = enc r.state.psk = psk r.state.pskID = pskID return r.allSetup() } // SetupAuthPSK generates a new HPKE context used for Auth-PSK Mode encryption. // SetupAuthPSK takes an encapsulated key, a public key, and a pre-shared key; // and returns an Opener. func (r *Receiver) SetupAuthPSK( enc, psk, pskID []byte, pkS kem.PublicKey, ) (Opener, error) { r.modeID = modeAuthPSK r.enc = enc r.state.psk = psk r.state.pskID = pskID r.state.pkS = pkS return r.allSetup() } func (s *Sender) allSetup(rnd io.Reader) ([]byte, Sealer, error) { scheme := s.kemID.Scheme() if rnd == nil { rnd = rand.Reader } seed := make([]byte, scheme.EncapsulationSeedSize()) _, err := io.ReadFull(rnd, seed) if err != nil { return nil, nil, err } var enc, ss []byte switch s.modeID { case modeBase, modePSK: enc, ss, err = scheme.EncapsulateDeterministically(s.pkR, seed) case modeAuth, modeAuthPSK: enc, ss, err = scheme.AuthEncapsulateDeterministically(s.pkR, s.skS, seed) } if err != nil { return nil, nil, err } ctx, err := s.keySchedule(ss, s.info, s.psk, s.pskID) if err != nil { return nil, nil, err } return enc, &sealContext{ctx}, nil } func (r *Receiver) allSetup() (Opener, error) { var err error var ss []byte scheme := r.kemID.Scheme() switch r.modeID { case modeBase, modePSK: ss, err = scheme.Decapsulate(r.skR, r.enc) case modeAuth, modeAuthPSK: ss, err = scheme.AuthDecapsulate(r.skR, r.enc, r.pkS) } if err != nil { return nil, err } ctx, err := r.keySchedule(ss, r.info, r.psk, r.pskID) if err != nil { return nil, err } return &openContext{ctx}, nil } var ( ErrInvalidHPKESuite = errors.New("hpke: invalid HPKE suite") ErrInvalidKDF = errors.New("hpke: invalid KDF identifier") ErrInvalidKEM = errors.New("hpke: invalid KEM identifier") ErrInvalidAEAD = errors.New("hpke: invalid AEAD identifier") ErrInvalidKEMPublicKey = errors.New("hpke: invalid KEM public key") ErrInvalidKEMPrivateKey = errors.New("hpke: invalid KEM private key") ErrInvalidKEMSharedSecret = errors.New("hpke: invalid KEM shared secret") ErrAEADSeqOverflows = errors.New("hpke: AEAD sequence number overflows") ) golang-github-cloudflare-circl-1.3.7/hpke/hpke_test.go000066400000000000000000000071271454601126700227420ustar00rootroot00000000000000package hpke_test import ( "bytes" "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/hpke" ) func Example() { // import "github.com/cloudflare/circl/hpke" // import "crypto/rand" // HPKE suite is a domain parameter. kemID := hpke.KEM_P384_HKDF_SHA384 kdfID := hpke.KDF_HKDF_SHA384 aeadID := hpke.AEAD_AES256GCM suite := hpke.NewSuite(kemID, kdfID, aeadID) info := []byte("public info string, known to both Alice and Bob") // Bob prepares to receive messages and announces his public key. publicBob, privateBob, err := kemID.Scheme().GenerateKeyPair() if err != nil { panic(err) } Bob, err := suite.NewReceiver(privateBob, info) if err != nil { panic(err) } // Alice gets Bob's public key. Alice, err := suite.NewSender(publicBob, info) if err != nil { panic(err) } enc, sealer, err := Alice.Setup(rand.Reader) if err != nil { panic(err) } // Alice encrypts some plaintext and sends the ciphertext to Bob. ptAlice := []byte("text encrypted to Bob's public key") aad := []byte("additional public data") ct, err := sealer.Seal(ptAlice, aad) if err != nil { panic(err) } // Bob decrypts the ciphertext. opener, err := Bob.Setup(enc) if err != nil { panic(err) } ptBob, err := opener.Open(ct, aad) if err != nil { panic(err) } // Plaintext was sent successfully. fmt.Println(bytes.Equal(ptAlice, ptBob)) // Output: true } func runHpkeBenchmark(b *testing.B, kem hpke.KEM, kdf hpke.KDF, aead hpke.AEAD) { suite := hpke.NewSuite(kem, kdf, aead) pkR, skR, err := kem.Scheme().GenerateKeyPair() if err != nil { b.Fatal(err) } info := []byte("public info string") sender, err := suite.NewSender(pkR, info) if err != nil { b.Fatal(err) } b.Run(fmt.Sprintf("SetupSender-%04x-%04x-%04x", kem, kdf, aead), func(b *testing.B) { for i := 0; i < b.N; i++ { _, _, err = sender.Setup(rand.Reader) if err != nil { b.Fatal(err) } } }) enc, _, err := sender.Setup(rand.Reader) if err != nil { b.Fatal(err) } receiver, err := suite.NewReceiver(skR, info) if err != nil { b.Fatal(err) } b.Run(fmt.Sprintf("SetupReceiver-%04x-%04x-%04x", kem, kdf, aead), func(b *testing.B) { for i := 0; i < b.N; i++ { _, err := receiver.Setup(enc) if err != nil { b.Fatal(err) } } }) b.Run(fmt.Sprintf("Encrypt-%04x-%04x-%04x", kem, kdf, aead), func(b *testing.B) { pt := []byte("plaintext") aad := []byte("additional authenticated data") cts := make([][]byte, b.N) _, sealer, err := sender.Setup(rand.Reader) if err != nil { b.Fatal(err) } b.ResetTimer() for i := 0; i < b.N; i++ { cts[i], err = sealer.Seal(pt, aad) if err != nil { b.Fatal(err) } } }) b.Run(fmt.Sprintf("Decrypt-%04x-%04x-%04x", kem, kdf, aead), func(b *testing.B) { pt := []byte("plaintext") aad := []byte("additional authenticated data") cts := make([][]byte, b.N) enc, sealer, err := sender.Setup(rand.Reader) if err != nil { b.Fatal(err) } opener, err := receiver.Setup(enc) if err != nil { b.Fatal(err) } for i := 0; i < b.N; i++ { cts[i], err = sealer.Seal(pt, aad) if err != nil { b.Fatal(err) } } b.ResetTimer() for i := 0; i < b.N; i++ { _, err = opener.Open(cts[i], aad) if err != nil { b.Log(i) b.Fatal(err) } } }) } func BenchmarkHpkeRoundTrip(b *testing.B) { tests := []struct { kem hpke.KEM kdf hpke.KDF aead hpke.AEAD }{ {hpke.KEM_X25519_HKDF_SHA256, hpke.KDF_HKDF_SHA256, hpke.AEAD_AES128GCM}, {hpke.KEM_X25519_KYBER768_DRAFT00, hpke.KDF_HKDF_SHA256, hpke.AEAD_AES128GCM}, } for _, test := range tests { runHpkeBenchmark(b, test.kem, test.kdf, test.aead) } } golang-github-cloudflare-circl-1.3.7/hpke/hybridkem.go000066400000000000000000000135531454601126700227320ustar00rootroot00000000000000package hpke // This file implements a hybrid KEM for HPKE using a simple concatenation // combiner. // // WARNING It is not safe to combine arbitrary KEMs using this combiner. // See the draft specification for more details: // https://bwesterb.github.io/draft-westerbaan-cfrg-hpke-xyber768d00/draft-westerbaan-cfrg-hpke-xyber768d00.html#name-security-considerations import ( "crypto/rand" "github.com/cloudflare/circl/kem" ) type hybridKEM struct { kemBase kemA kem.Scheme kemB kem.Scheme } func (h hybridKEM) PrivateKeySize() int { return h.kemA.PrivateKeySize() + h.kemB.PrivateKeySize() } func (h hybridKEM) SeedSize() int { return 32 } func (h hybridKEM) CiphertextSize() int { return h.kemA.CiphertextSize() + h.kemB.CiphertextSize() } func (h hybridKEM) PublicKeySize() int { return h.kemA.PublicKeySize() + h.kemB.PublicKeySize() } func (h hybridKEM) EncapsulationSeedSize() int { return h.kemA.EncapsulationSeedSize() + h.kemB.EncapsulationSeedSize() } func (h hybridKEM) SharedKeySize() int { return h.kemA.SharedKeySize() + h.kemB.SharedKeySize() } func (h hybridKEM) Name() string { return h.name } func (h hybridKEM) AuthDecapsulate(skR kem.PrivateKey, ct []byte, pkS kem.PublicKey, ) ([]byte, error) { panic("AuthDecapsulate is not supported for this KEM") } func (h hybridKEM) AuthEncapsulate(pkr kem.PublicKey, sks kem.PrivateKey) ( ct []byte, ss []byte, err error, ) { panic("AuthEncapsulate is not supported for this KEM") } func (h hybridKEM) AuthEncapsulateDeterministically(pkr kem.PublicKey, sks kem.PrivateKey, seed []byte) (ct, ss []byte, err error) { panic("AuthEncapsulateDeterministically is not supported for this KEM") } func (h hybridKEM) Encapsulate(pkr kem.PublicKey) ( ct []byte, ss []byte, err error, ) { panic("Encapsulate is not implemented") } func (h hybridKEM) Decapsulate(skr kem.PrivateKey, ct []byte) ([]byte, error) { hybridSk := skr.(*hybridKEMPrivKey) ssA, err := h.kemA.Decapsulate(hybridSk.privA, ct[0:h.kemA.CiphertextSize()]) if err != nil { return nil, err } ssB, err := h.kemB.Decapsulate(hybridSk.privB, ct[h.kemA.CiphertextSize():]) if err != nil { return nil, err } ss := append(ssA, ssB...) return ss, nil } func (h hybridKEM) EncapsulateDeterministically( pkr kem.PublicKey, seed []byte, ) (ct, ss []byte, err error) { hybridPk := pkr.(*hybridKEMPubKey) encA, ssA, err := h.kemA.EncapsulateDeterministically(hybridPk.pubA, seed[0:h.kemA.EncapsulationSeedSize()]) if err != nil { return nil, nil, err } encB, ssB, err := h.kemB.EncapsulateDeterministically(hybridPk.pubB, seed[h.kemA.EncapsulationSeedSize():]) if err != nil { return nil, nil, err } ct = append(encA, encB...) ss = append(ssA, ssB...) return ct, ss, nil } type hybridKEMPrivKey struct { scheme kem.Scheme privA kem.PrivateKey privB kem.PrivateKey } func (k *hybridKEMPrivKey) Scheme() kem.Scheme { return k.scheme } func (k *hybridKEMPrivKey) MarshalBinary() ([]byte, error) { skA, err := k.privA.MarshalBinary() if err != nil { return nil, err } skB, err := k.privB.MarshalBinary() if err != nil { return nil, err } return append(skA, skB...), nil } func (k *hybridKEMPrivKey) Equal(sk kem.PrivateKey) bool { k1, ok := sk.(*hybridKEMPrivKey) return ok && k.privA.Equal(k1.privA) && k.privB.Equal(k1.privB) } func (k *hybridKEMPrivKey) Public() kem.PublicKey { return &hybridKEMPubKey{ scheme: k.scheme, pubA: k.privA.Public(), pubB: k.privB.Public(), } } type hybridKEMPubKey struct { scheme kem.Scheme pubA kem.PublicKey pubB kem.PublicKey } func (k *hybridKEMPubKey) Scheme() kem.Scheme { return k.scheme } func (k hybridKEMPubKey) MarshalBinary() ([]byte, error) { pkA, err := k.pubA.MarshalBinary() if err != nil { return nil, err } pkB, err := k.pubB.MarshalBinary() if err != nil { return nil, err } return append(pkA, pkB...), nil } func (k *hybridKEMPubKey) Equal(pk kem.PublicKey) bool { k1, ok := pk.(*hybridKEMPubKey) return ok && k.pubA.Equal(k1.pubA) && k.pubB.Equal(k1.pubB) } // Deterministically derives a keypair from a seed. If you're unsure, // you're better off using GenerateKey(). // // Panics if seed is not of length SeedSize(). func (h hybridKEM) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { // Implementation based on // https://www.ietf.org/archive/id/draft-irtf-cfrg-hpke-07.html#name-derivekeypair if len(seed) != h.SeedSize() { panic(kem.ErrSeedSize) } outputSeedSize := h.kemA.SeedSize() + h.kemB.SeedSize() dkpPrk := h.labeledExtract([]byte(""), []byte("dkp_prk"), seed) bytes := h.labeledExpand( dkpPrk, []byte("sk"), nil, uint16(outputSeedSize), ) seedA := bytes[0:h.kemA.SeedSize()] seedB := bytes[h.kemA.SeedSize():] pubA, privA := h.kemA.DeriveKeyPair(seedA) pubB, privB := h.kemB.DeriveKeyPair(seedB) privKey := &hybridKEMPrivKey{ privA: privA, privB: privB, } pubKey := &hybridKEMPubKey{ pubA: pubA, pubB: pubB, } return pubKey, privKey } func (h hybridKEM) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { seed := make([]byte, h.SeedSize()) _, err := rand.Read(seed) if err != nil { return nil, nil, err } pk, sk := h.DeriveKeyPair(seed) return pk, sk, nil } func (h hybridKEM) UnmarshalBinaryPrivateKey(data []byte) (kem.PrivateKey, error) { skA, err := h.kemA.UnmarshalBinaryPrivateKey(data[0:h.kemA.PrivateKeySize()]) if err != nil { return nil, err } skB, err := h.kemB.UnmarshalBinaryPrivateKey(data[h.kemA.PrivateKeySize():]) if err != nil { return nil, err } return &hybridKEMPrivKey{ privA: skA, privB: skB, }, nil } func (h hybridKEM) UnmarshalBinaryPublicKey(data []byte) (kem.PublicKey, error) { pkA, err := h.kemA.UnmarshalBinaryPublicKey(data[0:h.kemA.PublicKeySize()]) if err != nil { return nil, err } pkB, err := h.kemB.UnmarshalBinaryPublicKey(data[h.kemA.PublicKeySize():]) if err != nil { return nil, err } return &hybridKEMPubKey{ pubA: pkA, pubB: pkB, }, nil } golang-github-cloudflare-circl-1.3.7/hpke/kembase.go000066400000000000000000000117421454601126700223610ustar00rootroot00000000000000package hpke import ( "crypto" "crypto/rand" "encoding/binary" "io" "github.com/cloudflare/circl/kem" "golang.org/x/crypto/hkdf" ) type dhKEM interface { sizeDH() int calcDH(dh []byte, sk kem.PrivateKey, pk kem.PublicKey) error SeedSize() int DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) UnmarshalBinaryPrivateKey(data []byte) (kem.PrivateKey, error) UnmarshalBinaryPublicKey(data []byte) (kem.PublicKey, error) } type kemBase struct { id KEM name string crypto.Hash } type dhKemBase struct { kemBase dhKEM } func (k kemBase) Name() string { return k.name } func (k kemBase) SharedKeySize() int { return k.Hash.Size() } func (k kemBase) getSuiteID() (sid [5]byte) { sid[0], sid[1], sid[2] = 'K', 'E', 'M' binary.BigEndian.PutUint16(sid[3:5], uint16(k.id)) return } func (k kemBase) extractExpand(dh, kemCtx []byte) []byte { eaePkr := k.labeledExtract([]byte(""), []byte("eae_prk"), dh) return k.labeledExpand( eaePkr, []byte("shared_secret"), kemCtx, uint16(k.Size()), ) } func (k kemBase) labeledExtract(salt, label, info []byte) []byte { suiteID := k.getSuiteID() labeledIKM := append(append(append(append( make([]byte, 0, len(versionLabel)+len(suiteID)+len(label)+len(info)), versionLabel...), suiteID[:]...), label...), info...) return hkdf.Extract(k.New, labeledIKM, salt) } func (k kemBase) labeledExpand(prk, label, info []byte, l uint16) []byte { suiteID := k.getSuiteID() labeledInfo := make( []byte, 2, 2+len(versionLabel)+len(suiteID)+len(label)+len(info), ) binary.BigEndian.PutUint16(labeledInfo[0:2], l) labeledInfo = append(append(append(append(labeledInfo, versionLabel...), suiteID[:]...), label...), info...) b := make([]byte, l) rd := hkdf.Expand(k.New, prk, labeledInfo) if _, err := io.ReadFull(rd, b); err != nil { panic(err) } return b } func (k dhKemBase) AuthEncapsulate(pkr kem.PublicKey, sks kem.PrivateKey) ( ct []byte, ss []byte, err error, ) { seed := make([]byte, k.SeedSize()) _, err = io.ReadFull(rand.Reader, seed) if err != nil { return nil, nil, err } return k.authEncap(pkr, sks, seed) } func (k dhKemBase) Encapsulate(pkr kem.PublicKey) ( ct []byte, ss []byte, err error, ) { seed := make([]byte, k.SeedSize()) _, err = io.ReadFull(rand.Reader, seed) if err != nil { return nil, nil, err } return k.encap(pkr, seed) } func (k dhKemBase) AuthEncapsulateDeterministically( pkr kem.PublicKey, sks kem.PrivateKey, seed []byte, ) (ct, ss []byte, err error) { return k.authEncap(pkr, sks, seed) } func (k dhKemBase) EncapsulateDeterministically( pkr kem.PublicKey, seed []byte, ) (ct, ss []byte, err error) { return k.encap(pkr, seed) } func (k dhKemBase) encap( pkR kem.PublicKey, seed []byte, ) (ct []byte, ss []byte, err error) { dh := make([]byte, k.sizeDH()) enc, kemCtx, err := k.coreEncap(dh, pkR, seed) if err != nil { return nil, nil, err } ss = k.extractExpand(dh, kemCtx) return enc, ss, nil } func (k dhKemBase) authEncap( pkR kem.PublicKey, skS kem.PrivateKey, seed []byte, ) (ct []byte, ss []byte, err error) { dhLen := k.sizeDH() dh := make([]byte, 2*dhLen) enc, kemCtx, err := k.coreEncap(dh[:dhLen], pkR, seed) if err != nil { return nil, nil, err } err = k.calcDH(dh[dhLen:], skS, pkR) if err != nil { return nil, nil, err } pkS := skS.Public() pkSm, err := pkS.MarshalBinary() if err != nil { return nil, nil, err } kemCtx = append(kemCtx, pkSm...) ss = k.extractExpand(dh, kemCtx) return enc, ss, nil } func (k dhKemBase) coreEncap( dh []byte, pkR kem.PublicKey, seed []byte, ) (enc []byte, kemCtx []byte, err error) { pkE, skE := k.DeriveKeyPair(seed) err = k.calcDH(dh, skE, pkR) if err != nil { return nil, nil, err } enc, err = pkE.MarshalBinary() if err != nil { return nil, nil, err } pkRm, err := pkR.MarshalBinary() if err != nil { return nil, nil, err } kemCtx = append(append([]byte{}, enc...), pkRm...) return enc, kemCtx, nil } func (k dhKemBase) Decapsulate(skr kem.PrivateKey, ct []byte) ([]byte, error) { dh := make([]byte, k.sizeDH()) kemCtx, err := k.coreDecap(dh, skr, ct) if err != nil { return nil, err } return k.extractExpand(dh, kemCtx), nil } func (k dhKemBase) AuthDecapsulate( skR kem.PrivateKey, ct []byte, pkS kem.PublicKey, ) ([]byte, error) { dhLen := k.sizeDH() dh := make([]byte, 2*dhLen) kemCtx, err := k.coreDecap(dh[:dhLen], skR, ct) if err != nil { return nil, err } err = k.calcDH(dh[dhLen:], skR, pkS) if err != nil { return nil, err } pkSm, err := pkS.MarshalBinary() if err != nil { return nil, err } kemCtx = append(kemCtx, pkSm...) return k.extractExpand(dh, kemCtx), nil } func (k dhKemBase) coreDecap( dh []byte, skR kem.PrivateKey, ct []byte, ) ([]byte, error) { pkE, err := k.UnmarshalBinaryPublicKey(ct) if err != nil { return nil, err } err = k.calcDH(dh, skR, pkE) if err != nil { return nil, err } pkR := skR.Public() pkRm, err := pkR.MarshalBinary() if err != nil { return nil, err } return append(append([]byte{}, ct...), pkRm...), nil } golang-github-cloudflare-circl-1.3.7/hpke/marshal.go000066400000000000000000000075101454601126700223770ustar00rootroot00000000000000package hpke import ( "errors" "golang.org/x/crypto/cryptobyte" ) // marshal serializes an HPKE context. func (c *encdecContext) marshal() ([]byte, error) { var b cryptobyte.Builder b.AddUint16(uint16(c.suite.kemID)) b.AddUint16(uint16(c.suite.kdfID)) b.AddUint16(uint16(c.suite.aeadID)) b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { b.AddBytes(c.exporterSecret) }) b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { b.AddBytes(c.key) }) b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { b.AddBytes(c.baseNonce) }) b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { b.AddBytes(c.sequenceNumber) }) return b.Bytes() } // unmarshalContext parses an HPKE context. func unmarshalContext(raw []byte) (*encdecContext, error) { var ( err error t cryptobyte.String ) c := new(encdecContext) s := cryptobyte.String(raw) if !s.ReadUint16((*uint16)(&c.suite.kemID)) || !s.ReadUint16((*uint16)(&c.suite.kdfID)) || !s.ReadUint16((*uint16)(&c.suite.aeadID)) || !s.ReadUint8LengthPrefixed(&t) || !t.ReadBytes(&c.exporterSecret, len(t)) || !s.ReadUint8LengthPrefixed(&t) || !t.ReadBytes(&c.key, len(t)) || !s.ReadUint8LengthPrefixed(&t) || !t.ReadBytes(&c.baseNonce, len(t)) || !s.ReadUint8LengthPrefixed(&t) || !t.ReadBytes(&c.sequenceNumber, len(t)) { return nil, errors.New("failed to parse context") } if !c.suite.isValid() { return nil, ErrInvalidHPKESuite } Nh := c.suite.kdfID.ExtractSize() if len(c.exporterSecret) != Nh { return nil, errors.New("invalid exporter secret length") } Nk := int(c.suite.aeadID.KeySize()) if len(c.key) != Nk { return nil, errors.New("invalid key length") } c.AEAD, err = c.suite.aeadID.New(c.key) if err != nil { return nil, err } Nn := int(c.suite.aeadID.NonceSize()) if len(c.baseNonce) != Nn { return nil, errors.New("invalid base nonce length") } if len(c.sequenceNumber) != Nn { return nil, errors.New("invalid sequence number length") } c.nonce = make([]byte, Nn) return c, nil } // MarshalBinary serializes an HPKE sealer according to the format specified // below. (Expressed in TLS syntax.) Note that this format is not defined by // the HPKE standard. // // enum { sealer(0), opener(1) } HpkeRole; // // struct { // HpkeKemId kem_id; // draft-irtf-cfrg-hpke-07 // HpkeKdfId kdf_id; // draft-irtf-cfrg-hpke-07 // HpkeAeadId aead_id; // draft-irtf-cfrg-hpke-07 // opaque exporter_secret<0..255>; // opaque key<0..255>; // opaque base_nonce<0..255>; // opaque seq<0..255>; // } HpkeContext; // // struct { // HpkeRole role = 0; // sealer // HpkeContext context; // } HpkeSealer; func (c *sealContext) MarshalBinary() ([]byte, error) { rawContext, err := c.encdecContext.marshal() if err != nil { return nil, err } return append([]byte{0}, rawContext...), nil } // UnmarshalSealer parses an HPKE sealer. func UnmarshalSealer(raw []byte) (Sealer, error) { if raw[0] != 0 { return nil, errors.New("incorrect role") } context, err := unmarshalContext(raw[1:]) if err != nil { return nil, err } return &sealContext{context}, nil } // MarshalBinary serializes an HPKE opener according to the format specified // below. (Expressed in TLS syntax.) Note that this format is not defined by the // HPKE standard. // // struct { // HpkeRole role = 1; // opener // HpkeContext context; // } HpkeOpener; func (c *openContext) MarshalBinary() ([]byte, error) { rawContext, err := c.encdecContext.marshal() if err != nil { return nil, err } return append([]byte{1}, rawContext...), nil } // UnmarshalOpener parses a serialized HPKE opener and returns the corresponding // Opener. func UnmarshalOpener(raw []byte) (Opener, error) { if raw[0] != 1 { return nil, errors.New("incorrect role") } context, err := unmarshalContext(raw[1:]) if err != nil { return nil, err } return &openContext{context}, nil } golang-github-cloudflare-circl-1.3.7/hpke/marshal_test.go000066400000000000000000000037121454601126700234360ustar00rootroot00000000000000package hpke import ( "bytes" "crypto/rand" "testing" ) func contextEqual(a, b *encdecContext) bool { an := make([]byte, a.NonceSize()) bn := make([]byte, b.NonceSize()) ac := a.AEAD.Seal(nil, an, nil, nil) bc := b.AEAD.Seal(nil, bn, nil, nil) return a.suite == b.suite && bytes.Equal(a.exporterSecret, b.exporterSecret) && bytes.Equal(a.key, b.key) && bytes.Equal(a.baseNonce, b.baseNonce) && bytes.Equal(a.sequenceNumber, b.sequenceNumber) && bytes.Equal(ac, bc) && len(a.nonce) == len(b.nonce) && len(a.nonce) == len(a.baseNonce) } func TestContextSerialization(t *testing.T) { s := NewSuite(KEM_P384_HKDF_SHA384, KDF_HKDF_SHA384, AEAD_AES256GCM) info := []byte("some info string") pk, sk, err := s.kemID.Scheme().GenerateKeyPair() if err != nil { t.Fatal(err) } receiver, err := s.NewReceiver(sk, info) if err != nil { t.Fatal(err) } sender, err := s.NewSender(pk, info) if err != nil { t.Fatal(err) } enc, sealer, err := sender.Setup(rand.Reader) if err != nil { t.Fatal(err) } opener, err := receiver.Setup(enc) if err != nil { t.Fatal(err) } rawSealer, err := sealer.MarshalBinary() if err != nil { t.Fatal(err) } parsedSealer, err := UnmarshalSealer(rawSealer) if err != nil { t.Fatal(err) } if !contextEqual( sealer.(*sealContext).encdecContext, parsedSealer.(*sealContext).encdecContext) { t.Error("parsed sealer does not match original") } _, err = UnmarshalOpener(rawSealer) if err == nil { t.Error("parsing a sealer as an opener succeeded; want failure") } rawOpener, err := opener.MarshalBinary() if err != nil { t.Fatal(err) } parsedOpener, err := UnmarshalOpener(rawOpener) if err != nil { t.Fatal(err) } if !contextEqual( opener.(*openContext).encdecContext, parsedOpener.(*openContext).encdecContext) { t.Error("parsed opener does not match original") } _, err = UnmarshalSealer(rawOpener) if err == nil { t.Error("parsing an opener as a sealer succeeded; want failure") } } golang-github-cloudflare-circl-1.3.7/hpke/shortkem.go000066400000000000000000000110441454601126700226010ustar00rootroot00000000000000package hpke import ( "crypto/elliptic" "crypto/rand" "crypto/subtle" "fmt" "math/big" "github.com/cloudflare/circl/kem" ) type shortKEM struct { dhKemBase elliptic.Curve } func (s shortKEM) PrivateKeySize() int { return s.byteSize() } func (s shortKEM) SeedSize() int { return s.byteSize() } func (s shortKEM) CiphertextSize() int { return 1 + 2*s.byteSize() } func (s shortKEM) PublicKeySize() int { return 1 + 2*s.byteSize() } func (s shortKEM) EncapsulationSeedSize() int { return s.byteSize() } func (s shortKEM) byteSize() int { return (s.Params().BitSize + 7) / 8 } func (s shortKEM) sizeDH() int { return s.byteSize() } func (s shortKEM) calcDH(dh []byte, sk kem.PrivateKey, pk kem.PublicKey) error { PK := pk.(*shortKEMPubKey) SK := sk.(*shortKEMPrivKey) l := len(dh) x, _ := s.ScalarMult(PK.x, PK.y, SK.priv) // only x-coordinate is used. if x.Sign() == 0 { return ErrInvalidKEMSharedSecret } b := x.Bytes() copy(dh[l-len(b):l], b) return nil } // Deterministically derives a keypair from a seed. If you're unsure, // you're better off using GenerateKey(). // // Panics if seed is not of length SeedSize(). func (s shortKEM) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { // Implementation based on // https://www.ietf.org/archive/id/draft-irtf-cfrg-hpke-07.html#name-derivekeypair if len(seed) != s.SeedSize() { panic(kem.ErrSeedSize) } bitmask := byte(0xFF) if s.Params().BitSize == 521 { bitmask = 0x01 } dkpPrk := s.labeledExtract([]byte(""), []byte("dkp_prk"), seed) var bytes []byte ctr := 0 for skBig := new(big.Int); skBig.Sign() == 0 || skBig.Cmp(s.Params().N) >= 0; ctr++ { if ctr > 255 { panic("derive key error") } bytes = s.labeledExpand( dkpPrk, []byte("candidate"), []byte{byte(ctr)}, uint16(s.byteSize()), ) bytes[0] &= bitmask skBig.SetBytes(bytes) } l := s.PrivateKeySize() sk := &shortKEMPrivKey{s, make([]byte, l), nil} copy(sk.priv[l-len(bytes):], bytes) return sk.Public(), sk } func (s shortKEM) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { sk, x, y, err := elliptic.GenerateKey(s, rand.Reader) pub := &shortKEMPubKey{s, x, y} return pub, &shortKEMPrivKey{s, sk, pub}, err } func (s shortKEM) UnmarshalBinaryPrivateKey(data []byte) (kem.PrivateKey, error) { l := s.PrivateKeySize() if len(data) < l { return nil, ErrInvalidKEMPrivateKey } sk := &shortKEMPrivKey{s, make([]byte, l), nil} copy(sk.priv[l-len(data):l], data[:l]) if !sk.validate() { return nil, ErrInvalidKEMPrivateKey } return sk, nil } func (s shortKEM) UnmarshalBinaryPublicKey(data []byte) (kem.PublicKey, error) { x, y := elliptic.Unmarshal(s, data) if x == nil { return nil, ErrInvalidKEMPublicKey } key := &shortKEMPubKey{s, x, y} if !key.validate() { return nil, ErrInvalidKEMPublicKey } return key, nil } type shortKEMPubKey struct { scheme shortKEM x, y *big.Int } func (k *shortKEMPubKey) String() string { return fmt.Sprintf("x: %v\ny: %v", k.x.Text(16), k.y.Text(16)) } func (k *shortKEMPubKey) Scheme() kem.Scheme { return k.scheme } func (k *shortKEMPubKey) MarshalBinary() ([]byte, error) { return elliptic.Marshal(k.scheme, k.x, k.y), nil } func (k *shortKEMPubKey) Equal(pk kem.PublicKey) bool { k1, ok := pk.(*shortKEMPubKey) return ok && k.scheme.Params().Name == k1.scheme.Params().Name && k.x.Cmp(k1.x) == 0 && k.y.Cmp(k1.y) == 0 } func (k *shortKEMPubKey) validate() bool { p := k.scheme.Params().P notAtInfinity := k.x.Sign() > 0 && k.y.Sign() > 0 lessThanP := k.x.Cmp(p) < 0 && k.y.Cmp(p) < 0 onCurve := k.scheme.IsOnCurve(k.x, k.y) return notAtInfinity && lessThanP && onCurve } type shortKEMPrivKey struct { scheme shortKEM priv []byte pub *shortKEMPubKey } func (k *shortKEMPrivKey) String() string { return fmt.Sprintf("%x", k.priv) } func (k *shortKEMPrivKey) Scheme() kem.Scheme { return k.scheme } func (k *shortKEMPrivKey) MarshalBinary() ([]byte, error) { return append(make([]byte, 0, k.scheme.PrivateKeySize()), k.priv...), nil } func (k *shortKEMPrivKey) Equal(pk kem.PrivateKey) bool { k1, ok := pk.(*shortKEMPrivKey) return ok && k.scheme.Params().Name == k1.scheme.Params().Name && subtle.ConstantTimeCompare(k.priv, k1.priv) == 1 } func (k *shortKEMPrivKey) Public() kem.PublicKey { if k.pub == nil { x, y := k.scheme.ScalarBaseMult(k.priv) k.pub = &shortKEMPubKey{k.scheme, x, y} } return k.pub } func (k *shortKEMPrivKey) validate() bool { n := new(big.Int).SetBytes(k.priv) order := k.scheme.Curve.Params().N return len(k.priv) == k.scheme.PrivateKeySize() && n.Cmp(order) < 0 } 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hpke import ( "encoding/binary" "errors" "fmt" ) func (st state) keySchedule(ss, info, psk, pskID []byte) (*encdecContext, error) { if err := st.verifyPSKInputs(psk, pskID); err != nil { return nil, err } pskIDHash := st.labeledExtract(nil, []byte("psk_id_hash"), pskID) infoHash := st.labeledExtract(nil, []byte("info_hash"), info) keySchCtx := append(append( []byte{st.modeID}, pskIDHash...), infoHash...) secret := st.labeledExtract(ss, []byte("secret"), psk) Nk := uint16(st.aeadID.KeySize()) key := st.labeledExpand(secret, []byte("key"), keySchCtx, Nk) aead, err := st.aeadID.New(key) if err != nil { return nil, err } Nn := uint16(aead.NonceSize()) baseNonce := st.labeledExpand(secret, []byte("base_nonce"), keySchCtx, Nn) exporterSecret := st.labeledExpand( secret, []byte("exp"), keySchCtx, uint16(st.kdfID.ExtractSize()), ) return &encdecContext{ st.Suite, ss, secret, keySchCtx, exporterSecret, key, baseNonce, make([]byte, Nn), aead, make([]byte, Nn), }, nil } func (st state) verifyPSKInputs(psk, pskID []byte) error { gotPSK := psk != nil gotPSKID := pskID != nil if gotPSK != gotPSKID { return errors.New("inconsistent PSK inputs") } switch st.modeID { case modeBase | modeAuth: if gotPSK { return errors.New("PSK input provided when not needed") } case modePSK | modeAuthPSK: if !gotPSK { return errors.New("missing required PSK input") } } return nil } // Params returns the codepoints for the algorithms comprising the suite. func (suite Suite) Params() (KEM, KDF, AEAD) { return suite.kemID, suite.kdfID, suite.aeadID } func (suite Suite) String() string { return fmt.Sprintf( "kem_id: %v kdf_id: %v aead_id: %v", suite.kemID, suite.kdfID, suite.aeadID, ) } func (suite Suite) getSuiteID() (id [10]byte) { id[0], id[1], id[2], id[3] = 'H', 'P', 'K', 'E' binary.BigEndian.PutUint16(id[4:6], uint16(suite.kemID)) binary.BigEndian.PutUint16(id[6:8], uint16(suite.kdfID)) binary.BigEndian.PutUint16(id[8:10], uint16(suite.aeadID)) return } func (suite Suite) isValid() bool { return suite.kemID.IsValid() && suite.kdfID.IsValid() && suite.aeadID.IsValid() } func (suite Suite) labeledExtract(salt, label, ikm []byte) []byte { suiteID := suite.getSuiteID() labeledIKM := append(append(append(append( make([]byte, 0, len(versionLabel)+len(suiteID)+len(label)+len(ikm)), versionLabel...), suiteID[:]...), label...), ikm...) return suite.kdfID.Extract(labeledIKM, salt) } func (suite Suite) labeledExpand(prk, label, info []byte, l uint16) []byte { suiteID := suite.getSuiteID() labeledInfo := make([]byte, 2, 2+len(versionLabel)+len(suiteID)+len(label)+len(info)) binary.BigEndian.PutUint16(labeledInfo[0:2], l) labeledInfo = append(append(append(append(labeledInfo, versionLabel...), suiteID[:]...), label...), info...) return suite.kdfID.Expand(prk, labeledInfo, uint(l)) } golang-github-cloudflare-circl-1.3.7/hpke/vectors_test.go000066400000000000000000000275531454601126700235050ustar00rootroot00000000000000package hpke import ( "bytes" "encoding/hex" "encoding/json" "fmt" "io" "os" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/kem" "golang.org/x/crypto/sha3" ) var ( outputTestVectorEnvironmentKey = "HPKE_TEST_VECTORS_OUT" testVectorEncryptionCount = 257 testVectorExportLength = 32 ) func TestVectors(t *testing.T) { // Test vectors from // https://github.com/cfrg/draft-irtf-cfrg-hpke/blob/master/test-vectors.json vectors := readFile(t, "testdata/vectors_rfc9180_5f503c5.json") for i, v := range vectors { t.Run(fmt.Sprintf("v%v", i), v.verify) } } func (v *vector) verify(t *testing.T) { m := v.ModeID kem, kdf, aead := KEM(v.KemID), KDF(v.KdfID), AEAD(v.AeadID) if !kem.IsValid() { t.Skipf("Skipping test with unknown KEM: %x", kem) } if !kdf.IsValid() { t.Skipf("Skipping test with unknown KDF: %x", kdf) } if !aead.IsValid() { t.Skipf("Skipping test with unknown AEAD: %x", aead) } s := NewSuite(kem, kdf, aead) sender, recv := v.getActors(t, kem.Scheme(), s) sealer, opener := v.setup(t, kem.Scheme(), sender, recv, m, s) v.checkAead(t, (sealer.(*sealContext)).encdecContext, m) v.checkAead(t, (opener.(*openContext)).encdecContext, m) v.checkEncryptions(t, sealer, opener, m) v.checkExports(t, sealer, m) v.checkExports(t, opener, m) } func (v *vector) getActors( t *testing.T, dhkem kem.Scheme, s Suite, ) (*Sender, *Receiver) { h := s.String() + "\n" pkR, err := dhkem.UnmarshalBinaryPublicKey(hexB(t, v.PkRm)) test.CheckNoErr(t, err, h+"bad public key") skR, err := dhkem.UnmarshalBinaryPrivateKey(hexB(t, v.SkRm)) test.CheckNoErr(t, err, h+"bad private key") info := hexB(t, v.Info) sender, err := s.NewSender(pkR, info) test.CheckNoErr(t, err, h+"err sender") recv, err := s.NewReceiver(skR, info) test.CheckNoErr(t, err, h+"err receiver") return sender, recv } func (v *vector) setup(t *testing.T, k kem.Scheme, se *Sender, re *Receiver, m modeID, s Suite, ) (sealer Sealer, opener Opener) { seed := hexB(t, v.IkmE) rd := bytes.NewReader(seed) var enc []byte var skS kem.PrivateKey var pkS kem.PublicKey var errS, errR, errPK, errSK error switch v.ModeID { case modeBase: enc, sealer, errS = se.Setup(rd) if errS == nil { opener, errR = re.Setup(enc) } case modePSK: psk, pskid := hexB(t, v.Psk), hexB(t, v.PskID) enc, sealer, errS = se.SetupPSK(rd, psk, pskid) if errS == nil { opener, errR = re.SetupPSK(enc, psk, pskid) } case modeAuth: skS, errSK = k.UnmarshalBinaryPrivateKey(hexB(t, v.SkSm)) if errSK == nil { pkS, errPK = k.UnmarshalBinaryPublicKey(hexB(t, v.PkSm)) if errPK == nil { enc, sealer, errS = se.SetupAuth(rd, skS) if errS == nil { opener, errR = re.SetupAuth(enc, pkS) } } } case modeAuthPSK: psk, pskid := hexB(t, v.Psk), hexB(t, v.PskID) skS, errSK = k.UnmarshalBinaryPrivateKey(hexB(t, v.SkSm)) if errSK == nil { pkS, errPK = k.UnmarshalBinaryPublicKey(hexB(t, v.PkSm)) if errPK == nil { enc, sealer, errS = se.SetupAuthPSK(rd, skS, psk, pskid) if errS == nil { opener, errR = re.SetupAuthPSK(enc, psk, pskid, pkS) } } } } h := fmt.Sprintf("mode: %v %v\n", m, s) test.CheckNoErr(t, errS, h+"error on sender setup") test.CheckNoErr(t, errR, h+"error on receiver setup") test.CheckNoErr(t, errSK, h+"bad private key") test.CheckNoErr(t, errPK, h+"bad public key") return sealer, opener } func (v *vector) checkAead(t *testing.T, e *encdecContext, m modeID) { got := e.baseNonce want := hexB(t, v.BaseNonce) if !bytes.Equal(got, want) { test.ReportError(t, got, want, m, e.Suite()) } got = e.exporterSecret want = hexB(t, v.ExporterSecret) if !bytes.Equal(got, want) { test.ReportError(t, got, want, m, e.Suite()) } } func (v *vector) checkEncryptions( t *testing.T, se Sealer, op Opener, m modeID, ) { for j, encv := range v.Encryptions { pt := hexB(t, encv.Plaintext) aad := hexB(t, encv.Aad) ct, err := se.Seal(pt, aad) test.CheckNoErr(t, err, "error on sealing") got, err := op.Open(ct, aad) test.CheckNoErr(t, err, "error on opening") want := pt if !bytes.Equal(got, want) { test.ReportError(t, got, want, m, se.Suite(), j) } } } func (v *vector) checkExports(t *testing.T, context Context, m modeID) { for j, expv := range v.Exports { ctx := hexB(t, expv.ExportContext) want := hexB(t, expv.ExportValue) got := context.Export(ctx, uint(expv.ExportLength)) if !bytes.Equal(got, want) { test.ReportError(t, got, want, m, context.Suite(), j) } } } func hexB(t *testing.T, x string) []byte { t.Helper() z, err := hex.DecodeString(x) test.CheckNoErr(t, err, "") return z } func readFile(t *testing.T, fileName string) []vector { jsonFile, err := os.Open(fileName) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", fileName, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", fileName, err) } var vectors []vector err = json.Unmarshal(input, &vectors) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) } return vectors } type encryptionVector struct { Aad string `json:"aad"` Ciphertext string `json:"ct"` Nonce string `json:"nonce"` Plaintext string `json:"pt"` } type exportVector struct { ExportContext string `json:"exporter_context"` ExportLength int `json:"L"` ExportValue string `json:"exported_value"` } type vector struct { ModeID uint8 `json:"mode"` KemID uint16 `json:"kem_id"` KdfID uint16 `json:"kdf_id"` AeadID uint16 `json:"aead_id"` Info string `json:"info"` Ier string `json:"ier,omitempty"` IkmR string `json:"ikmR"` IkmE string `json:"ikmE,omitempty"` SkRm string `json:"skRm"` SkEm string `json:"skEm,omitempty"` SkSm string `json:"skSm,omitempty"` Psk string `json:"psk,omitempty"` PskID string `json:"psk_id,omitempty"` PkSm string `json:"pkSm,omitempty"` PkRm string `json:"pkRm"` PkEm string `json:"pkEm,omitempty"` Enc string `json:"enc"` SharedSecret string `json:"shared_secret"` KeyScheduleContext string `json:"key_schedule_context"` Secret string `json:"secret"` Key string `json:"key"` BaseNonce string `json:"base_nonce"` ExporterSecret string `json:"exporter_secret"` Encryptions []encryptionVector `json:"encryptions"` Exports []exportVector `json:"exports"` } func generateHybridKeyPair(rnd io.Reader, h kem.Scheme) ([]byte, kem.PublicKey, kem.PrivateKey, error) { seed := make([]byte, h.SeedSize()) _, err := rnd.Read(seed) if err != nil { return nil, nil, nil, err } pk, sk := h.DeriveKeyPair(seed) return seed, pk, sk, nil } func mustEncodePublicKey(pk kem.PublicKey) []byte { enc, err := pk.MarshalBinary() if err != nil { panic(err) } return enc } func mustEncodePrivateKey(sk kem.PrivateKey) []byte { enc, err := sk.MarshalBinary() if err != nil { panic(err) } return enc } func generateEncryptions(sealer Sealer, opener Opener, msg []byte) ([]encryptionVector, error) { vectors := make([]encryptionVector, testVectorEncryptionCount) for i := 0; i < len(vectors); i++ { aad := []byte(fmt.Sprintf("Count-%d", i)) innerSealer := sealer.(*sealContext) nonce := innerSealer.calcNonce() encrypted, err := sealer.Seal(msg, aad) if err != nil { return nil, err } decrypted, err := opener.Open(encrypted, aad) if err != nil { return nil, err } if !bytes.Equal(decrypted, msg) { return nil, fmt.Errorf("Mismatch messages %d", i) } vectors[i] = encryptionVector{ Plaintext: hex.EncodeToString(msg), Aad: hex.EncodeToString(aad), Nonce: hex.EncodeToString(nonce), Ciphertext: hex.EncodeToString(encrypted), } } return vectors, nil } func generateExports(sealer Sealer, opener Opener) ([]exportVector, error) { exportContexts := [][]byte{ []byte(""), {0x00}, []byte("TestContext"), } vectors := make([]exportVector, len(exportContexts)) for i := 0; i < len(vectors); i++ { senderValue := sealer.Export(exportContexts[i], uint(testVectorExportLength)) receiverValue := opener.Export(exportContexts[i], uint(testVectorExportLength)) if !bytes.Equal(senderValue, receiverValue) { return nil, fmt.Errorf("Mismatch export values") } vectors[i] = exportVector{ ExportContext: hex.EncodeToString(exportContexts[i]), ExportLength: testVectorExportLength, ExportValue: hex.EncodeToString(senderValue), } } return vectors, nil } func TestHybridKemRoundTrip(t *testing.T) { kemID := KEM_X25519_KYBER768_DRAFT00 kdfID := KDF_HKDF_SHA256 aeadID := AEAD_AES128GCM rnd := sha3.NewShake128() suite := NewSuite(kemID, kdfID, aeadID) msg := []byte("To the universal deployment of PQC") info := []byte("Hear hear") pskid := []byte("before everybody for everybody for everything") psk := make([]byte, 32) _, _ = rnd.Read(psk) ikmR, pkR, skR, err := generateHybridKeyPair(rnd, kemID.Scheme()) if err != nil { t.Error(err) } ier := make([]byte, 64) _, _ = rnd.Read(ier) receiver, err := suite.NewReceiver(skR, info) if err != nil { t.Error(err) } sender, err := suite.NewSender(pkR, info) if err != nil { t.Error(err) } generateVector := func(mode uint8) vector { var ( err2 error sealer Sealer opener Opener enc []byte ) rnd2 := bytes.NewBuffer(ier) switch mode { case modeBase: enc, sealer, err2 = sender.Setup(rnd2) if err2 != nil { t.Error(err2) } opener, err2 = receiver.Setup(enc) if err2 != nil { t.Error(err2) } case modePSK: enc, sealer, err2 = sender.SetupPSK(rnd2, psk, pskid) if err2 != nil { t.Error(err2) } opener, err2 = receiver.SetupPSK(enc, psk, pskid) if err2 != nil { t.Error(err2) } default: panic("unsupported mode") } if rnd2.Len() != 0 { t.Fatal() } innerSealer := sealer.(*sealContext) encryptions, err2 := generateEncryptions(sealer, opener, msg) if err2 != nil { t.Error(err2) } exports, err2 := generateExports(sealer, opener) if err2 != nil { t.Error(err2) } ret := vector{ ModeID: mode, KemID: uint16(kemID), KdfID: uint16(kdfID), AeadID: uint16(aeadID), Ier: hex.EncodeToString(ier), Info: hex.EncodeToString(info), IkmR: hex.EncodeToString(ikmR), SkRm: hex.EncodeToString(mustEncodePrivateKey(skR)), PkRm: hex.EncodeToString(mustEncodePublicKey(pkR)), Enc: hex.EncodeToString(enc), SharedSecret: hex.EncodeToString(innerSealer.sharedSecret), KeyScheduleContext: hex.EncodeToString(innerSealer.keyScheduleContext), Secret: hex.EncodeToString(innerSealer.secret), Key: hex.EncodeToString(innerSealer.key), BaseNonce: hex.EncodeToString(innerSealer.baseNonce), ExporterSecret: hex.EncodeToString(innerSealer.exporterSecret), Encryptions: encryptions, Exports: exports, } if mode == modePSK { ret.Psk = hex.EncodeToString(psk) ret.PskID = hex.EncodeToString(pskid) } return ret } encodedVector, err := json.Marshal([]vector{ generateVector(modeBase), generateVector(modePSK), }) if err != nil { t.Error(err) } var outputFile string if outputFile = os.Getenv(outputTestVectorEnvironmentKey); len(outputFile) > 0 { // nolint: gosec err = os.WriteFile(outputFile, encodedVector, 0o644) if err != nil { t.Error(err) } } } golang-github-cloudflare-circl-1.3.7/hpke/xkem.go000066400000000000000000000103361454601126700217140ustar00rootroot00000000000000package hpke import ( "bytes" "crypto/rand" "crypto/subtle" "fmt" "io" "github.com/cloudflare/circl/dh/x25519" "github.com/cloudflare/circl/dh/x448" "github.com/cloudflare/circl/kem" ) type xKEM struct { dhKemBase size int } func (x xKEM) PrivateKeySize() int { return x.size } func (x xKEM) SeedSize() int { return x.size } func (x xKEM) CiphertextSize() int { return x.size } func (x xKEM) PublicKeySize() int { return x.size } func (x xKEM) EncapsulationSeedSize() int { return x.size } func (x xKEM) sizeDH() int { return x.size } func (x xKEM) calcDH(dh []byte, sk kem.PrivateKey, pk kem.PublicKey) error { PK := pk.(*xKEMPubKey) SK := sk.(*xKEMPrivKey) switch x.size { case x25519.Size: var ss, sKey, pKey x25519.Key copy(sKey[:], SK.priv) copy(pKey[:], PK.pub) if !x25519.Shared(&ss, &sKey, &pKey) { return ErrInvalidKEMSharedSecret } copy(dh, ss[:]) case x448.Size: var ss, sKey, pKey x448.Key copy(sKey[:], SK.priv) copy(pKey[:], PK.pub) if !x448.Shared(&ss, &sKey, &pKey) { return ErrInvalidKEMSharedSecret } copy(dh, ss[:]) } return nil } // Deterministically derives a keypair from a seed. If you're unsure, // you're better off using GenerateKey(). // // Panics if seed is not of length SeedSize(). func (x xKEM) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { // Implementation based on // https://www.ietf.org/archive/id/draft-irtf-cfrg-hpke-07.html#name-derivekeypair if len(seed) != x.SeedSize() { panic(kem.ErrSeedSize) } sk := &xKEMPrivKey{scheme: x, priv: make([]byte, x.size)} dkpPrk := x.labeledExtract([]byte(""), []byte("dkp_prk"), seed) bytes := x.labeledExpand( dkpPrk, []byte("sk"), nil, uint16(x.PrivateKeySize()), ) copy(sk.priv, bytes) return sk.Public(), sk } func (x xKEM) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { sk := &xKEMPrivKey{scheme: x, priv: make([]byte, x.PrivateKeySize())} _, err := io.ReadFull(rand.Reader, sk.priv) if err != nil { return nil, nil, err } return sk.Public(), sk, nil } func (x xKEM) UnmarshalBinaryPrivateKey(data []byte) (kem.PrivateKey, error) { l := x.PrivateKeySize() if len(data) < l { return nil, ErrInvalidKEMPrivateKey } sk := &xKEMPrivKey{x, make([]byte, l), nil} copy(sk.priv, data[:l]) if !sk.validate() { return nil, ErrInvalidKEMPrivateKey } return sk, nil } func (x xKEM) UnmarshalBinaryPublicKey(data []byte) (kem.PublicKey, error) { l := x.PublicKeySize() if len(data) < l { return nil, ErrInvalidKEMPublicKey } pk := &xKEMPubKey{x, make([]byte, l)} copy(pk.pub, data[:l]) if !pk.validate() { return nil, ErrInvalidKEMPublicKey } return pk, nil } type xKEMPubKey struct { scheme xKEM pub []byte } func (k *xKEMPubKey) String() string { return fmt.Sprintf("%x", k.pub) } func (k *xKEMPubKey) Scheme() kem.Scheme { return k.scheme } func (k *xKEMPubKey) MarshalBinary() ([]byte, error) { return append(make([]byte, 0, k.scheme.PublicKeySize()), k.pub...), nil } func (k *xKEMPubKey) Equal(pk kem.PublicKey) bool { k1, ok := pk.(*xKEMPubKey) return ok && k.scheme.id == k1.scheme.id && bytes.Equal(k.pub, k1.pub) } func (k *xKEMPubKey) validate() bool { return len(k.pub) == k.scheme.PublicKeySize() } type xKEMPrivKey struct { scheme xKEM priv []byte pub *xKEMPubKey } func (k *xKEMPrivKey) String() string { return fmt.Sprintf("%x", k.priv) } func (k *xKEMPrivKey) Scheme() kem.Scheme { return k.scheme } func (k *xKEMPrivKey) MarshalBinary() ([]byte, error) { return append(make([]byte, 0, k.scheme.PrivateKeySize()), k.priv...), nil } func (k *xKEMPrivKey) Equal(pk kem.PrivateKey) bool { k1, ok := pk.(*xKEMPrivKey) return ok && k.scheme.id == k1.scheme.id && subtle.ConstantTimeCompare(k.priv, k1.priv) == 1 } func (k *xKEMPrivKey) Public() kem.PublicKey { if k.pub == nil { k.pub = &xKEMPubKey{scheme: k.scheme, pub: make([]byte, k.scheme.size)} switch k.scheme.size { case x25519.Size: var sk, pk x25519.Key copy(sk[:], k.priv) x25519.KeyGen(&pk, &sk) copy(k.pub.pub, pk[:]) case x448.Size: var sk, pk x448.Key copy(sk[:], k.priv) x448.KeyGen(&pk, &sk) copy(k.pub.pub, pk[:]) } } return k.pub } func (k *xKEMPrivKey) validate() bool { return len(k.priv) == k.scheme.PrivateKeySize() } golang-github-cloudflare-circl-1.3.7/internal/000077500000000000000000000000001454601126700213035ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/internal/conv/000077500000000000000000000000001454601126700222505ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/internal/conv/conv.go000066400000000000000000000064251454601126700235530ustar00rootroot00000000000000package conv import ( "encoding/binary" "fmt" "math/big" "strings" ) // BytesLe2Hex returns an hexadecimal string of a number stored in a // little-endian order slice x. func BytesLe2Hex(x []byte) string { b := &strings.Builder{} b.Grow(2*len(x) + 2) fmt.Fprint(b, "0x") if len(x) == 0 { fmt.Fprint(b, "00") } for i := len(x) - 1; i >= 0; i-- { fmt.Fprintf(b, "%02x", x[i]) } return b.String() } // BytesLe2BigInt converts a little-endian slice x into a big-endian // math/big.Int. func BytesLe2BigInt(x []byte) *big.Int { n := len(x) b := new(big.Int) if len(x) > 0 { y := make([]byte, n) for i := 0; i < n; i++ { y[n-1-i] = x[i] } b.SetBytes(y) } return b } // BytesBe2Uint64Le converts a big-endian slice x to a little-endian slice of uint64. func BytesBe2Uint64Le(x []byte) []uint64 { l := len(x) z := make([]uint64, (l+7)/8) blocks := l / 8 for i := 0; i < blocks; i++ { z[i] = binary.BigEndian.Uint64(x[l-8*(i+1):]) } remBytes := l % 8 for i := 0; i < remBytes; i++ { z[blocks] |= uint64(x[l-1-8*blocks-i]) << uint(8*i) } return z } // BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z. // The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). // If x does not fit in the slice or is negative, z is not modified. func BigInt2BytesLe(z []byte, x *big.Int) { xLen := (x.BitLen() + 7) >> 3 zLen := len(z) if zLen >= xLen && x.Sign() >= 0 { y := x.Bytes() for i := 0; i < xLen; i++ { z[i] = y[xLen-1-i] } for i := xLen; i < zLen; i++ { z[i] = 0 } } } // Uint64Le2BigInt converts a little-endian slice x into a big number. func Uint64Le2BigInt(x []uint64) *big.Int { n := len(x) b := new(big.Int) var bi big.Int for i := n - 1; i >= 0; i-- { bi.SetUint64(x[i]) b.Lsh(b, 64) b.Add(b, &bi) } return b } // Uint64Le2BytesLe converts a little-endian slice x to a little-endian slice of bytes. func Uint64Le2BytesLe(x []uint64) []byte { b := make([]byte, 8*len(x)) n := len(x) for i := 0; i < n; i++ { binary.LittleEndian.PutUint64(b[i*8:], x[i]) } return b } // Uint64Le2BytesBe converts a little-endian slice x to a big-endian slice of bytes. func Uint64Le2BytesBe(x []uint64) []byte { b := make([]byte, 8*len(x)) n := len(x) for i := 0; i < n; i++ { binary.BigEndian.PutUint64(b[i*8:], x[n-1-i]) } return b } // Uint64Le2Hex returns an hexadecimal string of a number stored in a // little-endian order slice x. func Uint64Le2Hex(x []uint64) string { b := new(strings.Builder) b.Grow(16*len(x) + 2) fmt.Fprint(b, "0x") if len(x) == 0 { fmt.Fprint(b, "00") } for i := len(x) - 1; i >= 0; i-- { fmt.Fprintf(b, "%016x", x[i]) } return b.String() } // BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z. // The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). // If x does not fit in the slice or is negative, z is not modified. func BigInt2Uint64Le(z []uint64, x *big.Int) { xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words zLen := len(z) if zLen >= xLen && x.Sign() > 0 { var y, yi big.Int y.Set(x) two64 := big.NewInt(1) two64.Lsh(two64, 64).Sub(two64, big.NewInt(1)) for i := 0; i < xLen; i++ { yi.And(&y, two64) z[i] = yi.Uint64() y.Rsh(&y, 64) } } for i := xLen; i < zLen; i++ { z[i] = 0 } } golang-github-cloudflare-circl-1.3.7/internal/nist/000077500000000000000000000000001454601126700222605ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/internal/nist/drbg.go000066400000000000000000000020271454601126700235260ustar00rootroot00000000000000// Package nist implements helpers to generate NIST's Known Answer Tests (KATs). package nist import ( "crypto/aes" ) // See NIST's PQCgenKAT.c. type DRBG struct { key [32]byte v [16]byte } func (g *DRBG) incV() { for j := 15; j >= 0; j-- { if g.v[j] == 255 { g.v[j] = 0 } else { g.v[j]++ break } } } // AES256_CTR_DRBG_Update(pd, &g.key, &g.v). func (g *DRBG) update(pd *[48]byte) { var buf [48]byte b, _ := aes.NewCipher(g.key[:]) for i := 0; i < 3; i++ { g.incV() b.Encrypt(buf[i*16:(i+1)*16], g.v[:]) } if pd != nil { for i := 0; i < 48; i++ { buf[i] ^= pd[i] } } copy(g.key[:], buf[:32]) copy(g.v[:], buf[32:]) } // randombyte_init(seed, NULL, 256). func NewDRBG(seed *[48]byte) (g DRBG) { g.update(seed) return } // randombytes. func (g *DRBG) Fill(x []byte) { var block [16]byte b, _ := aes.NewCipher(g.key[:]) for len(x) > 0 { g.incV() b.Encrypt(block[:], g.v[:]) if len(x) < 16 { copy(x[:], block[:len(x)]) break } copy(x[:], block[:]) x = x[16:] } g.update(nil) } golang-github-cloudflare-circl-1.3.7/internal/sha3/000077500000000000000000000000001454601126700221415ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/internal/sha3/doc.go000066400000000000000000000061061454601126700232400ustar00rootroot00000000000000// Copyright 2014 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // Package sha3 implements the SHA-3 fixed-output-length hash functions and // the SHAKE variable-output-length hash functions defined by FIPS-202. // // Both types of hash function use the "sponge" construction and the Keccak // permutation. For a detailed specification see http://keccak.noekeon.org/ // // # Guidance // // If you aren't sure what function you need, use SHAKE256 with at least 64 // bytes of output. The SHAKE instances are faster than the SHA3 instances; // the latter have to allocate memory to conform to the hash.Hash interface. // // If you need a secret-key MAC (message authentication code), prepend the // secret key to the input, hash with SHAKE256 and read at least 32 bytes of // output. // // # Security strengths // // The SHA3-x (x equals 224, 256, 384, or 512) functions have a security // strength against preimage attacks of x bits. Since they only produce "x" // bits of output, their collision-resistance is only "x/2" bits. // // The SHAKE-256 and -128 functions have a generic security strength of 256 and // 128 bits against all attacks, provided that at least 2x bits of their output // is used. Requesting more than 64 or 32 bytes of output, respectively, does // not increase the collision-resistance of the SHAKE functions. // // # The sponge construction // // A sponge builds a pseudo-random function from a public pseudo-random // permutation, by applying the permutation to a state of "rate + capacity" // bytes, but hiding "capacity" of the bytes. // // A sponge starts out with a zero state. To hash an input using a sponge, up // to "rate" bytes of the input are XORed into the sponge's state. The sponge // is then "full" and the permutation is applied to "empty" it. This process is // repeated until all the input has been "absorbed". The input is then padded. // The digest is "squeezed" from the sponge in the same way, except that output // is copied out instead of input being XORed in. // // A sponge is parameterized by its generic security strength, which is equal // to half its capacity; capacity + rate is equal to the permutation's width. // Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means // that the security strength of a sponge instance is equal to (1600 - bitrate) / 2. // // # Recommendations // // The SHAKE functions are recommended for most new uses. They can produce // output of arbitrary length. SHAKE256, with an output length of at least // 64 bytes, provides 256-bit security against all attacks. The Keccak team // recommends it for most applications upgrading from SHA2-512. (NIST chose a // much stronger, but much slower, sponge instance for SHA3-512.) // // The SHA-3 functions are "drop-in" replacements for the SHA-2 functions. // They produce output of the same length, with the same security strengths // against all attacks. This means, in particular, that SHA3-256 only has // 128-bit collision resistance, because its output length is 32 bytes. package sha3 golang-github-cloudflare-circl-1.3.7/internal/sha3/hashes.go000066400000000000000000000035551454601126700237530ustar00rootroot00000000000000// Copyright 2014 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package sha3 // This file provides functions for creating instances of the SHA-3 // and SHAKE hash functions, as well as utility functions for hashing // bytes. // New224 creates a new SHA3-224 hash. // Its generic security strength is 224 bits against preimage attacks, // and 112 bits against collision attacks. func New224() State { return State{rate: 144, outputLen: 28, dsbyte: 0x06} } // New256 creates a new SHA3-256 hash. // Its generic security strength is 256 bits against preimage attacks, // and 128 bits against collision attacks. func New256() State { return State{rate: 136, outputLen: 32, dsbyte: 0x06} } // New384 creates a new SHA3-384 hash. // Its generic security strength is 384 bits against preimage attacks, // and 192 bits against collision attacks. func New384() State { return State{rate: 104, outputLen: 48, dsbyte: 0x06} } // New512 creates a new SHA3-512 hash. // Its generic security strength is 512 bits against preimage attacks, // and 256 bits against collision attacks. func New512() State { return State{rate: 72, outputLen: 64, dsbyte: 0x06} } // Sum224 returns the SHA3-224 digest of the data. func Sum224(data []byte) (digest [28]byte) { h := New224() _, _ = h.Write(data) h.Sum(digest[:0]) return } // Sum256 returns the SHA3-256 digest of the data. func Sum256(data []byte) (digest [32]byte) { h := New256() _, _ = h.Write(data) h.Sum(digest[:0]) return } // Sum384 returns the SHA3-384 digest of the data. func Sum384(data []byte) (digest [48]byte) { h := New384() _, _ = h.Write(data) h.Sum(digest[:0]) return } // Sum512 returns the SHA3-512 digest of the data. func Sum512(data []byte) (digest [64]byte) { h := New512() _, _ = h.Write(data) h.Sum(digest[:0]) return } golang-github-cloudflare-circl-1.3.7/internal/sha3/keccakf.go000066400000000000000000000224161454601126700240640ustar00rootroot00000000000000// Copyright 2014 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package sha3 // KeccakF1600 applies the Keccak permutation to a 1600b-wide // state represented as a slice of 25 uint64s. // If turbo is true, applies the 12-round variant instead of the // regular 24-round variant. // nolint:funlen func KeccakF1600(a *[25]uint64, turbo bool) { // Implementation translated from Keccak-inplace.c // in the keccak reference code. var t, bc0, bc1, bc2, bc3, bc4, d0, d1, d2, d3, d4 uint64 i := 0 if turbo { i = 12 } for ; i < 24; i += 4 { // Combines the 5 steps in each round into 2 steps. // Unrolls 4 rounds per loop and spreads some steps across rounds. // Round 1 bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] d0 = bc4 ^ (bc1<<1 | bc1>>63) d1 = bc0 ^ (bc2<<1 | bc2>>63) d2 = bc1 ^ (bc3<<1 | bc3>>63) d3 = bc2 ^ (bc4<<1 | bc4>>63) d4 = bc3 ^ (bc0<<1 | bc0>>63) bc0 = a[0] ^ d0 t = a[6] ^ d1 bc1 = t<<44 | t>>(64-44) t = a[12] ^ d2 bc2 = t<<43 | t>>(64-43) t = a[18] ^ d3 bc3 = t<<21 | t>>(64-21) t = a[24] ^ d4 bc4 = t<<14 | t>>(64-14) a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i] a[6] = bc1 ^ (bc3 &^ bc2) a[12] = bc2 ^ (bc4 &^ bc3) a[18] = bc3 ^ (bc0 &^ bc4) a[24] = bc4 ^ (bc1 &^ bc0) t = a[10] ^ d0 bc2 = t<<3 | t>>(64-3) t = a[16] ^ d1 bc3 = t<<45 | t>>(64-45) t = a[22] ^ d2 bc4 = t<<61 | t>>(64-61) t = a[3] ^ d3 bc0 = t<<28 | t>>(64-28) t = a[9] ^ d4 bc1 = t<<20 | t>>(64-20) a[10] = bc0 ^ (bc2 &^ bc1) a[16] = bc1 ^ (bc3 &^ bc2) a[22] = bc2 ^ (bc4 &^ bc3) a[3] = bc3 ^ (bc0 &^ bc4) a[9] = bc4 ^ (bc1 &^ bc0) t = a[20] ^ d0 bc4 = t<<18 | t>>(64-18) t = a[1] ^ d1 bc0 = t<<1 | t>>(64-1) t = a[7] ^ d2 bc1 = t<<6 | t>>(64-6) t = a[13] ^ d3 bc2 = t<<25 | t>>(64-25) t = a[19] ^ d4 bc3 = t<<8 | t>>(64-8) a[20] = bc0 ^ (bc2 &^ bc1) a[1] = bc1 ^ (bc3 &^ bc2) a[7] = bc2 ^ (bc4 &^ bc3) a[13] = bc3 ^ (bc0 &^ bc4) a[19] = bc4 ^ (bc1 &^ bc0) t = a[5] ^ d0 bc1 = t<<36 | t>>(64-36) t = a[11] ^ d1 bc2 = t<<10 | t>>(64-10) t = a[17] ^ d2 bc3 = t<<15 | t>>(64-15) t = a[23] ^ d3 bc4 = t<<56 | t>>(64-56) t = a[4] ^ d4 bc0 = t<<27 | t>>(64-27) a[5] = bc0 ^ (bc2 &^ bc1) a[11] = bc1 ^ (bc3 &^ bc2) a[17] = bc2 ^ (bc4 &^ bc3) a[23] = bc3 ^ (bc0 &^ bc4) a[4] = bc4 ^ (bc1 &^ bc0) t = a[15] ^ d0 bc3 = t<<41 | t>>(64-41) t = a[21] ^ d1 bc4 = t<<2 | t>>(64-2) t = a[2] ^ d2 bc0 = t<<62 | t>>(64-62) t = a[8] ^ d3 bc1 = t<<55 | t>>(64-55) t = a[14] ^ d4 bc2 = t<<39 | t>>(64-39) a[15] = bc0 ^ (bc2 &^ bc1) a[21] = bc1 ^ (bc3 &^ bc2) a[2] = bc2 ^ (bc4 &^ bc3) a[8] = bc3 ^ (bc0 &^ bc4) a[14] = bc4 ^ (bc1 &^ bc0) // Round 2 bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] d0 = bc4 ^ (bc1<<1 | bc1>>63) d1 = bc0 ^ (bc2<<1 | bc2>>63) d2 = bc1 ^ (bc3<<1 | bc3>>63) d3 = bc2 ^ (bc4<<1 | bc4>>63) d4 = bc3 ^ (bc0<<1 | bc0>>63) bc0 = a[0] ^ d0 t = a[16] ^ d1 bc1 = t<<44 | t>>(64-44) t = a[7] ^ d2 bc2 = t<<43 | t>>(64-43) t = a[23] ^ d3 bc3 = t<<21 | t>>(64-21) t = a[14] ^ d4 bc4 = t<<14 | t>>(64-14) a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+1] a[16] = bc1 ^ (bc3 &^ bc2) a[7] = bc2 ^ (bc4 &^ bc3) a[23] = bc3 ^ (bc0 &^ bc4) a[14] = bc4 ^ (bc1 &^ bc0) t = a[20] ^ d0 bc2 = t<<3 | t>>(64-3) t = a[11] ^ d1 bc3 = t<<45 | t>>(64-45) t = a[2] ^ d2 bc4 = t<<61 | t>>(64-61) t = a[18] ^ d3 bc0 = t<<28 | t>>(64-28) t = a[9] ^ d4 bc1 = t<<20 | t>>(64-20) a[20] = bc0 ^ (bc2 &^ bc1) a[11] = bc1 ^ (bc3 &^ bc2) a[2] = bc2 ^ (bc4 &^ bc3) a[18] = bc3 ^ (bc0 &^ bc4) a[9] = bc4 ^ (bc1 &^ bc0) t = a[15] ^ d0 bc4 = t<<18 | t>>(64-18) t = a[6] ^ d1 bc0 = t<<1 | t>>(64-1) t = a[22] ^ d2 bc1 = t<<6 | t>>(64-6) t = a[13] ^ d3 bc2 = t<<25 | t>>(64-25) t = a[4] ^ d4 bc3 = t<<8 | t>>(64-8) a[15] = bc0 ^ (bc2 &^ bc1) a[6] = bc1 ^ (bc3 &^ bc2) a[22] = bc2 ^ (bc4 &^ bc3) a[13] = bc3 ^ (bc0 &^ bc4) a[4] = bc4 ^ (bc1 &^ bc0) t = a[10] ^ d0 bc1 = t<<36 | t>>(64-36) t = a[1] ^ d1 bc2 = t<<10 | t>>(64-10) t = a[17] ^ d2 bc3 = t<<15 | t>>(64-15) t = a[8] ^ d3 bc4 = t<<56 | t>>(64-56) t = a[24] ^ d4 bc0 = t<<27 | t>>(64-27) a[10] = bc0 ^ (bc2 &^ bc1) a[1] = bc1 ^ (bc3 &^ bc2) a[17] = bc2 ^ (bc4 &^ bc3) a[8] = bc3 ^ (bc0 &^ bc4) a[24] = bc4 ^ (bc1 &^ bc0) t = a[5] ^ d0 bc3 = t<<41 | t>>(64-41) t = a[21] ^ d1 bc4 = t<<2 | t>>(64-2) t = a[12] ^ d2 bc0 = t<<62 | t>>(64-62) t = a[3] ^ d3 bc1 = t<<55 | t>>(64-55) t = a[19] ^ d4 bc2 = t<<39 | t>>(64-39) a[5] = bc0 ^ (bc2 &^ bc1) a[21] = bc1 ^ (bc3 &^ bc2) a[12] = bc2 ^ (bc4 &^ bc3) a[3] = bc3 ^ (bc0 &^ bc4) a[19] = bc4 ^ (bc1 &^ bc0) // Round 3 bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] d0 = bc4 ^ (bc1<<1 | bc1>>63) d1 = bc0 ^ (bc2<<1 | bc2>>63) d2 = bc1 ^ (bc3<<1 | bc3>>63) d3 = bc2 ^ (bc4<<1 | bc4>>63) d4 = bc3 ^ (bc0<<1 | bc0>>63) bc0 = a[0] ^ d0 t = a[11] ^ d1 bc1 = t<<44 | t>>(64-44) t = a[22] ^ d2 bc2 = t<<43 | t>>(64-43) t = a[8] ^ d3 bc3 = t<<21 | t>>(64-21) t = a[19] ^ d4 bc4 = t<<14 | t>>(64-14) a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+2] a[11] = bc1 ^ (bc3 &^ bc2) a[22] = bc2 ^ (bc4 &^ bc3) a[8] = bc3 ^ (bc0 &^ bc4) a[19] = bc4 ^ (bc1 &^ bc0) t = a[15] ^ d0 bc2 = t<<3 | t>>(64-3) t = a[1] ^ d1 bc3 = t<<45 | t>>(64-45) t = a[12] ^ d2 bc4 = t<<61 | t>>(64-61) t = a[23] ^ d3 bc0 = t<<28 | t>>(64-28) t = a[9] ^ d4 bc1 = t<<20 | t>>(64-20) a[15] = bc0 ^ (bc2 &^ bc1) a[1] = bc1 ^ (bc3 &^ bc2) a[12] = bc2 ^ (bc4 &^ bc3) a[23] = bc3 ^ (bc0 &^ bc4) a[9] = bc4 ^ (bc1 &^ bc0) t = a[5] ^ d0 bc4 = t<<18 | t>>(64-18) t = a[16] ^ d1 bc0 = t<<1 | t>>(64-1) t = a[2] ^ d2 bc1 = t<<6 | t>>(64-6) t = a[13] ^ d3 bc2 = t<<25 | t>>(64-25) t = a[24] ^ d4 bc3 = t<<8 | t>>(64-8) a[5] = bc0 ^ (bc2 &^ bc1) a[16] = bc1 ^ (bc3 &^ bc2) a[2] = bc2 ^ (bc4 &^ bc3) a[13] = bc3 ^ (bc0 &^ bc4) a[24] = bc4 ^ (bc1 &^ bc0) t = a[20] ^ d0 bc1 = t<<36 | t>>(64-36) t = a[6] ^ d1 bc2 = t<<10 | t>>(64-10) t = a[17] ^ d2 bc3 = t<<15 | t>>(64-15) t = a[3] ^ d3 bc4 = t<<56 | t>>(64-56) t = a[14] ^ d4 bc0 = t<<27 | t>>(64-27) a[20] = bc0 ^ (bc2 &^ bc1) a[6] = bc1 ^ (bc3 &^ bc2) a[17] = bc2 ^ (bc4 &^ bc3) a[3] = bc3 ^ (bc0 &^ bc4) a[14] = bc4 ^ (bc1 &^ bc0) t = a[10] ^ d0 bc3 = t<<41 | t>>(64-41) t = a[21] ^ d1 bc4 = t<<2 | t>>(64-2) t = a[7] ^ d2 bc0 = t<<62 | t>>(64-62) t = a[18] ^ d3 bc1 = t<<55 | t>>(64-55) t = a[4] ^ d4 bc2 = t<<39 | t>>(64-39) a[10] = bc0 ^ (bc2 &^ bc1) a[21] = bc1 ^ (bc3 &^ bc2) a[7] = bc2 ^ (bc4 &^ bc3) a[18] = bc3 ^ (bc0 &^ bc4) a[4] = bc4 ^ (bc1 &^ bc0) // Round 4 bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] d0 = bc4 ^ (bc1<<1 | bc1>>63) d1 = bc0 ^ (bc2<<1 | bc2>>63) d2 = bc1 ^ (bc3<<1 | bc3>>63) d3 = bc2 ^ (bc4<<1 | bc4>>63) d4 = bc3 ^ (bc0<<1 | bc0>>63) bc0 = a[0] ^ d0 t = a[1] ^ d1 bc1 = t<<44 | t>>(64-44) t = a[2] ^ d2 bc2 = t<<43 | t>>(64-43) t = a[3] ^ d3 bc3 = t<<21 | t>>(64-21) t = a[4] ^ d4 bc4 = t<<14 | t>>(64-14) a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+3] a[1] = bc1 ^ (bc3 &^ bc2) a[2] = bc2 ^ (bc4 &^ bc3) a[3] = bc3 ^ (bc0 &^ bc4) a[4] = bc4 ^ (bc1 &^ bc0) t = a[5] ^ d0 bc2 = t<<3 | t>>(64-3) t = a[6] ^ d1 bc3 = t<<45 | t>>(64-45) t = a[7] ^ d2 bc4 = t<<61 | t>>(64-61) t = a[8] ^ d3 bc0 = t<<28 | t>>(64-28) t = a[9] ^ d4 bc1 = t<<20 | t>>(64-20) a[5] = bc0 ^ (bc2 &^ bc1) a[6] = bc1 ^ (bc3 &^ bc2) a[7] = bc2 ^ (bc4 &^ bc3) a[8] = bc3 ^ (bc0 &^ bc4) a[9] = bc4 ^ (bc1 &^ bc0) t = a[10] ^ d0 bc4 = t<<18 | t>>(64-18) t = a[11] ^ d1 bc0 = t<<1 | t>>(64-1) t = a[12] ^ d2 bc1 = t<<6 | t>>(64-6) t = a[13] ^ d3 bc2 = t<<25 | t>>(64-25) t = a[14] ^ d4 bc3 = t<<8 | t>>(64-8) a[10] = bc0 ^ (bc2 &^ bc1) a[11] = bc1 ^ (bc3 &^ bc2) a[12] = bc2 ^ (bc4 &^ bc3) a[13] = bc3 ^ (bc0 &^ bc4) a[14] = bc4 ^ (bc1 &^ bc0) t = a[15] ^ d0 bc1 = t<<36 | t>>(64-36) t = a[16] ^ d1 bc2 = t<<10 | t>>(64-10) t = a[17] ^ d2 bc3 = t<<15 | t>>(64-15) t = a[18] ^ d3 bc4 = t<<56 | t>>(64-56) t = a[19] ^ d4 bc0 = t<<27 | t>>(64-27) a[15] = bc0 ^ (bc2 &^ bc1) a[16] = bc1 ^ (bc3 &^ bc2) a[17] = bc2 ^ (bc4 &^ bc3) a[18] = bc3 ^ (bc0 &^ bc4) a[19] = bc4 ^ (bc1 &^ bc0) t = a[20] ^ d0 bc3 = t<<41 | t>>(64-41) t = a[21] ^ d1 bc4 = t<<2 | t>>(64-2) t = a[22] ^ d2 bc0 = t<<62 | t>>(64-62) t = a[23] ^ d3 bc1 = t<<55 | t>>(64-55) t = a[24] ^ d4 bc2 = t<<39 | t>>(64-39) a[20] = bc0 ^ (bc2 &^ bc1) a[21] = bc1 ^ (bc3 &^ bc2) a[22] = bc2 ^ (bc4 &^ bc3) a[23] = bc3 ^ (bc0 &^ bc4) a[24] = bc4 ^ (bc1 &^ bc0) } } golang-github-cloudflare-circl-1.3.7/internal/sha3/rc.go000066400000000000000000000011261454601126700230740ustar00rootroot00000000000000package sha3 // RC stores the round constants for use in the ι step. var RC = [24]uint64{ 0x0000000000000001, 0x0000000000008082, 0x800000000000808A, 0x8000000080008000, 0x000000000000808B, 0x0000000080000001, 0x8000000080008081, 0x8000000000008009, 0x000000000000008A, 0x0000000000000088, 0x0000000080008009, 0x000000008000000A, 0x000000008000808B, 0x800000000000008B, 0x8000000000008089, 0x8000000000008003, 0x8000000000008002, 0x8000000000000080, 0x000000000000800A, 0x800000008000000A, 0x8000000080008081, 0x8000000000008080, 0x0000000080000001, 0x8000000080008008, } golang-github-cloudflare-circl-1.3.7/internal/sha3/sha3.go000066400000000000000000000133461454601126700233350ustar00rootroot00000000000000// Copyright 2014 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package sha3 // spongeDirection indicates the direction bytes are flowing through the sponge. type spongeDirection int const ( // spongeAbsorbing indicates that the sponge is absorbing input. spongeAbsorbing spongeDirection = iota // spongeSqueezing indicates that the sponge is being squeezed. spongeSqueezing ) const ( // maxRate is the maximum size of the internal buffer. SHAKE-256 // currently needs the largest buffer. maxRate = 168 ) func (d *State) buf() []byte { return d.storage.asBytes()[d.bufo:d.bufe] } type State struct { // Generic sponge components. a [25]uint64 // main state of the hash rate int // the number of bytes of state to use bufo int // offset of buffer in storage bufe int // end of buffer in storage // dsbyte contains the "domain separation" bits and the first bit of // the padding. Sections 6.1 and 6.2 of [1] separate the outputs of the // SHA-3 and SHAKE functions by appending bitstrings to the message. // Using a little-endian bit-ordering convention, these are "01" for SHA-3 // and "1111" for SHAKE, or 00000010b and 00001111b, respectively. Then the // padding rule from section 5.1 is applied to pad the message to a multiple // of the rate, which involves adding a "1" bit, zero or more "0" bits, and // a final "1" bit. We merge the first "1" bit from the padding into dsbyte, // giving 00000110b (0x06) and 00011111b (0x1f). // [1] http://csrc.nist.gov/publications/drafts/fips-202/fips_202_draft.pdf // "Draft FIPS 202: SHA-3 Standard: Permutation-Based Hash and // Extendable-Output Functions (May 2014)" dsbyte byte storage storageBuf // Specific to SHA-3 and SHAKE. outputLen int // the default output size in bytes state spongeDirection // whether the sponge is absorbing or squeezing turbo bool // Whether we're using 12 rounds instead of 24 } // BlockSize returns the rate of sponge underlying this hash function. func (d *State) BlockSize() int { return d.rate } // Size returns the output size of the hash function in bytes. func (d *State) Size() int { return d.outputLen } // Reset clears the internal state by zeroing the sponge state and // the byte buffer, and setting Sponge.state to absorbing. func (d *State) Reset() { // Zero the permutation's state. for i := range d.a { d.a[i] = 0 } d.state = spongeAbsorbing d.bufo = 0 d.bufe = 0 } func (d *State) clone() *State { ret := *d return &ret } // permute applies the KeccakF-1600 permutation. It handles // any input-output buffering. func (d *State) permute() { switch d.state { case spongeAbsorbing: // If we're absorbing, we need to xor the input into the state // before applying the permutation. xorIn(d, d.buf()) d.bufe = 0 d.bufo = 0 KeccakF1600(&d.a, d.turbo) case spongeSqueezing: // If we're squeezing, we need to apply the permutation before // copying more output. KeccakF1600(&d.a, d.turbo) d.bufe = d.rate d.bufo = 0 copyOut(d, d.buf()) } } // pads appends the domain separation bits in dsbyte, applies // the multi-bitrate 10..1 padding rule, and permutes the state. func (d *State) padAndPermute(dsbyte byte) { // Pad with this instance's domain-separator bits. We know that there's // at least one byte of space in d.buf() because, if it were full, // permute would have been called to empty it. dsbyte also contains the // first one bit for the padding. See the comment in the state struct. zerosStart := d.bufe + 1 d.bufe = d.rate buf := d.buf() buf[zerosStart-1] = dsbyte for i := zerosStart; i < d.rate; i++ { buf[i] = 0 } // This adds the final one bit for the padding. Because of the way that // bits are numbered from the LSB upwards, the final bit is the MSB of // the last byte. buf[d.rate-1] ^= 0x80 // Apply the permutation d.permute() d.state = spongeSqueezing d.bufe = d.rate copyOut(d, buf) } // Write absorbs more data into the hash's state. It produces an error // if more data is written to the ShakeHash after writing func (d *State) Write(p []byte) (written int, err error) { if d.state != spongeAbsorbing { panic("sha3: write to sponge after read") } written = len(p) for len(p) > 0 { bufl := d.bufe - d.bufo if bufl == 0 && len(p) >= d.rate { // The fast path; absorb a full "rate" bytes of input and apply the permutation. xorIn(d, p[:d.rate]) p = p[d.rate:] KeccakF1600(&d.a, d.turbo) } else { // The slow path; buffer the input until we can fill the sponge, and then xor it in. todo := d.rate - bufl if todo > len(p) { todo = len(p) } d.bufe += todo buf := d.buf() copy(buf[bufl:], p[:todo]) p = p[todo:] // If the sponge is full, apply the permutation. if d.bufe == d.rate { d.permute() } } } return written, nil } // Read squeezes an arbitrary number of bytes from the sponge. func (d *State) Read(out []byte) (n int, err error) { // If we're still absorbing, pad and apply the permutation. if d.state == spongeAbsorbing { d.padAndPermute(d.dsbyte) } n = len(out) // Now, do the squeezing. for len(out) > 0 { buf := d.buf() n := copy(out, buf) d.bufo += n out = out[n:] // Apply the permutation if we've squeezed the sponge dry. if d.bufo == d.bufe { d.permute() } } return } // Sum applies padding to the hash state and then squeezes out the desired // number of output bytes. func (d *State) Sum(in []byte) []byte { // Make a copy of the original hash so that caller can keep writing // and summing. dup := d.clone() hash := make([]byte, dup.outputLen) _, _ = dup.Read(hash) return append(in, hash...) } func (d *State) IsAbsorbing() bool { return d.state == spongeAbsorbing } golang-github-cloudflare-circl-1.3.7/internal/sha3/sha3_s390x.s000066400000000000000000000017001454601126700241270ustar00rootroot00000000000000// Copyright 2017 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // +build !gccgo,!appengine #include "textflag.h" // func kimd(function code, chain *[200]byte, src []byte) TEXT ·kimd(SB), NOFRAME|NOSPLIT, $0-40 MOVD function+0(FP), R0 MOVD chain+8(FP), R1 LMG src+16(FP), R2, R3 // R2=base, R3=len continue: WORD $0xB93E0002 // KIMD --, R2 BVS continue // continue if interrupted MOVD $0, R0 // reset R0 for pre-go1.8 compilers RET // func klmd(function code, chain *[200]byte, dst, src []byte) TEXT ·klmd(SB), NOFRAME|NOSPLIT, $0-64 // TODO: SHAKE support MOVD function+0(FP), R0 MOVD chain+8(FP), R1 LMG dst+16(FP), R2, R3 // R2=base, R3=len LMG src+40(FP), R4, R5 // R4=base, R5=len continue: WORD $0xB93F0024 // KLMD R2, R4 BVS continue // continue if interrupted MOVD $0, R0 // reset R0 for pre-go1.8 compilers RET golang-github-cloudflare-circl-1.3.7/internal/sha3/sha3_test.go000066400000000000000000000207041454601126700243700ustar00rootroot00000000000000// Copyright 2014 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package sha3 // Tests include all the ShortMsgKATs provided by the Keccak team at // https://github.com/gvanas/KeccakCodePackage // // They only include the zero-bit case of the bitwise testvectors // published by NIST in the draft of FIPS-202. import ( "bytes" "compress/flate" "encoding/hex" "encoding/json" "fmt" "math/rand" "os" "strings" "testing" ) const ( katFilename = "testdata/keccakKats.json.deflate" ) // testDigests contains functions returning hash.Hash instances // with output-length equal to the KAT length for SHA-3, Keccak // and SHAKE instances. var testDigests = map[string]func() State{ "SHA3-224": New224, "SHA3-256": New256, "SHA3-384": New384, "SHA3-512": New512, } // structs used to marshal JSON test-cases. type KeccakKats struct { Kats map[string][]struct { Digest string `json:"digest"` Length int64 `json:"length"` Message string `json:"message"` // Defined only for cSHAKE N string `json:"N"` S string `json:"S"` } } // TestKeccakKats tests the SHA-3 and Shake implementations against all the // ShortMsgKATs from https://github.com/gvanas/KeccakCodePackage // (The testvectors are stored in keccakKats.json.deflate due to their length.) func TestKeccakKats(t *testing.T) { // Read the KATs. deflated, err := os.Open(katFilename) if err != nil { t.Errorf("error opening %s: %s", katFilename, err) } file := flate.NewReader(deflated) dec := json.NewDecoder(file) var katSet KeccakKats err = dec.Decode(&katSet) if err != nil { t.Errorf("error decoding KATs: %s", err) } for algo, function := range testDigests { d := function() for _, kat := range katSet.Kats[algo] { d.Reset() in, err := hex.DecodeString(kat.Message) if err != nil { t.Errorf("error decoding KAT: %s", err) } _, _ = d.Write(in[:kat.Length/8]) got := strings.ToUpper(hex.EncodeToString(d.Sum(nil))) if got != kat.Digest { t.Errorf("function=%s, length=%d\nmessage:\n %s\ngot:\n %s\nwanted:\n %s", algo, kat.Length, kat.Message, got, kat.Digest) t.Logf("wanted %+v", kat) t.FailNow() } continue } } } // TestUnalignedWrite tests that writing data in an arbitrary pattern with // small input buffers. func TestUnalignedWrite(t *testing.T) { buf := sequentialBytes(0x10000) for alg, df := range testDigests { d := df() d.Reset() _, _ = d.Write(buf) want := d.Sum(nil) d.Reset() for i := 0; i < len(buf); { // Cycle through offsets which make a 137 byte sequence. // Because 137 is prime this sequence should exercise all corner cases. offsets := [17]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1} for _, j := range offsets { if v := len(buf) - i; v < j { j = v } _, _ = d.Write(buf[i : i+j]) i += j } } got := d.Sum(nil) if !bytes.Equal(got, want) { t.Errorf("Unaligned writes, alg=%s\ngot %q, want %q", alg, got, want) } } } // TestAppend checks that appending works when reallocation is necessary. func TestAppend(t *testing.T) { d := New224() for capacity := 2; capacity <= 66; capacity += 64 { // The first time around the loop, Sum will have to reallocate. // The second time, it will not. buf := make([]byte, 2, capacity) d.Reset() _, _ = d.Write([]byte{0xcc}) buf = d.Sum(buf) expected := "0000DF70ADC49B2E76EEE3A6931B93FA41841C3AF2CDF5B32A18B5478C39" if got := strings.ToUpper(hex.EncodeToString(buf)); got != expected { t.Errorf("got %s, want %s", got, expected) } } } // TestAppendNoRealloc tests that appending works when no reallocation is necessary. func TestAppendNoRealloc(t *testing.T) { buf := make([]byte, 1, 200) d := New224() _, _ = d.Write([]byte{0xcc}) buf = d.Sum(buf) expected := "00DF70ADC49B2E76EEE3A6931B93FA41841C3AF2CDF5B32A18B5478C39" if got := strings.ToUpper(hex.EncodeToString(buf)); got != expected { t.Errorf("got %s, want %s", got, expected) } } // sequentialBytes produces a buffer of size consecutive bytes 0x00, 0x01, ..., used for testing. // // The alignment of each slice is intentionally randomized to detect alignment // issues in the implementation. See https://golang.org/issue/37644. // Ideally, the compiler should fuzz the alignment itself. // (See https://golang.org/issue/35128.) func sequentialBytes(size int) []byte { alignmentOffset := rand.Intn(8) // nolint:gosec result := make([]byte, size+alignmentOffset)[alignmentOffset:] for i := range result { result[i] = byte(i) } return result } // BenchmarkPermutationFunctionTurbo measures the speed of the permutation // function with no input data. func BenchmarkPermutationFunctionTurbo(b *testing.B) { b.SetBytes(int64(200)) var lanes [25]uint64 for i := 0; i < b.N; i++ { KeccakF1600(&lanes, true) } } // BenchmarkPermutationFunction measures the speed of the permutation function // with no input data. func BenchmarkPermutationFunction(b *testing.B) { b.SetBytes(int64(200)) var lanes [25]uint64 for i := 0; i < b.N; i++ { KeccakF1600(&lanes, false) } } // benchmarkHash tests the speed to hash num buffers of buflen each. func benchmarkHash(b *testing.B, h State, size, num int) { b.StopTimer() h.Reset() data := sequentialBytes(size) b.SetBytes(int64(size * num)) b.StartTimer() var state []byte for i := 0; i < b.N; i++ { for j := 0; j < num; j++ { _, _ = h.Write(data) } state = h.Sum(state[:0]) } b.StopTimer() h.Reset() } // benchmarkShake is specialized to the Shake instances, which don't // require a copy on reading output. func benchmarkShake(b *testing.B, h State, size, num int) { b.StopTimer() h.Reset() data := sequentialBytes(size) d := make([]byte, 32) b.SetBytes(int64(size * num)) b.StartTimer() for i := 0; i < b.N; i++ { h.Reset() for j := 0; j < num; j++ { _, _ = h.Write(data) } _, _ = h.Read(d) } } func BenchmarkSha3_512_MTU(b *testing.B) { benchmarkHash(b, New512(), 1350, 1) } func BenchmarkSha3_384_MTU(b *testing.B) { benchmarkHash(b, New384(), 1350, 1) } func BenchmarkSha3_256_MTU(b *testing.B) { benchmarkHash(b, New256(), 1350, 1) } func BenchmarkSha3_224_MTU(b *testing.B) { benchmarkHash(b, New224(), 1350, 1) } func BenchmarkShake128_MTU(b *testing.B) { benchmarkShake(b, NewShake128(), 1350, 1) } func BenchmarkShake256_MTU(b *testing.B) { benchmarkShake(b, NewShake256(), 1350, 1) } func BenchmarkShake256_16x(b *testing.B) { benchmarkShake(b, NewShake256(), 16, 1024) } func BenchmarkShake256_1MiB(b *testing.B) { benchmarkShake(b, NewShake256(), 1024, 1024) } func BenchmarkTurboShake128_1MiB(b *testing.B) { benchmarkShake(b, NewTurboShake128(0x37), 1024, 1024) } func BenchmarkTurboShake256_1MiB(b *testing.B) { benchmarkShake(b, NewTurboShake256(0x37), 1024, 1024) } func BenchmarkSha3_512_1MiB(b *testing.B) { benchmarkHash(b, New512(), 1024, 1024) } func Example_sum() { buf := []byte("some data to hash") // A hash needs to be 64 bytes long to have 256-bit collision resistance. h := make([]byte, 64) // Compute a 64-byte hash of buf and put it in h. ShakeSum256(h, buf) fmt.Printf("%x\n", h) // Output: 0f65fe41fc353e52c55667bb9e2b27bfcc8476f2c413e9437d272ee3194a4e3146d05ec04a25d16b8f577c19b82d16b1424c3e022e783d2b4da98de3658d363d } func Example_mac() { k := []byte("this is a secret key; you should generate a strong random key that's at least 32 bytes long") buf := []byte("and this is some data to authenticate") // A MAC with 32 bytes of output has 256-bit security strength -- if you use at least a 32-byte-long key. h := make([]byte, 32) d := NewShake256() // Write the key into the hash. _, _ = d.Write(k) // Now write the data. _, _ = d.Write(buf) // Read 32 bytes of output from the hash into h. _, _ = d.Read(h) fmt.Printf("%x\n", h) // Output: 78de2974bd2711d5549ffd32b753ef0f5fa80a0db2556db60f0987eb8a9218ff } func TestTurboShake128(t *testing.T) { out := make([]byte, 64) TurboShakeSum128(out, []byte{}, 0x07) if hex.EncodeToString(out) != "5a223ad30b3b8c66a243048cfced430f54e7529287d15150b973133adfac6a2ffe2708e73061e09a4000168ba9c8ca1813198f7bbed4984b4185f2c2580ee623" { t.Fatal() } h := NewTurboShake128(0x07) out = make([]byte, 10032) _, _ = h.Read(out) if hex.EncodeToString(out[len(out)-32:]) != "7593a28020a3c4ae0d605fd61f5eb56eccd27cc3d12ff09f78369772a460c55d" { t.Fatal() } out = make([]byte, 32) TurboShakeSum128(out, []byte{0xff}, 0x06) if hex.EncodeToString(out) != "8ec9c66465ed0d4a6c35d13506718d687a25cb05c74cca1e42501abd83874a67" { t.Fatal() } // TODO all tests } golang-github-cloudflare-circl-1.3.7/internal/sha3/shake.go000066400000000000000000000070511454601126700235660ustar00rootroot00000000000000// Copyright 2014 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package sha3 // This file defines the ShakeHash interface, and provides // functions for creating SHAKE and cSHAKE instances, as well as utility // functions for hashing bytes to arbitrary-length output. // // // SHAKE implementation is based on FIPS PUB 202 [1] // cSHAKE implementations is based on NIST SP 800-185 [2] // // [1] https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf // [2] https://doi.org/10.6028/NIST.SP.800-185 import ( "io" ) // ShakeHash defines the interface to hash functions that // support arbitrary-length output. type ShakeHash interface { // Write absorbs more data into the hash's state. It panics if input is // written to it after output has been read from it. io.Writer // Read reads more output from the hash; reading affects the hash's // state. (ShakeHash.Read is thus very different from Hash.Sum) // It never returns an error. io.Reader // Clone returns a copy of the ShakeHash in its current state. Clone() ShakeHash // Reset resets the ShakeHash to its initial state. Reset() } // Consts for configuring initial SHA-3 state const ( dsbyteShake = 0x1f rate128 = 168 rate256 = 136 ) // Clone returns copy of SHAKE context within its current state. func (d *State) Clone() ShakeHash { return d.clone() } // NewShake128 creates a new SHAKE128 variable-output-length ShakeHash. // Its generic security strength is 128 bits against all attacks if at // least 32 bytes of its output are used. func NewShake128() State { return State{rate: rate128, dsbyte: dsbyteShake} } // NewTurboShake128 creates a new TurboSHAKE128 variable-output-length ShakeHash. // Its generic security strength is 128 bits against all attacks if at // least 32 bytes of its output are used. // D is the domain separation byte and must be between 0x01 and 0x7f inclusive. func NewTurboShake128(D byte) State { if D == 0 || D > 0x7f { panic("turboshake: D out of range") } return State{rate: rate128, dsbyte: D, turbo: true} } // NewShake256 creates a new SHAKE256 variable-output-length ShakeHash. // Its generic security strength is 256 bits against all attacks if // at least 64 bytes of its output are used. func NewShake256() State { return State{rate: rate256, dsbyte: dsbyteShake} } // NewTurboShake256 creates a new TurboSHAKE256 variable-output-length ShakeHash. // Its generic security strength is 256 bits against all attacks if // at least 64 bytes of its output are used. // D is the domain separation byte and must be between 0x01 and 0x7f inclusive. func NewTurboShake256(D byte) State { if D == 0 || D > 0x7f { panic("turboshake: D out of range") } return State{rate: rate256, dsbyte: D, turbo: true} } // ShakeSum128 writes an arbitrary-length digest of data into hash. func ShakeSum128(hash, data []byte) { h := NewShake128() _, _ = h.Write(data) _, _ = h.Read(hash) } // ShakeSum256 writes an arbitrary-length digest of data into hash. func ShakeSum256(hash, data []byte) { h := NewShake256() _, _ = h.Write(data) _, _ = h.Read(hash) } // TurboShakeSum128 writes an arbitrary-length digest of data into hash. func TurboShakeSum128(hash, data []byte, D byte) { h := NewTurboShake128(D) _, _ = h.Write(data) _, _ = h.Read(hash) } // TurboShakeSum256 writes an arbitrary-length digest of data into hash. func TurboShakeSum256(hash, data []byte, D byte) { h := NewTurboShake256(D) _, _ = h.Write(data) _, _ = h.Read(hash) } func (d *State) SwitchDS(D byte) { d.dsbyte = D } golang-github-cloudflare-circl-1.3.7/internal/sha3/testdata/000077500000000000000000000000001454601126700237525ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/internal/sha3/testdata/keccakKats.json.deflate000066400000000000000000020402341454601126700303210ustar00rootroot00000000000000uK5[@dyBLY Kũk݅X 5>cs9\$#?_?9_߾??㟚<Iva=,~\ZI ͺ_??,'P1bJX _+ ˂,]t1%{OŃl, 1^v(n_ 2wF2L{*]ˤAavY'1,JG߽ӕg2"U?" )"lJ1wS/>zbz{jXd/R]pD0]QB x \lӽ%,ޱil˰{G&:0*s]α;κ R)Q+8/! .%ߛ 2~Axލ@SnvvNv䜣{ _RPJ)|q FvflȚr9V6>i19O~ZhYPsL rZpgmޛYDvs={~ "-鹆pĴcZ#YŅ29 Ň+~ه>w>aZAWvL/ȉF RcۊwO</3>QW(/BL?ngcOL@v$뜕3WɤH9:<;,d6b&5,`3fB̝ jcfYr}$^;|~Z=m]=]`2v1ߌyXD orjH;-|=:݇pvϲ~z=&Ͽ4kqf$mD\S#ةmLS\ȚE\Fvi$yHiӮ}滊c'gY]ĨB8xj(\։ׇN813c/tYdDJ$zlsW81F?[ ##0^afxlx(՞jkGx WYC/;5+qJ@4VrMmnwH`3xG,#FVF=v~x`_;Y/RY 0lnh%cD7U{xµjwm0퐜)3#(Gh4E縹n?wl!F'0aɟ3eu9;։6cSI`&aM=$aVFEȐ=t+):u"m {6¿ }WV\1awws鈞H99b,=i] <1d/tmcZ"Ka窣nI1B(kx-sm߸G!pRk jȅm})F{hy2nϝ;rKGILν)Tn9Bð]UmG+xa5zJcbٗNc|QI9׼,ȻrE,e^9r{{o7* TI>4*#+ܳD[0`ʪg\<}(${`۩GJὃyq^oxIr?YdT@6)d-rcajCޔm&MʹiT#^4#[wzKBy3Ww> -Dd]m*Jƪ.5(±Ci=wl&UF\Rg* 0MJY.؝-])Qil2x2Os:jN1ܺת[H!W/,կfd(.ȩ!ޫ}7۩]龤.t?Vw2= E)4"{4{Ls;)eB(!t1l{fl %Wӊr]xc|oUEɺ8NEY';ޣUWϕ3-i!):lv(-h]VHj7^@:yIKmb ~xBk<0/Xrۗ:8j<#W;wWO2+;*/5\ Lf"`YNAOٜyTPɇH"nU8Q~V"T;gN`=2Fg|b_+gr]Tz} kXҤPEX9?'DZKMN-=8OuvoS/D}l$AahmN8Q= ~x:!{[Si|I Wn 9e!1%xH쒲2 /Bmf9(!B=HvY<hyWRۗx?Zsqg=[xm!Ix{t /<~l.WAM]9bŃK:!r&;K@[QK±J˼gʹͿࠏ<ѕg$]sZK }dٽJnVQFhvpZKH/sEM{zرsah^L(p$uo9#a<[ s/@r$N֪>y~V^n=1Iێd^=[^4A뚂(!(W+un2w( `uS-49k]2  av KhPS\s 騎ӵnaO2_2;'sd1oTd7% 8;: KR8% f+9/{G ;(riA ciQ[n™hw r'Maq>󆎒JIk(yۢ$Cbtߙ74d2EA1X\ Ri(g=橓pQCxXn1< {g!B|y-z ý?Z[(g}V\sm*zx|T+{He֕4HQbYbpc6$?^l͡P!--.QtiTQnu Z*c,Y2 S36#N4;~XAyrCuC_2N-ȳs_F)N=Vpzc!i2.!) 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All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. //go:build (!amd64 && !386 && !ppc64le) || appengine // +build !amd64,!386,!ppc64le appengine package sha3 // A storageBuf is an aligned array of maxRate bytes. type storageBuf [maxRate]byte func (b *storageBuf) asBytes() *[maxRate]byte { return (*[maxRate]byte)(b) } golang-github-cloudflare-circl-1.3.7/internal/sha3/xor_generic.go000066400000000000000000000014611454601126700247760ustar00rootroot00000000000000// Copyright 2015 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. //go:build (!amd64 || appengine) && (!386 || appengine) && (!ppc64le || appengine) // +build !amd64 appengine // +build !386 appengine // +build !ppc64le appengine package sha3 import "encoding/binary" // xorIn xors the bytes in buf into the state; it // makes no non-portable assumptions about memory layout // or alignment. func xorIn(d *State, buf []byte) { n := len(buf) / 8 for i := 0; i < n; i++ { a := binary.LittleEndian.Uint64(buf) d.a[i] ^= a buf = buf[8:] } } // copyOut copies ulint64s to a byte buffer. func copyOut(d *State, b []byte) { for i := 0; len(b) >= 8; i++ { binary.LittleEndian.PutUint64(b, d.a[i]) b = b[8:] } } golang-github-cloudflare-circl-1.3.7/internal/sha3/xor_unaligned.go000066400000000000000000000023741454601126700253340ustar00rootroot00000000000000// Copyright 2015 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. //go:build (amd64 || 386 || ppc64le) && !appengine // +build amd64 386 ppc64le // +build !appengine package sha3 import "unsafe" // A storageBuf is an aligned array of maxRate bytes. type storageBuf [maxRate / 8]uint64 func (b *storageBuf) asBytes() *[maxRate]byte { return (*[maxRate]byte)(unsafe.Pointer(b)) } // xorInuses unaligned reads and writes to update d.a to contain d.a // XOR buf. func xorIn(d *State, buf []byte) { n := len(buf) bw := (*[maxRate / 8]uint64)(unsafe.Pointer(&buf[0]))[: n/8 : n/8] if n >= 72 { d.a[0] ^= bw[0] d.a[1] ^= bw[1] d.a[2] ^= bw[2] d.a[3] ^= bw[3] d.a[4] ^= bw[4] d.a[5] ^= bw[5] d.a[6] ^= bw[6] d.a[7] ^= bw[7] d.a[8] ^= bw[8] } if n >= 104 { d.a[9] ^= bw[9] d.a[10] ^= bw[10] d.a[11] ^= bw[11] d.a[12] ^= bw[12] } if n >= 136 { d.a[13] ^= bw[13] d.a[14] ^= bw[14] d.a[15] ^= bw[15] d.a[16] ^= bw[16] } if n >= 144 { d.a[17] ^= bw[17] } if n >= 168 { d.a[18] ^= bw[18] d.a[19] ^= bw[19] d.a[20] ^= bw[20] } } func copyOut(d *State, buf []byte) { ab := (*[maxRate]uint8)(unsafe.Pointer(&d.a[0])) copy(buf, ab[:]) } golang-github-cloudflare-circl-1.3.7/internal/test/000077500000000000000000000000001454601126700222625ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/internal/test/test.go000066400000000000000000000026771454601126700236040ustar00rootroot00000000000000package test import ( "errors" "fmt" "strings" "testing" ) // ReportError reports an error if got is different from want. func ReportError(t testing.TB, got, want interface{}, inputs ...interface{}) { b := &strings.Builder{} fmt.Fprint(b, "\n") for i, in := range inputs { fmt.Fprintf(b, "in[%v]: %v\n", i, in) } fmt.Fprintf(b, "got: %v\nwant: %v", got, want) t.Helper() t.Fatalf(b.String()) } // CheckOk fails the test if result == false. func CheckOk(result bool, msg string, t testing.TB) { t.Helper() if !result { t.Fatal(msg) } } // checkErr fails on error condition. mustFail indicates whether err is expected // to be nil or not. func checkErr(t testing.TB, err error, mustFail bool, msg string) { t.Helper() if err != nil && !mustFail { t.Fatalf("msg: %v\nerr: %v", msg, err) } if err == nil && mustFail { t.Fatalf("msg: %v\nerr: %v", msg, err) } } // CheckNoErr fails if err !=nil. Print msg as an error message. func CheckNoErr(t testing.TB, err error, msg string) { t.Helper(); checkErr(t, err, false, msg) } // CheckIsErr fails if err ==nil. Print msg as an error message. func CheckIsErr(t testing.TB, err error, msg string) { t.Helper(); checkErr(t, err, true, msg) } // CheckPanic returns true if call to function 'f' caused panic. func CheckPanic(f func()) error { hasPanicked := errors.New("no panic detected") defer func() { if r := recover(); r != nil { hasPanicked = nil } }() f() return hasPanicked } golang-github-cloudflare-circl-1.3.7/kem/000077500000000000000000000000001454601126700202435ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/frodo/000077500000000000000000000000001454601126700213545ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/frodo/doc.go000066400000000000000000000006611454601126700224530ustar00rootroot00000000000000// Package frodo provides the key encapsulation mechanism FrodoKEM. // // Compatible with the implementation submitted to round 3 of the // NIST PQC competition [1]. This implementation draws heavily from the PQClean // implementation [2]. // // References: // // [1] https://frodokem.org/files/FrodoKEM-specification-20210604.pdf // [2] https://github.com/PQClean/PQClean/tree/master/crypto_kem/frodokem640shake/clean package frodo golang-github-cloudflare-circl-1.3.7/kem/frodo/frodo640shake/000077500000000000000000000000001454601126700237335ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/frodo/frodo640shake/frodo.go000066400000000000000000000326501454601126700254010ustar00rootroot00000000000000// Package frodo640shake implements the variant FrodoKEM-640 with SHAKE. package frodo640shake import ( "bytes" cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" ) const ( paramN = 640 // Denoted by 'mbar' in the FrodoKEM spec. paramNbar = 8 logQ = 15 logQMask = ((1 << logQ) - 1) seedASize = 16 pkHashSize = 16 // Denoted by 'B' in the FrodoKEM spec. extractedBits = 2 messageSize = 16 matrixBpPackedSize = (logQ * (paramN * paramNbar)) / 8 ) const ( // Size of seed for NewKeyFromSeed. // = len(s) + len(seedSE) + len(z). KeySeedSize = SharedKeySize + SharedKeySize + 16 // Size of seed for EncapsulateTo. EncapsulationSeedSize = 16 // Size of the established shared key. SharedKeySize = 16 // Size of the encapsulated shared key. CiphertextSize = 9720 // Size of a packed public key. PublicKeySize = 9616 // Size of a packed private key. PrivateKeySize = 19888 ) // Multi-dimensional arrays are stored in 1-dimensional arrays in // row-major order. type ( nByNU16 [paramN * paramN]uint16 nByNbarU16 [paramN * paramNbar]uint16 nbarByNU16 [paramNbar * paramN]uint16 nbarByNbarU16 [paramNbar * paramNbar]uint16 ) // Type of a FrodoKEM-640-SHAKE public key type PublicKey struct { seedA [seedASize]byte matrixB nByNbarU16 } // Type of a FrodoKEM-640-SHAKE private key type PrivateKey struct { hashInputIfDecapsFail [SharedKeySize]byte pk *PublicKey // matrixS stores transpose(S) matrixS nByNbarU16 // H(packed(pk)) hpk [pkHashSize]byte } // NewKeyFromSeed derives a public/private keypair deterministically // from the given seed. // // Panics if seed is not of length KeySeedSize. func newKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } var sk PrivateKey var pk PublicKey var E nByNbarU16 var byteSE [2 * (len(sk.matrixS) + len(E))]byte var A nByNU16 // Generate the secret value s, and the seed for S, E, and A. Add seedA to the public key shake128 := sha3.NewShake128() _, _ = shake128.Write(seed[2*SharedKeySize:]) _, _ = shake128.Read(pk.seedA[:]) shake128.Reset() _, _ = shake128.Write([]byte{0x5F}) _, _ = shake128.Write(seed[SharedKeySize : 2*SharedKeySize]) _, _ = shake128.Read(byteSE[:]) i := 0 for i < len(sk.matrixS) { sk.matrixS[i] = uint16(byteSE[i*2]) | (uint16(byteSE[(i*2)+1]) << 8) i++ } sample(sk.matrixS[:]) for j := range E { E[j] = uint16(byteSE[i*2]) | (uint16(byteSE[(i*2)+1]) << 8) i++ } sample(E[:]) expandSeedIntoA(&A, &pk.seedA, &shake128) mulAddASPlusE(&pk.matrixB, &A, &sk.matrixS, &E) // Populate the private key copy(sk.hashInputIfDecapsFail[:], seed[0:SharedKeySize]) sk.pk = &pk // Add H(pk) to the private key shake128.Reset() var ppk [PublicKeySize]byte pk.Pack(ppk[:]) _, _ = shake128.Write(ppk[:]) _, _ = shake128.Read(sk.hpk[:]) return &pk, &sk } // GenerateKeyPair generates public and private keys using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func generateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := newKeyFromSeed(seed[:]) return pk, sk, err } // EncapsulateTo generates a shared key and a ciphertext containing said key // from the public key and the randomness from seed and writes the shared key // to ss and ciphertext to ct. // // Panics if ss, ct, or seed are not of length SharedKeySize, CiphertextSize // and EncapsulationSeedSize respectively. // // seed may be nil, in which case crypto/rand.Reader is used to generate one. func (pk *PublicKey) EncapsulateTo(ct []byte, ss []byte, seed []byte) { if seed == nil { seed = make([]byte, EncapsulationSeedSize) if _, err := cryptoRand.Read(seed[:]); err != nil { panic(err) } } if len(seed) != EncapsulationSeedSize { panic("seed must be of length EncapsulationSeedSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } var G2out [2 * SharedKeySize]byte var SpEpEpp [(paramN * paramNbar) + (paramN * paramNbar) + (paramNbar * paramNbar)]uint16 var byteSpEpEpp [2 * len(SpEpEpp)]byte Sp := SpEpEpp[:paramN*paramNbar] Ep := SpEpEpp[paramN*paramNbar : 2*paramN*paramNbar] Epp := SpEpEpp[2*paramN*paramNbar:] var Bp nbarByNU16 var V nbarByNbarU16 var C nbarByNbarU16 var A nByNU16 var hpk [pkHashSize]byte var mu [messageSize]byte copy(mu[:], seed[:messageSize]) // compute hpk = G_1(packed(pk)) shake128 := sha3.NewShake128() var ppk [PublicKeySize]byte pk.Pack(ppk[:]) _, _ = shake128.Write(ppk[:]) _, _ = shake128.Read(hpk[:]) // compute (seedSE || k) = G_2(hpk || mu) shake128.Reset() _, _ = shake128.Write(hpk[:]) _, _ = shake128.Write(mu[:]) _, _ = shake128.Read(G2out[:]) // Generate Sp, Ep, Epp, and A, and compute: // Bp = Sp*A + Ep // V = Sp*B + Epp shake128.Reset() _, _ = shake128.Write([]byte{0x96}) _, _ = shake128.Write(G2out[:SharedKeySize]) _, _ = shake128.Read(byteSpEpEpp[:]) for i := range SpEpEpp { SpEpEpp[i] = uint16(byteSpEpEpp[i*2]) | (uint16(byteSpEpEpp[(i*2)+1]) << 8) } sample(SpEpEpp[:]) expandSeedIntoA(&A, &pk.seedA, &shake128) mulAddSAPlusE(&Bp, Sp, &A, Ep) mulAddSBPlusE(&V, Sp, &pk.matrixB, Epp) // Encode mu, and compute C = V + enc(mu) (mod q) encodeMessage(&C, &mu) add(&C, &V, &C) // Prepare the ciphertext pack(ct[:matrixBpPackedSize], Bp[:]) pack(ct[matrixBpPackedSize:], C[:]) // Compute ss = F(ct||k) shake128.Reset() _, _ = shake128.Write(ct[:]) _, _ = shake128.Write(G2out[SharedKeySize:]) _, _ = shake128.Read(ss[:]) } // DecapsulateTo computes the shared key that is encapsulated in ct // from the private key. // // Panics if ct or ss are not of length CiphertextSize and SharedKeySize // respectively. func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } var Bp nbarByNU16 var C nbarByNbarU16 var W nbarByNbarU16 var CC nbarByNbarU16 var BBp nbarByNU16 var SpEpEpp [(paramN * paramNbar) + (paramN * paramNbar) + (paramNbar * paramNbar)]uint16 var byteSpEpEpp [2 * len(SpEpEpp)]byte Sp := SpEpEpp[:paramN*paramNbar] Ep := SpEpEpp[paramN*paramNbar : 2*paramN*paramNbar] Epp := SpEpEpp[2*paramN*paramNbar:] var A nByNU16 var muprime [messageSize]byte var G2out [2 * SharedKeySize]byte kprime := G2out[SharedKeySize:] // Compute W = C - Bp*S (mod q), and decode the randomness mu unpack(Bp[:], ct[0:matrixBpPackedSize]) unpack(C[:], ct[matrixBpPackedSize:]) mulBS(&W, &Bp, &sk.matrixS) sub(&W, &C, &W) decodeMessage(&muprime, &W) // Generate (seedSE' || k') = G_2(hpk || mu') shake128 := sha3.NewShake128() _, _ = shake128.Write(sk.hpk[:]) _, _ = shake128.Write(muprime[:]) _, _ = shake128.Read(G2out[:]) // Generate Sp, Ep, Epp, A, and compute BBp = Sp*A + Ep. shake128.Reset() _, _ = shake128.Write([]byte{0x96}) _, _ = shake128.Write(G2out[:SharedKeySize]) _, _ = shake128.Read(byteSpEpEpp[:]) for i := range SpEpEpp { SpEpEpp[i] = uint16(byteSpEpEpp[i*2]) | (uint16(byteSpEpEpp[(i*2)+1]) << 8) } sample(SpEpEpp[:]) expandSeedIntoA(&A, &sk.pk.seedA, &shake128) mulAddSAPlusE(&BBp, Sp[:], &A, Ep[:]) // Reduce BBp modulo q for i := range BBp { BBp[i] = BBp[i] & logQMask } // compute W = Sp*B + Epp mulAddSBPlusE(&W, Sp, &sk.pk.matrixB, Epp) // Encode mu, and compute CC = W + enc(mu') (mod q) encodeMessage(&CC, &muprime) add(&CC, &W, &CC) // Prepare input to F // If (Bp == BBp & C == CC) then ss = F(ct || k'), else ss = F(ct || s) // Needs to avoid branching on secret data as per: // Qian Guo, Thomas Johansson, Alexander Nilsson. A key-recovery timing attack on post-quantum // primitives using the Fujisaki-Okamoto transformation and its application on FrodoKEM. In CRYPTO 2020. selector := ctCompareU16(Bp[:], BBp[:]) | ctCompareU16(C[:], CC[:]) // If (selector == 0) then load k' to do ss = F(ct || k'), else if (selector == 1) load s to do ss = F(ct || s) subtle.ConstantTimeCopy(selector, kprime[:], sk.hashInputIfDecapsFail[:]) shake128.Reset() _, _ = shake128.Write(ct[:]) _, _ = shake128.Write(kprime[:]) _, _ = shake128.Read(ss[:]) } // Packs sk to buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } copy(buf[:SharedKeySize], sk.hashInputIfDecapsFail[:]) buf = buf[SharedKeySize:] sk.pk.Pack(buf[:PublicKeySize]) buf = buf[PublicKeySize:] j := 0 for i := range sk.matrixS { buf[j] = byte(sk.matrixS[i]) buf[j+1] = byte(sk.matrixS[i] >> 8) j += 2 } buf = buf[j:] copy(buf[:], sk.hpk[:]) } // Unpacks sk from buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } copy(sk.hashInputIfDecapsFail[:], buf[:SharedKeySize]) buf = buf[SharedKeySize:] sk.pk = new(PublicKey) sk.pk.Unpack(buf[:PublicKeySize]) buf = buf[PublicKeySize:] for i := range sk.matrixS { sk.matrixS[i] = uint16(buf[i*2]) | (uint16(buf[(i*2)+1]) << 8) } buf = buf[len(sk.matrixS)*2:] copy(sk.hpk[:], buf[:]) } // Packs pk to buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } copy(buf[:seedASize], pk.seedA[:]) pack(buf[seedASize:], pk.matrixB[:]) } // TODO: Unpacks pk from buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } copy(pk.seedA[:], buf[:seedASize]) unpack(pk.matrixB[:], buf[seedASize:]) } // Boilerplate down below for the KEM scheme API. type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. func Scheme() kem.Scheme { return sch } func (scheme) Name() string { return "FrodoKEM-640-SHAKE" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SeedSize() int { return KeySeedSize } func (*scheme) SharedKeySize() int { return SharedKeySize } func (*scheme) CiphertextSize() int { return CiphertextSize } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { var ret [PrivateKeySize]byte sk.Pack(ret[:]) return ret[:], nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } if sk.pk == nil && oth.pk == nil { return true } if sk.pk == nil || oth.pk == nil { return false } return ctCompareU16(sk.matrixS[:], oth.matrixS[:]) == 0 && subtle.ConstantTimeCompare(sk.hashInputIfDecapsFail[:], oth.hashInputIfDecapsFail[:]) == 1 && sk.pk.Equal(oth.pk) && bytes.Equal(sk.hpk[:], oth.hpk[:]) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } if pk == nil && oth == nil { return true } if pk == nil || oth == nil { return false } for i := range pk.matrixB { if (pk.matrixB[i] & logQMask) != (oth.matrixB[i] & logQMask) { return false } } return bytes.Equal(pk.seedA[:], oth.seedA[:]) } func (sk *PrivateKey) Public() kem.PublicKey { return sk.pk } func (pk *PublicKey) MarshalBinary() ([]byte, error) { var ret [PublicKeySize]byte pk.Pack(ret[:]) return ret[:], nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return generateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != KeySeedSize { panic(kem.ErrSeedSize) } return newKeyFromSeed(seed[:]) } func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, nil) return } func (*scheme) EncapsulateDeterministically( pk kem.PublicKey, seed []byte, ) (ct, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, seed) return } func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != CiphertextSize { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } ss := make([]byte, SharedKeySize) priv.DecapsulateTo(ss, ct) return ss, nil } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != PublicKeySize { return nil, kem.ErrPubKeySize } var ret PublicKey ret.Unpack(buf) return &ret, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != PrivateKeySize { return nil, kem.ErrPrivKeySize } var ret PrivateKey ret.Unpack(buf) return &ret, nil } golang-github-cloudflare-circl-1.3.7/kem/frodo/frodo640shake/matrix_shake.go000066400000000000000000000026421454601126700267450ustar00rootroot00000000000000package frodo640shake import ( "github.com/cloudflare/circl/internal/sha3" ) func expandSeedIntoA(A *nByNU16, seed *[seedASize]byte, xof *sha3.State) { var ARow [paramN * 2]byte var seedSeparated [2 + seedASize]byte copy(seedSeparated[2:], seed[:]) for i := 0; i < paramN; i++ { seedSeparated[0] = byte(i) seedSeparated[1] = byte(i >> 8) xof.Reset() _, _ = xof.Write(seedSeparated[:]) _, _ = xof.Read(ARow[:]) for j := 0; j < paramN; j++ { // No need to reduce modulo 2^15, extra bits are removed // later on via packing or explicit reduction. A[(i*paramN)+j] = uint16(ARow[j*2]) | (uint16(ARow[(j*2)+1]) << 8) } } } func mulAddASPlusE(out *nByNbarU16, A *nByNU16, s *nByNbarU16, e *nByNbarU16) { for i := 0; i < paramN; i++ { for k := 0; k < paramNbar; k++ { sum := e[i*paramNbar+k] for j := 0; j < paramN; j++ { sum += A[i*paramN+j] * s[k*paramN+j] } // No need to reduce modulo 2^15, extra bits are removed // later on via packing or explicit reduction. out[i*paramNbar+k] += sum } } } func mulAddSAPlusE(out *nbarByNU16, s []uint16, A *nByNU16, e []uint16) { for i := 0; i < paramN; i++ { for k := 0; k < paramNbar; k++ { sum := e[k*paramN+i] for j := 0; j < paramN; j++ { sum += A[j*paramN+i] * s[k*paramN+j] } // No need to reduce modulo 2^15, extra bits are removed // later on via packing or explicit reduction. out[k*paramN+i] += sum } } } golang-github-cloudflare-circl-1.3.7/kem/frodo/frodo640shake/noise.go000066400000000000000000000016051454601126700254010ustar00rootroot00000000000000package frodo640shake const cdfTableLen = 13 var cdfTable [cdfTableLen]uint16 = [cdfTableLen]uint16{4643, 13363, 20579, 25843, 29227, 31145, 32103, 32525, 32689, 32745, 32762, 32766, 32767} // Take a uniformly distributed sample, and produce a sample in the FrodoKEM // discrete Gaussian distribution using inverse transform sampling. func sample(sampled []uint16) { for i := 0; i < len(sampled); i++ { var gaussianSample uint16 = 0 sign := sampled[i] & 1 unifSample := sampled[i] >> 1 for j := 0; j < cdfTableLen-1; j++ { gaussianSample += (cdfTable[j] - unifSample) >> 15 } // If sign = 1, -sign = 0xFFFF and the bits of gaussianSample // are flipped. Since gaussianSample is uint16, we have: // // flippedBits(gaussianSample) + 1 ≡ -gaussianSample (mod 2^16), // // and so the sign of gaussianSample is flipped. sampled[i] = ((-sign) ^ gaussianSample) + sign } } golang-github-cloudflare-circl-1.3.7/kem/frodo/frodo640shake/util.go000066400000000000000000000102101454601126700252310ustar00rootroot00000000000000package frodo640shake func add(out *nbarByNbarU16, lhs *nbarByNbarU16, rhs *nbarByNbarU16) { for i := 0; i < len(out); i++ { out[i] = (lhs[i] + rhs[i]) & logQMask } } func sub(out *nbarByNbarU16, lhs *nbarByNbarU16, rhs *nbarByNbarU16) { for i := 0; i < len(out); i++ { out[i] = (lhs[i] - rhs[i]) & logQMask } } func pack(out []byte, in []uint16) { j := 0 for i := 0; (i * 8) < len(in); i++ { in0 := in[i*8] & logQMask in1 := in[(i*8)+1] & logQMask in2 := in[(i*8)+2] & logQMask in3 := in[(i*8)+3] & logQMask in4 := in[(i*8)+4] & logQMask in5 := in[(i*8)+5] & logQMask in6 := in[(i*8)+6] & logQMask in7 := in[(i*8)+7] & logQMask out[j] |= byte(in0 >> 7) out[j+1] = (byte(in0&0x7F) << 1) | byte(in1>>14) out[j+2] = byte(in1 >> 6) out[j+3] = (byte(in1&0x3F) << 2) | byte(in2>>13) out[j+4] = byte(in2 >> 5) out[j+5] = (byte(in2&0x1F) << 3) | byte(in3>>12) out[j+6] = byte(in3 >> 4) out[j+7] = (byte(in3&0x0F) << 4) | byte(in4>>11) out[j+8] = byte(in4 >> 3) out[j+9] = (byte(in4&0x07) << 5) | byte(in5>>10) out[j+10] = byte(in5 >> 2) out[j+11] = (byte(in5&0x03) << 6) | byte(in6>>9) out[j+12] = byte(in6 >> 1) out[j+13] = (byte(in6&0x01) << 7) | byte(in7>>8) out[j+14] = byte(in7) j += 15 } } func unpack(out []uint16, in []byte) { j := 0 for i := 0; (i * 15) < len(in); i++ { in0 := in[i*15] in1 := in[(i*15)+1] in2 := in[(i*15)+2] in3 := in[(i*15)+3] in4 := in[(i*15)+4] in5 := in[(i*15)+5] in6 := in[(i*15)+6] in7 := in[(i*15)+7] in8 := in[(i*15)+8] in9 := in[(i*15)+9] in10 := in[(i*15)+10] in11 := in[(i*15)+11] in12 := in[(i*15)+12] in13 := in[(i*15)+13] in14 := in[(i*15)+14] out[j] = (uint16(in0) << 7) | (uint16(in1&0xFE) >> 1) out[j+1] = (uint16(in1&0x1) << 14) | (uint16(in2) << 6) | (uint16(in3&0xFC) >> 2) out[j+2] = (uint16(in3&0x03) << 13) | (uint16(in4) << 5) | (uint16(in5&0xF8) >> 3) out[j+3] = (uint16(in5&0x07) << 12) | (uint16(in6) << 4) | (uint16(in7&0xF0) >> 4) out[j+4] = (uint16(in7&0x0F) << 11) | (uint16(in8) << 3) | (uint16(in9&0xE0) >> 5) out[j+5] = (uint16(in9&0x1F) << 10) | (uint16(in10) << 2) | (uint16(in11&0xC0) >> 6) out[j+6] = (uint16(in11&0x3F) << 9) | (uint16(in12) << 1) | (uint16(in13&0x80) >> 7) out[j+7] = (uint16(in13&0x7F) << 8) | uint16(in14) j += 8 } } func encodeMessage(out *nbarByNbarU16, msg *[messageSize]byte) { extractedBitsMask := uint16((1 << extractedBits) - 1) outPos := 0 for i := 0; (i * 2) < len(msg); i++ { in := uint16(msg[i*2]) | (uint16(msg[(i*2)+1]) << 8) for j := 0; j < (16 / extractedBits); j++ { // 16 = bit size of out[i] out[outPos] = (in & extractedBitsMask) << (logQ - extractedBits) outPos++ in >>= extractedBits } } } func decodeMessage(out *[messageSize]byte, msg *nbarByNbarU16) { extractedBitsMask := uint16((1 << extractedBits) - 1) msgPos := 0 for i := 0; i < len(out); i++ { for j := 0; j < (8 / extractedBits); j++ { temp := (msg[msgPos] & logQMask) + (1 << (logQ - extractedBits - 1)) temp >>= (logQ - extractedBits) temp &= extractedBitsMask out[i] |= byte(temp) << (j * extractedBits) msgPos++ } } } func mulAddSBPlusE(out *nbarByNbarU16, s []uint16, b *nByNbarU16, e []uint16) { // Multiply by s on the left // Inputs: b (N x N_BAR), s (N_BAR x N), e (N_BAR x N_BAR) // Output: out = s*b + e (N_BAR x N_BAR) for k := 0; k < paramNbar; k++ { for i := 0; i < paramNbar; i++ { out[k*paramNbar+i] = e[k*paramNbar+i] for j := 0; j < paramN; j++ { out[k*paramNbar+i] += s[k*paramN+j] * b[j*paramNbar+i] } out[k*paramNbar+i] = out[k*paramNbar+i] & logQMask } } } func mulBS(out *nbarByNbarU16, b *nbarByNU16, s *nByNbarU16) { for i := 0; i < paramNbar; i++ { for j := 0; j < paramNbar; j++ { out[i*paramNbar+j] = 0 for k := 0; k < paramN; k++ { out[i*paramNbar+j] += b[i*paramN+k] * s[j*paramN+k] } out[i*paramNbar+j] = out[i*paramNbar+j] & logQMask } } } func ctCompareU16(lhs []uint16, rhs []uint16) int { // Compare lhs and rhs in constant time. // Returns 0 if they are equal, 1 otherwise. if len(lhs) != len(rhs) { return 1 } var v uint16 for i := range lhs { v |= lhs[i] ^ rhs[i] } return int((v | -v) >> 15) } golang-github-cloudflare-circl-1.3.7/kem/frodo/kat_test.go000066400000000000000000000034321454601126700235230ustar00rootroot00000000000000package frodo // Code to generate the NIST "PQCsignKAT" test vectors. // See PQCsignKAT_sign.c and randombytes.c in the reference implementation. import ( "bytes" "crypto/sha256" "fmt" "testing" "github.com/cloudflare/circl/internal/nist" "github.com/cloudflare/circl/kem/schemes" ) func TestPQCgenKATKem(t *testing.T) { kats := []struct { name string want string }{ // Computed from: // https://github.com/microsoft/PQCrypto-LWEKE/blob/66fc7744c3aae6acfc5fcc587ec7f2cdec48d216/KAT/PQCkemKAT_19888_shake.rsp {"FrodoKEM-640-SHAKE", "604a10cfc871dfaed9cb5b057c644ab03b16852cea7f39bc7f9831513b5b1cfa"}, } for _, kat := range kats { kat := kat t.Run(kat.name, func(t *testing.T) { testPQCgenKATKem(t, kat.name, kat.want) }) } } func testPQCgenKATKem(t *testing.T, name, expected string) { scheme := schemes.ByName(name) if scheme == nil { t.Fatal() } var seed [48]byte kseed := make([]byte, scheme.SeedSize()) eseed := make([]byte, scheme.EncapsulationSeedSize()) for i := 0; i < 48; i++ { seed[i] = byte(i) } f := sha256.New() g := nist.NewDRBG(&seed) fmt.Fprintf(f, "# %s\n\n", name) for i := 0; i < 100; i++ { g.Fill(seed[:]) fmt.Fprintf(f, "count = %d\n", i) fmt.Fprintf(f, "seed = %X\n", seed) g2 := nist.NewDRBG(&seed) g2.Fill(kseed[:]) pk, sk := scheme.DeriveKeyPair(kseed) ppk, _ := pk.MarshalBinary() psk, _ := sk.MarshalBinary() g2.Fill(eseed) ct, ss, err := scheme.EncapsulateDeterministically(pk, eseed) if err != nil { t.Fatal(err) } ss2, _ := scheme.Decapsulate(sk, ct) if !bytes.Equal(ss, ss2) { t.Fatal() } fmt.Fprintf(f, "pk = %X\n", ppk) fmt.Fprintf(f, "sk = %X\n", psk) fmt.Fprintf(f, "ct = %X\n", ct) fmt.Fprintf(f, "ss = %X\n\n", ss) } if fmt.Sprintf("%x", f.Sum(nil)) != expected { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/kem/hybrid/000077500000000000000000000000001454601126700215245ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/hybrid/ckem.go000066400000000000000000000106731454601126700230010ustar00rootroot00000000000000package hybrid // TODO move over to crypto/ecdh once we can assume Go 1.20. import ( "crypto/elliptic" cryptoRand "crypto/rand" "crypto/subtle" "math/big" "github.com/cloudflare/circl/kem" "github.com/cloudflare/circl/xof" ) type cPublicKey struct { scheme *cScheme x, y *big.Int } type cPrivateKey struct { scheme *cScheme key []byte } type cScheme struct { curve elliptic.Curve } var p256Kem = &cScheme{elliptic.P256()} func (sch *cScheme) scSize() int { return (sch.curve.Params().N.BitLen() + 7) / 8 } func (sch *cScheme) ptSize() int { return (sch.curve.Params().BitSize + 7) / 8 } func (sch *cScheme) Name() string { return sch.curve.Params().Name } func (sch *cScheme) PublicKeySize() int { return 2*sch.ptSize() + 1 } func (sch *cScheme) PrivateKeySize() int { return sch.scSize() } func (sch *cScheme) SeedSize() int { return sch.PrivateKeySize() } func (sch *cScheme) SharedKeySize() int { return sch.ptSize() } func (sch *cScheme) CiphertextSize() int { return sch.PublicKeySize() } func (sch *cScheme) EncapsulationSeedSize() int { return sch.SeedSize() } func (sk *cPrivateKey) Scheme() kem.Scheme { return sk.scheme } func (pk *cPublicKey) Scheme() kem.Scheme { return pk.scheme } func (sk *cPrivateKey) MarshalBinary() ([]byte, error) { ret := make([]byte, len(sk.key)) copy(ret, sk.key) return ret, nil } func (sk *cPrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*cPrivateKey) if !ok { return false } if oth.scheme != sk.scheme { return false } return subtle.ConstantTimeCompare(oth.key, sk.key) == 1 } func (sk *cPrivateKey) Public() kem.PublicKey { x, y := sk.scheme.curve.ScalarBaseMult(sk.key) return &cPublicKey{ sk.scheme, x, y, } } func (pk *cPublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*cPublicKey) if !ok { return false } if oth.scheme != pk.scheme { return false } return oth.x.Cmp(pk.x) == 0 && oth.y.Cmp(pk.y) == 0 } func (pk *cPublicKey) MarshalBinary() ([]byte, error) { return elliptic.Marshal(pk.scheme.curve, pk.x, pk.y), nil } func (sch *cScheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { seed := make([]byte, sch.SeedSize()) _, err := cryptoRand.Read(seed) if err != nil { return nil, nil, err } pk, sk := sch.DeriveKeyPair(seed) return pk, sk, nil } func (sch *cScheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != sch.SeedSize() { panic(kem.ErrSeedSize) } h := xof.SHAKE256.New() _, _ = h.Write(seed) key, x, y, err := elliptic.GenerateKey(sch.curve, h) if err != nil { panic(err) } sk := cPrivateKey{scheme: sch, key: key} pk := cPublicKey{scheme: sch, x: x, y: y} return &pk, &sk } func (sch *cScheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { seed := make([]byte, sch.EncapsulationSeedSize()) _, err = cryptoRand.Read(seed) if err != nil { return } return sch.EncapsulateDeterministically(pk, seed) } func (pk *cPublicKey) X(sk *cPrivateKey) []byte { if pk.scheme != sk.scheme { panic(kem.ErrTypeMismatch) } sharedKey := make([]byte, pk.scheme.SharedKeySize()) xShared, _ := pk.scheme.curve.ScalarMult(pk.x, pk.y, sk.key) xShared.FillBytes(sharedKey) return sharedKey } func (sch *cScheme) EncapsulateDeterministically( pk kem.PublicKey, seed []byte, ) (ct, ss []byte, err error) { if len(seed) != sch.EncapsulationSeedSize() { return nil, nil, kem.ErrSeedSize } pub, ok := pk.(*cPublicKey) if !ok || pub.scheme != sch { return nil, nil, kem.ErrTypeMismatch } pk2, sk2 := sch.DeriveKeyPair(seed) ss = pub.X(sk2.(*cPrivateKey)) ct, _ = pk2.MarshalBinary() return } func (sch *cScheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != sch.CiphertextSize() { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*cPrivateKey) if !ok || priv.scheme != sch { return nil, kem.ErrTypeMismatch } pk, err := sch.UnmarshalBinaryPublicKey(ct) if err != nil { return nil, err } ss := pk.(*cPublicKey).X(priv) return ss, nil } func (sch *cScheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != sch.PublicKeySize() { return nil, kem.ErrPubKeySize } x, y := elliptic.Unmarshal(sch.curve, buf) return &cPublicKey{sch, x, y}, nil } func (sch *cScheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != sch.PrivateKeySize() { return nil, kem.ErrPrivKeySize } ret := cPrivateKey{sch, make([]byte, sch.PrivateKeySize())} copy(ret.key, buf) return &ret, nil } golang-github-cloudflare-circl-1.3.7/kem/hybrid/hybrid.go000066400000000000000000000216371454601126700233450ustar00rootroot00000000000000// Package hybrid defines several hybrid classical/quantum KEMs. // // KEMs are combined by simple concatenation of shared secrets, cipher texts, // public keys, etc, see // // https://datatracker.ietf.org/doc/draft-ietf-tls-hybrid-design/ // https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Cr2.pdf // // Note that this is only fine if the shared secret is used in its entirety // in a next step, such as being hashed or used as key. // // For deriving a KEM keypair deterministically and encapsulating // deterministically, we expand a single seed to both using SHAKE256, // so that a non-uniform seed (such as a shared secret generated by a hybrid // KEM where one of the KEMs is weak) doesn't impact just one of the KEMs. // // Of our XOF (SHAKE256), we desire two security properties: // // 1. The internal state of the XOF should be big enough so that we // do not loose entropy. // 2. From one of the new seeds, we shouldn't be able to derive // the other or the original seed. // // SHAKE256, and all siblings in the SHA3 family, have a 200B internal // state, so (1) is fine if our seeds are less than 200B. // If SHAKE256 is computationally indistinguishable from a random // sponge, then it affords us 256b security against (2) by the // flat sponge claim [https://keccak.team/files/SpongeFunctions.pdf]. // None of the implemented schemes claim more than 256b security // and so SHAKE256 will do fine. package hybrid import ( "errors" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" "github.com/cloudflare/circl/kem/kyber/kyber1024" "github.com/cloudflare/circl/kem/kyber/kyber512" "github.com/cloudflare/circl/kem/kyber/kyber768" ) var ErrUninitialized = errors.New("public or private key not initialized") // Returns the hybrid KEM of Kyber512Draft00 and X25519. func Kyber512X25519() kem.Scheme { return kyber512X } // Returns the hybrid KEM of Kyber768Draft00 and X25519. func Kyber768X25519() kem.Scheme { return kyber768X } // Returns the hybrid KEM of Kyber768Draft00 and X448. func Kyber768X448() kem.Scheme { return kyber768X4 } // Returns the hybrid KEM of Kyber1024Draft00 and X448. func Kyber1024X448() kem.Scheme { return kyber1024X } // Returns the hybrid KEM of Kyber768Draft00 and P-256. func P256Kyber768Draft00() kem.Scheme { return p256Kyber768Draft00 } var p256Kyber768Draft00 kem.Scheme = &scheme{ "P256Kyber768Draft00", p256Kem, kyber768.Scheme(), } var kyber512X kem.Scheme = &scheme{ "Kyber512-X25519", x25519Kem, kyber512.Scheme(), } var kyber768X kem.Scheme = &scheme{ "Kyber768-X25519", x25519Kem, kyber768.Scheme(), } var kyber768X4 kem.Scheme = &scheme{ "Kyber768-X448", x448Kem, kyber768.Scheme(), } var kyber1024X kem.Scheme = &scheme{ "Kyber1024-X448", x448Kem, kyber1024.Scheme(), } // Public key of a hybrid KEM. type publicKey struct { scheme *scheme first kem.PublicKey second kem.PublicKey } // Private key of a hybrid KEM. type privateKey struct { scheme *scheme first kem.PrivateKey second kem.PrivateKey } // Scheme for a hybrid KEM. type scheme struct { name string first kem.Scheme second kem.Scheme } func (sch *scheme) Name() string { return sch.name } func (sch *scheme) PublicKeySize() int { return sch.first.PublicKeySize() + sch.second.PublicKeySize() } func (sch *scheme) PrivateKeySize() int { return sch.first.PrivateKeySize() + sch.second.PrivateKeySize() } func (sch *scheme) SeedSize() int { first := sch.first.SeedSize() second := sch.second.SeedSize() ret := second if first > second { ret = first } return ret } func (sch *scheme) SharedKeySize() int { return sch.first.SharedKeySize() + sch.second.SharedKeySize() } func (sch *scheme) CiphertextSize() int { return sch.first.CiphertextSize() + sch.second.CiphertextSize() } func (sch *scheme) EncapsulationSeedSize() int { first := sch.first.EncapsulationSeedSize() second := sch.second.EncapsulationSeedSize() ret := second if first > second { ret = first } return ret } func (sk *privateKey) Scheme() kem.Scheme { return sk.scheme } func (pk *publicKey) Scheme() kem.Scheme { return pk.scheme } func (sk *privateKey) MarshalBinary() ([]byte, error) { if sk.first == nil || sk.second == nil { return nil, ErrUninitialized } first, err := sk.first.MarshalBinary() if err != nil { return nil, err } second, err := sk.second.MarshalBinary() if err != nil { return nil, err } return append(first, second...), nil } func (sk *privateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*privateKey) if !ok { return false } if sk.first == nil && sk.second == nil && oth.first == nil && oth.second == nil { return true } if sk.first == nil || sk.second == nil || oth.first == nil || oth.second == nil { return false } return sk.first.Equal(oth.first) && sk.second.Equal(oth.second) } func (sk *privateKey) Public() kem.PublicKey { return &publicKey{sk.scheme, sk.first.Public(), sk.second.Public()} } func (pk *publicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*publicKey) if !ok { return false } if pk.first == nil && pk.second == nil && oth.first == nil && oth.second == nil { return true } if pk.first == nil || pk.second == nil || oth.first == nil || oth.second == nil { return false } return pk.first.Equal(oth.first) && pk.second.Equal(oth.second) } func (pk *publicKey) MarshalBinary() ([]byte, error) { if pk.first == nil || pk.second == nil { return nil, ErrUninitialized } first, err := pk.first.MarshalBinary() if err != nil { return nil, err } second, err := pk.second.MarshalBinary() if err != nil { return nil, err } return append(first, second...), nil } func (sch *scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { pk1, sk1, err := sch.first.GenerateKeyPair() if err != nil { return nil, nil, err } pk2, sk2, err := sch.second.GenerateKeyPair() if err != nil { return nil, nil, err } return &publicKey{sch, pk1, pk2}, &privateKey{sch, sk1, sk2}, nil } func (sch *scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != sch.SeedSize() { panic(kem.ErrSeedSize) } h := sha3.NewShake256() _, _ = h.Write(seed) first := make([]byte, sch.first.SeedSize()) second := make([]byte, sch.second.SeedSize()) _, _ = h.Read(first) _, _ = h.Read(second) pk1, sk1 := sch.first.DeriveKeyPair(first) pk2, sk2 := sch.second.DeriveKeyPair(second) return &publicKey{sch, pk1, pk2}, &privateKey{sch, sk1, sk2} } func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { pub, ok := pk.(*publicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } ct1, ss1, err := sch.first.Encapsulate(pub.first) if err != nil { return nil, nil, err } ct2, ss2, err := sch.second.Encapsulate(pub.second) if err != nil { return nil, nil, err } return append(ct1, ct2...), append(ss1, ss2...), nil } func (sch *scheme) EncapsulateDeterministically( pk kem.PublicKey, seed []byte, ) (ct, ss []byte, err error) { if len(seed) != sch.EncapsulationSeedSize() { return nil, nil, kem.ErrSeedSize } h := sha3.NewShake256() _, _ = h.Write(seed) first := make([]byte, sch.first.EncapsulationSeedSize()) second := make([]byte, sch.second.EncapsulationSeedSize()) _, _ = h.Read(first) _, _ = h.Read(second) pub, ok := pk.(*publicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } ct1, ss1, err := sch.first.EncapsulateDeterministically(pub.first, first) if err != nil { return nil, nil, err } ct2, ss2, err := sch.second.EncapsulateDeterministically(pub.second, second) if err != nil { return nil, nil, err } return append(ct1, ct2...), append(ss1, ss2...), nil } func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != sch.CiphertextSize() { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*privateKey) if !ok { return nil, kem.ErrTypeMismatch } firstSize := sch.first.CiphertextSize() ss1, err := sch.first.Decapsulate(priv.first, ct[:firstSize]) if err != nil { return nil, err } ss2, err := sch.second.Decapsulate(priv.second, ct[firstSize:]) if err != nil { return nil, err } return append(ss1, ss2...), nil } func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != sch.PublicKeySize() { return nil, kem.ErrPubKeySize } firstSize := sch.first.PublicKeySize() pk1, err := sch.first.UnmarshalBinaryPublicKey(buf[:firstSize]) if err != nil { return nil, err } pk2, err := sch.second.UnmarshalBinaryPublicKey(buf[firstSize:]) if err != nil { return nil, err } return &publicKey{sch, pk1, pk2}, nil } func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != sch.PrivateKeySize() { return nil, kem.ErrPrivKeySize } firstSize := sch.first.PrivateKeySize() sk1, err := sch.first.UnmarshalBinaryPrivateKey(buf[:firstSize]) if err != nil { return nil, err } sk2, err := sch.second.UnmarshalBinaryPrivateKey(buf[firstSize:]) if err != nil { return nil, err } return &privateKey{sch, sk1, sk2}, nil } golang-github-cloudflare-circl-1.3.7/kem/hybrid/xkem.go000066400000000000000000000112751454601126700230250ustar00rootroot00000000000000package hybrid import ( "bytes" cryptoRand "crypto/rand" "crypto/subtle" "github.com/cloudflare/circl/dh/x25519" "github.com/cloudflare/circl/dh/x448" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" ) type xPublicKey struct { scheme *xScheme key []byte } type xPrivateKey struct { scheme *xScheme key []byte } type xScheme struct { size int } var ( x25519Kem = &xScheme{x25519.Size} x448Kem = &xScheme{x448.Size} ) func (sch *xScheme) Name() string { switch sch.size { case x25519.Size: return "X25519" case x448.Size: return "X448" } panic(kem.ErrTypeMismatch) } func (sch *xScheme) PublicKeySize() int { return sch.size } func (sch *xScheme) PrivateKeySize() int { return sch.size } func (sch *xScheme) SeedSize() int { return sch.size } func (sch *xScheme) SharedKeySize() int { return sch.size } func (sch *xScheme) CiphertextSize() int { return sch.size } func (sch *xScheme) EncapsulationSeedSize() int { return sch.size } func (sk *xPrivateKey) Scheme() kem.Scheme { return sk.scheme } func (pk *xPublicKey) Scheme() kem.Scheme { return pk.scheme } func (sk *xPrivateKey) MarshalBinary() ([]byte, error) { ret := make([]byte, len(sk.key)) copy(ret, sk.key) return ret, nil } func (sk *xPrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*xPrivateKey) if !ok { return false } if oth.scheme != sk.scheme { return false } return subtle.ConstantTimeCompare(oth.key, sk.key) == 1 } func (sk *xPrivateKey) Public() kem.PublicKey { pk := xPublicKey{sk.scheme, make([]byte, sk.scheme.size)} switch sk.scheme.size { case x25519.Size: var sk2, pk2 x25519.Key copy(sk2[:], sk.key) x25519.KeyGen(&pk2, &sk2) copy(pk.key, pk2[:]) case x448.Size: var sk2, pk2 x448.Key copy(sk2[:], sk.key) x448.KeyGen(&pk2, &sk2) copy(pk.key, pk2[:]) } return &pk } func (pk *xPublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*xPublicKey) if !ok { return false } if oth.scheme != pk.scheme { return false } return bytes.Equal(oth.key, pk.key) } func (pk *xPublicKey) MarshalBinary() ([]byte, error) { ret := make([]byte, pk.scheme.size) copy(ret, pk.key) return ret, nil } func (sch *xScheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { seed := make([]byte, sch.SeedSize()) _, err := cryptoRand.Read(seed) if err != nil { return nil, nil, err } pk, sk := sch.DeriveKeyPair(seed) return pk, sk, nil } func (sch *xScheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != sch.SeedSize() { panic(kem.ErrSeedSize) } sk := xPrivateKey{scheme: sch, key: make([]byte, sch.size)} h := sha3.NewShake256() _, _ = h.Write(seed) _, _ = h.Read(sk.key) return sk.Public(), &sk } func (sch *xScheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { seed := make([]byte, sch.EncapsulationSeedSize()) _, err = cryptoRand.Read(seed) if err != nil { return } return sch.EncapsulateDeterministically(pk, seed) } func (pk *xPublicKey) X(sk *xPrivateKey) []byte { if pk.scheme != sk.scheme { panic(kem.ErrTypeMismatch) } switch pk.scheme.size { case x25519.Size: var ss2, pk2, sk2 x25519.Key copy(pk2[:], pk.key) copy(sk2[:], sk.key) x25519.Shared(&ss2, &sk2, &pk2) return ss2[:] case x448.Size: var ss2, pk2, sk2 x448.Key copy(pk2[:], pk.key) copy(sk2[:], sk.key) x448.Shared(&ss2, &sk2, &pk2) return ss2[:] } panic(kem.ErrTypeMismatch) } func (sch *xScheme) EncapsulateDeterministically( pk kem.PublicKey, seed []byte, ) (ct, ss []byte, err error) { if len(seed) != sch.EncapsulationSeedSize() { return nil, nil, kem.ErrSeedSize } pub, ok := pk.(*xPublicKey) if !ok || pub.scheme != sch { return nil, nil, kem.ErrTypeMismatch } pk2, sk2 := sch.DeriveKeyPair(seed) ss = pub.X(sk2.(*xPrivateKey)) ct, _ = pk2.MarshalBinary() return } func (sch *xScheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != sch.CiphertextSize() { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*xPrivateKey) if !ok || priv.scheme != sch { return nil, kem.ErrTypeMismatch } pk, err := sch.UnmarshalBinaryPublicKey(ct) if err != nil { return nil, err } ss := pk.(*xPublicKey).X(priv) return ss, nil } func (sch *xScheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != sch.PublicKeySize() { return nil, kem.ErrPubKeySize } ret := xPublicKey{sch, make([]byte, sch.size)} copy(ret.key, buf) return &ret, nil } func (sch *xScheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != sch.PrivateKeySize() { return nil, kem.ErrPrivKeySize } ret := xPrivateKey{sch, make([]byte, sch.size)} copy(ret.key, buf) return &ret, nil } golang-github-cloudflare-circl-1.3.7/kem/kem.go000066400000000000000000000067001454601126700213510ustar00rootroot00000000000000// Package kem provides a unified interface for KEM schemes. // // A register of schemes is available in the package // // github.com/cloudflare/circl/kem/schemes package kem import ( "encoding" "errors" ) // A KEM public key type PublicKey interface { // Returns the scheme for this public key Scheme() Scheme encoding.BinaryMarshaler Equal(PublicKey) bool } // A KEM private key type PrivateKey interface { // Returns the scheme for this private key Scheme() Scheme encoding.BinaryMarshaler Equal(PrivateKey) bool Public() PublicKey } // A Scheme represents a specific instance of a KEM. type Scheme interface { // Name of the scheme Name() string // GenerateKeyPair creates a new key pair. GenerateKeyPair() (PublicKey, PrivateKey, error) // Encapsulate generates a shared key ss for the public key and // encapsulates it into a ciphertext ct. Encapsulate(pk PublicKey) (ct, ss []byte, err error) // Returns the shared key encapsulated in ciphertext ct for the // private key sk. Decapsulate(sk PrivateKey, ct []byte) ([]byte, error) // Unmarshals a PublicKey from the provided buffer. UnmarshalBinaryPublicKey([]byte) (PublicKey, error) // Unmarshals a PrivateKey from the provided buffer. UnmarshalBinaryPrivateKey([]byte) (PrivateKey, error) // Size of encapsulated keys. CiphertextSize() int // Size of established shared keys. SharedKeySize() int // Size of packed private keys. PrivateKeySize() int // Size of packed public keys. PublicKeySize() int // DeriveKeyPair deterministically derives a pair of keys from a seed. // Panics if the length of seed is not equal to the value returned by // SeedSize. DeriveKeyPair(seed []byte) (PublicKey, PrivateKey) // Size of seed used in DeriveKey SeedSize() int // EncapsulateDeterministically generates a shared key ss for the public // key deterministically from the given seed and encapsulates it into // a ciphertext ct. If unsure, you're better off using Encapsulate(). EncapsulateDeterministically(pk PublicKey, seed []byte) ( ct, ss []byte, err error) // Size of seed used in EncapsulateDeterministically(). EncapsulationSeedSize() int } // AuthScheme represents a KEM that supports authenticated key encapsulation. type AuthScheme interface { Scheme AuthEncapsulate(pkr PublicKey, sks PrivateKey) (ct, ss []byte, err error) AuthEncapsulateDeterministically(pkr PublicKey, sks PrivateKey, seed []byte) (ct, ss []byte, err error) AuthDecapsulate(skr PrivateKey, ct []byte, pks PublicKey) ([]byte, error) } var ( // ErrTypeMismatch is the error used if types of, for instance, private // and public keys don't match ErrTypeMismatch = errors.New("types mismatch") // ErrSeedSize is the error used if the provided seed is of the wrong // size. ErrSeedSize = errors.New("wrong seed size") // ErrPubKeySize is the error used if the provided public key is of // the wrong size. ErrPubKeySize = errors.New("wrong size for public key") // ErrCiphertextSize is the error used if the provided ciphertext // is of the wrong size. ErrCiphertextSize = errors.New("wrong size for ciphertext") // ErrPrivKeySize is the error used if the provided private key is of // the wrong size. ErrPrivKeySize = errors.New("wrong size for private key") // ErrPubKey is the error used if the provided public key is invalid. ErrPubKey = errors.New("invalid public key") // ErrCipherText is the error used if the provided ciphertext is invalid. ErrCipherText = errors.New("invalid ciphertext") ) golang-github-cloudflare-circl-1.3.7/kem/kyber/000077500000000000000000000000001454601126700213575ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/kyber/doc.go000066400000000000000000000006611454601126700224560ustar00rootroot00000000000000//go:generate go run gen.go // Package kyber implements the CRYSTALS-Kyber.CCAKEM IND-CCA2 secure // key encapsulation mechanism (KEM) as submitted to round 3 of the NIST PQC // competition and described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf // // The related public key encryption scheme CRYSTALS-Kyber.CPAPKE can be // found in the package github.com/cloudflare/circl/pke/kyber. package kyber golang-github-cloudflare-circl-1.3.7/kem/kyber/gen.go000066400000000000000000000023301454601126700224550ustar00rootroot00000000000000//go:build ignore // +build ignore // Autogenerates wrappers from templates to prevent too much duplicated code // between the code for different modes. package main import ( "bytes" "go/format" "io/ioutil" "strings" "text/template" ) type Instance struct { Name string } func (m Instance) Pkg() string { return strings.ToLower(m.Name) } var ( Instances = []Instance{ {Name: "Kyber512"}, {Name: "Kyber768"}, {Name: "Kyber1024"}, } TemplateWarning = "// Code generated from" ) func main() { generatePackageFiles() } // Generates instance/kyber.go from templates/pkg.templ.go func generatePackageFiles() { tl, err := template.ParseFiles("templates/pkg.templ.go") if err != nil { panic(err) } for _, mode := range Instances { buf := new(bytes.Buffer) err := tl.Execute(buf, mode) if err != nil { panic(err) } // Formating output code code, err := format.Source(buf.Bytes()) if err != nil { panic("error formating code") } res := string(code) offset := strings.Index(res, TemplateWarning) if offset == -1 { panic("Missing template warning in pkg.templ.go") } err = ioutil.WriteFile(mode.Pkg()+"/kyber.go", []byte(res[offset:]), 0o644) if err != nil { panic(err) } } } golang-github-cloudflare-circl-1.3.7/kem/kyber/kat_test.go000066400000000000000000000037541454601126700235350ustar00rootroot00000000000000package kyber // Code to generate the NIST "PQCsignKAT" test vectors. // See PQCsignKAT_sign.c and randombytes.c in the reference implementation. import ( "bytes" "crypto/sha256" "fmt" "testing" "github.com/cloudflare/circl/internal/nist" "github.com/cloudflare/circl/kem/schemes" ) func TestPQCgenKATKem(t *testing.T) { kats := []struct { name string want string }{ // Computed from reference implementation {"Kyber1024", "89248f2f33f7f4f7051729111f3049c409a933ec904aedadf035f30fa5646cd5"}, {"Kyber768", "a1e122cad3c24bc51622e4c242d8b8acbcd3f618fee4220400605ca8f9ea02c2"}, {"Kyber512", "e9c2bd37133fcb40772f81559f14b1f58dccd1c816701be9ba6214d43baf4547"}, } for _, kat := range kats { kat := kat t.Run(kat.name, func(t *testing.T) { testPQCgenKATKem(t, kat.name, kat.want) }) } } func testPQCgenKATKem(t *testing.T, name, expected string) { scheme := schemes.ByName(name) if scheme == nil { t.Fatal() } var seed [48]byte kseed := make([]byte, scheme.SeedSize()) eseed := make([]byte, scheme.EncapsulationSeedSize()) for i := 0; i < 48; i++ { seed[i] = byte(i) } f := sha256.New() g := nist.NewDRBG(&seed) fmt.Fprintf(f, "# %s\n\n", name) for i := 0; i < 100; i++ { g.Fill(seed[:]) fmt.Fprintf(f, "count = %d\n", i) fmt.Fprintf(f, "seed = %X\n", seed) g2 := nist.NewDRBG(&seed) // This is not equivalent to g2.Fill(kseed[:]). As the reference // implementation calls randombytes twice generating the keypair, // we have to do that as well. g2.Fill(kseed[:32]) g2.Fill(kseed[32:]) g2.Fill(eseed) pk, sk := scheme.DeriveKeyPair(kseed) ppk, _ := pk.MarshalBinary() psk, _ := sk.MarshalBinary() ct, ss, _ := scheme.EncapsulateDeterministically(pk, eseed) ss2, _ := scheme.Decapsulate(sk, ct) if !bytes.Equal(ss, ss2) { t.Fatal() } fmt.Fprintf(f, "pk = %X\n", ppk) fmt.Fprintf(f, "sk = %X\n", psk) fmt.Fprintf(f, "ct = %X\n", ct) fmt.Fprintf(f, "ss = %X\n\n", ss) } if fmt.Sprintf("%x", f.Sum(nil)) != expected { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/kem/kyber/kyber1024/000077500000000000000000000000001454601126700230025ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/kyber/kyber1024/kyber.go000066400000000000000000000227011454601126700244470ustar00rootroot00000000000000// Code generated from pkg.templ.go. DO NOT EDIT. // Package kyber1024 implements the IND-CCA2 secure key encapsulation mechanism // Kyber1024.CCAKEM as submitted to round 3 of the NIST PQC competition and // described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package kyber1024 import ( "bytes" "crypto/subtle" "io" cryptoRand "crypto/rand" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" cpapke "github.com/cloudflare/circl/pke/kyber/kyber1024" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = cpapke.KeySeedSize + 32 // Size of seed for EncapsulateTo. EncapsulationSeedSize = 32 // Size of the established shared key. SharedKeySize = 32 // Size of the encapsulated shared key. CiphertextSize = cpapke.CiphertextSize // Size of a packed public key. PublicKeySize = cpapke.PublicKeySize // Size of a packed private key. PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 ) // Type of a Kyber1024.CCAKEM public key type PublicKey struct { pk *cpapke.PublicKey hpk [32]byte // H(pk) } // Type of a Kyber1024.CCAKEM private key type PrivateKey struct { sk *cpapke.PrivateKey pk *cpapke.PublicKey hpk [32]byte // H(pk) z [32]byte } // NewKeyFromSeed derives a public/private keypair deterministically // from the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { var sk PrivateKey var pk PublicKey if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) sk.pk = pk.pk copy(sk.z[:], seed[cpapke.KeySeedSize:]) // Compute H(pk) var ppk [cpapke.PublicKeySize]byte sk.pk.Pack(ppk[:]) h := sha3.New256() h.Write(ppk[:]) h.Read(sk.hpk[:]) copy(pk.hpk[:], sk.hpk[:]) return &pk, &sk } // GenerateKeyPair generates public and private keys using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(seed[:]) return pk, sk, nil } // EncapsulateTo generates a shared key and ciphertext that contains it // for the public key using randomness from seed and writes the shared key // to ss and ciphertext to ct. // // Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize // and EncapsulationSeedSize respectively. // // seed may be nil, in which case crypto/rand.Reader is used to generate one. func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { if seed == nil { seed = make([]byte, EncapsulationSeedSize) if _, err := cryptoRand.Read(seed[:]); err != nil { panic(err) } } else { if len(seed) != EncapsulationSeedSize { panic("seed must be of length EncapsulationSeedSize") } } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m = H(seed) var m [32]byte h := sha3.New256() h.Write(seed[:]) h.Read(m[:]) // (K', r) = G(m ‖ H(pk)) var kr [64]byte g := sha3.New512() g.Write(m[:]) g.Write(pk.hpk[:]) g.Read(kr[:]) // c = Kyber.CPAPKE.Enc(pk, m, r) pk.pk.EncryptTo(ct, m[:], kr[32:]) // Compute H(c) and put in second slot of kr, which will be (K', H(c)). h.Reset() h.Write(ct[:CiphertextSize]) h.Read(kr[32:]) // K = KDF(K' ‖ H(c)) kdf := sha3.NewShake256() kdf.Write(kr[:]) kdf.Read(ss[:SharedKeySize]) } // DecapsulateTo computes the shared key which is encapsulated in ct // for the private key. // // Panics if ct or ss are not of length CiphertextSize and SharedKeySize // respectively. func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m' = Kyber.CPAPKE.Dec(sk, ct) var m2 [32]byte sk.sk.DecryptTo(m2[:], ct) // (K'', r') = G(m' ‖ H(pk)) var kr2 [64]byte g := sha3.New512() g.Write(m2[:]) g.Write(sk.hpk[:]) g.Read(kr2[:]) // c' = Kyber.CPAPKE.Enc(pk, m', r') var ct2 [CiphertextSize]byte sk.pk.EncryptTo(ct2[:], m2[:], kr2[32:]) // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). h := sha3.New256() h.Write(ct[:CiphertextSize]) h.Read(kr2[32:]) // Replace K'' by z in the first slot of kr2 if c ≠ c'. subtle.ConstantTimeCopy( 1-subtle.ConstantTimeCompare(ct, ct2[:]), kr2[:32], sk.z[:], ) // K = KDF(K''/z, H(c)) kdf := sha3.NewShake256() kdf.Write(kr2[:]) kdf.Read(ss[:SharedKeySize]) } // Packs sk to buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk.Pack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk.Pack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(buf, sk.hpk[:]) buf = buf[32:] copy(buf, sk.z[:]) } // Unpacks sk from buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk = new(cpapke.PrivateKey) sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk = new(cpapke.PublicKey) sk.pk.Unpack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(sk.hpk[:], buf[:32]) copy(sk.z[:], buf[32:]) } // Packs pk to buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk.Pack(buf) } // Unpacks pk from buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk = new(cpapke.PublicKey) pk.pk.Unpack(buf) // Compute cached H(pk) h := sha3.New256() h.Write(buf) h.Read(pk.hpk[:]) } // Boilerplate down below for the KEM scheme API. type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. func Scheme() kem.Scheme { return sch } func (*scheme) Name() string { return "Kyber1024" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SeedSize() int { return KeySeedSize } func (*scheme) SharedKeySize() int { return SharedKeySize } func (*scheme) CiphertextSize() int { return CiphertextSize } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { var ret [PrivateKeySize]byte sk.Pack(ret[:]) return ret[:], nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } if sk.pk == nil && oth.pk == nil { return true } if sk.pk == nil || oth.pk == nil { return false } if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || subtle.ConstantTimeCompare(sk.z[:], oth.z[:]) != 1 { return false } return sk.sk.Equal(oth.sk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } if pk.pk == nil && oth.pk == nil { return true } if pk.pk == nil || oth.pk == nil { return false } return bytes.Equal(pk.hpk[:], oth.hpk[:]) } func (sk *PrivateKey) Public() kem.PublicKey { pk := new(PublicKey) pk.pk = sk.pk copy(pk.hpk[:], sk.hpk[:]) return pk } func (pk *PublicKey) MarshalBinary() ([]byte, error) { var ret [PublicKeySize]byte pk.Pack(ret[:]) return ret[:], nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != KeySeedSize { panic(kem.ErrSeedSize) } return NewKeyFromSeed(seed[:]) } func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, nil) return } func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( ct, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, seed) return } func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != CiphertextSize { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } ss := make([]byte, SharedKeySize) priv.DecapsulateTo(ss, ct) return ss, nil } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != PublicKeySize { return nil, kem.ErrPubKeySize } var ret PublicKey ret.Unpack(buf) return &ret, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != PrivateKeySize { return nil, kem.ErrPrivKeySize } var ret PrivateKey ret.Unpack(buf) return &ret, nil } golang-github-cloudflare-circl-1.3.7/kem/kyber/kyber512/000077500000000000000000000000001454601126700227235ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/kyber/kyber512/kyber.go000066400000000000000000000226721454601126700243770ustar00rootroot00000000000000// Code generated from pkg.templ.go. DO NOT EDIT. // Package kyber512 implements the IND-CCA2 secure key encapsulation mechanism // Kyber512.CCAKEM as submitted to round 3 of the NIST PQC competition and // described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package kyber512 import ( "bytes" "crypto/subtle" "io" cryptoRand "crypto/rand" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" cpapke "github.com/cloudflare/circl/pke/kyber/kyber512" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = cpapke.KeySeedSize + 32 // Size of seed for EncapsulateTo. EncapsulationSeedSize = 32 // Size of the established shared key. SharedKeySize = 32 // Size of the encapsulated shared key. CiphertextSize = cpapke.CiphertextSize // Size of a packed public key. PublicKeySize = cpapke.PublicKeySize // Size of a packed private key. PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 ) // Type of a Kyber512.CCAKEM public key type PublicKey struct { pk *cpapke.PublicKey hpk [32]byte // H(pk) } // Type of a Kyber512.CCAKEM private key type PrivateKey struct { sk *cpapke.PrivateKey pk *cpapke.PublicKey hpk [32]byte // H(pk) z [32]byte } // NewKeyFromSeed derives a public/private keypair deterministically // from the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { var sk PrivateKey var pk PublicKey if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) sk.pk = pk.pk copy(sk.z[:], seed[cpapke.KeySeedSize:]) // Compute H(pk) var ppk [cpapke.PublicKeySize]byte sk.pk.Pack(ppk[:]) h := sha3.New256() h.Write(ppk[:]) h.Read(sk.hpk[:]) copy(pk.hpk[:], sk.hpk[:]) return &pk, &sk } // GenerateKeyPair generates public and private keys using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(seed[:]) return pk, sk, nil } // EncapsulateTo generates a shared key and ciphertext that contains it // for the public key using randomness from seed and writes the shared key // to ss and ciphertext to ct. // // Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize // and EncapsulationSeedSize respectively. // // seed may be nil, in which case crypto/rand.Reader is used to generate one. func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { if seed == nil { seed = make([]byte, EncapsulationSeedSize) if _, err := cryptoRand.Read(seed[:]); err != nil { panic(err) } } else { if len(seed) != EncapsulationSeedSize { panic("seed must be of length EncapsulationSeedSize") } } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m = H(seed) var m [32]byte h := sha3.New256() h.Write(seed[:]) h.Read(m[:]) // (K', r) = G(m ‖ H(pk)) var kr [64]byte g := sha3.New512() g.Write(m[:]) g.Write(pk.hpk[:]) g.Read(kr[:]) // c = Kyber.CPAPKE.Enc(pk, m, r) pk.pk.EncryptTo(ct, m[:], kr[32:]) // Compute H(c) and put in second slot of kr, which will be (K', H(c)). h.Reset() h.Write(ct[:CiphertextSize]) h.Read(kr[32:]) // K = KDF(K' ‖ H(c)) kdf := sha3.NewShake256() kdf.Write(kr[:]) kdf.Read(ss[:SharedKeySize]) } // DecapsulateTo computes the shared key which is encapsulated in ct // for the private key. // // Panics if ct or ss are not of length CiphertextSize and SharedKeySize // respectively. func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m' = Kyber.CPAPKE.Dec(sk, ct) var m2 [32]byte sk.sk.DecryptTo(m2[:], ct) // (K'', r') = G(m' ‖ H(pk)) var kr2 [64]byte g := sha3.New512() g.Write(m2[:]) g.Write(sk.hpk[:]) g.Read(kr2[:]) // c' = Kyber.CPAPKE.Enc(pk, m', r') var ct2 [CiphertextSize]byte sk.pk.EncryptTo(ct2[:], m2[:], kr2[32:]) // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). h := sha3.New256() h.Write(ct[:CiphertextSize]) h.Read(kr2[32:]) // Replace K'' by z in the first slot of kr2 if c ≠ c'. subtle.ConstantTimeCopy( 1-subtle.ConstantTimeCompare(ct, ct2[:]), kr2[:32], sk.z[:], ) // K = KDF(K''/z, H(c)) kdf := sha3.NewShake256() kdf.Write(kr2[:]) kdf.Read(ss[:SharedKeySize]) } // Packs sk to buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk.Pack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk.Pack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(buf, sk.hpk[:]) buf = buf[32:] copy(buf, sk.z[:]) } // Unpacks sk from buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk = new(cpapke.PrivateKey) sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk = new(cpapke.PublicKey) sk.pk.Unpack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(sk.hpk[:], buf[:32]) copy(sk.z[:], buf[32:]) } // Packs pk to buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk.Pack(buf) } // Unpacks pk from buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk = new(cpapke.PublicKey) pk.pk.Unpack(buf) // Compute cached H(pk) h := sha3.New256() h.Write(buf) h.Read(pk.hpk[:]) } // Boilerplate down below for the KEM scheme API. type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. func Scheme() kem.Scheme { return sch } func (*scheme) Name() string { return "Kyber512" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SeedSize() int { return KeySeedSize } func (*scheme) SharedKeySize() int { return SharedKeySize } func (*scheme) CiphertextSize() int { return CiphertextSize } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { var ret [PrivateKeySize]byte sk.Pack(ret[:]) return ret[:], nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } if sk.pk == nil && oth.pk == nil { return true } if sk.pk == nil || oth.pk == nil { return false } if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || subtle.ConstantTimeCompare(sk.z[:], oth.z[:]) != 1 { return false } return sk.sk.Equal(oth.sk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } if pk.pk == nil && oth.pk == nil { return true } if pk.pk == nil || oth.pk == nil { return false } return bytes.Equal(pk.hpk[:], oth.hpk[:]) } func (sk *PrivateKey) Public() kem.PublicKey { pk := new(PublicKey) pk.pk = sk.pk copy(pk.hpk[:], sk.hpk[:]) return pk } func (pk *PublicKey) MarshalBinary() ([]byte, error) { var ret [PublicKeySize]byte pk.Pack(ret[:]) return ret[:], nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != KeySeedSize { panic(kem.ErrSeedSize) } return NewKeyFromSeed(seed[:]) } func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, nil) return } func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( ct, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, seed) return } func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != CiphertextSize { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } ss := make([]byte, SharedKeySize) priv.DecapsulateTo(ss, ct) return ss, nil } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != PublicKeySize { return nil, kem.ErrPubKeySize } var ret PublicKey ret.Unpack(buf) return &ret, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != PrivateKeySize { return nil, kem.ErrPrivKeySize } var ret PrivateKey ret.Unpack(buf) return &ret, nil } golang-github-cloudflare-circl-1.3.7/kem/kyber/kyber768/000077500000000000000000000000001454601126700227405ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/kyber/kyber768/kyber.go000066400000000000000000000226721454601126700244140ustar00rootroot00000000000000// Code generated from pkg.templ.go. DO NOT EDIT. // Package kyber768 implements the IND-CCA2 secure key encapsulation mechanism // Kyber768.CCAKEM as submitted to round 3 of the NIST PQC competition and // described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package kyber768 import ( "bytes" "crypto/subtle" "io" cryptoRand "crypto/rand" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" cpapke "github.com/cloudflare/circl/pke/kyber/kyber768" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = cpapke.KeySeedSize + 32 // Size of seed for EncapsulateTo. EncapsulationSeedSize = 32 // Size of the established shared key. SharedKeySize = 32 // Size of the encapsulated shared key. CiphertextSize = cpapke.CiphertextSize // Size of a packed public key. PublicKeySize = cpapke.PublicKeySize // Size of a packed private key. PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 ) // Type of a Kyber768.CCAKEM public key type PublicKey struct { pk *cpapke.PublicKey hpk [32]byte // H(pk) } // Type of a Kyber768.CCAKEM private key type PrivateKey struct { sk *cpapke.PrivateKey pk *cpapke.PublicKey hpk [32]byte // H(pk) z [32]byte } // NewKeyFromSeed derives a public/private keypair deterministically // from the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { var sk PrivateKey var pk PublicKey if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) sk.pk = pk.pk copy(sk.z[:], seed[cpapke.KeySeedSize:]) // Compute H(pk) var ppk [cpapke.PublicKeySize]byte sk.pk.Pack(ppk[:]) h := sha3.New256() h.Write(ppk[:]) h.Read(sk.hpk[:]) copy(pk.hpk[:], sk.hpk[:]) return &pk, &sk } // GenerateKeyPair generates public and private keys using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(seed[:]) return pk, sk, nil } // EncapsulateTo generates a shared key and ciphertext that contains it // for the public key using randomness from seed and writes the shared key // to ss and ciphertext to ct. // // Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize // and EncapsulationSeedSize respectively. // // seed may be nil, in which case crypto/rand.Reader is used to generate one. func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { if seed == nil { seed = make([]byte, EncapsulationSeedSize) if _, err := cryptoRand.Read(seed[:]); err != nil { panic(err) } } else { if len(seed) != EncapsulationSeedSize { panic("seed must be of length EncapsulationSeedSize") } } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m = H(seed) var m [32]byte h := sha3.New256() h.Write(seed[:]) h.Read(m[:]) // (K', r) = G(m ‖ H(pk)) var kr [64]byte g := sha3.New512() g.Write(m[:]) g.Write(pk.hpk[:]) g.Read(kr[:]) // c = Kyber.CPAPKE.Enc(pk, m, r) pk.pk.EncryptTo(ct, m[:], kr[32:]) // Compute H(c) and put in second slot of kr, which will be (K', H(c)). h.Reset() h.Write(ct[:CiphertextSize]) h.Read(kr[32:]) // K = KDF(K' ‖ H(c)) kdf := sha3.NewShake256() kdf.Write(kr[:]) kdf.Read(ss[:SharedKeySize]) } // DecapsulateTo computes the shared key which is encapsulated in ct // for the private key. // // Panics if ct or ss are not of length CiphertextSize and SharedKeySize // respectively. func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m' = Kyber.CPAPKE.Dec(sk, ct) var m2 [32]byte sk.sk.DecryptTo(m2[:], ct) // (K'', r') = G(m' ‖ H(pk)) var kr2 [64]byte g := sha3.New512() g.Write(m2[:]) g.Write(sk.hpk[:]) g.Read(kr2[:]) // c' = Kyber.CPAPKE.Enc(pk, m', r') var ct2 [CiphertextSize]byte sk.pk.EncryptTo(ct2[:], m2[:], kr2[32:]) // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). h := sha3.New256() h.Write(ct[:CiphertextSize]) h.Read(kr2[32:]) // Replace K'' by z in the first slot of kr2 if c ≠ c'. subtle.ConstantTimeCopy( 1-subtle.ConstantTimeCompare(ct, ct2[:]), kr2[:32], sk.z[:], ) // K = KDF(K''/z, H(c)) kdf := sha3.NewShake256() kdf.Write(kr2[:]) kdf.Read(ss[:SharedKeySize]) } // Packs sk to buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk.Pack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk.Pack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(buf, sk.hpk[:]) buf = buf[32:] copy(buf, sk.z[:]) } // Unpacks sk from buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk = new(cpapke.PrivateKey) sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk = new(cpapke.PublicKey) sk.pk.Unpack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(sk.hpk[:], buf[:32]) copy(sk.z[:], buf[32:]) } // Packs pk to buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk.Pack(buf) } // Unpacks pk from buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk = new(cpapke.PublicKey) pk.pk.Unpack(buf) // Compute cached H(pk) h := sha3.New256() h.Write(buf) h.Read(pk.hpk[:]) } // Boilerplate down below for the KEM scheme API. type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. func Scheme() kem.Scheme { return sch } func (*scheme) Name() string { return "Kyber768" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SeedSize() int { return KeySeedSize } func (*scheme) SharedKeySize() int { return SharedKeySize } func (*scheme) CiphertextSize() int { return CiphertextSize } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { var ret [PrivateKeySize]byte sk.Pack(ret[:]) return ret[:], nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } if sk.pk == nil && oth.pk == nil { return true } if sk.pk == nil || oth.pk == nil { return false } if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || subtle.ConstantTimeCompare(sk.z[:], oth.z[:]) != 1 { return false } return sk.sk.Equal(oth.sk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } if pk.pk == nil && oth.pk == nil { return true } if pk.pk == nil || oth.pk == nil { return false } return bytes.Equal(pk.hpk[:], oth.hpk[:]) } func (sk *PrivateKey) Public() kem.PublicKey { pk := new(PublicKey) pk.pk = sk.pk copy(pk.hpk[:], sk.hpk[:]) return pk } func (pk *PublicKey) MarshalBinary() ([]byte, error) { var ret [PublicKeySize]byte pk.Pack(ret[:]) return ret[:], nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != KeySeedSize { panic(kem.ErrSeedSize) } return NewKeyFromSeed(seed[:]) } func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, nil) return } func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( ct, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, seed) return } func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != CiphertextSize { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } ss := make([]byte, SharedKeySize) priv.DecapsulateTo(ss, ct) return ss, nil } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != PublicKeySize { return nil, kem.ErrPubKeySize } var ret PublicKey ret.Unpack(buf) return &ret, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != PrivateKeySize { return nil, kem.ErrPrivKeySize } var ret PrivateKey ret.Unpack(buf) return &ret, nil } golang-github-cloudflare-circl-1.3.7/kem/kyber/templates/000077500000000000000000000000001454601126700233555ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/kyber/templates/pkg.templ.go000066400000000000000000000230651454601126700256130ustar00rootroot00000000000000// +build ignore // The previous line (and this one up to the warning below) is removed by the // template generator. // Code generated from pkg.templ.go. DO NOT EDIT. // Package {{.Pkg}} implements the IND-CCA2 secure key encapsulation mechanism // {{.Name}}.CCAKEM as submitted to round 3 of the NIST PQC competition and // described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package {{.Pkg}} import ( "bytes" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" cpapke "github.com/cloudflare/circl/pke/kyber/{{.Pkg}}" cryptoRand "crypto/rand" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = cpapke.KeySeedSize + 32 // Size of seed for EncapsulateTo. EncapsulationSeedSize = 32 // Size of the established shared key. SharedKeySize = 32 // Size of the encapsulated shared key. CiphertextSize = cpapke.CiphertextSize // Size of a packed public key. PublicKeySize = cpapke.PublicKeySize // Size of a packed private key. PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 ) // Type of a {{.Name}}.CCAKEM public key type PublicKey struct { pk *cpapke.PublicKey hpk [32]byte // H(pk) } // Type of a {{.Name}}.CCAKEM private key type PrivateKey struct { sk *cpapke.PrivateKey pk *cpapke.PublicKey hpk [32]byte // H(pk) z [32]byte } // NewKeyFromSeed derives a public/private keypair deterministically // from the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { var sk PrivateKey var pk PublicKey if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) sk.pk = pk.pk copy(sk.z[:], seed[cpapke.KeySeedSize:]) // Compute H(pk) var ppk [cpapke.PublicKeySize]byte sk.pk.Pack(ppk[:]) h := sha3.New256() h.Write(ppk[:]) h.Read(sk.hpk[:]) copy(pk.hpk[:], sk.hpk[:]) return &pk, &sk } // GenerateKeyPair generates public and private keys using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(seed[:]) return pk, sk, nil } // EncapsulateTo generates a shared key and ciphertext that contains it // for the public key using randomness from seed and writes the shared key // to ss and ciphertext to ct. // // Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize // and EncapsulationSeedSize respectively. // // seed may be nil, in which case crypto/rand.Reader is used to generate one. func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { if seed == nil { seed = make([]byte, EncapsulationSeedSize) if _, err := cryptoRand.Read(seed[:]); err != nil { panic(err) } } else { if len(seed) != EncapsulationSeedSize { panic("seed must be of length EncapsulationSeedSize") } } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m = H(seed) var m [32]byte h := sha3.New256() h.Write(seed[:]) h.Read(m[:]) // (K', r) = G(m ‖ H(pk)) var kr [64]byte g := sha3.New512() g.Write(m[:]) g.Write(pk.hpk[:]) g.Read(kr[:]) // c = Kyber.CPAPKE.Enc(pk, m, r) pk.pk.EncryptTo(ct, m[:], kr[32:]) // Compute H(c) and put in second slot of kr, which will be (K', H(c)). h.Reset() h.Write(ct[:CiphertextSize]) h.Read(kr[32:]) // K = KDF(K' ‖ H(c)) kdf := sha3.NewShake256() kdf.Write(kr[:]) kdf.Read(ss[:SharedKeySize]) } // DecapsulateTo computes the shared key which is encapsulated in ct // for the private key. // // Panics if ct or ss are not of length CiphertextSize and SharedKeySize // respectively. func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(ss) != SharedKeySize { panic("ss must be of length SharedKeySize") } // m' = Kyber.CPAPKE.Dec(sk, ct) var m2 [32]byte sk.sk.DecryptTo(m2[:], ct) // (K'', r') = G(m' ‖ H(pk)) var kr2 [64]byte g := sha3.New512() g.Write(m2[:]) g.Write(sk.hpk[:]) g.Read(kr2[:]) // c' = Kyber.CPAPKE.Enc(pk, m', r') var ct2 [CiphertextSize]byte sk.pk.EncryptTo(ct2[:], m2[:], kr2[32:]) // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). h := sha3.New256() h.Write(ct[:CiphertextSize]) h.Read(kr2[32:]) // Replace K'' by z in the first slot of kr2 if c ≠ c'. subtle.ConstantTimeCopy( 1-subtle.ConstantTimeCompare(ct, ct2[:]), kr2[:32], sk.z[:], ) // K = KDF(K''/z, H(c)) kdf := sha3.NewShake256() kdf.Write(kr2[:]) kdf.Read(ss[:SharedKeySize]) } // Packs sk to buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk.Pack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk.Pack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(buf, sk.hpk[:]) buf = buf[32:] copy(buf, sk.z[:]) } // Unpacks sk from buf. // // Panics if buf is not of size PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of length PrivateKeySize") } sk.sk = new(cpapke.PrivateKey) sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) buf = buf[cpapke.PrivateKeySize:] sk.pk = new(cpapke.PublicKey) sk.pk.Unpack(buf[:cpapke.PublicKeySize]) buf = buf[cpapke.PublicKeySize:] copy(sk.hpk[:], buf[:32]) copy(sk.z[:], buf[32:]) } // Packs pk to buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk.Pack(buf) } // Unpacks pk from buf. // // Panics if buf is not of size PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of length PublicKeySize") } pk.pk = new(cpapke.PublicKey) pk.pk.Unpack(buf) // Compute cached H(pk) h := sha3.New256() h.Write(buf) h.Read(pk.hpk[:]) } // Boilerplate down below for the KEM scheme API. type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. func Scheme() kem.Scheme { return sch } func (*scheme) Name() string { return "{{.Name}}" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SeedSize() int { return KeySeedSize } func (*scheme) SharedKeySize() int { return SharedKeySize } func (*scheme) CiphertextSize() int { return CiphertextSize } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { var ret [PrivateKeySize]byte sk.Pack(ret[:]) return ret[:], nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } if sk.pk == nil && oth.pk == nil { return true } if sk.pk == nil || oth.pk == nil { return false } if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || subtle.ConstantTimeCompare(sk.z[:], oth.z[:]) != 1 { return false } return sk.sk.Equal(oth.sk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } if pk.pk == nil && oth.pk == nil { return true } if pk.pk == nil || oth.pk == nil { return false } return bytes.Equal(pk.hpk[:], oth.hpk[:]) } func (sk *PrivateKey) Public() kem.PublicKey { pk := new(PublicKey) pk.pk = sk.pk copy(pk.hpk[:], sk.hpk[:]) return pk } func (pk *PublicKey) MarshalBinary() ([]byte, error) { var ret [PublicKeySize]byte pk.Pack(ret[:]) return ret[:], nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != KeySeedSize { panic(kem.ErrSeedSize) } return NewKeyFromSeed(seed[:]) } func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, nil) return } func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( ct, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } ct = make([]byte, CiphertextSize) ss = make([]byte, SharedKeySize) pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } pub.EncapsulateTo(ct, ss, seed) return } func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != CiphertextSize { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } ss := make([]byte, SharedKeySize) priv.DecapsulateTo(ss, ct) return ss, nil } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != PublicKeySize { return nil, kem.ErrPubKeySize } var ret PublicKey ret.Unpack(buf) return &ret, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != PrivateKeySize { return nil, kem.ErrPrivKeySize } var ret PrivateKey ret.Unpack(buf) return &ret, nil } golang-github-cloudflare-circl-1.3.7/kem/schemes/000077500000000000000000000000001454601126700216725ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/schemes/schemes.go000066400000000000000000000032611454601126700236520ustar00rootroot00000000000000// Package schemes contains a register of KEM schemes. // // # Schemes Implemented // // Based on standard elliptic curves: // // HPKE_KEM_P256_HKDF_SHA256, HPKE_KEM_P384_HKDF_SHA384, HPKE_KEM_P521_HKDF_SHA512 // // Based on standard Diffie-Hellman functions: // // HPKE_KEM_X25519_HKDF_SHA256, HPKE_KEM_X448_HKDF_SHA512 // // Post-quantum kems: // // FrodoKEM-640-SHAKE // Kyber512, Kyber768, Kyber1024 package schemes import ( "strings" "github.com/cloudflare/circl/hpke" "github.com/cloudflare/circl/kem" "github.com/cloudflare/circl/kem/frodo/frodo640shake" "github.com/cloudflare/circl/kem/hybrid" "github.com/cloudflare/circl/kem/kyber/kyber1024" "github.com/cloudflare/circl/kem/kyber/kyber512" "github.com/cloudflare/circl/kem/kyber/kyber768" ) var allSchemes = [...]kem.Scheme{ hpke.KEM_P256_HKDF_SHA256.Scheme(), hpke.KEM_P384_HKDF_SHA384.Scheme(), hpke.KEM_P521_HKDF_SHA512.Scheme(), hpke.KEM_X25519_HKDF_SHA256.Scheme(), hpke.KEM_X448_HKDF_SHA512.Scheme(), frodo640shake.Scheme(), kyber512.Scheme(), kyber768.Scheme(), kyber1024.Scheme(), hybrid.Kyber512X25519(), hybrid.Kyber768X25519(), hybrid.Kyber768X448(), hybrid.Kyber1024X448(), hybrid.P256Kyber768Draft00(), } var allSchemeNames map[string]kem.Scheme func init() { allSchemeNames = make(map[string]kem.Scheme) for _, scheme := range allSchemes { allSchemeNames[strings.ToLower(scheme.Name())] = scheme } } // ByName returns the scheme with the given name and nil if it is not // supported. // // Names are case insensitive. func ByName(name string) kem.Scheme { return allSchemeNames[strings.ToLower(name)] } // All returns all KEM schemes supported. func All() []kem.Scheme { a := allSchemes; return a[:] } golang-github-cloudflare-circl-1.3.7/kem/schemes/schemes_test.go000066400000000000000000000057361454601126700247220ustar00rootroot00000000000000package schemes_test import ( "bytes" "fmt" "testing" "github.com/cloudflare/circl/kem/schemes" ) func TestCaseSensitivity(t *testing.T) { if schemes.ByName("kyber512") != schemes.ByName("Kyber512") { t.Fatal() } } func BenchmarkGenerateKeyPair(b *testing.B) { allSchemes := schemes.All() for _, scheme := range allSchemes { scheme := scheme b.Run(scheme.Name(), func(b *testing.B) { for i := 0; i < b.N; i++ { _, _, _ = scheme.GenerateKeyPair() } }) } } func BenchmarkEncapsulate(b *testing.B) { allSchemes := schemes.All() for _, scheme := range allSchemes { scheme := scheme pk, _, _ := scheme.GenerateKeyPair() b.Run(scheme.Name(), func(b *testing.B) { for i := 0; i < b.N; i++ { _, _, _ = scheme.Encapsulate(pk) } }) } } func BenchmarkDecapsulate(b *testing.B) { allSchemes := schemes.All() for _, scheme := range allSchemes { scheme := scheme pk, sk, _ := scheme.GenerateKeyPair() ct, _, _ := scheme.Encapsulate(pk) b.Run(scheme.Name(), func(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = scheme.Decapsulate(sk, ct) } }) } } func TestApi(t *testing.T) { allSchemes := schemes.All() for _, scheme := range allSchemes { scheme := scheme t.Run(scheme.Name(), func(t *testing.T) { if scheme == nil { t.Fatal() } _ = scheme.SeedSize() _ = scheme.EncapsulationSeedSize() pk, sk, err := scheme.GenerateKeyPair() if err != nil { t.Fatal() } packedPk, err := pk.MarshalBinary() if err != nil { t.Fatal() } if len(packedPk) != scheme.PublicKeySize() { t.Fatal() } packedSk, err := sk.MarshalBinary() if err != nil { t.Fatal() } if len(packedSk) != scheme.PrivateKeySize() { t.Fatal() } pk2, err := scheme.UnmarshalBinaryPublicKey(packedPk) if err != nil { t.Fatal() } sk2, err := scheme.UnmarshalBinaryPrivateKey(packedSk) if err != nil { t.Fatal() } if !sk.Equal(sk2) { t.Fatal() } if !pk.Equal(pk2) { t.Fatal() } ct, ss, err := scheme.Encapsulate(pk2) if err != nil { t.Fatal(err) } if len(ct) != scheme.CiphertextSize() { t.Fatal() } if len(ss) != scheme.SharedKeySize() { t.Fatal() } ct3, ss3, err := scheme.Encapsulate(pk2) if err != nil { t.Fatal(err) } if bytes.Equal(ss3, ss) { t.Fatal() } if bytes.Equal(ct3, ct) { t.Fatal() } ss2, err := scheme.Decapsulate(sk2, ct) if err != nil { t.Fatal(err) } if !bytes.Equal(ss, ss2) { t.Fatal() } }) } } func Example_schemes() { // import "github.com/cloudflare/circl/kem/schemes" for _, sch := range schemes.All() { fmt.Println(sch.Name()) } // Output: // HPKE_KEM_P256_HKDF_SHA256 // HPKE_KEM_P384_HKDF_SHA384 // HPKE_KEM_P521_HKDF_SHA512 // HPKE_KEM_X25519_HKDF_SHA256 // HPKE_KEM_X448_HKDF_SHA512 // FrodoKEM-640-SHAKE // Kyber512 // Kyber768 // Kyber1024 // Kyber512-X25519 // Kyber768-X25519 // Kyber768-X448 // Kyber1024-X448 // P256Kyber768Draft00 } golang-github-cloudflare-circl-1.3.7/kem/sike/000077500000000000000000000000001454601126700211765ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/sike/doc.go000066400000000000000000000005641454601126700222770ustar00rootroot00000000000000//go:generate go run gen.go // Package sike is deprecated, it contains the SIKE key encapsulation mechanism. // // # DEPRECATION NOTICE // // SIDH and SIKE are deprecated as were shown vulnerable to a key recovery // attack by Castryck-Decru's paper (https://eprint.iacr.org/2022/975). New // systems should not rely on this package. This package is frozen. package sike golang-github-cloudflare-circl-1.3.7/kem/sike/gen.go000066400000000000000000000025341454601126700223020ustar00rootroot00000000000000//go:build ignore // +build ignore // Autogenerates wrappers from templates to prevent too much duplicated code // between the code for different modes. package main import ( "bytes" "fmt" "go/format" "io/ioutil" "strings" "text/template" ) type Instance struct { Bits int } func (m Instance) Pkg() string { return strings.ToLower(m.Name()) } func (m Instance) Name() string { return fmt.Sprintf("SIKEp%d", m.Bits) } func (m Instance) Field() string { return fmt.Sprintf("Fp%d", m.Bits) } var ( Instances = []Instance{ {Bits: 434}, {Bits: 503}, {Bits: 751}, } TemplateWarning = "// Code generated from" ) func main() { generatePackageFiles() } // Generates instance/sike.go from templates/pkg.templ.go func generatePackageFiles() { tl, err := template.ParseFiles("templates/pkg.templ.go") if err != nil { panic(err) } for _, mode := range Instances { buf := new(bytes.Buffer) err := tl.Execute(buf, mode) if err != nil { panic(err) } // Formating output code code, err := format.Source(buf.Bytes()) if err != nil { panic("error formating code") } res := string(code) offset := strings.Index(res, TemplateWarning) if offset == -1 { panic("Missing template warning in pkg.templ.go") } err = ioutil.WriteFile(mode.Pkg()+"/sike.go", []byte(res[offset:]), 0o644) if err != nil { panic(err) } } } golang-github-cloudflare-circl-1.3.7/kem/sike/sikep434/000077500000000000000000000000001454601126700225445ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/sike/sikep434/sike.go000066400000000000000000000122631454601126700240320ustar00rootroot00000000000000// Code generated from pkg.templ.go. DO NOT EDIT. // Package sikep434 is deprecated, it implements the key encapsulation mechanism SIKEp434. // // # DEPRECATION NOTICE // // SIDH and SIKE are deprecated as were shown vulnerable to a key recovery // attack by Castryck-Decru's paper (https://eprint.iacr.org/2022/975). New // systems should not rely on this package. This package is frozen. package sikep434 import ( "bytes" cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/dh/sidh" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" ) // Deprecated: not cryptographically secure. type PrivateKey struct { sk *sidh.PrivateKey pk *sidh.PublicKey } // Deprecated: not cryptographically secure. type PublicKey sidh.PublicKey const ( SeedSize = 32 EncapsulationSeedSize = 32 ) type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. // // Deprecated: not cryptographically secure. func Scheme() kem.Scheme { return sch } var params *sidh.KEM func (*scheme) Name() string { return "SIKEp434" } func (*scheme) PublicKeySize() int { return params.PublicKeySize() } func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } func (*scheme) CiphertextSize() int { return params.CiphertextSize() } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { ret := make([]byte, sk.sk.Size()) sk.sk.Export(ret) return ret, nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } a, _ := sk.MarshalBinary() b, _ := oth.MarshalBinary() return subtle.ConstantTimeCompare(a, b) == 1 } func (sk *PrivateKey) Public() kem.PublicKey { if sk.pk == nil { sk.pk = sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) sk.sk.GeneratePublicKey(sk.pk) } return (*PublicKey)(sk.pk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } a, _ := pk.MarshalBinary() b, _ := oth.MarshalBinary() return bytes.Equal(a, b) } func (pk *PublicKey) MarshalBinary() ([]byte, error) { cpk := (*sidh.PublicKey)(pk) ret := make([]byte, cpk.Size()) cpk.Export(ret) return ret, nil } // Deprecated: not cryptographically secure. func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { sk := sidh.NewPrivateKey(sidh.Fp434, sidh.KeyVariantSike) if err := sk.Generate(rand); err != nil { return nil, nil, err } priv := &PrivateKey{sk: sk} return priv.Public(), priv, nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != SeedSize { panic(kem.ErrSeedSize) } h := sha3.NewShake256() _, _ = h.Write(seed[:]) pk, sk, err := GenerateKeyPair(&h) if err != nil { panic(err) } return pk, sk } func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { var seed [EncapsulationSeedSize]byte if _, err := cryptoRand.Read(seed[:]); err != nil { return nil, nil, err } return sch.EncapsulateDeterministically(pk, seed[:]) } func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } ct = make([]byte, sch.CiphertextSize()) ss = make([]byte, sch.SharedKeySize()) h := sha3.NewShake256() _, _ = h.Write(seed[:]) ctx := sidh.NewSike434(&h) if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { return nil, nil, err } return ct, ss, nil } func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != sch.CiphertextSize() { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } sikePub := sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) priv.sk.GeneratePublicKey(sikePub) ss := make([]byte, sch.SharedKeySize()) ctx := sidh.NewSike434(nil) if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { return nil, err } return ss, nil } func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != sch.PublicKeySize() { return nil, kem.ErrPubKeySize } pk := sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) if err := pk.Import(buf); err != nil { return nil, err } return (*PublicKey)(pk), nil } func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != sch.PrivateKeySize() { return nil, kem.ErrPrivKeySize } sk := sidh.NewPrivateKey(sidh.Fp434, sidh.KeyVariantSike) if err := sk.Import(buf); err != nil { return nil, err } return &PrivateKey{sk: sk}, nil } func init() { params = sidh.NewSike434(nil) } golang-github-cloudflare-circl-1.3.7/kem/sike/sikep503/000077500000000000000000000000001454601126700225415ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/sike/sikep503/sike.go000066400000000000000000000122631454601126700240270ustar00rootroot00000000000000// Code generated from pkg.templ.go. DO NOT EDIT. // Package sikep503 is deprecated, it implements the key encapsulation mechanism SIKEp503. // // # DEPRECATION NOTICE // // SIDH and SIKE are deprecated as were shown vulnerable to a key recovery // attack by Castryck-Decru's paper (https://eprint.iacr.org/2022/975). New // systems should not rely on this package. This package is frozen. package sikep503 import ( "bytes" cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/dh/sidh" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" ) // Deprecated: not cryptographically secure. type PrivateKey struct { sk *sidh.PrivateKey pk *sidh.PublicKey } // Deprecated: not cryptographically secure. type PublicKey sidh.PublicKey const ( SeedSize = 32 EncapsulationSeedSize = 32 ) type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. // // Deprecated: not cryptographically secure. func Scheme() kem.Scheme { return sch } var params *sidh.KEM func (*scheme) Name() string { return "SIKEp503" } func (*scheme) PublicKeySize() int { return params.PublicKeySize() } func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } func (*scheme) CiphertextSize() int { return params.CiphertextSize() } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { ret := make([]byte, sk.sk.Size()) sk.sk.Export(ret) return ret, nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } a, _ := sk.MarshalBinary() b, _ := oth.MarshalBinary() return subtle.ConstantTimeCompare(a, b) == 1 } func (sk *PrivateKey) Public() kem.PublicKey { if sk.pk == nil { sk.pk = sidh.NewPublicKey(sidh.Fp503, sidh.KeyVariantSike) sk.sk.GeneratePublicKey(sk.pk) } return (*PublicKey)(sk.pk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } a, _ := pk.MarshalBinary() b, _ := oth.MarshalBinary() return bytes.Equal(a, b) } func (pk *PublicKey) MarshalBinary() ([]byte, error) { cpk := (*sidh.PublicKey)(pk) ret := make([]byte, cpk.Size()) cpk.Export(ret) return ret, nil } // Deprecated: not cryptographically secure. func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { sk := sidh.NewPrivateKey(sidh.Fp503, sidh.KeyVariantSike) if err := sk.Generate(rand); err != nil { return nil, nil, err } priv := &PrivateKey{sk: sk} return priv.Public(), priv, nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != SeedSize { panic(kem.ErrSeedSize) } h := sha3.NewShake256() _, _ = h.Write(seed[:]) pk, sk, err := GenerateKeyPair(&h) if err != nil { panic(err) } return pk, sk } func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { var seed [EncapsulationSeedSize]byte if _, err := cryptoRand.Read(seed[:]); err != nil { return nil, nil, err } return sch.EncapsulateDeterministically(pk, seed[:]) } func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } ct = make([]byte, sch.CiphertextSize()) ss = make([]byte, sch.SharedKeySize()) h := sha3.NewShake256() _, _ = h.Write(seed[:]) ctx := sidh.NewSike503(&h) if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { return nil, nil, err } return ct, ss, nil } func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != sch.CiphertextSize() { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } sikePub := sidh.NewPublicKey(sidh.Fp503, sidh.KeyVariantSike) priv.sk.GeneratePublicKey(sikePub) ss := make([]byte, sch.SharedKeySize()) ctx := sidh.NewSike503(nil) if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { return nil, err } return ss, nil } func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != sch.PublicKeySize() { return nil, kem.ErrPubKeySize } pk := sidh.NewPublicKey(sidh.Fp503, sidh.KeyVariantSike) if err := pk.Import(buf); err != nil { return nil, err } return (*PublicKey)(pk), nil } func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != sch.PrivateKeySize() { return nil, kem.ErrPrivKeySize } sk := sidh.NewPrivateKey(sidh.Fp503, sidh.KeyVariantSike) if err := sk.Import(buf); err != nil { return nil, err } return &PrivateKey{sk: sk}, nil } func init() { params = sidh.NewSike503(nil) } golang-github-cloudflare-circl-1.3.7/kem/sike/sikep751/000077500000000000000000000000001454601126700225465ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/sike/sikep751/sike.go000066400000000000000000000122631454601126700240340ustar00rootroot00000000000000// Code generated from pkg.templ.go. DO NOT EDIT. // Package sikep751 is deprecated, it implements the key encapsulation mechanism SIKEp751. // // # DEPRECATION NOTICE // // SIDH and SIKE are deprecated as were shown vulnerable to a key recovery // attack by Castryck-Decru's paper (https://eprint.iacr.org/2022/975). New // systems should not rely on this package. This package is frozen. package sikep751 import ( "bytes" cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/dh/sidh" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" ) // Deprecated: not cryptographically secure. type PrivateKey struct { sk *sidh.PrivateKey pk *sidh.PublicKey } // Deprecated: not cryptographically secure. type PublicKey sidh.PublicKey const ( SeedSize = 32 EncapsulationSeedSize = 32 ) type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. // // Deprecated: not cryptographically secure. func Scheme() kem.Scheme { return sch } var params *sidh.KEM func (*scheme) Name() string { return "SIKEp751" } func (*scheme) PublicKeySize() int { return params.PublicKeySize() } func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } func (*scheme) CiphertextSize() int { return params.CiphertextSize() } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { ret := make([]byte, sk.sk.Size()) sk.sk.Export(ret) return ret, nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } a, _ := sk.MarshalBinary() b, _ := oth.MarshalBinary() return subtle.ConstantTimeCompare(a, b) == 1 } func (sk *PrivateKey) Public() kem.PublicKey { if sk.pk == nil { sk.pk = sidh.NewPublicKey(sidh.Fp751, sidh.KeyVariantSike) sk.sk.GeneratePublicKey(sk.pk) } return (*PublicKey)(sk.pk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } a, _ := pk.MarshalBinary() b, _ := oth.MarshalBinary() return bytes.Equal(a, b) } func (pk *PublicKey) MarshalBinary() ([]byte, error) { cpk := (*sidh.PublicKey)(pk) ret := make([]byte, cpk.Size()) cpk.Export(ret) return ret, nil } // Deprecated: not cryptographically secure. func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { sk := sidh.NewPrivateKey(sidh.Fp751, sidh.KeyVariantSike) if err := sk.Generate(rand); err != nil { return nil, nil, err } priv := &PrivateKey{sk: sk} return priv.Public(), priv, nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != SeedSize { panic(kem.ErrSeedSize) } h := sha3.NewShake256() _, _ = h.Write(seed[:]) pk, sk, err := GenerateKeyPair(&h) if err != nil { panic(err) } return pk, sk } func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { var seed [EncapsulationSeedSize]byte if _, err := cryptoRand.Read(seed[:]); err != nil { return nil, nil, err } return sch.EncapsulateDeterministically(pk, seed[:]) } func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } ct = make([]byte, sch.CiphertextSize()) ss = make([]byte, sch.SharedKeySize()) h := sha3.NewShake256() _, _ = h.Write(seed[:]) ctx := sidh.NewSike751(&h) if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { return nil, nil, err } return ct, ss, nil } func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != sch.CiphertextSize() { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } sikePub := sidh.NewPublicKey(sidh.Fp751, sidh.KeyVariantSike) priv.sk.GeneratePublicKey(sikePub) ss := make([]byte, sch.SharedKeySize()) ctx := sidh.NewSike751(nil) if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { return nil, err } return ss, nil } func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != sch.PublicKeySize() { return nil, kem.ErrPubKeySize } pk := sidh.NewPublicKey(sidh.Fp751, sidh.KeyVariantSike) if err := pk.Import(buf); err != nil { return nil, err } return (*PublicKey)(pk), nil } func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != sch.PrivateKeySize() { return nil, kem.ErrPrivKeySize } sk := sidh.NewPrivateKey(sidh.Fp751, sidh.KeyVariantSike) if err := sk.Import(buf); err != nil { return nil, err } return &PrivateKey{sk: sk}, nil } func init() { params = sidh.NewSike751(nil) } golang-github-cloudflare-circl-1.3.7/kem/sike/templates/000077500000000000000000000000001454601126700231745ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/kem/sike/templates/pkg.templ.go000066400000000000000000000125301454601126700254250ustar00rootroot00000000000000// +build ignore // The previous line (and this one up to the warning below) is removed by the // template generator. // Code generated from pkg.templ.go. DO NOT EDIT. // Package {{.Pkg}} is deprecated, it implements the key encapsulation mechanism {{.Name}}. // // # DEPRECATION NOTICE // // SIDH and SIKE are deprecated as were shown vulnerable to a key recovery // attack by Castryck-Decru's paper (https://eprint.iacr.org/2022/975). New // systems should not rely on this package. This package is frozen. package {{.Pkg}} import ( "bytes" cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/dh/sidh" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/kem" ) // Deprecated: not cryptographically secure. type PrivateKey struct { sk *sidh.PrivateKey pk *sidh.PublicKey } // Deprecated: not cryptographically secure. type PublicKey sidh.PublicKey const ( SeedSize = 32 EncapsulationSeedSize = 32 ) type scheme struct{} var sch kem.Scheme = &scheme{} // Scheme returns a KEM interface. // // Deprecated: not cryptographically secure. func Scheme() kem.Scheme { return sch } var params *sidh.KEM func (*scheme) Name() string { return "{{.Name}}" } func (*scheme) PublicKeySize() int { return params.PublicKeySize() } func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } func (*scheme) CiphertextSize() int { return params.CiphertextSize() } func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } func (sk *PrivateKey) Scheme() kem.Scheme { return sch } func (pk *PublicKey) Scheme() kem.Scheme { return sch } func (sk *PrivateKey) MarshalBinary() ([]byte, error) { ret := make([]byte, sk.sk.Size()) sk.sk.Export(ret) return ret, nil } func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { oth, ok := other.(*PrivateKey) if !ok { return false } a, _ := sk.MarshalBinary() b, _ := oth.MarshalBinary() return subtle.ConstantTimeCompare(a, b) == 1 } func (sk *PrivateKey) Public() kem.PublicKey { if sk.pk == nil { sk.pk = sidh.NewPublicKey(sidh.{{.Field}}, sidh.KeyVariantSike) sk.sk.GeneratePublicKey(sk.pk) } return (*PublicKey)(sk.pk) } func (pk *PublicKey) Equal(other kem.PublicKey) bool { oth, ok := other.(*PublicKey) if !ok { return false } a, _ := pk.MarshalBinary() b, _ := oth.MarshalBinary() return bytes.Equal(a, b) } func (pk *PublicKey) MarshalBinary() ([]byte, error) { cpk := (*sidh.PublicKey)(pk) ret := make([]byte, cpk.Size()) cpk.Export(ret) return ret, nil } // Deprecated: not cryptographically secure. func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { sk := sidh.NewPrivateKey(sidh.{{.Field}}, sidh.KeyVariantSike) if err := sk.Generate(rand); err != nil { return nil, nil, err } priv := &PrivateKey{sk: sk} return priv.Public(), priv, nil } func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { return GenerateKeyPair(cryptoRand.Reader) } func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { if len(seed) != SeedSize { panic(kem.ErrSeedSize) } h := sha3.NewShake256() _, _ = h.Write(seed[:]) pk, sk, err := GenerateKeyPair(&h) if err != nil { panic(err) } return pk, sk } func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { var seed [EncapsulationSeedSize]byte if _, err := cryptoRand.Read(seed[:]); err != nil { return nil, nil, err } return sch.EncapsulateDeterministically(pk, seed[:]) } func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { if len(seed) != EncapsulationSeedSize { return nil, nil, kem.ErrSeedSize } pub, ok := pk.(*PublicKey) if !ok { return nil, nil, kem.ErrTypeMismatch } ct = make([]byte, sch.CiphertextSize()) ss = make([]byte, sch.SharedKeySize()) h := sha3.NewShake256() _, _ = h.Write(seed[:]) ctx := sidh.NewSike{{.Bits}}(&h) if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { return nil, nil, err } return ct, ss, nil } func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { if len(ct) != sch.CiphertextSize() { return nil, kem.ErrCiphertextSize } priv, ok := sk.(*PrivateKey) if !ok { return nil, kem.ErrTypeMismatch } sikePub := sidh.NewPublicKey(sidh.{{.Field}}, sidh.KeyVariantSike) priv.sk.GeneratePublicKey(sikePub) ss := make([]byte, sch.SharedKeySize()) ctx := sidh.NewSike{{.Bits}}(nil) if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { return nil, err } return ss, nil } func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { if len(buf) != sch.PublicKeySize() { return nil, kem.ErrPubKeySize } pk := sidh.NewPublicKey(sidh.{{.Field}}, sidh.KeyVariantSike) if err := pk.Import(buf); err != nil { return nil, err } return (*PublicKey)(pk), nil } func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { if len(buf) != sch.PrivateKeySize() { return nil, kem.ErrPrivKeySize } sk := sidh.NewPrivateKey(sidh.{{.Field}}, sidh.KeyVariantSike) if err := sk.Import(buf); err != nil { return nil, err } return &PrivateKey{sk: sk}, nil } func init() { params = sidh.NewSike{{.Bits}}(nil) } golang-github-cloudflare-circl-1.3.7/math/000077500000000000000000000000001454601126700204205ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/math/fp25519/000077500000000000000000000000001454601126700214335ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/math/fp25519/fp.go000066400000000000000000000106361454601126700223750ustar00rootroot00000000000000// Package fp25519 provides prime field arithmetic over GF(2^255-19). package fp25519 import ( "errors" "github.com/cloudflare/circl/internal/conv" ) // Size in bytes of an element. const Size = 32 // Elt is a prime field element. type Elt [Size]byte func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } // p is the prime modulus 2^255-19. var p = Elt{ 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, } // P returns the prime modulus 2^255-19. func P() Elt { return p } // ToBytes stores in b the little-endian byte representation of x. func ToBytes(b []byte, x *Elt) error { if len(b) != Size { return errors.New("wrong size") } Modp(x) copy(b, x[:]) return nil } // IsZero returns true if x is equal to 0. func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } // SetOne assigns x=1. func SetOne(x *Elt) { *x = Elt{}; x[0] = 1 } // Neg calculates z = -x. func Neg(z, x *Elt) { Sub(z, &p, x) } // InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue, which is // indicated by returning isQR = true. Otherwise, when x/y is a quadratic // non-residue, z will have an undetermined value and isQR = false. func InvSqrt(z, x, y *Elt) (isQR bool) { sqrtMinusOne := &Elt{ 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f, 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b, 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b, } t0, t1, t2, t3 := &Elt{}, &Elt{}, &Elt{}, &Elt{} Mul(t0, x, y) // t0 = u*v Sqr(t1, y) // t1 = v^2 Mul(t2, t0, t1) // t2 = u*v^3 Sqr(t0, t1) // t0 = v^4 Mul(t1, t0, t2) // t1 = u*v^7 var Tab [4]*Elt Tab[0] = &Elt{} Tab[1] = &Elt{} Tab[2] = t3 Tab[3] = t1 *Tab[0] = *t1 Sqr(Tab[0], Tab[0]) Sqr(Tab[1], Tab[0]) Sqr(Tab[1], Tab[1]) Mul(Tab[1], Tab[1], Tab[3]) Mul(Tab[0], Tab[0], Tab[1]) Sqr(Tab[0], Tab[0]) Mul(Tab[0], Tab[0], Tab[1]) Sqr(Tab[1], Tab[0]) for i := 0; i < 4; i++ { Sqr(Tab[1], Tab[1]) } Mul(Tab[1], Tab[1], Tab[0]) Sqr(Tab[2], Tab[1]) for i := 0; i < 4; i++ { Sqr(Tab[2], Tab[2]) } Mul(Tab[2], Tab[2], Tab[0]) Sqr(Tab[1], Tab[2]) for i := 0; i < 14; i++ { Sqr(Tab[1], Tab[1]) } Mul(Tab[1], Tab[1], Tab[2]) Sqr(Tab[2], Tab[1]) for i := 0; i < 29; i++ { Sqr(Tab[2], Tab[2]) } Mul(Tab[2], Tab[2], Tab[1]) Sqr(Tab[1], Tab[2]) for i := 0; i < 59; i++ { Sqr(Tab[1], Tab[1]) } Mul(Tab[1], Tab[1], Tab[2]) for i := 0; i < 5; i++ { Sqr(Tab[1], Tab[1]) } Mul(Tab[1], Tab[1], Tab[0]) Sqr(Tab[2], Tab[1]) for i := 0; i < 124; i++ { Sqr(Tab[2], Tab[2]) } Mul(Tab[2], Tab[2], Tab[1]) Sqr(Tab[2], Tab[2]) Sqr(Tab[2], Tab[2]) Mul(Tab[2], Tab[2], Tab[3]) Mul(z, t3, t2) // z = xy^(p+3)/8 = xy^3*(xy^7)^(p-5)/8 // Checking whether y z^2 == x Sqr(t0, z) // t0 = z^2 Mul(t0, t0, y) // t0 = yz^2 Sub(t1, t0, x) // t1 = t0-u Add(t2, t0, x) // t2 = t0+u if IsZero(t1) { return true } else if IsZero(t2) { Mul(z, z, sqrtMinusOne) // z = z*sqrt(-1) return true } else { return false } } // Inv calculates z = 1/x mod p. func Inv(z, x *Elt) { x0, x1, x2 := &Elt{}, &Elt{}, &Elt{} Sqr(x1, x) Sqr(x0, x1) Sqr(x0, x0) Mul(x0, x0, x) Mul(z, x0, x1) Sqr(x1, z) Mul(x0, x0, x1) Sqr(x1, x0) for i := 0; i < 4; i++ { Sqr(x1, x1) } Mul(x0, x0, x1) Sqr(x1, x0) for i := 0; i < 9; i++ { Sqr(x1, x1) } Mul(x1, x1, x0) Sqr(x2, x1) for i := 0; i < 19; i++ { Sqr(x2, x2) } Mul(x2, x2, x1) for i := 0; i < 10; i++ { Sqr(x2, x2) } Mul(x2, x2, x0) Sqr(x0, x2) for i := 0; i < 49; i++ { Sqr(x0, x0) } Mul(x0, x0, x2) Sqr(x1, x0) for i := 0; i < 99; i++ { Sqr(x1, x1) } Mul(x1, x1, x0) for i := 0; i < 50; i++ { Sqr(x1, x1) } Mul(x1, x1, x2) for i := 0; i < 5; i++ { Sqr(x1, x1) } Mul(z, z, x1) } // Cmov assigns y to x if n is 1. func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } // Cswap interchanges x and y if n is 1. func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } // Add calculates z = x+y mod p. func Add(z, x, y *Elt) { add(z, x, y) } // Sub calculates z = x-y mod p. func Sub(z, x, y *Elt) { sub(z, x, y) } // AddSub calculates (x,y) = (x+y mod p, x-y mod p). func AddSub(x, y *Elt) { addsub(x, y) } // Mul calculates z = x*y mod p. func Mul(z, x, y *Elt) { mul(z, x, y) } // Sqr calculates z = x^2 mod p. func Sqr(z, x *Elt) { sqr(z, x) } // Modp ensures that z is between [0,p-1]. func Modp(z *Elt) { modp(z) } golang-github-cloudflare-circl-1.3.7/math/fp25519/fp_amd64.go000066400000000000000000000016521454601126700233660ustar00rootroot00000000000000//go:build amd64 && !purego // +build amd64,!purego package fp25519 import ( "golang.org/x/sys/cpu" ) var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX var _ = hasBmi2Adx func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } func add(z, x, y *Elt) { addAmd64(z, x, y) } func sub(z, x, y *Elt) { subAmd64(z, x, y) } func addsub(x, y *Elt) { addsubAmd64(x, y) } func mul(z, x, y *Elt) { mulAmd64(z, x, y) } func sqr(z, x *Elt) { sqrAmd64(z, x) } func modp(z *Elt) { modpAmd64(z) } //go:noescape func cmovAmd64(x, y *Elt, n uint) //go:noescape func cswapAmd64(x, y *Elt, n uint) //go:noescape func addAmd64(z, x, y *Elt) //go:noescape func subAmd64(z, x, y *Elt) //go:noescape func addsubAmd64(x, y *Elt) //go:noescape func mulAmd64(z, x, y *Elt) //go:noescape func sqrAmd64(z, x *Elt) //go:noescape func modpAmd64(z *Elt) golang-github-cloudflare-circl-1.3.7/math/fp25519/fp_amd64.h000066400000000000000000000305371454601126700232140ustar00rootroot00000000000000// This code was imported from https://github.com/armfazh/rfc7748_precomputed // CHECK_BMI2ADX triggers bmi2adx if supported, // otherwise it fallbacks to legacy code. #define CHECK_BMI2ADX(label, legacy, bmi2adx) \ CMPB ·hasBmi2Adx(SB), $0 \ JE label \ bmi2adx \ RET \ label: \ legacy \ RET // cselect is a conditional move // if b=1: it copies y into x; // if b=0: x remains with the same value; // if b<> 0,1: undefined. // Uses: AX, DX, FLAGS // Instr: x86_64, cmov #define cselect(x,y,b) \ TESTQ b, b \ MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; // cswap is a conditional swap // if b=1: x,y <- y,x; // if b=0: x,y remain with the same values; // if b<> 0,1: undefined. // Uses: AX, DX, R8, FLAGS // Instr: x86_64, cmov #define cswap(x,y,b) \ TESTQ b, b \ MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; // additionLeg adds x and y and stores in z // Uses: AX, DX, R8-R11, FLAGS // Instr: x86_64, cmov #define additionLeg(z,x,y) \ MOVL $38, AX; \ MOVL $0, DX; \ MOVQ 0+x, R8; ADDQ 0+y, R8; \ MOVQ 8+x, R9; ADCQ 8+y, R9; \ MOVQ 16+x, R10; ADCQ 16+y, R10; \ MOVQ 24+x, R11; ADCQ 24+y, R11; \ CMOVQCS AX, DX; \ ADDQ DX, R8; \ ADCQ $0, R9; MOVQ R9, 8+z; \ ADCQ $0, R10; MOVQ R10, 16+z; \ ADCQ $0, R11; MOVQ R11, 24+z; \ MOVL $0, DX; \ CMOVQCS AX, DX; \ ADDQ DX, R8; MOVQ R8, 0+z; // additionAdx adds x and y and stores in z // Uses: AX, DX, R8-R11, FLAGS // Instr: x86_64, cmov, adx #define additionAdx(z,x,y) \ MOVL $38, AX; \ XORL DX, DX; \ MOVQ 0+x, R8; ADCXQ 0+y, R8; \ MOVQ 8+x, R9; ADCXQ 8+y, R9; \ MOVQ 16+x, R10; ADCXQ 16+y, R10; \ MOVQ 24+x, R11; ADCXQ 24+y, R11; \ CMOVQCS AX, DX ; \ XORL AX, AX; \ ADCXQ DX, R8; \ ADCXQ AX, R9; MOVQ R9, 8+z; \ ADCXQ AX, R10; MOVQ R10, 16+z; \ ADCXQ AX, R11; MOVQ R11, 24+z; \ MOVL $38, DX; \ CMOVQCS DX, AX; \ ADDQ AX, R8; MOVQ R8, 0+z; // subtraction subtracts y from x and stores in z // Uses: AX, DX, R8-R11, FLAGS // Instr: x86_64, cmov #define subtraction(z,x,y) \ MOVL $38, AX; \ MOVQ 0+x, R8; SUBQ 0+y, R8; \ MOVQ 8+x, R9; SBBQ 8+y, R9; \ MOVQ 16+x, R10; SBBQ 16+y, R10; \ MOVQ 24+x, R11; SBBQ 24+y, R11; \ MOVL $0, DX; \ CMOVQCS AX, DX; \ SUBQ DX, R8; \ SBBQ $0, R9; MOVQ R9, 8+z; \ SBBQ $0, R10; MOVQ R10, 16+z; \ SBBQ $0, R11; MOVQ R11, 24+z; \ MOVL $0, DX; \ CMOVQCS AX, DX; \ SUBQ DX, R8; MOVQ R8, 0+z; // integerMulAdx multiplies x and y and stores in z // Uses: AX, DX, R8-R15, FLAGS // Instr: x86_64, bmi2, adx #define integerMulAdx(z,x,y) \ MOVL $0,R15; \ MOVQ 0+y, DX; XORL AX, AX; \ MULXQ 0+x, AX, R8; MOVQ AX, 0+z; \ MULXQ 8+x, AX, R9; ADCXQ AX, R8; \ MULXQ 16+x, AX, R10; ADCXQ AX, R9; \ MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; \ MOVQ 8+y, DX; XORL AX, AX; \ MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 8+z; \ MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; \ MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; \ MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; \ MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; \ MOVQ 16+y, DX; XORL AX, AX; \ MULXQ 0+x, AX, R8; ADCXQ R12, AX; MOVQ AX, 16+z; \ MULXQ 8+x, AX, R9; ADCXQ R13, R8; ADOXQ AX, R8; \ MULXQ 16+x, AX, R10; ADCXQ R14, R9; ADOXQ AX, R9; \ MULXQ 24+x, AX, R11; ADCXQ R15, R10; ADOXQ AX, R10; \ MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; ADOXQ AX, R11; \ MOVQ 24+y, DX; XORL AX, AX; \ MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 24+z; \ MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; MOVQ R12, 32+z; \ MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; MOVQ R13, 40+z; \ MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; MOVQ R14, 48+z; \ MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; MOVQ R15, 56+z; // integerMulLeg multiplies x and y and stores in z // Uses: AX, DX, R8-R15, FLAGS // Instr: x86_64 #define integerMulLeg(z,x,y) \ MOVQ 0+y, R8; \ MOVQ 0+x, AX; MULQ R8; MOVQ AX, 0+z; MOVQ DX, R15; \ MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ MOVQ 24+x, AX; MULQ R8; \ ADDQ R13, R15; \ ADCQ R14, R10; MOVQ R10, 16+z; \ ADCQ AX, R11; MOVQ R11, 24+z; \ ADCQ $0, DX; MOVQ DX, 32+z; \ MOVQ 8+y, R8; \ MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ MOVQ 24+x, AX; MULQ R8; \ ADDQ R12, R15; MOVQ R15, 8+z; \ ADCQ R13, R9; \ ADCQ R14, R10; \ ADCQ AX, R11; \ ADCQ $0, DX; \ ADCQ 16+z, R9; MOVQ R9, R15; \ ADCQ 24+z, R10; MOVQ R10, 24+z; \ ADCQ 32+z, R11; MOVQ R11, 32+z; \ ADCQ $0, DX; MOVQ DX, 40+z; \ MOVQ 16+y, R8; \ MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ MOVQ 24+x, AX; MULQ R8; \ ADDQ R12, R15; MOVQ R15, 16+z; \ ADCQ R13, R9; \ ADCQ R14, R10; \ ADCQ AX, R11; \ ADCQ $0, DX; \ ADCQ 24+z, R9; MOVQ R9, R15; \ ADCQ 32+z, R10; MOVQ R10, 32+z; \ ADCQ 40+z, R11; MOVQ R11, 40+z; \ ADCQ $0, DX; MOVQ DX, 48+z; \ MOVQ 24+y, R8; \ MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ MOVQ 24+x, AX; MULQ R8; \ ADDQ R12, R15; MOVQ R15, 24+z; \ ADCQ R13, R9; \ ADCQ R14, R10; \ ADCQ AX, R11; \ ADCQ $0, DX; \ ADCQ 32+z, R9; MOVQ R9, 32+z; \ ADCQ 40+z, R10; MOVQ R10, 40+z; \ ADCQ 48+z, R11; MOVQ R11, 48+z; \ ADCQ $0, DX; MOVQ DX, 56+z; // integerSqrLeg squares x and stores in z // Uses: AX, CX, DX, R8-R15, FLAGS // Instr: x86_64 #define integerSqrLeg(z,x) \ MOVQ 0+x, R8; \ MOVQ 8+x, AX; MULQ R8; MOVQ AX, R9; MOVQ DX, R10; /* A[0]*A[1] */ \ MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; /* A[0]*A[2] */ \ MOVQ 24+x, AX; MULQ R8; MOVQ AX, R15; MOVQ DX, R12; /* A[0]*A[3] */ \ MOVQ 24+x, R8; \ MOVQ 8+x, AX; MULQ R8; MOVQ AX, CX; MOVQ DX, R13; /* A[3]*A[1] */ \ MOVQ 16+x, AX; MULQ R8; /* A[3]*A[2] */ \ \ ADDQ R14, R10;\ ADCQ R15, R11; MOVL $0, R15;\ ADCQ CX, R12;\ ADCQ AX, R13;\ ADCQ $0, DX; MOVQ DX, R14;\ MOVQ 8+x, AX; MULQ 16+x;\ \ ADDQ AX, R11;\ ADCQ DX, R12;\ ADCQ $0, R13;\ ADCQ $0, R14;\ ADCQ $0, R15;\ \ SHLQ $1, R14, R15; MOVQ R15, 56+z;\ SHLQ $1, R13, R14; MOVQ R14, 48+z;\ SHLQ $1, R12, R13; MOVQ R13, 40+z;\ SHLQ $1, R11, R12; MOVQ R12, 32+z;\ SHLQ $1, R10, R11; MOVQ R11, 24+z;\ SHLQ $1, R9, R10; MOVQ R10, 16+z;\ SHLQ $1, R9; MOVQ R9, 8+z;\ \ MOVQ 0+x,AX; MULQ AX; MOVQ AX, 0+z; MOVQ DX, R9;\ MOVQ 8+x,AX; MULQ AX; MOVQ AX, R10; MOVQ DX, R11;\ MOVQ 16+x,AX; MULQ AX; MOVQ AX, R12; MOVQ DX, R13;\ MOVQ 24+x,AX; MULQ AX; MOVQ AX, R14; MOVQ DX, R15;\ \ ADDQ 8+z, R9; MOVQ R9, 8+z;\ ADCQ 16+z, R10; MOVQ R10, 16+z;\ ADCQ 24+z, R11; MOVQ R11, 24+z;\ ADCQ 32+z, R12; MOVQ R12, 32+z;\ ADCQ 40+z, R13; MOVQ R13, 40+z;\ ADCQ 48+z, R14; MOVQ R14, 48+z;\ ADCQ 56+z, R15; MOVQ R15, 56+z; // integerSqrAdx squares x and stores in z // Uses: AX, CX, DX, R8-R15, FLAGS // Instr: x86_64, bmi2, adx #define integerSqrAdx(z,x) \ MOVQ 0+x, DX; /* A[0] */ \ MULXQ 8+x, R8, R14; /* A[1]*A[0] */ XORL R15, R15; \ MULXQ 16+x, R9, R10; /* A[2]*A[0] */ ADCXQ R14, R9; \ MULXQ 24+x, AX, CX; /* A[3]*A[0] */ ADCXQ AX, R10; \ MOVQ 24+x, DX; /* A[3] */ \ MULXQ 8+x, R11, R12; /* A[1]*A[3] */ ADCXQ CX, R11; \ MULXQ 16+x, AX, R13; /* A[2]*A[3] */ ADCXQ AX, R12; \ MOVQ 8+x, DX; /* A[1] */ ADCXQ R15, R13; \ MULXQ 16+x, AX, CX; /* A[2]*A[1] */ MOVL $0, R14; \ ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADCXQ R15, R14; \ XORL R15, R15; \ ADOXQ AX, R10; ADCXQ R8, R8; \ ADOXQ CX, R11; ADCXQ R9, R9; \ ADOXQ R15, R12; ADCXQ R10, R10; \ ADOXQ R15, R13; ADCXQ R11, R11; \ ADOXQ R15, R14; ADCXQ R12, R12; \ ;;;;;;;;;;;;;;; ADCXQ R13, R13; \ ;;;;;;;;;;;;;;; ADCXQ R14, R14; \ MOVQ 0+x, DX; MULXQ DX, AX, CX; /* A[0]^2 */ \ ;;;;;;;;;;;;;;; MOVQ AX, 0+z; \ ADDQ CX, R8; MOVQ R8, 8+z; \ MOVQ 8+x, DX; MULXQ DX, AX, CX; /* A[1]^2 */ \ ADCQ AX, R9; MOVQ R9, 16+z; \ ADCQ CX, R10; MOVQ R10, 24+z; \ MOVQ 16+x, DX; MULXQ DX, AX, CX; /* A[2]^2 */ \ ADCQ AX, R11; MOVQ R11, 32+z; \ ADCQ CX, R12; MOVQ R12, 40+z; \ MOVQ 24+x, DX; MULXQ DX, AX, CX; /* A[3]^2 */ \ ADCQ AX, R13; MOVQ R13, 48+z; \ ADCQ CX, R14; MOVQ R14, 56+z; // reduceFromDouble finds z congruent to x modulo p such that 0> 63) // PUT BIT 255 IN CARRY FLAG AND CLEAR x3 &^= 1 << 63 x0, c0 := bits.Add64(x0, cx, 0) x1, c1 := bits.Add64(x1, 0, c0) x2, c2 := bits.Add64(x2, 0, c1) x3, _ = bits.Add64(x3, 0, c2) // TEST FOR BIT 255 AGAIN; ONLY TRIGGERED ON OVERFLOW MODULO 2^255-19 // cx = C[255] ? 0 : 19 cx = uint64(19) &^ (-(x3 >> 63)) // CLEAR BIT 255 x3 &^= 1 << 63 x0, c0 = bits.Sub64(x0, cx, 0) x1, c1 = bits.Sub64(x1, 0, c0) x2, c2 = bits.Sub64(x2, 0, c1) x3, _ = bits.Sub64(x3, 0, c2) binary.LittleEndian.PutUint64(x[0*8:1*8], x0) binary.LittleEndian.PutUint64(x[1*8:2*8], x1) binary.LittleEndian.PutUint64(x[2*8:3*8], x2) binary.LittleEndian.PutUint64(x[3*8:4*8], x3) } func red64(z *Elt, x0, x1, x2, x3, x4, x5, x6, x7 uint64) { h0, l0 := bits.Mul64(x4, 38) h1, l1 := bits.Mul64(x5, 38) h2, l2 := bits.Mul64(x6, 38) h3, l3 := bits.Mul64(x7, 38) l1, c0 := bits.Add64(h0, l1, 0) l2, c1 := bits.Add64(h1, l2, c0) l3, c2 := bits.Add64(h2, l3, c1) l4, _ := bits.Add64(h3, 0, c2) l0, c0 = bits.Add64(l0, x0, 0) l1, c1 = bits.Add64(l1, x1, c0) l2, c2 = bits.Add64(l2, x2, c1) l3, c3 := bits.Add64(l3, x3, c2) l4, _ = bits.Add64(l4, 0, c3) _, l4 = bits.Mul64(l4, 38) l0, c0 = bits.Add64(l0, l4, 0) z1, c1 := bits.Add64(l1, 0, c0) z2, c2 := bits.Add64(l2, 0, c1) z3, c3 := bits.Add64(l3, 0, c2) z0, _ := bits.Add64(l0, (-c3)&38, 0) binary.LittleEndian.PutUint64(z[0*8:1*8], z0) binary.LittleEndian.PutUint64(z[1*8:2*8], z1) binary.LittleEndian.PutUint64(z[2*8:3*8], z2) binary.LittleEndian.PutUint64(z[3*8:4*8], z3) } golang-github-cloudflare-circl-1.3.7/math/fp25519/fp_noasm.go000066400000000000000000000007611454601126700235700ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package fp25519 func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } func add(z, x, y *Elt) { addGeneric(z, x, y) } func sub(z, x, y *Elt) { subGeneric(z, x, y) } func addsub(x, y *Elt) { addsubGeneric(x, y) } func mul(z, x, y *Elt) { mulGeneric(z, x, y) } func sqr(z, x *Elt) { sqrGeneric(z, x) } func modp(z *Elt) { modpGeneric(z) } golang-github-cloudflare-circl-1.3.7/math/fp25519/fp_test.go000066400000000000000000000222661454601126700234360ustar00rootroot00000000000000package fp25519 import ( "crypto/rand" "errors" "fmt" "math/big" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" ) type ( tcmov func(x, y *Elt, n uint) tcswap func(x, y *Elt, n uint) tadd func(z, x, y *Elt) tsub func(z, x, y *Elt) taddsub func(x, y *Elt) tmul func(z, x, y *Elt) tsqr func(z, x *Elt) tmodp func(z *Elt) ) func testCmov(t *testing.T, f tcmov) { const numTests = 1 << 9 var x, y Elt for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) b := uint(y[0] & 0x1) want := conv.BytesLe2BigInt(x[:]) if b != 0 { want = conv.BytesLe2BigInt(y[:]) } f(&x, &y, b) got := conv.BytesLe2BigInt(x[:]) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y, b) } } } func testCswap(t *testing.T, f tcswap) { const numTests = 1 << 9 var x, y Elt for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) b := uint(y[0] & 0x1) want0 := conv.BytesLe2BigInt(x[:]) want1 := conv.BytesLe2BigInt(y[:]) if b != 0 { want0 = conv.BytesLe2BigInt(y[:]) want1 = conv.BytesLe2BigInt(x[:]) } f(&x, &y, b) got0 := conv.BytesLe2BigInt(x[:]) got1 := conv.BytesLe2BigInt(y[:]) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, y, b) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, y, b) } } } func testAdd(t *testing.T, f tadd) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) f(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want := xx.Add(xx, yy).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testSub(t *testing.T, f tsub) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) f(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want := xx.Sub(xx, yy).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testAddSub(t *testing.T, f taddsub) { const numTests = 1 << 9 var x, y Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) want0, want1 := big.NewInt(0), big.NewInt(0) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want0.Add(xx, yy).Mod(want0, p) want1.Sub(xx, yy).Mod(want1, p) f(&x, &y) Modp(&x) Modp(&y) got0 := conv.BytesLe2BigInt(x[:]) got1 := conv.BytesLe2BigInt(y[:]) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, y) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, y) } } } func testMul(t *testing.T, f tmul) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) f(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want := xx.Mul(xx, yy).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testSqr(t *testing.T, f tsqr) { const numTests = 1 << 9 var x, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) f(&z, &x) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx := conv.BytesLe2BigInt(x[:]) want := xx.Mul(xx, xx).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func testModp(t *testing.T, f tmodp) { const numTests = 1 << 9 var x Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) two256 := big.NewInt(1) two256.Lsh(two256, 256) want := new(big.Int) for i := 0; i < numTests; i++ { bigX, _ := rand.Int(rand.Reader, two256) bigX.Add(bigX, p).Mod(bigX, two256) conv.BigInt2BytesLe(x[:], bigX) f(&x) got := conv.BytesLe2BigInt(x[:]) want.Mod(bigX, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, bigX) } } } func TestIsZero(t *testing.T) { var x Elt got := IsZero(&x) want := true if got != want { test.ReportError(t, got, want, x) } SetOne(&x) got = IsZero(&x) want = false if got != want { test.ReportError(t, got, want, x) } x = P() got = IsZero(&x) want = true if got != want { test.ReportError(t, got, want, x) } x = Elt{ // 2P 0xda, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, } got = IsZero(&x) want = true if got != want { test.ReportError(t, got, want, x) } } func TestToBytes(t *testing.T) { const numTests = 1 << 9 var x Elt var got, want [Size]byte for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) err := ToBytes(got[:], &x) conv.BigInt2BytesLe(want[:], conv.BytesLe2BigInt(x[:])) if got != want || err != nil { test.ReportError(t, got, want, x) } } { var small [Size + 1]byte got := ToBytes(small[:], &x) want := errors.New("wrong size") if got.Error() != want.Error() { test.ReportError(t, got, want) } } } func TestString(t *testing.T) { const numTests = 1 << 9 var x Elt var bigX big.Int for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) got, _ := bigX.SetString(fmt.Sprint(x), 0) want := conv.BytesLe2BigInt(x[:]) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestNeg(t *testing.T) { const numTests = 1 << 9 var x, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) Neg(&z, &x) Modp(&z) got := conv.BytesLe2BigInt(z[:]) bigX := conv.BytesLe2BigInt(x[:]) want := bigX.Neg(bigX).Mod(bigX, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, bigX) } } } func TestInv(t *testing.T) { const numTests = 1 << 9 var x, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) Inv(&z, &x) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx := conv.BytesLe2BigInt(x[:]) want := xx.ModInverse(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestInvSqrt(t *testing.T) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) exp := big.NewInt(3) exp.Add(p, exp).Rsh(exp, 3) var frac, root, sqRoot big.Int var wantQR bool var want *big.Int sqrtMinusOne, _ := new(big.Int).SetString("2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0", 16) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) gotQR := InvSqrt(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx := conv.BytesLe2BigInt(x[:]) yy := conv.BytesLe2BigInt(y[:]) frac.ModInverse(yy, p).Mul(&frac, xx).Mod(&frac, p) root.Exp(&frac, exp, p) sqRoot.Mul(&root, &root).Mod(&sqRoot, p) if sqRoot.Cmp(&frac) == 0 { want = &root wantQR = true } else { frac.Neg(&frac).Mod(&frac, p) if sqRoot.Cmp(&frac) == 0 { want = root.Mul(&root, sqrtMinusOne).Mod(&root, p) wantQR = true } else { want = big.NewInt(0) wantQR = false } } if wantQR { if gotQR != wantQR || got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } else { if gotQR != wantQR { test.ReportError(t, gotQR, wantQR, x, y) } } } } func TestGeneric(t *testing.T) { t.Run("Cmov", func(t *testing.T) { testCmov(t, cmovGeneric) }) t.Run("Cswap", func(t *testing.T) { testCswap(t, cswapGeneric) }) t.Run("Add", func(t *testing.T) { testAdd(t, addGeneric) }) t.Run("Sub", func(t *testing.T) { testSub(t, subGeneric) }) t.Run("AddSub", func(t *testing.T) { testAddSub(t, addsubGeneric) }) t.Run("Mul", func(t *testing.T) { testMul(t, mulGeneric) }) t.Run("Sqr", func(t *testing.T) { testSqr(t, sqrGeneric) }) t.Run("Modp", func(t *testing.T) { testModp(t, modpGeneric) }) } func TestNative(t *testing.T) { t.Run("Cmov", func(t *testing.T) { testCmov(t, Cmov) }) t.Run("Cswap", func(t *testing.T) { testCswap(t, Cswap) }) t.Run("Add", func(t *testing.T) { testAdd(t, Add) }) t.Run("Sub", func(t *testing.T) { testSub(t, Sub) }) t.Run("AddSub", func(t *testing.T) { testAddSub(t, AddSub) }) t.Run("Mul", func(t *testing.T) { testMul(t, Mul) }) t.Run("Sqr", func(t *testing.T) { testSqr(t, Sqr) }) t.Run("Modp", func(t *testing.T) { testModp(t, Modp) }) } func BenchmarkFp(b *testing.B) { var x, y, z Elt _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) _, _ = rand.Read(z[:]) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { Add(&x, &y, &z) } }) b.Run("Sub", func(b *testing.B) { for i := 0; i < b.N; i++ { Sub(&x, &y, &z) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { Mul(&x, &y, &z) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { Sqr(&x, &y) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { Inv(&x, &y) } }) b.Run("InvSqrt", func(b *testing.B) { for i := 0; i < b.N; i++ { InvSqrt(&z, &x, &y) } }) } golang-github-cloudflare-circl-1.3.7/math/fp448/000077500000000000000000000000001454601126700212655ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/math/fp448/edgecases_test.go000066400000000000000000000064051454601126700246030ustar00rootroot00000000000000package fp448 import ( "encoding/binary" "math/big" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" ) func TestEdgeCases(t *testing.T) { t.Run("red64", func(t *testing.T) { ecRed64(t) }) } func ecRed64(t *testing.T) { cases := [][2 * Size]byte{ { 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, }, { 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, }, { 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x45, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, }, } two448 := big.NewInt(1) two448.Lsh(two448, 448) // 2^448 mask448 := big.NewInt(1) mask448.Sub(two448, mask448) // 2^448-1 two224plus1 := big.NewInt(1) two224plus1.Lsh(two224plus1, 224) two224plus1.Add(two224plus1, big.NewInt(1)) // 2^224+1 var got, want Elt var lo, hi [7]uint64 for _, c := range cases { cLo := c[0*Size:] cHi := c[1*Size:] for i := range lo { lo[i] = binary.LittleEndian.Uint64(cLo[i*8 : (i+1)*8]) hi[i] = binary.LittleEndian.Uint64(cHi[i*8 : (i+1)*8]) } red64(&got, &lo, &hi) tt := conv.BytesLe2BigInt(c[:2*Size]) var loBig, hiBig big.Int for tt.Cmp(two448) >= 0 { loBig.And(tt, mask448) hiBig.Rsh(tt, 448) tt.Mul(&hiBig, two224plus1) tt.Add(tt, &loBig) } conv.BigInt2BytesLe(want[:], tt) if got != want { test.ReportError(t, got, want, conv.BytesLe2BigInt(c[:2*Size])) } } } golang-github-cloudflare-circl-1.3.7/math/fp448/fp.go000066400000000000000000000076711454601126700222340ustar00rootroot00000000000000// Package fp448 provides prime field arithmetic over GF(2^448-2^224-1). package fp448 import ( "errors" "github.com/cloudflare/circl/internal/conv" ) // Size in bytes of an element. const Size = 56 // Elt is a prime field element. type Elt [Size]byte func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } // p is the prime modulus 2^448-2^224-1. var p = Elt{ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, } // P returns the prime modulus 2^448-2^224-1. func P() Elt { return p } // ToBytes stores in b the little-endian byte representation of x. func ToBytes(b []byte, x *Elt) error { if len(b) != Size { return errors.New("wrong size") } Modp(x) copy(b, x[:]) return nil } // IsZero returns true if x is equal to 0. func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } // IsOne returns true if x is equal to 1. func IsOne(x *Elt) bool { Modp(x); return *x == Elt{1} } // SetOne assigns x=1. func SetOne(x *Elt) { *x = Elt{1} } // One returns the 1 element. func One() (x Elt) { x = Elt{1}; return } // Neg calculates z = -x. func Neg(z, x *Elt) { Sub(z, &p, x) } // Modp ensures that z is between [0,p-1]. func Modp(z *Elt) { Sub(z, z, &p) } // InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue. If so, // isQR = true; otherwise, isQR = false, since x/y is a quadratic non-residue, // and z = sqrt(-x/y). func InvSqrt(z, x, y *Elt) (isQR bool) { // First note that x^(2(k+1)) = x^(p-1)/2 * x = legendre(x) * x // so that's x if x is a quadratic residue and -x otherwise. // Next, y^(6k+3) = y^(4k+2) * y^(2k+1) = y^(p-1) * y^((p-1)/2) = legendre(y). // So the z we compute satisfies z^2 y = x^(2(k+1)) y^(6k+3) = legendre(x)*legendre(y). // Thus if x and y are quadratic residues, then z is indeed sqrt(x/y). t0, t1 := &Elt{}, &Elt{} Mul(t0, x, y) // x*y Sqr(t1, y) // y^2 Mul(t1, t0, t1) // x*y^3 powPminus3div4(z, t1) // (x*y^3)^k Mul(z, z, t0) // z = x*y*(x*y^3)^k = x^(k+1) * y^(3k+1) // Check if x/y is a quadratic residue Sqr(t0, z) // z^2 Mul(t0, t0, y) // y*z^2 Sub(t0, t0, x) // y*z^2-x return IsZero(t0) } // Inv calculates z = 1/x mod p. func Inv(z, x *Elt) { // Calculates z = x^(4k+1) = x^(p-3+1) = x^(p-2) = x^-1, where k = (p-3)/4. t := &Elt{} powPminus3div4(t, x) // t = x^k Sqr(t, t) // t = x^2k Sqr(t, t) // t = x^4k Mul(z, t, x) // z = x^(4k+1) } // powPminus3div4 calculates z = x^k mod p, where k = (p-3)/4. func powPminus3div4(z, x *Elt) { x0, x1 := &Elt{}, &Elt{} Sqr(z, x) Mul(z, z, x) Sqr(x0, z) Mul(x0, x0, x) Sqr(z, x0) Sqr(z, z) Sqr(z, z) Mul(z, z, x0) Sqr(x1, z) for i := 0; i < 5; i++ { Sqr(x1, x1) } Mul(x1, x1, z) Sqr(z, x1) for i := 0; i < 11; i++ { Sqr(z, z) } Mul(z, z, x1) Sqr(z, z) Sqr(z, z) Sqr(z, z) Mul(z, z, x0) Sqr(x1, z) for i := 0; i < 26; i++ { Sqr(x1, x1) } Mul(x1, x1, z) Sqr(z, x1) for i := 0; i < 53; i++ { Sqr(z, z) } Mul(z, z, x1) Sqr(z, z) Sqr(z, z) Sqr(z, z) Mul(z, z, x0) Sqr(x1, z) for i := 0; i < 110; i++ { Sqr(x1, x1) } Mul(x1, x1, z) Sqr(z, x1) Mul(z, z, x) for i := 0; i < 223; i++ { Sqr(z, z) } Mul(z, z, x1) } // Cmov assigns y to x if n is 1. func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } // Cswap interchanges x and y if n is 1. func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } // Add calculates z = x+y mod p. func Add(z, x, y *Elt) { add(z, x, y) } // Sub calculates z = x-y mod p. func Sub(z, x, y *Elt) { sub(z, x, y) } // AddSub calculates (x,y) = (x+y mod p, x-y mod p). func AddSub(x, y *Elt) { addsub(x, y) } // Mul calculates z = x*y mod p. func Mul(z, x, y *Elt) { mul(z, x, y) } // Sqr calculates z = x^2 mod p. func Sqr(z, x *Elt) { sqr(z, x) } golang-github-cloudflare-circl-1.3.7/math/fp448/fp_amd64.go000066400000000000000000000015721454601126700232210ustar00rootroot00000000000000//go:build amd64 && !purego // +build amd64,!purego package fp448 import ( "golang.org/x/sys/cpu" ) var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX var _ = hasBmi2Adx func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } func add(z, x, y *Elt) { addAmd64(z, x, y) } func sub(z, x, y *Elt) { subAmd64(z, x, y) } func addsub(x, y *Elt) { addsubAmd64(x, y) } func mul(z, x, y *Elt) { mulAmd64(z, x, y) } func sqr(z, x *Elt) { sqrAmd64(z, x) } /* Functions defined in fp_amd64.s */ //go:noescape func cmovAmd64(x, y *Elt, n uint) //go:noescape func cswapAmd64(x, y *Elt, n uint) //go:noescape func addAmd64(z, x, y *Elt) //go:noescape func subAmd64(z, x, y *Elt) //go:noescape func addsubAmd64(x, y *Elt) //go:noescape func mulAmd64(z, x, y *Elt) //go:noescape func sqrAmd64(z, x *Elt) golang-github-cloudflare-circl-1.3.7/math/fp448/fp_amd64.h000066400000000000000000000541751454601126700230520ustar00rootroot00000000000000// This code was imported from https://github.com/armfazh/rfc7748_precomputed // CHECK_BMI2ADX triggers bmi2adx if supported, // otherwise it fallbacks to legacy code. #define CHECK_BMI2ADX(label, legacy, bmi2adx) \ CMPB ·hasBmi2Adx(SB), $0 \ JE label \ bmi2adx \ RET \ label: \ legacy \ RET // cselect is a conditional move // if b=1: it copies y into x; // if b=0: x remains with the same value; // if b<> 0,1: undefined. // Uses: AX, DX, FLAGS // Instr: x86_64, cmov #define cselect(x,y,b) \ TESTQ b, b \ MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; \ MOVQ 32+x, AX; MOVQ 32+y, DX; CMOVQNE DX, AX; MOVQ AX, 32+x; \ MOVQ 40+x, AX; MOVQ 40+y, DX; CMOVQNE DX, AX; MOVQ AX, 40+x; \ MOVQ 48+x, AX; MOVQ 48+y, DX; CMOVQNE DX, AX; MOVQ AX, 48+x; // cswap is a conditional swap // if b=1: x,y <- y,x; // if b=0: x,y remain with the same values; // if b<> 0,1: undefined. // Uses: AX, DX, R8, FLAGS // Instr: x86_64, cmov #define cswap(x,y,b) \ TESTQ b, b \ MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; \ MOVQ 32+x, AX; MOVQ AX, R8; MOVQ 32+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 32+x; MOVQ DX, 32+y; \ MOVQ 40+x, AX; MOVQ AX, R8; MOVQ 40+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 40+x; MOVQ DX, 40+y; \ MOVQ 48+x, AX; MOVQ AX, R8; MOVQ 48+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 48+x; MOVQ DX, 48+y; // additionLeg adds x and y and stores in z // Uses: AX, DX, R8-R14, FLAGS // Instr: x86_64 #define additionLeg(z,x,y) \ MOVQ 0+x, R8; ADDQ 0+y, R8; \ MOVQ 8+x, R9; ADCQ 8+y, R9; \ MOVQ 16+x, R10; ADCQ 16+y, R10; \ MOVQ 24+x, R11; ADCQ 24+y, R11; \ MOVQ 32+x, R12; ADCQ 32+y, R12; \ MOVQ 40+x, R13; ADCQ 40+y, R13; \ MOVQ 48+x, R14; ADCQ 48+y, R14; \ MOVQ $0, AX; ADCQ $0, AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ ADDQ AX, R8; MOVQ $0, AX; \ ADCQ $0, R9; \ ADCQ $0, R10; \ ADCQ DX, R11; \ ADCQ $0, R12; \ ADCQ $0, R13; \ ADCQ $0, R14; \ ADCQ $0, AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ ADDQ AX, R8; MOVQ R8, 0+z; \ ADCQ $0, R9; MOVQ R9, 8+z; \ ADCQ $0, R10; MOVQ R10, 16+z; \ ADCQ DX, R11; MOVQ R11, 24+z; \ ADCQ $0, R12; MOVQ R12, 32+z; \ ADCQ $0, R13; MOVQ R13, 40+z; \ ADCQ $0, R14; MOVQ R14, 48+z; // additionAdx adds x and y and stores in z // Uses: AX, DX, R8-R15, FLAGS // Instr: x86_64, adx #define additionAdx(z,x,y) \ MOVL $32, R15; \ XORL DX, DX; \ MOVQ 0+x, R8; ADCXQ 0+y, R8; \ MOVQ 8+x, R9; ADCXQ 8+y, R9; \ MOVQ 16+x, R10; ADCXQ 16+y, R10; \ MOVQ 24+x, R11; ADCXQ 24+y, R11; \ MOVQ 32+x, R12; ADCXQ 32+y, R12; \ MOVQ 40+x, R13; ADCXQ 40+y, R13; \ MOVQ 48+x, R14; ADCXQ 48+y, R14; \ ;;;;;;;;;;;;;;; ADCXQ DX, DX; \ XORL AX, AX; \ ADCXQ DX, R8; SHLXQ R15, DX, DX; \ ADCXQ AX, R9; \ ADCXQ AX, R10; \ ADCXQ DX, R11; \ ADCXQ AX, R12; \ ADCXQ AX, R13; \ ADCXQ AX, R14; \ ADCXQ AX, AX; \ XORL DX, DX; \ ADCXQ AX, R8; MOVQ R8, 0+z; SHLXQ R15, AX, AX; \ ADCXQ DX, R9; MOVQ R9, 8+z; \ ADCXQ DX, R10; MOVQ R10, 16+z; \ ADCXQ AX, R11; MOVQ R11, 24+z; \ ADCXQ DX, R12; MOVQ R12, 32+z; \ ADCXQ DX, R13; MOVQ R13, 40+z; \ ADCXQ DX, R14; MOVQ R14, 48+z; // subtraction subtracts y from x and stores in z // Uses: AX, DX, R8-R14, FLAGS // Instr: x86_64 #define subtraction(z,x,y) \ MOVQ 0+x, R8; SUBQ 0+y, R8; \ MOVQ 8+x, R9; SBBQ 8+y, R9; \ MOVQ 16+x, R10; SBBQ 16+y, R10; \ MOVQ 24+x, R11; SBBQ 24+y, R11; \ MOVQ 32+x, R12; SBBQ 32+y, R12; \ MOVQ 40+x, R13; SBBQ 40+y, R13; \ MOVQ 48+x, R14; SBBQ 48+y, R14; \ MOVQ $0, AX; SETCS AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ SUBQ AX, R8; MOVQ $0, AX; \ SBBQ $0, R9; \ SBBQ $0, R10; \ SBBQ DX, R11; \ SBBQ $0, R12; \ SBBQ $0, R13; \ SBBQ $0, R14; \ SETCS AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ SUBQ AX, R8; MOVQ R8, 0+z; \ SBBQ $0, R9; MOVQ R9, 8+z; \ SBBQ $0, R10; MOVQ R10, 16+z; \ SBBQ DX, R11; MOVQ R11, 24+z; \ SBBQ $0, R12; MOVQ R12, 32+z; \ SBBQ $0, R13; MOVQ R13, 40+z; \ SBBQ $0, R14; MOVQ R14, 48+z; // maddBmi2Adx multiplies x and y and accumulates in z // Uses: AX, DX, R15, FLAGS // Instr: x86_64, bmi2, adx #define maddBmi2Adx(z,x,y,i,r0,r1,r2,r3,r4,r5,r6) \ MOVQ i+y, DX; XORL AX, AX; \ MULXQ 0+x, AX, R8; ADOXQ AX, r0; ADCXQ R8, r1; MOVQ r0,i+z; \ MULXQ 8+x, AX, r0; ADOXQ AX, r1; ADCXQ r0, r2; MOVQ $0, R8; \ MULXQ 16+x, AX, r0; ADOXQ AX, r2; ADCXQ r0, r3; \ MULXQ 24+x, AX, r0; ADOXQ AX, r3; ADCXQ r0, r4; \ MULXQ 32+x, AX, r0; ADOXQ AX, r4; ADCXQ r0, r5; \ MULXQ 40+x, AX, r0; ADOXQ AX, r5; ADCXQ r0, r6; \ MULXQ 48+x, AX, r0; ADOXQ AX, r6; ADCXQ R8, r0; \ ;;;;;;;;;;;;;;;;;;; ADOXQ R8, r0; // integerMulAdx multiplies x and y and stores in z // Uses: AX, DX, R8-R15, FLAGS // Instr: x86_64, bmi2, adx #define integerMulAdx(z,x,y) \ MOVL $0,R15; \ MOVQ 0+y, DX; XORL AX, AX; MOVQ $0, R8; \ MULXQ 0+x, AX, R9; MOVQ AX, 0+z; \ MULXQ 8+x, AX, R10; ADCXQ AX, R9; \ MULXQ 16+x, AX, R11; ADCXQ AX, R10; \ MULXQ 24+x, AX, R12; ADCXQ AX, R11; \ MULXQ 32+x, AX, R13; ADCXQ AX, R12; \ MULXQ 40+x, AX, R14; ADCXQ AX, R13; \ MULXQ 48+x, AX, R15; ADCXQ AX, R14; \ ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R15; \ maddBmi2Adx(z,x,y, 8, R9,R10,R11,R12,R13,R14,R15) \ maddBmi2Adx(z,x,y,16,R10,R11,R12,R13,R14,R15, R9) \ maddBmi2Adx(z,x,y,24,R11,R12,R13,R14,R15, R9,R10) \ maddBmi2Adx(z,x,y,32,R12,R13,R14,R15, R9,R10,R11) \ maddBmi2Adx(z,x,y,40,R13,R14,R15, R9,R10,R11,R12) \ maddBmi2Adx(z,x,y,48,R14,R15, R9,R10,R11,R12,R13) \ MOVQ R15, 56+z; \ MOVQ R9, 64+z; \ MOVQ R10, 72+z; \ MOVQ R11, 80+z; \ MOVQ R12, 88+z; \ MOVQ R13, 96+z; \ MOVQ R14, 104+z; // maddLegacy multiplies x and y and accumulates in z // Uses: AX, DX, R15, FLAGS // Instr: x86_64 #define maddLegacy(z,x,y,i) \ MOVQ i+y, R15; \ MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ ADDQ 0+i+z, R8; MOVQ R8, 0+i+z; \ ADCQ 8+i+z, R9; MOVQ R9, 8+i+z; \ ADCQ 16+i+z, R10; MOVQ R10, 16+i+z; \ ADCQ 24+i+z, R11; MOVQ R11, 24+i+z; \ ADCQ 32+i+z, R12; MOVQ R12, 32+i+z; \ ADCQ 40+i+z, R13; MOVQ R13, 40+i+z; \ ADCQ 48+i+z, R14; MOVQ R14, 48+i+z; \ ADCQ $0, DX; MOVQ DX, 56+i+z; // integerMulLeg multiplies x and y and stores in z // Uses: AX, DX, R8-R15, FLAGS // Instr: x86_64 #define integerMulLeg(z,x,y) \ MOVQ 0+y, R15; \ MOVQ 0+x, AX; MULQ R15; MOVQ AX, 0+z; ;;;;;;;;;;;; MOVQ DX, R8; \ MOVQ 8+x, AX; MULQ R15; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ MOVQ 16+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; MOVQ R9, 16+z; \ MOVQ 24+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; MOVQ R10, 24+z; \ MOVQ 32+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; MOVQ R11, 32+z; \ MOVQ 40+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; MOVQ R12, 40+z; \ MOVQ 48+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX,56+z; MOVQ R13, 48+z; \ maddLegacy(z,x,y, 8) \ maddLegacy(z,x,y,16) \ maddLegacy(z,x,y,24) \ maddLegacy(z,x,y,32) \ maddLegacy(z,x,y,40) \ maddLegacy(z,x,y,48) // integerSqrLeg squares x and stores in z // Uses: AX, CX, DX, R8-R15, FLAGS // Instr: x86_64 #define integerSqrLeg(z,x) \ XORL R15, R15; \ MOVQ 0+x, CX; \ MOVQ CX, AX; MULQ CX; MOVQ AX, 0+z; MOVQ DX, R8; \ ADDQ CX, CX; ADCQ $0, R15; \ MOVQ 8+x, AX; MULQ CX; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ MOVQ 16+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ MOVQ 24+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ MOVQ 32+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ MOVQ 40+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ MOVQ 48+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ \ MOVQ 8+x, CX; \ MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9,16+z; \ MOVQ R15, AX; NEGQ AX; ANDQ 8+x, AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ ADDQ 8+x, CX; ADCQ $0, R15; \ MOVQ 16+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 24+z; \ MOVQ 24+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX, R8; \ MOVQ 32+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; \ MOVQ 40+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ MOVQ 48+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R9; \ \ MOVQ 16+x, CX; \ MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 32+z; \ MOVQ R15, AX; NEGQ AX; ANDQ 16+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ ADDQ 16+x, CX; ADCQ $0, R15; \ MOVQ 24+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 40+z; \ MOVQ 32+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ MOVQ 40+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; \ MOVQ 48+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX,R10; \ \ MOVQ 24+x, CX; \ MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 48+z; \ MOVQ R15, AX; NEGQ AX; ANDQ 24+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ ADDQ 24+x, CX; ADCQ $0, R15; \ MOVQ 32+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; MOVQ R14, 56+z; \ MOVQ 40+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX, R8; \ MOVQ 48+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX,R11; \ \ MOVQ 32+x, CX; \ MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9, 64+z; \ MOVQ R15, AX; NEGQ AX; ANDQ 32+x,AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ ADDQ 32+x, CX; ADCQ $0, R15; \ MOVQ 40+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 72+z; \ MOVQ 48+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX,R12; \ \ XORL R13, R13; \ XORL R14, R14; \ MOVQ 40+x, CX; \ MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 80+z; \ MOVQ R15, AX; NEGQ AX; ANDQ 40+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ ADDQ 40+x, CX; ADCQ $0, R15; \ MOVQ 48+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 88+z; \ ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8, R13; ADCQ $0,R14; \ \ XORL R9, R9; \ MOVQ 48+x, CX; \ MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 96+z; \ MOVQ R15, AX; NEGQ AX; ANDQ 48+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8,R14; ADCQ $0, R9; MOVQ R14, 104+z; // integerSqrAdx squares x and stores in z // Uses: AX, CX, DX, R8-R15, FLAGS // Instr: x86_64, bmi2, adx #define integerSqrAdx(z,x) \ XORL R15, R15; \ MOVQ 0+x, DX; \ ;;;;;;;;;;;;;; MULXQ DX, AX, R8; MOVQ AX, 0+z; \ ADDQ DX, DX; ADCQ $0, R15; CLC; \ MULXQ 8+x, AX, R9; ADCXQ AX, R8; MOVQ R8, 8+z; \ MULXQ 16+x, AX, R10; ADCXQ AX, R9; MOVQ $0, R8;\ MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ MULXQ 32+x, AX, R12; ADCXQ AX, R11; \ MULXQ 40+x, AX, R13; ADCXQ AX, R12; \ MULXQ 48+x, AX, R14; ADCXQ AX, R13; \ ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R14; \ \ MOVQ 8+x, DX; \ MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ MULXQ AX, AX, CX; \ MOVQ R15, R8; NEGQ R8; ANDQ 8+x, R8; \ ADDQ AX, R9; MOVQ R9, 16+z; \ ADCQ CX, R8; \ ADCQ $0, R11; \ ADDQ 8+x, DX; \ ADCQ $0, R15; \ XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ MULXQ 16+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 24+z; \ MULXQ 24+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; MOVQ $0, R10; \ MULXQ 32+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; \ MULXQ 40+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; \ MULXQ 48+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ ;;;;;;;;;;;;;;;;;;; ADCXQ R10, R9; \ \ MOVQ 16+x, DX; \ MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ MULXQ AX, AX, CX; \ MOVQ R15, R8; NEGQ R8; ANDQ 16+x, R8; \ ADDQ AX, R11; MOVQ R11, 32+z; \ ADCQ CX, R8; \ ADCQ $0, R13; \ ADDQ 16+x, DX; \ ADCQ $0, R15; \ XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ MULXQ 24+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 40+z; \ MULXQ 32+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; MOVQ $0, R12; \ MULXQ 40+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ MULXQ 48+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; \ ;;;;;;;;;;;;;;;;;;; ADCXQ R11,R10; \ \ MOVQ 24+x, DX; \ MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ MULXQ AX, AX, CX; \ MOVQ R15, R8; NEGQ R8; ANDQ 24+x, R8; \ ADDQ AX, R13; MOVQ R13, 48+z; \ ADCQ CX, R8; \ ADCQ $0, R9; \ ADDQ 24+x, DX; \ ADCQ $0, R15; \ XORL R13, R13; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R14; \ MULXQ 32+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; MOVQ R14, 56+z; \ MULXQ 40+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; MOVQ $0, R14; \ MULXQ 48+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; \ ;;;;;;;;;;;;;;;;;;; ADCXQ R12,R11; \ \ MOVQ 32+x, DX; \ MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ MULXQ AX, AX, CX; \ MOVQ R15, R8; NEGQ R8; ANDQ 32+x, R8; \ ADDQ AX, R9; MOVQ R9, 64+z; \ ADCQ CX, R8; \ ADCQ $0, R11; \ ADDQ 32+x, DX; \ ADCQ $0, R15; \ XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ MULXQ 40+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 72+z; \ MULXQ 48+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; \ ;;;;;;;;;;;;;;;;;;; ADCXQ R13,R12; \ \ MOVQ 40+x, DX; \ MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ MULXQ AX, AX, CX; \ MOVQ R15, R8; NEGQ R8; ANDQ 40+x, R8; \ ADDQ AX, R11; MOVQ R11, 80+z; \ ADCQ CX, R8; \ ADCQ $0, R13; \ ADDQ 40+x, DX; \ ADCQ $0, R15; \ XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ MULXQ 48+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 88+z; \ ;;;;;;;;;;;;;;;;;;; ADCXQ R14,R13; \ \ MOVQ 48+x, DX; \ MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ MULXQ AX, AX, CX; \ MOVQ R15, R8; NEGQ R8; ANDQ 48+x, R8; \ XORL R10, R10; ;;;;;;;;;;;;;; ADOXQ CX, R14; \ ;;;;;;;;;;;;;; ADCXQ AX, R13; ;;;;;;;;;;;;;; MOVQ R13, 96+z; \ ;;;;;;;;;;;;;; ADCXQ R8, R14; MOVQ R14, 104+z; // reduceFromDoubleLeg finds a z=x modulo p such that z<2^448 and stores in z // Uses: AX, R8-R15, FLAGS // Instr: x86_64 #define reduceFromDoubleLeg(z,x) \ /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ MOVQ 80+x,AX; MOVQ AX,R10; \ MOVQ $0xFFFFFFFF00000000, R8; \ ANDQ R8,R10; \ \ MOVQ $0,R14; \ MOVQ 104+x,R13; SHLQ $1,R13,R14; \ MOVQ 96+x,R12; SHLQ $1,R12,R13; \ MOVQ 88+x,R11; SHLQ $1,R11,R12; \ MOVQ 72+x, R9; SHLQ $1,R10,R11; \ MOVQ 64+x, R8; SHLQ $1,R10; \ MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ MOVQ 56+x,R15; \ \ ADDQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ ADCQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ ADCQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ ADCQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ ADCQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ ADCQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ ADCQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ ADCQ $0,R14; \ /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ /* ( r9, r8, r15, r13, r12, r11, r10) */ \ MOVQ R10, AX; \ SHRQ $32,R11,R10; \ SHRQ $32,R12,R11; \ SHRQ $32,R13,R12; \ SHRQ $32,R15,R13; \ SHRQ $32, R8,R15; \ SHRQ $32, R9, R8; \ SHRQ $32, AX, R9; \ \ ADDQ 0+z,R10; \ ADCQ 8+z,R11; \ ADCQ 16+z,R12; \ ADCQ 24+z,R13; \ ADCQ 32+z,R15; \ ADCQ 40+z, R8; \ ADCQ 48+z, R9; \ ADCQ $0,R14; \ /* ( c7) + (c6,...,c0) */ \ /* (r14) */ \ MOVQ R14, AX; SHLQ $32, AX; \ ADDQ R14,R10; MOVQ $0,R14; \ ADCQ $0,R11; \ ADCQ $0,R12; \ ADCQ AX,R13; \ ADCQ $0,R15; \ ADCQ $0, R8; \ ADCQ $0, R9; \ ADCQ $0,R14; \ /* ( c7) + (c6,...,c0) */ \ /* (r14) */ \ MOVQ R14, AX; SHLQ $32,AX; \ ADDQ R14,R10; MOVQ R10, 0+z; \ ADCQ $0,R11; MOVQ R11, 8+z; \ ADCQ $0,R12; MOVQ R12,16+z; \ ADCQ AX,R13; MOVQ R13,24+z; \ ADCQ $0,R15; MOVQ R15,32+z; \ ADCQ $0, R8; MOVQ R8,40+z; \ ADCQ $0, R9; MOVQ R9,48+z; // reduceFromDoubleAdx finds a z=x modulo p such that z<2^448 and stores in z // Uses: AX, R8-R15, FLAGS // Instr: x86_64, adx #define reduceFromDoubleAdx(z,x) \ /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ MOVQ 80+x,AX; MOVQ AX,R10; \ MOVQ $0xFFFFFFFF00000000, R8; \ ANDQ R8,R10; \ \ MOVQ $0,R14; \ MOVQ 104+x,R13; SHLQ $1,R13,R14; \ MOVQ 96+x,R12; SHLQ $1,R12,R13; \ MOVQ 88+x,R11; SHLQ $1,R11,R12; \ MOVQ 72+x, R9; SHLQ $1,R10,R11; \ MOVQ 64+x, R8; SHLQ $1,R10; \ MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ MOVQ 56+x,R15; \ \ XORL AX,AX; \ ADCXQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ ADCXQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ ADCXQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ ADCXQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ ADCXQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ ADCXQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ ADCXQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ ADCXQ AX,R14; \ /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ /* ( r9, r8, r15, r13, r12, r11, r10) */ \ MOVQ R10, AX; \ SHRQ $32,R11,R10; \ SHRQ $32,R12,R11; \ SHRQ $32,R13,R12; \ SHRQ $32,R15,R13; \ SHRQ $32, R8,R15; \ SHRQ $32, R9, R8; \ SHRQ $32, AX, R9; \ \ XORL AX,AX; \ ADCXQ 0+z,R10; \ ADCXQ 8+z,R11; \ ADCXQ 16+z,R12; \ ADCXQ 24+z,R13; \ ADCXQ 32+z,R15; \ ADCXQ 40+z, R8; \ ADCXQ 48+z, R9; \ ADCXQ AX,R14; \ /* ( c7) + (c6,...,c0) */ \ /* (r14) */ \ MOVQ R14, AX; SHLQ $32, AX; \ CLC; \ ADCXQ R14,R10; MOVQ $0,R14; \ ADCXQ R14,R11; \ ADCXQ R14,R12; \ ADCXQ AX,R13; \ ADCXQ R14,R15; \ ADCXQ R14, R8; \ ADCXQ R14, R9; \ ADCXQ R14,R14; \ /* ( c7) + (c6,...,c0) */ \ /* (r14) */ \ MOVQ R14, AX; SHLQ $32, AX; \ CLC; \ ADCXQ R14,R10; MOVQ R10, 0+z; MOVQ $0,R14; \ ADCXQ R14,R11; MOVQ R11, 8+z; \ ADCXQ R14,R12; MOVQ R12,16+z; \ ADCXQ AX,R13; MOVQ R13,24+z; \ ADCXQ R14,R15; MOVQ R15,32+z; \ ADCXQ R14, R8; MOVQ R8,40+z; \ ADCXQ R14, R9; MOVQ R9,48+z; // addSub calculates two operations: x,y = x+y,x-y // Uses: AX, DX, R8-R15, FLAGS #define addSub(x,y) \ MOVQ 0+x, R8; ADDQ 0+y, R8; \ MOVQ 8+x, R9; ADCQ 8+y, R9; \ MOVQ 16+x, R10; ADCQ 16+y, R10; \ MOVQ 24+x, R11; ADCQ 24+y, R11; \ MOVQ 32+x, R12; ADCQ 32+y, R12; \ MOVQ 40+x, R13; ADCQ 40+y, R13; \ MOVQ 48+x, R14; ADCQ 48+y, R14; \ MOVQ $0, AX; ADCQ $0, AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ ADDQ AX, R8; MOVQ $0, AX; \ ADCQ $0, R9; \ ADCQ $0, R10; \ ADCQ DX, R11; \ ADCQ $0, R12; \ ADCQ $0, R13; \ ADCQ $0, R14; \ ADCQ $0, AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ ADDQ AX, R8; MOVQ 0+x,AX; MOVQ R8, 0+x; MOVQ AX, R8; \ ADCQ $0, R9; MOVQ 8+x,AX; MOVQ R9, 8+x; MOVQ AX, R9; \ ADCQ $0, R10; MOVQ 16+x,AX; MOVQ R10, 16+x; MOVQ AX, R10; \ ADCQ DX, R11; MOVQ 24+x,AX; MOVQ R11, 24+x; MOVQ AX, R11; \ ADCQ $0, R12; MOVQ 32+x,AX; MOVQ R12, 32+x; MOVQ AX, R12; \ ADCQ $0, R13; MOVQ 40+x,AX; MOVQ R13, 40+x; MOVQ AX, R13; \ ADCQ $0, R14; MOVQ 48+x,AX; MOVQ R14, 48+x; MOVQ AX, R14; \ SUBQ 0+y, R8; \ SBBQ 8+y, R9; \ SBBQ 16+y, R10; \ SBBQ 24+y, R11; \ SBBQ 32+y, R12; \ SBBQ 40+y, R13; \ SBBQ 48+y, R14; \ MOVQ $0, AX; SETCS AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ SUBQ AX, R8; MOVQ $0, AX; \ SBBQ $0, R9; \ SBBQ $0, R10; \ SBBQ DX, R11; \ SBBQ $0, R12; \ SBBQ $0, R13; \ SBBQ $0, R14; \ SETCS AX; \ MOVQ AX, DX; \ SHLQ $32, DX; \ SUBQ AX, R8; MOVQ R8, 0+y; \ SBBQ $0, R9; MOVQ R9, 8+y; \ SBBQ $0, R10; MOVQ R10, 16+y; \ SBBQ DX, R11; MOVQ R11, 24+y; \ SBBQ $0, R12; MOVQ R12, 32+y; \ SBBQ $0, R13; MOVQ R13, 40+y; \ SBBQ $0, R14; MOVQ R14, 48+y; golang-github-cloudflare-circl-1.3.7/math/fp448/fp_amd64.s000066400000000000000000000032711454601126700230540ustar00rootroot00000000000000// +build amd64 #include "textflag.h" #include "fp_amd64.h" // func cmovAmd64(x, y *Elt, n uint) TEXT ·cmovAmd64(SB),NOSPLIT,$0-24 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVQ n+16(FP), BX cselect(0(DI),0(SI),BX) RET // func cswapAmd64(x, y *Elt, n uint) TEXT ·cswapAmd64(SB),NOSPLIT,$0-24 MOVQ x+0(FP), DI MOVQ y+8(FP), SI MOVQ n+16(FP), BX cswap(0(DI),0(SI),BX) RET // func subAmd64(z, x, y *Elt) TEXT ·subAmd64(SB),NOSPLIT,$0-24 MOVQ z+0(FP), DI MOVQ x+8(FP), SI MOVQ y+16(FP), BX subtraction(0(DI),0(SI),0(BX)) RET // func addsubAmd64(x, y *Elt) TEXT ·addsubAmd64(SB),NOSPLIT,$0-16 MOVQ x+0(FP), DI MOVQ y+8(FP), SI addSub(0(DI),0(SI)) RET #define addLegacy \ additionLeg(0(DI),0(SI),0(BX)) #define addBmi2Adx \ additionAdx(0(DI),0(SI),0(BX)) #define mulLegacy \ integerMulLeg(0(SP),0(SI),0(BX)) \ reduceFromDoubleLeg(0(DI),0(SP)) #define mulBmi2Adx \ integerMulAdx(0(SP),0(SI),0(BX)) \ reduceFromDoubleAdx(0(DI),0(SP)) #define sqrLegacy \ integerSqrLeg(0(SP),0(SI)) \ reduceFromDoubleLeg(0(DI),0(SP)) #define sqrBmi2Adx \ integerSqrAdx(0(SP),0(SI)) \ reduceFromDoubleAdx(0(DI),0(SP)) // func addAmd64(z, x, y *Elt) TEXT ·addAmd64(SB),NOSPLIT,$0-24 MOVQ z+0(FP), DI MOVQ x+8(FP), SI MOVQ y+16(FP), BX CHECK_BMI2ADX(LADD, addLegacy, addBmi2Adx) // func mulAmd64(z, x, y *Elt) TEXT ·mulAmd64(SB),NOSPLIT,$112-24 MOVQ z+0(FP), DI MOVQ x+8(FP), SI MOVQ y+16(FP), BX CHECK_BMI2ADX(LMUL, mulLegacy, mulBmi2Adx) // func sqrAmd64(z, x *Elt) TEXT ·sqrAmd64(SB),NOSPLIT,$112-16 MOVQ z+0(FP), DI MOVQ x+8(FP), SI CHECK_BMI2ADX(LSQR, sqrLegacy, sqrBmi2Adx) golang-github-cloudflare-circl-1.3.7/math/fp448/fp_generic.go000066400000000000000000000246571454601126700237330ustar00rootroot00000000000000package fp448 import ( "encoding/binary" "math/bits" ) func cmovGeneric(x, y *Elt, n uint) { m := -uint64(n & 0x1) x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) x0 = (x0 &^ m) | (y0 & m) x1 = (x1 &^ m) | (y1 & m) x2 = (x2 &^ m) | (y2 & m) x3 = (x3 &^ m) | (y3 & m) x4 = (x4 &^ m) | (y4 & m) x5 = (x5 &^ m) | (y5 & m) x6 = (x6 &^ m) | (y6 & m) binary.LittleEndian.PutUint64(x[0*8:1*8], x0) binary.LittleEndian.PutUint64(x[1*8:2*8], x1) binary.LittleEndian.PutUint64(x[2*8:3*8], x2) binary.LittleEndian.PutUint64(x[3*8:4*8], x3) binary.LittleEndian.PutUint64(x[4*8:5*8], x4) binary.LittleEndian.PutUint64(x[5*8:6*8], x5) binary.LittleEndian.PutUint64(x[6*8:7*8], x6) } func cswapGeneric(x, y *Elt, n uint) { m := -uint64(n & 0x1) x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) t0 := m & (x0 ^ y0) t1 := m & (x1 ^ y1) t2 := m & (x2 ^ y2) t3 := m & (x3 ^ y3) t4 := m & (x4 ^ y4) t5 := m & (x5 ^ y5) t6 := m & (x6 ^ y6) x0 ^= t0 x1 ^= t1 x2 ^= t2 x3 ^= t3 x4 ^= t4 x5 ^= t5 x6 ^= t6 y0 ^= t0 y1 ^= t1 y2 ^= t2 y3 ^= t3 y4 ^= t4 y5 ^= t5 y6 ^= t6 binary.LittleEndian.PutUint64(x[0*8:1*8], x0) binary.LittleEndian.PutUint64(x[1*8:2*8], x1) binary.LittleEndian.PutUint64(x[2*8:3*8], x2) binary.LittleEndian.PutUint64(x[3*8:4*8], x3) binary.LittleEndian.PutUint64(x[4*8:5*8], x4) binary.LittleEndian.PutUint64(x[5*8:6*8], x5) binary.LittleEndian.PutUint64(x[6*8:7*8], x6) binary.LittleEndian.PutUint64(y[0*8:1*8], y0) binary.LittleEndian.PutUint64(y[1*8:2*8], y1) binary.LittleEndian.PutUint64(y[2*8:3*8], y2) binary.LittleEndian.PutUint64(y[3*8:4*8], y3) binary.LittleEndian.PutUint64(y[4*8:5*8], y4) binary.LittleEndian.PutUint64(y[5*8:6*8], y5) binary.LittleEndian.PutUint64(y[6*8:7*8], y6) } func addGeneric(z, x, y *Elt) { x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) z0, c0 := bits.Add64(x0, y0, 0) z1, c1 := bits.Add64(x1, y1, c0) z2, c2 := bits.Add64(x2, y2, c1) z3, c3 := bits.Add64(x3, y3, c2) z4, c4 := bits.Add64(x4, y4, c3) z5, c5 := bits.Add64(x5, y5, c4) z6, z7 := bits.Add64(x6, y6, c5) z0, c0 = bits.Add64(z0, z7, 0) z1, c1 = bits.Add64(z1, 0, c0) z2, c2 = bits.Add64(z2, 0, c1) z3, c3 = bits.Add64(z3, z7<<32, c2) z4, c4 = bits.Add64(z4, 0, c3) z5, c5 = bits.Add64(z5, 0, c4) z6, z7 = bits.Add64(z6, 0, c5) z0, c0 = bits.Add64(z0, z7, 0) z1, c1 = bits.Add64(z1, 0, c0) z2, c2 = bits.Add64(z2, 0, c1) z3, c3 = bits.Add64(z3, z7<<32, c2) z4, c4 = bits.Add64(z4, 0, c3) z5, c5 = bits.Add64(z5, 0, c4) z6, _ = bits.Add64(z6, 0, c5) binary.LittleEndian.PutUint64(z[0*8:1*8], z0) binary.LittleEndian.PutUint64(z[1*8:2*8], z1) binary.LittleEndian.PutUint64(z[2*8:3*8], z2) binary.LittleEndian.PutUint64(z[3*8:4*8], z3) binary.LittleEndian.PutUint64(z[4*8:5*8], z4) binary.LittleEndian.PutUint64(z[5*8:6*8], z5) binary.LittleEndian.PutUint64(z[6*8:7*8], z6) } func subGeneric(z, x, y *Elt) { x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) z0, c0 := bits.Sub64(x0, y0, 0) z1, c1 := bits.Sub64(x1, y1, c0) z2, c2 := bits.Sub64(x2, y2, c1) z3, c3 := bits.Sub64(x3, y3, c2) z4, c4 := bits.Sub64(x4, y4, c3) z5, c5 := bits.Sub64(x5, y5, c4) z6, z7 := bits.Sub64(x6, y6, c5) z0, c0 = bits.Sub64(z0, z7, 0) z1, c1 = bits.Sub64(z1, 0, c0) z2, c2 = bits.Sub64(z2, 0, c1) z3, c3 = bits.Sub64(z3, z7<<32, c2) z4, c4 = bits.Sub64(z4, 0, c3) z5, c5 = bits.Sub64(z5, 0, c4) z6, z7 = bits.Sub64(z6, 0, c5) z0, c0 = bits.Sub64(z0, z7, 0) z1, c1 = bits.Sub64(z1, 0, c0) z2, c2 = bits.Sub64(z2, 0, c1) z3, c3 = bits.Sub64(z3, z7<<32, c2) z4, c4 = bits.Sub64(z4, 0, c3) z5, c5 = bits.Sub64(z5, 0, c4) z6, _ = bits.Sub64(z6, 0, c5) binary.LittleEndian.PutUint64(z[0*8:1*8], z0) binary.LittleEndian.PutUint64(z[1*8:2*8], z1) binary.LittleEndian.PutUint64(z[2*8:3*8], z2) binary.LittleEndian.PutUint64(z[3*8:4*8], z3) binary.LittleEndian.PutUint64(z[4*8:5*8], z4) binary.LittleEndian.PutUint64(z[5*8:6*8], z5) binary.LittleEndian.PutUint64(z[6*8:7*8], z6) } func addsubGeneric(x, y *Elt) { z := &Elt{} addGeneric(z, x, y) subGeneric(y, x, y) *x = *z } func mulGeneric(z, x, y *Elt) { x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) yy := [7]uint64{y0, y1, y2, y3, y4, y5, y6} zz := [7]uint64{} yi := yy[0] h0, l0 := bits.Mul64(x0, yi) h1, l1 := bits.Mul64(x1, yi) h2, l2 := bits.Mul64(x2, yi) h3, l3 := bits.Mul64(x3, yi) h4, l4 := bits.Mul64(x4, yi) h5, l5 := bits.Mul64(x5, yi) h6, l6 := bits.Mul64(x6, yi) zz[0] = l0 a0, c0 := bits.Add64(h0, l1, 0) a1, c1 := bits.Add64(h1, l2, c0) a2, c2 := bits.Add64(h2, l3, c1) a3, c3 := bits.Add64(h3, l4, c2) a4, c4 := bits.Add64(h4, l5, c3) a5, c5 := bits.Add64(h5, l6, c4) a6, _ := bits.Add64(h6, 0, c5) for i := 1; i < 7; i++ { yi = yy[i] h0, l0 = bits.Mul64(x0, yi) h1, l1 = bits.Mul64(x1, yi) h2, l2 = bits.Mul64(x2, yi) h3, l3 = bits.Mul64(x3, yi) h4, l4 = bits.Mul64(x4, yi) h5, l5 = bits.Mul64(x5, yi) h6, l6 = bits.Mul64(x6, yi) zz[i], c0 = bits.Add64(a0, l0, 0) a0, c1 = bits.Add64(a1, l1, c0) a1, c2 = bits.Add64(a2, l2, c1) a2, c3 = bits.Add64(a3, l3, c2) a3, c4 = bits.Add64(a4, l4, c3) a4, c5 = bits.Add64(a5, l5, c4) a5, a6 = bits.Add64(a6, l6, c5) a0, c0 = bits.Add64(a0, h0, 0) a1, c1 = bits.Add64(a1, h1, c0) a2, c2 = bits.Add64(a2, h2, c1) a3, c3 = bits.Add64(a3, h3, c2) a4, c4 = bits.Add64(a4, h4, c3) a5, c5 = bits.Add64(a5, h5, c4) a6, _ = bits.Add64(a6, h6, c5) } red64(z, &zz, &[7]uint64{a0, a1, a2, a3, a4, a5, a6}) } func sqrGeneric(z, x *Elt) { mulGeneric(z, x, x) } func red64(z *Elt, l, h *[7]uint64) { /* (2C13, 2C12, 2C11, 2C10|C10, C9, C8, C7) + (C6,...,C0) */ h0 := h[0] h1 := h[1] h2 := h[2] h3 := ((h[3] & (0xFFFFFFFF << 32)) << 1) | (h[3] & 0xFFFFFFFF) h4 := (h[3] >> 63) | (h[4] << 1) h5 := (h[4] >> 63) | (h[5] << 1) h6 := (h[5] >> 63) | (h[6] << 1) h7 := (h[6] >> 63) l0, c0 := bits.Add64(h0, l[0], 0) l1, c1 := bits.Add64(h1, l[1], c0) l2, c2 := bits.Add64(h2, l[2], c1) l3, c3 := bits.Add64(h3, l[3], c2) l4, c4 := bits.Add64(h4, l[4], c3) l5, c5 := bits.Add64(h5, l[5], c4) l6, c6 := bits.Add64(h6, l[6], c5) l7, _ := bits.Add64(h7, 0, c6) /* (C10C9, C9C8,C8C7,C7C13,C13C12,C12C11,C11C10) + (C6,...,C0) */ h0 = (h[3] >> 32) | (h[4] << 32) h1 = (h[4] >> 32) | (h[5] << 32) h2 = (h[5] >> 32) | (h[6] << 32) h3 = (h[6] >> 32) | (h[0] << 32) h4 = (h[0] >> 32) | (h[1] << 32) h5 = (h[1] >> 32) | (h[2] << 32) h6 = (h[2] >> 32) | (h[3] << 32) l0, c0 = bits.Add64(l0, h0, 0) l1, c1 = bits.Add64(l1, h1, c0) l2, c2 = bits.Add64(l2, h2, c1) l3, c3 = bits.Add64(l3, h3, c2) l4, c4 = bits.Add64(l4, h4, c3) l5, c5 = bits.Add64(l5, h5, c4) l6, c6 = bits.Add64(l6, h6, c5) l7, _ = bits.Add64(l7, 0, c6) /* (C7) + (C6,...,C0) */ l0, c0 = bits.Add64(l0, l7, 0) l1, c1 = bits.Add64(l1, 0, c0) l2, c2 = bits.Add64(l2, 0, c1) l3, c3 = bits.Add64(l3, l7<<32, c2) l4, c4 = bits.Add64(l4, 0, c3) l5, c5 = bits.Add64(l5, 0, c4) l6, l7 = bits.Add64(l6, 0, c5) /* (C7) + (C6,...,C0) */ l0, c0 = bits.Add64(l0, l7, 0) l1, c1 = bits.Add64(l1, 0, c0) l2, c2 = bits.Add64(l2, 0, c1) l3, c3 = bits.Add64(l3, l7<<32, c2) l4, c4 = bits.Add64(l4, 0, c3) l5, c5 = bits.Add64(l5, 0, c4) l6, _ = bits.Add64(l6, 0, c5) binary.LittleEndian.PutUint64(z[0*8:1*8], l0) binary.LittleEndian.PutUint64(z[1*8:2*8], l1) binary.LittleEndian.PutUint64(z[2*8:3*8], l2) binary.LittleEndian.PutUint64(z[3*8:4*8], l3) binary.LittleEndian.PutUint64(z[4*8:5*8], l4) binary.LittleEndian.PutUint64(z[5*8:6*8], l5) binary.LittleEndian.PutUint64(z[6*8:7*8], l6) } golang-github-cloudflare-circl-1.3.7/math/fp448/fp_noasm.go000066400000000000000000000006761454601126700234270ustar00rootroot00000000000000//go:build !amd64 || purego // +build !amd64 purego package fp448 func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } func add(z, x, y *Elt) { addGeneric(z, x, y) } func sub(z, x, y *Elt) { subGeneric(z, x, y) } func addsub(x, y *Elt) { addsubGeneric(x, y) } func mul(z, x, y *Elt) { mulGeneric(z, x, y) } func sqr(z, x *Elt) { sqrGeneric(z, x) } golang-github-cloudflare-circl-1.3.7/math/fp448/fp_test.go000066400000000000000000000204731454601126700232660ustar00rootroot00000000000000package fp448 import ( "crypto/rand" "fmt" "math/big" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" ) func testCmov(t *testing.T, f func(x, y *Elt, n uint)) { const numTests = 1 << 9 var x, y Elt for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) b := uint(y[0] & 0x1) want := conv.BytesLe2BigInt(x[:]) if b != 0 { want = conv.BytesLe2BigInt(y[:]) } f(&x, &y, b) got := conv.BytesLe2BigInt(x[:]) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y, b) } } } func testCswap(t *testing.T, f func(x, y *Elt, n uint)) { const numTests = 1 << 9 var x, y Elt for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) b := uint(y[0] & 0x1) want0 := conv.BytesLe2BigInt(x[:]) want1 := conv.BytesLe2BigInt(y[:]) if b != 0 { want0 = conv.BytesLe2BigInt(y[:]) want1 = conv.BytesLe2BigInt(x[:]) } f(&x, &y, b) got0 := conv.BytesLe2BigInt(x[:]) got1 := conv.BytesLe2BigInt(y[:]) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, y, b) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, y, b) } } } func testAdd(t *testing.T, f func(z, x, y *Elt)) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) f(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want := xx.Add(xx, yy).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testSub(t *testing.T, f func(z, x, y *Elt)) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) f(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want := xx.Sub(xx, yy).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testAddSub(t *testing.T, f func(x, y *Elt)) { const numTests = 1 << 9 var x, y Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) want0, want1 := big.NewInt(0), big.NewInt(0) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want0.Add(xx, yy).Mod(want0, p) want1.Sub(xx, yy).Mod(want1, p) f(&x, &y) Modp(&x) Modp(&y) got0 := conv.BytesLe2BigInt(x[:]) got1 := conv.BytesLe2BigInt(y[:]) if got0.Cmp(want0) != 0 { test.ReportError(t, got0, want0, x, y) } if got1.Cmp(want1) != 0 { test.ReportError(t, got1, want1, x, y) } } } func testMul(t *testing.T, f func(z, x, y *Elt)) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) f(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) want := xx.Mul(xx, yy).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } } func testSqr(t *testing.T, f func(z, x *Elt)) { const numTests = 1 << 9 var x, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) f(&z, &x) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx := conv.BytesLe2BigInt(x[:]) want := xx.Mul(xx, xx).Mod(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestModp(t *testing.T) { const numTests = 1 << 9 var x Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) two256 := big.NewInt(1) two256.Lsh(two256, 256) want := new(big.Int) for i := 0; i < numTests; i++ { bigX, _ := rand.Int(rand.Reader, two256) bigX.Add(bigX, p).Mod(bigX, two256) conv.BigInt2BytesLe(x[:], bigX) Modp(&x) got := conv.BytesLe2BigInt(x[:]) want.Mod(bigX, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, bigX) } } } func TestIsZero(t *testing.T) { var x Elt got := IsZero(&x) want := true if got != want { test.ReportError(t, got, want, x) } SetOne(&x) got = IsZero(&x) want = false if got != want { test.ReportError(t, got, want, x) } x = P() got = IsZero(&x) want = true if got != want { test.ReportError(t, got, want, x) } } func TestToBytes(t *testing.T) { const numTests = 1 << 9 var x Elt var got, want [Size]byte for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) err := ToBytes(got[:], &x) conv.BigInt2BytesLe(want[:], conv.BytesLe2BigInt(x[:])) if err != nil || got != want { test.ReportError(t, got, want, x) } } var largeSlice [Size + 1]byte err := ToBytes(largeSlice[:], &x) if err == nil { test.ReportError(t, got, want, largeSlice) } } func TestString(t *testing.T) { const numTests = 1 << 9 var x Elt var bigX big.Int for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) got, _ := bigX.SetString(fmt.Sprint(x), 0) want := conv.BytesLe2BigInt(x[:]) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestNeg(t *testing.T) { const numTests = 1 << 9 var x, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) Neg(&z, &x) Modp(&z) got := conv.BytesLe2BigInt(z[:]) bigX := conv.BytesLe2BigInt(x[:]) want := bigX.Neg(bigX).Mod(bigX, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, bigX) } } } func TestInv(t *testing.T) { const numTests = 1 << 9 var x, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) Inv(&z, &x) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx := conv.BytesLe2BigInt(x[:]) want := xx.ModInverse(xx, p) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } func TestInvSqrt(t *testing.T) { const numTests = 1 << 9 var x, y, z Elt prime := P() p := conv.BytesLe2BigInt(prime[:]) exp := big.NewInt(1) exp.Add(p, exp).Rsh(exp, 2) var frac, root, sqRoot big.Int var wantQR bool var want *big.Int for i := 0; i < numTests; i++ { _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) gotQR := InvSqrt(&z, &x, &y) Modp(&z) got := conv.BytesLe2BigInt(z[:]) xx := conv.BytesLe2BigInt(x[:]) yy := conv.BytesLe2BigInt(y[:]) frac.ModInverse(yy, p).Mul(&frac, xx).Mod(&frac, p) root.Exp(&frac, exp, p) sqRoot.Mul(&root, &root).Mod(&sqRoot, p) if sqRoot.Cmp(&frac) == 0 { want = &root wantQR = true } else { want = big.NewInt(0) wantQR = false } if wantQR { if gotQR != wantQR || got.Cmp(want) != 0 { test.ReportError(t, got, want, x, y) } } else { if gotQR != wantQR { test.ReportError(t, gotQR, wantQR, x, y) } } } } func TestGeneric(t *testing.T) { t.Run("Cmov", func(t *testing.T) { testCmov(t, cmovGeneric) }) t.Run("Cswap", func(t *testing.T) { testCswap(t, cswapGeneric) }) t.Run("Add", func(t *testing.T) { testAdd(t, addGeneric) }) t.Run("Sub", func(t *testing.T) { testSub(t, subGeneric) }) t.Run("AddSub", func(t *testing.T) { testAddSub(t, addsubGeneric) }) t.Run("Mul", func(t *testing.T) { testMul(t, mulGeneric) }) t.Run("Sqr", func(t *testing.T) { testSqr(t, sqrGeneric) }) } func TestNative(t *testing.T) { t.Run("Cmov", func(t *testing.T) { testCmov(t, Cmov) }) t.Run("Cswap", func(t *testing.T) { testCswap(t, Cswap) }) t.Run("Add", func(t *testing.T) { testAdd(t, Add) }) t.Run("Sub", func(t *testing.T) { testSub(t, Sub) }) t.Run("AddSub", func(t *testing.T) { testAddSub(t, AddSub) }) t.Run("Mul", func(t *testing.T) { testMul(t, Mul) }) t.Run("Sqr", func(t *testing.T) { testSqr(t, Sqr) }) } func BenchmarkFp(b *testing.B) { var x, y, z Elt _, _ = rand.Read(x[:]) _, _ = rand.Read(y[:]) _, _ = rand.Read(z[:]) b.Run("Add", func(b *testing.B) { for i := 0; i < b.N; i++ { Add(&x, &y, &z) } }) b.Run("Sub", func(b *testing.B) { for i := 0; i < b.N; i++ { Sub(&x, &y, &z) } }) b.Run("Mul", func(b *testing.B) { for i := 0; i < b.N; i++ { Mul(&x, &y, &z) } }) b.Run("Sqr", func(b *testing.B) { for i := 0; i < b.N; i++ { Sqr(&x, &y) } }) b.Run("Inv", func(b *testing.B) { for i := 0; i < b.N; i++ { Inv(&x, &y) } }) b.Run("InvSqrt", func(b *testing.B) { for i := 0; i < b.N; i++ { _ = InvSqrt(&z, &x, &y) } }) } golang-github-cloudflare-circl-1.3.7/math/fp448/fuzzer.go000066400000000000000000000040271454601126700231440ustar00rootroot00000000000000//go:build gofuzz // +build gofuzz // How to run the fuzzer: // // $ go get -u github.com/dvyukov/go-fuzz/go-fuzz // $ go get -u github.com/dvyukov/go-fuzz/go-fuzz-build // $ go-fuzz-build -libfuzzer -func FuzzReduction -o lib.a // $ clang -fsanitize=fuzzer lib.a -o fu.exe // $ ./fu.exe package fp448 import ( "encoding/binary" "fmt" "math/big" "github.com/cloudflare/circl/internal/conv" ) // FuzzReduction is a fuzzer target for red64 function, which reduces t // (112 bits) to a number t' (56 bits) congruent modulo p448. func FuzzReduction(data []byte) int { if len(data) != 2*Size { return -1 } var got, want Elt var lo, hi [7]uint64 a := data[:Size] b := data[Size:] lo[0] = binary.LittleEndian.Uint64(a[0*8 : 1*8]) lo[1] = binary.LittleEndian.Uint64(a[1*8 : 2*8]) lo[2] = binary.LittleEndian.Uint64(a[2*8 : 3*8]) lo[3] = binary.LittleEndian.Uint64(a[3*8 : 4*8]) lo[4] = binary.LittleEndian.Uint64(a[4*8 : 5*8]) lo[5] = binary.LittleEndian.Uint64(a[5*8 : 6*8]) lo[6] = binary.LittleEndian.Uint64(a[6*8 : 7*8]) hi[0] = binary.LittleEndian.Uint64(b[0*8 : 1*8]) hi[1] = binary.LittleEndian.Uint64(b[1*8 : 2*8]) hi[2] = binary.LittleEndian.Uint64(b[2*8 : 3*8]) hi[3] = binary.LittleEndian.Uint64(b[3*8 : 4*8]) hi[4] = binary.LittleEndian.Uint64(b[4*8 : 5*8]) hi[5] = binary.LittleEndian.Uint64(b[5*8 : 6*8]) hi[6] = binary.LittleEndian.Uint64(b[6*8 : 7*8]) red64(&got, &lo, &hi) t := conv.BytesLe2BigInt(data[:2*Size]) two448 := big.NewInt(1) two448.Lsh(two448, 448) // 2^448 mask448 := big.NewInt(1) mask448.Sub(two448, mask448) // 2^448-1 two224plus1 := big.NewInt(1) two224plus1.Lsh(two224plus1, 224) two224plus1.Add(two224plus1, big.NewInt(1)) // 2^224+1 var loBig, hiBig big.Int for t.Cmp(two448) >= 0 { loBig.And(t, mask448) hiBig.Rsh(t, 448) t.Mul(&hiBig, two224plus1) t.Add(t, &loBig) } conv.BigInt2BytesLe(want[:], t) if got != want { fmt.Printf("in: %v\n", conv.BytesLe2BigInt(data[:2*Size])) fmt.Printf("got: %v\n", got) fmt.Printf("want: %v\n", want) panic("error found") } return 1 } golang-github-cloudflare-circl-1.3.7/math/mlsbset/000077500000000000000000000000001454601126700220715ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/math/mlsbset/mlsbset.go000066400000000000000000000071201454601126700240710ustar00rootroot00000000000000// Package mlsbset provides a constant-time exponentiation method with precomputation. // // References: "Efficient and secure algorithms for GLV-based scalar // multiplication and their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) // - https://doi.org/10.1007/s13389-014-0085-7 // - https://eprint.iacr.org/2013/158 package mlsbset import ( "errors" "fmt" "math/big" "github.com/cloudflare/circl/internal/conv" ) // EltG is a group element. type EltG interface{} // EltP is a precomputed group element. type EltP interface{} // Group defines the operations required by MLSBSet exponentiation method. type Group interface { Identity() EltG // Returns the identity of the group. Sqr(x EltG) // Calculates x = x^2. Mul(x EltG, y EltP) // Calculates x = x*y. NewEltP() EltP // Returns an arbitrary precomputed element. ExtendedEltP() EltP // Returns the precomputed element x^(2^(w*d)). Lookup(a EltP, v uint, s, u int32) // Sets a = s*T[v][u]. } // Params contains the parameters of the encoding. type Params struct { T uint // T is the maximum size (in bits) of exponents. V uint // V is the number of tables. W uint // W is the window size. E uint // E is the number of digits per table. D uint // D is the number of digits in total. L uint // L is the length of the code. } // Encoder allows to convert integers into valid powers. type Encoder struct{ p Params } // New produces an encoder of the MLSBSet algorithm. func New(t, v, w uint) (Encoder, error) { if !(t > 1 && v >= 1 && w >= 2) { return Encoder{}, errors.New("t>1, v>=1, w>=2") } e := (t + w*v - 1) / (w * v) d := e * v l := d * w return Encoder{Params{t, v, w, e, d, l}}, nil } // Encode converts an odd integer k into a valid power for exponentiation. func (m Encoder) Encode(k []byte) (*Power, error) { if len(k) == 0 { return nil, errors.New("empty slice") } if !(len(k) <= int(m.p.L+7)>>3) { return nil, errors.New("k too big") } if k[0]%2 == 0 { return nil, errors.New("k must be odd") } ap := int((m.p.L+7)/8) - len(k) k = append(k, make([]byte, ap)...) s := m.signs(k) b := make([]int32, m.p.L-m.p.D) c := conv.BytesLe2BigInt(k) c.Rsh(c, m.p.D) var bi big.Int for i := m.p.D; i < m.p.L; i++ { c0 := int32(c.Bit(0)) b[i-m.p.D] = s[i%m.p.D] * c0 bi.SetInt64(int64(b[i-m.p.D] >> 1)) c.Rsh(c, 1) c.Sub(c, &bi) } carry := int(c.Int64()) return &Power{m, s, b, carry}, nil } // signs calculates the set of signs. func (m Encoder) signs(k []byte) []int32 { s := make([]int32, m.p.D) s[m.p.D-1] = 1 for i := uint(1); i < m.p.D; i++ { ki := int32((k[i>>3] >> (i & 0x7)) & 0x1) s[i-1] = 2*ki - 1 } return s } // GetParams returns the complementary parameters of the encoding. func (m Encoder) GetParams() Params { return m.p } // tableSize returns the size of each table. func (m Encoder) tableSize() uint { return 1 << (m.p.W - 1) } // Elts returns the total number of elements that must be precomputed. func (m Encoder) Elts() uint { return m.p.V * m.tableSize() } // IsExtended returns true if the element x^(2^(wd)) must be calculated. func (m Encoder) IsExtended() bool { q := m.p.T / (m.p.V * m.p.W); return m.p.T == q*m.p.V*m.p.W } // Ops returns the number of squares and multiplications executed during an exponentiation. func (m Encoder) Ops() (S uint, M uint) { S = m.p.E M = m.p.E * m.p.V if m.IsExtended() { M++ } return } func (m Encoder) String() string { return fmt.Sprintf("T: %v W: %v V: %v e: %v d: %v l: %v wv|t: %v", m.p.T, m.p.W, m.p.V, m.p.E, m.p.D, m.p.L, m.IsExtended()) } golang-github-cloudflare-circl-1.3.7/math/mlsbset/mlsbset_test.go000066400000000000000000000062661454601126700251420ustar00rootroot00000000000000package mlsbset_test import ( "crypto/rand" "errors" "math/big" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/math/mlsbset" ) func TestExp(t *testing.T) { T := uint(126) for v := uint(1); v <= 5; v++ { for w := uint(2); w <= 5; w++ { m, err := mlsbset.New(T, v, w) if err != nil { test.ReportError(t, err, nil) } testExp(t, m) } } } func testExp(t *testing.T, m mlsbset.Encoder) { const testTimes = 1 << 8 params := m.GetParams() TBytes := (params.T + 7) / 8 topBits := (byte(1) << (params.T % 8)) - 1 k := make([]byte, TBytes) for i := 0; i < testTimes; i++ { _, _ = rand.Read(k) k[0] |= 1 k[TBytes-1] &= topBits c, err := m.Encode(k) if err != nil { test.ReportError(t, err, nil) } g := zzAdd{m.GetParams()} a := c.Exp(g) got := a.(*big.Int) want := conv.BytesLe2BigInt(k) if got.Cmp(want) != 0 { test.ReportError(t, got, want, m) } } } type zzAdd struct{ set mlsbset.Params } func (zzAdd) Identity() mlsbset.EltG { return big.NewInt(0) } func (zzAdd) NewEltP() mlsbset.EltP { return new(big.Int) } func (zzAdd) Sqr(x mlsbset.EltG) { a := x.(*big.Int) a.Add(a, a) } func (zzAdd) Mul(x mlsbset.EltG, y mlsbset.EltP) { a := x.(*big.Int) b := y.(*big.Int) a.Add(a, b) } func (z zzAdd) ExtendedEltP() mlsbset.EltP { a := big.NewInt(1) a.Lsh(a, z.set.W*z.set.D) return a } func (z zzAdd) Lookup(x mlsbset.EltP, idTable uint, sgnElt int32, idElt int32) { a := x.(*big.Int) a.SetInt64(1) a.Lsh(a, z.set.E*idTable) // 2^(e*v) sum := big.NewInt(0) for i := int(z.set.W - 2); i >= 0; i-- { ui := big.NewInt(int64((idElt >> uint(i)) & 0x1)) sum.Add(sum, ui) sum.Lsh(sum, z.set.D) } sum.Add(sum, big.NewInt(1)) a.Mul(a, sum) if sgnElt == -1 { a.Neg(a) } } func TestEncodeErr(t *testing.T) { t.Run("mArgs", func(t *testing.T) { _, got := mlsbset.New(0, 0, 0) want := errors.New("t>1, v>=1, w>=2") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) t.Run("kOdd", func(t *testing.T) { m, _ := mlsbset.New(16, 2, 2) k := make([]byte, 2) _, got := m.Encode(k) want := errors.New("k must be odd") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) t.Run("kBig", func(t *testing.T) { m, _ := mlsbset.New(16, 2, 2) k := make([]byte, 4) _, got := m.Encode(k) want := errors.New("k too big") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) t.Run("kEmpty", func(t *testing.T) { m, _ := mlsbset.New(16, 2, 2) k := []byte{} _, got := m.Encode(k) want := errors.New("empty slice") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) } func BenchmarkEncode(b *testing.B) { t, v, w := uint(256), uint(2), uint(3) m, _ := mlsbset.New(t, v, w) params := m.GetParams() TBytes := (params.T + 7) / 8 topBits := (byte(1) << (params.T % 8)) - 1 k := make([]byte, TBytes) _, _ = rand.Read(k) k[0] |= 1 k[TBytes-1] &= topBits c, _ := m.Encode(k) g := zzAdd{params} b.Run("Encode", func(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = m.Encode(k) } }) b.Run("Exp", func(b *testing.B) { for i := 0; i < b.N; i++ { c.Exp(g) } }) } golang-github-cloudflare-circl-1.3.7/math/mlsbset/power.go000066400000000000000000000030211454601126700235500ustar00rootroot00000000000000package mlsbset import "fmt" // Power is a valid exponent produced by the MLSBSet encoding algorithm. type Power struct { set Encoder // parameters of code. s []int32 // set of signs. b []int32 // set of digits. c int // carry is {0,1}. } // Exp is calculates x^k, where x is a predetermined element of a group G. func (p *Power) Exp(G Group) EltG { a, b := G.Identity(), G.NewEltP() for e := int(p.set.p.E - 1); e >= 0; e-- { G.Sqr(a) for v := uint(0); v < p.set.p.V; v++ { sgnElt, idElt := p.Digit(v, uint(e)) G.Lookup(b, v, sgnElt, idElt) G.Mul(a, b) } } if p.set.IsExtended() && p.c == 1 { G.Mul(a, G.ExtendedEltP()) } return a } // Digit returns the (v,e)-th digit and its sign. func (p *Power) Digit(v, e uint) (sgn, dig int32) { sgn = p.bit(0, v, e) dig = 0 for i := p.set.p.W - 1; i > 0; i-- { dig = 2*dig + p.bit(i, v, e) } mask := dig >> 31 dig = (dig + mask) ^ mask return sgn, dig } // bit returns the (w,v,e)-th bit of the code. func (p *Power) bit(w, v, e uint) int32 { if !(w < p.set.p.W && v < p.set.p.V && e < p.set.p.E) { panic(fmt.Errorf("indexes outside (%v,%v,%v)", w, v, e)) } if w == 0 { return p.s[p.set.p.E*v+e] } return p.b[p.set.p.D*(w-1)+p.set.p.E*v+e] } func (p *Power) String() string { dig := "" for j := uint(0); j < p.set.p.V; j++ { for i := uint(0); i < p.set.p.E; i++ { s, d := p.Digit(j, i) dig += fmt.Sprintf("(%2v,%2v) = %+2v %+2v\n", j, i, s, d) } } return fmt.Sprintf("len: %v\ncarry: %v\ndigits:\n%v", len(p.b)+len(p.s), p.c, dig) } golang-github-cloudflare-circl-1.3.7/math/polynomial/000077500000000000000000000000001454601126700226035ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/math/polynomial/polynomial.go000066400000000000000000000071651454601126700253260ustar00rootroot00000000000000// Package polynomial provides representations of polynomials over the scalars // of a group. package polynomial import "github.com/cloudflare/circl/group" // Polynomial stores a polynomial over the set of scalars of a group. type Polynomial struct { // Internal representation is in polynomial basis: // Thus, // p(x) = \sum_i^k c[i] x^i, // where k = len(c)-1 is the degree of the polynomial. c []group.Scalar } // New creates a new polynomial given its coefficients in ascending order. // Thus, // // p(x) = \sum_i^k c[i] x^i, // // where k = len(c)-1 is the degree of the polynomial. // // The zero polynomial has degree equal to -1 and can be instantiated passing // nil to New. func New(coeffs []group.Scalar) (p Polynomial) { if l := len(coeffs); l != 0 { p.c = make([]group.Scalar, l) for i := range coeffs { p.c[i] = coeffs[i].Copy() } } return } func (p Polynomial) Degree() int { i := len(p.c) - 1 for i > 0 && p.c[i].IsZero() { i-- } return i } func (p Polynomial) Evaluate(x group.Scalar) group.Scalar { px := x.Group().NewScalar() if l := len(p.c); l != 0 { px.Set(p.c[l-1]) for i := l - 2; i >= 0; i-- { px.Mul(px, x) px.Add(px, p.c[i]) } } return px } // LagrangePolynomial stores a Lagrange polynomial over the set of scalars of a group. type LagrangePolynomial struct { // Internal representation is in Lagrange basis: // Thus, // p(x) = \sum_i^k y[i] L_j(x), where k is the degree of the polynomial, // L_j(x) = \prod_i^k (x-x[i])/(x[j]-x[i]), // y[i] = p(x[i]), and // all x[i] are different. x, y []group.Scalar } // NewLagrangePolynomial creates a polynomial in Lagrange basis given a list // of nodes (x) and values (y), such that: // // p(x) = \sum_i^k y[i] L_j(x), where k is the degree of the polynomial, // L_j(x) = \prod_i^k (x-x[i])/(x[j]-x[i]), // y[i] = p(x[i]), and // all x[i] are different. // // It panics if one of these conditions does not hold. // // The zero polynomial has degree equal to -1 and can be instantiated passing // (nil,nil) to NewLagrangePolynomial. func NewLagrangePolynomial(x, y []group.Scalar) (l LagrangePolynomial) { if len(x) != len(y) { panic("lagrange: invalid length") } if !areAllDifferent(x) { panic("lagrange: x[i] must be different") } if n := len(x); n != 0 { l.x, l.y = make([]group.Scalar, n), make([]group.Scalar, n) for i := range x { l.x[i], l.y[i] = x[i].Copy(), y[i].Copy() } } return } func (l LagrangePolynomial) Degree() int { return len(l.x) - 1 } func (l LagrangePolynomial) Evaluate(x group.Scalar) group.Scalar { px := x.Group().NewScalar() tmp := x.Group().NewScalar() for i := range l.x { LjX := baseRatio(uint(i), l.x, x) tmp.Mul(l.y[i], LjX) px.Add(px, tmp) } return px } // LagrangeBase returns the j-th Lagrange polynomial base evaluated at x. // Thus, L_j(x) = \prod (x - x[i]) / (x[j] - x[i]) for 0 <= i < k, and i != j. func LagrangeBase(jth uint, xi []group.Scalar, x group.Scalar) group.Scalar { if jth >= uint(len(xi)) { panic("lagrange: invalid index") } return baseRatio(jth, xi, x) } func baseRatio(jth uint, xi []group.Scalar, x group.Scalar) group.Scalar { num := x.Copy() num.SetUint64(1) den := x.Copy() den.SetUint64(1) tmp := x.Copy() for i := range xi { if uint(i) != jth { num.Mul(num, tmp.Sub(x, xi[i])) den.Mul(den, tmp.Sub(xi[jth], xi[i])) } } return num.Mul(num, den.Inv(den)) } func areAllDifferent(x []group.Scalar) bool { m := make(map[string]struct{}) for i := range x { k, err := x[i].MarshalBinary() if err != nil { panic(err) } if _, exists := m[string(k)]; exists { return false } m[string(k)] = struct{}{} } return true } golang-github-cloudflare-circl-1.3.7/math/polynomial/polynomial_test.go000066400000000000000000000054211454601126700263560ustar00rootroot00000000000000package polynomial_test import ( "testing" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/math/polynomial" ) func TestPolyDegree(t *testing.T) { g := group.P256 t.Run("zeroPoly", func(t *testing.T) { p := polynomial.New(nil) test.CheckOk(p.Degree() == -1, "it should be -1", t) p = polynomial.New([]group.Scalar{}) test.CheckOk(p.Degree() == -1, "it should be -1", t) }) t.Run("constantPoly", func(t *testing.T) { c := []group.Scalar{ g.NewScalar().SetUint64(0), g.NewScalar().SetUint64(0), } p := polynomial.New(c) test.CheckOk(p.Degree() == 0, "it should be 0", t) }) t.Run("linearPoly", func(t *testing.T) { c := []group.Scalar{ g.NewScalar().SetUint64(0), g.NewScalar().SetUint64(1), g.NewScalar().SetUint64(0), } p := polynomial.New(c) test.CheckOk(p.Degree() == 1, "it should be 1", t) }) } func TestPolyEval(t *testing.T) { g := group.P256 c := []group.Scalar{ g.NewScalar(), g.NewScalar(), g.NewScalar(), } c[0].SetUint64(5) c[1].SetUint64(5) c[2].SetUint64(2) p := polynomial.New(c) x := g.NewScalar() x.SetUint64(10) got := p.Evaluate(x) want := g.NewScalar() want.SetUint64(255) if !got.IsEqual(want) { test.ReportError(t, got, want) } } func TestLagrange(t *testing.T) { g := group.P256 c := []group.Scalar{ g.NewScalar(), g.NewScalar(), g.NewScalar(), } c[0].SetUint64(1234) c[1].SetUint64(166) c[2].SetUint64(94) p := polynomial.New(c) x := []group.Scalar{g.NewScalar(), g.NewScalar(), g.NewScalar()} x[0].SetUint64(2) x[1].SetUint64(4) x[2].SetUint64(5) y := []group.Scalar{} for i := range x { y = append(y, p.Evaluate(x[i])) } zero := g.NewScalar() l := polynomial.NewLagrangePolynomial(x, y) test.CheckOk(l.Degree() == p.Degree(), "bad degree", t) got := l.Evaluate(zero) want := p.Evaluate(zero) if !got.IsEqual(want) { test.ReportError(t, got, want) } // Test Kronecker's delta of LagrangeBase. // Thus: // L_j(x[i]) = { 1, if i == j; // { 0, otherwise. one := g.NewScalar() one.SetUint64(1) for j := range x { for i := range x { got := polynomial.LagrangeBase(uint(j), x, x[i]) if i == j { want = one } else { want = zero } if !got.IsEqual(want) { test.ReportError(t, got, want) } } } // Test that inputs are different length err := test.CheckPanic(func() { polynomial.NewLagrangePolynomial(x, y[:1]) }) test.CheckNoErr(t, err, "should panic") // Test that nodes must be different. x[0].Set(x[1]) err = test.CheckPanic(func() { polynomial.NewLagrangePolynomial(x, y) }) test.CheckNoErr(t, err, "should panic") // Test LagrangeBase wrong index err = test.CheckPanic(func() { polynomial.LagrangeBase(10, x, zero) }) test.CheckNoErr(t, err, "should panic") } golang-github-cloudflare-circl-1.3.7/math/primes.go000066400000000000000000000016721454601126700222540ustar00rootroot00000000000000package math import ( "crypto/rand" "io" "math/big" ) // IsSafePrime reports whether p is (probably) a safe prime. // The prime p=2*q+1 is safe prime if both p and q are primes. // Note that ProbablyPrime is not suitable for judging primes // that an adversary may have crafted to fool the test. func IsSafePrime(p *big.Int) bool { pdiv2 := new(big.Int).Rsh(p, 1) return p.ProbablyPrime(20) && pdiv2.ProbablyPrime(20) } // SafePrime returns a number of the given bit length that is a safe prime with high probability. // The number returned p=2*q+1 is a safe prime if both p and q are primes. // SafePrime will return error for any error returned by rand.Read or if bits < 2. func SafePrime(random io.Reader, bits int) (*big.Int, error) { one := big.NewInt(1) p := new(big.Int) for { q, err := rand.Prime(random, bits-1) if err != nil { return nil, err } p.Lsh(q, 1).Add(p, one) if p.ProbablyPrime(20) { return p, nil } } } golang-github-cloudflare-circl-1.3.7/math/primes_test.go000066400000000000000000000025121454601126700233050ustar00rootroot00000000000000package math import ( "crypto/rand" "fmt" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) func TestSafePrime(t *testing.T) { firstSafePrimes := []int64{ 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903, 2963, 2999, 3023, 3119, 3167, 3203, 3467, 3623, 3779, 3803, 3863, 3947, 4007, 4079, 4127, 4139, 4259, 4283, 4547, 4679, 4703, 4787, 4799, 4919, 5087, 5099, 5387, 5399, 5483, 5507, 5639, 5807, 5879, 5927, 5939, 6047, 6599, 6659, 6719, 6779, 6827, 6899, 6983, 7079, 7187, 7247, 7523, 7559, 7607, 7643, 7703, 7727, } p := new(big.Int) for _, pi := range firstSafePrimes { p.SetInt64(pi) test.CheckOk(IsSafePrime(p), fmt.Sprintf("it should be a safe prime p=%v", p), t) } } func TestIsSafePrime(t *testing.T) { for i := 1; i < 5; i++ { bits := 128 * i t.Run(fmt.Sprint(bits), func(t *testing.T) { p, err := SafePrime(rand.Reader, bits) test.CheckNoErr(t, err, "safeprime failed") test.CheckOk(IsSafePrime(p), fmt.Sprintf("it should be a safe prime p=%v", p), t) }) } } func BenchmarkSafePrime(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = SafePrime(rand.Reader, 256) } } golang-github-cloudflare-circl-1.3.7/math/wnaf.go000066400000000000000000000042651454601126700217110ustar00rootroot00000000000000// Package math provides some utility functions for big integers. package math import "math/big" // SignedDigit obtains the signed-digit recoding of n and returns a list L of // digits such that n = sum( L[i]*2^(i*(w-1)) ), and each L[i] is an odd number // in the set {±1, ±3, ..., ±2^(w-1)-1}. The third parameter ensures that the // output has ceil(l/(w-1)) digits. // // Restrictions: // - n is odd and n > 0. // - 1 < w < 32. // - l >= bit length of n. // // References: // - Alg.6 in "Exponent Recoding and Regular Exponentiation Algorithms" // by Joye-Tunstall. http://doi.org/10.1007/978-3-642-02384-2_21 // - Alg.6 in "Selecting Elliptic Curves for Cryptography: An Efficiency and // Security Analysis" by Bos et al. http://doi.org/10.1007/s13389-015-0097-y func SignedDigit(n *big.Int, w, l uint) []int32 { if n.Sign() <= 0 || n.Bit(0) == 0 { panic("n must be non-zero, odd, and positive") } if w <= 1 || w >= 32 { panic("Verify that 1 < w < 32") } if uint(n.BitLen()) > l { panic("n is too big to fit in l digits") } lenN := (l + (w - 1) - 1) / (w - 1) // ceil(l/(w-1)) L := make([]int32, lenN+1) var k, v big.Int k.Set(n) var i uint for i = 0; i < lenN; i++ { words := k.Bits() value := int32(words[0] & ((1 << w) - 1)) value -= int32(1) << (w - 1) L[i] = value v.SetInt64(int64(value)) k.Sub(&k, &v) k.Rsh(&k, w-1) } L[i] = int32(k.Int64()) return L } // OmegaNAF obtains the window-w Non-Adjacent Form of a positive number n and // 1 < w < 32. The returned slice L holds n = sum( L[i]*2^i ). // // Reference: // - Alg.9 "Efficient arithmetic on Koblitz curves" by Solinas. // http://doi.org/10.1023/A:1008306223194 func OmegaNAF(n *big.Int, w uint) (L []int32) { if n.Sign() < 0 { panic("n must be positive") } if w <= 1 || w >= 32 { panic("Verify that 1 < w < 32") } L = make([]int32, n.BitLen()+1) var k, v big.Int k.Set(n) i := 0 for ; k.Sign() > 0; i++ { value := int32(0) if k.Bit(0) == 1 { words := k.Bits() value = int32(words[0] & ((1 << w) - 1)) if value >= (int32(1) << (w - 1)) { value -= int32(1) << w } v.SetInt64(int64(value)) k.Sub(&k, &v) } L[i] = value k.Rsh(&k, 1) } return L[:i] } golang-github-cloudflare-circl-1.3.7/math/wnaf_test.go000066400000000000000000000034211454601126700227410ustar00rootroot00000000000000package math import ( "crypto/rand" "fmt" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) func TestOmegaNAF(t *testing.T) { testTimes := 1 << 7 var max big.Int max.SetInt64(1) max.Lsh(&max, 128) for w := uint(2); w < 10; w++ { for j := 0; j < testTimes; j++ { x, _ := rand.Int(rand.Reader, &max) L := OmegaNAF(x, w) var y big.Int for i := len(L) - 1; i >= 0; i-- { y.Add(&y, &y).Add(&y, big.NewInt(int64(L[i]))) } want := x got := &y if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, w) } } } } func TestOmegaNAFRegular(t *testing.T) { testTimes := 1 << 7 Two128 := big.NewInt(1) Two128.Lsh(Two128, 128) for w := uint(2); w < 10; w++ { for j := 0; j < testTimes; j++ { x, _ := rand.Int(rand.Reader, Two128) x.SetBit(x, 0, uint(1)) // odd-numbers L := SignedDigit(x, w, 128) var y big.Int for i := len(L) - 1; i >= 0; i-- { y.Lsh(&y, w-1) y.Add(&y, big.NewInt(int64(L[i]))) } want := x got := &y if got.Cmp(want) != 0 { test.ReportError(t, got, want, x, w) } } } } func BenchmarkOmegaNAF(b *testing.B) { Two128 := big.NewInt(1) Two128.Lsh(Two128, 128) for w := uint(2); w < 6; w++ { w := w // pin variable b.Run(fmt.Sprintf("%v", w), func(b *testing.B) { x, _ := rand.Int(rand.Reader, Two128) b.ResetTimer() for i := 0; i < b.N; i++ { _ = OmegaNAF(x, w) } }) } } func BenchmarkOmegaNAFRegular(b *testing.B) { Two128 := big.NewInt(1) Two128.Lsh(Two128, 128) for w := uint(2); w < 6; w++ { w := w // pin variable b.Run(fmt.Sprintf("%v", w), func(b *testing.B) { x, _ := rand.Int(rand.Reader, Two128) x.SetBit(x, 0, uint(1)) // odd-numbers b.ResetTimer() for i := 0; i < b.N; i++ { _ = SignedDigit(x, w, 128) } }) } } golang-github-cloudflare-circl-1.3.7/oprf/000077500000000000000000000000001454601126700204355ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/oprf/client.go000066400000000000000000000074321454601126700222500ustar00rootroot00000000000000package oprf import ( "crypto/rand" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/zk/dleq" ) type client struct{ params } type Client struct { client } type VerifiableClient struct { client pkS *PublicKey } type PartialObliviousClient struct { client pkS *PublicKey } func (c client) Blind(inputs [][]byte) (*FinalizeData, *EvaluationRequest, error) { if len(inputs) == 0 { return nil, nil, ErrInvalidInput } blinds := make([]Blind, len(inputs)) for i := range inputs { blinds[i] = c.params.group.RandomScalar(rand.Reader) } return c.blind(inputs, blinds) } func (c client) DeterministicBlind(inputs [][]byte, blinds []Blind) (*FinalizeData, *EvaluationRequest, error) { if len(inputs) == 0 { return nil, nil, ErrInvalidInput } if len(inputs) != len(blinds) { return nil, nil, ErrInvalidInput } return c.blind(inputs, blinds) } func (c client) blind(inputs [][]byte, blinds []Blind) (*FinalizeData, *EvaluationRequest, error) { blindedElements := make([]Blinded, len(inputs)) dst := c.params.getDST(hashToGroupDST) for i := range inputs { point := c.params.group.HashToElement(inputs[i], dst) if point.IsIdentity() { return nil, nil, ErrInvalidInput } blindedElements[i] = c.params.group.NewElement().Mul(point, blinds[i]) } evalReq := &EvaluationRequest{blindedElements} finData := &FinalizeData{inputs, blinds, evalReq} return finData, evalReq, nil } func (c client) unblind(serUnblindeds [][]byte, blindeds []group.Element, blind []Blind) (err error) { invBlind := c.params.group.NewScalar() U := c.params.group.NewElement() for i := range blindeds { invBlind.Inv(blind[i]) U.Mul(blindeds[i], invBlind) serUnblindeds[i], err = U.MarshalBinaryCompress() if err != nil { return err } } return nil } func (c client) validate(f *FinalizeData, e *Evaluation) (err error) { if l := len(f.blinds); len(f.evalReq.Elements) != l || len(e.Elements) != l { err = ErrInvalidInput } return } func (c client) finalize(f *FinalizeData, e *Evaluation, info []byte) ([][]byte, error) { unblindedElements := make([][]byte, len(f.blinds)) err := c.unblind(unblindedElements, e.Elements, f.blinds) if err != nil { return nil, err } h := c.params.hash.New() outputs := make([][]byte, len(f.inputs)) for i := range f.inputs { outputs[i] = c.params.finalizeHash(h, f.inputs[i], info, unblindedElements[i]) } return outputs, nil } func (c Client) Finalize(f *FinalizeData, e *Evaluation) (outputs [][]byte, err error) { if err = c.validate(f, e); err != nil { return nil, err } return c.client.finalize(f, e, nil) } func (c VerifiableClient) Finalize(f *FinalizeData, e *Evaluation) (outputs [][]byte, err error) { if err := c.validate(f, e); err != nil { return nil, err } if !(dleq.Verifier{Params: c.getDLEQParams()}).VerifyBatch( c.params.group.Generator(), c.pkS.e, f.evalReq.Elements, e.Elements, e.Proof, ) { return nil, ErrInvalidProof } return c.client.finalize(f, e, nil) } func (c PartialObliviousClient) Finalize(f *FinalizeData, e *Evaluation, info []byte) (outputs [][]byte, err error) { if err = c.validate(f, e); err != nil { return nil, err } tweakedKey, err := c.pointFromInfo(info) if err != nil { return nil, err } if !(dleq.Verifier{Params: c.getDLEQParams()}).VerifyBatch( c.params.group.Generator(), tweakedKey, e.Elements, f.evalReq.Elements, e.Proof, ) { return nil, ErrInvalidProof } return c.client.finalize(f, e, info) } func (c PartialObliviousClient) pointFromInfo(info []byte) (group.Element, error) { m, err := c.params.scalarFromInfo(info) if err != nil { return nil, err } T := c.params.group.NewElement().MulGen(m) tweakedKey := c.params.group.NewElement().Add(T, c.pkS.e) if tweakedKey.IsIdentity() { return nil, ErrInvalidInfo } return tweakedKey, nil } golang-github-cloudflare-circl-1.3.7/oprf/keys.go000066400000000000000000000040711454601126700217410ustar00rootroot00000000000000package oprf import ( "encoding/binary" "io" "github.com/cloudflare/circl/group" ) type PrivateKey struct { p params k group.Scalar pub *PublicKey } type PublicKey struct { p params e group.Element } func (k *PrivateKey) MarshalBinary() ([]byte, error) { return k.k.MarshalBinary() } func (k *PublicKey) MarshalBinary() ([]byte, error) { return k.e.MarshalBinaryCompress() } func (k *PrivateKey) UnmarshalBinary(s Suite, data []byte) error { p, ok := s.(params) if !ok { return ErrInvalidSuite } k.p = p k.k = k.p.group.NewScalar() return k.k.UnmarshalBinary(data) } func (k *PublicKey) UnmarshalBinary(s Suite, data []byte) error { p, ok := s.(params) if !ok { return ErrInvalidSuite } k.p = p k.e = k.p.group.NewElement() return k.e.UnmarshalBinary(data) } func (k *PrivateKey) Public() *PublicKey { if k.pub == nil { k.pub = &PublicKey{k.p, k.p.group.NewElement().MulGen(k.k)} } return k.pub } // GenerateKey generates a private key compatible with the suite. func GenerateKey(s Suite, rnd io.Reader) (*PrivateKey, error) { if rnd == nil { return nil, io.ErrNoProgress } p, ok := s.(params) if !ok { return nil, ErrInvalidSuite } privateKey := p.group.RandomScalar(rnd) return &PrivateKey{p, privateKey, nil}, nil } // DeriveKey generates a private key from a given seed and optional info string. func DeriveKey(s Suite, mode Mode, seed, info []byte) (*PrivateKey, error) { const maxTries = 255 p, ok := s.(params) if !ok { return nil, ErrInvalidSuite } if !isValidMode(mode) { return nil, ErrInvalidMode } p.m = mode lenInfo := []byte{0, 0} binary.BigEndian.PutUint16(lenInfo, uint16(len(info))) deriveInput := append(append(append([]byte{}, seed...), lenInfo...), info...) dst := p.getDST(deriveKeyPairDST) zero := p.group.NewScalar() privateKey := p.group.NewScalar() for counter := byte(0); privateKey.IsEqual(zero); counter++ { if counter > maxTries { return nil, ErrDeriveKeyPairError } privateKey = p.group.HashToScalar(append(deriveInput, counter), dst) } return &PrivateKey{p, privateKey, nil}, nil } golang-github-cloudflare-circl-1.3.7/oprf/oprf.go000066400000000000000000000166531454601126700217450ustar00rootroot00000000000000// Package oprf provides Verifiable, Oblivious Pseudo-Random Functions. // // An Oblivious Pseudorandom Function (OPRFs) is a two-party protocol for // computing the output of a PRF. One party (the server) holds the PRF secret // key, and the other (the client) holds the PRF input. // // This package is compatible with the OPRF specification at draft-irtf-cfrg-voprf [1]. // // # Protocol Overview // // This diagram shows the steps of the protocol that are common for all operation modes. // // Client(info*) Server(sk, pk, info*) // ================================================================= // finData, evalReq = Blind(input) // // evalReq // ----------> // // evaluation = Evaluate(evalReq, info*) // // evaluation // <---------- // // output = Finalize(finData, evaluation, info*) // // # Operation Modes // // Each operation mode provides different properties to the PRF. // // Base Mode: Provides obliviousness to the PRF evaluation, i.e., it ensures // that the server does not learn anything about the client's input and output // during the Evaluation step. // // Verifiable Mode: Extends the Base mode allowing the client to verify that // Server used the private key that corresponds to the public key. // // Partial Oblivious Mode: Extends the Verifiable mode by including shared // public information to the PRF input. // // All three modes can perform batches of PRF evaluations, so passing an array // of inputs will produce an array of outputs. // // # References // // [1] draft-irtf-cfrg-voprf: https://datatracker.ietf.org/doc/draft-irtf-cfrg-voprf package oprf import ( "crypto" "encoding/binary" "errors" "hash" "io" "math" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/zk/dleq" ) const ( version = "OPRFV1-" finalizeDST = "Finalize" hashToGroupDST = "HashToGroup-" hashToScalarDST = "HashToScalar-" deriveKeyPairDST = "DeriveKeyPair" infoLabel = "Info" ) type Mode = uint8 const ( BaseMode Mode = 0x00 VerifiableMode Mode = 0x01 PartialObliviousMode Mode = 0x02 ) func isValidMode(m Mode) bool { return m == BaseMode || m == VerifiableMode || m == PartialObliviousMode } type Suite interface { Identifier() string Group() group.Group Hash() crypto.Hash cannotBeImplementedExternally() } var ( // SuiteRistretto255 represents the OPRF with Ristretto255 and SHA-512 SuiteRistretto255 Suite = params{identifier: "ristretto255-SHA512", group: group.Ristretto255, hash: crypto.SHA512} // SuiteP256 represents the OPRF with P-256 and SHA-256. SuiteP256 Suite = params{identifier: "P256-SHA256", group: group.P256, hash: crypto.SHA256} // SuiteP384 represents the OPRF with P-384 and SHA-384. SuiteP384 Suite = params{identifier: "P384-SHA384", group: group.P384, hash: crypto.SHA384} // SuiteP521 represents the OPRF with P-521 and SHA-512. SuiteP521 Suite = params{identifier: "P521-SHA512", group: group.P521, hash: crypto.SHA512} ) func GetSuite(identifier string) (Suite, error) { for _, suite := range []Suite{SuiteRistretto255, SuiteP256, SuiteP384, SuiteP521} { if suite.Identifier() == identifier { return suite, nil } } return nil, ErrInvalidSuite } func NewClient(s Suite) Client { p := s.(params) p.m = BaseMode return Client{client{p}} } func NewVerifiableClient(s Suite, server *PublicKey) VerifiableClient { p, ok := s.(params) if !ok || server == nil { panic(ErrNoKey) } p.m = VerifiableMode return VerifiableClient{client{p}, server} } func NewPartialObliviousClient(s Suite, server *PublicKey) PartialObliviousClient { p, ok := s.(params) if !ok || server == nil { panic(ErrNoKey) } p.m = PartialObliviousMode return PartialObliviousClient{client{p}, server} } func NewServer(s Suite, key *PrivateKey) Server { p, ok := s.(params) if !ok || key == nil { panic(ErrNoKey) } p.m = BaseMode return Server{server{p, key}} } func NewVerifiableServer(s Suite, key *PrivateKey) VerifiableServer { p, ok := s.(params) if !ok || key == nil { panic(ErrNoKey) } p.m = VerifiableMode return VerifiableServer{server{p, key}} } func NewPartialObliviousServer(s Suite, key *PrivateKey) PartialObliviousServer { p, ok := s.(params) if !ok || key == nil { panic(ErrNoKey) } p.m = PartialObliviousMode return PartialObliviousServer{server{p, key}} } type params struct { m Mode group group.Group hash crypto.Hash identifier string } func (p params) cannotBeImplementedExternally() {} func (p params) String() string { return p.Identifier() } func (p params) Group() group.Group { return p.group } func (p params) Hash() crypto.Hash { return p.hash } func (p params) Identifier() string { return p.identifier } func (p params) getDST(name string) []byte { return append(append(append(append( []byte{}, []byte(name)...), []byte(version)...), []byte{p.m, byte('-')}...), []byte(p.identifier)...) } func (p params) scalarFromInfo(info []byte) (group.Scalar, error) { if len(info) > math.MaxUint16 { return nil, ErrInvalidInfo } lenInfo := []byte{0, 0} binary.BigEndian.PutUint16(lenInfo, uint16(len(info))) framedInfo := append(append(append([]byte{}, []byte(infoLabel)...), lenInfo...), info...) return p.group.HashToScalar(framedInfo, p.getDST(hashToScalarDST)), nil } func (p params) finalizeHash(h hash.Hash, input, info, element []byte) []byte { h.Reset() lenBuf := []byte{0, 0} binary.BigEndian.PutUint16(lenBuf, uint16(len(input))) mustWrite(h, lenBuf) mustWrite(h, input) if p.m == PartialObliviousMode { binary.BigEndian.PutUint16(lenBuf, uint16(len(info))) mustWrite(h, lenBuf) mustWrite(h, info) } binary.BigEndian.PutUint16(lenBuf, uint16(len(element))) mustWrite(h, lenBuf) mustWrite(h, element) mustWrite(h, []byte(finalizeDST)) return h.Sum(nil) } func (p params) getDLEQParams() (out dleq.Params) { out.G = p.group out.H = p.hash out.DST = p.getDST("") return } func mustWrite(h io.Writer, bytes []byte) { bytesLen, err := h.Write(bytes) if err != nil { panic(err) } if len(bytes) != bytesLen { panic("failed to write") } } var ( ErrInvalidSuite = errors.New("invalid suite") ErrInvalidMode = errors.New("invalid mode") ErrDeriveKeyPairError = errors.New("key pair derivation failed") ErrInvalidInput = errors.New("invalid input") ErrInvalidInfo = errors.New("invalid info") ErrInvalidProof = errors.New("proof verification failed") ErrInverseZero = errors.New("inverting a zero value") ErrNoKey = errors.New("must provide a key") ) type ( Blind = group.Scalar Blinded = group.Element Evaluated = group.Element ) // FinalizeData encapsulates data needed for Finalize step. type FinalizeData struct { inputs [][]byte blinds []Blind evalReq *EvaluationRequest } // CopyBlinds copies the serialized blinds to use when deterministically // invoking DeterministicBlind. func (f FinalizeData) CopyBlinds() []Blind { out := make([]Blind, len(f.blinds)) for i, b := range f.blinds { out[i] = b.Copy() } return out } // EvaluationRequest contains the blinded elements to be evaluated by the Server. type EvaluationRequest struct { Elements []Blinded } // Evaluation contains a list of elements produced during server's evaluation, and // for verifiable modes it also includes a proof. type Evaluation struct { Elements []Evaluated Proof *dleq.Proof } golang-github-cloudflare-circl-1.3.7/oprf/oprf_test.go000066400000000000000000000236751454601126700230060ustar00rootroot00000000000000package oprf import ( "bytes" "crypto/rand" "encoding" "encoding/binary" "fmt" "testing" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/internal/test" ) type commonClient interface { blind(inputs [][]byte, blinds []Blind) (*FinalizeData, *EvaluationRequest, error) DeterministicBlind(inputs [][]byte, blinds []Blind) (*FinalizeData, *EvaluationRequest, error) Blind(inputs [][]byte) (*FinalizeData, *EvaluationRequest, error) Finalize(d *FinalizeData, e *Evaluation) ([][]byte, error) } type c1 struct { PartialObliviousClient info []byte } func (c *c1) Finalize(f *FinalizeData, e *Evaluation) ([][]byte, error) { return c.PartialObliviousClient.Finalize(f, e, c.info) } type commonServer interface { Evaluate(req *EvaluationRequest) (*Evaluation, error) FullEvaluate(input []byte) ([]byte, error) VerifyFinalize(input, expectedOutput []byte) bool PublicKey() *PublicKey } type s1 struct { PartialObliviousServer info []byte } func (s *s1) Evaluate(req *EvaluationRequest) (*Evaluation, error) { return s.PartialObliviousServer.Evaluate(req, s.info) } func (s *s1) FullEvaluate(input []byte) ([]byte, error) { return s.PartialObliviousServer.FullEvaluate(input, s.info) } func (s *s1) VerifyFinalize(input, expectedOutput []byte) bool { return s.PartialObliviousServer.VerifyFinalize(input, s.info, expectedOutput) } type canMarshal interface { encoding.BinaryMarshaler UnmarshalBinary(id Suite, data []byte) (err error) } func testMarshal(t *testing.T, suite Suite, x, y canMarshal, name string) { t.Helper() wantBytes, err := x.MarshalBinary() test.CheckNoErr(t, err, "error on marshaling "+name) err = y.UnmarshalBinary(suite, wantBytes) test.CheckNoErr(t, err, "error on unmarshaling "+name) gotBytes, err := x.MarshalBinary() test.CheckNoErr(t, err, "error on marshaling "+name) if !bytes.Equal(gotBytes, wantBytes) { test.ReportError(t, gotBytes, wantBytes) } } func elementsMarshalBinary(g group.Group, e []group.Element) ([]byte, error) { output := make([]byte, 2, 2+len(e)*int(g.Params().CompressedElementLength)) binary.BigEndian.PutUint16(output[0:2], uint16(len(e))) for i := range e { ei, err := e[i].MarshalBinaryCompress() if err != nil { return nil, err } output = append(output, ei...) } return output, nil } func testAPI(t *testing.T, server commonServer, client commonClient) { t.Helper() inputs := [][]byte{{0x00}, {0xFF}} finData, evalReq, err := client.Blind(inputs) test.CheckNoErr(t, err, "invalid blinding of client") blinds := finData.CopyBlinds() _, detEvalReq, err := client.DeterministicBlind(inputs, blinds) test.CheckNoErr(t, err, "invalid deterministic blinding of client") test.CheckOk(len(detEvalReq.Elements) == len(evalReq.Elements), "invalid number of evaluations", t) for i := range evalReq.Elements { test.CheckOk(evalReq.Elements[i].IsEqual(detEvalReq.Elements[i]), "invalid blinded element mismatch", t) } eval, err := server.Evaluate(evalReq) test.CheckNoErr(t, err, "invalid evaluation of server") test.CheckOk(eval != nil, "invalid evaluation of server: no evaluation", t) clientOutputs, err := client.Finalize(finData, eval) test.CheckNoErr(t, err, "invalid finalize of client") test.CheckOk(clientOutputs != nil, "invalid finalize of client: no outputs", t) for i := range inputs { valid := server.VerifyFinalize(inputs[i], clientOutputs[i]) test.CheckOk(valid, "invalid verification from the server", t) serverOutput, err := server.FullEvaluate(inputs[i]) test.CheckNoErr(t, err, "FullEvaluate failed") if !bytes.Equal(serverOutput, clientOutputs[i]) { test.ReportError(t, serverOutput, clientOutputs[i]) } } } func TestAPI(t *testing.T) { info := []byte("shared info") for _, suite := range []Suite{ SuiteRistretto255, SuiteP256, SuiteP384, SuiteP521, } { t.Run(suite.(fmt.Stringer).String(), func(t *testing.T) { private, err := GenerateKey(suite, rand.Reader) test.CheckNoErr(t, err, "failed private key generation") testMarshal(t, suite, private, new(PrivateKey), "PrivateKey") public := private.Public() testMarshal(t, suite, public, new(PublicKey), "PublicKey") t.Run("OPRF", func(t *testing.T) { s := NewServer(suite, private) c := NewClient(suite) testAPI(t, s, c) }) t.Run("VOPRF", func(t *testing.T) { s := NewVerifiableServer(suite, private) c := NewVerifiableClient(suite, s.PublicKey()) testAPI(t, s, c) }) t.Run("POPRF", func(t *testing.T) { s := &s1{NewPartialObliviousServer(suite, private), info} c := &c1{NewPartialObliviousClient(suite, s.PublicKey()), info} testAPI(t, s, c) }) }) } } func TestErrors(t *testing.T) { goodID := SuiteP256 strErrNil := "must be nil" strErrK := "must fail key" strErrC := "must fail client" strErrS := "must fail server" t.Run("badID", func(t *testing.T) { var badID Suite k, err := GenerateKey(badID, rand.Reader) test.CheckIsErr(t, err, strErrK) test.CheckOk(k == nil, strErrNil, t) k, err = DeriveKey(badID, BaseMode, nil, nil) test.CheckIsErr(t, err, strErrK) test.CheckOk(k == nil, strErrNil, t) err = new(PrivateKey).UnmarshalBinary(badID, nil) test.CheckIsErr(t, err, strErrK) err = new(PublicKey).UnmarshalBinary(badID, nil) test.CheckIsErr(t, err, strErrK) err = test.CheckPanic(func() { NewClient(badID) }) test.CheckNoErr(t, err, strErrC) err = test.CheckPanic(func() { NewServer(badID, nil) }) test.CheckNoErr(t, err, strErrS) err = test.CheckPanic(func() { NewVerifiableClient(badID, nil) }) test.CheckNoErr(t, err, strErrC) err = test.CheckPanic(func() { NewVerifiableServer(badID, nil) }) test.CheckNoErr(t, err, strErrS) err = test.CheckPanic(func() { NewPartialObliviousClient(badID, nil) }) test.CheckNoErr(t, err, strErrC) err = test.CheckPanic(func() { NewPartialObliviousServer(badID, nil) }) test.CheckNoErr(t, err, strErrS) }) t.Run("nilPubKey", func(t *testing.T) { err := test.CheckPanic(func() { NewVerifiableClient(goodID, nil) }) test.CheckNoErr(t, err, strErrC) }) t.Run("nilCalls", func(t *testing.T) { c := NewClient(goodID) finData, evalReq, err := c.Blind(nil) test.CheckIsErr(t, err, strErrC) test.CheckOk(finData == nil, strErrNil, t) test.CheckOk(evalReq == nil, strErrNil, t) var emptyEval Evaluation finData, _, _ = c.Blind([][]byte{[]byte("in0"), []byte("in1")}) out, err := c.Finalize(finData, &emptyEval) test.CheckIsErr(t, err, strErrC) test.CheckOk(out == nil, strErrNil, t) }) t.Run("invalidProof", func(t *testing.T) { key, _ := GenerateKey(goodID, rand.Reader) s := NewVerifiableServer(goodID, key) c := NewVerifiableClient(goodID, key.Public()) finData, evalReq, _ := c.Blind([][]byte{[]byte("in0"), []byte("in1")}) _, _ = s.Evaluate(evalReq) _, evalReq, _ = c.Blind([][]byte{[]byte("in0"), []byte("in2")}) badEV, _ := s.Evaluate(evalReq) _, err := c.Finalize(finData, badEV) test.CheckIsErr(t, err, strErrC) }) t.Run("badKeyGen", func(t *testing.T) { key, err := GenerateKey(goodID, nil) test.CheckIsErr(t, err, strErrNil) test.CheckOk(key == nil, strErrNil, t) key, err = DeriveKey(goodID, Mode(8), nil, nil) test.CheckIsErr(t, err, strErrK) test.CheckOk(key == nil, strErrNil, t) }) } func Example_oprf() { suite := SuiteP256 // Server(sk, pk, info*) private, _ := GenerateKey(suite, rand.Reader) server := NewServer(suite, private) // Client(info*) client := NewClient(suite) // ================================================================= // finData, evalReq = Blind(input) inputs := [][]byte{[]byte("first input"), []byte("second input")} finData, evalReq, _ := client.Blind(inputs) // // evalReq // ----------> // // evaluation = Evaluate(evalReq, info*) evaluation, _ := server.Evaluate(evalReq) // // evaluation // <---------- // // output = Finalize(finData, evaluation, info*) outputs, err := client.Finalize(finData, evaluation) fmt.Print(err == nil && len(inputs) == len(outputs)) // Output: true } func BenchmarkAPI(b *testing.B) { for _, suite := range []Suite{ SuiteRistretto255, SuiteP256, SuiteP384, SuiteP521, } { key, err := GenerateKey(suite, rand.Reader) test.CheckNoErr(b, err, "failed key generation") b.Run("OPRF/"+suite.Identifier(), func(b *testing.B) { s := NewServer(suite, key) c := NewClient(suite) benchAPI(b, s, c) }) b.Run("VOPRF/"+suite.Identifier(), func(b *testing.B) { s := NewVerifiableServer(suite, key) c := NewVerifiableClient(suite, s.PublicKey()) benchAPI(b, s, c) }) b.Run("POPRF/"+suite.Identifier(), func(b *testing.B) { info := []byte("shared info") s := &s1{NewPartialObliviousServer(suite, key), info} c := &c1{NewPartialObliviousClient(suite, s.PublicKey()), info} benchAPI(b, s, c) }) } } func benchAPI(b *testing.B, server commonServer, client commonClient) { b.Helper() inputs := [][]byte{[]byte("first input"), []byte("second input")} finData, evalReq, err := client.Blind(inputs) test.CheckNoErr(b, err, "failed client request") eval, err := server.Evaluate(evalReq) test.CheckNoErr(b, err, "failed server evaluate") clientOutputs, err := client.Finalize(finData, eval) test.CheckNoErr(b, err, "failed client finalize") b.Run("Client/Request", func(b *testing.B) { for i := 0; i < b.N; i++ { _, _, _ = client.Blind(inputs) } }) b.Run("Server/Evaluate", func(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = server.Evaluate(evalReq) } }) b.Run("Client/Finalize", func(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = client.Finalize(finData, eval) } }) b.Run("Server/VerifyFinalize", func(b *testing.B) { for i := 0; i < b.N; i++ { for j := range inputs { server.VerifyFinalize(inputs[j], clientOutputs[j]) } } }) b.Run("Server/FullEvaluate", func(b *testing.B) { for i := 0; i < b.N; i++ { for j := range inputs { _, _ = server.FullEvaluate(inputs[j]) } } }) } golang-github-cloudflare-circl-1.3.7/oprf/server.go000066400000000000000000000071741454601126700223030ustar00rootroot00000000000000package oprf import ( "crypto/rand" "crypto/subtle" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/zk/dleq" ) type server struct { params privateKey *PrivateKey } type Server struct{ server } type VerifiableServer struct{ server } type PartialObliviousServer struct{ server } func (s server) PublicKey() *PublicKey { return s.privateKey.Public() } func (s server) evaluate(elements []Blinded, secret Blind) []Evaluated { evaluations := make([]Evaluated, len(elements)) for i := range elements { evaluations[i] = s.params.group.NewElement().Mul(elements[i], secret) } return evaluations } func (s Server) Evaluate(req *EvaluationRequest) (*Evaluation, error) { evaluations := s.server.evaluate(req.Elements, s.privateKey.k) return &Evaluation{evaluations, nil}, nil } func (s VerifiableServer) Evaluate(req *EvaluationRequest) (*Evaluation, error) { evaluations := s.server.evaluate(req.Elements, s.privateKey.k) proof, err := dleq.Prover{Params: s.getDLEQParams()}.ProveBatch( s.privateKey.k, s.params.group.Generator(), s.PublicKey().e, req.Elements, evaluations, rand.Reader, ) if err != nil { return nil, err } return &Evaluation{evaluations, proof}, nil } func (s PartialObliviousServer) Evaluate(req *EvaluationRequest, info []byte) (*Evaluation, error) { keyProof, evalSecret, err := s.secretFromInfo(info) if err != nil { return nil, err } evaluations := s.server.evaluate(req.Elements, evalSecret) proof, err := dleq.Prover{Params: s.getDLEQParams()}.ProveBatch( keyProof, s.params.group.Generator(), s.params.group.NewElement().MulGen(keyProof), evaluations, req.Elements, rand.Reader, ) if err != nil { return nil, err } return &Evaluation{evaluations, proof}, nil } func (s server) secretFromInfo(info []byte) (t, tInv group.Scalar, err error) { m, err := s.params.scalarFromInfo(info) if err != nil { return nil, nil, err } t = s.params.group.NewScalar().Add(m, s.privateKey.k) if zero := s.params.group.NewScalar(); t.IsEqual(zero) { return nil, nil, ErrInverseZero } tInv = s.params.group.NewScalar().Inv(t) return t, tInv, nil } func (s server) fullEvaluate(input, info []byte) ([]byte, error) { evalSecret := s.privateKey.k if s.params.m == PartialObliviousMode { var err error _, evalSecret, err = s.secretFromInfo(info) if err != nil { return nil, err } } element := s.params.group.HashToElement(input, s.params.getDST(hashToGroupDST)) evaluation := s.params.group.NewElement().Mul(element, evalSecret) serEval, err := evaluation.MarshalBinaryCompress() if err != nil { return nil, err } return s.finalizeHash(s.params.hash.New(), input, info, serEval), nil } func (s Server) FullEvaluate(input []byte) (output []byte, err error) { return s.fullEvaluate(input, nil) } func (s VerifiableServer) FullEvaluate(input []byte) (output []byte, err error) { return s.fullEvaluate(input, nil) } func (s PartialObliviousServer) FullEvaluate(input, info []byte) (output []byte, err error) { return s.fullEvaluate(input, info) } func (s server) verifyFinalize(input, info, expectedOutput []byte) bool { gotOutput, err := s.fullEvaluate(input, info) if err != nil { return false } return subtle.ConstantTimeCompare(gotOutput, expectedOutput) == 1 } func (s Server) VerifyFinalize(input, expectedOutput []byte) bool { return s.verifyFinalize(input, nil, expectedOutput) } func (s VerifiableServer) VerifyFinalize(input, expectedOutput []byte) bool { return s.verifyFinalize(input, nil, expectedOutput) } func (s PartialObliviousServer) VerifyFinalize(input, info, expectedOutput []byte) bool { return s.verifyFinalize(input, info, expectedOutput) } golang-github-cloudflare-circl-1.3.7/oprf/testdata/000077500000000000000000000000001454601126700222465ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/oprf/testdata/allVectors.json000066400000000000000000001310201454601126700252540ustar00rootroot00000000000000[ { "groupDST": "48617368546f47726f75702d4f50524656312d002d72697374726574746f3235352d534841353132", "hash": "SHA512", "identifier": "ristretto255-SHA512", "keyInfo": "74657374206b6579", "mode": 0, "seed": "a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3", "skSm": "5ebcea5ee37023ccb9fc2d2019f9d7737be85591ae8652ffa9ef0f4d37063b0e", "vectors": [ { "Batch": 1, "Blind": "64d37aed22a27f5191de1c1d69fadb899d8862b58eb4220029e036ec4c1f6706", "BlindedElement": "609a0ae68c15a3cf6903766461307e5c8bb2f95e7e6550e1ffa2dc99e412803c", "EvaluationElement": "7ec6578ae5120958eb2db1745758ff379e77cb64fe77b0b2d8cc917ea0869c7e", "Input": "00", "Output": "527759c3d9366f277d8c6020418d96bb393ba2afb20ff90df23fb7708264e2f3ab9135e3bd69955851de4b1f9fe8a0973396719b7912ba9ee8aa7d0b5e24bcf6" }, { "Batch": 1, "Blind": "64d37aed22a27f5191de1c1d69fadb899d8862b58eb4220029e036ec4c1f6706", "BlindedElement": "da27ef466870f5f15296299850aa088629945a17d1f5b7f5ff043f76b3c06418", "EvaluationElement": "b4cbf5a4f1eeda5a63ce7b77c7d23f461db3fcab0dd28e4e17cecb5c90d02c25", "Input": "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "f4a74c9c592497375e796aa837e907b1a045d34306a749db9f34221f7e750cb4f2a6413a6bf6fa5e19ba6348eb673934a722a7ede2e7621306d18951e7cf2c73" } ] }, { "groupDST": "48617368546f47726f75702d4f50524656312d012d72697374726574746f3235352d534841353132", "hash": "SHA512", "identifier": "ristretto255-SHA512", "keyInfo": "74657374206b6579", "mode": 1, "pkSm": "c803e2cc6b05fc15064549b5920659ca4a77b2cca6f04f6b357009335476ad4e", "seed": "a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3", "skSm": "e6f73f344b79b379f1a0dd37e07ff62e38d9f71345ce62ae3a9bc60b04ccd909", "vectors": [ { "Batch": 1, "Blind": "64d37aed22a27f5191de1c1d69fadb899d8862b58eb4220029e036ec4c1f6706", "BlindedElement": "863f330cc1a1259ed5a5998a23acfd37fb4351a793a5b3c090b642ddc439b945", "EvaluationElement": "aa8fa048764d5623868679402ff6108d2521884fa138cd7f9c7669a9a014267e", "Input": "00", "Output": "b58cfbe118e0cb94d79b5fd6a6dafb98764dff49c14e1770b566e42402da1a7da4d8527693914139caee5bd03903af43a491351d23b430948dd50cde10d32b3c", "Proof": { "proof": "ddef93772692e535d1a53903db24367355cc2cc78de93b3be5a8ffcc6985dd066d4346421d17bf5117a2a1ff0fcb2a759f58a539dfbe857a40bce4cf49ec600d", "r": "222a5e897cf59db8145db8d16e597e8facb80ae7d4e26d9881aa6f61d645fc0e" } }, { "Batch": 1, "Blind": "64d37aed22a27f5191de1c1d69fadb899d8862b58eb4220029e036ec4c1f6706", "BlindedElement": "cc0b2a350101881d8a4cba4c80241d74fb7dcbfde4a61fde2f91443c2bf9ef0c", "EvaluationElement": "60a59a57208d48aca71e9e850d22674b611f752bed48b36f7a91b372bd7ad468", "Input": "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "8a9a2f3c7f085b65933594309041fc1898d42d0858e59f90814ae90571a6df60356f4610bf816f27afdd84f47719e480906d27ecd994985890e5f539e7ea74b6", "Proof": { "proof": "401a0da6264f8cf45bb2f5264bc31e109155600babb3cd4e5af7d181a2c9dc0a67154fabf031fd936051dec80b0b6ae29c9503493dde7393b722eafdf5a50b02", "r": "222a5e897cf59db8145db8d16e597e8facb80ae7d4e26d9881aa6f61d645fc0e" } }, { "Batch": 2, "Blind": "64d37aed22a27f5191de1c1d69fadb899d8862b58eb4220029e036ec4c1f6706,222a5e897cf59db8145db8d16e597e8facb80ae7d4e26d9881aa6f61d645fc0e", "BlindedElement": "863f330cc1a1259ed5a5998a23acfd37fb4351a793a5b3c090b642ddc439b945,90a0145ea9da29254c3a56be4fe185465ebb3bf2a1801f7124bbbadac751e654", "EvaluationElement": "aa8fa048764d5623868679402ff6108d2521884fa138cd7f9c7669a9a014267e,cc5ac221950a49ceaa73c8db41b82c20372a4c8d63e5dded2db920b7eee36a2a", "Input": "00,5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "b58cfbe118e0cb94d79b5fd6a6dafb98764dff49c14e1770b566e42402da1a7da4d8527693914139caee5bd03903af43a491351d23b430948dd50cde10d32b3c,8a9a2f3c7f085b65933594309041fc1898d42d0858e59f90814ae90571a6df60356f4610bf816f27afdd84f47719e480906d27ecd994985890e5f539e7ea74b6", "Proof": { "proof": 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"ca688351e88afb1d841fde4401c79efebb2eb75e7998fa9737bd5a82a152406d38bd29f680504e54fd4587eddcf2f37a2617ac2fbd2993f7bdf45442ace7d221", "Proof": { "proof": "41ad1a291aa02c80b0915fbfbb0c0afa15a57e2970067a602ddb9e8fd6b7100de32e1ecff943a36f0b10e3dae6bd266cdeb8adf825d86ef27dbc6c0e30c52206", "r": "222a5e897cf59db8145db8d16e597e8facb80ae7d4e26d9881aa6f61d645fc0e" } }, { "Batch": 1, "Blind": "64d37aed22a27f5191de1c1d69fadb899d8862b58eb4220029e036ec4c1f6706", "BlindedElement": "f0f0b209dd4d5f1844dac679acc7761b91a2e704879656cb7c201e82a99ab07d", "EvaluationElement": "8c3c9d064c334c6991e99f286ea2301d1bde170b54003fb9c44c6d7bd6fc1540", "Info": "7465737420696e666f", "Input": "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "7c6557b276a137922a0bcfc2aa2b35dd78322bd500235eb6d6b6f91bc5b56a52de2d65612d503236b321f5d0bebcbc52b64b92e426f29c9b8b69f52de98ae507", "Proof": { "proof": "4c39992d55ffba38232cdac88fe583af8a85441fefd7d1d4a8d0394cd1de77018bf135c174f20281b3341ab1f453fe72b0293a7398703384bed822bfdeec8908", 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"Input": "00,5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "0188653cfec38119a6c7dd7948b0f0720460b4310e40824e048bf82a16527303ed449a08caf84272c3bbc972ede797df,ff2a527a21cc43b251a567382677f078c6e356336aec069dea8ba36995343ca3b33bb5d6cf15be4d31a7e6d75b30d3f5", "Proof": { "proof": "4a0b2fe96d5b2a046a0447fe079b77859ef11a39a3520d6ff7c626aad9b473b724fb0cf188974ec961710a62162a83e97e0baa9eeada73397032d928b3e97b1ea92ad9458208302be3681b8ba78bcc17745bac00f84e0fdc98a6a8cba009c080", "r": "a097e722ed2427de86966910acba9f5c350e8040f828bf6ceca27405420cdf3d63cb3aef005f40ba51943c8026877963" } } ] }, { "groupDST": "48617368546f47726f75702d4f50524656312d002d503532312d534841353132", "hash": "SHA512", "identifier": "P521-SHA512", "keyInfo": "74657374206b6579", "mode": 0, "seed": "a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3", "skSm": "0153441b8faedb0340439036d6aed06d1217b34c42f17f8db4c5cc610a4a955d698a688831b16d0dc7713a1aa3611ec60703bffc7dc9c84e3ed673b3dbe1d5fccea6", "vectors": [ { "Batch": 1, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364", "BlindedElement": "0300e78bf846b0e1e1a3c320e353d758583cd876df56100a3a1e62bacba470fa6e0991be1be80b721c50c5fd0c672ba764457acc18c6200704e9294fbf28859d916351", "EvaluationElement": "030166371cf827cb2fb9b581f97907121a16e2dc5d8b10ce9f0ede7f7d76a0d047657735e8ad07bcda824907b3e5479bd72cdef6b839b967ba5c58b118b84d26f2ba07", "Input": "00", "Output": "26232de6fff83f812adadadb6cc05d7bbeee5dca043dbb16b03488abb9981d0a1ef4351fad52dbd7e759649af393348f7b9717566c19a6b8856284d69375c809" }, { "Batch": 1, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364", "BlindedElement": "0300c28e57e74361d87e0c1874e5f7cc1cc796d61f9cad50427cf54655cdb455613368d42b27f94bf66f59f53c816db3e95e68e1b113443d66a99b3693bab88afb556b", "EvaluationElement": "0301ad453607e12d0cc11a3359332a40c3a254eaa1afc64296528d55bed07ba322e72e22cf3bcb50570fd913cb54f7f09c17aff8787af75f6a7faf5640cbb2d9620a6e", "Input": "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "ad1f76ef939042175e007738906ac0336bbd1d51e287ebaa66901abdd324ea3ffa40bfc5a68e7939c2845e0fd37a5a6e76dadb9907c6cc8579629757fd4d04ba" } ] }, { "groupDST": "48617368546f47726f75702d4f50524656312d012d503532312d534841353132", "hash": "SHA512", "identifier": "P521-SHA512", "keyInfo": "74657374206b6579", "mode": 1, "pkSm": "0301505d646f6e4c9102451eb39730c4ba1c4087618641edbdba4a60896b07fd0c9414ce553cbf25b81dfcca50a8f6724ab7a2bc4d0cf736967a287bb6084cc0678ac0", "seed": "a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3", "skSm": "015c7fc1b4a0b1390925bae915bd9f3d72009d44d9241b962428aad5d13f22803311e7102632a39addc61ea440810222715c9d2f61f03ea424ec9ab1fe5e31cf9238", "vectors": [ { "Batch": 1, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364", "BlindedElement": "0301d6e4fb545e043ddb6aee5d5ceeee1b44102615ab04430c27dd0f56988dedcb1df32ef384f160e0e76e718605f14f3f582f9357553d153b996795b4b3628a4f6380", "EvaluationElement": "03013fdeaf887f3d3d283a79e696a54b66ff0edcb559265e204a958acf840e0930cc147e2a6835148d8199eebc26c03e9394c9762a1c991dde40bca0f8ca003eefb045", "Input": "00", "Output": "5e003d9b2fb540b3d4bab5fedd154912246da1ee5e557afd8f56415faa1a0fadff6517da802ee254437e4f60907b4cda146e7ba19e249eef7be405549f62954b", "Proof": { "proof": "0077fcc8ec6d059d7759b0a61f871e7c1dadc65333502e09a51994328f79e5bda3357b9a4f410a1760a3612c2f8f27cb7cb032951c047cc66da60da583df7b247edd0188e5eb99c71799af1d80d643af16ffa1545acd9e9233fbb370455b10eb257ea12a1667c1b4ee5b0ab7c93d50ae89602006960f083ca9adc4f6276c0ad60440393c", "r": "015e80ae32363b32cb76ad4b95a5a34e46bb803d955f0e073a04aa5d92b3fb739f56f9db001266677f62c095021db018cd8cbb55941d4073698ce45c405d1348b7b1" } }, { "Batch": 1, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364", "BlindedElement": "03005b05e656cb609ce5ff5faf063bb746d662d67bbd07c062638396f52f0392180cf2365cabb0ece8e19048961d35eeae5d5fa872328dce98df076ee154dd191c615e", "EvaluationElement": "0301b19fcf482b1fff04754e282292ed736c5f0aa080d4f42663cd3a416c6596f03129e8e096d8671fe5b0d19838312c511d2ce08d431e43e3ef06199d8cab7426238d", "Input": "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "fa15eebba81ecf40954f7135cb76f69ef22c6bae394d1a4362f9b03066b54b6604d39f2e53369ca6762a3d9787e230e832aa85955af40ecb8deebb009a8cf474", "Proof": { "proof": "01ec9fece444caa6a57032e8963df0e945286f88fbdf233fb5101f0924f7ea89c47023f5f72f240e61991fd33a299b5b38c45a5e2dd1a67b072e59dfe86708a359c701e38d383c60cf6969463bcf13251bedad47b7941f52e409a3591398e27924410b18a301c0e19f527cad504fa08388050ac634e1b05c5216d337742f2754e1fc502f", "r": "015e80ae32363b32cb76ad4b95a5a34e46bb803d955f0e073a04aa5d92b3fb739f56f9db001266677f62c095021db018cd8cbb55941d4073698ce45c405d1348b7b1" } }, { "Batch": 2, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364,015e80ae32363b32cb76ad4b95a5a34e46bb803d955f0e073a04aa5d92b3fb739f56f9db001266677f62c095021db018cd8cbb55941d4073698ce45c405d1348b7b1", "BlindedElement": "0301d6e4fb545e043ddb6aee5d5ceeee1b44102615ab04430c27dd0f56988dedcb1df32ef384f160e0e76e718605f14f3f582f9357553d153b996795b4b3628a4f6380,0301403b597538b939b450c93586ba275f9711ba07e42364bac1d5769c6824a8b55be6f9a536df46d952b11ab2188363b3d6737635d9543d4dba14a6e19421b9245bf5", "EvaluationElement": "03013fdeaf887f3d3d283a79e696a54b66ff0edcb559265e204a958acf840e0930cc147e2a6835148d8199eebc26c03e9394c9762a1c991dde40bca0f8ca003eefb045,03001f96424497e38c46c904978c2fa1636c5c3dd2e634a85d8a7265977c5dce1f02c7e6c118479f0751767b91a39cce6561998258591b5d7c1bb02445a9e08e4f3e8d", "Input": "00,5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "5e003d9b2fb540b3d4bab5fedd154912246da1ee5e557afd8f56415faa1a0fadff6517da802ee254437e4f60907b4cda146e7ba19e249eef7be405549f62954b,fa15eebba81ecf40954f7135cb76f69ef22c6bae394d1a4362f9b03066b54b6604d39f2e53369ca6762a3d9787e230e832aa85955af40ecb8deebb009a8cf474", "Proof": { "proof": "00b4d215c8405e57c7a4b53398caf55f1f1623aaeb22408ddb9ea29130909b3f95dbb1ff366e81e86e918f9f2fd8b80dbb344cd498c9499d112905e585417e0068c600fe5dea18b389ef6c4cc062935607b8ccbbb9a84fba3143868a3e8a58efa0bf6ca642804d09dc06e980f64837811227c4267b217f1099a4e28b0854f4e5ee659796", "r": "01ec21c7bb69b0734cb48dfd68433dd93b0fa097e722ed2427de86966910acba9f5c350e8040f828bf6ceca27405420cdf3d63cb3aef005f40ba51943c8026877963" } } ] }, { "groupDST": "48617368546f47726f75702d4f50524656312d022d503532312d534841353132", "hash": "SHA512", "identifier": "P521-SHA512", "keyInfo": "74657374206b6579", "mode": 2, "pkSm": "0301de8ceb9ffe9237b1bba87c320ea0bebcfc3447fe6f278065c6c69886d692d1126b79b6844f829940ace9b52a5e26882cf7cbc9e57503d4cca3cd834584729f812a", "seed": "a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3", "skSm": "014893130030ce69cf714f536498a02ff6b396888f9bb507985c32928c4427d6d39de10ef509aca4240e8569e3a88debc0d392e3361bcd934cb9bdd59e339dff7b27", "vectors": [ { "Batch": 1, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364", "BlindedElement": "020095cff9d7ecf65bdfee4ea92d6e748d60b02de34ad98094f82e25d33a8bf50138ccc2cc633556f1a97d7ea9438cbb394df612f041c485a515849d5ebb2238f2f0e2", "EvaluationElement": "0301408e9c5be3ffcc1c16e5ae8f8aa68446223b0804b11962e856af5a6d1c65ebbb5db7278c21db4e8cc06d89a35b6804fb1738a295b691638af77aa1327253f26d01", "Info": "7465737420696e666f", "Input": "00", "Output": "808ae5b87662eaaf0b39151dd85991b94c96ef214cb14a68bf5c143954882d330da8953a80eea20788e552bc8bbbfff3100e89f9d6e341197b122c46a208733b", "Proof": { "proof": "0106a89a61eee9dd2417d2849a8e2167bc5f56e3aed5a3ff23e22511fa1b37a29ed44d1bbfd6907d99cfbc558a56aec709282415a864a281e49dc53792a4a638a0660034306d64be12a94dcea5a6d664cf76681911c8b9a84d49bf12d4893307ec14436bd05f791f82446c0de4be6c582d373627b51886f76c4788256e3da7ec8fa18a86", "r": "015e80ae32363b32cb76ad4b95a5a34e46bb803d955f0e073a04aa5d92b3fb739f56f9db001266677f62c095021db018cd8cbb55941d4073698ce45c405d1348b7b1" } }, { "Batch": 1, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364", "BlindedElement": "030112ea89cf9cf589496189eafc5f9eb13c9f9e170d6ecde7c5b940541cb1a9c5cfeec908b67efe16b81ca00d0ce216e34b3d5f46a658d3fd8573d671bdb6515ed508", "EvaluationElement": "0200ebc49df1e6fa61f412e6c391e6f074400ecdd2f56c4a8c03fe0f91d9b551f40d4b5258fd891952e8c9b28003bcfa365122e54a5714c8949d5d202767b31b4bf1f6", "Info": "7465737420696e666f", "Input": "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "27032e24b1a52a82ab7f4646f3c5df0f070f499db98b9c5df33972bd5af5762c3638afae7912a6c1acdb1ae2ab2fa670bd5486c645a0e55412e08d33a4a0d6e3", "Proof": { "proof": "0082162c71a7765005cae202d4bd14b84dae63c29067e886b82506992bd994a1c3aac0c1c5309222fe1af8287b6443ed6df5c2e0b0991faddd3564c73c7597aecd9a003b1f1e3c65f28e58ab4e767cfb4adbcaf512441645f4c2aed8bf67d132d966006d35fa71a34145414bf3572c1de1a46c266a344dd9e22e7fb1e90ffba1caf556d9", "r": "015e80ae32363b32cb76ad4b95a5a34e46bb803d955f0e073a04aa5d92b3fb739f56f9db001266677f62c095021db018cd8cbb55941d4073698ce45c405d1348b7b1" } }, { "Batch": 2, "Blind": "00d1dccf7a51bafaf75d4a866d53d8cafe4d504650f53df8f16f6861633388936ea23338fa65ec36e0290022b48eb562889d89dbfa691d1cde91517fa222ed7ad364,015e80ae32363b32cb76ad4b95a5a34e46bb803d955f0e073a04aa5d92b3fb739f56f9db001266677f62c095021db018cd8cbb55941d4073698ce45c405d1348b7b1", "BlindedElement": "020095cff9d7ecf65bdfee4ea92d6e748d60b02de34ad98094f82e25d33a8bf50138ccc2cc633556f1a97d7ea9438cbb394df612f041c485a515849d5ebb2238f2f0e2,0201a328cf9f3fdeb86b6db242dd4cbb436b3a488b70b72d2fbbd1e5f50d7b0878b157d6f278c6a95c488f3ad52d6898a421658a82fe7ceb000b01aedea7967522d525", "EvaluationElement": "0301408e9c5be3ffcc1c16e5ae8f8aa68446223b0804b11962e856af5a6d1c65ebbb5db7278c21db4e8cc06d89a35b6804fb1738a295b691638af77aa1327253f26d01,020062ab51ac3aa829e0f5b7ae50688bcf5f63a18a83a6e0da538666b8d50c7ea2b4ef31f4ac669302318dbebe46660acdda695da30c22cee7ca21f6984a720504502e", "Info": "7465737420696e666f", "Input": "00,5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", "Output": "808ae5b87662eaaf0b39151dd85991b94c96ef214cb14a68bf5c143954882d330da8953a80eea20788e552bc8bbbfff3100e89f9d6e341197b122c46a208733b,27032e24b1a52a82ab7f4646f3c5df0f070f499db98b9c5df33972bd5af5762c3638afae7912a6c1acdb1ae2ab2fa670bd5486c645a0e55412e08d33a4a0d6e3", "Proof": { "proof": "00731738844f739bca0cca9d1c8bea204bed4fd00285785738b985763741de5cdfa275152d52b6a2fdf7792ef3779f39ba34581e56d62f78ecad5b7f8083f384961501cd4b43713253c022692669cf076b1d382ecd8293c1de69ea569737f37a24772ab73517983c1e3db5818754ba1f008076267b8058b6481949ae346cdc17a8455fe2", "r": "01ec21c7bb69b0734cb48dfd68433dd93b0fa097e722ed2427de86966910acba9f5c350e8040f828bf6ceca27405420cdf3d63cb3aef005f40ba51943c8026877963" } } ] } ] golang-github-cloudflare-circl-1.3.7/oprf/vectors_test.go000066400000000000000000000156531454601126700235220ustar00rootroot00000000000000package oprf import ( "bytes" "encoding" "encoding/binary" "encoding/hex" "encoding/json" "fmt" "io" "os" "strings" "testing" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/zk/dleq" ) type vector struct { Identifier string `json:"identifier"` Mode Mode `json:"mode"` Hash string `json:"hash"` PkSm string `json:"pkSm"` SkSm string `json:"skSm"` Seed string `json:"seed"` KeyInfo string `json:"keyInfo"` GroupDST string `json:"groupDST"` Vectors []struct { Batch int `json:"Batch"` Blind string `json:"Blind"` Info string `json:"Info"` BlindedElement string `json:"BlindedElement"` EvaluationElement string `json:"EvaluationElement"` Proof struct { Proof string `json:"proof"` R string `json:"r"` } `json:"Proof"` Input string `json:"Input"` Output string `json:"Output"` } `json:"vectors"` } func toBytes(t *testing.T, s, errMsg string) []byte { t.Helper() bytes, err := hex.DecodeString(s) test.CheckNoErr(t, err, "decoding "+errMsg) return bytes } func toListBytes(t *testing.T, s, errMsg string) [][]byte { t.Helper() strs := strings.Split(s, ",") out := make([][]byte, len(strs)) for i := range strs { out[i] = toBytes(t, strs[i], errMsg) } return out } func flattenList(t *testing.T, s, errMsg string) []byte { t.Helper() strs := strings.Split(s, ",") out := []byte{0, 0} binary.BigEndian.PutUint16(out, uint16(len(strs))) for i := range strs { out = append(out, toBytes(t, strs[i], errMsg)...) } return out } func toScalar(t *testing.T, g group.Group, s, errMsg string) group.Scalar { t.Helper() r := g.NewScalar() rBytes := toBytes(t, s, errMsg) err := r.UnmarshalBinary(rBytes) test.CheckNoErr(t, err, errMsg) return r } func readFile(t *testing.T, fileName string) []vector { t.Helper() jsonFile, err := os.Open(fileName) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", fileName, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", fileName, err) } var v []vector err = json.Unmarshal(input, &v) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) } return v } func (v *vector) SetUpParties(t *testing.T) (id params, s commonServer, c commonClient) { suite, err := GetSuite(v.Identifier) test.CheckNoErr(t, err, "suite id") seed := toBytes(t, v.Seed, "seed for key derivation") keyInfo := toBytes(t, v.KeyInfo, "info for key derivation") privateKey, err := DeriveKey(suite, v.Mode, seed, keyInfo) test.CheckNoErr(t, err, "deriving key") got, err := privateKey.MarshalBinary() test.CheckNoErr(t, err, "serializing private key") want := toBytes(t, v.SkSm, "private key") v.compareBytes(t, got, want) switch v.Mode { case BaseMode: s = NewServer(suite, privateKey) c = NewClient(suite) case VerifiableMode: s = NewVerifiableServer(suite, privateKey) c = NewVerifiableClient(suite, s.PublicKey()) case PartialObliviousMode: var info []byte s = &s1{NewPartialObliviousServer(suite, privateKey), info} c = &c1{NewPartialObliviousClient(suite, s.PublicKey()), info} } return suite.(params), s, c } func (v *vector) compareLists(t *testing.T, got, want [][]byte) { t.Helper() for i := range got { if !bytes.Equal(got[i], want[i]) { test.ReportError(t, got[i], want[i], v.Identifier, v.Mode, i) } } } func (v *vector) compareBytes(t *testing.T, got, want []byte) { t.Helper() if !bytes.Equal(got, want) { test.ReportError(t, got, want, v.Identifier, v.Mode) } } func (v *vector) test(t *testing.T) { params, server, client := v.SetUpParties(t) for i, vi := range v.Vectors { if v.Mode == PartialObliviousMode { info := toBytes(t, vi.Info, "info") ss := server.(*s1) cc := client.(*c1) ss.info = info cc.info = info } inputs := toListBytes(t, vi.Input, "input") blindsBytes := toListBytes(t, vi.Blind, "blind") blinds := make([]Blind, len(blindsBytes)) for j := range blindsBytes { blinds[j] = params.group.NewScalar() err := blinds[j].UnmarshalBinary(blindsBytes[j]) test.CheckNoErr(t, err, "invalid blind") } finData, evalReq, err := client.blind(inputs, blinds) test.CheckNoErr(t, err, "invalid client request") evalReqBytes, err := elementsMarshalBinary(params.group, evalReq.Elements) test.CheckNoErr(t, err, "bad serialization") v.compareBytes(t, evalReqBytes, flattenList(t, vi.BlindedElement, "blindedElement")) eval, err := server.Evaluate(evalReq) test.CheckNoErr(t, err, "invalid evaluation") elemBytes, err := elementsMarshalBinary(params.group, eval.Elements) test.CheckNoErr(t, err, "invalid evaluations marshaling") v.compareBytes(t, elemBytes, flattenList(t, vi.EvaluationElement, "evaluation")) if v.Mode == VerifiableMode || v.Mode == PartialObliviousMode { randomness := toScalar(t, params.group, vi.Proof.R, "invalid proof random scalar") var proof encoding.BinaryMarshaler switch v.Mode { case VerifiableMode: ss := server.(VerifiableServer) prover := dleq.Prover{Params: ss.getDLEQParams()} proof, err = prover.ProveBatchWithRandomness( ss.privateKey.k, ss.params.group.Generator(), server.PublicKey().e, evalReq.Elements, eval.Elements, randomness) case PartialObliviousMode: ss := server.(*s1) keyProof, _, _ := ss.secretFromInfo(ss.info) prover := dleq.Prover{Params: ss.getDLEQParams()} proof, err = prover.ProveBatchWithRandomness( keyProof, ss.params.group.Generator(), ss.params.group.NewElement().MulGen(keyProof), eval.Elements, evalReq.Elements, randomness) } test.CheckNoErr(t, err, "failed proof generation") proofBytes, errr := proof.MarshalBinary() test.CheckNoErr(t, errr, "failed proof marshaling") v.compareBytes(t, proofBytes, toBytes(t, vi.Proof.Proof, "proof")) } outputs, err := client.Finalize(finData, eval) test.CheckNoErr(t, err, "invalid finalize") expectedOutputs := toListBytes(t, vi.Output, "output") v.compareLists(t, outputs, expectedOutputs, ) for j := range inputs { output, err := server.FullEvaluate(inputs[j]) test.CheckNoErr(t, err, "invalid full evaluate") got := output want := expectedOutputs[j] if !bytes.Equal(got, want) { test.ReportError(t, got, want, v.Identifier, v.Mode, i, j) } test.CheckOk(server.VerifyFinalize(inputs[j], output), "verify finalize", t) } } } func TestVectors(t *testing.T) { // Draft published at https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-voprf-10 // Test vectors at https://github.com/cfrg/draft-irtf-cfrg-voprf // Version supported: v10 v := readFile(t, "testdata/allVectors.json") for i := range v { suite, err := GetSuite(v[i].Identifier) if err != nil { t.Logf(v[i].Identifier + " not supported yet") continue } t.Run(fmt.Sprintf("%v/Mode%v", suite, v[i].Mode), v[i].test) } } golang-github-cloudflare-circl-1.3.7/ot/000077500000000000000000000000001454601126700201115ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ot/doc.go000066400000000000000000000001001454601126700211740ustar00rootroot00000000000000// Package ot provides oblivious-transfer protocols. package ot golang-github-cloudflare-circl-1.3.7/ot/simot/000077500000000000000000000000001454601126700212445ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/ot/simot/simot_test.go000066400000000000000000000122601454601126700237660ustar00rootroot00000000000000// Reference: https://eprint.iacr.org/2015/267.pdf (1 out of 2 OT case) // Sender has 2 messages m0, m1 // Receiver receives mc based on the choice bit c package simot import ( "bytes" "crypto/rand" "testing" "github.com/cloudflare/circl/group" ) const testSimOTCount = 100 func simOT(myGroup group.Group, sender *Sender, receiver *Receiver, m0, m1 []byte, choice, index int) error { // Initialization A := sender.InitSender(myGroup, m0, m1, index) // Round 1 // Sender sends A to receiver B := receiver.Round1Receiver(myGroup, choice, index, A) // Round 2 // Receiver sends B to sender e0, e1 := sender.Round2Sender(B) // Round 3 // Sender sends e0 e1 to receiver errDec := receiver.Round3Receiver(e0, e1, receiver.c) if errDec != nil { return errDec } return nil } func testNegativeSimOT(t *testing.T, myGroup group.Group, choice int) { var sender Sender var receiver Receiver m0 := make([]byte, myGroup.Params().ScalarLength) m1 := make([]byte, myGroup.Params().ScalarLength) _, errRand := rand.Read(m0) if errRand != nil { panic(errRand) } _, errRand = rand.Read(m1) if errRand != nil { panic(errRand) } // Initialization A := sender.InitSender(myGroup, m0, m1, 0) // Round 1 B := receiver.Round1Receiver(myGroup, choice, 0, A) // Round 2 e0, e1 := sender.Round2Sender(B) // Round 3 // Here we pass in the flipped choice bit, to prove the decryption will fail // The receiver will not learn anything about m_{1-c} errDec := receiver.Round3Receiver(e0, e1, 1-choice) if errDec == nil { t.Error("SimOT decryption failed", errDec) } if choice == 0 { equal0 := bytes.Compare(sender.m0, receiver.mc) if equal0 == 0 { t.Error("Receiver decryption should fail") } equal1 := bytes.Compare(sender.m1, receiver.mc) if equal1 == 0 { t.Error("Receiver decryption should fail") } } else { equal0 := bytes.Compare(sender.m0, receiver.mc) if equal0 == 0 { t.Error("Receiver decryption should fail") } equal1 := bytes.Compare(sender.m1, receiver.mc) if equal1 == 0 { t.Error("Receiver decryption should fail") } } } // Input: myGroup, the group we operate in func testSimOT(t *testing.T, myGroup group.Group, choice int) { var sender Sender var receiver Receiver m0 := make([]byte, myGroup.Params().ScalarLength) m1 := make([]byte, myGroup.Params().ScalarLength) _, errRand := rand.Read(m0) if errRand != nil { panic(errRand) } _, errRand = rand.Read(m1) if errRand != nil { panic(errRand) } errDec := simOT(myGroup, &sender, &receiver, m0, m1, choice, 0) if errDec != nil { t.Error("AES GCM Decryption failed") } if choice == 0 { equal0 := bytes.Compare(sender.m0, receiver.mc) if equal0 != 0 { t.Error("Receiver decryption failed") } } else { equal1 := bytes.Compare(sender.m1, receiver.mc) if equal1 != 0 { t.Error("Receiver decryption failed") } } } func benchmarSimOT(b *testing.B, myGroup group.Group) { var sender Sender var receiver Receiver m0 := make([]byte, myGroup.Params().ScalarLength) m1 := make([]byte, myGroup.Params().ScalarLength) _, errRand := rand.Read(m0) if errRand != nil { panic(errRand) } _, errRand = rand.Read(m1) if errRand != nil { panic(errRand) } for iter := 0; iter < b.N; iter++ { errDec := simOT(myGroup, &sender, &receiver, m0, m1, iter%2, 0) if errDec != nil { b.Error("AES GCM Decryption failed") } } } func benchmarkSimOTRound(b *testing.B, myGroup group.Group) { var sender Sender var receiver Receiver m0 := make([]byte, myGroup.Params().ScalarLength) m1 := make([]byte, myGroup.Params().ScalarLength) _, errRand := rand.Read(m0) if errRand != nil { panic(errRand) } _, errRand = rand.Read(m1) if errRand != nil { panic(errRand) } b.Run("Sender-Initialization", func(b *testing.B) { for i := 0; i < b.N; i++ { sender.InitSender(myGroup, m0, m1, 0) } }) A := sender.InitSender(myGroup, m0, m1, 0) b.Run("Receiver-Round1", func(b *testing.B) { for i := 0; i < b.N; i++ { receiver.Round1Receiver(myGroup, 0, 0, A) } }) B := receiver.Round1Receiver(myGroup, 0, 0, A) b.Run("Sender-Round2", func(b *testing.B) { for i := 0; i < b.N; i++ { sender.Round2Sender(B) } }) e0, e1 := sender.Round2Sender(B) b.Run("Receiver-Round3", func(b *testing.B) { for i := 0; i < b.N; i++ { errDec := receiver.Round3Receiver(e0, e1, receiver.c) if errDec != nil { b.Error("Receiver-Round3 decryption failed") } } }) errDec := receiver.Round3Receiver(e0, e1, receiver.c) if errDec != nil { b.Error("Receiver-Round3 decryption failed") } // Confirm equal0 := bytes.Compare(sender.m0, receiver.mc) if equal0 != 0 { b.Error("Receiver decryption failed") } } func TestSimOT(t *testing.T) { t.Run("SimOT", func(t *testing.T) { for i := 0; i < testSimOTCount; i++ { currGroup := group.P256 choice := i % 2 testSimOT(t, currGroup, choice) } }) t.Run("SimOTNegative", func(t *testing.T) { for i := 0; i < testSimOTCount; i++ { currGroup := group.P256 choice := i % 2 testNegativeSimOT(t, currGroup, choice) } }) } func BenchmarkSimOT(b *testing.B) { currGroup := group.P256 benchmarSimOT(b, currGroup) } func BenchmarkSimOTRound(b *testing.B) { currGroup := group.P256 benchmarkSimOTRound(b, currGroup) } golang-github-cloudflare-circl-1.3.7/ot/simot/simotlocal.go000066400000000000000000000131371454601126700237460ustar00rootroot00000000000000package simot import ( "crypto/aes" "crypto/cipher" "crypto/rand" "crypto/subtle" "errors" "io" "github.com/cloudflare/circl/group" "golang.org/x/crypto/sha3" ) const keyLength = 16 // AES GCM encryption, we don't need to pad because our input is fixed length // Need to use authenticated encryption to defend against tampering on ciphertext // Input: key, plaintext message // Output: ciphertext func aesEncGCM(key, plaintext []byte) []byte { block, err := aes.NewCipher(key) if err != nil { panic(err) } aesgcm, err := cipher.NewGCM(block) if err != nil { panic(err.Error()) } nonce := make([]byte, aesgcm.NonceSize()) if _, err := io.ReadFull(rand.Reader, nonce); err != nil { panic(err) } ciphertext := aesgcm.Seal(nonce, nonce, plaintext, nil) return ciphertext } // AES GCM decryption // Input: key, ciphertext message // Output: plaintext func aesDecGCM(key, ciphertext []byte) ([]byte, error) { block, err := aes.NewCipher(key) if err != nil { panic(err) } aesgcm, err := cipher.NewGCM(block) if err != nil { panic(err.Error()) } nonceSize := aesgcm.NonceSize() if len(ciphertext) < nonceSize { return nil, errors.New("ciphertext too short") } nonce, encryptedMessage := ciphertext[:nonceSize], ciphertext[nonceSize:] plaintext, err := aesgcm.Open(nil, nonce, encryptedMessage, nil) return plaintext, err } // Initialization // Input: myGroup, the group we operate in // Input: m0, m1 the 2 message of the sender // Input: index, the index of this SimOT // Output: A = [a]G, a the sender randomness func (sender *Sender) InitSender(myGroup group.Group, m0, m1 []byte, index int) group.Element { sender.a = myGroup.RandomNonZeroScalar(rand.Reader) sender.k0 = make([]byte, keyLength) sender.k1 = make([]byte, keyLength) sender.m0 = m0 sender.m1 = m1 sender.index = index sender.A = myGroup.NewElement() sender.A.MulGen(sender.a) sender.myGroup = myGroup return sender.A.Copy() } // Round 1 // ---- sender should send A to receiver ---- // Input: myGroup, the group we operate in // Input: choice, the receiver choice bit // Input: index, the index of this SimOT // Input: A, from sender // Output: B = [b]G if c == 0, B = A+[b]G if c == 1 (Implementation in constant time). b, the receiver randomness func (receiver *Receiver) Round1Receiver(myGroup group.Group, choice int, index int, A group.Element) group.Element { receiver.b = myGroup.RandomNonZeroScalar(rand.Reader) receiver.c = choice receiver.kR = make([]byte, keyLength) receiver.index = index receiver.A = A receiver.myGroup = myGroup bG := myGroup.NewElement() bG.MulGen(receiver.b) AorI := myGroup.NewElement() AorI.CMov(choice, A) receiver.B = myGroup.NewElement() receiver.B.Add(bG, AorI) return receiver.B.Copy() } // Round 2 // ---- receiver should send B to sender ---- // Input: B from the receiver // Output: e0, e1, encryption of m0 and m1 under key k0, k1 func (sender *Sender) Round2Sender(B group.Element) ([]byte, []byte) { sender.B = B aB := sender.myGroup.NewElement() aB.Mul(sender.B, sender.a) maA := sender.myGroup.NewElement() maA.Mul(sender.A, sender.a) maA.Neg(maA) aBaA := sender.myGroup.NewElement() aBaA.Add(aB, maA) // Hash the whole transcript A|B|... AByte, errByte := sender.A.MarshalBinary() if errByte != nil { panic(errByte) } BByte, errByte := sender.B.MarshalBinary() if errByte != nil { panic(errByte) } aBByte, errByte := aB.MarshalBinary() if errByte != nil { panic(errByte) } hashByte0 := append(AByte, BByte...) hashByte0 = append(hashByte0, aBByte...) s := sha3.NewShake128() _, errWrite := s.Write(hashByte0) if errWrite != nil { panic(errWrite) } _, errRead := s.Read(sender.k0) if errRead != nil { panic(errRead) } aBaAByte, errByte := aBaA.MarshalBinary() if errByte != nil { panic(errByte) } hashByte1 := append(AByte, BByte...) hashByte1 = append(hashByte1, aBaAByte...) s = sha3.NewShake128() _, errWrite = s.Write(hashByte1) if errWrite != nil { panic(errWrite) } _, errRead = s.Read(sender.k1) if errRead != nil { panic(errRead) } e0 := aesEncGCM(sender.k0, sender.m0) sender.e0 = e0 e1 := aesEncGCM(sender.k1, sender.m1) sender.e1 = e1 return sender.e0, sender.e1 } // Round 3 // ---- sender should send e0, e1 to receiver ---- // Input: e0, e1: encryption of m0 and m1 from the sender // Input: choice, choice bit of receiver // Choose e0 or e1 based on choice bit in constant time func (receiver *Receiver) Round3Receiver(e0, e1 []byte, choice int) error { receiver.ec = make([]byte, len(e1)) // If c == 1, copy e1 subtle.ConstantTimeCopy(choice, receiver.ec, e1) // If c == 0, copy e0 subtle.ConstantTimeCopy(1-choice, receiver.ec, e0) AByte, errByte := receiver.A.MarshalBinary() if errByte != nil { panic(errByte) } BByte, errByte := receiver.B.MarshalBinary() if errByte != nil { panic(errByte) } bA := receiver.myGroup.NewElement() bA.Mul(receiver.A, receiver.b) bAByte, errByte := bA.MarshalBinary() if errByte != nil { panic(errByte) } // Hash the whole transcript so far hashByte := append(AByte, BByte...) hashByte = append(hashByte, bAByte...) s := sha3.NewShake128() _, errWrite := s.Write(hashByte) if errWrite != nil { panic(errWrite) } _, errRead := s.Read(receiver.kR) // kR, decryption key of mc if errRead != nil { panic(errRead) } mc, errDec := aesDecGCM(receiver.kR, receiver.ec) if errDec != nil { return errDec } receiver.mc = mc return nil } func (receiver *Receiver) Returnmc() []byte { return receiver.mc } func (sender *Sender) Returne0e1() ([]byte, []byte) { return sender.e0, sender.e1 } func (sender *Sender) Returnm0m1() ([]byte, []byte) { return sender.m0, sender.m1 } golang-github-cloudflare-circl-1.3.7/ot/simot/simotparty.go000066400000000000000000000022611454601126700240070ustar00rootroot00000000000000package simot import "github.com/cloudflare/circl/group" type Sender struct { index int // Indicate which OT m0 []byte // The M0 message from sender m1 []byte // The M1 message from sender a group.Scalar // The randomness of the sender A group.Element // [a]G B group.Element // The random group element from the receiver k0 []byte // The encryption key of M0 k1 []byte // The encryption key of M1 e0 []byte // The encryption of M0 under k0 e1 []byte // The encryption of M1 under k1 myGroup group.Group // The elliptic curve we operate in } type Receiver struct { index int // Indicate which OT c int // The choice bit of the receiver A group.Element // The random group element from the sender b group.Scalar // The randomness of the receiver B group.Element // B = [b]G if c == 0, B = A+[b]G if c == 1 kR []byte // The decryption key of receiver ec []byte // The encryption of mc mc []byte // The decrypted message from sender myGroup group.Group // The elliptic curve we operate in } golang-github-cloudflare-circl-1.3.7/pke/000077500000000000000000000000001454601126700202465ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/doc.go000066400000000000000000000001231454601126700213360ustar00rootroot00000000000000// Package pke provides a variety of public key encryption mechanisms. package pke golang-github-cloudflare-circl-1.3.7/pke/kyber/000077500000000000000000000000001454601126700213625ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/gen.go000066400000000000000000000100421454601126700224570ustar00rootroot00000000000000//go:build ignore // +build ignore // Autogenerates wrappers from templates to prevent too much duplicated code // between the code for different modes. package main import ( "bytes" "fmt" "go/format" "os" "path" "strings" "text/template" ) type Instance struct { Name string K int Eta1 int CiphertextSize int DU int DV int } func (m Instance) Pkg() string { return strings.ToLower(m.Name) } func (m Instance) Impl() string { return "impl" + m.Name } var ( Instances = []Instance{ { Name: "Kyber512", Eta1: 3, K: 2, CiphertextSize: 768, DU: 10, DV: 4, }, { Name: "Kyber768", Eta1: 2, K: 3, CiphertextSize: 1088, DU: 10, DV: 4, }, { Name: "Kyber1024", Eta1: 2, K: 4, CiphertextSize: 1568, DU: 11, DV: 5, }, } TemplateWarning = "// Code generated from" ) func main() { generatePackageFiles() generateParamsFiles() generateSourceFiles() } // Generates instance/internal/params.go from templates/params.templ.go func generateParamsFiles() { tl, err := template.ParseFiles("templates/params.templ.go") if err != nil { panic(err) } for _, mode := range Instances { buf := new(bytes.Buffer) err := tl.Execute(buf, mode) if err != nil { panic(err) } // Formating output code code, err := format.Source(buf.Bytes()) if err != nil { panic("error formating code") } res := string(code) offset := strings.Index(res, TemplateWarning) if offset == -1 { panic("Missing template warning in params.templ.go") } err = os.WriteFile(mode.Pkg()+"/internal/params.go", []byte(res[offset:]), 0o644) if err != nil { panic(err) } } } // Generates instance/kyber.go from templates/pkg.templ.go func generatePackageFiles() { tl, err := template.ParseFiles("templates/pkg.templ.go") if err != nil { panic(err) } for _, mode := range Instances { buf := new(bytes.Buffer) err := tl.Execute(buf, mode) if err != nil { panic(err) } res := string(buf.Bytes()) offset := strings.Index(res, TemplateWarning) if offset == -1 { panic("Missing template warning in pkg.templ.go") } err = os.WriteFile(mode.Pkg()+"/kyber.go", []byte(res[offset:]), 0o644) if err != nil { panic(err) } } } // Copies kyber512 source files to other modes func generateSourceFiles() { files := make(map[string][]byte) // Ignore mode specific files. ignored := func(x string) bool { return x == "params.go" || x == "params_test.go" } fs, err := os.ReadDir("kyber512/internal") if err != nil { panic(err) } // Read files for _, f := range fs { name := f.Name() if ignored(name) { continue } files[name], err = os.ReadFile(path.Join("kyber512/internal", name)) if err != nil { panic(err) } } // Go over modes for _, mode := range Instances { if mode.Name == "Kyber512" { continue } fs, err = os.ReadDir(path.Join(mode.Pkg(), "internal")) for _, f := range fs { name := f.Name() fn := path.Join(mode.Pkg(), "internal", name) if ignored(name) { continue } _, ok := files[name] if !ok { fmt.Printf("Removing superfluous file: %s\n", fn) err = os.Remove(fn) if err != nil { panic(err) } } if f.IsDir() { panic(fmt.Sprintf("%s: is a directory", fn)) } if f.Type()&os.ModeSymlink != 0 { fmt.Printf("Removing symlink: %s\n", fn) err = os.Remove(fn) if err != nil { panic(err) } } } for name, expected := range files { fn := path.Join(mode.Pkg(), "internal", name) expected = []byte(fmt.Sprintf( "%s kyber512/internal/%s by gen.go\n\n%s", TemplateWarning, name, string(expected), )) got, err := os.ReadFile(fn) if err == nil { if bytes.Equal(got, expected) { continue } } fmt.Printf("Updating %s\n", fn) err = os.WriteFile(fn, expected, 0o644) if err != nil { panic(err) } } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/000077500000000000000000000000001454601126700231765ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/000077500000000000000000000000001454601126700244665ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/amd64.go000066400000000000000000000251401454601126700257320ustar00rootroot00000000000000//go:build amd64 // +build amd64 package common import ( "golang.org/x/sys/cpu" ) // ZetasAVX2 contains all ζ used in NTT (like the Zetas array), but also // the values int16(zeta * 62209) for each zeta, which is used in // Montgomery reduction. There is some duplication and reordering as // compared to Zetas to make it more convenient for use with AVX2. var ZetasAVX2 = [...]int16{ // level 1: int16(Zetas[1]*62209) and Zetas[1] 31499, 2571, // level 2 // // int16(Zetas[2]*62209), Zetas[2], int16(Zetas[3]*62209), Zetas[3] 14746, 2970, 788, 1812, // level 3, like level 2. 13525, 1493, -12402, 1422, 28191, 287, -16694, 202, 0, 0, // padding // layer 4. offset: 1*16 // // The precomputed multiplication and zetas are grouped by 16 at a // time as used in the set of butterflies, etc. -20906, -20906, -20906, -20906, -20906, -20906, -20906, -20906, 27758, 27758, 27758, 27758, 27758, 27758, 27758, 27758, 3158, 3158, 3158, 3158, 3158, 3158, 3158, 3158, 622, 622, 622, 622, 622, 622, 622, 622, -3799, -3799, -3799, -3799, -3799, -3799, -3799, -3799, -15690, -15690, -15690, -15690, -15690, -15690, -15690, -15690, 1577, 1577, 1577, 1577, 1577, 1577, 1577, 1577, 182, 182, 182, 182, 182, 182, 182, 182, 10690, 10690, 10690, 10690, 10690, 10690, 10690, 10690, 1359, 1359, 1359, 1359, 1359, 1359, 1359, 1359, 962, 962, 962, 962, 962, 962, 962, 962, 2127, 2127, 2127, 2127, 2127, 2127, 2127, 2127, -11201, -11201, -11201, -11201, -11201, -11201, -11201, -11201, 31164, 31164, 31164, 31164, 31164, 31164, 31164, 31164, 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1468, 1468, 1468, 1468, 1468, 1468, 1468, 1468, // layer 5. offset: 9*16 -5827, -5827, -5827, -5827, 17364, 17364, 17364, 17364, -26360, -26360, -26360, -26360, -29057, -29057, -29057, -29057, 573, 573, 573, 573, 2004, 2004, 2004, 2004, 264, 264, 264, 264, 383, 383, 383, 383, 5572, 5572, 5572, 5572, -1102, -1102, -1102, -1102, 21439, 21439, 21439, 21439, -26241, -26241, -26241, -26241, 2500, 2500, 2500, 2500, 1458, 1458, 1458, 1458, 1727, 1727, 1727, 1727, 3199, 3199, 3199, 3199, -28072, -28072, -28072, -28072, 24313, 24313, 24313, 24313, -10532, -10532, -10532, -10532, 8800, 8800, 8800, 8800, 2648, 2648, 2648, 2648, 1017, 1017, 1017, 1017, 732, 732, 732, 732, 608, 608, 608, 608, 18427, 18427, 18427, 18427, 8859, 8859, 8859, 8859, 26676, 26676, 26676, 26676, -16162, -16162, -16162, -16162, 1787, 1787, 1787, 1787, 411, 411, 411, 411, 3124, 3124, 3124, 3124, 1758, 1758, 1758, 1758, // layer 6. offset: 17*16 -5689, -5689, -6516, -6516, 1497, 1497, 30967, 30967, -23564, -23564, 20179, 20179, 20711, 20711, 25081, 25081, 1223, 1223, 652, 652, 2777, 2777, 1015, 1015, 2036, 2036, 1491, 1491, 3047, 3047, 1785, 1785, -12796, -12796, 26617, 26617, 16065, 16065, -12441, -12441, 9135, 9135, -649, -649, -25986, -25986, 27837, 27837, 516, 516, 3321, 3321, 3009, 3009, 2663, 2663, 1711, 1711, 2167, 2167, 126, 126, 1469, 1469, 19884, 19884, -28249, -28249, -15886, -15886, -8898, -8898, -28309, -28309, 9076, 9076, -30198, -30198, 18250, 18250, 2476, 2476, 3239, 3239, 3058, 3058, 830, 830, 107, 107, 1908, 1908, 3082, 3082, 2378, 2378, 13427, 13427, 14017, 14017, -29155, -29155, -12756, -12756, 16832, 16832, 4312, 4312, -24155, -24155, -17914, -17914, 2931, 2931, 961, 961, 1821, 1821, 2604, 2604, 448, 448, 2264, 2264, 677, 677, 2054, 2054, // layer 7. offset: 25*16 -334, 11182, -11477, 13387, -32226, -14233, 20494, -21655, -27738, 13131, 945, -4586, -14882, 23093, 6182, 5493, 2226, 430, 555, 843, 2078, 871, 1550, 105, 422, 587, 177, 3094, 3038, 2869, 1574, 1653, 32011, -32502, 10631, 30318, 29176, -18741, -28761, 12639, -18485, 20100, 17561, 18525, -14430, 19529, -5275, -12618, 3083, 778, 1159, 3182, 2552, 1483, 2727, 1119, 1739, 644, 2457, 349, 418, 329, 3173, 3254, -31183, 20297, 25435, 2146, -7382, 15356, 24392, -32384, -20926, -6279, 10946, -14902, 24215, -11044, 16990, 14470, 817, 1097, 603, 610, 1322, 2044, 1864, 384, 2114, 3193, 1218, 1994, 2455, 220, 2142, 1670, 10336, -21497, -7933, -20198, -22501, 23211, 10907, -17442, 31637, -23859, 28644, -20257, 23998, 7757, -17422, 23132, 2144, 1799, 2051, 794, 1819, 2475, 2459, 478, 3221, 3021, 996, 991, 958, 1869, 1522, 1628, // layer 1 inverse 23132, -17422, 7757, 23998, -20257, 28644, -23859, 31637, -17442, 10907, 23211, -22501, -20198, -7933, -21497, 10336, 1628, 1522, 1869, 958, 991, 996, 3021, 3221, 478, 2459, 2475, 1819, 794, 2051, 1799, 2144, 14470, 16990, -11044, 24215, -14902, 10946, -6279, -20926, -32384, 24392, 15356, -7382, 2146, 25435, 20297, -31183, 1670, 2142, 220, 2455, 1994, 1218, 3193, 2114, 384, 1864, 2044, 1322, 610, 603, 1097, 817, -12618, -5275, 19529, -14430, 18525, 17561, 20100, -18485, 12639, -28761, -18741, 29176, 30318, 10631, -32502, 32011, 3254, 3173, 329, 418, 349, 2457, 644, 1739, 1119, 2727, 1483, 2552, 3182, 1159, 778, 3083, 5493, 6182, 23093, -14882, -4586, 945, 13131, -27738, -21655, 20494, -14233, -32226, 13387, -11477, 11182, -334, 1653, 1574, 2869, 3038, 3094, 177, 587, 422, 105, 1550, 871, 2078, 843, 555, 430, 2226, // layer 2 inverse -17914, -17914, -24155, -24155, 4312, 4312, 16832, 16832, -12756, -12756, -29155, -29155, 14017, 14017, 13427, 13427, 2054, 2054, 677, 677, 2264, 2264, 448, 448, 2604, 2604, 1821, 1821, 961, 961, 2931, 2931, 18250, 18250, -30198, -30198, 9076, 9076, -28309, -28309, -8898, -8898, -15886, -15886, -28249, -28249, 19884, 19884, 2378, 2378, 3082, 3082, 1908, 1908, 107, 107, 830, 830, 3058, 3058, 3239, 3239, 2476, 2476, 27837, 27837, -25986, -25986, -649, -649, 9135, 9135, -12441, -12441, 16065, 16065, 26617, 26617, -12796, -12796, 1469, 1469, 126, 126, 2167, 2167, 1711, 1711, 2663, 2663, 3009, 3009, 3321, 3321, 516, 516, 25081, 25081, 20711, 20711, 20179, 20179, -23564, -23564, 30967, 30967, 1497, 1497, -6516, -6516, -5689, -5689, 1785, 1785, 3047, 3047, 1491, 1491, 2036, 2036, 1015, 1015, 2777, 2777, 652, 652, 1223, 1223, // layer 3 inverse -16162, -16162, -16162, -16162, 26676, 26676, 26676, 26676, 8859, 8859, 8859, 8859, 18427, 18427, 18427, 18427, 1758, 1758, 1758, 1758, 3124, 3124, 3124, 3124, 411, 411, 411, 411, 1787, 1787, 1787, 1787, 8800, 8800, 8800, 8800, -10532, -10532, -10532, -10532, 24313, 24313, 24313, 24313, -28072, -28072, -28072, -28072, 608, 608, 608, 608, 732, 732, 732, 732, 1017, 1017, 1017, 1017, 2648, 2648, 2648, 2648, -26241, -26241, -26241, -26241, 21439, 21439, 21439, 21439, -1102, -1102, -1102, -1102, 5572, 5572, 5572, 5572, 3199, 3199, 3199, 3199, 1727, 1727, 1727, 1727, 1458, 1458, 1458, 1458, 2500, 2500, 2500, 2500, -29057, -29057, -29057, -29057, -26360, -26360, -26360, -26360, 17364, 17364, 17364, 17364, -5827, -5827, -5827, -5827, 383, 383, 383, 383, 264, 264, 264, 264, 2004, 2004, 2004, 2004, 573, 573, 573, 573, // layer 4 inverse 31164, 31164, 31164, 31164, 31164, 31164, 31164, 31164, -11201, -11201, -11201, -11201, -11201, -11201, -11201, -11201, 1468, 1468, 1468, 1468, 1468, 1468, 1468, 1468, 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1359, 1359, 1359, 1359, 1359, 1359, 1359, 1359, 10690, 10690, 10690, 10690, 10690, 10690, 10690, 10690, 2127, 2127, 2127, 2127, 2127, 2127, 2127, 2127, 962, 962, 962, 962, 962, 962, 962, 962, -15690, -15690, -15690, -15690, -15690, -15690, -15690, -15690, -3799, -3799, -3799, -3799, -3799, -3799, -3799, -3799, 182, 182, 182, 182, 182, 182, 182, 182, 1577, 1577, 1577, 1577, 1577, 1577, 1577, 1577, 27758, 27758, 27758, 27758, 27758, 27758, 27758, 27758, -20906, -20906, -20906, -20906, -20906, -20906, -20906, -20906, 622, 622, 622, 622, 622, 622, 622, 622, 3158, 3158, 3158, 3158, 3158, 3158, 3158, 3158, // layer 5 inverse -16694, 202, 28191, 287, -12402, 1422, 13525, 1493, // layer 6 inverse 788, 1812, 14746, 2970, // layer 7 inverse 31499, 2571, } // Sets p to a + b. Does not normalize coefficients. func (p *Poly) Add(a, b *Poly) { if cpu.X86.HasAVX2 { addAVX2( (*[N]int16)(p), (*[N]int16)(a), (*[N]int16)(b), ) } else { p.addGeneric(a, b) } } // Sets p to a - b. Does not normalize coefficients. func (p *Poly) Sub(a, b *Poly) { if cpu.X86.HasAVX2 { subAVX2( (*[N]int16)(p), (*[N]int16)(a), (*[N]int16)(b), ) } else { p.subGeneric(a, b) } } // Executes an in-place forward "NTT" on p. // // Assumes the coefficients are in absolute value ≤q. The resulting // coefficients are in absolute value ≤7q. If the input is in Montgomery // form, then the result is in Montgomery form and so (by linearity of the NTT) // if the input is in regular form, then the result is also in regular form. // The order of coefficients will be "tangled". These can be put back into // their proper order by calling Detangle(). func (p *Poly) NTT() { if cpu.X86.HasAVX2 { nttAVX2((*[N]int16)(p)) } else { p.nttGeneric() } } // Executes an in-place inverse "NTT" on p and multiply by the Montgomery // factor R. // // Requires coefficients to be in "tangled" order, see Tangle(). // Assumes the coefficients are in absolute value ≤q. The resulting // coefficients are in absolute value ≤q. If the input is in Montgomery // form, then the result is in Montgomery form and so (by linearity) // if the input is in regular form, then the result is also in regular form. func (p *Poly) InvNTT() { if cpu.X86.HasAVX2 { invNttAVX2((*[N]int16)(p)) } else { p.invNTTGeneric() } } // Sets p to the "pointwise" multiplication of a and b. // // That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in // Montgomery form. Products between coefficients of a and b must be strictly // bounded in absolute value by 2¹⁵q. p will be in Montgomery form and // bounded in absolute value by 2q. // // Requires a and b to be in "tangled" order, see Tangle(). p will be in // tangled order as well. func (p *Poly) MulHat(a, b *Poly) { if cpu.X86.HasAVX2 { mulHatAVX2( (*[N]int16)(p), (*[N]int16)(a), (*[N]int16)(b), ) } else { p.mulHatGeneric(a, b) } } // Puts p into the right form to be used with (among others) InvNTT(). func (p *Poly) Tangle() { if cpu.X86.HasAVX2 { tangleAVX2((*[N]int16)(p)) } // When AVX2 is not available, we use the standard order. } // Puts p back into standard form. func (p *Poly) Detangle() { if cpu.X86.HasAVX2 { detangleAVX2((*[N]int16)(p)) } // When AVX2 is not available, we use the standard order. } // Almost normalizes coefficients. // // Ensures each coefficient is in {0, …, q}. func (p *Poly) BarrettReduce() { if cpu.X86.HasAVX2 { barrettReduceAVX2((*[N]int16)(p)) } else { p.barrettReduceGeneric() } } // Normalizes coefficients. // // Ensures each coefficient is in {0, …, q-1}. func (p *Poly) Normalize() { if cpu.X86.HasAVX2 { normalizeAVX2((*[N]int16)(p)) } else { p.normalizeGeneric() } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/amd64.s000066400000000000000000001666001454601126700255760ustar00rootroot00000000000000// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. //go:build amd64 #include "textflag.h" // func addAVX2(p *[256]int16, a *[256]int16, b *[256]int16) // Requires: AVX, AVX2 TEXT ·addAVX2(SB), NOSPLIT, $0-24 MOVQ p+0(FP), AX MOVQ a+8(FP), CX MOVQ b+16(FP), DX VMOVDQU (CX), Y0 VMOVDQU 32(CX), Y2 VMOVDQU 64(CX), Y4 VMOVDQU 96(CX), Y6 VMOVDQU 128(CX), Y8 VMOVDQU 160(CX), Y10 VMOVDQU 192(CX), Y12 VMOVDQU 224(CX), Y14 VMOVDQU (DX), Y1 VMOVDQU 32(DX), Y3 VMOVDQU 64(DX), Y5 VMOVDQU 96(DX), Y7 VMOVDQU 128(DX), Y9 VMOVDQU 160(DX), Y11 VMOVDQU 192(DX), Y13 VMOVDQU 224(DX), Y15 VPADDW Y0, Y1, Y1 VPADDW Y2, Y3, Y3 VPADDW Y4, Y5, Y5 VPADDW Y6, Y7, Y7 VPADDW Y8, Y9, Y9 VPADDW Y10, Y11, Y11 VPADDW Y12, Y13, Y13 VPADDW Y14, Y15, Y15 VMOVDQU Y1, (AX) VMOVDQU Y3, 32(AX) VMOVDQU Y5, 64(AX) VMOVDQU Y7, 96(AX) VMOVDQU Y9, 128(AX) VMOVDQU Y11, 160(AX) VMOVDQU Y13, 192(AX) VMOVDQU Y15, 224(AX) VMOVDQU 256(CX), Y0 VMOVDQU 288(CX), Y2 VMOVDQU 320(CX), Y4 VMOVDQU 352(CX), Y6 VMOVDQU 384(CX), Y8 VMOVDQU 416(CX), Y10 VMOVDQU 448(CX), Y12 VMOVDQU 480(CX), Y14 VMOVDQU 256(DX), Y1 VMOVDQU 288(DX), Y3 VMOVDQU 320(DX), Y5 VMOVDQU 352(DX), Y7 VMOVDQU 384(DX), Y9 VMOVDQU 416(DX), Y11 VMOVDQU 448(DX), Y13 VMOVDQU 480(DX), Y15 VPADDW Y0, Y1, Y1 VPADDW Y2, Y3, Y3 VPADDW Y4, Y5, Y5 VPADDW Y6, Y7, Y7 VPADDW Y8, Y9, Y9 VPADDW Y10, Y11, Y11 VPADDW Y12, Y13, Y13 VPADDW Y14, Y15, Y15 VMOVDQU Y1, 256(AX) VMOVDQU Y3, 288(AX) VMOVDQU Y5, 320(AX) VMOVDQU Y7, 352(AX) VMOVDQU Y9, 384(AX) VMOVDQU Y11, 416(AX) VMOVDQU Y13, 448(AX) VMOVDQU Y15, 480(AX) RET // func subAVX2(p *[256]int16, a *[256]int16, b *[256]int16) // Requires: AVX, AVX2 TEXT ·subAVX2(SB), NOSPLIT, $0-24 MOVQ p+0(FP), AX MOVQ a+8(FP), CX MOVQ b+16(FP), DX VMOVDQU (CX), Y0 VMOVDQU 32(CX), Y2 VMOVDQU 64(CX), Y4 VMOVDQU 96(CX), Y6 VMOVDQU 128(CX), Y8 VMOVDQU 160(CX), Y10 VMOVDQU 192(CX), Y12 VMOVDQU 224(CX), Y14 VMOVDQU (DX), Y1 VMOVDQU 32(DX), Y3 VMOVDQU 64(DX), Y5 VMOVDQU 96(DX), Y7 VMOVDQU 128(DX), Y9 VMOVDQU 160(DX), Y11 VMOVDQU 192(DX), Y13 VMOVDQU 224(DX), Y15 VPSUBW Y1, Y0, Y1 VPSUBW Y3, Y2, Y3 VPSUBW Y5, Y4, Y5 VPSUBW Y7, Y6, Y7 VPSUBW Y9, Y8, Y9 VPSUBW Y11, Y10, Y11 VPSUBW Y13, Y12, Y13 VPSUBW Y15, Y14, Y15 VMOVDQU Y1, (AX) VMOVDQU Y3, 32(AX) VMOVDQU Y5, 64(AX) VMOVDQU Y7, 96(AX) VMOVDQU Y9, 128(AX) VMOVDQU Y11, 160(AX) VMOVDQU Y13, 192(AX) VMOVDQU Y15, 224(AX) VMOVDQU 256(CX), Y0 VMOVDQU 288(CX), Y2 VMOVDQU 320(CX), Y4 VMOVDQU 352(CX), Y6 VMOVDQU 384(CX), Y8 VMOVDQU 416(CX), Y10 VMOVDQU 448(CX), Y12 VMOVDQU 480(CX), Y14 VMOVDQU 256(DX), Y1 VMOVDQU 288(DX), Y3 VMOVDQU 320(DX), Y5 VMOVDQU 352(DX), Y7 VMOVDQU 384(DX), Y9 VMOVDQU 416(DX), Y11 VMOVDQU 448(DX), Y13 VMOVDQU 480(DX), Y15 VPSUBW Y1, Y0, Y1 VPSUBW Y3, Y2, Y3 VPSUBW Y5, Y4, Y5 VPSUBW Y7, Y6, Y7 VPSUBW Y9, Y8, Y9 VPSUBW Y11, Y10, Y11 VPSUBW Y13, Y12, Y13 VPSUBW Y15, Y14, Y15 VMOVDQU Y1, 256(AX) VMOVDQU Y3, 288(AX) VMOVDQU Y5, 320(AX) VMOVDQU Y7, 352(AX) VMOVDQU Y9, 384(AX) VMOVDQU Y11, 416(AX) VMOVDQU Y13, 448(AX) VMOVDQU Y15, 480(AX) RET // func nttAVX2(p *[256]int16) // Requires: AVX, AVX2 TEXT ·nttAVX2(SB), NOSPLIT, $0-8 MOVQ p+0(FP), AX LEAQ ·ZetasAVX2+0(SB), CX MOVL $0x00000d01, DX VMOVD DX, X0 VPBROADCASTW X0, Y15 VPBROADCASTW (CX), Y0 VPBROADCASTW 2(CX), Y1 VMOVDQU (AX), Y7 VMOVDQU 32(AX), Y8 VMOVDQU 64(AX), Y9 VMOVDQU 96(AX), Y10 VMOVDQU 256(AX), Y11 VMOVDQU 288(AX), Y12 VMOVDQU 320(AX), Y13 VMOVDQU 352(AX), Y14 VPMULLW Y11, Y0, Y2 VPMULLW Y12, Y0, Y3 VPMULLW Y13, Y0, Y4 VPMULLW Y14, Y0, Y5 VPMULHW Y11, Y1, Y11 VPMULHW Y12, Y1, Y12 VPMULHW Y13, Y1, Y13 VPMULHW Y14, Y1, Y14 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y11, Y2 VPSUBW Y3, Y12, Y3 VPSUBW Y4, Y13, Y4 VPSUBW Y5, Y14, Y5 VPSUBW Y2, Y7, Y11 VPSUBW Y3, Y8, Y12 VPSUBW Y4, Y9, Y13 VPSUBW Y5, Y10, Y14 VPADDW Y2, Y7, Y7 VPADDW Y3, Y8, Y8 VPADDW Y4, Y9, Y9 VPADDW Y5, Y10, Y10 VMOVDQU Y7, (AX) VMOVDQU Y8, 32(AX) VMOVDQU Y9, 64(AX) VMOVDQU Y10, 96(AX) VMOVDQU Y11, 256(AX) VMOVDQU Y12, 288(AX) VMOVDQU Y13, 320(AX) VMOVDQU Y14, 352(AX) VMOVDQU 128(AX), Y7 VMOVDQU 160(AX), Y8 VMOVDQU 192(AX), Y9 VMOVDQU 224(AX), Y10 VMOVDQU 384(AX), Y11 VMOVDQU 416(AX), Y12 VMOVDQU 448(AX), Y13 VMOVDQU 480(AX), Y14 VPMULLW Y11, Y0, Y2 VPMULLW Y12, Y0, Y3 VPMULLW Y13, Y0, Y4 VPMULLW Y14, Y0, Y5 VPMULHW Y11, Y1, Y11 VPMULHW Y12, Y1, Y12 VPMULHW Y13, Y1, Y13 VPMULHW Y14, Y1, Y14 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y11, Y2 VPSUBW Y3, Y12, Y3 VPSUBW Y4, Y13, Y4 VPSUBW Y5, Y14, Y5 VPSUBW Y2, Y7, Y11 VPSUBW Y3, Y8, Y12 VPSUBW Y4, Y9, Y13 VPSUBW Y5, Y10, Y14 VPADDW Y2, Y7, Y7 VPADDW Y3, Y8, Y8 VPADDW Y4, Y9, Y9 VPADDW Y5, Y10, Y10 VMOVDQU Y7, 128(AX) VMOVDQU Y8, 160(AX) VMOVDQU Y9, 192(AX) VMOVDQU Y10, 224(AX) VMOVDQU Y11, 384(AX) VMOVDQU Y12, 416(AX) VMOVDQU Y13, 448(AX) VMOVDQU Y14, 480(AX) VPBROADCASTW 4(CX), Y0 VPBROADCASTW 6(CX), Y1 VMOVDQU (AX), Y7 VMOVDQU 32(AX), Y8 VMOVDQU 64(AX), Y9 VMOVDQU 96(AX), Y10 VMOVDQU 128(AX), Y11 VMOVDQU 160(AX), Y12 VMOVDQU 192(AX), Y13 VMOVDQU 224(AX), Y14 VPMULLW Y11, Y0, Y2 VPMULLW Y12, Y0, Y3 VPMULLW Y13, Y0, Y4 VPMULLW Y14, Y0, Y5 VPMULHW Y11, Y1, Y11 VPMULHW Y12, Y1, Y12 VPMULHW Y13, Y1, Y13 VPMULHW Y14, Y1, Y14 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y11, Y2 VPSUBW Y3, Y12, Y3 VPSUBW Y4, Y13, Y4 VPSUBW Y5, Y14, Y5 VPSUBW Y2, Y7, Y11 VPSUBW Y3, Y8, Y12 VPSUBW Y4, Y9, Y13 VPSUBW Y5, Y10, Y14 VPADDW Y2, Y7, Y7 VPADDW Y3, Y8, Y8 VPADDW Y4, Y9, Y9 VPADDW Y5, Y10, Y10 VPBROADCASTW 12(CX), Y0 VPBROADCASTW 14(CX), Y1 VPBROADCASTW 16(CX), Y2 VPBROADCASTW 18(CX), Y3 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y13, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y13, Y3, Y13 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y9, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y13, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y9 VPSUBW Y5, Y8, Y10 VPSUBW Y6, Y11, Y13 VPSUBW Y0, Y12, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y8, Y8 VPADDW Y6, Y11, Y11 VPADDW Y0, Y12, Y12 VMOVDQU 32(CX), Y0 VMOVDQU 64(CX), Y1 VMOVDQU 96(CX), Y2 VMOVDQU 128(CX), Y3 VPERM2I128 $0x20, Y9, Y7, Y4 VPERM2I128 $0x31, Y9, Y7, Y9 VMOVDQA Y4, Y7 VPERM2I128 $0x20, Y10, Y8, Y4 VPERM2I128 $0x31, Y10, Y8, Y10 VMOVDQA Y4, Y8 VPERM2I128 $0x20, Y13, Y11, Y4 VPERM2I128 $0x31, Y13, Y11, Y13 VMOVDQA Y4, Y11 VPERM2I128 $0x20, Y14, Y12, Y4 VPERM2I128 $0x31, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPMULLW Y8, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y12, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y8, Y1, Y8 VPMULHW Y10, Y1, Y10 VPMULHW Y12, Y3, Y12 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y8, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y12, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y8 VPSUBW Y5, Y9, Y10 VPSUBW Y6, Y11, Y12 VPSUBW Y0, Y13, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y9, Y9 VPADDW Y6, Y11, Y11 VPADDW Y0, Y13, Y13 VMOVDQU 288(CX), Y0 VMOVDQU 320(CX), Y1 VMOVDQU 352(CX), Y2 VMOVDQU 384(CX), Y3 VPUNPCKLQDQ Y8, Y7, Y4 VPUNPCKHQDQ Y8, Y7, Y8 VMOVDQA Y4, Y7 VPUNPCKLQDQ Y10, Y9, Y4 VPUNPCKHQDQ Y10, Y9, Y10 VMOVDQA Y4, Y9 VPUNPCKLQDQ Y12, Y11, Y4 VPUNPCKHQDQ Y12, Y11, Y12 VMOVDQA Y4, Y11 VPUNPCKLQDQ Y14, Y13, Y4 VPUNPCKHQDQ Y14, Y13, Y14 VMOVDQA Y4, Y13 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y13, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y13, Y3, Y13 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y9, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y13, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y9 VPSUBW Y5, Y8, Y10 VPSUBW Y6, Y11, Y13 VPSUBW Y0, Y12, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y8, Y8 VPADDW Y6, Y11, Y11 VPADDW Y0, Y12, Y12 VMOVDQU 544(CX), Y0 VMOVDQU 576(CX), Y1 VMOVDQU 608(CX), Y2 VMOVDQU 640(CX), Y3 VMOVSLDUP Y9, Y4 VPBLENDD $0xaa, Y4, Y7, Y4 VPSRLQ $0x20, Y7, Y7 VPBLENDD $0xaa, Y9, Y7, Y9 VMOVDQA Y4, Y7 VMOVSLDUP Y10, Y4 VPBLENDD $0xaa, Y4, Y8, Y4 VPSRLQ $0x20, Y8, Y8 VPBLENDD $0xaa, Y10, Y8, Y10 VMOVDQA Y4, Y8 VMOVSLDUP Y13, Y4 VPBLENDD $0xaa, Y4, Y11, Y4 VPSRLQ $0x20, Y11, Y11 VPBLENDD $0xaa, Y13, Y11, Y13 VMOVDQA Y4, Y11 VMOVSLDUP Y14, Y4 VPBLENDD $0xaa, Y4, Y12, Y4 VPSRLQ $0x20, Y12, Y12 VPBLENDD $0xaa, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPMULLW Y8, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y12, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y8, Y1, Y8 VPMULHW Y10, Y1, Y10 VPMULHW Y12, Y3, Y12 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y8, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y12, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y8 VPSUBW Y5, Y9, Y10 VPSUBW Y6, Y11, Y12 VPSUBW Y0, Y13, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y9, Y9 VPADDW Y6, Y11, Y11 VPADDW Y0, Y13, Y13 VMOVDQU 800(CX), Y0 VMOVDQU 832(CX), Y1 VMOVDQU 864(CX), Y2 VMOVDQU 896(CX), Y3 VPSLLD $0x10, Y8, Y4 VPBLENDW $0xaa, Y4, Y7, Y4 VPSRLD $0x10, Y7, Y7 VPBLENDW $0xaa, Y8, Y7, Y8 VMOVDQA Y4, Y7 VPSLLD $0x10, Y10, Y4 VPBLENDW $0xaa, Y4, Y9, Y4 VPSRLD $0x10, Y9, Y9 VPBLENDW $0xaa, Y10, Y9, Y10 VMOVDQA Y4, Y9 VPSLLD $0x10, Y12, Y4 VPBLENDW $0xaa, Y4, Y11, Y4 VPSRLD $0x10, Y11, Y11 VPBLENDW $0xaa, Y12, Y11, Y12 VMOVDQA Y4, Y11 VPSLLD $0x10, Y14, Y4 VPBLENDW $0xaa, Y4, Y13, Y4 VPSRLD $0x10, Y13, Y13 VPBLENDW $0xaa, Y14, Y13, Y14 VMOVDQA Y4, Y13 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y13, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y13, Y3, Y13 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y9, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y13, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y9 VPSUBW Y5, Y8, Y10 VPSUBW Y6, Y11, Y13 VPSUBW Y0, Y12, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y8, Y8 VPADDW Y6, Y11, Y11 VPADDW Y0, Y12, Y12 VMOVDQU Y7, (AX) VMOVDQU Y8, 32(AX) VMOVDQU Y9, 64(AX) VMOVDQU Y10, 96(AX) VMOVDQU Y11, 128(AX) VMOVDQU Y12, 160(AX) VMOVDQU Y13, 192(AX) VMOVDQU Y14, 224(AX) VPBROADCASTW 8(CX), Y0 VPBROADCASTW 10(CX), Y1 VMOVDQU 256(AX), Y7 VMOVDQU 288(AX), Y8 VMOVDQU 320(AX), Y9 VMOVDQU 352(AX), Y10 VMOVDQU 384(AX), Y11 VMOVDQU 416(AX), Y12 VMOVDQU 448(AX), Y13 VMOVDQU 480(AX), Y14 VPMULLW Y11, Y0, Y2 VPMULLW Y12, Y0, Y3 VPMULLW Y13, Y0, Y4 VPMULLW Y14, Y0, Y5 VPMULHW Y11, Y1, Y11 VPMULHW Y12, Y1, Y12 VPMULHW Y13, Y1, Y13 VPMULHW Y14, Y1, Y14 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y11, Y2 VPSUBW Y3, Y12, Y3 VPSUBW Y4, Y13, Y4 VPSUBW Y5, Y14, Y5 VPSUBW Y2, Y7, Y11 VPSUBW Y3, Y8, Y12 VPSUBW Y4, Y9, Y13 VPSUBW Y5, Y10, Y14 VPADDW Y2, Y7, Y7 VPADDW Y3, Y8, Y8 VPADDW Y4, Y9, Y9 VPADDW Y5, Y10, Y10 VPBROADCASTW 20(CX), Y0 VPBROADCASTW 22(CX), Y1 VPBROADCASTW 24(CX), Y2 VPBROADCASTW 26(CX), Y3 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y13, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y13, Y3, Y13 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y9, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y13, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y9 VPSUBW Y5, Y8, Y10 VPSUBW Y6, Y11, Y13 VPSUBW Y0, Y12, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y8, Y8 VPADDW Y6, Y11, Y11 VPADDW Y0, Y12, Y12 VMOVDQU 160(CX), Y0 VMOVDQU 192(CX), Y1 VMOVDQU 224(CX), Y2 VMOVDQU 256(CX), Y3 VPERM2I128 $0x20, Y9, Y7, Y4 VPERM2I128 $0x31, Y9, Y7, Y9 VMOVDQA Y4, Y7 VPERM2I128 $0x20, Y10, Y8, Y4 VPERM2I128 $0x31, Y10, Y8, Y10 VMOVDQA Y4, Y8 VPERM2I128 $0x20, Y13, Y11, Y4 VPERM2I128 $0x31, Y13, Y11, Y13 VMOVDQA Y4, Y11 VPERM2I128 $0x20, Y14, Y12, Y4 VPERM2I128 $0x31, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPMULLW Y8, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y12, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y8, Y1, Y8 VPMULHW Y10, Y1, Y10 VPMULHW Y12, Y3, Y12 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y8, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y12, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y8 VPSUBW Y5, Y9, Y10 VPSUBW Y6, Y11, Y12 VPSUBW Y0, Y13, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y9, Y9 VPADDW Y6, Y11, Y11 VPADDW Y0, Y13, Y13 VMOVDQU 416(CX), Y0 VMOVDQU 448(CX), Y1 VMOVDQU 480(CX), Y2 VMOVDQU 512(CX), Y3 VPUNPCKLQDQ Y8, Y7, Y4 VPUNPCKHQDQ Y8, Y7, Y8 VMOVDQA Y4, Y7 VPUNPCKLQDQ Y10, Y9, Y4 VPUNPCKHQDQ Y10, Y9, Y10 VMOVDQA Y4, Y9 VPUNPCKLQDQ Y12, Y11, Y4 VPUNPCKHQDQ Y12, Y11, Y12 VMOVDQA Y4, Y11 VPUNPCKLQDQ Y14, Y13, Y4 VPUNPCKHQDQ Y14, Y13, Y14 VMOVDQA Y4, Y13 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y13, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y13, Y3, Y13 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y9, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y13, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y9 VPSUBW Y5, Y8, Y10 VPSUBW Y6, Y11, Y13 VPSUBW Y0, Y12, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y8, Y8 VPADDW Y6, Y11, Y11 VPADDW Y0, Y12, Y12 VMOVDQU 672(CX), Y0 VMOVDQU 704(CX), Y1 VMOVDQU 736(CX), Y2 VMOVDQU 768(CX), Y3 VMOVSLDUP Y9, Y4 VPBLENDD $0xaa, Y4, Y7, Y4 VPSRLQ $0x20, Y7, Y7 VPBLENDD $0xaa, Y9, Y7, Y9 VMOVDQA Y4, Y7 VMOVSLDUP Y10, Y4 VPBLENDD $0xaa, Y4, Y8, Y4 VPSRLQ $0x20, Y8, Y8 VPBLENDD $0xaa, Y10, Y8, Y10 VMOVDQA Y4, Y8 VMOVSLDUP Y13, Y4 VPBLENDD $0xaa, Y4, Y11, Y4 VPSRLQ $0x20, Y11, Y11 VPBLENDD $0xaa, Y13, Y11, Y13 VMOVDQA Y4, Y11 VMOVSLDUP Y14, Y4 VPBLENDD $0xaa, Y4, Y12, Y4 VPSRLQ $0x20, Y12, Y12 VPBLENDD $0xaa, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPMULLW Y8, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y12, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y8, Y1, Y8 VPMULHW Y10, Y1, Y10 VPMULHW Y12, Y3, Y12 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y8, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y12, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y8 VPSUBW Y5, Y9, Y10 VPSUBW Y6, Y11, Y12 VPSUBW Y0, Y13, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y9, Y9 VPADDW Y6, Y11, Y11 VPADDW Y0, Y13, Y13 VMOVDQU 928(CX), Y0 VMOVDQU 960(CX), Y1 VMOVDQU 992(CX), Y2 VMOVDQU 1024(CX), Y3 VPSLLD $0x10, Y8, Y4 VPBLENDW $0xaa, Y4, Y7, Y4 VPSRLD $0x10, Y7, Y7 VPBLENDW $0xaa, Y8, Y7, Y8 VMOVDQA Y4, Y7 VPSLLD $0x10, Y10, Y4 VPBLENDW $0xaa, Y4, Y9, Y4 VPSRLD $0x10, Y9, Y9 VPBLENDW $0xaa, Y10, Y9, Y10 VMOVDQA Y4, Y9 VPSLLD $0x10, Y12, Y4 VPBLENDW $0xaa, Y4, Y11, Y4 VPSRLD $0x10, Y11, Y11 VPBLENDW $0xaa, Y12, Y11, Y12 VMOVDQA Y4, Y11 VPSLLD $0x10, Y14, Y4 VPBLENDW $0xaa, Y4, Y13, Y4 VPSRLD $0x10, Y13, Y13 VPBLENDW $0xaa, Y14, Y13, Y14 VMOVDQA Y4, Y13 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULLW Y13, Y2, Y6 VPMULLW Y14, Y2, Y0 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y13, Y3, Y13 VPMULHW Y14, Y3, Y14 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPMULHW Y6, Y15, Y6 VPMULHW Y0, Y15, Y0 VPSUBW Y4, Y9, Y4 VPSUBW Y5, Y10, Y5 VPSUBW Y6, Y13, Y6 VPSUBW Y0, Y14, Y0 VPSUBW Y4, Y7, Y9 VPSUBW Y5, Y8, Y10 VPSUBW Y6, Y11, Y13 VPSUBW Y0, Y12, Y14 VPADDW Y4, Y7, Y7 VPADDW Y5, Y8, Y8 VPADDW Y6, Y11, Y11 VPADDW Y0, Y12, Y12 VMOVDQU Y7, 256(AX) VMOVDQU Y8, 288(AX) VMOVDQU Y9, 320(AX) VMOVDQU Y10, 352(AX) VMOVDQU Y11, 384(AX) VMOVDQU Y12, 416(AX) VMOVDQU Y13, 448(AX) VMOVDQU Y14, 480(AX) RET // func invNttAVX2(p *[256]int16) // Requires: AVX, AVX2 TEXT ·invNttAVX2(SB), NOSPLIT, $0-8 MOVQ p+0(FP), AX LEAQ ·ZetasAVX2+0(SB), CX MOVL $0x00000d01, DX VMOVD DX, X0 VPBROADCASTW X0, Y15 VMOVDQU (AX), Y7 VMOVDQU 32(AX), Y8 VMOVDQU 64(AX), Y9 VMOVDQU 96(AX), Y10 VMOVDQU 128(AX), Y11 VMOVDQU 160(AX), Y12 VMOVDQU 192(AX), Y13 VMOVDQU 224(AX), Y14 VMOVDQU 1056(CX), Y0 VMOVDQU 1088(CX), Y1 VMOVDQU 1120(CX), Y2 VMOVDQU 1152(CX), Y3 VPSUBW Y7, Y9, Y4 VPSUBW Y8, Y10, Y5 VPSUBW Y11, Y13, Y6 VPADDW Y7, Y9, Y7 VPADDW Y8, Y10, Y8 VPADDW Y11, Y13, Y11 VPMULLW Y4, Y0, Y9 VPMULLW Y5, Y0, Y10 VPSUBW Y12, Y14, Y0 VPMULLW Y6, Y2, Y13 VPADDW Y12, Y14, Y12 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y9, Y4, Y9 VPSUBW Y10, Y5, Y10 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y0, Y14 VMOVDQU 1312(CX), Y0 VMOVDQU 1344(CX), Y1 VMOVDQU 1376(CX), Y2 VMOVDQU 1408(CX), Y3 VPSLLD $0x10, Y8, Y4 VPBLENDW $0xaa, Y4, Y7, Y4 VPSRLD $0x10, Y7, Y7 VPBLENDW $0xaa, Y8, Y7, Y8 VMOVDQA Y4, Y7 VPSLLD $0x10, Y10, Y4 VPBLENDW $0xaa, Y4, Y9, Y4 VPSRLD $0x10, Y9, Y9 VPBLENDW $0xaa, Y10, Y9, Y10 VMOVDQA Y4, Y9 VPSLLD $0x10, Y12, Y4 VPBLENDW $0xaa, Y4, Y11, Y4 VPSRLD $0x10, Y11, Y11 VPBLENDW $0xaa, Y12, Y11, Y12 VMOVDQA Y4, Y11 VPSLLD $0x10, Y14, Y4 VPBLENDW $0xaa, Y4, Y13, Y4 VPSRLD $0x10, Y13, Y13 VPBLENDW $0xaa, Y14, Y13, Y14 VMOVDQA Y4, Y13 VPSUBW Y7, Y8, Y4 VPSUBW Y9, Y10, Y5 VPSUBW Y11, Y12, Y6 VPADDW Y7, Y8, Y7 VPADDW Y9, Y10, Y9 VPADDW Y11, Y12, Y11 VPMULLW Y4, Y0, Y8 VPMULLW Y5, Y0, Y10 VPSUBW Y13, Y14, Y0 VPMULLW Y6, Y2, Y12 VPADDW Y13, Y14, Y13 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y8, Y15, Y8 VPMULHW Y10, Y15, Y10 VPMULHW Y12, Y15, Y12 VPMULHW Y14, Y15, Y14 VPSUBW Y8, Y4, Y8 VPSUBW Y10, Y5, Y10 VPSUBW Y12, Y6, Y12 VPSUBW Y14, Y0, Y14 VMOVDQU 1568(CX), Y0 VMOVDQU 1600(CX), Y1 VMOVDQU 1632(CX), Y2 VMOVDQU 1664(CX), Y3 VMOVSLDUP Y9, Y4 VPBLENDD $0xaa, Y4, Y7, Y4 VPSRLQ $0x20, Y7, Y7 VPBLENDD $0xaa, Y9, Y7, Y9 VMOVDQA Y4, Y7 VMOVSLDUP Y10, Y4 VPBLENDD $0xaa, Y4, Y8, Y4 VPSRLQ $0x20, Y8, Y8 VPBLENDD $0xaa, Y10, Y8, Y10 VMOVDQA Y4, Y8 VMOVSLDUP Y13, Y4 VPBLENDD $0xaa, Y4, Y11, Y4 VPSRLQ $0x20, Y11, Y11 VPBLENDD $0xaa, Y13, Y11, Y13 VMOVDQA Y4, Y11 VMOVSLDUP Y14, Y4 VPBLENDD $0xaa, Y4, Y12, Y4 VPSRLQ $0x20, Y12, Y12 VPBLENDD $0xaa, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPSUBW Y7, Y9, Y4 VPSUBW Y8, Y10, Y5 VPSUBW Y11, Y13, Y6 VPADDW Y7, Y9, Y7 VPADDW Y8, Y10, Y8 VPADDW Y11, Y13, Y11 VPMULLW Y4, Y0, Y9 VPMULLW Y5, Y0, Y10 VPSUBW Y12, Y14, Y0 VPMULLW Y6, Y2, Y13 VPADDW Y12, Y14, Y12 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y9, Y4, Y9 VPSUBW Y10, Y5, Y10 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y0, Y14 MOVL $0x00004ebf, DX VMOVD DX, X0 VPBROADCASTW X0, Y4 VPMULHW Y4, Y7, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y7, Y7 VPMULHW Y4, Y11, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y11, Y11 VMOVDQU 1824(CX), Y0 VMOVDQU 1856(CX), Y1 VMOVDQU 1888(CX), Y2 VMOVDQU 1920(CX), Y3 VPUNPCKLQDQ Y8, Y7, Y4 VPUNPCKHQDQ Y8, Y7, Y8 VMOVDQA Y4, Y7 VPUNPCKLQDQ Y10, Y9, Y4 VPUNPCKHQDQ Y10, Y9, Y10 VMOVDQA Y4, Y9 VPUNPCKLQDQ Y12, Y11, Y4 VPUNPCKHQDQ Y12, Y11, Y12 VMOVDQA Y4, Y11 VPUNPCKLQDQ Y14, Y13, Y4 VPUNPCKHQDQ Y14, Y13, Y14 VMOVDQA Y4, Y13 VPSUBW Y7, Y8, Y4 VPSUBW Y9, Y10, Y5 VPSUBW Y11, Y12, Y6 VPADDW Y7, Y8, Y7 VPADDW Y9, Y10, Y9 VPADDW Y11, Y12, Y11 VPMULLW Y4, Y0, Y8 VPMULLW Y5, Y0, Y10 VPSUBW Y13, Y14, Y0 VPMULLW Y6, Y2, Y12 VPADDW Y13, Y14, Y13 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y8, Y15, Y8 VPMULHW Y10, Y15, Y10 VPMULHW Y12, Y15, Y12 VPMULHW Y14, Y15, Y14 VPSUBW Y8, Y4, Y8 VPSUBW Y10, Y5, Y10 VPSUBW Y12, Y6, Y12 VPSUBW Y14, Y0, Y14 VPBROADCASTW 2080(CX), Y0 VPBROADCASTW 2082(CX), Y1 VPBROADCASTW 2084(CX), Y2 VPBROADCASTW 2086(CX), Y3 VPERM2I128 $0x20, Y9, Y7, Y4 VPERM2I128 $0x31, Y9, Y7, Y9 VMOVDQA Y4, Y7 VPERM2I128 $0x20, Y10, Y8, Y4 VPERM2I128 $0x31, Y10, Y8, Y10 VMOVDQA Y4, Y8 VPERM2I128 $0x20, Y13, Y11, Y4 VPERM2I128 $0x31, Y13, Y11, Y13 VMOVDQA Y4, Y11 VPERM2I128 $0x20, Y14, Y12, Y4 VPERM2I128 $0x31, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPSUBW Y7, Y9, Y4 VPSUBW Y8, Y10, Y5 VPSUBW Y11, Y13, Y6 VPADDW Y7, Y9, Y7 VPADDW Y8, Y10, Y8 VPADDW Y11, Y13, Y11 VPMULLW Y4, Y0, Y9 VPMULLW Y5, Y0, Y10 VPSUBW Y12, Y14, Y0 VPMULLW Y6, Y2, Y13 VPADDW Y12, Y14, Y12 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y9, Y4, Y9 VPSUBW Y10, Y5, Y10 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y0, Y14 MOVL $0x00004ebf, DX VMOVD DX, X0 VPBROADCASTW X0, Y4 VPMULHW Y4, Y7, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y7, Y7 VPMULHW Y4, Y11, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y11, Y11 VPBROADCASTW 2096(CX), Y0 VPBROADCASTW 2098(CX), Y1 VPSUBW Y7, Y11, Y4 VPSUBW Y8, Y12, Y5 VPSUBW Y9, Y13, Y6 VPADDW Y7, Y11, Y7 VPADDW Y8, Y12, Y8 VPADDW Y9, Y13, Y9 VPMULLW Y4, Y0, Y11 VPMULLW Y5, Y0, Y12 VPSUBW Y10, Y14, Y2 VPMULLW Y6, Y0, Y13 VPADDW Y10, Y14, Y10 VPMULLW Y2, Y0, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y1, Y6 VPMULHW Y2, Y1, Y2 VPMULHW Y11, Y15, Y11 VPMULHW Y12, Y15, Y12 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y11, Y4, Y11 VPSUBW Y12, Y5, Y12 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y2, Y14 VMOVDQU Y7, (AX) VMOVDQU Y8, 32(AX) VMOVDQU Y9, 64(AX) VMOVDQU Y10, 96(AX) VMOVDQU Y11, 128(AX) VMOVDQU Y12, 160(AX) VMOVDQU Y13, 192(AX) VMOVDQU Y14, 224(AX) VMOVDQU 256(AX), Y7 VMOVDQU 288(AX), Y8 VMOVDQU 320(AX), Y9 VMOVDQU 352(AX), Y10 VMOVDQU 384(AX), Y11 VMOVDQU 416(AX), Y12 VMOVDQU 448(AX), Y13 VMOVDQU 480(AX), Y14 VMOVDQU 1184(CX), Y0 VMOVDQU 1216(CX), Y1 VMOVDQU 1248(CX), Y2 VMOVDQU 1280(CX), Y3 VPSUBW Y7, Y9, Y4 VPSUBW Y8, Y10, Y5 VPSUBW Y11, Y13, Y6 VPADDW Y7, Y9, Y7 VPADDW Y8, Y10, Y8 VPADDW Y11, Y13, Y11 VPMULLW Y4, Y0, Y9 VPMULLW Y5, Y0, Y10 VPSUBW Y12, Y14, Y0 VPMULLW Y6, Y2, Y13 VPADDW Y12, Y14, Y12 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y9, Y4, Y9 VPSUBW Y10, Y5, Y10 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y0, Y14 VMOVDQU 1440(CX), Y0 VMOVDQU 1472(CX), Y1 VMOVDQU 1504(CX), Y2 VMOVDQU 1536(CX), Y3 VPSLLD $0x10, Y8, Y4 VPBLENDW $0xaa, Y4, Y7, Y4 VPSRLD $0x10, Y7, Y7 VPBLENDW $0xaa, Y8, Y7, Y8 VMOVDQA Y4, Y7 VPSLLD $0x10, Y10, Y4 VPBLENDW $0xaa, Y4, Y9, Y4 VPSRLD $0x10, Y9, Y9 VPBLENDW $0xaa, Y10, Y9, Y10 VMOVDQA Y4, Y9 VPSLLD $0x10, Y12, Y4 VPBLENDW $0xaa, Y4, Y11, Y4 VPSRLD $0x10, Y11, Y11 VPBLENDW $0xaa, Y12, Y11, Y12 VMOVDQA Y4, Y11 VPSLLD $0x10, Y14, Y4 VPBLENDW $0xaa, Y4, Y13, Y4 VPSRLD $0x10, Y13, Y13 VPBLENDW $0xaa, Y14, Y13, Y14 VMOVDQA Y4, Y13 VPSUBW Y7, Y8, Y4 VPSUBW Y9, Y10, Y5 VPSUBW Y11, Y12, Y6 VPADDW Y7, Y8, Y7 VPADDW Y9, Y10, Y9 VPADDW Y11, Y12, Y11 VPMULLW Y4, Y0, Y8 VPMULLW Y5, Y0, Y10 VPSUBW Y13, Y14, Y0 VPMULLW Y6, Y2, Y12 VPADDW Y13, Y14, Y13 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y8, Y15, Y8 VPMULHW Y10, Y15, Y10 VPMULHW Y12, Y15, Y12 VPMULHW Y14, Y15, Y14 VPSUBW Y8, Y4, Y8 VPSUBW Y10, Y5, Y10 VPSUBW Y12, Y6, Y12 VPSUBW Y14, Y0, Y14 VMOVDQU 1696(CX), Y0 VMOVDQU 1728(CX), Y1 VMOVDQU 1760(CX), Y2 VMOVDQU 1792(CX), Y3 VMOVSLDUP Y9, Y4 VPBLENDD $0xaa, Y4, Y7, Y4 VPSRLQ $0x20, Y7, Y7 VPBLENDD $0xaa, Y9, Y7, Y9 VMOVDQA Y4, Y7 VMOVSLDUP Y10, Y4 VPBLENDD $0xaa, Y4, Y8, Y4 VPSRLQ $0x20, Y8, Y8 VPBLENDD $0xaa, Y10, Y8, Y10 VMOVDQA Y4, Y8 VMOVSLDUP Y13, Y4 VPBLENDD $0xaa, Y4, Y11, Y4 VPSRLQ $0x20, Y11, Y11 VPBLENDD $0xaa, Y13, Y11, Y13 VMOVDQA Y4, Y11 VMOVSLDUP Y14, Y4 VPBLENDD $0xaa, Y4, Y12, Y4 VPSRLQ $0x20, Y12, Y12 VPBLENDD $0xaa, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPSUBW Y7, Y9, Y4 VPSUBW Y8, Y10, Y5 VPSUBW Y11, Y13, Y6 VPADDW Y7, Y9, Y7 VPADDW Y8, Y10, Y8 VPADDW Y11, Y13, Y11 VPMULLW Y4, Y0, Y9 VPMULLW Y5, Y0, Y10 VPSUBW Y12, Y14, Y0 VPMULLW Y6, Y2, Y13 VPADDW Y12, Y14, Y12 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y9, Y4, Y9 VPSUBW Y10, Y5, Y10 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y0, Y14 MOVL $0x00004ebf, DX VMOVD DX, X0 VPBROADCASTW X0, Y4 VPMULHW Y4, Y7, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y7, Y7 VPMULHW Y4, Y11, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y11, Y11 VMOVDQU 1952(CX), Y0 VMOVDQU 1984(CX), Y1 VMOVDQU 2016(CX), Y2 VMOVDQU 2048(CX), Y3 VPUNPCKLQDQ Y8, Y7, Y4 VPUNPCKHQDQ Y8, Y7, Y8 VMOVDQA Y4, Y7 VPUNPCKLQDQ Y10, Y9, Y4 VPUNPCKHQDQ Y10, Y9, Y10 VMOVDQA Y4, Y9 VPUNPCKLQDQ Y12, Y11, Y4 VPUNPCKHQDQ Y12, Y11, Y12 VMOVDQA Y4, Y11 VPUNPCKLQDQ Y14, Y13, Y4 VPUNPCKHQDQ Y14, Y13, Y14 VMOVDQA Y4, Y13 VPSUBW Y7, Y8, Y4 VPSUBW Y9, Y10, Y5 VPSUBW Y11, Y12, Y6 VPADDW Y7, Y8, Y7 VPADDW Y9, Y10, Y9 VPADDW Y11, Y12, Y11 VPMULLW Y4, Y0, Y8 VPMULLW Y5, Y0, Y10 VPSUBW Y13, Y14, Y0 VPMULLW Y6, Y2, Y12 VPADDW Y13, Y14, Y13 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y8, Y15, Y8 VPMULHW Y10, Y15, Y10 VPMULHW Y12, Y15, Y12 VPMULHW Y14, Y15, Y14 VPSUBW Y8, Y4, Y8 VPSUBW Y10, Y5, Y10 VPSUBW Y12, Y6, Y12 VPSUBW Y14, Y0, Y14 VPBROADCASTW 2088(CX), Y0 VPBROADCASTW 2090(CX), Y1 VPBROADCASTW 2092(CX), Y2 VPBROADCASTW 2094(CX), Y3 VPERM2I128 $0x20, Y9, Y7, Y4 VPERM2I128 $0x31, Y9, Y7, Y9 VMOVDQA Y4, Y7 VPERM2I128 $0x20, Y10, Y8, Y4 VPERM2I128 $0x31, Y10, Y8, Y10 VMOVDQA Y4, Y8 VPERM2I128 $0x20, Y13, Y11, Y4 VPERM2I128 $0x31, Y13, Y11, Y13 VMOVDQA Y4, Y11 VPERM2I128 $0x20, Y14, Y12, Y4 VPERM2I128 $0x31, Y14, Y12, Y14 VMOVDQA Y4, Y12 VPSUBW Y7, Y9, Y4 VPSUBW Y8, Y10, Y5 VPSUBW Y11, Y13, Y6 VPADDW Y7, Y9, Y7 VPADDW Y8, Y10, Y8 VPADDW Y11, Y13, Y11 VPMULLW Y4, Y0, Y9 VPMULLW Y5, Y0, Y10 VPSUBW Y12, Y14, Y0 VPMULLW Y6, Y2, Y13 VPADDW Y12, Y14, Y12 VPMULLW Y0, Y2, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y3, Y6 VPMULHW Y0, Y3, Y0 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y9, Y4, Y9 VPSUBW Y10, Y5, Y10 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y0, Y14 MOVL $0x00004ebf, DX VMOVD DX, X0 VPBROADCASTW X0, Y4 VPMULHW Y4, Y7, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y7, Y7 VPMULHW Y4, Y11, Y5 VPSRAW $0x0a, Y5, Y5 VPMULLW Y15, Y5, Y5 VPSUBW Y5, Y11, Y11 VPBROADCASTW 2100(CX), Y0 VPBROADCASTW 2102(CX), Y1 VPSUBW Y7, Y11, Y4 VPSUBW Y8, Y12, Y5 VPSUBW Y9, Y13, Y6 VPADDW Y7, Y11, Y7 VPADDW Y8, Y12, Y8 VPADDW Y9, Y13, Y9 VPMULLW Y4, Y0, Y11 VPMULLW Y5, Y0, Y12 VPSUBW Y10, Y14, Y2 VPMULLW Y6, Y0, Y13 VPADDW Y10, Y14, Y10 VPMULLW Y2, Y0, Y14 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y6, Y1, Y6 VPMULHW Y2, Y1, Y2 VPMULHW Y11, Y15, Y11 VPMULHW Y12, Y15, Y12 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y11, Y4, Y11 VPSUBW Y12, Y5, Y12 VPSUBW Y13, Y6, Y13 VPSUBW Y14, Y2, Y14 VMOVDQU Y7, 256(AX) VMOVDQU Y8, 288(AX) VMOVDQU Y9, 320(AX) VMOVDQU Y10, 352(AX) VMOVDQU Y11, 384(AX) VMOVDQU Y12, 416(AX) VMOVDQU Y13, 448(AX) VMOVDQU Y14, 480(AX) VPBROADCASTW 2104(CX), Y0 VPBROADCASTW 2106(CX), Y1 VMOVDQU (AX), Y7 VMOVDQU 32(AX), Y8 VMOVDQU 64(AX), Y9 VMOVDQU 96(AX), Y10 VMOVDQU 256(AX), Y11 VMOVDQU 288(AX), Y12 VMOVDQU 320(AX), Y13 VMOVDQU 352(AX), Y14 VPSUBW Y7, Y11, Y2 VPSUBW Y8, Y12, Y3 VPSUBW Y9, Y13, Y4 VPADDW Y7, Y11, Y7 VPADDW Y8, Y12, Y8 VPADDW Y9, Y13, Y9 VPMULLW Y2, Y0, Y11 VPMULLW Y3, Y0, Y12 VPSUBW Y10, Y14, Y5 VPMULLW Y4, Y0, Y13 VPADDW Y10, Y14, Y10 VPMULLW Y5, Y0, Y14 VPMULHW Y2, Y1, Y2 VPMULHW Y3, Y1, Y3 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y11, Y15, Y11 VPMULHW Y12, Y15, Y12 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y11, Y2, Y11 VPSUBW Y12, Y3, Y12 VPSUBW Y13, Y4, Y13 VPSUBW Y14, Y5, Y14 MOVL $0xffffd8a1, DX VMOVD DX, X0 VPBROADCASTW X0, Y0 MOVL $0x000005a1, DX VMOVD DX, X1 VPBROADCASTW X1, Y1 VPMULLW Y7, Y0, Y2 VPMULLW Y8, Y0, Y3 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULHW Y7, Y1, Y7 VPMULHW Y8, Y1, Y8 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y7, Y7 VPSUBW Y3, Y8, Y8 VPSUBW Y4, Y9, Y9 VPSUBW Y5, Y10, Y10 VPMULLW Y11, Y0, Y2 VPMULLW Y12, Y0, Y3 VPMULLW Y13, Y0, Y4 VPMULLW Y14, Y0, Y5 VPMULHW Y11, Y1, Y11 VPMULHW Y12, Y1, Y12 VPMULHW Y13, Y1, Y13 VPMULHW Y14, Y1, Y14 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y11, Y11 VPSUBW Y3, Y12, Y12 VPSUBW Y4, Y13, Y13 VPSUBW Y5, Y14, Y14 VMOVDQU Y7, (AX) VMOVDQU Y8, 32(AX) VMOVDQU Y9, 64(AX) VMOVDQU Y10, 96(AX) VMOVDQU Y11, 256(AX) VMOVDQU Y12, 288(AX) VMOVDQU Y13, 320(AX) VMOVDQU Y14, 352(AX) VPBROADCASTW 2104(CX), Y0 VPBROADCASTW 2106(CX), Y1 VMOVDQU 128(AX), Y7 VMOVDQU 160(AX), Y8 VMOVDQU 192(AX), Y9 VMOVDQU 224(AX), Y10 VMOVDQU 384(AX), Y11 VMOVDQU 416(AX), Y12 VMOVDQU 448(AX), Y13 VMOVDQU 480(AX), Y14 VPSUBW Y7, Y11, Y2 VPSUBW Y8, Y12, Y3 VPSUBW Y9, Y13, Y4 VPADDW Y7, Y11, Y7 VPADDW Y8, Y12, Y8 VPADDW Y9, Y13, Y9 VPMULLW Y2, Y0, Y11 VPMULLW Y3, Y0, Y12 VPSUBW Y10, Y14, Y5 VPMULLW Y4, Y0, Y13 VPADDW Y10, Y14, Y10 VPMULLW Y5, Y0, Y14 VPMULHW Y2, Y1, Y2 VPMULHW Y3, Y1, Y3 VPMULHW Y4, Y1, Y4 VPMULHW Y5, Y1, Y5 VPMULHW Y11, Y15, Y11 VPMULHW Y12, Y15, Y12 VPMULHW Y13, Y15, Y13 VPMULHW Y14, Y15, Y14 VPSUBW Y11, Y2, Y11 VPSUBW Y12, Y3, Y12 VPSUBW Y13, Y4, Y13 VPSUBW Y14, Y5, Y14 MOVL $0xffffd8a1, CX VMOVD CX, X0 VPBROADCASTW X0, Y0 MOVL $0x000005a1, CX VMOVD CX, X1 VPBROADCASTW X1, Y1 VPMULLW Y7, Y0, Y2 VPMULLW Y8, Y0, Y3 VPMULLW Y9, Y0, Y4 VPMULLW Y10, Y0, Y5 VPMULHW Y7, Y1, Y7 VPMULHW Y8, Y1, Y8 VPMULHW Y9, Y1, Y9 VPMULHW Y10, Y1, Y10 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y7, Y7 VPSUBW Y3, Y8, Y8 VPSUBW Y4, Y9, Y9 VPSUBW Y5, Y10, Y10 VPMULLW Y11, Y0, Y2 VPMULLW Y12, Y0, Y3 VPMULLW Y13, Y0, Y4 VPMULLW Y14, Y0, Y5 VPMULHW Y11, Y1, Y11 VPMULHW Y12, Y1, Y12 VPMULHW Y13, Y1, Y13 VPMULHW Y14, Y1, Y14 VPMULHW Y2, Y15, Y2 VPMULHW Y3, Y15, Y3 VPMULHW Y4, Y15, Y4 VPMULHW Y5, Y15, Y5 VPSUBW Y2, Y11, Y11 VPSUBW Y3, Y12, Y12 VPSUBW Y4, Y13, Y13 VPSUBW Y5, Y14, Y14 VMOVDQU Y7, 128(AX) VMOVDQU Y8, 160(AX) VMOVDQU Y9, 192(AX) VMOVDQU Y10, 224(AX) VMOVDQU Y11, 384(AX) VMOVDQU Y12, 416(AX) VMOVDQU Y13, 448(AX) VMOVDQU Y14, 480(AX) RET // func mulHatAVX2(p *[256]int16, a *[256]int16, b *[256]int16) // Requires: AVX, AVX2 TEXT ·mulHatAVX2(SB), NOSPLIT, $8-24 MOVQ p+0(FP), AX MOVQ a+8(FP), CX MOVQ b+16(FP), DX LEAQ ·ZetasAVX2+0(SB), BX MOVL $0xfffff301, SI VMOVD SI, X0 VPBROADCASTW X0, Y14 MOVL $0x00000d01, SI VMOVD SI, X0 VPBROADCASTW X0, Y15 VMOVDQU (CX), Y0 VMOVDQU 32(CX), Y1 VMOVDQU 64(CX), Y2 VMOVDQU 96(CX), Y3 VMOVDQU (DX), Y4 VMOVDQU 32(DX), Y5 VMOVDQU 64(DX), Y6 VMOVDQU 96(DX), Y7 VPMULLW Y1, Y5, Y8 VPMULLW Y0, Y4, Y9 VPMULLW Y0, Y5, Y10 VPMULLW Y1, Y4, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y1, Y5, Y12 VPMULHW Y0, Y4, Y13 VPMULHW Y0, Y5, Y0 VPMULHW Y1, Y4, Y1 VMOVDQA Y12, Y4 VMOVDQA Y13, Y5 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y4, Y4 VPSUBW Y9, Y5, Y5 VPSUBW Y10, Y0, Y0 VPSUBW Y11, Y1, Y1 VMOVDQU 800(BX), Y12 VMOVDQU 832(BX), Y13 VPMULLW Y4, Y12, Y8 VPMULHW Y4, Y13, Y4 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y4, Y4 VPADDW Y4, Y5, Y4 VPADDW Y0, Y1, Y5 VPMULLW Y3, Y7, Y8 VPMULLW Y2, Y6, Y9 VPMULLW Y2, Y7, Y10 VPMULLW Y3, Y6, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y3, Y7, Y12 VPMULHW Y2, Y6, Y13 VPMULHW Y2, Y7, Y2 VPMULHW Y3, Y6, Y3 VMOVDQA Y12, Y6 VMOVDQA Y13, Y7 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y6, Y6 VPSUBW Y9, Y7, Y7 VPSUBW Y10, Y2, Y2 VPSUBW Y11, Y3, Y3 VMOVDQU 800(BX), Y12 VMOVDQU 832(BX), Y13 VPMULLW Y6, Y12, Y8 VPMULHW Y6, Y13, Y6 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y6, Y6 VPSUBW Y6, Y7, Y6 VPADDW Y2, Y3, Y7 VMOVDQU Y4, (AX) VMOVDQU Y5, 32(AX) VMOVDQU Y6, 64(AX) VMOVDQU Y7, 96(AX) VMOVDQU 128(CX), Y0 VMOVDQU 160(CX), Y1 VMOVDQU 192(CX), Y2 VMOVDQU 224(CX), Y3 VMOVDQU 128(DX), Y4 VMOVDQU 160(DX), Y5 VMOVDQU 192(DX), Y6 VMOVDQU 224(DX), Y7 VPMULLW Y1, Y5, Y8 VPMULLW Y0, Y4, Y9 VPMULLW Y0, Y5, Y10 VPMULLW Y1, Y4, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y1, Y5, Y12 VPMULHW Y0, Y4, Y13 VPMULHW Y0, Y5, Y0 VPMULHW Y1, Y4, Y1 VMOVDQA Y12, Y4 VMOVDQA Y13, Y5 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y4, Y4 VPSUBW Y9, Y5, Y5 VPSUBW Y10, Y0, Y0 VPSUBW Y11, Y1, Y1 VMOVDQU 864(BX), Y12 VMOVDQU 896(BX), Y13 VPMULLW Y4, Y12, Y8 VPMULHW Y4, Y13, Y4 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y4, Y4 VPADDW Y4, Y5, Y4 VPADDW Y0, Y1, Y5 VPMULLW Y3, Y7, Y8 VPMULLW Y2, Y6, Y9 VPMULLW Y2, Y7, Y10 VPMULLW Y3, Y6, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y3, Y7, Y12 VPMULHW Y2, Y6, Y13 VPMULHW Y2, Y7, Y2 VPMULHW Y3, Y6, Y3 VMOVDQA Y12, Y6 VMOVDQA Y13, Y7 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y6, Y6 VPSUBW Y9, Y7, Y7 VPSUBW Y10, Y2, Y2 VPSUBW Y11, Y3, Y3 VMOVDQU 864(BX), Y12 VMOVDQU 896(BX), Y13 VPMULLW Y6, Y12, Y8 VPMULHW Y6, Y13, Y6 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y6, Y6 VPSUBW Y6, Y7, Y6 VPADDW Y2, Y3, Y7 VMOVDQU Y4, 128(AX) VMOVDQU Y5, 160(AX) VMOVDQU Y6, 192(AX) VMOVDQU Y7, 224(AX) VMOVDQU 256(CX), Y0 VMOVDQU 288(CX), Y1 VMOVDQU 320(CX), Y2 VMOVDQU 352(CX), Y3 VMOVDQU 256(DX), Y4 VMOVDQU 288(DX), Y5 VMOVDQU 320(DX), Y6 VMOVDQU 352(DX), Y7 VPMULLW Y1, Y5, Y8 VPMULLW Y0, Y4, Y9 VPMULLW Y0, Y5, Y10 VPMULLW Y1, Y4, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y1, Y5, Y12 VPMULHW Y0, Y4, Y13 VPMULHW Y0, Y5, Y0 VPMULHW Y1, Y4, Y1 VMOVDQA Y12, Y4 VMOVDQA Y13, Y5 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y4, Y4 VPSUBW Y9, Y5, Y5 VPSUBW Y10, Y0, Y0 VPSUBW Y11, Y1, Y1 VMOVDQU 928(BX), Y12 VMOVDQU 960(BX), Y13 VPMULLW Y4, Y12, Y8 VPMULHW Y4, Y13, Y4 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y4, Y4 VPADDW Y4, Y5, Y4 VPADDW Y0, Y1, Y5 VPMULLW Y3, Y7, Y8 VPMULLW Y2, Y6, Y9 VPMULLW Y2, Y7, Y10 VPMULLW Y3, Y6, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y3, Y7, Y12 VPMULHW Y2, Y6, Y13 VPMULHW Y2, Y7, Y2 VPMULHW Y3, Y6, Y3 VMOVDQA Y12, Y6 VMOVDQA Y13, Y7 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y6, Y6 VPSUBW Y9, Y7, Y7 VPSUBW Y10, Y2, Y2 VPSUBW Y11, Y3, Y3 VMOVDQU 928(BX), Y12 VMOVDQU 960(BX), Y13 VPMULLW Y6, Y12, Y8 VPMULHW Y6, Y13, Y6 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y6, Y6 VPSUBW Y6, Y7, Y6 VPADDW Y2, Y3, Y7 VMOVDQU Y4, 256(AX) VMOVDQU Y5, 288(AX) VMOVDQU Y6, 320(AX) VMOVDQU Y7, 352(AX) VMOVDQU 384(CX), Y0 VMOVDQU 416(CX), Y1 VMOVDQU 448(CX), Y2 VMOVDQU 480(CX), Y3 VMOVDQU 384(DX), Y4 VMOVDQU 416(DX), Y5 VMOVDQU 448(DX), Y6 VMOVDQU 480(DX), Y7 VPMULLW Y1, Y5, Y8 VPMULLW Y0, Y4, Y9 VPMULLW Y0, Y5, Y10 VPMULLW Y1, Y4, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y1, Y5, Y12 VPMULHW Y0, Y4, Y13 VPMULHW Y0, Y5, Y0 VPMULHW Y1, Y4, Y1 VMOVDQA Y12, Y4 VMOVDQA Y13, Y5 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y4, Y4 VPSUBW Y9, Y5, Y5 VPSUBW Y10, Y0, Y0 VPSUBW Y11, Y1, Y1 VMOVDQU 992(BX), Y12 VMOVDQU 1024(BX), Y13 VPMULLW Y4, Y12, Y8 VPMULHW Y4, Y13, Y4 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y4, Y4 VPADDW Y4, Y5, Y4 VPADDW Y0, Y1, Y5 VPMULLW Y3, Y7, Y8 VPMULLW Y2, Y6, Y9 VPMULLW Y2, Y7, Y10 VPMULLW Y3, Y6, Y11 VPMULLW Y8, Y14, Y8 VPMULLW Y9, Y14, Y9 VPMULLW Y10, Y14, Y10 VPMULLW Y11, Y14, Y11 VPMULHW Y3, Y7, Y12 VPMULHW Y2, Y6, Y13 VPMULHW Y2, Y7, Y2 VPMULHW Y3, Y6, Y3 VMOVDQA Y12, Y6 VMOVDQA Y13, Y7 VPMULHW Y8, Y15, Y8 VPMULHW Y9, Y15, Y9 VPMULHW Y10, Y15, Y10 VPMULHW Y11, Y15, Y11 VPSUBW Y8, Y6, Y6 VPSUBW Y9, Y7, Y7 VPSUBW Y10, Y2, Y2 VPSUBW Y11, Y3, Y3 VMOVDQU 992(BX), Y12 VMOVDQU 1024(BX), Y13 VPMULLW Y6, Y12, Y8 VPMULHW Y6, Y13, Y6 VPMULHW Y8, Y15, Y8 VPSUBW Y8, Y6, Y6 VPSUBW Y6, Y7, Y6 VPADDW Y2, Y3, Y7 VMOVDQU Y4, 384(AX) VMOVDQU Y5, 416(AX) VMOVDQU Y6, 448(AX) VMOVDQU Y7, 480(AX) RET // func detangleAVX2(p *[256]int16) // Requires: AVX, AVX2 TEXT ·detangleAVX2(SB), NOSPLIT, $0-8 MOVQ p+0(FP), AX VMOVDQU (AX), Y0 VMOVDQU 32(AX), Y1 VMOVDQU 64(AX), Y2 VMOVDQU 96(AX), Y3 VMOVDQU 128(AX), Y4 VMOVDQU 160(AX), Y5 VMOVDQU 192(AX), Y6 VMOVDQU 224(AX), Y7 VPSLLD $0x10, Y1, Y8 VPBLENDW $0xaa, Y8, Y0, Y8 VPSRLD $0x10, Y0, Y0 VPBLENDW $0xaa, Y1, Y0, Y1 VMOVDQA Y8, Y0 VPSLLD $0x10, Y3, Y8 VPBLENDW $0xaa, Y8, Y2, Y8 VPSRLD $0x10, Y2, Y2 VPBLENDW $0xaa, Y3, Y2, Y3 VMOVDQA Y8, Y2 VPSLLD $0x10, Y5, Y8 VPBLENDW $0xaa, Y8, Y4, Y8 VPSRLD $0x10, Y4, Y4 VPBLENDW $0xaa, Y5, Y4, Y5 VMOVDQA Y8, Y4 VPSLLD $0x10, Y7, Y8 VPBLENDW $0xaa, Y8, Y6, Y8 VPSRLD $0x10, Y6, Y6 VPBLENDW $0xaa, Y7, Y6, Y7 VMOVDQA Y8, Y6 VMOVSLDUP Y2, Y8 VPBLENDD $0xaa, Y8, Y0, Y8 VPSRLQ $0x20, Y0, Y0 VPBLENDD $0xaa, Y2, Y0, Y2 VMOVDQA Y8, Y0 VMOVSLDUP Y3, Y8 VPBLENDD $0xaa, Y8, Y1, Y8 VPSRLQ $0x20, Y1, Y1 VPBLENDD $0xaa, Y3, Y1, Y3 VMOVDQA Y8, Y1 VMOVSLDUP Y6, Y8 VPBLENDD $0xaa, Y8, Y4, Y8 VPSRLQ $0x20, Y4, Y4 VPBLENDD $0xaa, Y6, Y4, Y6 VMOVDQA Y8, Y4 VMOVSLDUP Y7, Y8 VPBLENDD $0xaa, Y8, Y5, Y8 VPSRLQ $0x20, Y5, Y5 VPBLENDD $0xaa, Y7, Y5, Y7 VMOVDQA Y8, Y5 VPUNPCKLQDQ Y1, Y0, Y8 VPUNPCKHQDQ Y1, Y0, Y1 VMOVDQA Y8, Y0 VPUNPCKLQDQ Y3, Y2, Y8 VPUNPCKHQDQ Y3, Y2, Y3 VMOVDQA Y8, Y2 VPUNPCKLQDQ Y5, Y4, Y8 VPUNPCKHQDQ Y5, Y4, Y5 VMOVDQA Y8, Y4 VPUNPCKLQDQ Y7, Y6, Y8 VPUNPCKHQDQ Y7, Y6, Y7 VMOVDQA Y8, Y6 VPERM2I128 $0x20, Y2, Y0, Y8 VPERM2I128 $0x31, Y2, Y0, Y2 VMOVDQA Y8, Y0 VPERM2I128 $0x20, Y3, Y1, Y8 VPERM2I128 $0x31, Y3, Y1, Y3 VMOVDQA Y8, Y1 VPERM2I128 $0x20, Y6, Y4, Y8 VPERM2I128 $0x31, Y6, Y4, Y6 VMOVDQA Y8, Y4 VPERM2I128 $0x20, Y7, Y5, Y8 VPERM2I128 $0x31, Y7, Y5, Y7 VMOVDQA Y8, Y5 VMOVDQU Y0, (AX) VMOVDQU Y1, 32(AX) VMOVDQU Y2, 64(AX) VMOVDQU Y3, 96(AX) VMOVDQU Y4, 128(AX) VMOVDQU Y5, 160(AX) VMOVDQU Y6, 192(AX) VMOVDQU Y7, 224(AX) VMOVDQU 256(AX), Y0 VMOVDQU 288(AX), Y1 VMOVDQU 320(AX), Y2 VMOVDQU 352(AX), Y3 VMOVDQU 384(AX), Y4 VMOVDQU 416(AX), Y5 VMOVDQU 448(AX), Y6 VMOVDQU 480(AX), Y7 VPSLLD $0x10, Y1, Y8 VPBLENDW $0xaa, Y8, Y0, Y8 VPSRLD $0x10, Y0, Y0 VPBLENDW $0xaa, Y1, Y0, Y1 VMOVDQA Y8, Y0 VPSLLD $0x10, Y3, Y8 VPBLENDW $0xaa, Y8, Y2, Y8 VPSRLD $0x10, Y2, Y2 VPBLENDW $0xaa, Y3, Y2, Y3 VMOVDQA Y8, Y2 VPSLLD $0x10, Y5, Y8 VPBLENDW $0xaa, Y8, Y4, Y8 VPSRLD $0x10, Y4, Y4 VPBLENDW $0xaa, Y5, Y4, Y5 VMOVDQA Y8, Y4 VPSLLD $0x10, Y7, Y8 VPBLENDW $0xaa, Y8, Y6, Y8 VPSRLD $0x10, Y6, Y6 VPBLENDW $0xaa, Y7, Y6, Y7 VMOVDQA Y8, Y6 VMOVSLDUP Y2, Y8 VPBLENDD $0xaa, Y8, Y0, Y8 VPSRLQ $0x20, Y0, Y0 VPBLENDD $0xaa, Y2, Y0, Y2 VMOVDQA Y8, Y0 VMOVSLDUP Y3, Y8 VPBLENDD $0xaa, Y8, Y1, Y8 VPSRLQ $0x20, Y1, Y1 VPBLENDD $0xaa, Y3, Y1, Y3 VMOVDQA Y8, Y1 VMOVSLDUP Y6, Y8 VPBLENDD $0xaa, Y8, Y4, Y8 VPSRLQ $0x20, Y4, Y4 VPBLENDD $0xaa, Y6, Y4, Y6 VMOVDQA Y8, Y4 VMOVSLDUP Y7, Y8 VPBLENDD $0xaa, Y8, Y5, Y8 VPSRLQ $0x20, Y5, Y5 VPBLENDD $0xaa, Y7, Y5, Y7 VMOVDQA Y8, Y5 VPUNPCKLQDQ Y1, Y0, Y8 VPUNPCKHQDQ Y1, Y0, Y1 VMOVDQA Y8, Y0 VPUNPCKLQDQ Y3, Y2, Y8 VPUNPCKHQDQ Y3, Y2, Y3 VMOVDQA Y8, Y2 VPUNPCKLQDQ Y5, Y4, Y8 VPUNPCKHQDQ Y5, Y4, Y5 VMOVDQA Y8, Y4 VPUNPCKLQDQ Y7, Y6, Y8 VPUNPCKHQDQ Y7, Y6, Y7 VMOVDQA Y8, Y6 VPERM2I128 $0x20, Y2, Y0, Y8 VPERM2I128 $0x31, Y2, Y0, Y2 VMOVDQA Y8, Y0 VPERM2I128 $0x20, Y3, Y1, Y8 VPERM2I128 $0x31, Y3, Y1, Y3 VMOVDQA Y8, Y1 VPERM2I128 $0x20, Y6, Y4, Y8 VPERM2I128 $0x31, Y6, Y4, Y6 VMOVDQA Y8, Y4 VPERM2I128 $0x20, Y7, Y5, Y8 VPERM2I128 $0x31, Y7, Y5, Y7 VMOVDQA Y8, Y5 VMOVDQU Y0, 256(AX) VMOVDQU Y1, 288(AX) VMOVDQU Y2, 320(AX) VMOVDQU Y3, 352(AX) VMOVDQU Y4, 384(AX) VMOVDQU Y5, 416(AX) VMOVDQU Y6, 448(AX) VMOVDQU Y7, 480(AX) RET // func tangleAVX2(p *[256]int16) // Requires: AVX, AVX2 TEXT ·tangleAVX2(SB), NOSPLIT, $0-8 MOVQ p+0(FP), AX VMOVDQU (AX), Y0 VMOVDQU 32(AX), Y1 VMOVDQU 64(AX), Y2 VMOVDQU 96(AX), Y3 VMOVDQU 128(AX), Y4 VMOVDQU 160(AX), Y5 VMOVDQU 192(AX), Y6 VMOVDQU 224(AX), Y7 VPERM2I128 $0x20, Y2, Y0, Y8 VPERM2I128 $0x31, Y2, Y0, Y2 VMOVDQA Y8, Y0 VPERM2I128 $0x20, Y3, Y1, Y8 VPERM2I128 $0x31, Y3, Y1, Y3 VMOVDQA Y8, Y1 VPERM2I128 $0x20, Y6, Y4, Y8 VPERM2I128 $0x31, Y6, Y4, Y6 VMOVDQA Y8, Y4 VPERM2I128 $0x20, Y7, Y5, Y8 VPERM2I128 $0x31, Y7, Y5, Y7 VMOVDQA Y8, Y5 VPUNPCKLQDQ Y1, Y0, Y8 VPUNPCKHQDQ Y1, Y0, Y1 VMOVDQA Y8, Y0 VPUNPCKLQDQ Y3, Y2, Y8 VPUNPCKHQDQ Y3, Y2, Y3 VMOVDQA Y8, Y2 VPUNPCKLQDQ Y5, Y4, Y8 VPUNPCKHQDQ Y5, Y4, Y5 VMOVDQA Y8, Y4 VPUNPCKLQDQ Y7, Y6, Y8 VPUNPCKHQDQ Y7, Y6, Y7 VMOVDQA Y8, Y6 VMOVSLDUP Y2, Y8 VPBLENDD $0xaa, Y8, Y0, Y8 VPSRLQ $0x20, Y0, Y0 VPBLENDD $0xaa, Y2, Y0, Y2 VMOVDQA Y8, Y0 VMOVSLDUP Y3, Y8 VPBLENDD $0xaa, Y8, Y1, Y8 VPSRLQ $0x20, Y1, Y1 VPBLENDD $0xaa, Y3, Y1, Y3 VMOVDQA Y8, Y1 VMOVSLDUP Y6, Y8 VPBLENDD $0xaa, Y8, Y4, Y8 VPSRLQ $0x20, Y4, Y4 VPBLENDD $0xaa, Y6, Y4, Y6 VMOVDQA Y8, Y4 VMOVSLDUP Y7, Y8 VPBLENDD $0xaa, Y8, Y5, Y8 VPSRLQ $0x20, Y5, Y5 VPBLENDD $0xaa, Y7, Y5, Y7 VMOVDQA Y8, Y5 VPSLLD $0x10, Y1, Y8 VPBLENDW $0xaa, Y8, Y0, Y8 VPSRLD $0x10, Y0, Y0 VPBLENDW $0xaa, Y1, Y0, Y1 VMOVDQA Y8, Y0 VPSLLD $0x10, Y3, Y8 VPBLENDW $0xaa, Y8, Y2, Y8 VPSRLD $0x10, Y2, Y2 VPBLENDW $0xaa, Y3, Y2, Y3 VMOVDQA Y8, Y2 VPSLLD $0x10, Y5, Y8 VPBLENDW $0xaa, Y8, Y4, Y8 VPSRLD $0x10, Y4, Y4 VPBLENDW $0xaa, Y5, Y4, Y5 VMOVDQA Y8, Y4 VPSLLD $0x10, Y7, Y8 VPBLENDW $0xaa, Y8, Y6, Y8 VPSRLD $0x10, Y6, Y6 VPBLENDW $0xaa, Y7, Y6, Y7 VMOVDQA Y8, Y6 VMOVDQU Y0, (AX) VMOVDQU Y1, 32(AX) VMOVDQU Y2, 64(AX) VMOVDQU Y3, 96(AX) VMOVDQU Y4, 128(AX) VMOVDQU Y5, 160(AX) VMOVDQU Y6, 192(AX) VMOVDQU Y7, 224(AX) VMOVDQU 256(AX), Y0 VMOVDQU 288(AX), Y1 VMOVDQU 320(AX), Y2 VMOVDQU 352(AX), Y3 VMOVDQU 384(AX), Y4 VMOVDQU 416(AX), Y5 VMOVDQU 448(AX), Y6 VMOVDQU 480(AX), Y7 VPERM2I128 $0x20, Y2, Y0, Y8 VPERM2I128 $0x31, Y2, Y0, Y2 VMOVDQA Y8, Y0 VPERM2I128 $0x20, Y3, Y1, Y8 VPERM2I128 $0x31, Y3, Y1, Y3 VMOVDQA Y8, Y1 VPERM2I128 $0x20, Y6, Y4, Y8 VPERM2I128 $0x31, Y6, Y4, Y6 VMOVDQA Y8, Y4 VPERM2I128 $0x20, Y7, Y5, Y8 VPERM2I128 $0x31, Y7, Y5, Y7 VMOVDQA Y8, Y5 VPUNPCKLQDQ Y1, Y0, Y8 VPUNPCKHQDQ Y1, Y0, Y1 VMOVDQA Y8, Y0 VPUNPCKLQDQ Y3, Y2, Y8 VPUNPCKHQDQ Y3, Y2, Y3 VMOVDQA Y8, Y2 VPUNPCKLQDQ Y5, Y4, Y8 VPUNPCKHQDQ Y5, Y4, Y5 VMOVDQA Y8, Y4 VPUNPCKLQDQ Y7, Y6, Y8 VPUNPCKHQDQ Y7, Y6, Y7 VMOVDQA Y8, Y6 VMOVSLDUP Y2, Y8 VPBLENDD $0xaa, Y8, Y0, Y8 VPSRLQ $0x20, Y0, Y0 VPBLENDD $0xaa, Y2, Y0, Y2 VMOVDQA Y8, Y0 VMOVSLDUP Y3, Y8 VPBLENDD $0xaa, Y8, Y1, Y8 VPSRLQ $0x20, Y1, Y1 VPBLENDD $0xaa, Y3, Y1, Y3 VMOVDQA Y8, Y1 VMOVSLDUP Y6, Y8 VPBLENDD $0xaa, Y8, Y4, Y8 VPSRLQ $0x20, Y4, Y4 VPBLENDD $0xaa, Y6, Y4, Y6 VMOVDQA Y8, Y4 VMOVSLDUP Y7, Y8 VPBLENDD $0xaa, Y8, Y5, Y8 VPSRLQ $0x20, Y5, Y5 VPBLENDD $0xaa, Y7, Y5, Y7 VMOVDQA Y8, Y5 VPSLLD $0x10, Y1, Y8 VPBLENDW $0xaa, Y8, Y0, Y8 VPSRLD $0x10, Y0, Y0 VPBLENDW $0xaa, Y1, Y0, Y1 VMOVDQA Y8, Y0 VPSLLD $0x10, Y3, Y8 VPBLENDW $0xaa, Y8, Y2, Y8 VPSRLD $0x10, Y2, Y2 VPBLENDW $0xaa, Y3, Y2, Y3 VMOVDQA Y8, Y2 VPSLLD $0x10, Y5, Y8 VPBLENDW $0xaa, Y8, Y4, Y8 VPSRLD $0x10, Y4, Y4 VPBLENDW $0xaa, Y5, Y4, Y5 VMOVDQA Y8, Y4 VPSLLD $0x10, Y7, Y8 VPBLENDW $0xaa, Y8, Y6, Y8 VPSRLD $0x10, Y6, Y6 VPBLENDW $0xaa, Y7, Y6, Y7 VMOVDQA Y8, Y6 VMOVDQU Y0, 256(AX) VMOVDQU Y1, 288(AX) VMOVDQU Y2, 320(AX) VMOVDQU Y3, 352(AX) VMOVDQU Y4, 384(AX) VMOVDQU Y5, 416(AX) VMOVDQU Y6, 448(AX) VMOVDQU Y7, 480(AX) RET // func barrettReduceAVX2(p *[256]int16) // Requires: AVX, AVX2 TEXT ·barrettReduceAVX2(SB), NOSPLIT, $0-8 MOVQ p+0(FP), AX MOVL $0x00000d01, CX VMOVD CX, X0 VPBROADCASTW X0, Y9 MOVL $0x00004ebf, CX VMOVD CX, X0 VPBROADCASTW X0, Y8 VMOVDQU (AX), Y0 VMOVDQU 32(AX), Y1 VMOVDQU 64(AX), Y2 VMOVDQU 96(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VMOVDQU Y0, (AX) VMOVDQU Y1, 32(AX) VMOVDQU Y2, 64(AX) VMOVDQU Y3, 96(AX) VMOVDQU 128(AX), Y0 VMOVDQU 160(AX), Y1 VMOVDQU 192(AX), Y2 VMOVDQU 224(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VMOVDQU Y0, 128(AX) VMOVDQU Y1, 160(AX) VMOVDQU Y2, 192(AX) VMOVDQU Y3, 224(AX) VMOVDQU 256(AX), Y0 VMOVDQU 288(AX), Y1 VMOVDQU 320(AX), Y2 VMOVDQU 352(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VMOVDQU Y0, 256(AX) VMOVDQU Y1, 288(AX) VMOVDQU Y2, 320(AX) VMOVDQU Y3, 352(AX) VMOVDQU 384(AX), Y0 VMOVDQU 416(AX), Y1 VMOVDQU 448(AX), Y2 VMOVDQU 480(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VMOVDQU Y0, 384(AX) VMOVDQU Y1, 416(AX) VMOVDQU Y2, 448(AX) VMOVDQU Y3, 480(AX) RET // func normalizeAVX2(p *[256]int16) // Requires: AVX, AVX2 TEXT ·normalizeAVX2(SB), NOSPLIT, $0-8 MOVQ p+0(FP), AX MOVL $0x00000d01, CX VMOVD CX, X0 VPBROADCASTW X0, Y9 MOVL $0x00004ebf, CX VMOVD CX, X0 VPBROADCASTW X0, Y8 VMOVDQU (AX), Y0 VMOVDQU 32(AX), Y1 VMOVDQU 64(AX), Y2 VMOVDQU 96(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VPSUBW Y9, Y0, Y0 VPSUBW Y9, Y1, Y1 VPSUBW Y9, Y2, Y2 VPSUBW Y9, Y3, Y3 VPSRAW $0x0f, Y0, Y4 VPSRAW $0x0f, Y1, Y5 VPSRAW $0x0f, Y2, Y6 VPSRAW $0x0f, Y3, Y7 VPAND Y4, Y9, Y4 VPAND Y5, Y9, Y5 VPAND Y6, Y9, Y6 VPAND Y7, Y9, Y7 VPADDW Y0, Y4, Y0 VPADDW Y1, Y5, Y1 VPADDW Y2, Y6, Y2 VPADDW Y3, Y7, Y3 VMOVDQU Y0, (AX) VMOVDQU Y1, 32(AX) VMOVDQU Y2, 64(AX) VMOVDQU Y3, 96(AX) VMOVDQU 128(AX), Y0 VMOVDQU 160(AX), Y1 VMOVDQU 192(AX), Y2 VMOVDQU 224(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VPSUBW Y9, Y0, Y0 VPSUBW Y9, Y1, Y1 VPSUBW Y9, Y2, Y2 VPSUBW Y9, Y3, Y3 VPSRAW $0x0f, Y0, Y4 VPSRAW $0x0f, Y1, Y5 VPSRAW $0x0f, Y2, Y6 VPSRAW $0x0f, Y3, Y7 VPAND Y4, Y9, Y4 VPAND Y5, Y9, Y5 VPAND Y6, Y9, Y6 VPAND Y7, Y9, Y7 VPADDW Y0, Y4, Y0 VPADDW Y1, Y5, Y1 VPADDW Y2, Y6, Y2 VPADDW Y3, Y7, Y3 VMOVDQU Y0, 128(AX) VMOVDQU Y1, 160(AX) VMOVDQU Y2, 192(AX) VMOVDQU Y3, 224(AX) VMOVDQU 256(AX), Y0 VMOVDQU 288(AX), Y1 VMOVDQU 320(AX), Y2 VMOVDQU 352(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VPSUBW Y9, Y0, Y0 VPSUBW Y9, Y1, Y1 VPSUBW Y9, Y2, Y2 VPSUBW Y9, Y3, Y3 VPSRAW $0x0f, Y0, Y4 VPSRAW $0x0f, Y1, Y5 VPSRAW $0x0f, Y2, Y6 VPSRAW $0x0f, Y3, Y7 VPAND Y4, Y9, Y4 VPAND Y5, Y9, Y5 VPAND Y6, Y9, Y6 VPAND Y7, Y9, Y7 VPADDW Y0, Y4, Y0 VPADDW Y1, Y5, Y1 VPADDW Y2, Y6, Y2 VPADDW Y3, Y7, Y3 VMOVDQU Y0, 256(AX) VMOVDQU Y1, 288(AX) VMOVDQU Y2, 320(AX) VMOVDQU Y3, 352(AX) VMOVDQU 384(AX), Y0 VMOVDQU 416(AX), Y1 VMOVDQU 448(AX), Y2 VMOVDQU 480(AX), Y3 VPMULHW Y8, Y0, Y4 VPMULHW Y8, Y1, Y5 VPMULHW Y8, Y2, Y6 VPMULHW Y8, Y3, Y7 VPSRAW $0x0a, Y4, Y4 VPSRAW $0x0a, Y5, Y5 VPSRAW $0x0a, Y6, Y6 VPSRAW $0x0a, Y7, Y7 VPMULLW Y9, Y4, Y4 VPMULLW Y9, Y5, Y5 VPMULLW Y9, Y6, Y6 VPMULLW Y9, Y7, Y7 VPSUBW Y4, Y0, Y0 VPSUBW Y5, Y1, Y1 VPSUBW Y6, Y2, Y2 VPSUBW Y7, Y3, Y3 VPSUBW Y9, Y0, Y0 VPSUBW Y9, Y1, Y1 VPSUBW Y9, Y2, Y2 VPSUBW Y9, Y3, Y3 VPSRAW $0x0f, Y0, Y4 VPSRAW $0x0f, Y1, Y5 VPSRAW $0x0f, Y2, Y6 VPSRAW $0x0f, Y3, Y7 VPAND Y4, Y9, Y4 VPAND Y5, Y9, Y5 VPAND Y6, Y9, Y6 VPAND Y7, Y9, Y7 VPADDW Y0, Y4, Y0 VPADDW Y1, Y5, Y1 VPADDW Y2, Y6, Y2 VPADDW Y3, Y7, Y3 VMOVDQU Y0, 384(AX) VMOVDQU Y1, 416(AX) VMOVDQU Y2, 448(AX) VMOVDQU Y3, 480(AX) RET golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/asm/000077500000000000000000000000001454601126700252465ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/asm/go.mod000066400000000000000000000005251454601126700263560ustar00rootroot00000000000000module github.com/cloudflare/circl/pke/kyber/internal/common/asm go 1.19 require ( github.com/cloudflare/circl v1.3.3 github.com/mmcloughlin/avo v0.5.0 ) require ( golang.org/x/mod v0.10.0 // indirect golang.org/x/sys v0.8.0 // indirect golang.org/x/tools v0.9.1 // indirect ) replace github.com/cloudflare/circl => ../../../../../ golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/asm/go.sum000066400000000000000000000073001454601126700264010ustar00rootroot00000000000000github.com/mmcloughlin/avo v0.5.0 h1:nAco9/aI9Lg2kiuROBY6BhCI/z0t5jEvJfjWbL8qXLU= github.com/mmcloughlin/avo v0.5.0/go.mod h1:ChHFdoV7ql95Wi7vuq2YT1bwCJqiWdZrQ1im3VujLYM= github.com/yuin/goldmark v1.4.13/go.mod h1:6yULJ656Px+3vBD8DxQVa3kxgyrAnzto9xy5taEt/CY= golang.org/x/arch v0.1.0/go.mod h1:5om86z9Hs0C8fWVUuoMHwpExlXzs5Tkyp9hOrfG7pp8= golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w= golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= golang.org/x/crypto v0.1.0/go.mod h1:RecgLatLF4+eUMCP1PoPZQb+cVrJcOPbHkTkbkB9sbw= golang.org/x/mod v0.6.0-dev.0.20220419223038-86c51ed26bb4/go.mod h1:jJ57K6gSWd91VN4djpZkiMVwK6gcyfeH4XE8wZrZaV4= golang.org/x/mod v0.6.0/go.mod h1:4mET923SAdbXp2ki8ey+zGs1SLqsuM2Y0uvdZR/fUNI= golang.org/x/mod v0.10.0 h1:lFO9qtOdlre5W1jxS3r/4szv2/6iXxScdzjoBMXNhYk= golang.org/x/mod v0.10.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs= golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg= golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c= golang.org/x/net v0.1.0/go.mod h1:Cx3nUiGt4eDBEyega/BKRp+/AlGL8hYe7U9odMt2Cco= golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.2.0 h1:PUR+T4wwASmuSTYdKjYHI5TD22Wy5ogLU5qZCOLxBrI= golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY= golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.1.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.8.0 h1:EBmGv8NaZBZTWvrbjNoL6HVt+IVy3QDQpJs7VRIw3tU= golang.org/x/sys v0.8.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo= golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= golang.org/x/term v0.1.0/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ= golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ= golang.org/x/text v0.3.7/go.mod h1:u+2+/6zg+i71rQMx5EYifcz6MCKuco9NR6JIITiCfzQ= golang.org/x/text v0.4.0/go.mod h1:mrYo+phRRbMaCq/xk9113O4dZlRixOauAjOtrjsXDZ8= golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ= golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo= golang.org/x/tools v0.1.12/go.mod h1:hNGJHUnrk76NpqgfD5Aqm5Crs+Hm0VOH/i9J2+nxYbc= golang.org/x/tools v0.2.0/go.mod h1:y4OqIKeOV/fWJetJ8bXPU1sEVniLMIyDAZWeHdV+NTA= golang.org/x/tools v0.9.1 h1:8WMNJAz3zrtPmnYC7ISf5dEn3MT0gY7jBJfw27yrrLo= golang.org/x/tools v0.9.1/go.mod h1:owI94Op576fPu3cIGQeHs3joujW/2Oc6MtlxbF5dfNc= golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= rsc.io/pdf v0.1.1/go.mod h1:n8OzWcQ6Sp37PL01nO98y4iUCRdTGarVfzxY20ICaU4= golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/asm/src.go000066400000000000000000001020301454601126700263600ustar00rootroot00000000000000//go:generate go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common // AVX2 optimized version of polynomial operations. See the comments on the // generic implementation for the details of the maths involved. package main import ( . "github.com/mmcloughlin/avo/build" // nolint:golint,stylecheck . "github.com/mmcloughlin/avo/operand" // nolint:golint,stylecheck . "github.com/mmcloughlin/avo/reg" // nolint:golint,stylecheck "github.com/cloudflare/circl/pke/kyber/internal/common/params" ) // XXX align Poly on 16 bytes such that we can use aligned moves // XXX ensure Zetas and ZetasAVX2 are 16 byte aligned // Barrett reduces the int16x16 where q must contain {q, q, …}; // num must contain {20159, 20159, …} the numerator in the approximation // 20159/2²⁶ of 1/q and t is a temporary register that will be clobbered. func barrettReduceX16(x, q, num, t Op) { // Recall that the Barrett reduction of x is given by // // x - int16((int32(x)*20159)>>26)*q VPMULHW(num, x, t) // t := (int32(x) * 20159) >> 16 VPSRAW(U8(10), t, t) // t = int16(t)>>10 so that t = (int32(x)*20159) >> 26 VPMULLW(q, t, t) // t *= q VPSUBW(t, x, x) // x -= t } func broadcastImm16(c int16, out Op) { tmp1 := GP32() tmp2 := XMM() MOVL(U32(uint32(int32(c))), tmp1) VMOVD(tmp1, tmp2) VPBROADCASTW(tmp2, out) } func addAVX2() { TEXT("addAVX2", NOSPLIT, "func(p, a, b *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) aPtr := Load(Param("a"), GP64()) bPtr := Load(Param("b"), GP64()) var a [8]VecVirtual var b [8]VecVirtual for i := 0; i < 8; i++ { a[i] = YMM() b[i] = YMM() } for j := 0; j < 2; j++ { for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: aPtr, Disp: 32 * (8*j + i)}, a[i]) } for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: bPtr, Disp: 32 * (8*j + i)}, b[i]) } for i := 0; i < 8; i++ { VPADDW(a[i], b[i], b[i]) } for i := 0; i < 8; i++ { VMOVDQU(b[i], Mem{Base: pPtr, Disp: 32 * (8*j + i)}) } } RET() } func subAVX2() { TEXT("subAVX2", NOSPLIT, "func(p, a, b *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) aPtr := Load(Param("a"), GP64()) bPtr := Load(Param("b"), GP64()) var a [8]VecVirtual var b [8]VecVirtual for i := 0; i < 8; i++ { a[i] = YMM() b[i] = YMM() } for j := 0; j < 2; j++ { for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: aPtr, Disp: 32 * (8*j + i)}, a[i]) } for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: bPtr, Disp: 32 * (8*j + i)}, b[i]) } for i := 0; i < 8; i++ { VPSUBW(b[i], a[i], b[i]) } for i := 0; i < 8; i++ { VMOVDQU(b[i], Mem{Base: pPtr, Disp: 32 * (8*j + i)}) } } RET() } // For each lane in a that has a 1 on ith bit of its index, swap it with // the corresponding lane in b where this 1 has been replaced by a 0. // // For instance, if i=2, then this will swap // // a[0b0100] ↔ b[0b0000] a[0b0101] ↔ b[0b0001] // a[0b0110] ↔ b[0b0010] a[0b0111] ↔ b[0b0011] // a[0b1100] ↔ b[0b1000] a[0b1101] ↔ b[0b1001] // a[0b1110] ↔ b[0b1010] a[0b1111] ↔ b[0b1011] // // and keep all other lanes in their place. If we index the lanes of a and // b consecutively (i.e. 0wxyz is wxyz of a and 1wxyz = wxyz of b), then // this corresponds to mapping lane vwxyz to xwvyz -- that is: flipping the // fourth bit with the ith bit (where we start from zeroth.) Hence the name. // // Why these permutations? There are two reasons: these are reasonable // easy to implement and they pull sequential butterflies in the NTT apart. // Recall, namely, that on the fifth layer of the NTT we're computing // butterflies between indices // // abcd0fgh abcd1fgh // // Applying bitflip with i=3 beforehand, the butterflies become // // abc0dfgh abc1dfgh // // which allows for 16 consecutive butterflies, which is convenient for AVX2. // What we'll actually end up doing is a bit different: we'll apply both // an i=3 and i=2 bitflip before then to also interleave the ζs correctly // for the fourth layer. // // See the diagram linked to in the documentation of nttAVX2(). func bitflip(i int, a, b, t Op) { switch i { case 3: VPERM2I128(U8(0x20), b, a, t) VPERM2I128(U8(0x31), b, a, b) VMOVDQA(t, a) case 2: VPUNPCKLQDQ(b, a, t) VPUNPCKHQDQ(b, a, b) VMOVDQA(t, a) case 1: VMOVSLDUP(b, t) VPBLENDD(U8(0xaa), t, a, t) VPSRLQ(U8(32), a, a) VPBLENDD(U8(0xaa), b, a, b) VMOVDQA(t, a) case 0: VPSLLD(U8(16), b, t) VPBLENDW(U8(0xaa), t, a, t) VPSRLD(U8(16), a, a) VPBLENDW(U8(0xaa), b, a, b) VMOVDQA(t, a) } } func invNttAVX2() { // This AVX2-optimized inverse NTT is close, but more disimilar from // the generic inverse NTT, then the AVX2-optimized forward NTT is // from the generic. // // 1. Just like in the AVX2-optimized forward NTT, we shuffle the // coefficients around to ensure we can do consecutive butterflies and // 2. we use the same preshuffled and duplicated ZetasAVX2 table. // 3. Barrett reductions are computed at different moments as it's very // efficient to do 16 at a time. // The butterflies and swaps are in the exact reverse order as those // of the AVX2-optimized forward NTT. See the comments on nttAVX2() // and bitflip() for documentation on the shufflings. // A diagram of the order of the butterflies and swaps can be found here: // // https://github.com/cloudflare/circl/wiki/images/kyber-invntt-avx2.svg // // The vertical lines with circles on the end represent butterflies. // The number in those butterflies refers to the index into the Zetas // array of which ζ is used. (Note that this array is different from // the ZetasAVX2 array, which contains the elements of Zetas many times // over in a way that is efficient for our implementation.) // // The green squares represent Barrett reductions. The green numbers after // the butterflies show the multiple of q that bounds the coefficient in // absolute value. (Recall that the lower coefficient is always bounded // by one when computing the inverse butterflies in the obvious way.) // The vertical lines with crosses on them represent a swap. TEXT("invNttAVX2", NOSPLIT, "func(p *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) zetasPtr := GP64() LEAQ(NewDataAddr(Symbol{Name: "·ZetasAVX2"}, 0), zetasPtr) // Compute 4x16 Gentleman--Sande butterflies (a, b) ↦ (a + b, ζ(a - b)). // // There is a catch: the first two and the last two sets of butterflies // have to use the same sets of zetas, as we don't have enough registers // to keep everything around. t1 up to t4 are temporary registers that // will be clobbered. gsButterfly := func(a1, b1, a2, b2, zeta12l, zeta12h, a3, b3, a4, b4, zeta34l, zeta34h, t1, t2, t3, t4, q Op) { // In the generic implementation, a single butterfly is computed as // follows (unfolding the definition of montReduce and recalling // zeta stores -ζ.) // // t := b - a // a += b // m := int16(zeta * t * 62209) // b = int16(uint32(zeta * int32(t) - m * int32(Q)) >> 16) // // As ζt ≡ mq (mod 2¹⁶), see comments on montReduce(), we can // also compute b as // // b = (uint32(zeta * int32(t)) >> 16) - (uint32(m * int32(Q)) >> 16) // // m (x16) can be computed using a single VPMULLW with zeta * 62209 // as the second operand stored in a table. The two multiplications // and bitshifts for b can be performed using two VPMULHWs (again // for 16 at a time.) VPSUBW(a1, b1, t1) // t = b - a VPSUBW(a2, b2, t2) VPSUBW(a3, b3, t3) // We don't use t4 yet, so that zeta12l may be used as t4. VPADDW(a1, b1, a1) // a += b VPADDW(a2, b2, a2) VPADDW(a3, b3, a3) VPMULLW(t1, zeta12l, b1) // m = int16(zeta * t * 62209) VPMULLW(t2, zeta12l, b2) // At this point zeta12l (which might equal t4) is free. VPSUBW(a4, b4, t4) VPMULLW(t3, zeta34l, b3) VPADDW(a4, b4, a4) VPMULLW(t4, zeta34l, b4) VPMULHW(t1, zeta12h, t1) // uint32(zeta*int32(t)) >> 16 VPMULHW(t2, zeta12h, t2) VPMULHW(t3, zeta34h, t3) VPMULHW(t4, zeta34h, t4) VPMULHW(b1, q, b1) // uint32(m*int32(Q)) >> 16 VPMULHW(b2, q, b2) VPMULHW(b3, q, b3) VPMULHW(b4, q, b4) VPSUBW(b1, t1, b1) // Compute b VPSUBW(b2, t2, b2) VPSUBW(b3, t3, b3) VPSUBW(b4, t4, b4) } // Registers and constants var xs [8]VecVirtual zs := [4]VecVirtual{YMM(), YMM(), YMM(), YMM()} ts := [3]VecVirtual{YMM(), YMM(), YMM()} for i := 0; i < 8; i++ { xs[i] = YMM() } q := YMM() broadcastImm16(params.Q, q) // Layers 1 - 6 for offset := 0; offset < 2; offset++ { for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*8)}, xs[i]) } VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (33 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (33 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (33 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (33 + offset*4 + 3)}, zs[3]) // Layer 1 (inverse of 7) gsButterfly( xs[0], xs[2], // a1, b1 xs[1], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[6], // a3, b3, xs[5], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (41 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (41 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (41 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (41 + offset*4 + 3)}, zs[3]) bitflip(0, xs[0], xs[1], ts[0]) bitflip(0, xs[2], xs[3], ts[0]) bitflip(0, xs[4], xs[5], ts[0]) bitflip(0, xs[6], xs[7], ts[0]) // Layer 2 (inverse of 6) gsButterfly( xs[0], xs[1], // a1, b1 xs[2], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[5], // a3, b3, xs[6], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (49 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (49 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (49 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (49 + offset*4 + 3)}, zs[3]) bitflip(1, xs[0], xs[2], ts[0]) bitflip(1, xs[1], xs[3], ts[0]) bitflip(1, xs[4], xs[6], ts[0]) bitflip(1, xs[5], xs[7], ts[0]) // Layer 3 (inverse of 5) gsButterfly( xs[0], xs[2], // a1, b1 xs[1], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[6], // a3, b3, xs[5], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) broadcastImm16(20159, ts[0]) barrettReduceX16(xs[0], q, ts[0], ts[1]) barrettReduceX16(xs[4], q, ts[0], ts[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (57 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (57 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (57 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (57 + offset*4 + 3)}, zs[3]) bitflip(2, xs[0], xs[1], ts[0]) bitflip(2, xs[2], xs[3], ts[0]) bitflip(2, xs[4], xs[5], ts[0]) bitflip(2, xs[6], xs[7], ts[0]) // Layer 4 (inverse of 4) gsButterfly( xs[0], xs[1], // a1, b1 xs[2], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[5], // a3, b3, xs[6], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(4*offset)}, zs[0]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(4*offset+1)}, zs[1]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(4*offset+2)}, zs[2]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(4*offset+3)}, zs[3]) bitflip(3, xs[0], xs[2], ts[0]) bitflip(3, xs[1], xs[3], ts[0]) bitflip(3, xs[4], xs[6], ts[0]) bitflip(3, xs[5], xs[7], ts[0]) // Layer 5 (inverse of 3) gsButterfly( xs[0], xs[2], // a1, b1 xs[1], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[6], // a3, b3, xs[5], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) broadcastImm16(20159, ts[0]) barrettReduceX16(xs[0], q, ts[0], ts[1]) barrettReduceX16(xs[4], q, ts[0], ts[1]) // Layer 6 (inverse of 2) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(8+2*offset)}, zs[0]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(8+2*offset+1)}, zs[1]) gsButterfly( xs[0], xs[4], // a1, b1 xs[1], xs[5], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[2], xs[6], // a3, b3, xs[3], xs[7], // a4, b4, zs[0], zs[1], // zs34l, zs34h ts[0], ts[1], ts[2], zs[2], // t1, t2, t3, t4 q, // q ) for i := 0; i < 8; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*8)}) } } // Layers 7 (inverse of 1) for offset := 0; offset < 2; offset++ { VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(12)}, zs[0]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 32*65 + 2*(12+1)}, zs[1]) for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*4)}, xs[i]) } for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + 8 + offset*4)}, xs[4+i]) } gsButterfly( xs[0], xs[4], // a1, b1 xs[1], xs[5], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[2], xs[6], // a3, b3, xs[3], xs[7], // a4, b4, zs[0], zs[1], // zs34l, zs34h zs[2], zs[3], ts[0], ts[1], // t1, t2, t3, t4 q, // q ) // Finally, we set x = montgomeryReduce(x * 1441). Just like in the // the butterflies we compute the Montgomery reduction using // VPMULHWs and VPMULLWs by observing: // // m := int16(1441 * x * 62209) = int16(-10079 * x) // x' = int16(uint32(1441 * int32(x) - m * int32(Q)) >> 16) // = (uint32(1441 * int32(x)) >> 16) - (uint32(m * int32(Q)) >> 16) broadcastImm16(-10079, zs[0]) broadcastImm16(1441, zs[1]) for j := 0; j < 2; j++ { VPMULLW(xs[4*j+0], zs[0], zs[2]) // m = int16(-10079 * x) VPMULLW(xs[4*j+1], zs[0], zs[3]) VPMULLW(xs[4*j+2], zs[0], ts[0]) VPMULLW(xs[4*j+3], zs[0], ts[1]) VPMULHW(xs[4*j+0], zs[1], xs[4*j+0]) // uint32(1441*int32(x)) >> 16 VPMULHW(xs[4*j+1], zs[1], xs[4*j+1]) VPMULHW(xs[4*j+2], zs[1], xs[4*j+2]) VPMULHW(xs[4*j+3], zs[1], xs[4*j+3]) VPMULHW(zs[2], q, zs[2]) // uint32(m*int32(Q)) >> 16 VPMULHW(zs[3], q, zs[3]) VPMULHW(ts[0], q, ts[0]) VPMULHW(ts[1], q, ts[1]) VPSUBW(zs[2], xs[4*j+0], xs[4*j+0]) // computes t VPSUBW(zs[3], xs[4*j+1], xs[4*j+1]) VPSUBW(ts[0], xs[4*j+2], xs[4*j+2]) VPSUBW(ts[1], xs[4*j+3], xs[4*j+3]) } for i := 0; i < 4; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*4)}) } for i := 0; i < 4; i++ { VMOVDQU(xs[4+i], Mem{Base: pPtr, Disp: 32 * (i + 8 + offset*4)}) } } RET() } func nttAVX2() { // We perform almost the same operations as the generic implementation of NTT, // but use AVX2 to perform 64 butterflies at the same time. We can keep // 128 coefficients in registers at the same time. We do the first level // separately writing back to memory. Then we do levels 2 through 7 for // 128 coefficients in registers all at the same time. // As we can only perform butterflies of 8 consecutive coefficients, // we need to shuffle coefficients around. Similarly parallel // multiplication in the NTT-domain (as implemented by MulHat) requires // sequential coefficients to be pulled apart. Thus we will use a // different order of coefficients than the reference implementation. // A diagram of the order of butterflies and swaps can be found here: // // https://github.com/cloudflare/circl/wiki/images/kyber-ntt-avx2.svg // // The vertical lines with circles on the end represent butterflies. // The number in those butterflies refers to the index into the Zetas // array of which ζ is used. (Note that this array is different from // the ZetasAVX2 array, which contains the elements of Zetas many times // over in a way that is efficient for our implementation.) // // The vertical lines with crosses on them represent a swap. // Related reading: https://eprint.iacr.org/2018/039.pdf TEXT("nttAVX2", NOSPLIT, "func(p *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) zetasPtr := GP64() LEAQ(NewDataAddr(Symbol{Name: "·ZetasAVX2"}, 0), zetasPtr) // Compute 4x16 Cooley--Tukey butterflies (a, b) ↦ (a + ζb, a - ζb). // // There is a catch: the first two and the last two sets of butterflies // have to use the same sets of zetas, as we don't have enough registers // to keep everything around. t1 up to t4 are temporary registers that // will be clobbered. ctButterfly := func(a1, b1, a2, b2, zeta12l, zeta12h, a3, b3, a4, b4, zeta34l, zeta34h, t1, t2, t3, t4, q Op) { // In the generic implementation, a single butterfly is computed as // follows (unfolding the definition of montReduce): // // m := int16(zeta * b * 62209) // t := int16(uint32(zeta * int32(b) - m * int32(Q)) >> 16) // b = a - t // a += t // // As ζb ≡ mq (mod 2¹⁶), see comments on montReduce(), we can // also compute t as // // t := (uint32(zeta * int32(b)) >> 16) - (uint32(m * int32(Q)) >> 16) // // m (x16) can be computed using a single VPMULLW with zeta * 62209 // as the second operand stored in a table. The two multiplications // and bitshifts for t can be performed using two VPMULHWs (again // for 16 at a time.) VPMULLW(b1, zeta12l, t1) // m = int16(zeta * b * 62209) VPMULLW(b2, zeta12l, t2) VPMULLW(b3, zeta34l, t3) VPMULLW(b4, zeta34l, t4) VPMULHW(b1, zeta12h, b1) // uint32(zeta*int32(b)) >> 16 VPMULHW(b2, zeta12h, b2) VPMULHW(b3, zeta34h, b3) VPMULHW(b4, zeta34h, b4) VPMULHW(t1, q, t1) // uint32(m*int32(Q)) >> 16 VPMULHW(t2, q, t2) VPMULHW(t3, q, t3) VPMULHW(t4, q, t4) VPSUBW(t1, b1, t1) // computes t VPSUBW(t2, b2, t2) VPSUBW(t3, b3, t3) VPSUBW(t4, b4, t4) VPSUBW(t1, a1, b1) // b = a - t VPSUBW(t2, a2, b2) VPSUBW(t3, a3, b3) VPSUBW(t4, a4, b4) VPADDW(t1, a1, a1) // a = a + t VPADDW(t2, a2, a2) VPADDW(t3, a3, a3) VPADDW(t4, a4, a4) } // First level: var xs [8]VecVirtual zs := [4]VecVirtual{YMM(), YMM(), YMM(), YMM()} ts := [3]VecVirtual{YMM(), YMM(), YMM()} for i := 0; i < 8; i++ { xs[i] = YMM() } q := YMM() broadcastImm16(params.Q, q) VPBROADCASTW(Mem{Base: zetasPtr}, zs[0]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 2}, zs[1]) for offset := 0; offset < 2; offset++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*4)}, xs[i]) } for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + 8 + offset*4)}, xs[4+i]) } ctButterfly( xs[0], xs[4], // a1, b1 xs[1], xs[5], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[2], xs[6], // a3, b3, xs[3], xs[7], // a4, b4, zs[0], zs[1], // zs34l, zs34h zs[2], zs[3], ts[0], ts[1], // t1, t2, t3, t4 q, // q ) for i := 0; i < 4; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*4)}) } for i := 0; i < 4; i++ { VMOVDQU(xs[4+i], Mem{Base: pPtr, Disp: 32 * (i + 8 + offset*4)}) } } // Layers 2 - 7 // // Layers 2 and 3 are straight forward. From layers 4 onwards, the // shuffling begins. for offset := 0; offset < 2; offset++ { VPBROADCASTW(Mem{Base: zetasPtr, Disp: 2 * (2 * (1 + offset))}, zs[0]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 2 * (2*(1+offset) + 1)}, zs[1]) for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*8)}, xs[i]) } // Layer 2 ctButterfly( xs[0], xs[4], // a1, b1 xs[1], xs[5], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[2], xs[6], // a3, b3, xs[3], xs[7], // a4, b4, zs[0], zs[1], // zs34l, zs34h zs[2], zs[3], ts[0], ts[1], // t1, t2, t3, t4 q, // q ) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 2 * (6 + 4*offset)}, zs[0]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 2 * ((6 + 4*offset) + 1)}, zs[1]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 2 * ((6 + 4*offset) + 2)}, zs[2]) VPBROADCASTW(Mem{Base: zetasPtr, Disp: 2 * ((6 + 4*offset) + 3)}, zs[3]) // Layer 3 ctButterfly( xs[0], xs[2], // a1, b1 xs[1], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[6], // a3, b3, xs[5], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) // Layer 4 // // On this layer, the butterflies are of length 16 and so would still // fit. However, the first set of butterflies uses Zetas[8], whereas // the second set uses Zetas[9]. On the next layer the butterflies // are each of length 8 and wouldn't fit. We solve both issues now // by swapping the second part of the first set with the first part // of the second set, etc. This is a bitflip() with i=4. VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (1 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (1 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (1 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (1 + offset*4 + 3)}, zs[3]) bitflip(3, xs[0], xs[2], ts[0]) bitflip(3, xs[1], xs[3], ts[0]) bitflip(3, xs[4], xs[6], ts[0]) bitflip(3, xs[5], xs[7], ts[0]) ctButterfly( xs[0], xs[1], // a1, b1 xs[2], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[5], // a3, b3, xs[6], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) // Layer 5 // // On this layer, the butterflies are of length 8 and wouldn't fit // directly. However, because of the previous shuffling we have // sets of 16 consecutive butterflies. However, just like in the // previous layer, the ζs required by the two sets are different: // the first sets uses 16 & 17 whereas the second uses 18 - 19. // We solve the issue by swapping two pairs of quarters. At the same // time this swapping also ensures that the next layer has consecutive // butterflies. This is bitflip() with i=3. There is some freedom // which pairs to flip. We try to keep the permutations as local // as possible: there is only mixing between xs[0], xs[1], xs[2] // and xs[3]. As an added benefit this ensures that the final // complete permutation is convenient for multiplication. VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (9 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (9 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (9 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (9 + offset*4 + 3)}, zs[3]) bitflip(2, xs[0], xs[1], ts[0]) bitflip(2, xs[2], xs[3], ts[0]) bitflip(2, xs[4], xs[5], ts[0]) bitflip(2, xs[6], xs[7], ts[0]) ctButterfly( xs[0], xs[2], // a1, b1 xs[1], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[6], // a3, b3, xs[5], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) // Layer 6 // // We continue on with the same principle. VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (17 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (17 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (17 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (17 + offset*4 + 3)}, zs[3]) bitflip(1, xs[0], xs[2], ts[0]) bitflip(1, xs[1], xs[3], ts[0]) bitflip(1, xs[4], xs[6], ts[0]) bitflip(1, xs[5], xs[7], ts[0]) ctButterfly( xs[0], xs[1], // a1, b1 xs[2], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[5], // a3, b3, xs[6], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) // Layer 7 VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + offset*4)}, zs[0]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + offset*4 + 1)}, zs[1]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + offset*4 + 2)}, zs[2]) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + offset*4 + 3)}, zs[3]) bitflip(0, xs[0], xs[1], ts[0]) bitflip(0, xs[2], xs[3], ts[0]) bitflip(0, xs[4], xs[5], ts[0]) bitflip(0, xs[6], xs[7], ts[0]) ctButterfly( xs[0], xs[2], // a1, b1 xs[1], xs[3], // a2, b2 zs[0], zs[1], // zs12l, zs12h xs[4], xs[6], // a3, b3, xs[5], xs[7], // a4, b4, zs[2], zs[3], // zs34l, zs34h ts[0], ts[1], ts[2], zs[0], // t1, t2, t3, t4 q, // q ) for i := 0; i < 8; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*8)}) } } RET() } func mulHatAVX2() { TEXT("mulHatAVX2", NOSPLIT, "func(p, a, b *[256]int16)") Pragma("noescape") AllocLocal(8) // In case BP register is needed. pPtr := Load(Param("p"), GP64()) aPtr := Load(Param("a"), GP64()) bPtr := Load(Param("b"), GP64()) zetasPtr := GP64() LEAQ(NewDataAddr(Symbol{Name: "·ZetasAVX2"}, 0), zetasPtr) a := []Op{YMM(), YMM(), YMM(), YMM()} b := []Op{YMM(), YMM(), YMM(), YMM()} t := []Op{YMM(), YMM(), YMM(), YMM()} zl := YMM() zh := YMM() qinv := YMM() q := YMM() broadcastImm16(-3327, qinv) // = q⁻¹ (mod 2¹⁶) broadcastImm16(params.Q, q) for j := 0; j < 4; j++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: aPtr, Disp: 32 * (4*j + i)}, a[i]) } for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: bPtr, Disp: 32 * (4*j + i)}, b[i]) } // Recall that quite conveniently for this computation (when j=0), // // a[0] contains a₀, a₄, ..., a₆₀, // a[1] contains a₁, a₅, ..., a₆₁, // a[2] contains a₂, a₆, ..., a₆₂ and // a[3] contains a₃, a₇, ..., a₆₃ // // and a similar thing for b, p and j>0. // We have to compute several products of the form t=montReduce(a*b). // From the discussion in AVX2-optimized NTT, recall that we can // compute this as follows. // // m := int16(a * b * 62209) = int16(a * b * -3227) // t := int16(uint32(int32(a) * int32(b) - m * int32(Q)) >> 16) // = (uint32(int32(a) * int32(b))>>16) - (uint32(m * int32(Q))>>16) // We start with the first four lines of // // p0 := montReduce(int32(a[i+1]) * int32(b[i+1])) // p2 := montReduce(int32(a[i]) * int32(b[i])) // p1 := montReduce(int32(a[i]) * int32(b[i+1])) // p1 += montReduce(int32(a[i+1]) * int32(b[i])) // p0 = montReduce(int32(p0) * zeta) + p2 VPMULLW(a[1], b[1], t[0]) VPMULLW(a[0], b[0], t[1]) VPMULLW(a[0], b[1], t[2]) VPMULLW(a[1], b[0], t[3]) VPMULLW(t[0], qinv, t[0]) VPMULLW(t[1], qinv, t[1]) VPMULLW(t[2], qinv, t[2]) VPMULLW(t[3], qinv, t[3]) // zl and zh are used as temporary registers here VPMULHW(a[1], b[1], zl) // will end up in b[0] VPMULHW(a[0], b[0], zh) // will end up in b[1] VPMULHW(a[0], b[1], a[0]) VPMULHW(a[1], b[0], a[1]) VMOVDQA(zl, b[0]) VMOVDQA(zh, b[1]) VPMULHW(t[0], q, t[0]) VPMULHW(t[1], q, t[1]) VPMULHW(t[2], q, t[2]) VPMULHW(t[3], q, t[3]) VPSUBW(t[0], b[0], b[0]) // a[i+1]*b[i+1] VPSUBW(t[1], b[1], b[1]) // a[i]*b[i] VPSUBW(t[2], a[0], a[0]) // a[i]*b[i+1] VPSUBW(t[3], a[1], a[1]) // a[i+1]*b[i] VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + j*2)}, zl) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + j*2 + 1)}, zh) // Compute p0 = montReduce(int32(p0) * zeta) + p2 VPMULLW(b[0], zl, t[0]) VPMULHW(b[0], zh, b[0]) VPMULHW(t[0], q, t[0]) VPSUBW(t[0], b[0], b[0]) VPADDW(b[0], b[1], b[0]) // p1 VPADDW(a[0], a[1], b[1]) // Now the same but then for the next two VPMULLW(a[3], b[3], t[0]) VPMULLW(a[2], b[2], t[1]) VPMULLW(a[2], b[3], t[2]) VPMULLW(a[3], b[2], t[3]) VPMULLW(t[0], qinv, t[0]) VPMULLW(t[1], qinv, t[1]) VPMULLW(t[2], qinv, t[2]) VPMULLW(t[3], qinv, t[3]) // zl and zh are used as temporary registers here VPMULHW(a[3], b[3], zl) // will end up in b[2] VPMULHW(a[2], b[2], zh) // will end up in b[3] VPMULHW(a[2], b[3], a[2]) VPMULHW(a[3], b[2], a[3]) VMOVDQA(zl, b[2]) VMOVDQA(zh, b[3]) VPMULHW(t[0], q, t[0]) VPMULHW(t[1], q, t[1]) VPMULHW(t[2], q, t[2]) VPMULHW(t[3], q, t[3]) VPSUBW(t[0], b[2], b[2]) // a[i+1]*b[i+1] VPSUBW(t[1], b[3], b[3]) // a[i]*b[i] VPSUBW(t[2], a[2], a[2]) // a[i]*b[i+1] VPSUBW(t[3], a[3], a[3]) // a[i+1]*b[i] VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + j*2)}, zl) VMOVDQU(Mem{Base: zetasPtr, Disp: 32 * (25 + j*2 + 1)}, zh) // Compute p0 = p2 - montReduce(int32(p0) * zeta) VPMULLW(b[2], zl, t[0]) VPMULHW(b[2], zh, b[2]) VPMULHW(t[0], q, t[0]) VPSUBW(t[0], b[2], b[2]) VPSUBW(b[2], b[3], b[2]) // p1 VPADDW(a[2], a[3], b[3]) for i := 0; i < 4; i++ { VMOVDQU(b[i], Mem{Base: pPtr, Disp: 32 * (4*j + i)}) } } RET() } func tangleAVX2() { TEXT("tangleAVX2", NOSPLIT, "func(p *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) var xs [8]VecVirtual for i := 0; i < 8; i++ { xs[i] = YMM() } t := YMM() for offset := 0; offset < 2; offset++ { for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*8)}, xs[i]) } bitflip(3, xs[0], xs[2], t) bitflip(3, xs[1], xs[3], t) bitflip(3, xs[4], xs[6], t) bitflip(3, xs[5], xs[7], t) bitflip(2, xs[0], xs[1], t) bitflip(2, xs[2], xs[3], t) bitflip(2, xs[4], xs[5], t) bitflip(2, xs[6], xs[7], t) bitflip(1, xs[0], xs[2], t) bitflip(1, xs[1], xs[3], t) bitflip(1, xs[4], xs[6], t) bitflip(1, xs[5], xs[7], t) bitflip(0, xs[0], xs[1], t) bitflip(0, xs[2], xs[3], t) bitflip(0, xs[4], xs[5], t) bitflip(0, xs[6], xs[7], t) for i := 0; i < 8; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*8)}) } } RET() } func detangleAVX2() { TEXT("detangleAVX2", NOSPLIT, "func(p *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) var xs [8]VecVirtual for i := 0; i < 8; i++ { xs[i] = YMM() } t := YMM() for offset := 0; offset < 2; offset++ { for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*8)}, xs[i]) } bitflip(0, xs[0], xs[1], t) bitflip(0, xs[2], xs[3], t) bitflip(0, xs[4], xs[5], t) bitflip(0, xs[6], xs[7], t) bitflip(1, xs[0], xs[2], t) bitflip(1, xs[1], xs[3], t) bitflip(1, xs[4], xs[6], t) bitflip(1, xs[5], xs[7], t) bitflip(2, xs[0], xs[1], t) bitflip(2, xs[2], xs[3], t) bitflip(2, xs[4], xs[5], t) bitflip(2, xs[6], xs[7], t) bitflip(3, xs[0], xs[2], t) bitflip(3, xs[1], xs[3], t) bitflip(3, xs[4], xs[6], t) bitflip(3, xs[5], xs[7], t) for i := 0; i < 8; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*8)}) } } RET() } func barrettReduceAVX2() { TEXT("barrettReduceAVX2", NOSPLIT, "func(p *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) xs := [4]Op{YMM(), YMM(), YMM(), YMM()} ts := [4]Op{YMM(), YMM(), YMM(), YMM()} num := YMM() q := YMM() broadcastImm16(params.Q, q) broadcastImm16(20159, num) for offset := 0; offset < 4; offset++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*4)}, xs[i]) } // Recall that the Barrett reduction of x is given by // // x - int16((int32(x)*20159)>>26)*q VPMULHW(num, xs[0], ts[0]) // t := (int32(x) * 20159) >> 16 VPMULHW(num, xs[1], ts[1]) VPMULHW(num, xs[2], ts[2]) VPMULHW(num, xs[3], ts[3]) // t = int16(t)>>10 so that t = (int32(x)*20159) >> 26 VPSRAW(U8(10), ts[0], ts[0]) VPSRAW(U8(10), ts[1], ts[1]) VPSRAW(U8(10), ts[2], ts[2]) VPSRAW(U8(10), ts[3], ts[3]) VPMULLW(q, ts[0], ts[0]) // t *= q VPMULLW(q, ts[1], ts[1]) VPMULLW(q, ts[2], ts[2]) VPMULLW(q, ts[3], ts[3]) VPSUBW(ts[0], xs[0], xs[0]) // x -= t VPSUBW(ts[1], xs[1], xs[1]) VPSUBW(ts[2], xs[2], xs[2]) VPSUBW(ts[3], xs[3], xs[3]) for i := 0; i < 4; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*4)}) } } RET() } func normalizeAVX2() { TEXT("normalizeAVX2", NOSPLIT, "func(p *[256]int16)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) xs := [4]Op{YMM(), YMM(), YMM(), YMM()} ts := [4]Op{YMM(), YMM(), YMM(), YMM()} num := YMM() q := YMM() broadcastImm16(params.Q, q) broadcastImm16(20159, num) for offset := 0; offset < 4; offset++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (i + offset*4)}, xs[i]) } // Just like the generic implementation, we do a Barrett reduction // followed by a conditional subtraction. // Recall that the Barrett reduction of x is given by // // x - int16((int32(x)*20159)>>26)*q VPMULHW(num, xs[0], ts[0]) // t := (int32(x) * 20159) >> 16 VPMULHW(num, xs[1], ts[1]) VPMULHW(num, xs[2], ts[2]) VPMULHW(num, xs[3], ts[3]) // t = int16(t)>>10 so that t = (int32(x)*20159) >> 26 VPSRAW(U8(10), ts[0], ts[0]) VPSRAW(U8(10), ts[1], ts[1]) VPSRAW(U8(10), ts[2], ts[2]) VPSRAW(U8(10), ts[3], ts[3]) VPMULLW(q, ts[0], ts[0]) // t *= q VPMULLW(q, ts[1], ts[1]) VPMULLW(q, ts[2], ts[2]) VPMULLW(q, ts[3], ts[3]) VPSUBW(ts[0], xs[0], xs[0]) // x -= t VPSUBW(ts[1], xs[1], xs[1]) VPSUBW(ts[2], xs[2], xs[2]) VPSUBW(ts[3], xs[3], xs[3]) // x is now Barrett reduced. Next we conditionally subtract q to // normalize it. // // x -= Q // x += (x >> 15) & Q VPSUBW(q, xs[0], xs[0]) // x -= q VPSUBW(q, xs[1], xs[1]) VPSUBW(q, xs[2], xs[2]) VPSUBW(q, xs[3], xs[3]) VPSRAW(U8(15), xs[0], ts[0]) // t := x >> 15 VPSRAW(U8(15), xs[1], ts[1]) VPSRAW(U8(15), xs[2], ts[2]) VPSRAW(U8(15), xs[3], ts[3]) VPAND(ts[0], q, ts[0]) // t &= q VPAND(ts[1], q, ts[1]) VPAND(ts[2], q, ts[2]) VPAND(ts[3], q, ts[3]) VPADDW(xs[0], ts[0], xs[0]) // x += t VPADDW(xs[1], ts[1], xs[1]) VPADDW(xs[2], ts[2], xs[2]) VPADDW(xs[3], ts[3], xs[3]) for i := 0; i < 4; i++ { VMOVDQU(xs[i], Mem{Base: pPtr, Disp: 32 * (i + offset*4)}) } } RET() } func main() { ConstraintExpr("amd64") addAVX2() subAVX2() nttAVX2() invNttAVX2() mulHatAVX2() detangleAVX2() tangleAVX2() barrettReduceAVX2() normalizeAVX2() Generate() } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/field.go000066400000000000000000000054511454601126700261050ustar00rootroot00000000000000package common // Given -2¹⁵ q ≤ x < 2¹⁵ q, returns -q < y < q with x 2⁻¹⁶ = y (mod q). func montReduce(x int32) int16 { // This is Montgomery reduction with R=2¹⁶. // // Note gcd(2¹⁶, q) = 1 as q is prime. Write q' := 62209 = q⁻¹ mod R. // First we compute // // m := ((x mod R) q') mod R // = x q' mod R // = int16(x q') // = int16(int32(x) * int32(q')) // // Note that x q' might be as big as 2³² and could overflow the int32 // multiplication in the last line. However for any int32s a and b, // we have int32(int64(a)*int64(b)) = int32(a*b) and so the result is ok. m := int16(x * 62209) // Note that x - m q is divisible by R; indeed modulo R we have // // x - m q ≡ x - x q' q ≡ x - x q⁻¹ q ≡ x - x = 0. // // We return y := (x - m q) / R. Note that y is indeed correct as // modulo q we have // // y ≡ x R⁻¹ - m q R⁻¹ = x R⁻¹ // // and as both 2¹⁵ q ≤ m q, x < 2¹⁵ q, we have // 2¹⁶ q ≤ x - m q < 2¹⁶ and so q ≤ (x - m q) / R < q as desired. return int16(uint32(x-int32(m)*int32(Q)) >> 16) } // Given any x, returns x R mod q where R=2¹⁶. func toMont(x int16) int16 { // Note |1353 x| ≤ 1353 2¹⁵ ≤ 13318 q ≤ 2¹⁵ q and so we're within // the bounds of montReduce. return montReduce(int32(x) * 1353) // 1353 = R² mod q. } // Given any x, compute 0 ≤ y ≤ q with x = y (mod q). // // Beware: we might have barrettReduce(x) = q ≠ 0 for some x. In fact, // this happens if and only if x = -nq for some positive integer n. func barrettReduce(x int16) int16 { // This is standard Barrett reduction. // // For any x we have x mod q = x - ⌊x/q⌋ q. We will use 20159/2²⁶ as // an approximation of 1/q. Note that 0 ≤ 20159/2²⁶ - 1/q ≤ 0.135/2²⁶ // and so | x 20156/2²⁶ - x/q | ≤ 2⁻¹⁰ for |x| ≤ 2¹⁶. For all x // not a multiple of q, the number x/q is further than 1/q from any integer // and so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋. If x is a multiple of q and x is positive, // then x 20156/2²⁶ is larger than x/q so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋ as well. // Finally, if x is negative multiple of q, then ⌊x 20156/2²⁶⌋ = ⌊x/q⌋-1. // Thus // [ q if x=-nq for pos. integer n // x - ⌊x 20156/2²⁶⌋ q = [ // [ x mod q otherwise // // To compute actually compute this, note that // // ⌊x 20156/2²⁶⌋ = (20159 x) >> 26. return x - int16((int32(x)*20159)>>26)*Q } // Returns x if x < q and x - q otherwise. Assumes x ≥ -29439. func csubq(x int16) int16 { x -= Q // no overflow due to assumption x ≥ -29439. // If x is positive, then x >> 15 = 0. If x is negative, // then uint16(x >> 15) = 2¹⁶-1. So this will add back in q // if x was smaller than q. x += (x >> 15) & Q return x } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/field_test.go000066400000000000000000000035631454601126700271460ustar00rootroot00000000000000package common import ( "crypto/rand" "encoding/binary" "flag" "testing" ) var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") func modQ32(x int32) int16 { y := int16(x % int32(Q)) if y < 0 { y += Q } return y } func TestBarrettReduceFull(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for x := -1 << 15; x <= 1<<15; x++ { y1 := barrettReduce(int16(x)) y2 := int16(x) % Q if y2 < 0 { y2 += Q } if x < 0 && int16(-x)%Q == 0 { y1 -= Q } if y1 != y2 { t.Fatalf("%d %d %d", x, y1, y2) } } } func randSliceUint32WithMax(length uint, max uint32) []uint32 { bytes := make([]uint8, 4*length) n, err := rand.Read(bytes) if err != nil { panic(err) } else if n < len(bytes) { panic("short read from RNG") } x := make([]uint32, length) for i := range x { x[i] = binary.LittleEndian.Uint32(bytes[4*i:]) % max } return x } func TestMontReduce(t *testing.T) { size := 1000 max := uint32(Q) * (1 << 16) mid := int32(Q) * (1 << 15) r := randSliceUint32WithMax(uint(size), max) for i := 0; i < size; i++ { x := int32(r[i]) - mid y := montReduce(x) if modQ32(x) != modQ32(int32(y)*(1<<16)) { t.Fatalf("%d", x) } } } func TestToMontFull(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for x := -(1 << 15); x < 1<<15; x++ { y := toMont(int16(x)) if modQ32(int32(y)) != modQ32(int32(x*2285)) { t.Fatalf("%d", x) } } } func TestMontReduceFull(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for x := -int32(Q) * (1 << 15); x <= int32(Q)*(1<<15); x++ { y := montReduce(x) if modQ32(x) != modQ32(int32(y)*(1<<16)) { t.Fatalf("%d", x) } } } func TestCSubQFull(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for x := -29439; x < 1<<15; x++ { y1 := csubq(int16(x)) y2 := x if int16(x) >= Q { y2 -= int(Q) } if y1 != int16(y2) { t.Fatalf("%d", x) } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/generic.go000066400000000000000000000046451454601126700264420ustar00rootroot00000000000000//go:build !amd64 // +build !amd64 package common // Sets p to a + b. Does not normalize coefficients. func (p *Poly) Add(a, b *Poly) { p.addGeneric(a, b) } // Sets p to a - b. Does not normalize coefficients. func (p *Poly) Sub(a, b *Poly) { p.subGeneric(a, b) } // Executes an in-place forward "NTT" on p. // // Assumes the coefficients are in absolute value ≤q. The resulting // coefficients are in absolute value ≤7q. If the input is in Montgomery // form, then the result is in Montgomery form and so (by linearity of the NTT) // if the input is in regular form, then the result is also in regular form. // The order of coefficients will be "tangled". These can be put back into // their proper order by calling Detangle(). func (p *Poly) NTT() { p.nttGeneric() } // Executes an in-place inverse "NTT" on p and multiply by the Montgomery // factor R. // // Requires coefficients to be in "tangled" order, see Tangle(). // Assumes the coefficients are in absolute value ≤q. The resulting // coefficients are in absolute value ≤q. If the input is in Montgomery // form, then the result is in Montgomery form and so (by linearity) // if the input is in regular form, then the result is also in regular form. func (p *Poly) InvNTT() { p.invNTTGeneric() } // Sets p to the "pointwise" multiplication of a and b. // // That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in // Montgomery form. Products between coefficients of a and b must be strictly // bounded in absolute value by 2¹⁵q. p will be in Montgomery form and // bounded in absolute value by 2q. // // Requires a and b to be in "tangled" order, see Tangle(). p will be in // tangled order as well. func (p *Poly) MulHat(a, b *Poly) { p.mulHatGeneric(a, b) } // Puts p into the right form to be used with (among others) InvNTT(). func (p *Poly) Tangle() { // In the generic implementation there is no advantage to using a // different order, so we use the standard order everywhere. } // Puts p back into standard form. func (p *Poly) Detangle() { // In the generic implementation there is no advantage to using a // different order, so we use the standard order everywhere. } // Almost normalizes coefficients. // // Ensures each coefficient is in {0, …, q}. func (p *Poly) BarrettReduce() { p.barrettReduceGeneric() } // Normalizes coefficients. // // Ensures each coefficient is in {0, …, q-1}. func (p *Poly) Normalize() { p.normalizeGeneric() } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/ntt.go000066400000000000000000000165631454601126700256350ustar00rootroot00000000000000package common // Zetas lists precomputed powers of the primitive root of unity in // Montgomery representation used for the NTT: // // Zetas[i] = ζᵇʳᵛ⁽ⁱ⁾ R mod q // // where ζ = 17, brv(i) is the bitreversal of a 7-bit number and R=2¹⁶ mod q. // // The following Python code generates the Zetas arrays: // // q = 13*2**8 + 1; zeta = 17 // R = 2**16 % q # Montgomery const. // def brv(x): return int(''.join(reversed(bin(x)[2:].zfill(7))),2) // print([(pow(zeta, brv(i), q)*R)%q for i in range(128)]) var Zetas = [128]int16{ 2285, 2571, 2970, 1812, 1493, 1422, 287, 202, 3158, 622, 1577, 182, 962, 2127, 1855, 1468, 573, 2004, 264, 383, 2500, 1458, 1727, 3199, 2648, 1017, 732, 608, 1787, 411, 3124, 1758, 1223, 652, 2777, 1015, 2036, 1491, 3047, 1785, 516, 3321, 3009, 2663, 1711, 2167, 126, 1469, 2476, 3239, 3058, 830, 107, 1908, 3082, 2378, 2931, 961, 1821, 2604, 448, 2264, 677, 2054, 2226, 430, 555, 843, 2078, 871, 1550, 105, 422, 587, 177, 3094, 3038, 2869, 1574, 1653, 3083, 778, 1159, 3182, 2552, 1483, 2727, 1119, 1739, 644, 2457, 349, 418, 329, 3173, 3254, 817, 1097, 603, 610, 1322, 2044, 1864, 384, 2114, 3193, 1218, 1994, 2455, 220, 2142, 1670, 2144, 1799, 2051, 794, 1819, 2475, 2459, 478, 3221, 3021, 996, 991, 958, 1869, 1522, 1628, } // InvNTTReductions keeps track of which coefficients to apply Barrett // reduction to in Poly.InvNTT(). // // Generated in a lazily: once a butterfly is computed which is about to // overflow the int16, the largest coefficient is reduced. If that is // not enough, the other coefficient is reduced as well. // // This is actually optimal, as proven in https://eprint.iacr.org/2020/1377.pdf var InvNTTReductions = [...]int{ -1, // after layer 1 -1, // after layer 2 16, 17, 48, 49, 80, 81, 112, 113, 144, 145, 176, 177, 208, 209, 240, 241, -1, // after layer 3 0, 1, 32, 33, 34, 35, 64, 65, 96, 97, 98, 99, 128, 129, 160, 161, 162, 163, 192, 193, 224, 225, 226, 227, -1, // after layer 4 2, 3, 66, 67, 68, 69, 70, 71, 130, 131, 194, 195, 196, 197, 198, 199, -1, // after layer 5 4, 5, 6, 7, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, -1, // after layer 6 -1, // after layer 7 } // Executes an in-place forward "NTT" on p. // // Assumes the coefficients are in absolute value ≤q. The resulting // coefficients are in absolute value ≤7q. If the input is in Montgomery // form, then the result is in Montgomery form and so (by linearity of the NTT) // if the input is in regular form, then the result is also in regular form. // The order of coefficients will be "tangled". These can be put back into // their proper order by calling Detangle(). func (p *Poly) nttGeneric() { // Note that ℤ_q does not have a primitive 512ᵗʰ root of unity (as 512 // does not divide into q-1) and so we cannot do a regular NTT. ℤ_q // does have a primitive 256ᵗʰ root of unity, the smallest of which // is ζ := 17. // // Recall that our base ring R := ℤ_q[x] / (x²⁵⁶ + 1). The polynomial // x²⁵⁶+1 will not split completely (as its roots would be 512ᵗʰ roots // of unity.) However, it does split almost (using ζ¹²⁸ = -1): // // x²⁵⁶ + 1 = (x²)¹²⁸ - ζ¹²⁸ // = ((x²)⁶⁴ - ζ⁶⁴)((x²)⁶⁴ + ζ⁶⁴) // = ((x²)³² - ζ³²)((x²)³² + ζ³²)((x²)³² - ζ⁹⁶)((x²)³² + ζ⁹⁶) // ⋮ // = (x² - ζ)(x² + ζ)(x² - ζ⁶⁵)(x² + ζ⁶⁵) … (x² + ζ¹²⁷) // // Note that the powers of ζ that appear (from the second line down) are // in binary // // 0100000 1100000 // 0010000 1010000 0110000 1110000 // 0001000 1001000 0101000 1101000 0011000 1011000 0111000 1111000 // … // // That is: brv(2), brv(3), brv(4), …, where brv(x) denotes the 7-bit // bitreversal of x. These powers of ζ are given by the Zetas array. // // The polynomials x² ± ζⁱ are irreducible and coprime, hence by // the Chinese Remainder Theorem we know // // ℤ_q[x]/(x²⁵⁶+1) → ℤ_q[x]/(x²-ζ) x … x ℤ_q[x]/(x²+ζ¹²⁷) // // given by a ↦ ( a mod x²-ζ, …, a mod x²+ζ¹²⁷ ) // is an isomorphism, which is the "NTT". It can be efficiently computed by // // // a ↦ ( a mod (x²)⁶⁴ - ζ⁶⁴, a mod (x²)⁶⁴ + ζ⁶⁴ ) // ↦ ( a mod (x²)³² - ζ³², a mod (x²)³² + ζ³², // a mod (x²)⁹⁶ - ζ⁹⁶, a mod (x²)⁹⁶ + ζ⁹⁶ ) // // et cetera // // If N was 8 then this can be pictured in the following diagram: // // https://cnx.org/resources/17ee4dfe517a6adda05377b25a00bf6e6c93c334/File0026.png // // Each cross is a Cooley-Tukey butterfly: it's the map // // (a, b) ↦ (a + ζb, a - ζb) // // for the appropriate power ζ for that column and row group. k := 0 // Index into Zetas // l runs effectively over the columns in the diagram above; it is half the // height of a row group, i.e. the number of butterflies in each row group. // In the diagram above it would be 4, 2, 1. for l := N / 2; l > 1; l >>= 1 { // On the nᵗʰ iteration of the l-loop, the absolute value of the // coefficients are bounded by nq. // offset effectively loops over the row groups in this column; it is // the first row in the row group. for offset := 0; offset < N-l; offset += 2 * l { k++ zeta := int32(Zetas[k]) // j loops over each butterfly in the row group. for j := offset; j < offset+l; j++ { t := montReduce(zeta * int32(p[j+l])) p[j+l] = p[j] - t p[j] += t } } } } // Executes an in-place inverse "NTT" on p and multiply by the Montgomery // factor R. // // Requires coefficients to be in "tangled" order, see Tangle(). // Assumes the coefficients are in absolute value ≤q. The resulting // coefficients are in absolute value ≤q. If the input is in Montgomery // form, then the result is in Montgomery form and so (by linearity) // if the input is in regular form, then the result is also in regular form. func (p *Poly) invNTTGeneric() { k := 127 // Index into Zetas r := -1 // Index into InvNTTReductions. // We basically do the opposite of NTT, but postpone dividing by 2 in the // inverse of the Cooley-Tukey butterfly and accumulate that into a big // division by 2⁷ at the end. See the comments in the NTT() function. for l := 2; l < N; l <<= 1 { for offset := 0; offset < N-l; offset += 2 * l { // As we're inverting, we need powers of ζ⁻¹ (instead of ζ). // To be precise, we need ζᵇʳᵛ⁽ᵏ⁾⁻¹²⁸. However, as ζ⁻¹²⁸ = -1, // we can use the existing Zetas table instead of // keeping a separate InvZetas table as in Dilithium. minZeta := int32(Zetas[k]) k-- for j := offset; j < offset+l; j++ { // Gentleman-Sande butterfly: (a, b) ↦ (a + b, ζ(a-b)) t := p[j+l] - p[j] p[j] += p[j+l] p[j+l] = montReduce(minZeta * int32(t)) // Note that if we had |a| < αq and |b| < βq before the // butterfly, then now we have |a| < (α+β)q and |b| < q. } } // We let the InvNTTReductions instruct us which coefficients to // Barrett reduce. See TestInvNTTReductions, which tests whether // there is an overflow. for { r++ i := InvNTTReductions[r] if i < 0 { break } p[i] = barrettReduce(p[i]) } } for j := 0; j < N; j++ { // Note 1441 = (128)⁻¹ R². The coefficients are bounded by 9q, so // as 1441 * 9 ≈ 2¹⁴ < 2¹⁵, we're within the required bounds // for montReduce(). p[j] = montReduce(1441 * int32(p[j])) } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/ntt_test.go000066400000000000000000000042171454601126700266650ustar00rootroot00000000000000package common import "testing" func BenchmarkNTT(b *testing.B) { var a Poly for i := 0; i < b.N; i++ { a.NTT() } } func BenchmarkNTTGeneric(b *testing.B) { var a Poly for i := 0; i < b.N; i++ { a.nttGeneric() } } func BenchmarkInvNTT(b *testing.B) { var a Poly for i := 0; i < b.N; i++ { a.InvNTT() } } func BenchmarkInvNTTGeneric(b *testing.B) { var a Poly for i := 0; i < b.N; i++ { a.invNTTGeneric() } } func (p *Poly) Rand() { max := uint32(Q) r := randSliceUint32WithMax(uint(N), max) for i := 0; i < N; i++ { p[i] = int16(r[i]) } } func (p *Poly) RandAbsLeQ() { max := 2 * uint32(Q) r := randSliceUint32WithMax(uint(N), max) for i := 0; i < N; i++ { p[i] = int16(int32(r[i]) - int32(Q)) } } func TestNTTAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p, q1, q2 Poly p.RandAbsLeQ() q1 = p q2 = p q1.NTT() q1.Detangle() q2.nttGeneric() if q1 != q2 { t.Fatalf("NTT(%v) = \n%v \n!= %v", p, q2, q1) } } } func TestInvNTTAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p, q1, q2 Poly p.RandAbsLeQ() q1 = p q2 = p q1.Tangle() q1.InvNTT() q2.invNTTGeneric() q1.Normalize() q2.Normalize() if q1 != q2 { t.Fatalf("InvNTT(%v) = \n%v \n!= %v", p, q2, q1) } } } func TestNTT(t *testing.T) { for k := 0; k < 1000; k++ { var p, q Poly p.RandAbsLeQ() q = p q.Normalize() p.NTT() for i := 0; i < N; i++ { if p[i] > 7*Q || 7*Q < p[i] { t.Fatal() } } p.Normalize() p.InvNTT() for i := 0; i < N; i++ { if p[i] > Q || p[i] < -Q { t.Fatal() } } p.Normalize() for i := 0; i < N; i++ { if int32(p[i]) != (int32(q[i])*(1<<16))%int32(Q) { t.Fatal() } } } } func TestInvNTTReductions(t *testing.T) { // Simulates bounds on coefficients in InvNTT. xs := [256]int{} for i := 0; i < 256; i++ { xs[i] = 1 } r := -1 for layer := 1; layer < 8; layer++ { w := 1 << uint(layer) i := 0 for i+w < 256 { xs[i] = xs[i] + xs[i+w] if xs[i] > 9 { t.Fatal() } xs[i+w] = 1 i++ if i%w == 0 { i += w } } for { r++ i := InvNTTReductions[r] if i < 0 { break } xs[i] = 1 } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/params.go000066400000000000000000000007231454601126700263020ustar00rootroot00000000000000package common import ( "github.com/cloudflare/circl/pke/kyber/internal/common/params" ) const ( // Q is the parameter q ≡ 3329 = 2¹¹ + 2¹⁰ + 2⁸ + 1. Q = params.Q // N is the parameter N: the length of the polynomials N = params.N // PolySize is the size of a packed polynomial. PolySize = params.PolySize // PlaintextSize is the size of the plaintext PlaintextSize = params.PlaintextSize // Eta2 is the parameter η₂ Eta2 = params.Eta2 ) golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/params/000077500000000000000000000000001454601126700257515ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/params/params.go000066400000000000000000000007421454601126700275660ustar00rootroot00000000000000package params // We put these parameters in a separate package so that the Go code, // such as asm/src.go, that generates assembler can import it. const ( // Q is the parameter q ≡ 3329 = 2¹¹ + 2¹⁰ + 2⁸ + 1. Q int16 = 3329 // N is the parameter N: the length of the polynomials N = 256 // PolySize is the size of a packed polynomial. PolySize = 384 // PlaintextSize is the size of the plaintext PlaintextSize = 32 // Eta2 is the parameter η₂ Eta2 = 2 ) golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/poly.go000066400000000000000000000226601454601126700260060ustar00rootroot00000000000000package common // An element of our base ring R which are polynomials over ℤ_q // modulo the equation Xᴺ = -1, where q=3329 and N=256. // // This type is also used to store NTT-transformed polynomials, // see Poly.NTT(). // // Coefficients aren't always reduced. See Normalize(). type Poly [N]int16 // Sets p to a + b. Does not normalize coefficients. func (p *Poly) addGeneric(a, b *Poly) { for i := 0; i < N; i++ { p[i] = a[i] + b[i] } } // Sets p to a - b. Does not normalize coefficients. func (p *Poly) subGeneric(a, b *Poly) { for i := 0; i < N; i++ { p[i] = a[i] - b[i] } } // Almost normalizes coefficients. // // Ensures each coefficient is in {0, …, q}. func (p *Poly) barrettReduceGeneric() { for i := 0; i < N; i++ { p[i] = barrettReduce(p[i]) } } // Normalizes coefficients. // // Ensures each coefficient is in {0, …, q-1}. func (p *Poly) normalizeGeneric() { for i := 0; i < N; i++ { p[i] = csubq(barrettReduce(p[i])) } } // Multiplies p in-place by the Montgomery factor 2¹⁶. // // Coefficients of p can be arbitrary. Resulting coefficients are bounded // in absolute value by q. func (p *Poly) ToMont() { for i := 0; i < N; i++ { p[i] = toMont(p[i]) } } // Sets p to the "pointwise" multiplication of a and b. // // That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in // Montgomery form. Products between coefficients of a and b must be strictly // bounded in absolute value by 2¹⁵q. p will be in Montgomery form and // bounded in absolute value by 2q. // // Requires a and b to be in "tangled" order, see Tangle(). p will be in // tangled order as well. func (p *Poly) mulHatGeneric(a, b *Poly) { // Recall from the discussion in NTT(), that a transformed polynomial is // an element of ℤ_q[x]/(x²-ζ) x … x ℤ_q[x]/(x²+ζ¹²⁷); // that is: 128 degree-one polynomials instead of simply 256 elements // from ℤ_q as in the regular NTT. So instead of pointwise multiplication, // we multiply the 128 pairs of degree-one polynomials modulo the // right equation: // // (a₁ + a₂x)(b₁ + b₂x) = a₁b₁ + a₂b₂ζ' + (a₁b₂ + a₂b₁)x, // // where ζ' is the appropriate power of ζ. k := 64 for i := 0; i < N; i += 4 { zeta := int32(Zetas[k]) k++ p0 := montReduce(int32(a[i+1]) * int32(b[i+1])) p0 = montReduce(int32(p0) * zeta) p0 += montReduce(int32(a[i]) * int32(b[i])) p1 := montReduce(int32(a[i]) * int32(b[i+1])) p1 += montReduce(int32(a[i+1]) * int32(b[i])) p[i] = p0 p[i+1] = p1 p2 := montReduce(int32(a[i+3]) * int32(b[i+3])) p2 = -montReduce(int32(p2) * zeta) p2 += montReduce(int32(a[i+2]) * int32(b[i+2])) p3 := montReduce(int32(a[i+2]) * int32(b[i+3])) p3 += montReduce(int32(a[i+3]) * int32(b[i+2])) p[i+2] = p2 p[i+3] = p3 } } // Packs p into buf. buf should be of length PolySize. // // Assumes p is normalized (and not just Barrett reduced) and "tangled", // see Tangle(). func (p *Poly) Pack(buf []byte) { q := *p q.Detangle() for i := 0; i < 128; i++ { t0 := q[2*i] t1 := q[2*i+1] buf[3*i] = byte(t0) buf[3*i+1] = byte(t0>>8) | byte(t1<<4) buf[3*i+2] = byte(t1 >> 4) } } // Unpacks p from buf. // // buf should be of length PolySize. p will be "tangled", see Detangle(). // // p will not be normalized; instead 0 ≤ p[i] < 4096. func (p *Poly) Unpack(buf []byte) { for i := 0; i < 128; i++ { p[2*i] = int16(buf[3*i]) | ((int16(buf[3*i+1]) << 8) & 0xfff) p[2*i+1] = int16(buf[3*i+1]>>4) | (int16(buf[3*i+2]) << 4) } p.Tangle() } // Set p to Decompress_q(m, 1). // // p will be normalized. m has to be of PlaintextSize. func (p *Poly) DecompressMessage(m []byte) { // Decompress_q(x, 1) = ⌈xq/2⌋ = ⌊xq/2+½⌋ = (xq+1) >> 1 and so // Decompress_q(0, 1) = 0 and Decompress_q(1, 1) = (q+1)/2. for i := 0; i < 32; i++ { for j := 0; j < 8; j++ { bit := (m[i] >> uint(j)) & 1 // Set coefficient to either 0 or (q+1)/2 depending on the bit. p[8*i+j] = -int16(bit) & ((Q + 1) / 2) } } } // Writes Compress_q(p, 1) to m. // // Assumes p is normalized. m has to be of length at least PlaintextSize. func (p *Poly) CompressMessageTo(m []byte) { // Compress_q(x, 1) is 1 on {833, …, 2496} and zero elsewhere. for i := 0; i < 32; i++ { m[i] = 0 for j := 0; j < 8; j++ { x := 1664 - p[8*i+j] // With the previous substitution, we want to return 1 if // and only if x is in {831, …, -832}. x = (x >> 15) ^ x // Note (x >> 15)ˣ if x≥0 and -x-1 otherwise. Thus now we want // to return 1 iff x ≤ 831, ie. x - 832 < 0. x -= 832 m[i] |= ((byte(x >> 15)) & 1) << uint(j) } } } // Set p to Decompress_q(m, 1). // // Assumes d is in {4, 5, 10, 11}. p will be normalized. func (p *Poly) Decompress(m []byte, d int) { // Decompress_q(x, d) = ⌈(q/2ᵈ)x⌋ // = ⌊(q/2ᵈ)x+½⌋ // = ⌊(qx + 2ᵈ⁻¹)/2ᵈ⌋ // = (qx + (1<<(d-1))) >> d switch d { case 4: for i := 0; i < N/2; i++ { p[2*i] = int16(((1 << 3) + uint32(m[i]&15)*uint32(Q)) >> 4) p[2*i+1] = int16(((1 << 3) + uint32(m[i]>>4)*uint32(Q)) >> 4) } case 5: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { t[0] = uint16(m[idx]) t[1] = (uint16(m[idx]) >> 5) | (uint16(m[idx+1] << 3)) t[2] = uint16(m[idx+1]) >> 2 t[3] = (uint16(m[idx+1]) >> 7) | (uint16(m[idx+2] << 1)) t[4] = (uint16(m[idx+2]) >> 4) | (uint16(m[idx+3] << 4)) t[5] = uint16(m[idx+3]) >> 1 t[6] = (uint16(m[idx+3]) >> 6) | (uint16(m[idx+4] << 2)) t[7] = uint16(m[idx+4]) >> 3 for j := 0; j < 8; j++ { p[8*i+j] = int16(((1 << 4) + uint32(t[j]&((1<<5)-1))*uint32(Q)) >> 5) } idx += 5 } case 10: var t [4]uint16 idx := 0 for i := 0; i < N/4; i++ { t[0] = uint16(m[idx]) | (uint16(m[idx+1]) << 8) t[1] = (uint16(m[idx+1]) >> 2) | (uint16(m[idx+2]) << 6) t[2] = (uint16(m[idx+2]) >> 4) | (uint16(m[idx+3]) << 4) t[3] = (uint16(m[idx+3]) >> 6) | (uint16(m[idx+4]) << 2) for j := 0; j < 4; j++ { p[4*i+j] = int16(((1 << 9) + uint32(t[j]&((1<<10)-1))*uint32(Q)) >> 10) } idx += 5 } case 11: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { t[0] = uint16(m[idx]) | (uint16(m[idx+1]) << 8) t[1] = (uint16(m[idx+1]) >> 3) | (uint16(m[idx+2]) << 5) t[2] = (uint16(m[idx+2]) >> 6) | (uint16(m[idx+3]) << 2) | (uint16(m[idx+4]) << 10) t[3] = (uint16(m[idx+4]) >> 1) | (uint16(m[idx+5]) << 7) t[4] = (uint16(m[idx+5]) >> 4) | (uint16(m[idx+6]) << 4) t[5] = (uint16(m[idx+6]) >> 7) | (uint16(m[idx+7]) << 1) | (uint16(m[idx+8]) << 9) t[6] = (uint16(m[idx+8]) >> 2) | (uint16(m[idx+9]) << 6) t[7] = (uint16(m[idx+9]) >> 5) | (uint16(m[idx+10]) << 3) for j := 0; j < 8; j++ { p[8*i+j] = int16(((1 << 10) + uint32(t[j]&((1<<11)-1))*uint32(Q)) >> 11) } idx += 11 } default: panic("unsupported d") } } // Writes Compress_q(p, d) to m. // // Assumes p is normalized and d is in {4, 5, 10, 11}. func (p *Poly) CompressTo(m []byte, d int) { // Compress_q(x, d) = ⌈(2ᵈ/q)x⌋ mod⁺ 2ᵈ // = ⌊(2ᵈ/q)x+½⌋ mod⁺ 2ᵈ // = ⌊((x << d) + q/2) / q⌋ mod⁺ 2ᵈ // = DIV((x << d) + q/2, q) & ((1<>e, where a/(2^e) ≈ 1/q. // For d in {10,11} we use 20,642,679/2^36, which computes division by x/q // correctly for 0 ≤ x < 41,522,616, which fits (q << 11) + q/2 comfortably. // For d in {4,5} we use 315/2^20, which doesn't compute division by x/q // correctly for all inputs, but it's close enough that the end result // of the compression is correct. The advantage is that we do not need // to use a 64-bit intermediate value. switch d { case 4: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { for j := 0; j < 8; j++ { t[j] = uint16((((uint32(p[8*i+j])<<4)+uint32(Q)/2)*315)>> 20) & ((1 << 4) - 1) } m[idx] = byte(t[0]) | byte(t[1]<<4) m[idx+1] = byte(t[2]) | byte(t[3]<<4) m[idx+2] = byte(t[4]) | byte(t[5]<<4) m[idx+3] = byte(t[6]) | byte(t[7]<<4) idx += 4 } case 5: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { for j := 0; j < 8; j++ { t[j] = uint16((((uint32(p[8*i+j])<<5)+uint32(Q)/2)*315)>> 20) & ((1 << 5) - 1) } m[idx] = byte(t[0]) | byte(t[1]<<5) m[idx+1] = byte(t[1]>>3) | byte(t[2]<<2) | byte(t[3]<<7) m[idx+2] = byte(t[3]>>1) | byte(t[4]<<4) m[idx+3] = byte(t[4]>>4) | byte(t[5]<<1) | byte(t[6]<<6) m[idx+4] = byte(t[6]>>2) | byte(t[7]<<3) idx += 5 } case 10: var t [4]uint16 idx := 0 for i := 0; i < N/4; i++ { for j := 0; j < 4; j++ { t[j] = uint16((uint64((uint32(p[4*i+j])<<10)+uint32(Q)/2)* 20642679)>>36) & ((1 << 10) - 1) } m[idx] = byte(t[0]) m[idx+1] = byte(t[0]>>8) | byte(t[1]<<2) m[idx+2] = byte(t[1]>>6) | byte(t[2]<<4) m[idx+3] = byte(t[2]>>4) | byte(t[3]<<6) m[idx+4] = byte(t[3] >> 2) idx += 5 } case 11: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { for j := 0; j < 8; j++ { t[j] = uint16((uint64((uint32(p[8*i+j])<<11)+uint32(Q)/2)* 20642679)>>36) & ((1 << 11) - 1) } m[idx] = byte(t[0]) m[idx+1] = byte(t[0]>>8) | byte(t[1]<<3) m[idx+2] = byte(t[1]>>5) | byte(t[2]<<6) m[idx+3] = byte(t[2] >> 2) m[idx+4] = byte(t[2]>>10) | byte(t[3]<<1) m[idx+5] = byte(t[3]>>7) | byte(t[4]<<4) m[idx+6] = byte(t[4]>>4) | byte(t[5]<<7) m[idx+7] = byte(t[5] >> 1) m[idx+8] = byte(t[5]>>9) | byte(t[6]<<2) m[idx+9] = byte(t[6]>>6) | byte(t[7]<<5) m[idx+10] = byte(t[7] >> 3) idx += 11 } default: panic("unsupported d") } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/poly_test.go000066400000000000000000000163411454601126700270440ustar00rootroot00000000000000package common import ( "bytes" "crypto/rand" "fmt" "testing" ) func (p *Poly) RandAbsLe9Q() { max := 9 * uint32(Q) r := randSliceUint32WithMax(uint(N), max) for i := 0; i < N; i++ { p[i] = int16(int32(r[i])) } } // Returns x mod^± q func sModQ(x int16) int16 { x = x % Q if x >= (Q-1)/2 { x = x - Q } return x } func TestDecompressMessage(t *testing.T) { var m, m2 [PlaintextSize]byte var p Poly for i := 0; i < 1000; i++ { if n, err := rand.Read(m[:]); err != nil { t.Error(err) } else if n != len(m) { t.Fatal("short read from RNG") } p.DecompressMessage(m[:]) p.CompressMessageTo(m2[:]) if m != m2 { t.Fatal() } } } func TestCompress(t *testing.T) { for _, d := range []int{4, 5, 10, 11} { d := d t.Run(fmt.Sprintf("d=%d", d), func(t *testing.T) { var p, q Poly bound := (Q + (1 << uint(d))) >> uint(d+1) buf := make([]byte, (N*d-1)/8+1) for i := 0; i < 1000; i++ { p.Rand() p.CompressTo(buf, d) q.Decompress(buf, d) for j := 0; j < N; j++ { diff := sModQ(p[j] - q[j]) if diff < 0 { diff = -diff } if diff > bound { t.Logf("%v\n", buf) t.Fatalf("|%d - %d mod^± q| = %d > %d, j=%d", p[i], q[j], diff, bound, j) } } } }) } } func TestCompressMessage(t *testing.T) { var p Poly var m [32]byte ok := true for i := 0; i < int(Q); i++ { p[0] = int16(i) p.CompressMessageTo(m[:]) want := byte(0) if i >= 833 && i < 2497 { want = 1 } if m[0] != want { ok = false t.Logf("%d %d %d", i, want, m[0]) } } if !ok { t.Fatal() } } func TestMulHat(t *testing.T) { for k := 0; k < 1000; k++ { var a, b, p, ah, bh, ph Poly a.RandAbsLeQ() b.RandAbsLeQ() b[0] = 1 ah = a bh = b ah.NTT() bh.NTT() ph.MulHat(&ah, &bh) ph.BarrettReduce() ph.InvNTT() for i := 0; i < N; i++ { for j := 0; j < N; j++ { v := montReduce(int32(a[i]) * int32(b[j])) k := i + j if k >= N { // Recall xᴺ = -1. k -= N v = -v } p[k] = barrettReduce(v + p[k]) } } for i := 0; i < N; i++ { p[i] = int16((int32(p[i]) * ((1 << 16) % int32(Q))) % int32(Q)) } p.Normalize() ph.Normalize() a.Normalize() b.Normalize() if p != ph { t.Fatalf("%v\n%v\n%v\n%v", a, b, p, ph) } } } func TestAddAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a, b Poly a.RandAbsLeQ() b.RandAbsLeQ() p1.Add(&a, &b) p2.addGeneric(&a, &b) if p1 != p2 { t.Fatalf("Add(%v, %v) = \n%v \n!= %v", a, b, p1, p2) } } } func BenchmarkAdd(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.Add(&p, &p) } } func BenchmarkAddGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.addGeneric(&p, &p) } } func TestSubAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a, b Poly a.RandAbsLeQ() b.RandAbsLeQ() p1.Sub(&a, &b) p2.subGeneric(&a, &b) if p1 != p2 { t.Fatalf("Sub(%v, %v) = \n%v \n!= %v", a, b, p1, p2) } } } func BenchmarkSub(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.Sub(&p, &p) } } func BenchmarkSubGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.subGeneric(&p, &p) } } func TestMulHatAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a, b Poly a.RandAbsLeQ() b.RandAbsLeQ() a2 := a b2 := b a2.Tangle() b2.Tangle() p1.MulHat(&a2, &b2) p1.Detangle() p2.mulHatGeneric(&a, &b) if p1 != p2 { t.Fatalf("MulHat(%v, %v) = \n%v \n!= %v", a, b, p1, p2) } } } func BenchmarkMulHat(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.MulHat(&p, &p) } } func BenchmarkMulHatGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.mulHatGeneric(&p, &p) } } func BenchmarkBarrettReduce(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.BarrettReduce() } } func BenchmarkBarrettReduceGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.barrettReduceGeneric() } } func TestBarrettReduceAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a Poly a.RandAbsLe9Q() p1 = a p2 = a p1.BarrettReduce() p2.barrettReduceGeneric() if p1 != p2 { t.Fatalf("BarrettReduce(%v) = \n%v \n!= %v", a, p1, p2) } } } func BenchmarkNormalize(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.Normalize() } } func BenchmarkNormalizeGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.barrettReduceGeneric() } } func TestNormalizeAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a Poly a.RandAbsLe9Q() p1 = a p2 = a p1.Normalize() p2.normalizeGeneric() if p1 != p2 { t.Fatalf("Normalize(%v) = \n%v \n!= %v", a, p1, p2) } } } func (p *Poly) OldCompressTo(m []byte, d int) { switch d { case 4: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { for j := 0; j < 8; j++ { t[j] = uint16(((uint32(p[8*i+j])<<4)+uint32(Q)/2)/ uint32(Q)) & ((1 << 4) - 1) } m[idx] = byte(t[0]) | byte(t[1]<<4) m[idx+1] = byte(t[2]) | byte(t[3]<<4) m[idx+2] = byte(t[4]) | byte(t[5]<<4) m[idx+3] = byte(t[6]) | byte(t[7]<<4) idx += 4 } case 5: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { for j := 0; j < 8; j++ { t[j] = uint16(((uint32(p[8*i+j])<<5)+uint32(Q)/2)/ uint32(Q)) & ((1 << 5) - 1) } m[idx] = byte(t[0]) | byte(t[1]<<5) m[idx+1] = byte(t[1]>>3) | byte(t[2]<<2) | byte(t[3]<<7) m[idx+2] = byte(t[3]>>1) | byte(t[4]<<4) m[idx+3] = byte(t[4]>>4) | byte(t[5]<<1) | byte(t[6]<<6) m[idx+4] = byte(t[6]>>2) | byte(t[7]<<3) idx += 5 } case 10: var t [4]uint16 idx := 0 for i := 0; i < N/4; i++ { for j := 0; j < 4; j++ { t[j] = uint16(((uint32(p[4*i+j])<<10)+uint32(Q)/2)/ uint32(Q)) & ((1 << 10) - 1) } m[idx] = byte(t[0]) m[idx+1] = byte(t[0]>>8) | byte(t[1]<<2) m[idx+2] = byte(t[1]>>6) | byte(t[2]<<4) m[idx+3] = byte(t[2]>>4) | byte(t[3]<<6) m[idx+4] = byte(t[3] >> 2) idx += 5 } case 11: var t [8]uint16 idx := 0 for i := 0; i < N/8; i++ { for j := 0; j < 8; j++ { t[j] = uint16(((uint32(p[8*i+j])<<11)+uint32(Q)/2)/ uint32(Q)) & ((1 << 11) - 1) } m[idx] = byte(t[0]) m[idx+1] = byte(t[0]>>8) | byte(t[1]<<3) m[idx+2] = byte(t[1]>>5) | byte(t[2]<<6) m[idx+3] = byte(t[2] >> 2) m[idx+4] = byte(t[2]>>10) | byte(t[3]<<1) m[idx+5] = byte(t[3]>>7) | byte(t[4]<<4) m[idx+6] = byte(t[4]>>4) | byte(t[5]<<7) m[idx+7] = byte(t[5] >> 1) m[idx+8] = byte(t[5]>>9) | byte(t[6]<<2) m[idx+9] = byte(t[6]>>6) | byte(t[7]<<5) m[idx+10] = byte(t[7] >> 3) idx += 11 } default: panic("unsupported d") } } func TestCompressFullInputFirstCoeff(t *testing.T) { for _, d := range []int{4, 5, 10, 11} { d := d t.Run(fmt.Sprintf("d=%d", d), func(t *testing.T) { var p, q Poly bound := (Q + (1 << uint(d))) >> uint(d+1) buf := make([]byte, (N*d-1)/8+1) buf2 := make([]byte, len(buf)) for i := int16(0); i < Q; i++ { p[0] = i p.CompressTo(buf, d) p.OldCompressTo(buf2, d) if !bytes.Equal(buf, buf2) { t.Fatalf("%d", i) } q.Decompress(buf, d) diff := sModQ(p[0] - q[0]) if diff < 0 { diff = -diff } if diff > bound { t.Logf("%v\n", buf) t.Fatalf("|%d - %d mod^± q| = %d > %d", p[0], q[0], diff, bound) } } }) } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/sample.go000066400000000000000000000133451454601126700263040ustar00rootroot00000000000000package common import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/simd/keccakf1600" ) // DeriveX4Available indicates whether the system supports the quick fourway // sampling variants like PolyDeriveUniformX4. var DeriveX4Available = keccakf1600.IsEnabledX4() // Samples p from a centered binomial distribution with given η. // // Essentially CBD_η(PRF(seed, nonce)) from the specification. func (p *Poly) DeriveNoise(seed []byte, nonce uint8, eta int) { switch eta { case 2: p.DeriveNoise2(seed, nonce) case 3: p.DeriveNoise3(seed, nonce) default: panic("unsupported eta") } } // Sample p from a centered binomial distribution with n=6 and p=½ - that is: // coefficients are in {-3, -2, -1, 0, 1, 2, 3} with probabilities {1/64, 3/32, // 15/64, 5/16, 16/64, 3/32, 1/64}. func (p *Poly) DeriveNoise3(seed []byte, nonce uint8) { keySuffix := [1]byte{nonce} h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Write(keySuffix[:]) // The distribution at hand is exactly the same as that // of (a₁ + a₂ + a₃) - (b₁ + b₂+b₃) where a_i,b_i~U(1). Thus we need // 6 bits per coefficients, thus 192 bytes of input entropy. // We add two extra zero bytes in the buffer to be able to read 8 bytes // at the same time (while using only 6.) var buf [192 + 2]byte _, _ = h.Read(buf[:192]) for i := 0; i < 32; i++ { // t is interpreted as a₁ + 2a₂ + 4a₃ + 8b₁ + 16b₂ + …. t := binary.LittleEndian.Uint64(buf[6*i:]) d := t & 0x249249249249 // a₁ + 8b₁ + … d += (t >> 1) & 0x249249249249 // a₁ + a₂ + 8(b₁ + b₂) + … d += (t >> 2) & 0x249249249249 // a₁ + a₂ + a₃ + 4(b₁ + b₂ + b₃) + … for j := 0; j < 8; j++ { a := int16(d) & 0x7 // a₁ + a₂ + a₃ d >>= 3 b := int16(d) & 0x7 // b₁ + b₂ + b₃ d >>= 3 p[8*i+j] = a - b } } } // Sample p from a centered binomial distribution with n=4 and p=½ - that is: // coefficients are in {-2, -1, 0, 1, 2} with probabilities {1/16, 1/4, // 3/8, 1/4, 1/16}. func (p *Poly) DeriveNoise2(seed []byte, nonce uint8) { keySuffix := [1]byte{nonce} h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Write(keySuffix[:]) // The distribution at hand is exactly the same as that // of (a + a') - (b + b') where a,a',b,b'~U(1). Thus we need 4 bits per // coefficients, thus 128 bytes of input entropy. var buf [128]byte _, _ = h.Read(buf[:]) for i := 0; i < 16; i++ { // t is interpreted as a + 2a' + 4b + 8b' + …. t := binary.LittleEndian.Uint64(buf[8*i:]) d := t & 0x5555555555555555 // a + 4b + … d += (t >> 1) & 0x5555555555555555 // a+a' + 4(b + b') + … for j := 0; j < 16; j++ { a := int16(d) & 0x3 d >>= 2 b := int16(d) & 0x3 d >>= 2 p[16*i+j] = a - b } } } // For each i, sample ps[i] uniformly from the given seed for coordinates // xs[i] and ys[i]. ps[i] may be nil and is ignored in that case. // // Can only be called when DeriveX4Available is true. func PolyDeriveUniformX4(ps [4]*Poly, seed *[32]byte, xs, ys [4]uint8) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // Absorb the coordinates, the SHAKE128 domain separator (0b1111), the // start of the padding (0b…001) and the end of the padding 0b100…. // Recall that the rate of SHAKE128 is 168; ie. 21 uint64s. for j := 0; j < 4; j++ { state[4*4+j] = uint64(xs[j]) | (uint64(ys[j]) << 8) | (0x1f << 16) state[20*4+j] = 0x80 << 56 } var idx [4]int // indices into ps for j := 0; j < 4; j++ { if ps[j] == nil { idx[j] = N // mark nil polynomials as completed } } done := false for !done { // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each of // the four SHAKE128 streams. perm.Permute() done = true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == N { continue } for i := 0; i < 7; i++ { var t [16]uint16 v1 := state[i*3*4+j] v2 := state[(i*3+1)*4+j] v3 := state[(i*3+2)*4+j] t[0] = uint16(v1) & 0xfff t[1] = uint16(v1>>12) & 0xfff t[2] = uint16(v1>>24) & 0xfff t[3] = uint16(v1>>36) & 0xfff t[4] = uint16(v1>>48) & 0xfff t[5] = uint16((v1>>60)|(v2<<4)) & 0xfff t[6] = uint16(v2>>8) & 0xfff t[7] = uint16(v2>>20) & 0xfff t[8] = uint16(v2>>32) & 0xfff t[9] = uint16(v2>>44) & 0xfff t[10] = uint16((v2>>56)|(v3<<8)) & 0xfff t[11] = uint16(v3>>4) & 0xfff t[12] = uint16(v3>>16) & 0xfff t[13] = uint16(v3>>28) & 0xfff t[14] = uint16(v3>>40) & 0xfff t[15] = uint16(v3>>52) & 0xfff for k := 0; k < 16; k++ { if t[k] < uint16(Q) { ps[j][idx[j]] = int16(t[k]) idx[j]++ if idx[j] == N { continue PolyLoop } } } } done = false } } for i := 0; i < 4; i++ { if ps[i] != nil { ps[i].Tangle() } } } // Sample p uniformly from the given seed and x and y coordinates. // // Coefficients are reduced and will be in "tangled" order. See Tangle(). func (p *Poly) DeriveUniform(seed *[32]byte, x, y uint8) { var seedSuffix [2]byte var buf [168]byte // rate of SHAKE-128 seedSuffix[0] = x seedSuffix[1] = y h := sha3.NewShake128() _, _ = h.Write(seed[:]) _, _ = h.Write(seedSuffix[:]) i := 0 for { _, _ = h.Read(buf[:]) for j := 0; j < 168; j += 3 { t1 := (uint16(buf[j]) | (uint16(buf[j+1]) << 8)) & 0xfff t2 := (uint16(buf[j+1]>>4) | (uint16(buf[j+2]) << 4)) & 0xfff if t1 < uint16(Q) { p[i] = int16(t1) i++ if i == N { break } } if t2 < uint16(Q) { p[i] = int16(t2) i++ if i == N { break } } } if i == N { break } } p.Tangle() } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/sample_test.go000066400000000000000000000120341454601126700273350ustar00rootroot00000000000000package common import ( "testing" ) func BenchmarkDeriveNoise2(b *testing.B) { var p Poly var seed [32]byte for i := 0; i < b.N; i++ { p.DeriveNoise2(seed[:], 37) } } func BenchmarkDeriveNoise3(b *testing.B) { var p Poly var seed [32]byte for i := 0; i < b.N; i++ { p.DeriveNoise3(seed[:], 37) } } func TestPolyDeriveNoise3Ref(t *testing.T) { var p Poly want := Poly{ 0, 0, 1, -1, 0, 2, 0, -1, -1, 3, 0, 1, -2, -2, 0, 1, -2, 1, 0, -2, 3, 0, 0, 0, 1, 3, 1, 1, 2, 1, -1, -1, -1, 0, 1, 0, 1, 0, 2, 0, 1, -2, 0, -1, -1, -2, 1, -1, -1, 2, -1, 1, 1, 2, -3, -1, -1, 0, 0, 0, 0, 1, -1, -2, -2, 0, -2, 0, 0, 0, 1, 0, -1, -1, 1, -2, 2, 0, 0, 2, -2, 0, 1, 0, 1, 1, 1, 0, 1, -2, -1, -2, -1, 1, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, -1, 1, 0, 1, 0, -1, -1, 0, -2, 2, 0, -2, 1, -1, 0, 1, -1, -1, 2, 1, 0, 0, -2, -1, 2, 0, 0, 0, -1, -1, 3, 1, 0, 1, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, -1, -1, -1, 0, 1, 3, 1, 0, 1, 0, 1, -1, -1, -1, -1, 0, 0, -2, -1, -1, 2, 0, 1, 0, 1, 0, 2, -2, 0, 1, 1, -3, -1, -2, -1, 0, 1, 0, 1, -2, 2, 2, 1, 1, 0, -1, 0, -1, -1, 1, 0, -1, 2, 1, -1, 1, 2, -2, 1, 2, 0, 1, 2, 1, 0, 0, 2, 1, 2, 1, 0, 2, 1, 0, 0, -1, -1, 1, -1, 0, 1, -1, 2, 2, 0, 0, -1, 1, 1, 1, 1, 0, 0, -2, 0, -1, 1, 2, 0, 0, 1, 1, -1, 1, 0, 1, } var seed [32]byte for i := 0; i < 32; i++ { seed[i] = byte(i) } p.DeriveNoise3(seed[:], 37) if p != want { t.Fatal() } } func TestPolyDeriveNoise2Ref(t *testing.T) { var p Poly want := Poly{ 1, 0, 1, -1, -1, -2, -1, -1, 2, 0, -1, 0, 0, -1, 1, 1, -1, 1, 0, 2, -2, 0, 1, 2, 0, 0, -1, 1, 0, -1, 1, -1, 1, 2, 1, 1, 0, -1, 1, -1, -2, -1, 1, -1, -1, -1, 2, -1, -1, 0, 0, 1, 1, -1, 1, 1, 1, 1, -1, -2, 0, 1, 0, 0, 2, 1, -1, 2, 0, 0, 1, 1, 0, -1, 0, 0, -1, -1, 2, 0, 1, -1, 2, -1, -1, -1, -1, 0, -2, 0, 2, 1, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, -1, -1, 0, -1, 0, 0, -2, 1, 1, 0, 1, 0, 1, 0, 1, 1, -1, 2, 0, 1, -1, 1, 2, 0, 0, 0, 0, -1, -1, -1, 0, 1, 0, -1, 2, 0, 0, 1, 1, 1, 0, 1, -1, 1, 2, 1, 0, 2, -1, 1, -1, -2, -1, -2, -1, 1, 0, -2, -2, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 0, -1, -1, 0, 2, 0, 0, -2, 1, 0, 2, 1, -1, -2, 0, 0, -1, 1, 1, 0, 0, 2, 0, 1, 1, -2, 1, -2, 1, 1, 0, 2, 0, -1, 0, -1, 0, 1, 2, 0, 1, 0, -2, 1, -2, -2, 1, -1, 0, -1, 1, 1, 0, 0, 0, 1, 0, -1, 1, 1, 0, 0, 0, 0, 1, 0, 1, -1, 0, 1, -1, -1, 2, 0, 0, 1, -1, 0, 1, -1, 0, } var seed [32]byte for i := 0; i < 32; i++ { seed[i] = byte(i) } p.DeriveNoise2(seed[:], 37) if p != want { t.Fatal() } } func TestPolyDeriveUniformRef(t *testing.T) { var p Poly // Generated by reference implementation. want := Poly{ 797, 993, 161, 6, 2608, 2385, 2096, 2661, 1676, 247, 2440, 342, 634, 194, 1570, 2848, 986, 684, 3148, 3208, 2018, 351, 2288, 612, 1394, 170, 1521, 3119, 58, 596, 2093, 1549, 409, 2156, 1934, 1730, 1324, 388, 446, 418, 1719, 2202, 1812, 98, 1019, 2369, 214, 2699, 28, 1523, 2824, 273, 402, 2899, 246, 210, 1288, 863, 2708, 177, 3076, 349, 44, 949, 854, 1371, 957, 292, 2502, 1617, 1501, 254, 7, 1761, 2581, 2206, 2655, 1211, 629, 1274, 2358, 816, 2766, 2115, 2985, 1006, 2433, 856, 2596, 3192, 1, 1378, 2345, 707, 1891, 1669, 536, 1221, 710, 2511, 120, 1176, 322, 1897, 2309, 595, 2950, 1171, 801, 1848, 695, 2912, 1396, 1931, 1775, 2904, 893, 2507, 1810, 2873, 253, 1529, 1047, 2615, 1687, 831, 1414, 965, 3169, 1887, 753, 3246, 1937, 115, 2953, 586, 545, 1621, 1667, 3187, 1654, 1988, 1857, 512, 1239, 1219, 898, 3106, 391, 1331, 2228, 3169, 586, 2412, 845, 768, 156, 662, 478, 1693, 2632, 573, 2434, 1671, 173, 969, 364, 1663, 2701, 2169, 813, 1000, 1471, 720, 2431, 2530, 3161, 733, 1691, 527, 2634, 335, 26, 2377, 1707, 767, 3020, 950, 502, 426, 1138, 3208, 2607, 2389, 44, 1358, 1392, 2334, 875, 2097, 173, 1697, 2578, 942, 1817, 974, 1165, 2853, 1958, 2973, 3282, 271, 1236, 1677, 2230, 673, 1554, 96, 242, 1729, 2518, 1884, 2272, 71, 1382, 924, 1807, 1610, 456, 1148, 2479, 2152, 238, 2208, 2329, 713, 1175, 1196, 757, 1078, 3190, 3169, 708, 3117, 154, 1751, 3225, 1364, 154, 23, 2842, 1105, 1419, 79, 5, 2013, } var seed [32]byte for i := 0; i < 32; i++ { seed[i] = byte(i) } p.DeriveUniform(&seed, 1, 0) p.Detangle() p.Normalize() if p != want { t.Fatalf("%v\n%v", p, want) } } func BenchmarkPolyDeriveUniform(b *testing.B) { var p Poly var seed [32]byte for i := 0; i < b.N; i++ { p.DeriveUniform(&seed, 0, 0) } } func BenchmarkPolyDeriveUniformX4(b *testing.B) { if !DeriveX4Available { b.SkipNow() } var p [4]Poly var seed [32]byte for i := 0; i < b.N; i++ { PolyDeriveUniformX4( [4]*Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint8{0, 1, 2, 3}, [4]uint8{4, 5, 6, 7}, ) } } func TestPolyDeriveUniformX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var p2 Poly var p [4]Poly var seed [32]byte for i := 0; i < 32; i++ { seed[i] = byte(i) } PolyDeriveUniformX4( [4]*Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint8{0, 1, 2, 3}, [4]uint8{4, 5, 6, 7}, ) for i := 0; i < 4; i++ { p2.DeriveUniform(&seed, uint8(i), uint8(i+4)) if p2 != p[i] { t.Fatalf("%d\n%v\n%v", i, p2, p[i]) } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/internal/common/stubs_amd64.go000066400000000000000000000012141454601126700271460ustar00rootroot00000000000000// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. //go:build amd64 package common //go:noescape func addAVX2(p *[256]int16, a *[256]int16, b *[256]int16) //go:noescape func subAVX2(p *[256]int16, a *[256]int16, b *[256]int16) //go:noescape func nttAVX2(p *[256]int16) //go:noescape func invNttAVX2(p *[256]int16) //go:noescape func mulHatAVX2(p *[256]int16, a *[256]int16, b *[256]int16) //go:noescape func detangleAVX2(p *[256]int16) //go:noescape func tangleAVX2(p *[256]int16) //go:noescape func barrettReduceAVX2(p *[256]int16) //go:noescape func normalizeAVX2(p *[256]int16) golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber.go000066400000000000000000000006271454601126700230320ustar00rootroot00000000000000//go:generate go run gen.go // Package kyber implements the CRYSTALS-Kyber.CPAPKE public key encryption // as submitted to round 3 of the NIST PQC competition and described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf // // The related key encapsulation mechanism (KEM) CRYSTALS-Kyber.CCAKEM can // be found in the package github.com/cloudflare/circl/kem/kyber. package kyber golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/000077500000000000000000000000001454601126700230055ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/internal/000077500000000000000000000000001454601126700246215ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/internal/cpapke.go000066400000000000000000000103021454601126700264070ustar00rootroot00000000000000// Code generated from kyber512/internal/cpapke.go by gen.go package internal import ( "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A Kyber.CPAPKE private key. type PrivateKey struct { sh Vec // NTT(s), normalized } // A Kyber.CPAPKE public key. type PublicKey struct { rho [32]byte // ρ, the seed for the matrix A th Vec // NTT(t), normalized // cached values aT Mat // the matrix Aᵀ } // Packs the private key to buf. func (sk *PrivateKey) Pack(buf []byte) { sk.sh.Pack(buf) } // Unpacks the private key from buf. func (sk *PrivateKey) Unpack(buf []byte) { sk.sh.Unpack(buf) sk.sh.Normalize() } // Packs the public key to buf. func (pk *PublicKey) Pack(buf []byte) { pk.th.Pack(buf) copy(buf[K*common.PolySize:], pk.rho[:]) } // Unpacks the public key from buf. func (pk *PublicKey) Unpack(buf []byte) { pk.th.Unpack(buf) pk.th.Normalize() copy(pk.rho[:], buf[K*common.PolySize:]) pk.aT.Derive(&pk.rho, true) } // Derives a new Kyber.CPAPKE keypair from the given seed. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { var pk PublicKey var sk PrivateKey var expandedSeed [64]byte h := sha3.New512() _, _ = h.Write(seed) // This writes hash into expandedSeed. Yes, this is idiomatic Go. _, _ = h.Read(expandedSeed[:]) copy(pk.rho[:], expandedSeed[:32]) sigma := expandedSeed[32:] // σ, the noise seed pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later var eh Vec sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s sk.sh.NTT() sk.sh.Normalize() eh.DeriveNoise(sigma, K, Eta1) // Sample blind e eh.NTT() // Next, we compute t = A s + e. for i := 0; i < K; i++ { // Note that coefficients of s are bounded by q and those of A // are bounded by 4.5q and so their product is bounded by 2¹⁵q // as required for multiplication. PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) // A and s were not in Montgomery form, so the Montgomery // multiplications in the inner product added a factor R⁻¹ which // we'll cancel out now. This will also ensure the coefficients of // t are bounded in absolute value by q. pk.th[i].ToMont() } pk.th.Add(&pk.th, &eh) // bounded by 8q. pk.th.Normalize() pk.aT.Transpose() return &pk, &sk } // Decrypts ciphertext ct meant for private key sk to plaintext pt. func (sk *PrivateKey) DecryptTo(pt, ct []byte) { var u Vec var v, m common.Poly u.Decompress(ct, DU) v.Decompress(ct[K*compressedPolySize(DU):], DV) // Compute m = v - u.NTT() PolyDotHat(&m, &sk.sh, &u) m.BarrettReduce() m.InvNTT() m.Sub(&v, &m) m.Normalize() // Compress polynomial m to original message m.CompressMessageTo(pt) } // Encrypts message pt for the public key to ciphertext ct using randomness // from seed. // // seed has to be of length SeedSize, pt of PlaintextSize and ct of // CiphertextSize. func (pk *PublicKey) EncryptTo(ct, pt, seed []byte) { var rh, e1, u Vec var e2, v, m common.Poly // Sample r, e₁ and e₂ from B_η rh.DeriveNoise(seed, 0, Eta1) rh.NTT() rh.BarrettReduce() e1.DeriveNoise(seed, K, common.Eta2) e2.DeriveNoise(seed, 2*K, common.Eta2) // Next we compute u = Aᵀ r + e₁. First Aᵀ. for i := 0; i < K; i++ { // Note that coefficients of r are bounded by q and those of Aᵀ // are bounded by 4.5q and so their product is bounded by 2¹⁵q // as required for multiplication. PolyDotHat(&u[i], &pk.aT[i], &rh) } u.BarrettReduce() // Aᵀ and r were not in Montgomery form, so the Montgomery // multiplications in the inner product added a factor R⁻¹ which // the InvNTT cancels out. u.InvNTT() u.Add(&u, &e1) // u = Aᵀ r + e₁ // Next compute v = + e₂ + Decompress_q(m, 1). PolyDotHat(&v, &pk.th, &rh) v.BarrettReduce() v.InvNTT() m.DecompressMessage(pt) v.Add(&v, &m) v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) // Pack ciphertext u.Normalize() v.Normalize() u.CompressTo(ct, DU) v.CompressTo(ct[K*compressedPolySize(DU):], DV) } // Returns whether sk equals other. func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := int16(0) for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { ret |= sk.sh[i][j] ^ other.sh[i][j] } } return ret == 0 } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/internal/cpapke_test.go000066400000000000000000000012371454601126700274550ustar00rootroot00000000000000// Code generated from kyber512/internal/cpapke_test.go by gen.go package internal import ( "crypto/rand" "testing" ) func TestEncryptThenDecrypt(t *testing.T) { var seed [32]byte var coin [SeedSize]byte for i := 0; i < 32; i++ { seed[i] = byte(i) coin[i] = byte(i) } for i := 0; i < 100; i++ { seed[0] = byte(i) pk, sk := NewKeyFromSeed(seed[:]) for j := 0; j < 100; j++ { var msg, msg2 [PlaintextSize]byte var ct [CiphertextSize]byte _, _ = rand.Read(msg[:]) _, _ = rand.Read(coin[:]) pk.EncryptTo(ct[:], msg[:], coin[:]) sk.DecryptTo(msg2[:], ct[:]) if msg != msg2 { t.Fatalf("%v %v %v", ct, msg, msg2) } } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/internal/mat.go000066400000000000000000000027031454601126700257330ustar00rootroot00000000000000// Code generated from kyber512/internal/mat.go by gen.go package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A k by k matrix of polynomials. type Mat [K]Vec // Expands the given seed to the corresponding matrix A or its transpose Aᵀ. func (m *Mat) Derive(seed *[32]byte, transpose bool) { if !common.DeriveX4Available { if transpose { for i := 0; i < K; i++ { for j := 0; j < K; j++ { m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) } } } else { for i := 0; i < K; i++ { for j := 0; j < K; j++ { m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) } } } return } var ps [4]*common.Poly var xs [4]uint8 var ys [4]uint8 x := uint8(0) y := uint8(0) for x != K { idx := 0 for ; idx < 4; idx++ { ps[idx] = &m[x][y] if transpose { xs[idx] = x ys[idx] = y } else { xs[idx] = y ys[idx] = x } y++ if y == K { x++ y = 0 if x == K { if idx == 0 { // If there is just one left, then a plain DeriveUniform // is quicker than the X4 variant. ps[0].DeriveUniform(seed, xs[0], ys[0]) return } for idx++; idx < 4; idx++ { ps[idx] = nil } break } } } common.PolyDeriveUniformX4(ps, seed, xs, ys) } } // Transposes A in place. func (m *Mat) Transpose() { for i := 0; i < K-1; i++ { for j := i + 1; j < K; j++ { t := m[i][j] m[i][j] = m[j][i] m[j][i] = t } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/internal/params.go000066400000000000000000000006071454601126700264360ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) const ( K = 4 Eta1 = 2 DU = 11 DV = 5 PublicKeySize = 32 + K*common.PolySize PrivateKeySize = K * common.PolySize PlaintextSize = common.PlaintextSize SeedSize = 32 CiphertextSize = 1568 ) golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/internal/vec.go000066400000000000000000000054461454601126700257360ustar00rootroot00000000000000// Code generated from kyber512/internal/vec.go by gen.go package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A vector of K polynomials type Vec [K]common.Poly // Samples v[i] from a centered binomial distribution with given η, // seed and nonce+i. // // Essentially CBD_η(PRF(seed, nonce+i)) from the specification. func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { for i := 0; i < K; i++ { v[i].DeriveNoise(seed, nonce+uint8(i), eta) } } // Sets p to the inner product of a and b using "pointwise" multiplication. // // See MulHat() and NTT() for a description of the multiplication. // Assumes a and b are in Montgomery form. p will be in Montgomery form, // and its coefficients will be bounded in absolute value by 2kq. // If a and b are not in Montgomery form, then the action is the same // as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse // of the Montgomery factor. func PolyDotHat(p *common.Poly, a, b *Vec) { var t common.Poly *p = common.Poly{} // set p to zero for i := 0; i < K; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } // Almost normalizes coefficients in-place. // // Ensures each coefficient is in {0, …, q}. func (v *Vec) BarrettReduce() { for i := 0; i < K; i++ { v[i].BarrettReduce() } } // Normalizes coefficients in-place. // // Ensures each coefficient is in {0, …, q-1}. func (v *Vec) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. func (v *Vec) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies in-place forward NTT(). See Poly.NTT() for assumptions. func (v *Vec) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sets v to a + b. func (v *Vec) Add(a, b *Vec) { for i := 0; i < K; i++ { v[i].Add(&a[i], &b[i]) } } // Packs v into buf, which must be of length K*PolySize. func (v *Vec) Pack(buf []byte) { for i := 0; i < K; i++ { v[i].Pack(buf[common.PolySize*i:]) } } // Unpacks v from buf which must be of length K*PolySize. func (v *Vec) Unpack(buf []byte) { for i := 0; i < K; i++ { v[i].Unpack(buf[common.PolySize*i:]) } } // Writes Compress_q(v, d) to m. // // Assumes v is normalized and d is in {3, 4, 5, 10, 11}. func (v *Vec) CompressTo(m []byte, d int) { size := compressedPolySize(d) for i := 0; i < K; i++ { v[i].CompressTo(m[size*i:], d) } } // Set v to Decompress_q(m, 1). // // Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. func (v *Vec) Decompress(m []byte, d int) { size := compressedPolySize(d) for i := 0; i < K; i++ { v[i].Decompress(m[size*i:], d) } } // ⌈(256 d)/8⌉ func compressedPolySize(d int) int { switch d { case 4: return 128 case 5: return 160 case 10: return 320 case 11: return 352 } panic("unsupported d") } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber1024/kyber.go000066400000000000000000000100371454601126700244510ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // kyber1024 implements the IND-CPA-secure Public Key Encryption // scheme Kyber1024.CPAPKE as submitted to round 3 of the NIST PQC competition // and described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package kyber1024 import ( cryptoRand "crypto/rand" "io" "github.com/cloudflare/circl/pke/kyber/kyber1024/internal" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = internal.SeedSize // Size of seed for EncryptTo EncryptionSeedSize = internal.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a ciphertext CiphertextSize = internal.CiphertextSize // Size of a plaintext PlaintextSize = internal.PlaintextSize ) // PublicKey is the type of Kyber1024.CPAPKE public key type PublicKey internal.PublicKey // PrivateKey is the type of Kyber1024.CPAPKE private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := internal.NewKeyFromSeed(seed[:]) return (*PublicKey)(pk), (*PrivateKey)(sk), nil } // NewKeyFromSeed derives a public/private key pair using the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // EncryptTo encrypts message pt for the public key and writes the ciphertext // to ct using randomness from seed. // // This function panics if the lengths of pt, seed, and ct are not // PlaintextSize, EncryptionSeedSize, and CiphertextSize respectively. func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(seed) != EncryptionSeedSize { panic("seed must be of length EncryptionSeedSize") } (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) } // DecryptTo decrypts message ct for the private key and writes the // plaintext to pt. // // This function panics if the lengths of ct and pt are not // CiphertextSize and PlaintextSize respectively. func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } (*internal.PrivateKey)(sk).DecryptTo(pt, ct) } // Packs pk into the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Pack(buf) } // Packs sk into the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Pack(buf) } // Unpacks pk from the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Unpack(buf) } // Unpacks sk from the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Unpack(buf) } // Returns whether the two private keys are equal. func (sk *PrivateKey) Equal(other *PrivateKey) bool { return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/000077500000000000000000000000001454601126700227265ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/internal/000077500000000000000000000000001454601126700245425ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/internal/cpapke.go000066400000000000000000000102041454601126700263310ustar00rootroot00000000000000package internal import ( "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A Kyber.CPAPKE private key. type PrivateKey struct { sh Vec // NTT(s), normalized } // A Kyber.CPAPKE public key. type PublicKey struct { rho [32]byte // ρ, the seed for the matrix A th Vec // NTT(t), normalized // cached values aT Mat // the matrix Aᵀ } // Packs the private key to buf. func (sk *PrivateKey) Pack(buf []byte) { sk.sh.Pack(buf) } // Unpacks the private key from buf. func (sk *PrivateKey) Unpack(buf []byte) { sk.sh.Unpack(buf) sk.sh.Normalize() } // Packs the public key to buf. func (pk *PublicKey) Pack(buf []byte) { pk.th.Pack(buf) copy(buf[K*common.PolySize:], pk.rho[:]) } // Unpacks the public key from buf. func (pk *PublicKey) Unpack(buf []byte) { pk.th.Unpack(buf) pk.th.Normalize() copy(pk.rho[:], buf[K*common.PolySize:]) pk.aT.Derive(&pk.rho, true) } // Derives a new Kyber.CPAPKE keypair from the given seed. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { var pk PublicKey var sk PrivateKey var expandedSeed [64]byte h := sha3.New512() _, _ = h.Write(seed) // This writes hash into expandedSeed. Yes, this is idiomatic Go. _, _ = h.Read(expandedSeed[:]) copy(pk.rho[:], expandedSeed[:32]) sigma := expandedSeed[32:] // σ, the noise seed pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later var eh Vec sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s sk.sh.NTT() sk.sh.Normalize() eh.DeriveNoise(sigma, K, Eta1) // Sample blind e eh.NTT() // Next, we compute t = A s + e. for i := 0; i < K; i++ { // Note that coefficients of s are bounded by q and those of A // are bounded by 4.5q and so their product is bounded by 2¹⁵q // as required for multiplication. PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) // A and s were not in Montgomery form, so the Montgomery // multiplications in the inner product added a factor R⁻¹ which // we'll cancel out now. This will also ensure the coefficients of // t are bounded in absolute value by q. pk.th[i].ToMont() } pk.th.Add(&pk.th, &eh) // bounded by 8q. pk.th.Normalize() pk.aT.Transpose() return &pk, &sk } // Decrypts ciphertext ct meant for private key sk to plaintext pt. func (sk *PrivateKey) DecryptTo(pt, ct []byte) { var u Vec var v, m common.Poly u.Decompress(ct, DU) v.Decompress(ct[K*compressedPolySize(DU):], DV) // Compute m = v - u.NTT() PolyDotHat(&m, &sk.sh, &u) m.BarrettReduce() m.InvNTT() m.Sub(&v, &m) m.Normalize() // Compress polynomial m to original message m.CompressMessageTo(pt) } // Encrypts message pt for the public key to ciphertext ct using randomness // from seed. // // seed has to be of length SeedSize, pt of PlaintextSize and ct of // CiphertextSize. func (pk *PublicKey) EncryptTo(ct, pt, seed []byte) { var rh, e1, u Vec var e2, v, m common.Poly // Sample r, e₁ and e₂ from B_η rh.DeriveNoise(seed, 0, Eta1) rh.NTT() rh.BarrettReduce() e1.DeriveNoise(seed, K, common.Eta2) e2.DeriveNoise(seed, 2*K, common.Eta2) // Next we compute u = Aᵀ r + e₁. First Aᵀ. for i := 0; i < K; i++ { // Note that coefficients of r are bounded by q and those of Aᵀ // are bounded by 4.5q and so their product is bounded by 2¹⁵q // as required for multiplication. PolyDotHat(&u[i], &pk.aT[i], &rh) } u.BarrettReduce() // Aᵀ and r were not in Montgomery form, so the Montgomery // multiplications in the inner product added a factor R⁻¹ which // the InvNTT cancels out. u.InvNTT() u.Add(&u, &e1) // u = Aᵀ r + e₁ // Next compute v = + e₂ + Decompress_q(m, 1). PolyDotHat(&v, &pk.th, &rh) v.BarrettReduce() v.InvNTT() m.DecompressMessage(pt) v.Add(&v, &m) v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) // Pack ciphertext u.Normalize() v.Normalize() u.CompressTo(ct, DU) v.CompressTo(ct[K*compressedPolySize(DU):], DV) } // Returns whether sk equals other. func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := int16(0) for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { ret |= sk.sh[i][j] ^ other.sh[i][j] } } return ret == 0 } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/internal/cpapke_test.go000066400000000000000000000011341454601126700273720ustar00rootroot00000000000000package internal import ( "crypto/rand" "testing" ) func TestEncryptThenDecrypt(t *testing.T) { var seed [32]byte var coin [SeedSize]byte for i := 0; i < 32; i++ { seed[i] = byte(i) coin[i] = byte(i) } for i := 0; i < 100; i++ { seed[0] = byte(i) pk, sk := NewKeyFromSeed(seed[:]) for j := 0; j < 100; j++ { var msg, msg2 [PlaintextSize]byte var ct [CiphertextSize]byte _, _ = rand.Read(msg[:]) _, _ = rand.Read(coin[:]) pk.EncryptTo(ct[:], msg[:], coin[:]) sk.DecryptTo(msg2[:], ct[:]) if msg != msg2 { t.Fatalf("%v %v %v", ct, msg, msg2) } } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/internal/mat.go000066400000000000000000000026101454601126700256510ustar00rootroot00000000000000package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A k by k matrix of polynomials. type Mat [K]Vec // Expands the given seed to the corresponding matrix A or its transpose Aᵀ. func (m *Mat) Derive(seed *[32]byte, transpose bool) { if !common.DeriveX4Available { if transpose { for i := 0; i < K; i++ { for j := 0; j < K; j++ { m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) } } } else { for i := 0; i < K; i++ { for j := 0; j < K; j++ { m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) } } } return } var ps [4]*common.Poly var xs [4]uint8 var ys [4]uint8 x := uint8(0) y := uint8(0) for x != K { idx := 0 for ; idx < 4; idx++ { ps[idx] = &m[x][y] if transpose { xs[idx] = x ys[idx] = y } else { xs[idx] = y ys[idx] = x } y++ if y == K { x++ y = 0 if x == K { if idx == 0 { // If there is just one left, then a plain DeriveUniform // is quicker than the X4 variant. ps[0].DeriveUniform(seed, xs[0], ys[0]) return } for idx++; idx < 4; idx++ { ps[idx] = nil } break } } } common.PolyDeriveUniformX4(ps, seed, xs, ys) } } // Transposes A in place. func (m *Mat) Transpose() { for i := 0; i < K-1; i++ { for j := i + 1; j < K; j++ { t := m[i][j] m[i][j] = m[j][i] m[j][i] = t } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/internal/params.go000066400000000000000000000006061454601126700263560ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) const ( K = 2 Eta1 = 3 DU = 10 DV = 4 PublicKeySize = 32 + K*common.PolySize PrivateKeySize = K * common.PolySize PlaintextSize = common.PlaintextSize SeedSize = 32 CiphertextSize = 768 ) golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/internal/vec.go000066400000000000000000000053531454601126700256540ustar00rootroot00000000000000package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A vector of K polynomials type Vec [K]common.Poly // Samples v[i] from a centered binomial distribution with given η, // seed and nonce+i. // // Essentially CBD_η(PRF(seed, nonce+i)) from the specification. func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { for i := 0; i < K; i++ { v[i].DeriveNoise(seed, nonce+uint8(i), eta) } } // Sets p to the inner product of a and b using "pointwise" multiplication. // // See MulHat() and NTT() for a description of the multiplication. // Assumes a and b are in Montgomery form. p will be in Montgomery form, // and its coefficients will be bounded in absolute value by 2kq. // If a and b are not in Montgomery form, then the action is the same // as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse // of the Montgomery factor. func PolyDotHat(p *common.Poly, a, b *Vec) { var t common.Poly *p = common.Poly{} // set p to zero for i := 0; i < K; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } // Almost normalizes coefficients in-place. // // Ensures each coefficient is in {0, …, q}. func (v *Vec) BarrettReduce() { for i := 0; i < K; i++ { v[i].BarrettReduce() } } // Normalizes coefficients in-place. // // Ensures each coefficient is in {0, …, q-1}. func (v *Vec) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. func (v *Vec) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies in-place forward NTT(). See Poly.NTT() for assumptions. func (v *Vec) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sets v to a + b. func (v *Vec) Add(a, b *Vec) { for i := 0; i < K; i++ { v[i].Add(&a[i], &b[i]) } } // Packs v into buf, which must be of length K*PolySize. func (v *Vec) Pack(buf []byte) { for i := 0; i < K; i++ { v[i].Pack(buf[common.PolySize*i:]) } } // Unpacks v from buf which must be of length K*PolySize. func (v *Vec) Unpack(buf []byte) { for i := 0; i < K; i++ { v[i].Unpack(buf[common.PolySize*i:]) } } // Writes Compress_q(v, d) to m. // // Assumes v is normalized and d is in {3, 4, 5, 10, 11}. func (v *Vec) CompressTo(m []byte, d int) { size := compressedPolySize(d) for i := 0; i < K; i++ { v[i].CompressTo(m[size*i:], d) } } // Set v to Decompress_q(m, 1). // // Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. func (v *Vec) Decompress(m []byte, d int) { size := compressedPolySize(d) for i := 0; i < K; i++ { v[i].Decompress(m[size*i:], d) } } // ⌈(256 d)/8⌉ func compressedPolySize(d int) int { switch d { case 4: return 128 case 5: return 160 case 10: return 320 case 11: return 352 } panic("unsupported d") } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber512/kyber.go000066400000000000000000000100311454601126700243640ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // kyber512 implements the IND-CPA-secure Public Key Encryption // scheme Kyber512.CPAPKE as submitted to round 3 of the NIST PQC competition // and described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package kyber512 import ( cryptoRand "crypto/rand" "io" "github.com/cloudflare/circl/pke/kyber/kyber512/internal" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = internal.SeedSize // Size of seed for EncryptTo EncryptionSeedSize = internal.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a ciphertext CiphertextSize = internal.CiphertextSize // Size of a plaintext PlaintextSize = internal.PlaintextSize ) // PublicKey is the type of Kyber512.CPAPKE public key type PublicKey internal.PublicKey // PrivateKey is the type of Kyber512.CPAPKE private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := internal.NewKeyFromSeed(seed[:]) return (*PublicKey)(pk), (*PrivateKey)(sk), nil } // NewKeyFromSeed derives a public/private key pair using the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // EncryptTo encrypts message pt for the public key and writes the ciphertext // to ct using randomness from seed. // // This function panics if the lengths of pt, seed, and ct are not // PlaintextSize, EncryptionSeedSize, and CiphertextSize respectively. func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(seed) != EncryptionSeedSize { panic("seed must be of length EncryptionSeedSize") } (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) } // DecryptTo decrypts message ct for the private key and writes the // plaintext to pt. // // This function panics if the lengths of ct and pt are not // CiphertextSize and PlaintextSize respectively. func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } (*internal.PrivateKey)(sk).DecryptTo(pt, ct) } // Packs pk into the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Pack(buf) } // Packs sk into the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Pack(buf) } // Unpacks pk from the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Unpack(buf) } // Unpacks sk from the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Unpack(buf) } // Returns whether the two private keys are equal. func (sk *PrivateKey) Equal(other *PrivateKey) bool { return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/000077500000000000000000000000001454601126700227435ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/internal/000077500000000000000000000000001454601126700245575ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/internal/cpapke.go000066400000000000000000000103021454601126700263450ustar00rootroot00000000000000// Code generated from kyber512/internal/cpapke.go by gen.go package internal import ( "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A Kyber.CPAPKE private key. type PrivateKey struct { sh Vec // NTT(s), normalized } // A Kyber.CPAPKE public key. type PublicKey struct { rho [32]byte // ρ, the seed for the matrix A th Vec // NTT(t), normalized // cached values aT Mat // the matrix Aᵀ } // Packs the private key to buf. func (sk *PrivateKey) Pack(buf []byte) { sk.sh.Pack(buf) } // Unpacks the private key from buf. func (sk *PrivateKey) Unpack(buf []byte) { sk.sh.Unpack(buf) sk.sh.Normalize() } // Packs the public key to buf. func (pk *PublicKey) Pack(buf []byte) { pk.th.Pack(buf) copy(buf[K*common.PolySize:], pk.rho[:]) } // Unpacks the public key from buf. func (pk *PublicKey) Unpack(buf []byte) { pk.th.Unpack(buf) pk.th.Normalize() copy(pk.rho[:], buf[K*common.PolySize:]) pk.aT.Derive(&pk.rho, true) } // Derives a new Kyber.CPAPKE keypair from the given seed. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { var pk PublicKey var sk PrivateKey var expandedSeed [64]byte h := sha3.New512() _, _ = h.Write(seed) // This writes hash into expandedSeed. Yes, this is idiomatic Go. _, _ = h.Read(expandedSeed[:]) copy(pk.rho[:], expandedSeed[:32]) sigma := expandedSeed[32:] // σ, the noise seed pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later var eh Vec sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s sk.sh.NTT() sk.sh.Normalize() eh.DeriveNoise(sigma, K, Eta1) // Sample blind e eh.NTT() // Next, we compute t = A s + e. for i := 0; i < K; i++ { // Note that coefficients of s are bounded by q and those of A // are bounded by 4.5q and so their product is bounded by 2¹⁵q // as required for multiplication. PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) // A and s were not in Montgomery form, so the Montgomery // multiplications in the inner product added a factor R⁻¹ which // we'll cancel out now. This will also ensure the coefficients of // t are bounded in absolute value by q. pk.th[i].ToMont() } pk.th.Add(&pk.th, &eh) // bounded by 8q. pk.th.Normalize() pk.aT.Transpose() return &pk, &sk } // Decrypts ciphertext ct meant for private key sk to plaintext pt. func (sk *PrivateKey) DecryptTo(pt, ct []byte) { var u Vec var v, m common.Poly u.Decompress(ct, DU) v.Decompress(ct[K*compressedPolySize(DU):], DV) // Compute m = v - u.NTT() PolyDotHat(&m, &sk.sh, &u) m.BarrettReduce() m.InvNTT() m.Sub(&v, &m) m.Normalize() // Compress polynomial m to original message m.CompressMessageTo(pt) } // Encrypts message pt for the public key to ciphertext ct using randomness // from seed. // // seed has to be of length SeedSize, pt of PlaintextSize and ct of // CiphertextSize. func (pk *PublicKey) EncryptTo(ct, pt, seed []byte) { var rh, e1, u Vec var e2, v, m common.Poly // Sample r, e₁ and e₂ from B_η rh.DeriveNoise(seed, 0, Eta1) rh.NTT() rh.BarrettReduce() e1.DeriveNoise(seed, K, common.Eta2) e2.DeriveNoise(seed, 2*K, common.Eta2) // Next we compute u = Aᵀ r + e₁. First Aᵀ. for i := 0; i < K; i++ { // Note that coefficients of r are bounded by q and those of Aᵀ // are bounded by 4.5q and so their product is bounded by 2¹⁵q // as required for multiplication. PolyDotHat(&u[i], &pk.aT[i], &rh) } u.BarrettReduce() // Aᵀ and r were not in Montgomery form, so the Montgomery // multiplications in the inner product added a factor R⁻¹ which // the InvNTT cancels out. u.InvNTT() u.Add(&u, &e1) // u = Aᵀ r + e₁ // Next compute v = + e₂ + Decompress_q(m, 1). PolyDotHat(&v, &pk.th, &rh) v.BarrettReduce() v.InvNTT() m.DecompressMessage(pt) v.Add(&v, &m) v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) // Pack ciphertext u.Normalize() v.Normalize() u.CompressTo(ct, DU) v.CompressTo(ct[K*compressedPolySize(DU):], DV) } // Returns whether sk equals other. func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := int16(0) for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { ret |= sk.sh[i][j] ^ other.sh[i][j] } } return ret == 0 } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/internal/cpapke_test.go000066400000000000000000000012371454601126700274130ustar00rootroot00000000000000// Code generated from kyber512/internal/cpapke_test.go by gen.go package internal import ( "crypto/rand" "testing" ) func TestEncryptThenDecrypt(t *testing.T) { var seed [32]byte var coin [SeedSize]byte for i := 0; i < 32; i++ { seed[i] = byte(i) coin[i] = byte(i) } for i := 0; i < 100; i++ { seed[0] = byte(i) pk, sk := NewKeyFromSeed(seed[:]) for j := 0; j < 100; j++ { var msg, msg2 [PlaintextSize]byte var ct [CiphertextSize]byte _, _ = rand.Read(msg[:]) _, _ = rand.Read(coin[:]) pk.EncryptTo(ct[:], msg[:], coin[:]) sk.DecryptTo(msg2[:], ct[:]) if msg != msg2 { t.Fatalf("%v %v %v", ct, msg, msg2) } } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/internal/mat.go000066400000000000000000000027031454601126700256710ustar00rootroot00000000000000// Code generated from kyber512/internal/mat.go by gen.go package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A k by k matrix of polynomials. type Mat [K]Vec // Expands the given seed to the corresponding matrix A or its transpose Aᵀ. func (m *Mat) Derive(seed *[32]byte, transpose bool) { if !common.DeriveX4Available { if transpose { for i := 0; i < K; i++ { for j := 0; j < K; j++ { m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) } } } else { for i := 0; i < K; i++ { for j := 0; j < K; j++ { m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) } } } return } var ps [4]*common.Poly var xs [4]uint8 var ys [4]uint8 x := uint8(0) y := uint8(0) for x != K { idx := 0 for ; idx < 4; idx++ { ps[idx] = &m[x][y] if transpose { xs[idx] = x ys[idx] = y } else { xs[idx] = y ys[idx] = x } y++ if y == K { x++ y = 0 if x == K { if idx == 0 { // If there is just one left, then a plain DeriveUniform // is quicker than the X4 variant. ps[0].DeriveUniform(seed, xs[0], ys[0]) return } for idx++; idx < 4; idx++ { ps[idx] = nil } break } } } common.PolyDeriveUniformX4(ps, seed, xs, ys) } } // Transposes A in place. func (m *Mat) Transpose() { for i := 0; i < K-1; i++ { for j := i + 1; j < K; j++ { t := m[i][j] m[i][j] = m[j][i] m[j][i] = t } } } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/internal/params.go000066400000000000000000000006071454601126700263740ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) const ( K = 3 Eta1 = 2 DU = 10 DV = 4 PublicKeySize = 32 + K*common.PolySize PrivateKeySize = K * common.PolySize PlaintextSize = common.PlaintextSize SeedSize = 32 CiphertextSize = 1088 ) golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/internal/vec.go000066400000000000000000000054461454601126700256740ustar00rootroot00000000000000// Code generated from kyber512/internal/vec.go by gen.go package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) // A vector of K polynomials type Vec [K]common.Poly // Samples v[i] from a centered binomial distribution with given η, // seed and nonce+i. // // Essentially CBD_η(PRF(seed, nonce+i)) from the specification. func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { for i := 0; i < K; i++ { v[i].DeriveNoise(seed, nonce+uint8(i), eta) } } // Sets p to the inner product of a and b using "pointwise" multiplication. // // See MulHat() and NTT() for a description of the multiplication. // Assumes a and b are in Montgomery form. p will be in Montgomery form, // and its coefficients will be bounded in absolute value by 2kq. // If a and b are not in Montgomery form, then the action is the same // as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse // of the Montgomery factor. func PolyDotHat(p *common.Poly, a, b *Vec) { var t common.Poly *p = common.Poly{} // set p to zero for i := 0; i < K; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } // Almost normalizes coefficients in-place. // // Ensures each coefficient is in {0, …, q}. func (v *Vec) BarrettReduce() { for i := 0; i < K; i++ { v[i].BarrettReduce() } } // Normalizes coefficients in-place. // // Ensures each coefficient is in {0, …, q-1}. func (v *Vec) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. func (v *Vec) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies in-place forward NTT(). See Poly.NTT() for assumptions. func (v *Vec) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sets v to a + b. func (v *Vec) Add(a, b *Vec) { for i := 0; i < K; i++ { v[i].Add(&a[i], &b[i]) } } // Packs v into buf, which must be of length K*PolySize. func (v *Vec) Pack(buf []byte) { for i := 0; i < K; i++ { v[i].Pack(buf[common.PolySize*i:]) } } // Unpacks v from buf which must be of length K*PolySize. func (v *Vec) Unpack(buf []byte) { for i := 0; i < K; i++ { v[i].Unpack(buf[common.PolySize*i:]) } } // Writes Compress_q(v, d) to m. // // Assumes v is normalized and d is in {3, 4, 5, 10, 11}. func (v *Vec) CompressTo(m []byte, d int) { size := compressedPolySize(d) for i := 0; i < K; i++ { v[i].CompressTo(m[size*i:], d) } } // Set v to Decompress_q(m, 1). // // Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. func (v *Vec) Decompress(m []byte, d int) { size := compressedPolySize(d) for i := 0; i < K; i++ { v[i].Decompress(m[size*i:], d) } } // ⌈(256 d)/8⌉ func compressedPolySize(d int) int { switch d { case 4: return 128 case 5: return 160 case 10: return 320 case 11: return 352 } panic("unsupported d") } golang-github-cloudflare-circl-1.3.7/pke/kyber/kyber768/kyber.go000066400000000000000000000100311454601126700244010ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // kyber768 implements the IND-CPA-secure Public Key Encryption // scheme Kyber768.CPAPKE as submitted to round 3 of the NIST PQC competition // and described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package kyber768 import ( cryptoRand "crypto/rand" "io" "github.com/cloudflare/circl/pke/kyber/kyber768/internal" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = internal.SeedSize // Size of seed for EncryptTo EncryptionSeedSize = internal.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a ciphertext CiphertextSize = internal.CiphertextSize // Size of a plaintext PlaintextSize = internal.PlaintextSize ) // PublicKey is the type of Kyber768.CPAPKE public key type PublicKey internal.PublicKey // PrivateKey is the type of Kyber768.CPAPKE private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := internal.NewKeyFromSeed(seed[:]) return (*PublicKey)(pk), (*PrivateKey)(sk), nil } // NewKeyFromSeed derives a public/private key pair using the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // EncryptTo encrypts message pt for the public key and writes the ciphertext // to ct using randomness from seed. // // This function panics if the lengths of pt, seed, and ct are not // PlaintextSize, EncryptionSeedSize, and CiphertextSize respectively. func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(seed) != EncryptionSeedSize { panic("seed must be of length EncryptionSeedSize") } (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) } // DecryptTo decrypts message ct for the private key and writes the // plaintext to pt. // // This function panics if the lengths of ct and pt are not // CiphertextSize and PlaintextSize respectively. func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } (*internal.PrivateKey)(sk).DecryptTo(pt, ct) } // Packs pk into the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Pack(buf) } // Packs sk into the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Pack(buf) } // Unpacks pk from the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Unpack(buf) } // Unpacks sk from the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Unpack(buf) } // Returns whether the two private keys are equal. func (sk *PrivateKey) Equal(other *PrivateKey) bool { return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) } golang-github-cloudflare-circl-1.3.7/pke/kyber/templates/000077500000000000000000000000001454601126700233605ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pke/kyber/templates/params.templ.go000066400000000000000000000010451454601126700263120ustar00rootroot00000000000000// +build ignore // The previous line (and this one up to the warning below) is removed by the // template generator. // Code generated from params.templ.go. DO NOT EDIT. package internal import ( "github.com/cloudflare/circl/pke/kyber/internal/common" ) const ( K = {{.K}} Eta1 = {{.Eta1}} DU = {{.DU}} DV = {{.DV}} PublicKeySize = 32 + K*common.PolySize PrivateKeySize = K * common.PolySize PlaintextSize = common.PlaintextSize SeedSize = 32 CiphertextSize = {{.CiphertextSize}} ) golang-github-cloudflare-circl-1.3.7/pke/kyber/templates/pkg.templ.go000066400000000000000000000102231454601126700256060ustar00rootroot00000000000000// +build ignore // The previous line (and this one up to the warning below) is removed by the // template generator. // Code generated from modePkg.templ.go. DO NOT EDIT. // {{.Pkg}} implements the IND-CPA-secure Public Key Encryption // scheme {{.Name}}.CPAPKE as submitted to round 3 of the NIST PQC competition // and described in // // https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf package {{.Pkg}} import ( cryptoRand "crypto/rand" "io" "github.com/cloudflare/circl/pke/kyber/{{.Pkg}}/internal" ) const ( // Size of seed for NewKeyFromSeed KeySeedSize = internal.SeedSize // Size of seed for EncryptTo EncryptionSeedSize = internal.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a ciphertext CiphertextSize = internal.CiphertextSize // Size of a plaintext PlaintextSize = internal.PlaintextSize ) // PublicKey is the type of {{.Name}}.CPAPKE public key type PublicKey internal.PublicKey // PrivateKey is the type of {{.Name}}.CPAPKE private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [KeySeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := internal.NewKeyFromSeed(seed[:]) return (*PublicKey)(pk), (*PrivateKey)(sk), nil } // NewKeyFromSeed derives a public/private key pair using the given seed. // // Panics if seed is not of length KeySeedSize. func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { if len(seed) != KeySeedSize { panic("seed must be of length KeySeedSize") } pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // EncryptTo encrypts message pt for the public key and writes the ciphertext // to ct using randomness from seed. // // This function panics if the lengths of pt, seed, and ct are not // PlaintextSize, EncryptionSeedSize, and CiphertextSize respectively. func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } if len(seed) != EncryptionSeedSize { panic("seed must be of length EncryptionSeedSize") } (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) } // DecryptTo decrypts message ct for the private key and writes the // plaintext to pt. // // This function panics if the lengths of ct and pt are not // CiphertextSize and PlaintextSize respectively. func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { if len(pt) != PlaintextSize { panic("pt must be of length PlaintextSize") } if len(ct) != CiphertextSize { panic("ct must be of length CiphertextSize") } (*internal.PrivateKey)(sk).DecryptTo(pt, ct) } // Packs pk into the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Pack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Pack(buf) } // Packs sk into the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Pack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Pack(buf) } // Unpacks pk from the given buffer. // // Panics if buf is not of length PublicKeySize. func (pk *PublicKey) Unpack(buf []byte) { if len(buf) != PublicKeySize { panic("buf must be of size PublicKeySize") } (*internal.PublicKey)(pk).Unpack(buf) } // Unpacks sk from the given buffer. // // Panics if buf is not of length PrivateKeySize. func (sk *PrivateKey) Unpack(buf []byte) { if len(buf) != PrivateKeySize { panic("buf must be of size PrivateKeySize") } (*internal.PrivateKey)(sk).Unpack(buf) } // Returns whether the two private keys are equal. func (sk *PrivateKey) Equal(other *PrivateKey) bool { return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) } golang-github-cloudflare-circl-1.3.7/pki/000077500000000000000000000000001454601126700202525ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/pki/pki.go000066400000000000000000000104541454601126700213700ustar00rootroot00000000000000package pki import ( "crypto/x509/pkix" "encoding/asn1" "encoding/pem" "errors" "strings" "github.com/cloudflare/circl/sign" "github.com/cloudflare/circl/sign/schemes" ) var ( allSchemesByOID map[string]sign.Scheme allSchemesByTLS map[uint]sign.Scheme ) type pkixPrivKey struct { Version int Algorithm pkix.AlgorithmIdentifier PrivateKey []byte } func init() { allSchemesByOID = make(map[string]sign.Scheme) allSchemesByTLS = make(map[uint]sign.Scheme) for _, scheme := range schemes.All() { if cert, ok := scheme.(CertificateScheme); ok { allSchemesByOID[cert.Oid().String()] = scheme } if tlsScheme, ok := scheme.(TLSScheme); ok { allSchemesByTLS[tlsScheme.TLSIdentifier()] = scheme } } } func SchemeByOid(oid asn1.ObjectIdentifier) sign.Scheme { return allSchemesByOID[oid.String()] } func SchemeByTLSID(id uint) sign.Scheme { return allSchemesByTLS[id] } // Additional methods when the signature scheme is supported in X509. type CertificateScheme interface { // Return the appropriate OIDs for this instance. It is implicitly // assumed that the encoding is simple: e.g. uses the same OID for // signature and public key like Ed25519. Oid() asn1.ObjectIdentifier } // Additional methods when the signature scheme is supported in TLS. type TLSScheme interface { TLSIdentifier() uint } func UnmarshalPEMPublicKey(data []byte) (sign.PublicKey, error) { block, rest := pem.Decode(data) if len(rest) != 0 { return nil, errors.New("trailing data") } if !strings.HasSuffix(block.Type, "PUBLIC KEY") { return nil, errors.New("pem block type is not public key") } return UnmarshalPKIXPublicKey(block.Bytes) } func UnmarshalPKIXPublicKey(data []byte) (sign.PublicKey, error) { var pkix struct { Raw asn1.RawContent Algorithm pkix.AlgorithmIdentifier PublicKey asn1.BitString } if rest, err := asn1.Unmarshal(data, &pkix); err != nil { return nil, err } else if len(rest) != 0 { return nil, errors.New("trailing data") } scheme := SchemeByOid(pkix.Algorithm.Algorithm) if scheme == nil { return nil, errors.New("unsupported public key algorithm") } return scheme.UnmarshalBinaryPublicKey(pkix.PublicKey.RightAlign()) } func UnmarshalPEMPrivateKey(data []byte) (sign.PrivateKey, error) { block, rest := pem.Decode(data) if len(rest) != 0 { return nil, errors.New("trailing") } if !strings.HasSuffix(block.Type, "PRIVATE KEY") { return nil, errors.New("pem block type is not private key") } return UnmarshalPKIXPrivateKey(block.Bytes) } func UnmarshalPKIXPrivateKey(data []byte) (sign.PrivateKey, error) { var pkix pkixPrivKey if rest, err := asn1.Unmarshal(data, &pkix); err != nil { return nil, err } else if len(rest) != 0 { return nil, errors.New("trailing data") } scheme := SchemeByOid(pkix.Algorithm.Algorithm) if scheme == nil { return nil, errors.New("unsupported public key algorithm") } var sk []byte if rest, err := asn1.Unmarshal(pkix.PrivateKey, &sk); err != nil { return nil, err } else if len(rest) > 0 { return nil, errors.New("trailing data") } return scheme.UnmarshalBinaryPrivateKey(sk) } func MarshalPEMPublicKey(pk sign.PublicKey) ([]byte, error) { data, err := MarshalPKIXPublicKey(pk) if err != nil { return nil, err } str := pem.EncodeToMemory(&pem.Block{ Type: "PUBLIC KEY", Bytes: data, }) return str, nil } func MarshalPKIXPublicKey(pk sign.PublicKey) ([]byte, error) { data, err := pk.MarshalBinary() if err != nil { return nil, err } scheme := pk.Scheme() return asn1.Marshal(struct { pkix.AlgorithmIdentifier asn1.BitString }{ pkix.AlgorithmIdentifier{ Algorithm: scheme.(CertificateScheme).Oid(), }, asn1.BitString{ Bytes: data, BitLength: len(data) * 8, }, }) } func MarshalPEMPrivateKey(sk sign.PrivateKey) ([]byte, error) { data, err := MarshalPKIXPrivateKey(sk) if err != nil { return nil, err } str := pem.EncodeToMemory(&pem.Block{ Type: sk.Scheme().Name() + " PRIVATE KEY", Bytes: data, }, ) return str, nil } func MarshalPKIXPrivateKey(sk sign.PrivateKey) ([]byte, error) { data, err := sk.MarshalBinary() if err != nil { return nil, err } data, err = asn1.Marshal(data) if err != nil { return nil, err } scheme := sk.Scheme() return asn1.Marshal(pkixPrivKey{ 0, pkix.AlgorithmIdentifier{ Algorithm: scheme.(CertificateScheme).Oid(), }, data, }) } golang-github-cloudflare-circl-1.3.7/pki/pki_test.go000066400000000000000000000016161454601126700224270ustar00rootroot00000000000000package pki_test import ( "testing" "github.com/cloudflare/circl/pki" "github.com/cloudflare/circl/sign/schemes" ) func TestPEM(t *testing.T) { for _, scheme := range schemes.All() { scheme := scheme t.Run(scheme.Name(), func(t *testing.T) { if scheme == nil { t.Fatal() } _, ok := scheme.(pki.CertificateScheme) if !ok { return } pk, sk, err := scheme.GenerateKey() if err != nil { t.Fatal(err) } packedPk, err := pki.MarshalPEMPublicKey(pk) if err != nil { t.Fatal(err) } pk2, err := pki.UnmarshalPEMPublicKey(packedPk) if err != nil { t.Fatal(err) } if !pk.Equal(pk2) { t.Fatal() } packedSk, err := pki.MarshalPEMPrivateKey(sk) if err != nil { t.Fatal(err) } sk2, err := pki.UnmarshalPEMPrivateKey(packedSk) if err != nil { t.Fatal(err) } if !sk.Equal(sk2) { t.Fatal() } }) } } golang-github-cloudflare-circl-1.3.7/sign/000077500000000000000000000000001454601126700204275ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/000077500000000000000000000000001454601126700224175ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/dilithium.go000066400000000000000000000066641454601126700247520ustar00rootroot00000000000000//go:generate go run gen.go // dilithium implements the CRYSTALS-Dilithium signature schemes // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf // // Each of the eight different modes of Dilithium is implemented by a // subpackage. For instance, Dilithium2 (the recommended mode) // can be found in // // github.com/cloudflare/circl/sign/dilithium/mode2 // // If your choice for mode is fixed compile-time, use the subpackages. // This package provides a convenient wrapper around all of the subpackages // so one can be chosen at runtime. // // The authors of Dilithium recommend to combine it with a "pre-quantum" // signature scheme. The packages // // github.com/cloudflare/circl/sign/eddilithium2 // github.com/cloudflare/circl/sign/eddilithium3 // // implement such hybrids of Dilithium2 with Ed25519 respectively and // Dilithium3 with Ed448. These packages are a drop in replacements for the // mode subpackages of this package. package dilithium import ( "crypto" "io" ) // PublicKey is a Dilithium public key. // // The structure contains values precomputed during unpacking/key generation // and is therefore significantly larger than a packed public key. type PublicKey interface { // Packs public key Bytes() []byte } // PrivateKey is a Dilithium public key. // // The structure contains values precomputed during unpacking/key generation // and is therefore significantly larger than a packed private key. type PrivateKey interface { // Packs private key Bytes() []byte crypto.Signer } // Mode is a certain configuration of the Dilithium signature scheme. type Mode interface { // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) // NewKeyFromSeed derives a public/private key pair using the given seed. // Panics if len(seed) != SeedSize() NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) // Sign signs the given message and returns the signature. // It will panic if sk has not been generated for this mode. Sign(sk PrivateKey, msg []byte) []byte // Verify checks whether the given signature by pk on msg is valid. // It will panic if pk is of the wrong mode. Verify(pk PublicKey, msg []byte, signature []byte) bool // Unpacks a public key. Panics if the buffer is not of PublicKeySize() // length. Precomputes values to speed up subsequent calls to Verify. PublicKeyFromBytes([]byte) PublicKey // Unpacks a private key. Panics if the buffer is not // of PrivateKeySize() length. Precomputes values to speed up subsequent // calls to Sign(To). PrivateKeyFromBytes([]byte) PrivateKey // SeedSize returns the size of the seed for NewKeyFromSeed SeedSize() int // PublicKeySize returns the size of a packed PublicKey PublicKeySize() int // PrivateKeySize returns the size of a packed PrivateKey PrivateKeySize() int // SignatureSize returns the size of a signature SignatureSize() int // Name returns the name of this mode Name() string } var modes = make(map[string]Mode) // ModeNames returns the list of supported modes. func ModeNames() []string { names := []string{} for name := range modes { names = append(names, name) } return names } // ModeByName returns the mode with the given name or nil when not supported. func ModeByName(name string) Mode { return modes[name] } golang-github-cloudflare-circl-1.3.7/sign/dilithium/dilithium_test.go000066400000000000000000000027151454601126700260020ustar00rootroot00000000000000package dilithium import ( "encoding/hex" "testing" "github.com/cloudflare/circl/internal/sha3" ) func hexHash(in []byte) string { var ret [16]byte h := sha3.NewShake256() _, _ = h.Write(in[:]) _, _ = h.Read(ret[:]) return hex.EncodeToString(ret[:]) } func TestNewKeyFromSeed(t *testing.T) { // Test vectors generated from reference implementation for _, tc := range []struct { name string esk string epk string }{ { "Dilithium2", "afe2e91f5f5899354230744c18410498", "7522162619f3329b5312322d3ee45b87", }, { "Dilithium3", "8ad3142e08b718b33f7c2668cd9d053c", "3562fc184dce1a10aad099051705b5d3", }, { "Dilithium5", "3956d812a7961af6e5dad16af15c736c", "665388291aa01e12e7f94bdc7769db18", }, { "Dilithium2-AES", "8466a752b0a09e63e42f66d3174a6471", "c3f8e705a0d8dfd489b98b205670f393", }, { "Dilithium3-AES", "2bb713ba7cb15f3ebf05c4c1fbb1b03c", "eb2bd8d98630835a3b18594ac436368b", }, { "Dilithium5-AES", "a613a08b564ee8717ba4f5ccfddc2693", "2f541bf6fedd12854d06a6b80090932a", }, } { t.Run(tc.name, func(t *testing.T) { mode := ModeByName(tc.name) if mode == nil { t.Fatal() } var seed [32]byte pk, sk := mode.NewKeyFromSeed(seed[:]) pkh := hexHash(pk.Bytes()) skh := hexHash(sk.Bytes()) if pkh != tc.epk { t.Fatalf("%s expected pk %s, got %s", tc.name, tc.epk, pkh) } if skh != tc.esk { t.Fatalf("%s expected pk %s, got %s", tc.name, tc.esk, skh) } }) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/example_test.go000066400000000000000000000022731454601126700254440ustar00rootroot00000000000000package dilithium_test import ( "fmt" "sort" "github.com/cloudflare/circl/sign/dilithium" ) func Example() { // Check supported modes modes := dilithium.ModeNames() sort.Strings(modes) fmt.Printf("Supported modes: %v\n", modes) // Pick Dilithium mode III. mode := dilithium.ModeByName("Dilithium3") if mode == nil { panic("Mode3 not supported") } // Alternatively one could simply write // // mode := dilithium.Mode3 // Generates a keypair. pk, sk, err := mode.GenerateKey(nil) if err != nil { panic(err) } // (Alternatively one can derive a keypair from a seed, // see mode.NewKeyFromSeed().) // Packs public and private key packedSk := sk.Bytes() packedPk := pk.Bytes() // Load it again sk2 := mode.PrivateKeyFromBytes(packedSk) pk2 := mode.PublicKeyFromBytes(packedPk) // Creates a signature on our message with the generated private key. msg := []byte("Some message") signature := mode.Sign(sk2, msg) // Checks whether a signature is correct if !mode.Verify(pk2, msg, signature) { panic("incorrect signature") } fmt.Printf("O.K.") // Output: // Supported modes: [Dilithium2 Dilithium2-AES Dilithium3 Dilithium3-AES Dilithium5 Dilithium5-AES] // O.K. } golang-github-cloudflare-circl-1.3.7/sign/dilithium/gen.go000066400000000000000000000137131454601126700235240ustar00rootroot00000000000000//go:build ignore // +build ignore // Autogenerates wrappers from templates to prevent too much duplicated code // between the code for different modes. package main import ( "bytes" "fmt" "go/format" "os" "path" "strings" "text/template" "github.com/cloudflare/circl/sign/dilithium/internal/common/params" ) type Mode struct { Name string UseAES bool K int L int Eta int DoubleEtaBits int Omega int Tau int Gamma1Bits int Gamma2 int } func (m Mode) Pkg() string { return strings.ToLower(m.Mode()) } func (m Mode) Impl() string { return "impl" + m.Mode() } func (m Mode) Mode() string { return strings.ReplaceAll(strings.ReplaceAll(m.Name, "Dilithium", "Mode"), "-AES", "AES") } var ( Modes = []Mode{ { Name: "Dilithium2", UseAES: false, K: 4, L: 4, Eta: 2, DoubleEtaBits: 3, Omega: 80, Tau: 39, Gamma1Bits: 17, Gamma2: (params.Q - 1) / 88, }, { Name: "Dilithium2-AES", UseAES: true, K: 4, L: 4, Eta: 2, DoubleEtaBits: 3, Omega: 80, Tau: 39, Gamma1Bits: 17, Gamma2: (params.Q - 1) / 88, }, { Name: "Dilithium3", UseAES: false, K: 6, L: 5, Eta: 4, DoubleEtaBits: 4, Omega: 55, Tau: 49, Gamma1Bits: 19, Gamma2: (params.Q - 1) / 32, }, { Name: "Dilithium3-AES", UseAES: true, K: 6, L: 5, Eta: 4, DoubleEtaBits: 4, Omega: 55, Tau: 49, Gamma1Bits: 19, Gamma2: (params.Q - 1) / 32, }, { Name: "Dilithium5", UseAES: false, K: 8, L: 7, Eta: 2, DoubleEtaBits: 3, Omega: 75, Tau: 60, Gamma1Bits: 19, Gamma2: (params.Q - 1) / 32, }, { Name: "Dilithium5-AES", UseAES: true, K: 8, L: 7, Eta: 2, DoubleEtaBits: 3, Omega: 75, Tau: 60, Gamma1Bits: 19, Gamma2: (params.Q - 1) / 32, }, } TemplateWarning = "// Code generated from" ) func main() { generateModePackageFiles() generateModeToplevelFiles() generateParamsFiles() generateSourceFiles() } // Generates modeX/internal/params.go from templates/params.templ.go func generateParamsFiles() { tl, err := template.ParseFiles("templates/params.templ.go") if err != nil { panic(err) } for _, mode := range Modes { buf := new(bytes.Buffer) err := tl.Execute(buf, mode) if err != nil { panic(err) } // Formating output code code, err := format.Source(buf.Bytes()) if err != nil { panic("error formating code") } res := string(code) offset := strings.Index(res, TemplateWarning) if offset == -1 { panic("Missing template warning in params.templ.go") } err = os.WriteFile(mode.Pkg()+"/internal/params.go", []byte(res[offset:]), 0o644) if err != nil { panic(err) } } } // Generates modeX.go from templates/mode.templ.go func generateModeToplevelFiles() { tl, err := template.ParseFiles("templates/mode.templ.go") if err != nil { panic(err) } for _, mode := range Modes { buf := new(bytes.Buffer) err := tl.Execute(buf, mode) if err != nil { panic(err) } res := string(buf.Bytes()) offset := strings.Index(res, TemplateWarning) if offset == -1 { panic("Missing template warning in mode.templ.go") } err = os.WriteFile(mode.Pkg()+".go", []byte(res[offset:]), 0o644) if err != nil { panic(err) } } } // Generates modeX/dilithium.go from templates/modePkg.templ.go func generateModePackageFiles() { tl, err := template.ParseFiles("templates/modePkg.templ.go") if err != nil { panic(err) } for _, mode := range Modes { buf := new(bytes.Buffer) err := tl.Execute(buf, mode) if err != nil { panic(err) } res := string(buf.Bytes()) offset := strings.Index(res, TemplateWarning) if offset == -1 { panic("Missing template warning in modePkg.templ.go") } err = os.WriteFile(mode.Pkg()+"/dilithium.go", []byte(res[offset:]), 0o644) if err != nil { panic(err) } } } // Copies mode3 source files to other modes func generateSourceFiles() { files := make(map[string][]byte) // Ignore mode specific files. ignored := func(x string) bool { return x == "params.go" || x == "params_test.go" || strings.HasSuffix(x, ".swp") } fs, err := os.ReadDir("mode3/internal") if err != nil { panic(err) } // Read files for _, f := range fs { name := f.Name() if ignored(name) { continue } files[name], err = os.ReadFile(path.Join("mode3/internal", name)) if err != nil { panic(err) } } // Go over modes for _, mode := range Modes { if mode.Name == "Dilithium3" { continue } fs, err = os.ReadDir(path.Join(mode.Pkg(), "internal")) for _, f := range fs { name := f.Name() fn := path.Join(mode.Pkg(), "internal", name) if ignored(name) { continue } _, ok := files[name] if !ok { fmt.Printf("Removing superfluous file: %s\n", fn) err = os.Remove(fn) if err != nil { panic(err) } } if f.IsDir() { panic(fmt.Sprintf("%s: is a directory", fn)) } if f.Type()&os.ModeSymlink != 0 { fmt.Printf("Removing symlink: %s\n", fn) err = os.Remove(fn) if err != nil { panic(err) } } } for name, expected := range files { fn := path.Join(mode.Pkg(), "internal", name) expected = []byte(fmt.Sprintf( "%s mode3/internal/%s by gen.go\n\n%s", TemplateWarning, name, string(expected), )) got, err := os.ReadFile(fn) if err == nil { if bytes.Equal(got, expected) { continue } } fmt.Printf("Updating %s\n", fn) err = os.WriteFile(fn, expected, 0o644) if err != nil { panic(err) } } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/000077500000000000000000000000001454601126700242335ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/000077500000000000000000000000001454601126700255235ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/aes.go000066400000000000000000000024261454601126700266260ustar00rootroot00000000000000package common import ( "crypto/aes" "crypto/cipher" "encoding/binary" ) // AES CTR stream used as a replacement for SHAKE in Dilithium[1234]-AES. type AesStream struct { c cipher.Block counter uint64 nonce uint16 } // Create a new AesStream as a replacement of SHAKE128. (Note that // not all occurrences of SHAKE are replaced by AES in the AES-variants). func NewAesStream128(key *[32]byte, nonce uint16) AesStream { c, _ := aes.NewCipher(key[:]) return AesStream{c: c, nonce: nonce} } // Create a new AesStream as a replacement of SHAKE256. (Note that // not all occurrences of SHAKE are replaced by AES in the AES-variants.) // // Yes, in an AES mode, Dilithium throws away the last 32 bytes of a seed ... // See the remark at the end of the caption of Figure 4 in the Round 2 spec. func NewAesStream256(key *[64]byte, nonce uint16) AesStream { c, _ := aes.NewCipher(key[:32]) return AesStream{c: c, nonce: nonce} } // Squeeze some more blocks from the AES CTR stream into buf. // // Assumes length of buf is a multiple of 16. func (s *AesStream) SqueezeInto(buf []byte) { var tmp [16]byte binary.LittleEndian.PutUint16(tmp[:], s.nonce) for len(buf) != 0 { binary.BigEndian.PutUint64(tmp[8:], s.counter) s.counter++ s.c.Encrypt(buf, tmp[:]) buf = buf[16:] } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/amd64.go000066400000000000000000000062351454601126700267730ustar00rootroot00000000000000//go:build amd64 // +build amd64 package common import ( "golang.org/x/sys/cpu" ) // Execute an in-place forward NTT on as. // // Assumes the coefficients are in Montgomery representation and bounded // by 2*Q. The resulting coefficients are again in Montgomery representation, // but are only bounded bt 18*Q. func (p *Poly) NTT() { if cpu.X86.HasAVX2 { nttAVX2( (*[N]uint32)(p), ) } else { p.nttGeneric() } } // Execute an in-place inverse NTT and multiply by Montgomery factor R // // Assumes the coefficients are in Montgomery representation and bounded // by 2*Q. The resulting coefficients are again in Montgomery representation // and bounded by 2*Q. func (p *Poly) InvNTT() { if cpu.X86.HasAVX2 { invNttAVX2( (*[N]uint32)(p), ) } else { p.invNttGeneric() } } // Sets p to the polynomial whose coefficients are the pointwise multiplication // of those of a and b. The coefficients of p are bounded by 2q. // // Assumes a and b are in Montgomery form and that the pointwise product // of each coefficient is below 2³² q. func (p *Poly) MulHat(a, b *Poly) { if cpu.X86.HasAVX2 { mulHatAVX2( (*[N]uint32)(p), (*[N]uint32)(a), (*[N]uint32)(b), ) } else { p.mulHatGeneric(a, b) } } // Sets p to a + b. Does not normalize polynomials. func (p *Poly) Add(a, b *Poly) { if cpu.X86.HasAVX2 { addAVX2( (*[N]uint32)(p), (*[N]uint32)(a), (*[N]uint32)(b), ) } else { p.addGeneric(a, b) } } // Sets p to a - b. // // Warning: assumes coefficients of b are less than 2q. // Sets p to a + b. Does not normalize polynomials. func (p *Poly) Sub(a, b *Poly) { if cpu.X86.HasAVX2 { subAVX2( (*[N]uint32)(p), (*[N]uint32)(a), (*[N]uint32)(b), ) } else { p.subGeneric(a, b) } } // Writes p whose coefficients are in [0, 16) to buf, which must be of // length N/2. func (p *Poly) PackLe16(buf []byte) { if cpu.X86.HasAVX2 { if len(buf) < PolyLe16Size { panic("buf too small") } packLe16AVX2( (*[N]uint32)(p), &buf[0], ) } else { p.packLe16Generic(buf) } } // Reduces each of the coefficients to <2q. func (p *Poly) ReduceLe2Q() { if cpu.X86.HasAVX2 { reduceLe2QAVX2((*[N]uint32)(p)) } else { p.reduceLe2QGeneric() } } // Reduce each of the coefficients to ../../../../../ golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/asm/go.sum000066400000000000000000000073001454601126700274360ustar00rootroot00000000000000github.com/mmcloughlin/avo v0.5.0 h1:nAco9/aI9Lg2kiuROBY6BhCI/z0t5jEvJfjWbL8qXLU= github.com/mmcloughlin/avo v0.5.0/go.mod h1:ChHFdoV7ql95Wi7vuq2YT1bwCJqiWdZrQ1im3VujLYM= github.com/yuin/goldmark v1.4.13/go.mod h1:6yULJ656Px+3vBD8DxQVa3kxgyrAnzto9xy5taEt/CY= golang.org/x/arch v0.1.0/go.mod h1:5om86z9Hs0C8fWVUuoMHwpExlXzs5Tkyp9hOrfG7pp8= golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w= golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= golang.org/x/crypto v0.1.0/go.mod h1:RecgLatLF4+eUMCP1PoPZQb+cVrJcOPbHkTkbkB9sbw= golang.org/x/mod v0.6.0-dev.0.20220419223038-86c51ed26bb4/go.mod h1:jJ57K6gSWd91VN4djpZkiMVwK6gcyfeH4XE8wZrZaV4= golang.org/x/mod v0.6.0/go.mod h1:4mET923SAdbXp2ki8ey+zGs1SLqsuM2Y0uvdZR/fUNI= golang.org/x/mod v0.10.0 h1:lFO9qtOdlre5W1jxS3r/4szv2/6iXxScdzjoBMXNhYk= golang.org/x/mod v0.10.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs= golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg= golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c= golang.org/x/net v0.1.0/go.mod h1:Cx3nUiGt4eDBEyega/BKRp+/AlGL8hYe7U9odMt2Cco= golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.2.0 h1:PUR+T4wwASmuSTYdKjYHI5TD22Wy5ogLU5qZCOLxBrI= golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY= golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.1.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.8.0 h1:EBmGv8NaZBZTWvrbjNoL6HVt+IVy3QDQpJs7VRIw3tU= golang.org/x/sys v0.8.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo= golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= golang.org/x/term v0.1.0/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ= golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ= golang.org/x/text v0.3.7/go.mod h1:u+2+/6zg+i71rQMx5EYifcz6MCKuco9NR6JIITiCfzQ= golang.org/x/text v0.4.0/go.mod h1:mrYo+phRRbMaCq/xk9113O4dZlRixOauAjOtrjsXDZ8= golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ= golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo= golang.org/x/tools v0.1.12/go.mod h1:hNGJHUnrk76NpqgfD5Aqm5Crs+Hm0VOH/i9J2+nxYbc= golang.org/x/tools v0.2.0/go.mod h1:y4OqIKeOV/fWJetJ8bXPU1sEVniLMIyDAZWeHdV+NTA= golang.org/x/tools v0.9.1 h1:8WMNJAz3zrtPmnYC7ISf5dEn3MT0gY7jBJfw27yrrLo= golang.org/x/tools v0.9.1/go.mod h1:owI94Op576fPu3cIGQeHs3joujW/2Oc6MtlxbF5dfNc= golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= rsc.io/pdf v0.1.1/go.mod h1:n8OzWcQ6Sp37PL01nO98y4iUCRdTGarVfzxY20ICaU4= golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/asm/src.go000066400000000000000000000657411454601126700274360ustar00rootroot00000000000000//go:generate go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common // AVX2 optimized version of Poly.[Inv]NTT(). See the comments on the generic // implementation for details on the maths involved. package main import ( . "github.com/mmcloughlin/avo/build" // nolint:golint,stylecheck . "github.com/mmcloughlin/avo/operand" // nolint:golint,stylecheck . "github.com/mmcloughlin/avo/reg" // nolint:golint,stylecheck "github.com/cloudflare/circl/sign/dilithium/internal/common/params" ) // XXX align Poly on 16 bytes such that we can use aligned moves // XXX ensure Zetas and InvZetas are 16 byte aligned. func broadcastImm32(c uint32, out Op) { tmp1 := GP32() tmp2 := XMM() MOVL(U32(c), tmp1) VMOVD(tmp1, tmp2) VPBROADCASTD(tmp2, out) } // Performs AND with an 64b immediate. func andImm64(c uint64, inout Op) { tmp := GP64() MOVQ(U64(c), tmp) ANDQ(tmp, inout) } // Executes the permutation (a[2] b[0]) (a[3] b[1]) when considering only the // even positions of a and b seen as [8]uint32. func swapInner(a, b Op) { tmp := YMM() VPERM2I128(U8(32), b, a, tmp) // 0 + 2*16 VPERM2I128(U8(49), b, a, b) // 1 + 3*16 VMOVDQA(tmp, a) } // Executes the permutation (a[1] b[0]) (a[3] b[2]) when considering only the // even positions of a and b seen as [8]uint32. func oddCrossing(a, b Op) { tmp := YMM() VPUNPCKLQDQ(b, a, tmp) VPUNPCKHQDQ(b, a, b) VMOVDQA(tmp, a) } // nolint:funlen func nttAVX2() { // We perform the same operations as the generic implementation of NTT, // but use AVX2 to perform 16 butterflies at the same time. For the // first few levels this is straight forward. For the final levels we // need to move some coefficients around to be able to use the AVX2 // instructions. TEXT("nttAVX2", 0, "func(p *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) zetasPtr := GP64() LEAQ(NewDataAddr(Symbol{Name: "·Zetas"}, 0), zetasPtr) // We allocate a [256]uint64 on the stack aligned to 32 bytes to hold // "buf" which contains intermediate coefficients like "p" in the generic // algorithm, but then in uint64s instead of uint32s. bufPtr := GP64() LEAQ(AllocLocal(256*8+32), bufPtr) // +32 to be able to align andImm64(0xffffffffffffffe0, bufPtr) q := YMM() broadcastImm32(params.Q, q) doubleQ := YMM() broadcastImm32(2*params.Q, doubleQ) qinv := YMM() broadcastImm32(params.Qinv, qinv) // 4236238847 = -(q^-1) mod 2³² // Computes 4x4 Cooley--Tukey butterflies (a,b) ↦ (a + ζb, a - ζb). ctButterfly := func(a1, b1, zeta1, a2, b2, zeta2, a3, b3, zeta3, a4, b4, zeta4 Op) { t := [4]Op{YMM(), YMM(), YMM(), YMM()} a := [4]Op{a1, a2, a3, a4} b := [4]Op{b1, b2, b3, b4} zeta := [4]Op{zeta1, zeta2, zeta3, zeta4} // Set b = bζ. for i := 0; i < 4; i++ { VPMULUDQ(b[i], zeta[i], b[i]) } // Now we reduce b below 2Q with the method of reduceLe2Q(): // // t := ((b * 4236238847) & 0xffffffff) * uint64(Q) // return uint32((b + t) >> 32) for i := 0; i < 4; i++ { // t = b * 4236238847. VPMULUDQ(qinv, b[i], t[i]) } // t = (t & 0xffffffff) * Q. The and is implicit as VPMULUDQ // is a parallel 32b x 32b -> 64b multiplication. for i := 0; i < 4; i++ { VPMULUDQ(q, t[i], t[i]) } // t = b + t for i := 0; i < 4; i++ { VPADDQ(t[i], b[i], t[i]) } // t = t >> 32 for i := 0; i < 4; i++ { VPSRLQ(U8(32), t[i], t[i]) } // b = a + 2Q for i := 0; i < 4; i++ { VPADDD(a[i], doubleQ, b[i]) } // a += t for i := 0; i < 4; i++ { VPADDD(t[i], a[i], a[i]) } // b = b - t for i := 0; i < 4; i++ { VPSUBD(t[i], b[i], b[i]) } } zs := [4]Op{YMM(), YMM(), YMM(), YMM()} var xs [8]VecVirtual for i := 0; i < 8; i++ { xs[i] = YMM() } // With AVX2 we can compute 4*4 Cooley--Tukey butterflies at the same time. // As loading and storing from memory is expensive, we try to compute // as much at the same time. // First, second and third level. // The first butterfly at the third level is (0, 32). To compute it, we // need to compute some butterflies on the second level and in turn // the butterflies (0, 128), (32, 160), (64, 192) and (96, 224) on the // first level. As we need to compute them anyway, we compute the // butterflies (0, 32), (64, 96), (128, 160) and (192, 224) on the // third level at the same time. Using the uint64x4 AVX2 registers, // we compute (0, 32), (1, 33), ..., (4, 36), (64, 96), (64, 97), ... // in one go. This is one eighth of the third level. We repeat another // seven times with a shifted offset to compute the third level. // XXX should we really unroll this loop? for offset := 0; offset < 8; offset++ { // First level. // Load the coefficients. First uint32s of xs[0], xs[1], ... // contains p[0], p[32], p[64], ..., p[224]. for i := 0; i < 8; i++ { // Loads 4 32b coefficients at the same time; zeropads them to 64b // and puts them in xs[i]. VPMOVZXDQ(Mem{Base: pPtr, Disp: 4 * (32*i + 4*offset)}, xs[i]) } // XXX At the moment we've completely unrolled, so we could, if we want, // hardcode the Zetas here instead of looking them up from memory. // Is that worth it? VPBROADCASTD(Mem{Base: zetasPtr, Disp: 1 * 4}, zs[0]) // Zetas[1] ctButterfly( xs[0], xs[4], zs[0], xs[1], xs[5], zs[0], xs[2], xs[6], zs[0], xs[3], xs[7], zs[0], ) // Second level VPBROADCASTD(Mem{Base: zetasPtr, Disp: 2 * 4}, zs[0]) // Zetas[2] VPBROADCASTD(Mem{Base: zetasPtr, Disp: 3 * 4}, zs[1]) // Zetas[3] ctButterfly( xs[0], xs[2], zs[0], xs[1], xs[3], zs[0], xs[4], xs[6], zs[1], xs[5], xs[7], zs[1], ) // Third level VPBROADCASTD(Mem{Base: zetasPtr, Disp: 4 * 4}, zs[0]) // Zetas[4] VPBROADCASTD(Mem{Base: zetasPtr, Disp: 5 * 4}, zs[1]) // Zetas[5] VPBROADCASTD(Mem{Base: zetasPtr, Disp: 6 * 4}, zs[2]) // Zetas[6] VPBROADCASTD(Mem{Base: zetasPtr, Disp: 7 * 4}, zs[3]) // Zetas[7] ctButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) for i := 0; i < 8; i++ { VMOVDQA(xs[i], Mem{Base: bufPtr, Disp: 8 * (32*i + 4*offset)}) } } // Fourth, fifth, sixth, seventh and eighth level. // If we want to compute the butterfly (0, 1) in the eighth level, we need // to compute the first 2 butterflies in the seventh level; the first 4 // of the sixth, ... and the first 16 in the fourth level which needs the // first 32 coefficients already computed in the third level. // Going forward again, we see that we can use these to compute the first // 32 coefficients. As each level requires 16 butterflies, we can // conveniently perform these all in our YMM registers. // After that we repeat the same method for the next 32 coefficients and // continue for a total of eight times to finish the computation of // the NTT. // XXX should we really unroll this loop? for offset := 0; offset < 8; offset++ { // Load the first 32 coefficients from level 3. Recall that bufPtr // has 64 bits of space for each coefficient. for i := 0; i < 8; i++ { VMOVDQA(Mem{Base: bufPtr, Disp: 8 * 4 * (8*offset + i)}, xs[i]) } // Fourth level VPBROADCASTD(Mem{Base: zetasPtr, Disp: (8 + offset) * 4}, zs[0]) ctButterfly( xs[0], xs[4], zs[0], xs[1], xs[5], zs[0], xs[2], xs[6], zs[0], xs[3], xs[7], zs[0], ) // Fifth level VPBROADCASTD(Mem{Base: zetasPtr, Disp: (16 + offset*2) * 4}, zs[0]) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (16 + offset*2 + 1) * 4}, zs[1]) ctButterfly( xs[0], xs[2], zs[0], xs[1], xs[3], zs[0], xs[4], xs[6], zs[1], xs[5], xs[7], zs[1], ) // Sixth level for i := 0; i < 4; i++ { VPBROADCASTD(Mem{Base: zetasPtr, Disp: (32 + offset*4 + i) * 4}, zs[i]) } ctButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) // Seventh level // Now things get a bit trickier. We have to compute the butterflies // (0, 2), (1, 3), (4, 6), (5, 7), etc which don't fit our ctButterfly() // routine, which likes to have four consecutive butterflies. // To work around this, we swap 2 with 4 and 3 with 5, etc., which // allows us to use our old routine. tmp := YMM() // XXX optimize? We might want to add a small extra table for just // these zetas so that we don't have to blend them. for i := 0; i < 4; i++ { VPBROADCASTD(Mem{Base: zetasPtr, Disp: (64 + offset*8 + i*2) * 4}, tmp) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (64 + offset*8 + i*2 + 1) * 4}, zs[i]) VPBLENDD(U8(240), zs[i], tmp, zs[i]) } swapInner(xs[0], xs[1]) swapInner(xs[2], xs[3]) swapInner(xs[4], xs[5]) swapInner(xs[6], xs[7]) ctButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) // Eighth level // Finally, we have to perform the butterflies (0, 1), (2, 3), etc. // Swapping 1 with 4 and 3 with 6 (etc.) will ensure that a // straight-forward call to our ctButterfly() routine will do the right // thing. oddCrossing(xs[0], xs[1]) oddCrossing(xs[2], xs[3]) oddCrossing(xs[4], xs[5]) oddCrossing(xs[6], xs[7]) for i := 0; i < 4; i++ { VPMOVZXDQ(Mem{Base: zetasPtr, Disp: (128 + 4*i + offset*16) * 4}, zs[i]) } ctButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) // Packing. // Due to swapInner() and oddCrossing() our coefficients are laid out // as 0, 2, 4, 6, 1, 3, 5, 7, 8, 10, ... in xs[0], xs[1], ... // with junk 32b in between. By shifting the odd xss 32b to the // left and merging them with the even xss, we get the desired // order 0, 1, 2, 3, ... without any padding, which can then be // moved out into memory. VPSLLQ(U8(32), xs[1], xs[1]) VPSLLQ(U8(32), xs[3], xs[3]) VPSLLQ(U8(32), xs[5], xs[5]) VPSLLQ(U8(32), xs[7], xs[7]) VPBLENDD(U8(170), xs[1], xs[0], xs[0]) VPBLENDD(U8(170), xs[3], xs[2], xs[2]) VPBLENDD(U8(170), xs[5], xs[4], xs[4]) VPBLENDD(U8(170), xs[7], xs[6], xs[6]) for i := 0; i < 4; i++ { VMOVDQU(xs[2*i], Mem{Base: pPtr, Disp: 8 * 4 * (4*offset + i)}) } } RET() } // nolint:funlen func invNttAVX2() { // Just like with the generic implementation, we do the operations of // NTT in reverse, except for two things: we hoist out all divisions by // two from the Gentleman-Sande butterflies and accumulate them to one // big division by 2⁸ at the end. TEXT("invNttAVX2", 0, "func(p *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) zetasPtr := GP64() LEAQ(NewDataAddr(Symbol{Name: "·InvZetas"}, 0), zetasPtr) // We allocate a [256]uint64 on the stack aligned to 32 bytes to hold // "buf" which contains intermediate coefficients like "p" in the generic // algorithm, but then in uint64s instead of uint32s. bufPtr := GP64() LEAQ(AllocLocal(256*8+32), bufPtr) // +32 to be able to align andImm64(0xffffffffffffffe0, bufPtr) q := YMM() broadcastImm32(params.Q, q) q256 := YMM() broadcastImm32(256*params.Q, q256) qinv := YMM() broadcastImm32(params.Qinv, qinv) // Computes 4x4 doubled Gentleman--Sande butterflies (a,b) ↦ (a+b, ζ(a-b)). gsButterfly := func(a1, b1, zeta1, a2, b2, zeta2, a3, b3, zeta3, a4, b4, zeta4 Op) { t := [4]Op{YMM(), YMM(), YMM(), YMM()} a := [4]Op{a1, a2, a3, a4} b := [4]Op{b1, b2, b3, b4} zeta := [4]Op{zeta1, zeta2, zeta3, zeta4} // XXX be more parallel when we have more registers available, when // we don't use the full four registers for zetas. for i := 0; i < 4; i++ { // Set t = 256Q + a in preparation of subtracting b VPADDD(a[i], q256, t[i]) // Set t = t - b VPSUBD(b[i], t[i], t[i]) // Set a = a + b VPADDD(a[i], b[i], a[i]) // Set b = tζ VPMULUDQ(t[i], zeta[i], b[i]) } // Now we reduce b below 2Q with the method of reduceLe2Q(): // // t := ((b * 4236238847) & 0xffffffff) * uint64(Q) // return uint32((b + t) >> 32) for i := 0; i < 4; i++ { // t = b * 4236238847. VPMULUDQ(qinv, b[i], t[i]) } // t = (t & 0xffffffff) * Q. The and is implicit as VPMULUDQ // is a parallel 32b x 32b -> 64b multiplication. for i := 0; i < 4; i++ { VPMULUDQ(q, t[i], t[i]) } // t = b + t for i := 0; i < 4; i++ { VPADDQ(t[i], b[i], t[i]) } // b = t >> 32 for i := 0; i < 4; i++ { VPSRLQ(U8(32), t[i], b[i]) } } zs := [4]Op{YMM(), YMM(), YMM(), YMM()} var xs [8]VecVirtual for i := 0; i < 8; i++ { xs[i] = YMM() } // XXX should we really unroll this loop? for offset := 0; offset < 8; offset++ { // Load coeffs 0 1 2 3 4 5 6 7 into xs[0], 8 ... 16 into xs[1], etc. for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 8 * 4 * (4*offset + i)}, xs[2*i]) } // Move odd coeffs of xs[2*i] into xs[2*i+1] and shift down. Ignoring // the odd coefficients, we have 0 2 4 6 in xs[0] and 1 3 4 5 in xs[1]. for i := 0; i < 4; i++ { VPSRLQ(U8(32), xs[2*i], xs[2*i+1]) } // Eighth level for i := 0; i < 4; i++ { VPMOVZXDQ(Mem{Base: zetasPtr, Disp: 4 * 4 * (4*offset + i)}, zs[i]) } gsButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) // See comments in nttAVX2() above about oddCrossing() and swapInner(). oddCrossing(xs[0], xs[1]) oddCrossing(xs[2], xs[3]) oddCrossing(xs[4], xs[5]) oddCrossing(xs[6], xs[7]) // Seventh level tmp := YMM() // XXX optimize? We might want to add a small extra table for just // these zetas so that we don't have to blend them. for i := 0; i < 4; i++ { VPBROADCASTD(Mem{Base: zetasPtr, Disp: (128 + offset*8 + i*2) * 4}, tmp) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (128 + offset*8 + i*2 + 1) * 4}, zs[i]) VPBLENDD(U8(240), zs[i], tmp, zs[i]) } gsButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) // See comments in nttAVX2() above about oddCrossing() and swapInner() swapInner(xs[0], xs[1]) swapInner(xs[2], xs[3]) swapInner(xs[4], xs[5]) swapInner(xs[6], xs[7]) // Sixth level for i := 0; i < 4; i++ { VPBROADCASTD(Mem{Base: zetasPtr, Disp: (192 + offset*4 + i) * 4}, zs[i]) } gsButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) // Fifth level VPBROADCASTD(Mem{Base: zetasPtr, Disp: (224 + offset*2) * 4}, zs[0]) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (224 + offset*2 + 1) * 4}, zs[1]) gsButterfly( xs[0], xs[2], zs[0], xs[1], xs[3], zs[0], xs[4], xs[6], zs[1], xs[5], xs[7], zs[1], ) // Fourth level VPBROADCASTD(Mem{Base: zetasPtr, Disp: (240 + offset) * 4}, zs[0]) gsButterfly( xs[0], xs[4], zs[0], xs[1], xs[5], zs[0], xs[2], xs[6], zs[0], xs[3], xs[7], zs[0], ) for i := 0; i < 8; i++ { VMOVDQA(xs[i], Mem{Base: bufPtr, Disp: 8 * 4 * (8*offset + i)}) } } // XXX should we really unroll this loop? for offset := 0; offset < 8; offset++ { for i := 0; i < 8; i++ { VMOVDQA(Mem{Base: bufPtr, Disp: 8 * (32*i + 4*offset)}, xs[i]) } // Third level VPBROADCASTD(Mem{Base: zetasPtr, Disp: (248 * 4)}, zs[0]) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (249 * 4)}, zs[1]) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (250 * 4)}, zs[2]) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (251 * 4)}, zs[3]) gsButterfly( xs[0], xs[1], zs[0], xs[2], xs[3], zs[1], xs[4], xs[5], zs[2], xs[6], xs[7], zs[3], ) // Second level VPBROADCASTD(Mem{Base: zetasPtr, Disp: (252 * 4)}, zs[0]) VPBROADCASTD(Mem{Base: zetasPtr, Disp: (253 * 4)}, zs[1]) gsButterfly( xs[0], xs[2], zs[0], xs[1], xs[3], zs[0], xs[4], xs[6], zs[1], xs[5], xs[7], zs[1], ) // First level VPBROADCASTD(Mem{Base: zetasPtr, Disp: (254 * 4)}, zs[0]) gsButterfly( xs[0], xs[4], zs[0], xs[1], xs[5], zs[0], xs[2], xs[6], zs[0], xs[3], xs[7], zs[0], ) // Finally, we multiply by 41978 = (256)^-1 R² ... rOver256 := YMM() broadcastImm32(params.ROver256, rOver256) for i := 0; i < 8; i++ { VPMULUDQ(xs[i], rOver256, xs[i]) } var t [8]VecVirtual // (we need this loop, otherwise we run out of YMM registers.) for j := 0; j <= 4; j += 4 { // ... and reduce below 2Q with the method of reduceLe2Q(): // // t := ((x * 4236238847) & 0xffffffff) * uint64(Q) // return uint32((x + t) >> 32) for i := j; i < 4+j; i++ { t[i] = YMM() // t = x * 4236238847. VPMULUDQ(qinv, xs[i], t[i]) } // t = (t & 0xffffffff) * Q. The and is implicit as VPMULUDQ // is a parallel 32b x 32b -> 64b multiplication. for i := j; i < 4+j; i++ { VPMULUDQ(q, t[i], t[i]) } // t = x + t for i := j; i < 4+j; i++ { VPADDQ(t[i], xs[i], t[i]) } // x = t >> 32 for i := j; i < 4+j; i++ { VPSRLQ(U8(32), t[i], xs[i]) } } for i := 0; i < 8; i++ { VMOVDQA(xs[i], Mem{Base: bufPtr, Disp: 8 * (32*i + 4*offset)}) } } // Finally, we copy the 32b results from the [256]uint64 buf to // the [256]uint32 p. // XXX is this the most efficient way? for j := 0; j < 8; j++ { for i := 0; i < 8; i++ { VMOVDQA(Mem{Base: bufPtr, Disp: 32 * (8*j + i)}, xs[i]) } // Recall that oddCrossing after swapInner will permute the // even coefficients from 0 1 2 3 4 5 6 7 to 0 2 4 6 1 3 5 7 and so // then we can simply shift and blend the last four into the first four // as we did at the end of nttAVX2(). for i := 0; i < 4; i++ { swapInner(xs[2*i], xs[2*i+1]) } for i := 0; i < 4; i++ { oddCrossing(xs[2*i], xs[2*i+1]) } for i := 0; i < 4; i++ { VPSLLQ(U8(32), xs[2*i+1], xs[2*i+1]) } for i := 0; i < 4; i++ { VPBLENDD(U8(170), xs[2*i+1], xs[2*i], xs[2*i]) } for i := 0; i < 4; i++ { VMOVDQU(xs[2*i], Mem{Base: pPtr, Disp: 32 * (4*j + i)}) } } RET() } // XXX Split out into separate file. To do this we need to figure out how // to share code properly between avo modules. func mulHatAVX2() { TEXT("mulHatAVX2", NOSPLIT, "func(p, a, b *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) aPtr := Load(Param("a"), GP64()) bPtr := Load(Param("b"), GP64()) q := YMM() broadcastImm32(params.Q, q) qinv := YMM() broadcastImm32(params.Qinv, qinv) var a [4]VecVirtual var b [4]VecVirtual for i := 0; i < 4; i++ { a[i] = YMM() b[i] = YMM() } // XXX Is this loop unrolling worthwhile? for j := 0; j < 16; j++ { // XXX We could use 6 registers each (instead of 4). Does that make // it faster? for i := 0; i < 4; i++ { VPMOVZXDQ(Mem{Base: aPtr, Disp: 16 * (4*j + i)}, a[i]) } for i := 0; i < 4; i++ { VPMOVZXDQ(Mem{Base: bPtr, Disp: 16 * (4*j + i)}, b[i]) } for i := 0; i < 4; i++ { VPMULUDQ(a[i], b[i], b[i]) } // Now we reduce b below 2Q with the method of reduceLe2Q(): // // a := ((b * 4236238847) & 0xffffffff) * uint64(Q) // return uint32((b + a) >> 32) for i := 0; i < 4; i++ { // a = b * 4236238847. VPMULUDQ(qinv, b[i], a[i]) } // t = (t & 0xffffffff) * Q. The and is implicit as VPMULUDQ // is a parallel 32b x 32b -> 64b multiplication. for i := 0; i < 4; i++ { VPMULUDQ(q, a[i], a[i]) } // t = b + a for i := 0; i < 4; i++ { VPADDQ(a[i], b[i], a[i]) } // b = a >> 32 for i := 0; i < 4; i++ { VPSRLQ(U8(32), a[i], b[i]) } // Pack into p. See end of invNttAvx2() for a description of the method. // XXX is there a better way to do this that avoids the PERM // in oddCrossing? for i := 0; i < 2; i++ { swapInner(b[2*i], b[2*i+1]) } for i := 0; i < 2; i++ { oddCrossing(b[2*i], b[2*i+1]) } for i := 0; i < 2; i++ { VPSLLQ(U8(32), b[2*i+1], b[2*i+1]) } for i := 0; i < 2; i++ { VPBLENDD(U8(170), b[2*i+1], b[2*i], b[2*i]) } for i := 0; i < 2; i++ { VMOVDQU(b[2*i], Mem{Base: pPtr, Disp: 32 * (2*j + i)}) } } RET() } func addAVX2() { TEXT("addAVX2", NOSPLIT, "func(p, a, b *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) aPtr := Load(Param("a"), GP64()) bPtr := Load(Param("b"), GP64()) var a [8]VecVirtual var b [8]VecVirtual for i := 0; i < 8; i++ { a[i] = YMM() b[i] = YMM() } // XXX is unrolling worth it? for j := 0; j < 4; j++ { for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: aPtr, Disp: 32 * (8*j + i)}, a[i]) } for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: bPtr, Disp: 32 * (8*j + i)}, b[i]) } for i := 0; i < 8; i++ { VPADDD(a[i], b[i], b[i]) } for i := 0; i < 8; i++ { VMOVDQU(b[i], Mem{Base: pPtr, Disp: 32 * (8*j + i)}) } } RET() } func subAVX2() { TEXT("subAVX2", NOSPLIT, "func(p, a, b *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) aPtr := Load(Param("a"), GP64()) bPtr := Load(Param("b"), GP64()) var a [4]VecVirtual var b [4]VecVirtual for i := 0; i < 4; i++ { a[i] = YMM() b[i] = YMM() } doubleQ := YMM() broadcastImm32(2*params.Q, doubleQ) // XXX is unrolling worth it? for j := 0; j < 8; j++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: aPtr, Disp: 32 * (4*j + i)}, a[i]) } for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: bPtr, Disp: 32 * (4*j + i)}, b[i]) } for i := 0; i < 4; i++ { VPSUBD(b[i], doubleQ, b[i]) } for i := 0; i < 4; i++ { VPADDD(a[i], b[i], b[i]) } for i := 0; i < 4; i++ { VMOVDQU(b[i], Mem{Base: pPtr, Disp: 32 * (4*j + i)}) } } RET() } func packLe16AVX2() { TEXT("packLe16AVX2", NOSPLIT, "func(p *[256]uint32, buf *byte)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) bufPtr := Load(Param("buf"), GP64()) var a [8]VecVirtual var b [8]VecVirtual for i := 0; i < 8; i++ { a[i] = YMM() b[i] = YMM() } for j := 0; j < 4; j++ { // We load p[0], ..., p[7] into a[0], p[8], ..., p[15] into a[1], etc., // so we may consider a as a matrix. We transpose a in the usual way. for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (8*j + 2*i)}, a[2*i]) VPUNPCKLDQ(Mem{Base: pPtr, Disp: 32 * (8*j + 2*i + 1)}, a[2*i], a[2*i]) VMOVDQU(Mem{Base: pPtr, Disp: 32 * (8*j + 2*i)}, a[2*i+1]) VPUNPCKHDQ(Mem{Base: pPtr, Disp: 32 * (8*j + 2*i + 1)}, a[2*i+1], a[2*i+1]) } VPUNPCKLQDQ(a[2], a[0], b[0]) VPUNPCKHQDQ(a[2], a[0], b[1]) VPUNPCKLQDQ(a[3], a[1], b[2]) VPUNPCKHQDQ(a[3], a[1], b[3]) VPUNPCKLQDQ(a[6], a[4], b[4]) VPUNPCKHQDQ(a[6], a[4], b[5]) VPUNPCKLQDQ(a[7], a[5], b[6]) VPUNPCKHQDQ(a[7], a[5], b[7]) VPERM2I128(U8(32), b[4], b[0], a[0]) VPERM2I128(U8(32), b[5], b[1], a[1]) VPERM2I128(U8(32), b[6], b[2], a[2]) VPERM2I128(U8(32), b[7], b[3], a[3]) VPERM2I128(U8(49), b[4], b[0], a[4]) VPERM2I128(U8(49), b[5], b[1], a[5]) VPERM2I128(U8(49), b[6], b[2], a[6]) VPERM2I128(U8(49), b[7], b[3], a[7]) // a has been transposed, so a[0] contains p[0], p[8], ... and // a[1] contains p[1], p[9], ..., etc. We shift a[i] by 4*i to the left // and or them together. for i := 1; i < 8; i++ { VPSLLD(U8(4*i), a[i], a[i]) } VPOR(a[0], a[1], a[1]) VPOR(a[2], a[3], a[3]) VPOR(a[4], a[5], a[5]) VPOR(a[6], a[7], a[7]) VPOR(a[1], a[3], a[3]) VPOR(a[5], a[7], a[7]) VPOR(a[3], a[7], a[7]) VMOVDQU(a[7], Mem{Base: bufPtr, Disp: 32 * j}) } RET() } func reduceLe2QAVX2() { TEXT("reduceLe2QAVX2", NOSPLIT, "func(p *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) var a, b, c [4]VecVirtual for i := 0; i < 4; i++ { a[i] = YMM() b[i] = YMM() c[i] = YMM() } twoToThe23MinusOne := YMM() broadcastImm32((1<<23)-1, twoToThe23MinusOne) // We use the same computation as used in reduceLe2Q() for the separate // coefficients. for j := 0; j < 8; j++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (4*j + i)}, a[i]) } // b = a >> 23 for i := 0; i < 4; i++ { VPSRLD(U8(23), a[i], b[i]) } // a = a & 2²³-1 for i := 0; i < 4; i++ { VPAND(a[i], twoToThe23MinusOne, a[i]) } // c = (b << 13) - b for i := 0; i < 4; i++ { VPSLLD(U8(13), b[i], c[i]) } for i := 0; i < 4; i++ { VPSUBD(b[i], c[i], c[i]) } // a = a + c for i := 0; i < 4; i++ { VPADDD(a[i], c[i], a[i]) } // Write back for i := 0; i < 4; i++ { VMOVDQU(a[i], Mem{Base: pPtr, Disp: 32 * (4*j + i)}) } } RET() } func le2qModQAVX2() { TEXT("le2qModQAVX2", NOSPLIT, "func(p *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) // We use the same method as le2qModQ(). var a, m [4]VecVirtual for i := 0; i < 4; i++ { a[i] = YMM() m[i] = YMM() } q := YMM() broadcastImm32(params.Q, q) for j := 0; j < 8; j++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (4*j + i)}, a[i]) } // a -= Q for i := 0; i < 4; i++ { VPSUBD(q, a[i], a[i]) } // m = uint32(int32(a) >> 31) for i := 0; i < 4; i++ { VPSRAD(U8(31), a[i], m[i]) } // m &= q for i := 0; i < 4; i++ { VPAND(m[i], q, m[i]) } // a += m for i := 0; i < 4; i++ { VPADDD(a[i], m[i], a[i]) } for i := 0; i < 4; i++ { VMOVDQU(a[i], Mem{Base: pPtr, Disp: 32 * (4*j + i)}) } } RET() } func exceedsAVX2() { TEXT("exceedsAVX2", NOSPLIT, "func(p *[256]uint32, bound uint32) uint8") Pragma("noescape") pPtr := Load(Param("p"), GP64()) bound := Load(Param("bound"), GP32()) var a, b [4]VecVirtual for i := 0; i < 4; i++ { a[i] = YMM() b[i] = YMM() } boundX4 := XMM() boundX8 := YMM() VMOVD(bound, boundX4) VPBROADCASTD(boundX4, boundX8) qMinusOneDiv2 := YMM() broadcastImm32((params.Q-1)/2, qMinusOneDiv2) signMaskX8 := YMM() broadcastImm32(0x80000000, signMaskX8) signsMask := GP32() MOVL(U32(0x88888888), signsMask) for j := 0; j < 8; j++ { for i := 0; i < 4; i++ { VMOVDQU(Mem{Base: pPtr, Disp: 32 * (4*j + i)}, a[i]) } // We use the same method as Poly.exceedsGeneric(). // a = (Q-1)/2 - a for i := 0; i < 4; i++ { VPSUBD(a[i], qMinusOneDiv2, a[i]) } // b = a >> 31 for i := 0; i < 4; i++ { VPSRAD(U8(31), a[i], b[i]) } // a = a ^ b for i := 0; i < 4; i++ { VPXOR(a[i], b[i], a[i]) } // a = (Q-1)/2 - a for i := 0; i < 4; i++ { VPSUBD(a[i], qMinusOneDiv2, a[i]) } // Here exceedsGeneric() checks if a ⩾ bound. We'll be more clever. // a ⩾ bound iff a - bound ⩾ 0, so set a = a - bound first. for i := 0; i < 4; i++ { VPSUBD(boundX8, a[i], a[i]) } // a &= 0x80000000. Leaves the sign. Should be zero. for i := 0; i < 4; i++ { VPAND(a[i], signMaskX8, a[i]) } for i := 0; i < 4; i++ { // Move the high bits, which are all zero except possibly for // the sign bits, into tmp. tmp := GP32() VPMOVMSKB(a[i], tmp) // If one of the sign bits is zero, then one of the as is // positive hence the bound is exceeded. XORL(signsMask, tmp) // 0b10001000100010001000100010001000 TESTL(tmp, tmp) JNZ(LabelRef("exceeded")) } } ret := GP8() XORB(ret, ret) Store(ret, ReturnIndex(0)) RET() Label("exceeded") MOVB(U8(1), ret) Store(ret, ReturnIndex(0)) RET() } func mulBy2toDAVX2() { TEXT("mulBy2toDAVX2", NOSPLIT, "func(p, q *[256]uint32)") Pragma("noescape") pPtr := Load(Param("p"), GP64()) qPtr := Load(Param("q"), GP64()) var x [8]VecVirtual for i := 0; i < 8; i++ { x[i] = YMM() } for j := 0; j < 4; j++ { for i := 0; i < 8; i++ { VMOVDQU(Mem{Base: qPtr, Disp: 32 * (8*j + i)}, x[i]) } for i := 0; i < 8; i++ { VPSLLD(U8(params.D), x[i], x[i]) } for i := 0; i < 8; i++ { VMOVDQU(x[i], Mem{Base: pPtr, Disp: 32 * (8*j + i)}) } } RET() } func main() { ConstraintExpr("amd64") nttAVX2() invNttAVX2() mulHatAVX2() addAVX2() subAVX2() packLe16AVX2() reduceLe2QAVX2() le2qModQAVX2() exceedsAVX2() mulBy2toDAVX2() Generate() } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/field.go000066400000000000000000000033411454601126700271360ustar00rootroot00000000000000package common // Returns a y with y < 2q and y = x mod q. // Note that in general *not*: ReduceLe2Q(ReduceLe2Q(x)) == x. func ReduceLe2Q(x uint32) uint32 { // Note 2²³ = 2¹³ - 1 mod q. So, writing x = x₁ 2²³ + x₂ with x₂ < 2²³ // and x₁ < 2⁹, we have x = y (mod q) where // y = x₂ + x₁ 2¹³ - x₁ ≤ 2²³ + 2¹³ < 2q. x1 := x >> 23 x2 := x & 0x7FFFFF // 2²³-1 return x2 + (x1 << 13) - x1 } // Returns x mod q. func modQ(x uint32) uint32 { return le2qModQ(ReduceLe2Q(x)) } // For x R ≤ q 2³², find y ≤ 2q with y = x mod q. func montReduceLe2Q(x uint64) uint32 { // Qinv = 4236238847 = -(q⁻¹) mod 2³² m := (x * Qinv) & 0xffffffff return uint32((x + m*uint64(Q)) >> 32) } // Returns x mod q for 0 ≤ x < 2q. func le2qModQ(x uint32) uint32 { x -= Q mask := uint32(int32(x) >> 31) // mask is 2³²-1 if x was neg.; 0 otherwise return x + (mask & Q) } // Splits 0 ≤ a < Q into a0 and a1 with a = a1*2ᴰ + a0 // and -2ᴰ⁻¹ < a0 < 2ᴰ⁻¹. Returns a0 + Q and a1. func power2round(a uint32) (a0plusQ, a1 uint32) { // We effectively compute a0 = a mod± 2ᵈ // and a1 = (a - a0) / 2ᵈ. a0 := a & ((1 << D) - 1) // a mod 2ᵈ // a0 is one of 0, 1, ..., 2ᵈ⁻¹-1, 2ᵈ⁻¹, 2ᵈ⁻¹+1, ..., 2ᵈ-1 a0 -= (1 << (D - 1)) + 1 // now a0 is -2ᵈ⁻¹-1, -2ᵈ⁻¹, ..., -2, -1, 0, ..., 2ᵈ⁻¹-2 // Next, we add 2ᴰ to those a0 that are negative (seen as int32). a0 += uint32(int32(a0)>>31) & (1 << D) // now a0 is 2ᵈ⁻¹-1, 2ᵈ⁻¹, ..., 2ᵈ-2, 2ᵈ-1, 0, ..., 2ᵈ⁻¹-2 a0 -= (1 << (D - 1)) - 1 // now a0 id 0, 1, 2, ..., 2ᵈ⁻¹-1, 2ᵈ⁻¹-1, -2ᵈ⁻¹-1, ... // which is what we want. a0plusQ = Q + a0 a1 = (a - a0) >> D return } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/field_test.go000066400000000000000000000027521454601126700302020ustar00rootroot00000000000000package common import ( "crypto/rand" "encoding/binary" "math" "testing" ) func randSliceUint32(length uint) []uint32 { return randSliceUint32WithMax(length, math.MaxUint32) } func randSliceUint32WithMax(length uint, max uint32) []uint32 { bytes := make([]uint8, 4*length) if n, err := rand.Read(bytes); err != nil { panic(err) } else if n < len(bytes) { panic("short read from RNG") } x := make([]uint32, length) for i := range x { x[i] = binary.LittleEndian.Uint32(bytes[4*i:]) % max } return x } func TestModQ(t *testing.T) { const testTimes = 1000 r := randSliceUint32(testTimes) for i := 0; i < testTimes; i++ { x := r[i] y := modQ(x) if y > Q { t.Fatalf("modQ(%d) > Q", x) } if y != x%Q { t.Fatalf("modQ(%d) != %d (mod Q)", x, x) } } } func TestReduceLe2Q(t *testing.T) { const testTimes = 1000 r := randSliceUint32(testTimes) for i := 0; i < testTimes; i++ { x := r[i] y := ReduceLe2Q(x) if y > 2*Q { t.Fatalf("reduce_le2q(%d) > 2Q", x) } if y%Q != x%Q { t.Fatalf("reduce_le2q(%d) != %d (mod Q)", x, x) } } } func TestPower2Round(t *testing.T) { for a := uint32(0); a < Q; a++ { a0PlusQ, a1 := power2round(a) a0 := int32(a0PlusQ) - int32(Q) if int32(a) != a0+int32((1<= a0) || (a0 > 1<<(D-1)) { t.Fatalf("power2round(%v): a0 out of bounds", a) } if a1 > (1 << (QBits - D)) { t.Fatalf("power2round(%v): a1 out of bounds", a) } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/generic.go000066400000000000000000000041761454601126700274760ustar00rootroot00000000000000//go:build !amd64 // +build !amd64 package common // Execute an in-place forward NTT on as. // // Assumes the coefficients are in Montgomery representation and bounded // by 2*Q. The resulting coefficients are again in Montgomery representation, // but are only bounded bt 18*Q. func (p *Poly) NTT() { p.nttGeneric() } // Execute an in-place inverse NTT and multiply by Montgomery factor R // // Assumes the coefficients are in Montgomery representation and bounded // by 2*Q. The resulting coefficients are again in Montgomery representation // and bounded by 2*Q. func (p *Poly) InvNTT() { p.invNttGeneric() } // Sets p to the polynomial whose coefficients are the pointwise multiplication // of those of a and b. The coefficients of p are bounded by 2q. // // Assumes a and b are in Montgomery form and that the pointwise product // of each coefficient is below 2³² q. func (p *Poly) MulHat(a, b *Poly) { p.mulHatGeneric(a, b) } // Sets p to a + b. Does not normalize polynomials. func (p *Poly) Add(a, b *Poly) { p.addGeneric(a, b) } // Sets p to a - b. // // Warning: assumes coefficients of b are less than 2q. // Sets p to a + b. Does not normalize polynomials. func (p *Poly) Sub(a, b *Poly) { p.subGeneric(a, b) } // Writes p whose coefficients are in [0, 16) to buf, which must be of // length N/2. func (p *Poly) PackLe16(buf []byte) { p.packLe16Generic(buf) } // Reduces each of the coefficients to <2q. func (p *Poly) ReduceLe2Q() { p.reduceLe2QGeneric() } // Reduce each of the coefficients to 0; l >>= 1 { // On the n-th iteration of the l-loop, the coefficients start off // bounded by n*2*Q. // // offset effectively loops over the row groups in this column; it // is the first row in the row group. for offset := uint(0); offset < N-l; offset += 2 * l { k++ zeta := uint64(Zetas[k]) // j loops over each butterfly in the row group. for j := offset; j < offset+l; j++ { t := montReduceLe2Q(zeta * uint64(p[j+l])) p[j+l] = p[j] + (2*Q - t) // Cooley--Tukey butterfly p[j] += t } } } } // Execute an in-place inverse NTT and multiply by Montgomery factor R // // Assumes the coefficients are in Montgomery representation and bounded // by 2*Q. The resulting coefficients are again in Montgomery representation // and bounded by 2*Q. func (p *Poly) invNttGeneric() { k := 0 // Index into InvZetas // We basically do the opposite of NTT, but postpone dividing by 2 in the // inverse of the Cooley--Tukey butterfly and accumulate that to a big // division by 2⁸ at the end. See comments in the NTT() function. for l := uint(1); l < N; l <<= 1 { // On the n-th iteration of the l-loop, the coefficients start off // bounded by 2ⁿ⁻¹*2*Q, so by 256*Q on the last. for offset := uint(0); offset < N-l; offset += 2 * l { zeta := uint64(InvZetas[k]) k++ for j := offset; j < offset+l; j++ { t := p[j] // Gentleman--Sande butterfly p[j] = t + p[j+l] t += 256*Q - p[j+l] p[j+l] = montReduceLe2Q(zeta * uint64(t)) } } } for j := uint(0); j < N; j++ { // ROver256 = 41978 = (256)⁻¹ R² p[j] = montReduceLe2Q(ROver256 * uint64(p[j])) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/ntt_test.go000066400000000000000000000023771454601126700277270ustar00rootroot00000000000000package common import "testing" func (p *Poly) RandLe2Q() { max := 2 * uint32(Q) r := randSliceUint32WithMax(N, max) copy(p[:], r) } func TestNTTAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p Poly p.RandLe2Q() q1 := p q2 := p q1.NTT() q2.nttGeneric() if q1 != q2 { t.Fatalf("NTT(%v) = %v != %v", p, q1, q2) } } } func TestNTT(t *testing.T) { for k := 0; k < 1000; k++ { var p, q Poly p.RandLe2Q() q = p q.Normalize() p.NTT() for i := uint(0); i < N; i++ { if p[i] > 18*Q { t.Fatalf("NTT(%v)[%d] = %d > 18*Q", q, i, p[i]) } } p.ReduceLe2Q() p.InvNTT() for i := uint(0); i < N; i++ { if p[i] > 2*Q { t.Fatalf("InvNTT(%v)[%d] > 2*Q", q, i) } } p.Normalize() for i := uint(0); i < N; i++ { if p[i] != uint32((uint64(q[i])*uint64(1<<32))%Q) { t.Fatalf("%v != %v", p, q) } } } } func BenchmarkNTTGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.nttGeneric() } } func BenchmarkInvNTTGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.invNttGeneric() } } func BenchmarkNTT(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.NTT() } } func BenchmarkInvNTT(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.InvNTT() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/pack.go000066400000000000000000000112021454601126700267640ustar00rootroot00000000000000package common // Sets p to the polynomial whose coefficients are less than 1024 encoded // into buf (which must be of size PolyT1Size). // // p will be normalized. func (p *Poly) UnpackT1(buf []byte) { j := 0 for i := 0; i < PolyT1Size; i += 5 { p[j] = (uint32(buf[i]) | (uint32(buf[i+1]) << 8)) & 0x3ff p[j+1] = (uint32(buf[i+1]>>2) | (uint32(buf[i+2]) << 6)) & 0x3ff p[j+2] = (uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4)) & 0x3ff p[j+3] = (uint32(buf[i+3]>>6) | (uint32(buf[i+4]) << 2)) & 0x3ff j += 4 } } // Writes p whose coefficients are in (-2ᵈ⁻¹, 2ᵈ⁻¹] into buf which // has to be of length at least PolyT0Size. // // Assumes that the coefficients are not normalized, but lie in the // range (q-2ᵈ⁻¹, q+2ᵈ⁻¹]. func (p *Poly) PackT0(buf []byte) { j := 0 for i := 0; i < PolyT0Size; i += 13 { p0 := Q + (1 << (D - 1)) - p[j] p1 := Q + (1 << (D - 1)) - p[j+1] p2 := Q + (1 << (D - 1)) - p[j+2] p3 := Q + (1 << (D - 1)) - p[j+3] p4 := Q + (1 << (D - 1)) - p[j+4] p5 := Q + (1 << (D - 1)) - p[j+5] p6 := Q + (1 << (D - 1)) - p[j+6] p7 := Q + (1 << (D - 1)) - p[j+7] buf[i] = byte(p0 >> 0) buf[i+1] = byte(p0>>8) | byte(p1<<5) buf[i+2] = byte(p1 >> 3) buf[i+3] = byte(p1>>11) | byte(p2<<2) buf[i+4] = byte(p2>>6) | byte(p3<<7) buf[i+5] = byte(p3 >> 1) buf[i+6] = byte(p3>>9) | byte(p4<<4) buf[i+7] = byte(p4 >> 4) buf[i+8] = byte(p4>>12) | byte(p5<<1) buf[i+9] = byte(p5>>7) | byte(p6<<6) buf[i+10] = byte(p6 >> 2) buf[i+11] = byte(p6>>10) | byte(p7<<3) buf[i+12] = byte(p7 >> 5) j += 8 } } // Sets p to the polynomial packed into buf by PackT0. // // The coefficients of p will not be normalized, but will lie // in (-2ᵈ⁻¹, 2ᵈ⁻¹]. func (p *Poly) UnpackT0(buf []byte) { j := 0 for i := 0; i < PolyT0Size; i += 13 { p[j] = Q + (1 << (D - 1)) - ((uint32(buf[i]) | (uint32(buf[i+1]) << 8)) & 0x1fff) p[j+1] = Q + (1 << (D - 1)) - (((uint32(buf[i+1]) >> 5) | (uint32(buf[i+2]) << 3) | (uint32(buf[i+3]) << 11)) & 0x1fff) p[j+2] = Q + (1 << (D - 1)) - (((uint32(buf[i+3]) >> 2) | (uint32(buf[i+4]) << 6)) & 0x1fff) p[j+3] = Q + (1 << (D - 1)) - (((uint32(buf[i+4]) >> 7) | (uint32(buf[i+5]) << 1) | (uint32(buf[i+6]) << 9)) & 0x1fff) p[j+4] = Q + (1 << (D - 1)) - (((uint32(buf[i+6]) >> 4) | (uint32(buf[i+7]) << 4) | (uint32(buf[i+8]) << 12)) & 0x1fff) p[j+5] = Q + (1 << (D - 1)) - (((uint32(buf[i+8]) >> 1) | (uint32(buf[i+9]) << 7)) & 0x1fff) p[j+6] = Q + (1 << (D - 1)) - (((uint32(buf[i+9]) >> 6) | (uint32(buf[i+10]) << 2) | (uint32(buf[i+11]) << 10)) & 0x1fff) p[j+7] = Q + (1 << (D - 1)) - ((uint32(buf[i+11]) >> 3) | (uint32(buf[i+12]) << 5)) j += 8 } } // Writes p whose coefficients are less than 1024 into buf, which must be // of size at least PolyT1Size . // // Assumes coefficients of p are normalized. func (p *Poly) PackT1(buf []byte) { j := 0 for i := 0; i < PolyT1Size; i += 5 { buf[i] = byte(p[j]) buf[i+1] = byte(p[j]>>8) | byte(p[j+1]<<2) buf[i+2] = byte(p[j+1]>>6) | byte(p[j+2]<<4) buf[i+3] = byte(p[j+2]>>4) | byte(p[j+3]<<6) buf[i+4] = byte(p[j+3] >> 2) j += 4 } } // Writes p whose coefficients are in [0, 16) to buf, which must be of // length N/2. func (p *Poly) packLe16Generic(buf []byte) { j := 0 for i := 0; i < PolyLe16Size; i++ { buf[i] = byte(p[j]) | byte(p[j+1]<<4) j += 2 } } // Writes p with 60 non-zero coefficients {-1,1} to buf, which must have // length 40. func (p *Poly) PackB60(buf []byte) { // We start with a mask of the non-zero positions of p (which is 32 bytes) // and then append 60 packed bits, where a one indicates a negative // coefficients. var signs uint64 mask := uint64(1) for i := 0; i < 32; i++ { buf[i] = 0 for j := 0; j < 8; j++ { if p[8*i+j] != 0 { buf[i] |= 1 << uint(j) if p[8*i+j] == Q-1 { signs |= mask } mask <<= 1 } } } for i := uint64(0); i < 8; i++ { buf[i+32] = uint8(signs >> (8 * i)) } } // UnpackB60 sets p to the polynomial packed into buf with Poly.PackB60(). // // Returns whether unpacking was successful. func (p *Poly) UnpackB60(buf []byte) bool { *p = Poly{} // zero p signs := (uint64(buf[32]) | (uint64(buf[33]) << 8) | (uint64(buf[34]) << 16) | (uint64(buf[35]) << 24) | (uint64(buf[36]) << 32) | (uint64(buf[37]) << 40) | (uint64(buf[38]) << 48) | (uint64(buf[39]) << 56)) if signs>>60 != 0 { return false // ensure unused bits are zero for strong unforgeability } for i := 0; i < 32; i++ { for j := 0; j < 8; j++ { if (buf[i]>>uint(j))&1 == 1 { p[8*i+j] = 1 // Note 1 ^ (1 | (Q-1)) = Q-1 and (-1)&x = x p[8*i+j] ^= uint32(-(signs & 1)) & (1 | (Q - 1)) signs >>= 1 } } } return true } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/pack_test.go000066400000000000000000000011151454601126700300250ustar00rootroot00000000000000package common import "testing" func TestPackLe16AgainstGeneric(t *testing.T) { var p Poly var buf1, buf2 [PolyLe16Size]byte for j := 0; j < 1000; j++ { pp := randSliceUint32WithMax(N, 16) copy(p[:], pp) p.PackLe16(buf1[:]) p.packLe16Generic(buf2[:]) if buf1 != buf2 { t.Fatal() } } } func BenchmarkPackLe16(b *testing.B) { var p Poly var buf [PolyLe16Size]byte for i := 0; i < b.N; i++ { p.PackLe16(buf[:]) } } func BenchmarkPackLe16Generic(b *testing.B) { var p Poly var buf [PolyLe16Size]byte for i := 0; i < b.N; i++ { p.packLe16Generic(buf[:]) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/params.go000066400000000000000000000006271454601126700273420ustar00rootroot00000000000000package common import ( "github.com/cloudflare/circl/sign/dilithium/internal/common/params" ) const ( SeedSize = params.SeedSize N = params.N Q = params.Q QBits = params.QBits Qinv = params.Qinv ROver256 = params.ROver256 D = params.D PolyT1Size = params.PolyT1Size PolyT0Size = params.PolyT0Size PolyLe16Size = params.PolyLe16Size ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/params/000077500000000000000000000000001454601126700270065ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/params/params.go000066400000000000000000000014471454601126700306260ustar00rootroot00000000000000package params // We put these parameters in a separate package so that the Go code, // such as ntt_amd64_src.go, that generates assembler can import it. const ( SeedSize = 32 N = 256 Q = 8380417 // 2²³ - 2¹³ + 1 QBits = 23 Qinv = 4236238847 // = -(q^-1) mod 2³² ROver256 = 41978 // = (256)⁻¹ R² mod q, where R=2³² D = 13 // Size of T1 packed. (Note that the formula is not valid in general, // but it is for the parameters used in the modes of Dilithium.) PolyT1Size = (N * (QBits - D)) / 8 // Size of T0 packed. (Note that the formula is not valid in general, // but it is for the parameters used in the modes of Dilithium.) PolyT0Size = (N * D) / 8 // Size of a packed polynomial whose coefficients are in [0,16). PolyLe16Size = N / 2 ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/poly.go000066400000000000000000000055511454601126700270430ustar00rootroot00000000000000package common // An element of our base ring R which are polynomials over Z_q modulo // the equation Xᴺ = -1, where q=2²³ - 2¹³ + 1 and N=256. // // Coefficients aren't always reduced. See Normalize(). type Poly [N]uint32 // Reduces each of the coefficients to <2q. func (p *Poly) reduceLe2QGeneric() { for i := uint(0); i < N; i++ { p[i] = ReduceLe2Q(p[i]) } } // Reduce each of the coefficients to > 31) // Sets x to {0, 1, ..., (Q-1)/2, (Q-1)/2, ..., 1} x = int32((Q-1)/2) - x if uint32(x) >= bound { return true } } return false } // Splits p into p1 and p0 such that [i]p1 * 2ᴰ + [i]p0 = [i]p // with -2ᴰ⁻¹ < [i]p0 ≤ 2ᴰ⁻¹. Returns p0 + Q and p1. // // Requires the coefficients of p to be normalized. func (p *Poly) Power2Round(p0PlusQ, p1 *Poly) { for i := 0; i < N; i++ { p0PlusQ[i], p1[i] = power2round(p[i]) } } // Sets p to the polynomial whose coefficients are the pointwise multiplication // of those of a and b. The coefficients of p are bounded by 2q. // // Assumes a and b are in Montgomery form and that the pointwise product // of each coefficient is below 2³² q. func (p *Poly) mulHatGeneric(a, b *Poly) { for i := 0; i < N; i++ { p[i] = montReduceLe2Q(uint64(a[i]) * uint64(b[i])) } } // Sets p to 2ᵈ q without reducing. // // So it requires the coefficients of p to be less than 2³²⁻ᴰ. func (p *Poly) mulBy2toDGeneric(q *Poly) { for i := 0; i < N; i++ { p[i] = q[i] << D } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/poly_test.go000066400000000000000000000072541454601126700301040ustar00rootroot00000000000000package common import "testing" func TestExceeds(t *testing.T) { for i := 0; i < N; i++ { var p Poly for v := 0; v < 10; v++ { p[i] = uint32(v) if p.Exceeds(uint32(10)) { t.Fatal() } p[i] = Q - uint32(v) if p.Exceeds(uint32(10)) { t.Fatal() } } for v := 10; v < 20; v++ { p[i] = uint32(v) if !p.Exceeds(uint32(10)) { t.Fatal() } p[i] = Q - uint32(v) if !p.Exceeds(uint32(10)) { t.Fatal() } } } } func TestSubAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a, b Poly a.RandLe2Q() b.RandLe2Q() p1.Sub(&a, &b) p2.subGeneric(&a, &b) if p1 != p2 { t.Fatalf("Sub(%v, %v) =\n%v\n!= %v", a, b, p1, p2) } } } func TestAddAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a, b Poly a.RandLe2Q() b.RandLe2Q() p1.Add(&a, &b) p2.addGeneric(&a, &b) if p1 != p2 { t.Fatalf("Add(%v, %v) =\n%v\n!= %v", a, b, p1, p2) } } } func TestMulHatAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, a, b Poly a.RandLe2Q() b.RandLe2Q() p1.MulHat(&a, &b) p2.mulHatGeneric(&a, &b) if p1 != p2 { t.Fatalf("MulHat(%v, %v) =\n%v\n!= %v", a, b, p1, p2) } } } func TestReduceLe2QAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var a Poly r := randSliceUint32(N) copy(a[:], r) p1 := a p2 := a p1.reduceLe2QGeneric() p2.ReduceLe2Q() if p1 != p2 { t.Fatalf("%v !=\n%v", p1, p2) } } } func TestNormalizeAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var a Poly r := randSliceUint32(N) copy(a[:], r) p1 := a p2 := a p1.normalizeGeneric() p2.Normalize() if p1 != p2 { t.Fatalf("%v !=\n%v", p1, p2) } } } func TestMulBy2ToDAgainstGeneric(t *testing.T) { for k := 0; k < 1000; k++ { var p1, p2, q Poly q.RandLe2Q() p1.mulBy2toDGeneric(&q) p2.MulBy2toD(&q) if p1 != p2 { t.Fatalf("MulBy2ToD(%v) =\n%v\n!= %v", q, p1, p2) } } } func BenchmarkNormalizeGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.normalizeGeneric() } } func BenchmarkMulHatGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.mulHatGeneric(&p, &p) } } func BenchmarkAddGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.addGeneric(&p, &p) } } func BenchmarkSubGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.subGeneric(&p, &p) } } func BenchmarkReduceLe2QGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.reduceLe2QGeneric() } } func BenchmarkNormalizeAssumingLe2QGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.normalizeAssumingLe2QGeneric() } } func BenchmarkExceedsGeneric(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.exceedsGeneric(uint32(10)) } } func BenchmarkMulBy2toDGeneric(b *testing.B) { var p, q Poly for i := 0; i < b.N; i++ { p.mulBy2toDGeneric(&q) } } func BenchmarkMulHat(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.MulHat(&p, &p) } } func BenchmarkAdd(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.Add(&p, &p) } } func BenchmarkSub(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.Sub(&p, &p) } } func BenchmarkReduceLe2Q(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.ReduceLe2Q() } } func BenchmarkNormalize(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.Normalize() } } func BenchmarkNormalizeAssumingLe2Q(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.NormalizeAssumingLe2Q() } } func BenchmarkExceeds(b *testing.B) { var p Poly for i := 0; i < b.N; i++ { p.Exceeds(uint32(10)) } } func BenchmarkMulBy2toD(b *testing.B) { var p, q Poly for i := 0; i < b.N; i++ { p.MulBy2toD(&q) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/internal/common/stubs_amd64.go000066400000000000000000000013711454601126700302070ustar00rootroot00000000000000// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. //go:build amd64 package common //go:noescape func nttAVX2(p *[256]uint32) //go:noescape func invNttAVX2(p *[256]uint32) //go:noescape func mulHatAVX2(p *[256]uint32, a *[256]uint32, b *[256]uint32) //go:noescape func addAVX2(p *[256]uint32, a *[256]uint32, b *[256]uint32) //go:noescape func subAVX2(p *[256]uint32, a *[256]uint32, b *[256]uint32) //go:noescape func packLe16AVX2(p *[256]uint32, buf *byte) //go:noescape func reduceLe2QAVX2(p *[256]uint32) //go:noescape func le2qModQAVX2(p *[256]uint32) //go:noescape func exceedsAVX2(p *[256]uint32, bound uint32) uint8 //go:noescape func mulBy2toDAVX2(p *[256]uint32, q *[256]uint32) golang-github-cloudflare-circl-1.3.7/sign/dilithium/kat_test.go000066400000000000000000000040321454601126700245630ustar00rootroot00000000000000package dilithium // Code to generate the NIST "PQCsignKAT" test vectors. // See PQCsignKAT_sign.c and randombytes.c in the reference implementation. import ( "crypto/sha256" "fmt" "testing" "github.com/cloudflare/circl/internal/nist" ) func TestPQCgenKATSign(t *testing.T) { // Generated from reference implementation commit 61b51a71701b8ae9f546a1e5, // which can be found at https://github.com/pq-crystals/dilithium for _, tc := range []struct { name string want string }{ {"Dilithium2", "38ed991c5ca11e39ab23945ca37af89e059d16c5474bf8ba96b15cb4e948af2a"}, {"Dilithium3", "8196b32212753f525346201ffec1c7a0a852596fa0b57bd4e2746231dab44d55"}, {"Dilithium5", "7ded97a6e6c809b43b54c248171d7504fa6a0cab651bf288bb00034782667481"}, {"Dilithium2-AES", "b6673f8da5bba7dfae63adbbdf559f4fcfb715d1f91da98d4b52e26203d69196"}, {"Dilithium3-AES", "482f4d672a9f1dc38cc8bcf8b1731b03fe99fcb6f2b73aa4a376b99faf89ccbe"}, {"Dilithium5-AES", "54dfa85013d1b3da4f1d7c6dd270bc91a083cfece3d320c97906da125fd2a48f"}, } { t.Run(tc.name, func(t *testing.T) { mode := ModeByName(tc.name) if mode == nil { t.Fatal() } var seed [48]byte var eseed [32]byte for i := 0; i < 48; i++ { seed[i] = byte(i) } f := sha256.New() g := nist.NewDRBG(&seed) fmt.Fprintf(f, "# %s\n\n", tc.name) for i := 0; i < 100; i++ { mlen := 33 * (i + 1) g.Fill(seed[:]) msg := make([]byte, mlen) g.Fill(msg[:]) fmt.Fprintf(f, "count = %d\n", i) fmt.Fprintf(f, "seed = %X\n", seed) fmt.Fprintf(f, "mlen = %d\n", mlen) fmt.Fprintf(f, "msg = %X\n", msg) g2 := nist.NewDRBG(&seed) g2.Fill(eseed[:]) pk, sk := mode.NewKeyFromSeed(eseed[:]) fmt.Fprintf(f, "pk = %X\n", pk.Bytes()) fmt.Fprintf(f, "sk = %X\n", sk.Bytes()) fmt.Fprintf(f, "smlen = %d\n", mlen+mode.SignatureSize()) sig := mode.Sign(sk, msg[:]) fmt.Fprintf(f, "sm = %X%X\n\n", sig, msg) if !mode.Verify(pk, msg[:], sig) { t.Fatal() } } if fmt.Sprintf("%x", f.Sum(nil)) != tc.want { t.Fatal() } }) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2.go000066400000000000000000000040321454601126700237530ustar00rootroot00000000000000// Code generated from mode.templ.go. DO NOT EDIT. package dilithium import ( "fmt" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode2" ) // implMode2 implements the mode.Mode interface for Dilithium2. type implMode2 struct{} // Mode2 is Dilithium in mode "Dilithium2". var Mode2 Mode = &implMode2{} func (m *implMode2) GenerateKey(rand io.Reader) ( PublicKey, PrivateKey, error) { return mode2.GenerateKey(rand) } func (m *implMode2) NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) { if len(seed) != common.SeedSize { panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) } seedBuf := [common.SeedSize]byte{} copy(seedBuf[:], seed) return mode2.NewKeyFromSeed(&seedBuf) } func (m *implMode2) Sign(sk PrivateKey, msg []byte) []byte { isk := sk.(*mode2.PrivateKey) ret := [mode2.SignatureSize]byte{} mode2.SignTo(isk, msg, ret[:]) return ret[:] } func (m *implMode2) Verify(pk PublicKey, msg []byte, signature []byte) bool { ipk := pk.(*mode2.PublicKey) return mode2.Verify(ipk, msg, signature) } func (m *implMode2) PublicKeyFromBytes(data []byte) PublicKey { var ret mode2.PublicKey if len(data) != mode2.PublicKeySize { panic("packed public key must be of mode2.PublicKeySize bytes") } var buf [mode2.PublicKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode2) PrivateKeyFromBytes(data []byte) PrivateKey { var ret mode2.PrivateKey if len(data) != mode2.PrivateKeySize { panic("packed public key must be of mode2.PrivateKeySize bytes") } var buf [mode2.PrivateKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode2) SeedSize() int { return common.SeedSize } func (m *implMode2) PublicKeySize() int { return mode2.PublicKeySize } func (m *implMode2) PrivateKeySize() int { return mode2.PrivateKeySize } func (m *implMode2) SignatureSize() int { return mode2.SignatureSize } func (m *implMode2) Name() string { return "Dilithium2" } func init() { modes["Dilithium2"] = Mode2 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/000077500000000000000000000000001454601126700234255ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/dilithium.go000066400000000000000000000116411454601126700257470ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // mode2 implements the CRYSTALS-Dilithium signature scheme Dilithium2 // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf package mode2 import ( "crypto" "errors" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode2/internal" ) const ( // Size of seed for NewKeyFromSeed SeedSize = common.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a signature SignatureSize = internal.SignatureSize ) // PublicKey is the type of Dilithium2 public key type PublicKey internal.PublicKey // PrivateKey is the type of Dilithium2 private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { pk, sk, err := internal.GenerateKey(rand) return (*PublicKey)(pk), (*PrivateKey)(sk), err } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { internal.SignTo( (*internal.PrivateKey)(sk), msg, signature, ) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { return internal.Verify( (*internal.PublicKey)(pk), msg, signature, ) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Unpack(buf) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Unpack(buf) } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Pack(buf) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Pack(buf) } // Packs the public key. func (pk *PublicKey) Bytes() []byte { var buf [PublicKeySize]byte pk.Pack(&buf) return buf[:] } // Packs the private key. func (sk *PrivateKey) Bytes() []byte { var buf [PrivateKeySize]byte sk.Pack(&buf) return buf[:] } // Packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // Packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // Unpacks the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of mode2.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // Unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of mode2.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("dilithium: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return (*PublicKey)((*internal.PrivateKey)(sk).Public()) } // Equal returns whether the two private keys equal. func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) } // Equal returns whether the two public keys equal. func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/000077500000000000000000000000001454601126700252415ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/dilithium.go000066400000000000000000000260461454601126700275700ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium.go by gen.go package internal import ( cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) const ( // Size of a packed polynomial of norm ≤η. // (Note that the formula is not valid in general.) PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 // β = τη, the maximum size of c s₂. Beta = Tau * Eta // γ₁ range of y Gamma1 = 1 << Gamma1Bits // Size of packed polynomial of norm <γ₁ such as z PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8 // α = 2γ₂ parameter for decompose Alpha = 2 * Gamma2 // Size of a packed private key PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K // Size of a packed public key PublicKeySize = 32 + common.PolyT1Size*K // Size of a packed signature SignatureSize = L*PolyLeGamma1Size + Omega + K + 32 // Size of packed w₁ PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8 ) // PublicKey is the type of Dilithium public keys. type PublicKey struct { rho [32]byte t1 VecK // Cached values t1p [common.PolyT1Size * K]byte A *Mat tr *[32]byte } // PrivateKey is the type of Dilithium private keys. type PrivateKey struct { rho [32]byte key [32]byte s1 VecL s2 VecK t0 VecK tr [32]byte // Cached values A Mat // ExpandA(ρ) s1h VecL // NTT(s₁) s2h VecK // NTT(s₂) t0h VecK // NTT(t₀) } type unpackedSignature struct { z VecL hint VecK c [32]byte } // Packs the signature into buf. func (sig *unpackedSignature) Pack(buf []byte) { copy(buf[:], sig.c[:]) sig.z.PackLeGamma1(buf[32:]) sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:]) } // Sets sig to the signature encoded in the buffer. // // Returns whether buf contains a properly packed signature. func (sig *unpackedSignature) Unpack(buf []byte) bool { if len(buf) < SignatureSize { return false } copy(sig.c[:], buf[:]) sig.z.UnpackLeGamma1(buf[32:]) if sig.z.Exceeds(Gamma1 - Beta) { return false } if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) { return false } return true } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { copy(buf[:32], pk.rho[:]) copy(buf[32:], pk.t1p[:]) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { copy(pk.rho[:], buf[:32]) copy(pk.t1p[:], buf[32:]) pk.t1.UnpackT1(pk.t1p[:]) pk.A = new(Mat) pk.A.Derive(&pk.rho) // tr = CRH(ρ ‖ t1) = CRH(pk) pk.tr = new([32]byte) h := sha3.NewShake256() _, _ = h.Write(buf[:]) _, _ = h.Read(pk.tr[:]) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { copy(buf[:32], sk.rho[:]) copy(buf[32:64], sk.key[:]) copy(buf[64:96], sk.tr[:]) offset := 96 sk.s1.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.PackT0(buf[offset:]) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { copy(sk.rho[:], buf[:32]) copy(sk.key[:], buf[32:64]) copy(sk.tr[:], buf[64:96]) offset := 96 sk.s1.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.UnpackT0(buf[offset:]) // Cached values sk.A.Derive(&sk.rho) sk.t0h = sk.t0 sk.t0h.NTT() sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [32]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { var eSeed [128]byte // expanded seed var pk PublicKey var sk PrivateKey var sSeed [64]byte h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(eSeed[:]) copy(pk.rho[:], eSeed[:32]) copy(sSeed[:], eSeed[32:96]) copy(sk.key[:], eSeed[96:]) copy(sk.rho[:], pk.rho[:]) sk.A.Derive(&pk.rho) for i := uint16(0); i < L; i++ { PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) } for i := uint16(0); i < K; i++ { PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) } sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() sk.computeT0andT1(&sk.t0, &pk.t1) sk.t0h = sk.t0 sk.t0h.NTT() // Complete public key far enough to be packed pk.t1.PackT1(pk.t1p[:]) pk.A = &sk.A // Finish private key var packedPk [PublicKeySize]byte pk.Pack(&packedPk) // tr = CRH(ρ ‖ t1) = CRH(pk) h.Reset() _, _ = h.Write(packedPk[:]) _, _ = h.Read(sk.tr[:]) // Finish cache of public key pk.tr = &sk.tr return &pk, &sk } // Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { var t VecK // Set t to A s₁ + s₂ for i := 0; i < K; i++ { PolyDotHat(&t[i], &sk.A[i], &sk.s1h) t[i].ReduceLe2Q() t[i].InvNTT() } t.Add(&t, &sk.s2) t.Normalize() // Compute t₀, t₁ = Power2Round(t) t.Power2Round(t0, t1) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { var sig unpackedSignature var mu [64]byte var zh VecL var Az, Az2dct1, w1 VecK var ch common.Poly var cp [32]byte var w1Packed [PolyW1Size * K]byte // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β // and ensured that there at most ω ones in pk.hint. if !sig.Unpack(signature) { return false } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(pk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // Compute Az zh = sig.z zh.NTT() for i := 0; i < K; i++ { PolyDotHat(&Az[i], &pk.A[i], &zh) } // Next, we compute Az - 2ᵈ·c·t₁. // Note that the coefficients of t₁ are bounded by 256 = 2⁹, // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, // which is small enough for NTT(). Az2dct1.MulBy2toD(&pk.t1) Az2dct1.NTT() PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() for i := 0; i < K; i++ { Az2dct1[i].MulHat(&Az2dct1[i], &ch) } Az2dct1.Sub(&Az, &Az2dct1) Az2dct1.ReduceLe2Q() Az2dct1.InvNTT() Az2dct1.NormalizeAssumingLe2Q() // UseHint(pk.hint, Az - 2ᵈ·c·t₁) // = UseHint(pk.hint, w - c·s₂ + c·t₀) // = UseHint(pk.hint, r + c·t₀) // = r₁ = w₁. w1.UseHint(&Az2dct1, &sig.hint) w1.PackW1(w1Packed[:]) // c' = H(μ, w₁) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(cp[:]) return sig.c == cp } // SignTo signs the given message and writes the signature into signature. // //nolint:funlen func SignTo(sk *PrivateKey, msg []byte, signature []byte) { var mu, rhop [64]byte var w1Packed [PolyW1Size * K]byte var y, yh VecL var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK var ch common.Poly var yNonce uint16 var sig unpackedSignature if len(signature) < SignatureSize { panic("Signature does not fit in that byteslice") } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(sk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // ρ' = CRH(key ‖ μ) h.Reset() _, _ = h.Write(sk.key[:]) _, _ = h.Write(mu[:]) _, _ = h.Read(rhop[:]) // Main rejection loop attempt := 0 for { attempt++ if attempt >= 576 { // Depending on the mode, one try has a chance between 1/7 and 1/4 // of succeeding. Thus it is safe to say that 576 iterations // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. panic("This should only happen 1 in 2^{128}: something is wrong.") } // y = ExpandMask(ρ', key) VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) yNonce += uint16(L) // Set w to A y yh = y yh.NTT() for i := 0; i < K; i++ { PolyDotHat(&w[i], &sk.A[i], &yh) w[i].ReduceLe2Q() w[i].InvNTT() } // Decompose w into w₀ and w₁ w.NormalizeAssumingLe2Q() w.Decompose(&w0, &w1) // c~ = H(μ ‖ w₁) w1.PackW1(w1Packed[:]) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(sig.c[:]) PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. // // By Lemma 3 of the specification this is equivalent to checking that // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition // w - c·s₂ = r₁ α + r₀ as computed by decompose(). // See also §4.1 of the specification. for i := 0; i < K; i++ { w0mcs2[i].MulHat(&ch, &sk.s2h[i]) w0mcs2[i].InvNTT() } w0mcs2.Sub(&w0, &w0mcs2) w0mcs2.Normalize() if w0mcs2.Exceeds(Gamma2 - Beta) { continue } // z = y + c·s₁ for i := 0; i < L; i++ { sig.z[i].MulHat(&ch, &sk.s1h[i]) sig.z[i].InvNTT() } sig.z.Add(&sig.z, &y) sig.z.Normalize() // Ensure ‖z‖_∞ < γ₁ - β if sig.z.Exceeds(Gamma1 - Beta) { continue } // Compute c·t₀ for i := 0; i < K; i++ { ct0[i].MulHat(&ch, &sk.t0h[i]) ct0[i].InvNTT() } ct0.NormalizeAssumingLe2Q() // Ensure ‖c·t₀‖_∞ < γ₂. if ct0.Exceeds(Gamma2) { continue } // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. // Note that we're not using makeHint() in the obvious way as we // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note // that our makeHint() is actually the same as a makeHint for a // different decomposition: // // Earlier we ensured indirectly with a check that r₁ = w₁ where // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. w0mcs2pct0.Add(&w0mcs2, &ct0) w0mcs2pct0.NormalizeAssumingLe2Q() hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) if hintPop > Omega { continue } break } sig.Pack(signature[:]) } // Computes the public key corresponding to this private key. func (sk *PrivateKey) Public() *PublicKey { var t0 VecK pk := &PublicKey{ rho: sk.rho, A: &sk.A, tr: &sk.tr, } sk.computeT0andT1(&t0, &pk.t1) pk.t1.PackT1(pk.t1p[:]) return pk } // Equal returns whether the two public keys are equal func (pk *PublicKey) Equal(other *PublicKey) bool { return pk.rho == other.rho && pk.t1 == other.t1 } // Equal returns whether the two private keys are equal func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) acc := uint32(0) for i := 0; i < L; i++ { for j := 0; j < common.N; j++ { acc |= sk.s1[i][j] ^ other.s1[i][j] } } for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { acc |= sk.s2[i][j] ^ other.s2[i][j] acc |= sk.t0[i][j] ^ other.t0[i][j] } } return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/dilithium_test.go000066400000000000000000000062731454601126700306270ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Checks whether p is normalized. Only used in tests. func PolyNormalized(p *common.Poly) bool { p2 := *p p2.Normalize() return p2 == *p } func BenchmarkSkUnpack(b *testing.B) { var buf [PrivateKeySize]byte var sk PrivateKey for i := 0; i < b.N; i++ { sk.Unpack(&buf) } } func BenchmarkPkUnpack(b *testing.B) { var buf [PublicKeySize]byte var pk PublicKey for i := 0; i < b.N; i++ { pk.Unpack(&buf) } } func BenchmarkVerify(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of verification (as in the reference // implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte pk, sk := NewKeyFromSeed(&seed) SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of signing (as in the reference implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte _, sk := NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [common.SeedSize]byte var sig [SignatureSize]byte var msg [8]byte var pkb [PublicKeySize]byte var skb [PrivateKeySize]byte var pk2 PublicKey var sk2 PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) if !sk.Equal(sk) { t.Fatal() } for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) SignTo(sk, msg[:], sig[:]) if !Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb) pk2.Unpack(&pkb) if !pk.Equal(&pk2) { t.Fatal() } sk.Pack(&skb) sk2.Unpack(&skb) if !sk.Equal(&sk2) { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [common.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) pk2 := sk.Public() if !pk.Equal(pk2) { t.Fatal() } } } func TestGamma1Size(t *testing.T) { var expected int switch Gamma1Bits { case 17: expected = 576 case 19: expected = 640 } if expected != PolyLeGamma1Size { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/mat.go000066400000000000000000000024411454601126700263520ustar00rootroot00000000000000// Code generated from mode3/internal/mat.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A k by l matrix of polynomials. type Mat [K]VecL // Expands the given seed to a complete matrix. // // This function is called ExpandA in the specification. func (m *Mat) Derive(seed *[32]byte) { if !DeriveX4Available { for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) } } return } idx := 0 var nonces [4]uint16 var ps [4]*common.Poly for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { nonces[idx] = (i << 8) + j ps[idx] = &m[i][j] idx++ if idx == 4 { idx = 0 PolyDeriveUniformX4(ps, seed, nonces) } } } if idx != 0 { for i := idx; i < 4; i++ { ps[i] = nil } PolyDeriveUniformX4(ps, seed, nonces) } } // Set p to the inner product of a and b using pointwise multiplication. // // Assumes a and b are in Montgomery form and their coefficients are // pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting // coefficients are bounded by 2Lq. func PolyDotHat(p *common.Poly, a, b *VecL) { var t common.Poly *p = common.Poly{} // zero p for i := 0; i < L; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/pack.go000066400000000000000000000164511454601126700265150ustar00rootroot00000000000000// Code generated from mode3/internal/pack.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Writes p with norm less than or equal η into buf, which must be of // size PolyLeqEtaSize. // // Assumes coefficients of p are not normalized, but in [q-η,q+η]. func PolyPackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { buf[i] = (byte(common.Q+Eta-p[j]) | byte(common.Q+Eta-p[j+1])<<4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { buf[i] = (byte(common.Q+Eta-p[j]) | (byte(common.Q+Eta-p[j+1]) << 3) | (byte(common.Q+Eta-p[j+2]) << 6)) buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | (byte(common.Q+Eta-p[j+3]) << 1) | (byte(common.Q+Eta-p[j+4]) << 4) | (byte(common.Q+Eta-p[j+5]) << 7)) buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | (byte(common.Q+Eta-p[j+6]) << 2) | (byte(common.Q+Eta-p[j+7]) << 5)) j += 8 } } else { panic("eta not supported") } } // Sets p to the polynomial of norm less than or equal η encoded in the // given buffer of size PolyLeqEtaSize. // // Output coefficients of p are not normalized, but in [q-η,q+η] provided // buf was created using PackLeqEta. // // Beware, for arbitrary buf the coefficients of p might end up in // the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. func PolyUnpackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { p[j] = common.Q + Eta - uint32(buf[i]&15) p[j+1] = common.Q + Eta - uint32(buf[i]>>4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { p[j] = common.Q + Eta - uint32(buf[i]&7) p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) j += 8 } } else { panic("eta not supported") } } // Writes v with coefficients in {0, 1} of which at most ω non-zero // to buf, which must have length ω+k. func (v *VecK) PackHint(buf []byte) { // The packed hint starts with the indices of the non-zero coefficients // For instance: // // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) // // Yields // // 56, 100, 255, 2, 23, 1 // // Then we pad with zeroes until we have a list of ω items: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 // // Then we finish with a list of the switch-over-indices in this // list between polynomials, so: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 off := uint8(0) for i := 0; i < K; i++ { for j := uint16(0); j < common.N; j++ { if v[i][j] != 0 { buf[off] = uint8(j) off++ } } buf[Omega+i] = off } for ; off < Omega; off++ { buf[off] = 0 } } // Sets v to the vector encoded using VecK.PackHint() // // Returns whether unpacking was successful. func (v *VecK) UnpackHint(buf []byte) bool { // A priori, there would be several reasonable ways to encode the same // hint vector. We take care to only allow only one encoding, to ensure // "strong unforgeability". // // See PackHint() source for description of the encoding. *v = VecK{} // zero v prevSOP := uint8(0) // previous switch-over-point for i := 0; i < K; i++ { SOP := buf[Omega+i] if SOP < prevSOP || SOP > Omega { return false // ensures switch-over-points are increasing } for j := prevSOP; j < SOP; j++ { if j > prevSOP && buf[j] <= buf[j-1] { return false // ensures indices are increasing (within a poly) } v[i][buf[j]] = 1 } prevSOP = SOP } for j := prevSOP; j < Omega; j++ { if buf[j] != 0 { return false // ensures padding indices are zero } } return true } // Sets p to the polynomial packed into buf by PolyPackLeGamma1. // // p will be normalized. func PolyUnpackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0x3) << 16) p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) | (uint32(buf[i+4]&0xf) << 14) p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) | (uint32(buf[i+6]&0x3f) << 12) p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) | (uint32(buf[i+8]) << 10) // coefficients in [0,…,2γ₁) p0 = Gamma1 - p0 // (-γ₁,…,γ₁] p1 = Gamma1 - p1 p2 = Gamma1 - p2 p3 = Gamma1 - p3 p0 += uint32(int32(p0)>>31) & common.Q // normalize p1 += uint32(int32(p1)>>31) & common.Q p2 += uint32(int32(p2)>>31) & common.Q p3 += uint32(int32(p3)>>31) & common.Q p[j] = p0 p[j+1] = p1 p[j+2] = p2 p[j+3] = p3 j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0xf) << 16) p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) | (uint32(buf[i+4]) << 12) p0 = Gamma1 - p0 p1 = Gamma1 - p1 p0 += uint32(int32(p0)>>31) & common.Q p1 += uint32(int32(p1)>>31) & common.Q p[j] = p0 p[j+1] = p1 j += 2 } } else { panic("γ₁ not supported") } } // Writes p whose coefficients are in (-γ₁,γ₁] into buf // which has to be of length PolyLeGamma1Size. // // Assumes p is normalized. func PolyPackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 // coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q) for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := Gamma1 - p[j] // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q) p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁) p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q p2 := Gamma1 - p[j+2] p2 += uint32(int32(p2)>>31) & common.Q p3 := Gamma1 - p[j+3] p3 += uint32(int32(p3)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<2) buf[i+3] = byte(p1 >> 6) buf[i+4] = byte(p1>>14) | byte(p2<<4) buf[i+5] = byte(p2 >> 4) buf[i+6] = byte(p2>>12) | byte(p3<<6) buf[i+7] = byte(p3 >> 2) buf[i+8] = byte(p3 >> 10) j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { // Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q) p0 := Gamma1 - p[j] p0 += uint32(int32(p0)>>31) & common.Q p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<4) buf[i+3] = byte(p1 >> 4) buf[i+4] = byte(p1 >> 12) j += 2 } } else { panic("γ₁ not supported") } } // Pack w₁ into buf, which must be of length PolyW1Size. // // Assumes w₁ is normalized. func PolyPackW1(p *common.Poly, buf []byte) { if Gamma1Bits == 19 { p.PackLe16(buf) } else if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyW1Size; i += 3 { buf[i] = byte(p[j]) | byte(p[j+1]<<6) buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4) buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2) j += 4 } } else { panic("unsupported γ₁") } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/pack_test.go000066400000000000000000000035651454601126700275560ustar00rootroot00000000000000// Code generated from mode3/internal/pack_test.go by gen.go package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestPolyPackLeqEta(t *testing.T) { var p1, p2 common.Poly var seed [64]byte var buf [PolyLeqEtaSize]byte for i := uint16(0); i < 100; i++ { // Note that DeriveUniformLeqEta sets p to the right kind of // unnormalized vector. PolyDeriveUniformLeqEta(&p1, &seed, i) for j := 0; j < PolyLeqEtaSize; j++ { if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { t.Fatalf("DerveUniformLeqEta out of bounds") } } PolyPackLeqEta(&p1, buf[:]) PolyUnpackLeqEta(&p2, buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT1(t *testing.T) { var p1, p2 common.Poly var seed [32]byte var buf [common.PolyT1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p1, &seed, i) p1.Normalize() for j := 0; j < common.N; j++ { p1[j] &= 0x1ff } p1.PackT1(buf[:]) p2.UnpackT1(buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT0(t *testing.T) { var p, p0, p1, p2 common.Poly var seed [32]byte var buf [common.PolyT0Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p, &seed, i) p.Normalize() p.Power2Round(&p0, &p1) p0.PackT0(buf[:]) p2.UnpackT0(buf[:]) if p0 != p2 { t.Fatalf("%v !=\n%v", p0, p2) } } } func BenchmarkUnpackLeGamma1(b *testing.B) { var p common.Poly var buf [PolyLeGamma1Size]byte for i := 0; i < b.N; i++ { PolyUnpackLeGamma1(&p, buf[:]) } } func TestPolyPackLeGamma1(t *testing.T) { var p0, p1 common.Poly var seed [64]byte var buf [PolyLeGamma1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniformLeGamma1(&p0, &seed, i) p0.Normalize() PolyPackLeGamma1(&p0, buf[:]) PolyUnpackLeGamma1(&p1, buf[:]) if p0 != p1 { t.Fatalf("%v != %v", p0, p1) } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/params.go000066400000000000000000000004461454601126700270570ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal const ( Name = "Dilithium2" UseAES = false K = 4 L = 4 Eta = 2 DoubleEtaBits = 3 Omega = 80 Tau = 39 Gamma1Bits = 17 Gamma2 = 95232 ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/params_test.go000066400000000000000000000102771454601126700301210ustar00rootroot00000000000000package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Tests specific to the current mode func TestVectorDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte p2 := common.Poly{ 8380415, 1, 8380415, 8380416, 1, 8380415, 8380416, 8380415, 8380415, 8380416, 8380416, 2, 2, 1, 8380415, 8380415, 8380416, 1, 8380416, 8380415, 2, 0, 0, 1, 1, 2, 2, 8380415, 0, 8380416, 8380416, 8380416, 8380415, 1, 2, 0, 1, 8380415, 0, 1, 8380415, 1, 0, 8380415, 2, 1, 2, 0, 1, 0, 8380416, 1, 8380416, 1, 0, 1, 1, 0, 1, 8380416, 0, 0, 8380416, 8380415, 8380416, 2, 0, 0, 8380415, 1, 1, 0, 0, 1, 8380415, 1, 8380416, 1, 8380415, 8380416, 8380416, 8380415, 0, 1, 8380415, 8380415, 1, 8380415, 0, 2, 2, 8380415, 1, 2, 8380415, 8380415, 0, 2, 2, 1, 8380415, 8380416, 0, 8380415, 2, 1, 8380415, 2, 2, 8380416, 8380416, 0, 8380416, 0, 2, 8380416, 1, 8380415, 8380416, 8380415, 1, 8380416, 8380416, 2, 2, 0, 0, 0, 8380415, 8380415, 2, 8380416, 2, 2, 8380415, 8380415, 2, 2, 2, 8380415, 1, 2, 1, 2, 8380415, 0, 2, 1, 8380415, 2, 8380415, 8380415, 8380416, 0, 8380416, 8380415, 8380415, 8380416, 8380416, 2, 8380416, 2, 0, 0, 1, 1, 1, 8380416, 0, 8380416, 8380416, 1, 1, 1, 0, 8380416, 2, 0, 8380415, 8380415, 0, 0, 2, 8380416, 1, 0, 0, 8380415, 8380415, 1, 0, 8380416, 1, 2, 8380415, 0, 8380416, 8380415, 1, 1, 0, 1, 8380416, 8380415, 1, 0, 0, 8380416, 1, 0, 2, 8380416, 2, 2, 0, 0, 1, 1, 2, 8380415, 2, 8380416, 8380416, 2, 1, 2, 8380416, 8380415, 8380415, 8380415, 0, 8380416, 1, 0, 2, 8380416, 2, 8380415, 8380415, 2, 2, 8380415, 8380416, 0, 8380415, 8380415, 0, 2, 8380415, 1, 8380415, 8380415, 1, 1, 8380416, 8380416, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeqEta(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestVectorDeriveUniformLeGamma1(t *testing.T) { var p, p2 common.Poly var seed [64]byte p2 = common.Poly{ 24652, 8360658, 8306, 8359852, 10689, 106730, 8321632, 8295173, 8263144, 8362203, 8270304, 86550, 8352484, 112252, 8326622, 8263346, 1209, 8357433, 8276262, 106912, 111719, 8266410, 8001, 8249719, 8298833, 108641, 127143, 74178, 8266405, 27781, 128456, 8359778, 8337159, 8336455, 8380097, 8339564, 8275392, 8298630, 8257822, 5932, 233, 8367273, 8335081, 8257869, 8350642, 8317253, 8256389, 8341263, 8360509, 8368380, 33767, 81445, 8265057, 8353702, 8270465, 61206, 8309816, 8281560, 8295763, 6244, 8353442, 8378970, 72579, 8351700, 8341053, 104835, 8344333, 8313546, 8373167, 61430, 8339993, 113603, 8254406, 8302777, 99473, 8342736, 54456, 65097, 8255826, 8329025, 23031, 8328165, 57608, 30426, 98210, 8264076, 8267955, 8351117, 22980, 8302860, 42373, 8349139, 6523, 8375937, 13127, 8270690, 40178, 105482, 74831, 8261990, 8306279, 5925, 8260573, 55220, 110952, 8273377, 8267217, 8275798, 124100, 119164, 8360113, 67060, 8351620, 8364798, 59495, 8362276, 8285770, 8313138, 37321, 8379867, 56428, 45742, 46037, 18715, 8330440, 99372, 8270907, 8341031, 49485, 63571, 111869, 8339624, 8311220, 8277176, 8357815, 60583, 8356010, 98423, 8360878, 84829, 8264301, 63134, 8321092, 8279722, 8352609, 8261763, 62169, 8317324, 122488, 8373120, 8337853, 8300028, 50829, 64411, 8330934, 8363377, 91994, 7023, 5142, 94655, 8335648, 28257, 129346, 68918, 14273, 27103, 8323037, 104538, 8307539, 55606, 94886, 8272263, 77952, 8314535, 9544, 8253819, 46445, 8267118, 85028, 8357851, 105779, 32474, 8256782, 89388, 8265113, 8291502, 48133, 57355, 60120, 8281124, 8346594, 8255737, 41780, 67374, 80423, 86222, 8334625, 97415, 8288685, 81515, 98856, 8300724, 36434, 89698, 4154, 21804, 70249, 102464, 101103, 8277794, 72647, 67640, 8323688, 61139, 91234, 74869, 8368270, 8367469, 8373445, 8249916, 86939, 8254257, 12306, 8270129, 48350, 8345018, 8364752, 8327455, 14568, 8252624, 62944, 32561, 8258436, 96011, 8331595, 33812, 8303001, 2233, 28847, 13235, 23003, 40644, 8279857, 8261616, 46409, 8369530, 112030, 97207, 8269039, 102924, 75641, 85486, 8358768, 65209, 92920, 34770, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeGamma1(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/rounding.go000066400000000000000000000101471454601126700274200ustar00rootroot00000000000000// Code generated from mode3/internal/rounding.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2, // except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken // and -α/2 ≤ a₀ < 0. Returns a₀ + q. Note 0 ≤ a₁ < (q-1)/α. // Recall α = 2γ₂. func decompose(a uint32) (a0plusQ, a1 uint32) { // a₁ = ⌈a / 128⌉ a1 = (a + 127) >> 7 if Alpha == 523776 { // 1025/2²² is close enough to 1/4092 so that a₁ // becomes a/α rounded down. a1 = ((a1*1025 + (1 << 21)) >> 22) // For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0. a1 &= 15 } else if Alpha == 190464 { // 1488/2²⁴ is close enough to 1/1488 so that a₁ // becomes a/α rounded down. a1 = ((a1 * 11275) + (1 << 23)) >> 24 // For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0. a1 ^= uint32(int32(43-a1)>>31) & a1 } else { panic("unsupported α") } a0plusQ = a - a1*Alpha // In the corner-case, when we set a₁=0, we will incorrectly // have a₀ > (q-1)/2 and we'll need to subtract q. As we // return a₀ + q, that comes down to adding q if a₀ < (q-1)/2. a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q return } // Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2. Decompose r as r = r1*α + r0 as // computed by decompose(). Write r' := r - f (mod Q). Now, decompose // r'=r-f again as r' = r'1*α + r'0 using decompose(). As f is small, we // have r'1 = r1 + h, where h ∈ {-1, 0, 1}. makeHint() computes |h| // given z0 := r0 - f (mod Q) and r1. With |h|, which is called the hint, // we can reconstruct r1 using only r' = r - f, which is done by useHint(). // To wit: // // useHint( r - f, makeHint( r0 - f, r1 ) ) = r1. // // Assumes 0 ≤ z0 < Q. func makeHint(z0, r1 uint32) uint32 { // If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r' // with the restrictions of decompose() and so r'1 = r1. So the hint // should be 0. This is covered by the first two inequalities. // There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also // a valid decomposition if r1 = 0. In the other cases a one is carried // and the hint should be 1. if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) { return 0 } return 1 } // Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see // documentation of makeHint() for context. // Assumes 0 ≤ r' < Q. func useHint(rp uint32, hint uint32) uint32 { rp0plusQ, rp1 := decompose(rp) if hint == 0 { return rp1 } if rp0plusQ > common.Q { return (rp1 + 1) & 15 } return (rp1 - 1) & 15 } // Sets p to the hint polynomial for p0 the modified low bits and p1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint polynomial. func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) { for i := 0; i < common.N; i++ { h := makeHint(p0[i], p1[i]) pop += h p[i] = h } return } // Computes corrections to the high bits of the polynomial q according // to the hints in h and sets p to the corrected high bits. Returns p. func PolyUseHint(p, q, hint *common.Poly) { var q0PlusQ common.Poly // See useHint() and makeHint() for an explanation. We reimplement it // here so that we can call Poly.Decompose(), which might be way faster // than calling decompose() in a loop (for instance when having AVX2.) PolyDecompose(q, &q0PlusQ, p) for i := 0; i < common.N; i++ { if hint[i] == 0 { continue } if Gamma2 == 261888 { if q0PlusQ[i] > common.Q { p[i] = (p[i] + 1) & 15 } else { p[i] = (p[i] - 1) & 15 } } else if Gamma2 == 95232 { if q0PlusQ[i] > common.Q { if p[i] == 43 { p[i] = 0 } else { p[i]++ } } else { if p[i] == 0 { p[i] = 43 } else { p[i]-- } } } else { panic("unsupported γ₂") } } } // Splits each of the coefficients of p using decompose. func PolyDecompose(p, p0PlusQ, p1 *common.Poly) { for i := 0; i < common.N; i++ { p0PlusQ[i], p1[i] = decompose(p[i]) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/rounding_test.go000066400000000000000000000031341454601126700304550ustar00rootroot00000000000000// Code generated from mode3/internal/rounding_test.go by gen.go package internal import ( "flag" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") func TestDecompose(t *testing.T) { for a := uint32(0); a < common.Q; a++ { a0PlusQ, a1 := decompose(a) a0 := int32(a0PlusQ) - int32(common.Q) recombined := a0 + int32(Alpha*a1) if a1 == 0 && recombined < 0 { recombined += common.Q if -(Alpha/2) > a0 || a0 >= 0 { t.Fatalf("decompose(%v): a0 out of bounds", a) } } else { if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) { t.Fatalf("decompose(%v): a0 out of bounds", a) } } if int32(a) != recombined { t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1) } } } func TestMakeHint(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for w := uint32(0); w < common.Q; w++ { w0, w1 := decompose(w) for fn := uint32(0); fn <= Gamma2; fn++ { fsign := false for { var f uint32 if fsign { if fn == 0 { break } f = common.Q - fn } else { f = fn } hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1) w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint) if w1p != w1 { t.Fatal() } if fsign { break } fsign = true } } } } func BenchmarkDecompose(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyDecompose(&p, &p0, &p1) } } func BenchmarkMakeHint(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyMakeHint(&p, &p0, &p1) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/sample.go000066400000000000000000000206561454601126700270620ustar00rootroot00000000000000// Code generated from mode3/internal/sample.go by gen.go package internal import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/simd/keccakf1600" ) // DeriveX4Available indicates whether the system supports the quick fourway // sampling variants like PolyDeriveUniformX4. var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES // For each i, sample ps[i] uniformly from the given seed and nonces[i]. // ps[i] may be nil and is ignored in that case. // // Can only be called when DeriveX4Available is true. func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // Absorb the nonces, the SHAKE128 domain separator (0b1111), the // start of the padding (0b...001) and the end of the padding 0b100... // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. for j := 0; j < 4; j++ { state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) state[20*4+j] = 0x80 << 56 } var idx [4]int // indices into ps for j := 0; j < 4; j++ { if ps[j] == nil { idx[j] = common.N // mark nil polynomial as completed } } done := false for !done { // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each // of the four SHAKE128 streams. perm.Permute() done = true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := 0; i < 7; i++ { var t [8]uint32 t[0] = uint32(state[i*3*4+j] & 0x7fffff) t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) t[2] = uint32((state[i*3*4+j] >> 48) | ((state[(i*3+1)*4+j] & 0x7f) << 16)) t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) t[5] = uint32((state[(i*3+1)*4+j] >> 56) | ((state[(i*3+2)*4+j] & 0x7fff) << 8)) t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) for k := 0; k < 8; k++ { if t[k] < common.Q { ps[j][idx[j]] = t[k] idx[j]++ if idx[j] == common.N { continue PolyLoop } } } } done = false } } } // Sample p uniformly from the given seed and nonce. // // p will be normalized. func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { var i, length int var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks if UseAES { length = 12 * 16 } else { length = 168 } sample := func() { // Note that 3 divides into 168 and 12*16, so we use up buf completely. for j := 0; j < length && i < common.N; j += 3 { t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | (uint32(buf[j+2]) << 16)) & 0x7fffff // We use rejection sampling if t < common.Q { p[i] = t i++ } } } if UseAES { h := common.NewAesStream128(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [32 + 2]byte // 32 byte seed + uint16 nonce h := sha3.NewShake128() copy(iv[:32], seed[:]) iv[32] = uint8(nonce) iv[33] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:168]) sample() } } } // Sample p uniformly with coefficients of norm less than or equal η, // using the given seed and nonce. // // p will not be normalized, but will have coefficients in [q-η,q+η]. func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) { // Assumes 2 < η < 8. var i, length int var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks if UseAES { length = 9 * 16 } else { length = 136 } sample := func() { // We use rejection sampling for j := 0; j < length && i < common.N; j++ { t1 := uint32(buf[j]) & 15 t2 := uint32(buf[j]) >> 4 if Eta == 2 { // branch is eliminated by compiler if t1 <= 14 { t1 -= ((205 * t1) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t1 i++ } if t2 <= 14 && i < common.N { t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t2 i++ } } else if Eta == 4 { if t1 <= 2*Eta { p[i] = common.Q + Eta - t1 i++ } if t2 <= 2*Eta && i < common.N { p[i] = common.Q + Eta - t2 i++ } } else { panic("unsupported η") } } } if UseAES { h := common.NewAesStream256(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [64 + 2]byte // 64 byte seed + uint16 nonce h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) // 136 is SHAKE-256 rate _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:136]) sample() } } } // Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁] using the // given seed and nonce+i // // p will be normalized. func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) { for i := 0; i < L; i++ { PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) } } // Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the // given seed and nonce. // // p will be normalized. func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) { var buf [PolyLeGamma1Size]byte if UseAES { h := common.NewAesStream256(seed, nonce) h.SqueezeInto(buf[:]) } else { var iv [66]byte h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) _, _ = h.Read(buf[:]) } PolyUnpackLeGamma1(p, buf[:]) } // For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1} // using the given seed and w1[i]. ps[i] may be nil and is ignored // in that case. ps[i] will be normalized. // // Can only be called when DeriveX4Available is true. // // This function is currently not used (yet). func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // SHAKE256 domain separator and padding for j := 0; j < 4; j++ { state[4*4+j] ^= 0x1f state[16*4+j] ^= 0x80 << 56 } perm.Permute() var signs [4]uint64 var idx [4]uint16 // indices into ps for j := 0; j < 4; j++ { if ps[j] != nil { signs[j] = state[j] *ps[j] = common.Poly{} // zero ps[j] idx[j] = common.N - Tau } else { idx[j] = common.N // mark as completed } } stateOffset := 1 for { done := true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := stateOffset; i < 17; i++ { var bs [8]byte binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) for k := 0; k < 8; k++ { b := uint16(bs[k]) if b > idx[j] { continue } ps[j][idx[j]] = ps[j][b] ps[j][b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) signs[j] >>= 1 idx[j]++ if idx[j] == common.N { continue PolyLoop } } } done = false } if done { break } perm.Permute() stateOffset = 0 } } // Samples p uniformly with τ non-zero coefficients in {q-1,1}. // // The polynomial p will be normalized. func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) { var buf [136]byte // SHAKE-256 rate is 136 h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(buf[:]) // Essentially we generate a sequence of τ ones or minus ones, // prepend 196 zeroes and shuffle the concatenation using the // usual algorithm (Fisher--Yates.) signs := binary.LittleEndian.Uint64(buf[:]) bufOff := 8 // offset into buf *p = common.Poly{} // zero p for i := uint16(common.N - Tau); i < common.N; i++ { var b uint16 // Find location of where to move the new coefficient to using // rejection sampling. for { if bufOff >= 136 { _, _ = h.Read(buf[:]) bufOff = 0 } b = uint16(buf[bufOff]) bufOff++ if b <= i { break } } p[i] = p[b] p[b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) signs >>= 1 } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/sample_test.go000066400000000000000000000204651454601126700301170ustar00rootroot00000000000000// Code generated from mode3/internal/sample_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestVectorDeriveUniform(t *testing.T) { var p, p2 common.Poly var seed [32]byte if UseAES { p2 = common.Poly{ 6724291, 310295, 6949524, 4464039, 1482136, 2522903, 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, 583034, 4971409, 2259140, 7715362, 3975394, 2341624, 5481174, 8150082, 365246, 5491939, 1083120, 7517301, 3104783, 2475292, 184149, 6425226, 4591622, 5964030, 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, 1512596, 5245430, 5517392, 2814840, 932545, 6826733, 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, 4123492, 8124406, 4016949, 5478752, 2750895, 603525, 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, 7990594, 1105530, 7121836, 1170740, 7417431, 633146, 253820, 7235019, 3539504, 6807707, 451390, 5481526, 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, 5311519, 3057534, 5277666, 682843, 2070398, 2874278, 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, 710407, 713806, 175647, 4274571, 2655021, 7319503, 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, 649664, 1720514, 6497260, 2683517, 7672754, 7105190, 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, 4337416, 2202680, 2338714, 557467, 6752058, 2469794, 485071, 1617604, 3590498, 2151466, 2005823, 7727956, 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, 2280717, 2889355, 3233946, 5187812, 978685, 5177364, 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, 816553, 6041174, 8317591, 1459178, 5332455, 1835058, 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, 4310856, 7135453, 3481032, 652626, 1841361, 8126828, 6250018, 300536, 7380070, 8174419, 1418793, 6208185, 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, 4119736, 6584065, 441634, 6941656, } } else { p2 = common.Poly{ 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, 4352830, } } for i := 0; i < 32; i++ { seed[i] = byte(i) } PolyDeriveUniform(&p, &seed, 30000) if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestDeriveUniform(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniform(&p, &seed, uint16(i)) if !PolyNormalized(&p) { t.Fatal() } } } func TestDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if p[j] < common.Q-Eta || p[j] > common.Q+Eta { t.Fatal() } } } } func TestDeriveUniformLeGamma1(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q { t.Fatal() } } } } func TestDeriveUniformBall(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformBall(&p, &seed) nonzero := 0 for j := 0; j < common.N; j++ { if p[j] != 0 { if p[j] != 1 && p[j] != common.Q-1 { t.Fatal() } nonzero++ } } if nonzero != Tau { t.Fatal() } } } func TestDeriveUniformX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte nonces := [4]uint16{12345, 54321, 13532, 37377} for i := 0; i < len(seed); i++ { seed[i] = byte(i) } PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, nonces) for i := 0; i < 4; i++ { PolyDeriveUniform(&p, &seed, nonces[i]) if ps[i] != p { t.Fatal() } } } func TestDeriveUniformBallX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte PolyDeriveUniformBallX4( [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, ) for j := 0; j < 4; j++ { PolyDeriveUniformBall(&p, &seed) if ps[j] != p { t.Fatalf("%d\n%v\n%v", j, ps[j], p) } } } func BenchmarkPolyDeriveUniformBall(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBall(&p, &seed) } } func BenchmarkPolyDeriveUniformBallX4(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBallX4( [4]*common.Poly{&p, &p, &p, &p}, &seed, ) } } func BenchmarkPolyDeriveUniform(b *testing.B) { var seed [32]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniform(&p, &seed, uint16(i)) } } func BenchmarkPolyDeriveUniformX4(b *testing.B) { if !DeriveX4Available { b.SkipNow() } var seed [32]byte var p [4]common.Poly for i := 0; i < b.N; i++ { nonce := uint16(4 * i) PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) } } func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { var seed [64]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2/internal/vec.go000066400000000000000000000141671454601126700263560ustar00rootroot00000000000000// Code generated from mode3/internal/vec.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A vector of L polynomials. type VecL [L]common.Poly // A vector of K polynomials. type VecK [K]common.Poly // Normalize the polynomials in this vector. func (v *VecL) Normalize() { for i := 0; i < L; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecL) NormalizeAssumingLe2Q() { for i := 0; i < L; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecL) Add(w, u *VecL) { for i := 0; i < L; i++ { v[i].Add(&w[i], &u[i]) } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecL) NTT() { for i := 0; i < L; i++ { v[i].NTT() } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecL) Exceeds(bound uint32) bool { for i := 0; i < L; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecL) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecL.PackLeqEta(). func (v *VecL) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sequentially packs each polynomial using PolyPackLeGamma1(). func (v *VecL) PackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). func (v *VecL) UnpackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Normalize the polynomials in this vector. func (v *VecK) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecK) NormalizeAssumingLe2Q() { for i := 0; i < K; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecK) Add(w, u *VecK) { for i := 0; i < K; i++ { v[i].Add(&w[i], &u[i]) } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecK) Exceeds(bound uint32) bool { for i := 0; i < K; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sets v to the hint vector for v0 the modified low bits and v1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint vector. func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { for i := 0; i < K; i++ { pop += PolyMakeHint(&v[i], &v0[i], &v1[i]) } return } // Computes corrections to the high bits of the polynomials in the vector // w using the hints in h and sets v to the corrected high bits. Returns v. // See useHint(). func (v *VecK) UseHint(q, hint *VecK) *VecK { for i := 0; i < K; i++ { PolyUseHint(&v[i], &q[i], &hint[i]) } return v } // Sequentially packs each polynomial using Poly.PackT1(). func (v *VecK) PackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT1(buf[offset:]) offset += common.PolyT1Size } } // Sets v to the vector packed into buf by PackT1(). func (v *VecK) UnpackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT1(buf[offset:]) offset += common.PolyT1Size } } // Sequentially packs each polynomial using Poly.PackT0(). func (v *VecK) PackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT0(buf[offset:]) offset += common.PolyT0Size } } // Sets v to the vector packed into buf by PackT0(). func (v *VecK) UnpackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT0(buf[offset:]) offset += common.PolyT0Size } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecK) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecK.PackLeqEta(). func (v *VecK) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecK) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sequentially packs each polynomial using PolyPackW1(). func (v *VecK) PackW1(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackW1(&v[i], buf[offset:]) offset += PolyW1Size } } // Sets v to a - b. // // Warning: assumes coefficients of the polynomials of b are less than 2q. func (v *VecK) Sub(a, b *VecK) { for i := 0; i < K; i++ { v[i].Sub(&a[i], &b[i]) } } // Sets v to 2ᵈ w without reducing. func (v *VecK) MulBy2toD(w *VecK) { for i := 0; i < K; i++ { v[i].MulBy2toD(&w[i]) } } // Applies InvNTT componentwise. See Poly.InvNTT() for details. func (v *VecK) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies Poly.ReduceLe2Q() componentwise. func (v *VecK) ReduceLe2Q() { for i := 0; i < K; i++ { v[i].ReduceLe2Q() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes.go000066400000000000000000000042261454601126700244510ustar00rootroot00000000000000// Code generated from mode.templ.go. DO NOT EDIT. package dilithium import ( "fmt" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode2aes" ) // implMode2AES implements the mode.Mode interface for Dilithium2-AES. type implMode2AES struct{} // Mode2AES is Dilithium in mode "Dilithium2-AES". var Mode2AES Mode = &implMode2AES{} func (m *implMode2AES) GenerateKey(rand io.Reader) ( PublicKey, PrivateKey, error) { return mode2aes.GenerateKey(rand) } func (m *implMode2AES) NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) { if len(seed) != common.SeedSize { panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) } seedBuf := [common.SeedSize]byte{} copy(seedBuf[:], seed) return mode2aes.NewKeyFromSeed(&seedBuf) } func (m *implMode2AES) Sign(sk PrivateKey, msg []byte) []byte { isk := sk.(*mode2aes.PrivateKey) ret := [mode2aes.SignatureSize]byte{} mode2aes.SignTo(isk, msg, ret[:]) return ret[:] } func (m *implMode2AES) Verify(pk PublicKey, msg []byte, signature []byte) bool { ipk := pk.(*mode2aes.PublicKey) return mode2aes.Verify(ipk, msg, signature) } func (m *implMode2AES) PublicKeyFromBytes(data []byte) PublicKey { var ret mode2aes.PublicKey if len(data) != mode2aes.PublicKeySize { panic("packed public key must be of mode2aes.PublicKeySize bytes") } var buf [mode2aes.PublicKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode2AES) PrivateKeyFromBytes(data []byte) PrivateKey { var ret mode2aes.PrivateKey if len(data) != mode2aes.PrivateKeySize { panic("packed public key must be of mode2aes.PrivateKeySize bytes") } var buf [mode2aes.PrivateKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode2AES) SeedSize() int { return common.SeedSize } func (m *implMode2AES) PublicKeySize() int { return mode2aes.PublicKeySize } func (m *implMode2AES) PrivateKeySize() int { return mode2aes.PrivateKeySize } func (m *implMode2AES) SignatureSize() int { return mode2aes.SignatureSize } func (m *implMode2AES) Name() string { return "Dilithium2-AES" } func init() { modes["Dilithium2-AES"] = Mode2AES } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/000077500000000000000000000000001454601126700241165ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/dilithium.go000066400000000000000000000116741454601126700264460ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // mode2aes implements the CRYSTALS-Dilithium signature scheme Dilithium2-AES // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf package mode2aes import ( "crypto" "errors" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode2aes/internal" ) const ( // Size of seed for NewKeyFromSeed SeedSize = common.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a signature SignatureSize = internal.SignatureSize ) // PublicKey is the type of Dilithium2-AES public key type PublicKey internal.PublicKey // PrivateKey is the type of Dilithium2-AES private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { pk, sk, err := internal.GenerateKey(rand) return (*PublicKey)(pk), (*PrivateKey)(sk), err } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { internal.SignTo( (*internal.PrivateKey)(sk), msg, signature, ) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { return internal.Verify( (*internal.PublicKey)(pk), msg, signature, ) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Unpack(buf) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Unpack(buf) } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Pack(buf) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Pack(buf) } // Packs the public key. func (pk *PublicKey) Bytes() []byte { var buf [PublicKeySize]byte pk.Pack(&buf) return buf[:] } // Packs the private key. func (sk *PrivateKey) Bytes() []byte { var buf [PrivateKeySize]byte sk.Pack(&buf) return buf[:] } // Packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // Packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // Unpacks the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of mode2aes.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // Unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of mode2aes.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("dilithium: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return (*PublicKey)((*internal.PrivateKey)(sk).Public()) } // Equal returns whether the two private keys equal. func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) } // Equal returns whether the two public keys equal. func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/000077500000000000000000000000001454601126700257325ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/dilithium.go000066400000000000000000000260461454601126700302610ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium.go by gen.go package internal import ( cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) const ( // Size of a packed polynomial of norm ≤η. // (Note that the formula is not valid in general.) PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 // β = τη, the maximum size of c s₂. Beta = Tau * Eta // γ₁ range of y Gamma1 = 1 << Gamma1Bits // Size of packed polynomial of norm <γ₁ such as z PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8 // α = 2γ₂ parameter for decompose Alpha = 2 * Gamma2 // Size of a packed private key PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K // Size of a packed public key PublicKeySize = 32 + common.PolyT1Size*K // Size of a packed signature SignatureSize = L*PolyLeGamma1Size + Omega + K + 32 // Size of packed w₁ PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8 ) // PublicKey is the type of Dilithium public keys. type PublicKey struct { rho [32]byte t1 VecK // Cached values t1p [common.PolyT1Size * K]byte A *Mat tr *[32]byte } // PrivateKey is the type of Dilithium private keys. type PrivateKey struct { rho [32]byte key [32]byte s1 VecL s2 VecK t0 VecK tr [32]byte // Cached values A Mat // ExpandA(ρ) s1h VecL // NTT(s₁) s2h VecK // NTT(s₂) t0h VecK // NTT(t₀) } type unpackedSignature struct { z VecL hint VecK c [32]byte } // Packs the signature into buf. func (sig *unpackedSignature) Pack(buf []byte) { copy(buf[:], sig.c[:]) sig.z.PackLeGamma1(buf[32:]) sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:]) } // Sets sig to the signature encoded in the buffer. // // Returns whether buf contains a properly packed signature. func (sig *unpackedSignature) Unpack(buf []byte) bool { if len(buf) < SignatureSize { return false } copy(sig.c[:], buf[:]) sig.z.UnpackLeGamma1(buf[32:]) if sig.z.Exceeds(Gamma1 - Beta) { return false } if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) { return false } return true } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { copy(buf[:32], pk.rho[:]) copy(buf[32:], pk.t1p[:]) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { copy(pk.rho[:], buf[:32]) copy(pk.t1p[:], buf[32:]) pk.t1.UnpackT1(pk.t1p[:]) pk.A = new(Mat) pk.A.Derive(&pk.rho) // tr = CRH(ρ ‖ t1) = CRH(pk) pk.tr = new([32]byte) h := sha3.NewShake256() _, _ = h.Write(buf[:]) _, _ = h.Read(pk.tr[:]) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { copy(buf[:32], sk.rho[:]) copy(buf[32:64], sk.key[:]) copy(buf[64:96], sk.tr[:]) offset := 96 sk.s1.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.PackT0(buf[offset:]) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { copy(sk.rho[:], buf[:32]) copy(sk.key[:], buf[32:64]) copy(sk.tr[:], buf[64:96]) offset := 96 sk.s1.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.UnpackT0(buf[offset:]) // Cached values sk.A.Derive(&sk.rho) sk.t0h = sk.t0 sk.t0h.NTT() sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [32]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { var eSeed [128]byte // expanded seed var pk PublicKey var sk PrivateKey var sSeed [64]byte h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(eSeed[:]) copy(pk.rho[:], eSeed[:32]) copy(sSeed[:], eSeed[32:96]) copy(sk.key[:], eSeed[96:]) copy(sk.rho[:], pk.rho[:]) sk.A.Derive(&pk.rho) for i := uint16(0); i < L; i++ { PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) } for i := uint16(0); i < K; i++ { PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) } sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() sk.computeT0andT1(&sk.t0, &pk.t1) sk.t0h = sk.t0 sk.t0h.NTT() // Complete public key far enough to be packed pk.t1.PackT1(pk.t1p[:]) pk.A = &sk.A // Finish private key var packedPk [PublicKeySize]byte pk.Pack(&packedPk) // tr = CRH(ρ ‖ t1) = CRH(pk) h.Reset() _, _ = h.Write(packedPk[:]) _, _ = h.Read(sk.tr[:]) // Finish cache of public key pk.tr = &sk.tr return &pk, &sk } // Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { var t VecK // Set t to A s₁ + s₂ for i := 0; i < K; i++ { PolyDotHat(&t[i], &sk.A[i], &sk.s1h) t[i].ReduceLe2Q() t[i].InvNTT() } t.Add(&t, &sk.s2) t.Normalize() // Compute t₀, t₁ = Power2Round(t) t.Power2Round(t0, t1) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { var sig unpackedSignature var mu [64]byte var zh VecL var Az, Az2dct1, w1 VecK var ch common.Poly var cp [32]byte var w1Packed [PolyW1Size * K]byte // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β // and ensured that there at most ω ones in pk.hint. if !sig.Unpack(signature) { return false } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(pk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // Compute Az zh = sig.z zh.NTT() for i := 0; i < K; i++ { PolyDotHat(&Az[i], &pk.A[i], &zh) } // Next, we compute Az - 2ᵈ·c·t₁. // Note that the coefficients of t₁ are bounded by 256 = 2⁹, // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, // which is small enough for NTT(). Az2dct1.MulBy2toD(&pk.t1) Az2dct1.NTT() PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() for i := 0; i < K; i++ { Az2dct1[i].MulHat(&Az2dct1[i], &ch) } Az2dct1.Sub(&Az, &Az2dct1) Az2dct1.ReduceLe2Q() Az2dct1.InvNTT() Az2dct1.NormalizeAssumingLe2Q() // UseHint(pk.hint, Az - 2ᵈ·c·t₁) // = UseHint(pk.hint, w - c·s₂ + c·t₀) // = UseHint(pk.hint, r + c·t₀) // = r₁ = w₁. w1.UseHint(&Az2dct1, &sig.hint) w1.PackW1(w1Packed[:]) // c' = H(μ, w₁) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(cp[:]) return sig.c == cp } // SignTo signs the given message and writes the signature into signature. // //nolint:funlen func SignTo(sk *PrivateKey, msg []byte, signature []byte) { var mu, rhop [64]byte var w1Packed [PolyW1Size * K]byte var y, yh VecL var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK var ch common.Poly var yNonce uint16 var sig unpackedSignature if len(signature) < SignatureSize { panic("Signature does not fit in that byteslice") } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(sk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // ρ' = CRH(key ‖ μ) h.Reset() _, _ = h.Write(sk.key[:]) _, _ = h.Write(mu[:]) _, _ = h.Read(rhop[:]) // Main rejection loop attempt := 0 for { attempt++ if attempt >= 576 { // Depending on the mode, one try has a chance between 1/7 and 1/4 // of succeeding. Thus it is safe to say that 576 iterations // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. panic("This should only happen 1 in 2^{128}: something is wrong.") } // y = ExpandMask(ρ', key) VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) yNonce += uint16(L) // Set w to A y yh = y yh.NTT() for i := 0; i < K; i++ { PolyDotHat(&w[i], &sk.A[i], &yh) w[i].ReduceLe2Q() w[i].InvNTT() } // Decompose w into w₀ and w₁ w.NormalizeAssumingLe2Q() w.Decompose(&w0, &w1) // c~ = H(μ ‖ w₁) w1.PackW1(w1Packed[:]) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(sig.c[:]) PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. // // By Lemma 3 of the specification this is equivalent to checking that // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition // w - c·s₂ = r₁ α + r₀ as computed by decompose(). // See also §4.1 of the specification. for i := 0; i < K; i++ { w0mcs2[i].MulHat(&ch, &sk.s2h[i]) w0mcs2[i].InvNTT() } w0mcs2.Sub(&w0, &w0mcs2) w0mcs2.Normalize() if w0mcs2.Exceeds(Gamma2 - Beta) { continue } // z = y + c·s₁ for i := 0; i < L; i++ { sig.z[i].MulHat(&ch, &sk.s1h[i]) sig.z[i].InvNTT() } sig.z.Add(&sig.z, &y) sig.z.Normalize() // Ensure ‖z‖_∞ < γ₁ - β if sig.z.Exceeds(Gamma1 - Beta) { continue } // Compute c·t₀ for i := 0; i < K; i++ { ct0[i].MulHat(&ch, &sk.t0h[i]) ct0[i].InvNTT() } ct0.NormalizeAssumingLe2Q() // Ensure ‖c·t₀‖_∞ < γ₂. if ct0.Exceeds(Gamma2) { continue } // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. // Note that we're not using makeHint() in the obvious way as we // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note // that our makeHint() is actually the same as a makeHint for a // different decomposition: // // Earlier we ensured indirectly with a check that r₁ = w₁ where // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. w0mcs2pct0.Add(&w0mcs2, &ct0) w0mcs2pct0.NormalizeAssumingLe2Q() hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) if hintPop > Omega { continue } break } sig.Pack(signature[:]) } // Computes the public key corresponding to this private key. func (sk *PrivateKey) Public() *PublicKey { var t0 VecK pk := &PublicKey{ rho: sk.rho, A: &sk.A, tr: &sk.tr, } sk.computeT0andT1(&t0, &pk.t1) pk.t1.PackT1(pk.t1p[:]) return pk } // Equal returns whether the two public keys are equal func (pk *PublicKey) Equal(other *PublicKey) bool { return pk.rho == other.rho && pk.t1 == other.t1 } // Equal returns whether the two private keys are equal func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) acc := uint32(0) for i := 0; i < L; i++ { for j := 0; j < common.N; j++ { acc |= sk.s1[i][j] ^ other.s1[i][j] } } for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { acc |= sk.s2[i][j] ^ other.s2[i][j] acc |= sk.t0[i][j] ^ other.t0[i][j] } } return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/dilithium_test.go000066400000000000000000000062731454601126700313200ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Checks whether p is normalized. Only used in tests. func PolyNormalized(p *common.Poly) bool { p2 := *p p2.Normalize() return p2 == *p } func BenchmarkSkUnpack(b *testing.B) { var buf [PrivateKeySize]byte var sk PrivateKey for i := 0; i < b.N; i++ { sk.Unpack(&buf) } } func BenchmarkPkUnpack(b *testing.B) { var buf [PublicKeySize]byte var pk PublicKey for i := 0; i < b.N; i++ { pk.Unpack(&buf) } } func BenchmarkVerify(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of verification (as in the reference // implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte pk, sk := NewKeyFromSeed(&seed) SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of signing (as in the reference implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte _, sk := NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [common.SeedSize]byte var sig [SignatureSize]byte var msg [8]byte var pkb [PublicKeySize]byte var skb [PrivateKeySize]byte var pk2 PublicKey var sk2 PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) if !sk.Equal(sk) { t.Fatal() } for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) SignTo(sk, msg[:], sig[:]) if !Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb) pk2.Unpack(&pkb) if !pk.Equal(&pk2) { t.Fatal() } sk.Pack(&skb) sk2.Unpack(&skb) if !sk.Equal(&sk2) { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [common.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) pk2 := sk.Public() if !pk.Equal(pk2) { t.Fatal() } } } func TestGamma1Size(t *testing.T) { var expected int switch Gamma1Bits { case 17: expected = 576 case 19: expected = 640 } if expected != PolyLeGamma1Size { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/mat.go000066400000000000000000000024411454601126700270430ustar00rootroot00000000000000// Code generated from mode3/internal/mat.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A k by l matrix of polynomials. type Mat [K]VecL // Expands the given seed to a complete matrix. // // This function is called ExpandA in the specification. func (m *Mat) Derive(seed *[32]byte) { if !DeriveX4Available { for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) } } return } idx := 0 var nonces [4]uint16 var ps [4]*common.Poly for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { nonces[idx] = (i << 8) + j ps[idx] = &m[i][j] idx++ if idx == 4 { idx = 0 PolyDeriveUniformX4(ps, seed, nonces) } } } if idx != 0 { for i := idx; i < 4; i++ { ps[i] = nil } PolyDeriveUniformX4(ps, seed, nonces) } } // Set p to the inner product of a and b using pointwise multiplication. // // Assumes a and b are in Montgomery form and their coefficients are // pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting // coefficients are bounded by 2Lq. func PolyDotHat(p *common.Poly, a, b *VecL) { var t common.Poly *p = common.Poly{} // zero p for i := 0; i < L; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/pack.go000066400000000000000000000164511454601126700272060ustar00rootroot00000000000000// Code generated from mode3/internal/pack.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Writes p with norm less than or equal η into buf, which must be of // size PolyLeqEtaSize. // // Assumes coefficients of p are not normalized, but in [q-η,q+η]. func PolyPackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { buf[i] = (byte(common.Q+Eta-p[j]) | byte(common.Q+Eta-p[j+1])<<4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { buf[i] = (byte(common.Q+Eta-p[j]) | (byte(common.Q+Eta-p[j+1]) << 3) | (byte(common.Q+Eta-p[j+2]) << 6)) buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | (byte(common.Q+Eta-p[j+3]) << 1) | (byte(common.Q+Eta-p[j+4]) << 4) | (byte(common.Q+Eta-p[j+5]) << 7)) buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | (byte(common.Q+Eta-p[j+6]) << 2) | (byte(common.Q+Eta-p[j+7]) << 5)) j += 8 } } else { panic("eta not supported") } } // Sets p to the polynomial of norm less than or equal η encoded in the // given buffer of size PolyLeqEtaSize. // // Output coefficients of p are not normalized, but in [q-η,q+η] provided // buf was created using PackLeqEta. // // Beware, for arbitrary buf the coefficients of p might end up in // the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. func PolyUnpackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { p[j] = common.Q + Eta - uint32(buf[i]&15) p[j+1] = common.Q + Eta - uint32(buf[i]>>4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { p[j] = common.Q + Eta - uint32(buf[i]&7) p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) j += 8 } } else { panic("eta not supported") } } // Writes v with coefficients in {0, 1} of which at most ω non-zero // to buf, which must have length ω+k. func (v *VecK) PackHint(buf []byte) { // The packed hint starts with the indices of the non-zero coefficients // For instance: // // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) // // Yields // // 56, 100, 255, 2, 23, 1 // // Then we pad with zeroes until we have a list of ω items: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 // // Then we finish with a list of the switch-over-indices in this // list between polynomials, so: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 off := uint8(0) for i := 0; i < K; i++ { for j := uint16(0); j < common.N; j++ { if v[i][j] != 0 { buf[off] = uint8(j) off++ } } buf[Omega+i] = off } for ; off < Omega; off++ { buf[off] = 0 } } // Sets v to the vector encoded using VecK.PackHint() // // Returns whether unpacking was successful. func (v *VecK) UnpackHint(buf []byte) bool { // A priori, there would be several reasonable ways to encode the same // hint vector. We take care to only allow only one encoding, to ensure // "strong unforgeability". // // See PackHint() source for description of the encoding. *v = VecK{} // zero v prevSOP := uint8(0) // previous switch-over-point for i := 0; i < K; i++ { SOP := buf[Omega+i] if SOP < prevSOP || SOP > Omega { return false // ensures switch-over-points are increasing } for j := prevSOP; j < SOP; j++ { if j > prevSOP && buf[j] <= buf[j-1] { return false // ensures indices are increasing (within a poly) } v[i][buf[j]] = 1 } prevSOP = SOP } for j := prevSOP; j < Omega; j++ { if buf[j] != 0 { return false // ensures padding indices are zero } } return true } // Sets p to the polynomial packed into buf by PolyPackLeGamma1. // // p will be normalized. func PolyUnpackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0x3) << 16) p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) | (uint32(buf[i+4]&0xf) << 14) p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) | (uint32(buf[i+6]&0x3f) << 12) p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) | (uint32(buf[i+8]) << 10) // coefficients in [0,…,2γ₁) p0 = Gamma1 - p0 // (-γ₁,…,γ₁] p1 = Gamma1 - p1 p2 = Gamma1 - p2 p3 = Gamma1 - p3 p0 += uint32(int32(p0)>>31) & common.Q // normalize p1 += uint32(int32(p1)>>31) & common.Q p2 += uint32(int32(p2)>>31) & common.Q p3 += uint32(int32(p3)>>31) & common.Q p[j] = p0 p[j+1] = p1 p[j+2] = p2 p[j+3] = p3 j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0xf) << 16) p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) | (uint32(buf[i+4]) << 12) p0 = Gamma1 - p0 p1 = Gamma1 - p1 p0 += uint32(int32(p0)>>31) & common.Q p1 += uint32(int32(p1)>>31) & common.Q p[j] = p0 p[j+1] = p1 j += 2 } } else { panic("γ₁ not supported") } } // Writes p whose coefficients are in (-γ₁,γ₁] into buf // which has to be of length PolyLeGamma1Size. // // Assumes p is normalized. func PolyPackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 // coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q) for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := Gamma1 - p[j] // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q) p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁) p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q p2 := Gamma1 - p[j+2] p2 += uint32(int32(p2)>>31) & common.Q p3 := Gamma1 - p[j+3] p3 += uint32(int32(p3)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<2) buf[i+3] = byte(p1 >> 6) buf[i+4] = byte(p1>>14) | byte(p2<<4) buf[i+5] = byte(p2 >> 4) buf[i+6] = byte(p2>>12) | byte(p3<<6) buf[i+7] = byte(p3 >> 2) buf[i+8] = byte(p3 >> 10) j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { // Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q) p0 := Gamma1 - p[j] p0 += uint32(int32(p0)>>31) & common.Q p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<4) buf[i+3] = byte(p1 >> 4) buf[i+4] = byte(p1 >> 12) j += 2 } } else { panic("γ₁ not supported") } } // Pack w₁ into buf, which must be of length PolyW1Size. // // Assumes w₁ is normalized. func PolyPackW1(p *common.Poly, buf []byte) { if Gamma1Bits == 19 { p.PackLe16(buf) } else if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyW1Size; i += 3 { buf[i] = byte(p[j]) | byte(p[j+1]<<6) buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4) buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2) j += 4 } } else { panic("unsupported γ₁") } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/pack_test.go000066400000000000000000000035651454601126700302470ustar00rootroot00000000000000// Code generated from mode3/internal/pack_test.go by gen.go package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestPolyPackLeqEta(t *testing.T) { var p1, p2 common.Poly var seed [64]byte var buf [PolyLeqEtaSize]byte for i := uint16(0); i < 100; i++ { // Note that DeriveUniformLeqEta sets p to the right kind of // unnormalized vector. PolyDeriveUniformLeqEta(&p1, &seed, i) for j := 0; j < PolyLeqEtaSize; j++ { if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { t.Fatalf("DerveUniformLeqEta out of bounds") } } PolyPackLeqEta(&p1, buf[:]) PolyUnpackLeqEta(&p2, buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT1(t *testing.T) { var p1, p2 common.Poly var seed [32]byte var buf [common.PolyT1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p1, &seed, i) p1.Normalize() for j := 0; j < common.N; j++ { p1[j] &= 0x1ff } p1.PackT1(buf[:]) p2.UnpackT1(buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT0(t *testing.T) { var p, p0, p1, p2 common.Poly var seed [32]byte var buf [common.PolyT0Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p, &seed, i) p.Normalize() p.Power2Round(&p0, &p1) p0.PackT0(buf[:]) p2.UnpackT0(buf[:]) if p0 != p2 { t.Fatalf("%v !=\n%v", p0, p2) } } } func BenchmarkUnpackLeGamma1(b *testing.B) { var p common.Poly var buf [PolyLeGamma1Size]byte for i := 0; i < b.N; i++ { PolyUnpackLeGamma1(&p, buf[:]) } } func TestPolyPackLeGamma1(t *testing.T) { var p0, p1 common.Poly var seed [64]byte var buf [PolyLeGamma1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniformLeGamma1(&p0, &seed, i) p0.Normalize() PolyPackLeGamma1(&p0, buf[:]) PolyUnpackLeGamma1(&p1, buf[:]) if p0 != p1 { t.Fatalf("%v != %v", p0, p1) } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/params.go000066400000000000000000000004511454601126700275440ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal const ( Name = "Dilithium2-AES" UseAES = true K = 4 L = 4 Eta = 2 DoubleEtaBits = 3 Omega = 80 Tau = 39 Gamma1Bits = 17 Gamma2 = 95232 ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/params_test.go000066400000000000000000000101531454601126700306030ustar00rootroot00000000000000package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Tests specific to the current mode func TestVectorDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte p2 := common.Poly{ 8380416, 0, 2, 8380415, 1, 1, 0, 1, 0, 1, 8380415, 2, 8380415, 8380415, 2, 2, 2, 1, 0, 2, 8380416, 1, 8380415, 8380415, 8380416, 8380415, 8380416, 8380415, 1, 1, 0, 1, 0, 1, 2, 8380416, 2, 1, 8380416, 1, 1, 2, 0, 8380416, 8380416, 2, 0, 2, 8380415, 0, 1, 2, 1, 1, 1, 0, 8380415, 1, 2, 8380415, 8380416, 1, 8380415, 0, 1, 8380416, 8380416, 8380415, 0, 2, 8380415, 1, 8380416, 0, 8380416, 8380416, 8380416, 2, 2, 1, 2, 8380415, 2, 0, 8380415, 8380415, 0, 2, 8380415, 8380415, 1, 8380415, 2, 8380415, 0, 1, 2, 8380415, 8380416, 8380415, 0, 8380416, 1, 0, 2, 0, 2, 8380415, 8380416, 2, 1, 8380415, 1, 8380416, 1, 8380415, 8380415, 0, 8380416, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 8380415, 8380416, 2, 0, 1, 8380416, 2, 1, 8380416, 2, 1, 8380416, 0, 2, 8380416, 2, 0, 8380415, 0, 2, 0, 8380415, 1, 0, 8380415, 2, 8380416, 8380416, 8380415, 0, 0, 8380416, 2, 2, 1, 8380416, 2, 1, 2, 0, 8380415, 1, 0, 2, 2, 1, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 8380416, 2, 2, 0, 8380415, 1, 2, 2, 1, 1, 8380415, 8380415, 2, 2, 1, 8380416, 8380415, 2, 1, 0, 8380416, 8380415, 8380415, 0, 1, 0, 8380416, 8380416, 8380416, 8380416, 2, 8380415, 1, 8380415, 0, 1, 0, 8380416, 2, 8380415, 2, 1, 2, 1, 1, 0, 8380415, 2, 8380416, 8380416, 8380415, 8380415, 0, 2, 8380416, 1, 8380416, 8380415, 8380416, 8380415, 2, 8380416, 2, 8380415, 2, 2, 1, 8380415, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeqEta(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestVectorDeriveUniformLeGamma1(t *testing.T) { var p, p2 common.Poly var seed [64]byte p2 = common.Poly{ 8340798, 8313384, 49077, 22486, 123481, 8288752, 36503, 8340997, 8302174, 8258535, 13603, 17223, 8335009, 8345989, 91340, 8349862, 83710, 72846, 89691, 8272088, 26276, 6832, 29103, 8313655, 72326, 8321983, 113475, 95773, 17886, 8365924, 8279095, 8343830, 8273195, 8310637, 8253500, 8374711, 8262430, 17388, 8294137, 8262960, 8290290, 47349, 44452, 128195, 8377719, 130632, 8256416, 8287230, 120060, 8323823, 115401, 8351851, 97604, 47772, 8363419, 8353971, 1956, 8267893, 8362705, 17686, 122170, 101229, 3317, 14205, 8368014, 97101, 8360617, 111843, 8357331, 16215, 8346959, 8313944, 8309613, 8348252, 64256, 8294208, 8318089, 8335255, 8324894, 8273750, 27850, 8260308, 8258591, 80542, 8320495, 36517, 8340794, 8304320, 8320157, 625, 8292418, 8317653, 8275617, 8352781, 109921, 121642, 8291715, 129643, 111667, 8325995, 8368715, 8283849, 8281348, 1417, 8336033, 100081, 30984, 22277, 8307048, 55908, 50909, 8326533, 34891, 98542, 121511, 2614, 125602, 59900, 120456, 8351260, 30124, 52065, 124214, 48354, 8281081, 116665, 17218, 74568, 4798, 8274275, 8328948, 8269139, 8908, 8276509, 8270063, 8370525, 8257669, 36128, 8313115, 8325113, 8257382, 77895, 8288147, 8294769, 8273027, 8370871, 57085, 59514, 82308, 71173, 6475, 8313311, 27188, 35803, 8296637, 100553, 8333397, 19553, 8373991, 8361935, 62433, 8300, 8371479, 8297954, 8352934, 8286, 8355336, 8335507, 8370548, 8301039, 8270317, 26478, 113694, 8296283, 8271234, 8250245, 8372668, 8284012, 8264500, 85893, 8322354, 8358407, 130156, 52458, 8291251, 122476, 8308146, 4252, 118400, 74123, 8333546, 70542, 8325370, 60510, 1874, 8377673, 50805, 78992, 66936, 8266050, 8367830, 8342582, 8268085, 65238, 61045, 8312728, 70547, 8309034, 5696, 118654, 8330845, 29553, 68995, 70518, 8351920, 8269399, 128395, 122804, 10848, 8291860, 8324935, 3842, 8265342, 8266117, 8368377, 8311281, 24039, 8343875, 97893, 12670, 8370577, 92482, 8288562, 8269568, 8371831, 8324316, 76758, 8327193, 46615, 10323, 8337373, 101795, 88456, 25023, 8351520, 94650, 8264851, 14881, 104171, 22607, 8379204, 8310533, 8324603, 8299017, 128723, 8291421, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeGamma1(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/rounding.go000066400000000000000000000101471454601126700301110ustar00rootroot00000000000000// Code generated from mode3/internal/rounding.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2, // except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken // and -α/2 ≤ a₀ < 0. Returns a₀ + q. Note 0 ≤ a₁ < (q-1)/α. // Recall α = 2γ₂. func decompose(a uint32) (a0plusQ, a1 uint32) { // a₁ = ⌈a / 128⌉ a1 = (a + 127) >> 7 if Alpha == 523776 { // 1025/2²² is close enough to 1/4092 so that a₁ // becomes a/α rounded down. a1 = ((a1*1025 + (1 << 21)) >> 22) // For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0. a1 &= 15 } else if Alpha == 190464 { // 1488/2²⁴ is close enough to 1/1488 so that a₁ // becomes a/α rounded down. a1 = ((a1 * 11275) + (1 << 23)) >> 24 // For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0. a1 ^= uint32(int32(43-a1)>>31) & a1 } else { panic("unsupported α") } a0plusQ = a - a1*Alpha // In the corner-case, when we set a₁=0, we will incorrectly // have a₀ > (q-1)/2 and we'll need to subtract q. As we // return a₀ + q, that comes down to adding q if a₀ < (q-1)/2. a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q return } // Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2. Decompose r as r = r1*α + r0 as // computed by decompose(). Write r' := r - f (mod Q). Now, decompose // r'=r-f again as r' = r'1*α + r'0 using decompose(). As f is small, we // have r'1 = r1 + h, where h ∈ {-1, 0, 1}. makeHint() computes |h| // given z0 := r0 - f (mod Q) and r1. With |h|, which is called the hint, // we can reconstruct r1 using only r' = r - f, which is done by useHint(). // To wit: // // useHint( r - f, makeHint( r0 - f, r1 ) ) = r1. // // Assumes 0 ≤ z0 < Q. func makeHint(z0, r1 uint32) uint32 { // If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r' // with the restrictions of decompose() and so r'1 = r1. So the hint // should be 0. This is covered by the first two inequalities. // There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also // a valid decomposition if r1 = 0. In the other cases a one is carried // and the hint should be 1. if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) { return 0 } return 1 } // Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see // documentation of makeHint() for context. // Assumes 0 ≤ r' < Q. func useHint(rp uint32, hint uint32) uint32 { rp0plusQ, rp1 := decompose(rp) if hint == 0 { return rp1 } if rp0plusQ > common.Q { return (rp1 + 1) & 15 } return (rp1 - 1) & 15 } // Sets p to the hint polynomial for p0 the modified low bits and p1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint polynomial. func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) { for i := 0; i < common.N; i++ { h := makeHint(p0[i], p1[i]) pop += h p[i] = h } return } // Computes corrections to the high bits of the polynomial q according // to the hints in h and sets p to the corrected high bits. Returns p. func PolyUseHint(p, q, hint *common.Poly) { var q0PlusQ common.Poly // See useHint() and makeHint() for an explanation. We reimplement it // here so that we can call Poly.Decompose(), which might be way faster // than calling decompose() in a loop (for instance when having AVX2.) PolyDecompose(q, &q0PlusQ, p) for i := 0; i < common.N; i++ { if hint[i] == 0 { continue } if Gamma2 == 261888 { if q0PlusQ[i] > common.Q { p[i] = (p[i] + 1) & 15 } else { p[i] = (p[i] - 1) & 15 } } else if Gamma2 == 95232 { if q0PlusQ[i] > common.Q { if p[i] == 43 { p[i] = 0 } else { p[i]++ } } else { if p[i] == 0 { p[i] = 43 } else { p[i]-- } } } else { panic("unsupported γ₂") } } } // Splits each of the coefficients of p using decompose. func PolyDecompose(p, p0PlusQ, p1 *common.Poly) { for i := 0; i < common.N; i++ { p0PlusQ[i], p1[i] = decompose(p[i]) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/rounding_test.go000066400000000000000000000031341454601126700311460ustar00rootroot00000000000000// Code generated from mode3/internal/rounding_test.go by gen.go package internal import ( "flag" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") func TestDecompose(t *testing.T) { for a := uint32(0); a < common.Q; a++ { a0PlusQ, a1 := decompose(a) a0 := int32(a0PlusQ) - int32(common.Q) recombined := a0 + int32(Alpha*a1) if a1 == 0 && recombined < 0 { recombined += common.Q if -(Alpha/2) > a0 || a0 >= 0 { t.Fatalf("decompose(%v): a0 out of bounds", a) } } else { if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) { t.Fatalf("decompose(%v): a0 out of bounds", a) } } if int32(a) != recombined { t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1) } } } func TestMakeHint(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for w := uint32(0); w < common.Q; w++ { w0, w1 := decompose(w) for fn := uint32(0); fn <= Gamma2; fn++ { fsign := false for { var f uint32 if fsign { if fn == 0 { break } f = common.Q - fn } else { f = fn } hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1) w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint) if w1p != w1 { t.Fatal() } if fsign { break } fsign = true } } } } func BenchmarkDecompose(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyDecompose(&p, &p0, &p1) } } func BenchmarkMakeHint(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyMakeHint(&p, &p0, &p1) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/sample.go000066400000000000000000000206561454601126700275530ustar00rootroot00000000000000// Code generated from mode3/internal/sample.go by gen.go package internal import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/simd/keccakf1600" ) // DeriveX4Available indicates whether the system supports the quick fourway // sampling variants like PolyDeriveUniformX4. var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES // For each i, sample ps[i] uniformly from the given seed and nonces[i]. // ps[i] may be nil and is ignored in that case. // // Can only be called when DeriveX4Available is true. func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // Absorb the nonces, the SHAKE128 domain separator (0b1111), the // start of the padding (0b...001) and the end of the padding 0b100... // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. for j := 0; j < 4; j++ { state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) state[20*4+j] = 0x80 << 56 } var idx [4]int // indices into ps for j := 0; j < 4; j++ { if ps[j] == nil { idx[j] = common.N // mark nil polynomial as completed } } done := false for !done { // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each // of the four SHAKE128 streams. perm.Permute() done = true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := 0; i < 7; i++ { var t [8]uint32 t[0] = uint32(state[i*3*4+j] & 0x7fffff) t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) t[2] = uint32((state[i*3*4+j] >> 48) | ((state[(i*3+1)*4+j] & 0x7f) << 16)) t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) t[5] = uint32((state[(i*3+1)*4+j] >> 56) | ((state[(i*3+2)*4+j] & 0x7fff) << 8)) t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) for k := 0; k < 8; k++ { if t[k] < common.Q { ps[j][idx[j]] = t[k] idx[j]++ if idx[j] == common.N { continue PolyLoop } } } } done = false } } } // Sample p uniformly from the given seed and nonce. // // p will be normalized. func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { var i, length int var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks if UseAES { length = 12 * 16 } else { length = 168 } sample := func() { // Note that 3 divides into 168 and 12*16, so we use up buf completely. for j := 0; j < length && i < common.N; j += 3 { t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | (uint32(buf[j+2]) << 16)) & 0x7fffff // We use rejection sampling if t < common.Q { p[i] = t i++ } } } if UseAES { h := common.NewAesStream128(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [32 + 2]byte // 32 byte seed + uint16 nonce h := sha3.NewShake128() copy(iv[:32], seed[:]) iv[32] = uint8(nonce) iv[33] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:168]) sample() } } } // Sample p uniformly with coefficients of norm less than or equal η, // using the given seed and nonce. // // p will not be normalized, but will have coefficients in [q-η,q+η]. func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) { // Assumes 2 < η < 8. var i, length int var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks if UseAES { length = 9 * 16 } else { length = 136 } sample := func() { // We use rejection sampling for j := 0; j < length && i < common.N; j++ { t1 := uint32(buf[j]) & 15 t2 := uint32(buf[j]) >> 4 if Eta == 2 { // branch is eliminated by compiler if t1 <= 14 { t1 -= ((205 * t1) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t1 i++ } if t2 <= 14 && i < common.N { t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t2 i++ } } else if Eta == 4 { if t1 <= 2*Eta { p[i] = common.Q + Eta - t1 i++ } if t2 <= 2*Eta && i < common.N { p[i] = common.Q + Eta - t2 i++ } } else { panic("unsupported η") } } } if UseAES { h := common.NewAesStream256(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [64 + 2]byte // 64 byte seed + uint16 nonce h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) // 136 is SHAKE-256 rate _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:136]) sample() } } } // Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁] using the // given seed and nonce+i // // p will be normalized. func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) { for i := 0; i < L; i++ { PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) } } // Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the // given seed and nonce. // // p will be normalized. func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) { var buf [PolyLeGamma1Size]byte if UseAES { h := common.NewAesStream256(seed, nonce) h.SqueezeInto(buf[:]) } else { var iv [66]byte h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) _, _ = h.Read(buf[:]) } PolyUnpackLeGamma1(p, buf[:]) } // For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1} // using the given seed and w1[i]. ps[i] may be nil and is ignored // in that case. ps[i] will be normalized. // // Can only be called when DeriveX4Available is true. // // This function is currently not used (yet). func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // SHAKE256 domain separator and padding for j := 0; j < 4; j++ { state[4*4+j] ^= 0x1f state[16*4+j] ^= 0x80 << 56 } perm.Permute() var signs [4]uint64 var idx [4]uint16 // indices into ps for j := 0; j < 4; j++ { if ps[j] != nil { signs[j] = state[j] *ps[j] = common.Poly{} // zero ps[j] idx[j] = common.N - Tau } else { idx[j] = common.N // mark as completed } } stateOffset := 1 for { done := true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := stateOffset; i < 17; i++ { var bs [8]byte binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) for k := 0; k < 8; k++ { b := uint16(bs[k]) if b > idx[j] { continue } ps[j][idx[j]] = ps[j][b] ps[j][b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) signs[j] >>= 1 idx[j]++ if idx[j] == common.N { continue PolyLoop } } } done = false } if done { break } perm.Permute() stateOffset = 0 } } // Samples p uniformly with τ non-zero coefficients in {q-1,1}. // // The polynomial p will be normalized. func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) { var buf [136]byte // SHAKE-256 rate is 136 h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(buf[:]) // Essentially we generate a sequence of τ ones or minus ones, // prepend 196 zeroes and shuffle the concatenation using the // usual algorithm (Fisher--Yates.) signs := binary.LittleEndian.Uint64(buf[:]) bufOff := 8 // offset into buf *p = common.Poly{} // zero p for i := uint16(common.N - Tau); i < common.N; i++ { var b uint16 // Find location of where to move the new coefficient to using // rejection sampling. for { if bufOff >= 136 { _, _ = h.Read(buf[:]) bufOff = 0 } b = uint16(buf[bufOff]) bufOff++ if b <= i { break } } p[i] = p[b] p[b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) signs >>= 1 } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/sample_test.go000066400000000000000000000204651454601126700306100ustar00rootroot00000000000000// Code generated from mode3/internal/sample_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestVectorDeriveUniform(t *testing.T) { var p, p2 common.Poly var seed [32]byte if UseAES { p2 = common.Poly{ 6724291, 310295, 6949524, 4464039, 1482136, 2522903, 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, 583034, 4971409, 2259140, 7715362, 3975394, 2341624, 5481174, 8150082, 365246, 5491939, 1083120, 7517301, 3104783, 2475292, 184149, 6425226, 4591622, 5964030, 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, 1512596, 5245430, 5517392, 2814840, 932545, 6826733, 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, 4123492, 8124406, 4016949, 5478752, 2750895, 603525, 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, 7990594, 1105530, 7121836, 1170740, 7417431, 633146, 253820, 7235019, 3539504, 6807707, 451390, 5481526, 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, 5311519, 3057534, 5277666, 682843, 2070398, 2874278, 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, 710407, 713806, 175647, 4274571, 2655021, 7319503, 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, 649664, 1720514, 6497260, 2683517, 7672754, 7105190, 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, 4337416, 2202680, 2338714, 557467, 6752058, 2469794, 485071, 1617604, 3590498, 2151466, 2005823, 7727956, 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, 2280717, 2889355, 3233946, 5187812, 978685, 5177364, 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, 816553, 6041174, 8317591, 1459178, 5332455, 1835058, 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, 4310856, 7135453, 3481032, 652626, 1841361, 8126828, 6250018, 300536, 7380070, 8174419, 1418793, 6208185, 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, 4119736, 6584065, 441634, 6941656, } } else { p2 = common.Poly{ 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, 4352830, } } for i := 0; i < 32; i++ { seed[i] = byte(i) } PolyDeriveUniform(&p, &seed, 30000) if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestDeriveUniform(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniform(&p, &seed, uint16(i)) if !PolyNormalized(&p) { t.Fatal() } } } func TestDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if p[j] < common.Q-Eta || p[j] > common.Q+Eta { t.Fatal() } } } } func TestDeriveUniformLeGamma1(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q { t.Fatal() } } } } func TestDeriveUniformBall(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformBall(&p, &seed) nonzero := 0 for j := 0; j < common.N; j++ { if p[j] != 0 { if p[j] != 1 && p[j] != common.Q-1 { t.Fatal() } nonzero++ } } if nonzero != Tau { t.Fatal() } } } func TestDeriveUniformX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte nonces := [4]uint16{12345, 54321, 13532, 37377} for i := 0; i < len(seed); i++ { seed[i] = byte(i) } PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, nonces) for i := 0; i < 4; i++ { PolyDeriveUniform(&p, &seed, nonces[i]) if ps[i] != p { t.Fatal() } } } func TestDeriveUniformBallX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte PolyDeriveUniformBallX4( [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, ) for j := 0; j < 4; j++ { PolyDeriveUniformBall(&p, &seed) if ps[j] != p { t.Fatalf("%d\n%v\n%v", j, ps[j], p) } } } func BenchmarkPolyDeriveUniformBall(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBall(&p, &seed) } } func BenchmarkPolyDeriveUniformBallX4(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBallX4( [4]*common.Poly{&p, &p, &p, &p}, &seed, ) } } func BenchmarkPolyDeriveUniform(b *testing.B) { var seed [32]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniform(&p, &seed, uint16(i)) } } func BenchmarkPolyDeriveUniformX4(b *testing.B) { if !DeriveX4Available { b.SkipNow() } var seed [32]byte var p [4]common.Poly for i := 0; i < b.N; i++ { nonce := uint16(4 * i) PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) } } func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { var seed [64]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode2aes/internal/vec.go000066400000000000000000000141671454601126700270470ustar00rootroot00000000000000// Code generated from mode3/internal/vec.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A vector of L polynomials. type VecL [L]common.Poly // A vector of K polynomials. type VecK [K]common.Poly // Normalize the polynomials in this vector. func (v *VecL) Normalize() { for i := 0; i < L; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecL) NormalizeAssumingLe2Q() { for i := 0; i < L; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecL) Add(w, u *VecL) { for i := 0; i < L; i++ { v[i].Add(&w[i], &u[i]) } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecL) NTT() { for i := 0; i < L; i++ { v[i].NTT() } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecL) Exceeds(bound uint32) bool { for i := 0; i < L; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecL) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecL.PackLeqEta(). func (v *VecL) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sequentially packs each polynomial using PolyPackLeGamma1(). func (v *VecL) PackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). func (v *VecL) UnpackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Normalize the polynomials in this vector. func (v *VecK) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecK) NormalizeAssumingLe2Q() { for i := 0; i < K; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecK) Add(w, u *VecK) { for i := 0; i < K; i++ { v[i].Add(&w[i], &u[i]) } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecK) Exceeds(bound uint32) bool { for i := 0; i < K; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sets v to the hint vector for v0 the modified low bits and v1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint vector. func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { for i := 0; i < K; i++ { pop += PolyMakeHint(&v[i], &v0[i], &v1[i]) } return } // Computes corrections to the high bits of the polynomials in the vector // w using the hints in h and sets v to the corrected high bits. Returns v. // See useHint(). func (v *VecK) UseHint(q, hint *VecK) *VecK { for i := 0; i < K; i++ { PolyUseHint(&v[i], &q[i], &hint[i]) } return v } // Sequentially packs each polynomial using Poly.PackT1(). func (v *VecK) PackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT1(buf[offset:]) offset += common.PolyT1Size } } // Sets v to the vector packed into buf by PackT1(). func (v *VecK) UnpackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT1(buf[offset:]) offset += common.PolyT1Size } } // Sequentially packs each polynomial using Poly.PackT0(). func (v *VecK) PackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT0(buf[offset:]) offset += common.PolyT0Size } } // Sets v to the vector packed into buf by PackT0(). func (v *VecK) UnpackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT0(buf[offset:]) offset += common.PolyT0Size } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecK) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecK.PackLeqEta(). func (v *VecK) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecK) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sequentially packs each polynomial using PolyPackW1(). func (v *VecK) PackW1(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackW1(&v[i], buf[offset:]) offset += PolyW1Size } } // Sets v to a - b. // // Warning: assumes coefficients of the polynomials of b are less than 2q. func (v *VecK) Sub(a, b *VecK) { for i := 0; i < K; i++ { v[i].Sub(&a[i], &b[i]) } } // Sets v to 2ᵈ w without reducing. func (v *VecK) MulBy2toD(w *VecK) { for i := 0; i < K; i++ { v[i].MulBy2toD(&w[i]) } } // Applies InvNTT componentwise. See Poly.InvNTT() for details. func (v *VecK) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies Poly.ReduceLe2Q() componentwise. func (v *VecK) ReduceLe2Q() { for i := 0; i < K; i++ { v[i].ReduceLe2Q() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3.go000066400000000000000000000040321454601126700237540ustar00rootroot00000000000000// Code generated from mode.templ.go. DO NOT EDIT. package dilithium import ( "fmt" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode3" ) // implMode3 implements the mode.Mode interface for Dilithium3. type implMode3 struct{} // Mode3 is Dilithium in mode "Dilithium3". var Mode3 Mode = &implMode3{} func (m *implMode3) GenerateKey(rand io.Reader) ( PublicKey, PrivateKey, error) { return mode3.GenerateKey(rand) } func (m *implMode3) NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) { if len(seed) != common.SeedSize { panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) } seedBuf := [common.SeedSize]byte{} copy(seedBuf[:], seed) return mode3.NewKeyFromSeed(&seedBuf) } func (m *implMode3) Sign(sk PrivateKey, msg []byte) []byte { isk := sk.(*mode3.PrivateKey) ret := [mode3.SignatureSize]byte{} mode3.SignTo(isk, msg, ret[:]) return ret[:] } func (m *implMode3) Verify(pk PublicKey, msg []byte, signature []byte) bool { ipk := pk.(*mode3.PublicKey) return mode3.Verify(ipk, msg, signature) } func (m *implMode3) PublicKeyFromBytes(data []byte) PublicKey { var ret mode3.PublicKey if len(data) != mode3.PublicKeySize { panic("packed public key must be of mode3.PublicKeySize bytes") } var buf [mode3.PublicKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode3) PrivateKeyFromBytes(data []byte) PrivateKey { var ret mode3.PrivateKey if len(data) != mode3.PrivateKeySize { panic("packed public key must be of mode3.PrivateKeySize bytes") } var buf [mode3.PrivateKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode3) SeedSize() int { return common.SeedSize } func (m *implMode3) PublicKeySize() int { return mode3.PublicKeySize } func (m *implMode3) PrivateKeySize() int { return mode3.PrivateKeySize } func (m *implMode3) SignatureSize() int { return mode3.SignatureSize } func (m *implMode3) Name() string { return "Dilithium3" } func init() { modes["Dilithium3"] = Mode3 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/000077500000000000000000000000001454601126700234265ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/dilithium.go000066400000000000000000000116411454601126700257500ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // mode3 implements the CRYSTALS-Dilithium signature scheme Dilithium3 // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf package mode3 import ( "crypto" "errors" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode3/internal" ) const ( // Size of seed for NewKeyFromSeed SeedSize = common.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a signature SignatureSize = internal.SignatureSize ) // PublicKey is the type of Dilithium3 public key type PublicKey internal.PublicKey // PrivateKey is the type of Dilithium3 private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { pk, sk, err := internal.GenerateKey(rand) return (*PublicKey)(pk), (*PrivateKey)(sk), err } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { internal.SignTo( (*internal.PrivateKey)(sk), msg, signature, ) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { return internal.Verify( (*internal.PublicKey)(pk), msg, signature, ) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Unpack(buf) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Unpack(buf) } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Pack(buf) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Pack(buf) } // Packs the public key. func (pk *PublicKey) Bytes() []byte { var buf [PublicKeySize]byte pk.Pack(&buf) return buf[:] } // Packs the private key. func (sk *PrivateKey) Bytes() []byte { var buf [PrivateKeySize]byte sk.Pack(&buf) return buf[:] } // Packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // Packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // Unpacks the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of mode3.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // Unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of mode3.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("dilithium: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return (*PublicKey)((*internal.PrivateKey)(sk).Public()) } // Equal returns whether the two private keys equal. func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) } // Equal returns whether the two public keys equal. func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/000077500000000000000000000000001454601126700252425ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/dilithium.go000066400000000000000000000257501454601126700275720ustar00rootroot00000000000000package internal import ( cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) const ( // Size of a packed polynomial of norm ≤η. // (Note that the formula is not valid in general.) PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 // β = τη, the maximum size of c s₂. Beta = Tau * Eta // γ₁ range of y Gamma1 = 1 << Gamma1Bits // Size of packed polynomial of norm <γ₁ such as z PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8 // α = 2γ₂ parameter for decompose Alpha = 2 * Gamma2 // Size of a packed private key PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K // Size of a packed public key PublicKeySize = 32 + common.PolyT1Size*K // Size of a packed signature SignatureSize = L*PolyLeGamma1Size + Omega + K + 32 // Size of packed w₁ PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8 ) // PublicKey is the type of Dilithium public keys. type PublicKey struct { rho [32]byte t1 VecK // Cached values t1p [common.PolyT1Size * K]byte A *Mat tr *[32]byte } // PrivateKey is the type of Dilithium private keys. type PrivateKey struct { rho [32]byte key [32]byte s1 VecL s2 VecK t0 VecK tr [32]byte // Cached values A Mat // ExpandA(ρ) s1h VecL // NTT(s₁) s2h VecK // NTT(s₂) t0h VecK // NTT(t₀) } type unpackedSignature struct { z VecL hint VecK c [32]byte } // Packs the signature into buf. func (sig *unpackedSignature) Pack(buf []byte) { copy(buf[:], sig.c[:]) sig.z.PackLeGamma1(buf[32:]) sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:]) } // Sets sig to the signature encoded in the buffer. // // Returns whether buf contains a properly packed signature. func (sig *unpackedSignature) Unpack(buf []byte) bool { if len(buf) < SignatureSize { return false } copy(sig.c[:], buf[:]) sig.z.UnpackLeGamma1(buf[32:]) if sig.z.Exceeds(Gamma1 - Beta) { return false } if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) { return false } return true } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { copy(buf[:32], pk.rho[:]) copy(buf[32:], pk.t1p[:]) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { copy(pk.rho[:], buf[:32]) copy(pk.t1p[:], buf[32:]) pk.t1.UnpackT1(pk.t1p[:]) pk.A = new(Mat) pk.A.Derive(&pk.rho) // tr = CRH(ρ ‖ t1) = CRH(pk) pk.tr = new([32]byte) h := sha3.NewShake256() _, _ = h.Write(buf[:]) _, _ = h.Read(pk.tr[:]) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { copy(buf[:32], sk.rho[:]) copy(buf[32:64], sk.key[:]) copy(buf[64:96], sk.tr[:]) offset := 96 sk.s1.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.PackT0(buf[offset:]) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { copy(sk.rho[:], buf[:32]) copy(sk.key[:], buf[32:64]) copy(sk.tr[:], buf[64:96]) offset := 96 sk.s1.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.UnpackT0(buf[offset:]) // Cached values sk.A.Derive(&sk.rho) sk.t0h = sk.t0 sk.t0h.NTT() sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [32]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { var eSeed [128]byte // expanded seed var pk PublicKey var sk PrivateKey var sSeed [64]byte h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(eSeed[:]) copy(pk.rho[:], eSeed[:32]) copy(sSeed[:], eSeed[32:96]) copy(sk.key[:], eSeed[96:]) copy(sk.rho[:], pk.rho[:]) sk.A.Derive(&pk.rho) for i := uint16(0); i < L; i++ { PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) } for i := uint16(0); i < K; i++ { PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) } sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() sk.computeT0andT1(&sk.t0, &pk.t1) sk.t0h = sk.t0 sk.t0h.NTT() // Complete public key far enough to be packed pk.t1.PackT1(pk.t1p[:]) pk.A = &sk.A // Finish private key var packedPk [PublicKeySize]byte pk.Pack(&packedPk) // tr = CRH(ρ ‖ t1) = CRH(pk) h.Reset() _, _ = h.Write(packedPk[:]) _, _ = h.Read(sk.tr[:]) // Finish cache of public key pk.tr = &sk.tr return &pk, &sk } // Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { var t VecK // Set t to A s₁ + s₂ for i := 0; i < K; i++ { PolyDotHat(&t[i], &sk.A[i], &sk.s1h) t[i].ReduceLe2Q() t[i].InvNTT() } t.Add(&t, &sk.s2) t.Normalize() // Compute t₀, t₁ = Power2Round(t) t.Power2Round(t0, t1) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { var sig unpackedSignature var mu [64]byte var zh VecL var Az, Az2dct1, w1 VecK var ch common.Poly var cp [32]byte var w1Packed [PolyW1Size * K]byte // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β // and ensured that there at most ω ones in pk.hint. if !sig.Unpack(signature) { return false } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(pk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // Compute Az zh = sig.z zh.NTT() for i := 0; i < K; i++ { PolyDotHat(&Az[i], &pk.A[i], &zh) } // Next, we compute Az - 2ᵈ·c·t₁. // Note that the coefficients of t₁ are bounded by 256 = 2⁹, // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, // which is small enough for NTT(). Az2dct1.MulBy2toD(&pk.t1) Az2dct1.NTT() PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() for i := 0; i < K; i++ { Az2dct1[i].MulHat(&Az2dct1[i], &ch) } Az2dct1.Sub(&Az, &Az2dct1) Az2dct1.ReduceLe2Q() Az2dct1.InvNTT() Az2dct1.NormalizeAssumingLe2Q() // UseHint(pk.hint, Az - 2ᵈ·c·t₁) // = UseHint(pk.hint, w - c·s₂ + c·t₀) // = UseHint(pk.hint, r + c·t₀) // = r₁ = w₁. w1.UseHint(&Az2dct1, &sig.hint) w1.PackW1(w1Packed[:]) // c' = H(μ, w₁) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(cp[:]) return sig.c == cp } // SignTo signs the given message and writes the signature into signature. // //nolint:funlen func SignTo(sk *PrivateKey, msg []byte, signature []byte) { var mu, rhop [64]byte var w1Packed [PolyW1Size * K]byte var y, yh VecL var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK var ch common.Poly var yNonce uint16 var sig unpackedSignature if len(signature) < SignatureSize { panic("Signature does not fit in that byteslice") } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(sk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // ρ' = CRH(key ‖ μ) h.Reset() _, _ = h.Write(sk.key[:]) _, _ = h.Write(mu[:]) _, _ = h.Read(rhop[:]) // Main rejection loop attempt := 0 for { attempt++ if attempt >= 576 { // Depending on the mode, one try has a chance between 1/7 and 1/4 // of succeeding. Thus it is safe to say that 576 iterations // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. panic("This should only happen 1 in 2^{128}: something is wrong.") } // y = ExpandMask(ρ', key) VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) yNonce += uint16(L) // Set w to A y yh = y yh.NTT() for i := 0; i < K; i++ { PolyDotHat(&w[i], &sk.A[i], &yh) w[i].ReduceLe2Q() w[i].InvNTT() } // Decompose w into w₀ and w₁ w.NormalizeAssumingLe2Q() w.Decompose(&w0, &w1) // c~ = H(μ ‖ w₁) w1.PackW1(w1Packed[:]) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(sig.c[:]) PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. // // By Lemma 3 of the specification this is equivalent to checking that // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition // w - c·s₂ = r₁ α + r₀ as computed by decompose(). // See also §4.1 of the specification. for i := 0; i < K; i++ { w0mcs2[i].MulHat(&ch, &sk.s2h[i]) w0mcs2[i].InvNTT() } w0mcs2.Sub(&w0, &w0mcs2) w0mcs2.Normalize() if w0mcs2.Exceeds(Gamma2 - Beta) { continue } // z = y + c·s₁ for i := 0; i < L; i++ { sig.z[i].MulHat(&ch, &sk.s1h[i]) sig.z[i].InvNTT() } sig.z.Add(&sig.z, &y) sig.z.Normalize() // Ensure ‖z‖_∞ < γ₁ - β if sig.z.Exceeds(Gamma1 - Beta) { continue } // Compute c·t₀ for i := 0; i < K; i++ { ct0[i].MulHat(&ch, &sk.t0h[i]) ct0[i].InvNTT() } ct0.NormalizeAssumingLe2Q() // Ensure ‖c·t₀‖_∞ < γ₂. if ct0.Exceeds(Gamma2) { continue } // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. // Note that we're not using makeHint() in the obvious way as we // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note // that our makeHint() is actually the same as a makeHint for a // different decomposition: // // Earlier we ensured indirectly with a check that r₁ = w₁ where // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. w0mcs2pct0.Add(&w0mcs2, &ct0) w0mcs2pct0.NormalizeAssumingLe2Q() hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) if hintPop > Omega { continue } break } sig.Pack(signature[:]) } // Computes the public key corresponding to this private key. func (sk *PrivateKey) Public() *PublicKey { var t0 VecK pk := &PublicKey{ rho: sk.rho, A: &sk.A, tr: &sk.tr, } sk.computeT0andT1(&t0, &pk.t1) pk.t1.PackT1(pk.t1p[:]) return pk } // Equal returns whether the two public keys are equal func (pk *PublicKey) Equal(other *PublicKey) bool { return pk.rho == other.rho && pk.t1 == other.t1 } // Equal returns whether the two private keys are equal func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) acc := uint32(0) for i := 0; i < L; i++ { for j := 0; j < common.N; j++ { acc |= sk.s1[i][j] ^ other.s1[i][j] } } for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { acc |= sk.s2[i][j] ^ other.s2[i][j] acc |= sk.t0[i][j] ^ other.t0[i][j] } } return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/dilithium_test.go000066400000000000000000000061701454601126700306240ustar00rootroot00000000000000package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Checks whether p is normalized. Only used in tests. func PolyNormalized(p *common.Poly) bool { p2 := *p p2.Normalize() return p2 == *p } func BenchmarkSkUnpack(b *testing.B) { var buf [PrivateKeySize]byte var sk PrivateKey for i := 0; i < b.N; i++ { sk.Unpack(&buf) } } func BenchmarkPkUnpack(b *testing.B) { var buf [PublicKeySize]byte var pk PublicKey for i := 0; i < b.N; i++ { pk.Unpack(&buf) } } func BenchmarkVerify(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of verification (as in the reference // implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte pk, sk := NewKeyFromSeed(&seed) SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of signing (as in the reference implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte _, sk := NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [common.SeedSize]byte var sig [SignatureSize]byte var msg [8]byte var pkb [PublicKeySize]byte var skb [PrivateKeySize]byte var pk2 PublicKey var sk2 PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) if !sk.Equal(sk) { t.Fatal() } for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) SignTo(sk, msg[:], sig[:]) if !Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb) pk2.Unpack(&pkb) if !pk.Equal(&pk2) { t.Fatal() } sk.Pack(&skb) sk2.Unpack(&skb) if !sk.Equal(&sk2) { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [common.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) pk2 := sk.Public() if !pk.Equal(pk2) { t.Fatal() } } } func TestGamma1Size(t *testing.T) { var expected int switch Gamma1Bits { case 17: expected = 576 case 19: expected = 640 } if expected != PolyLeGamma1Size { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/mat.go000066400000000000000000000023511454601126700263530ustar00rootroot00000000000000package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A k by l matrix of polynomials. type Mat [K]VecL // Expands the given seed to a complete matrix. // // This function is called ExpandA in the specification. func (m *Mat) Derive(seed *[32]byte) { if !DeriveX4Available { for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) } } return } idx := 0 var nonces [4]uint16 var ps [4]*common.Poly for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { nonces[idx] = (i << 8) + j ps[idx] = &m[i][j] idx++ if idx == 4 { idx = 0 PolyDeriveUniformX4(ps, seed, nonces) } } } if idx != 0 { for i := idx; i < 4; i++ { ps[i] = nil } PolyDeriveUniformX4(ps, seed, nonces) } } // Set p to the inner product of a and b using pointwise multiplication. // // Assumes a and b are in Montgomery form and their coefficients are // pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting // coefficients are bounded by 2Lq. func PolyDotHat(p *common.Poly, a, b *VecL) { var t common.Poly *p = common.Poly{} // zero p for i := 0; i < L; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/pack.go000066400000000000000000000163601454601126700265150ustar00rootroot00000000000000package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Writes p with norm less than or equal η into buf, which must be of // size PolyLeqEtaSize. // // Assumes coefficients of p are not normalized, but in [q-η,q+η]. func PolyPackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { buf[i] = (byte(common.Q+Eta-p[j]) | byte(common.Q+Eta-p[j+1])<<4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { buf[i] = (byte(common.Q+Eta-p[j]) | (byte(common.Q+Eta-p[j+1]) << 3) | (byte(common.Q+Eta-p[j+2]) << 6)) buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | (byte(common.Q+Eta-p[j+3]) << 1) | (byte(common.Q+Eta-p[j+4]) << 4) | (byte(common.Q+Eta-p[j+5]) << 7)) buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | (byte(common.Q+Eta-p[j+6]) << 2) | (byte(common.Q+Eta-p[j+7]) << 5)) j += 8 } } else { panic("eta not supported") } } // Sets p to the polynomial of norm less than or equal η encoded in the // given buffer of size PolyLeqEtaSize. // // Output coefficients of p are not normalized, but in [q-η,q+η] provided // buf was created using PackLeqEta. // // Beware, for arbitrary buf the coefficients of p might end up in // the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. func PolyUnpackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { p[j] = common.Q + Eta - uint32(buf[i]&15) p[j+1] = common.Q + Eta - uint32(buf[i]>>4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { p[j] = common.Q + Eta - uint32(buf[i]&7) p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) j += 8 } } else { panic("eta not supported") } } // Writes v with coefficients in {0, 1} of which at most ω non-zero // to buf, which must have length ω+k. func (v *VecK) PackHint(buf []byte) { // The packed hint starts with the indices of the non-zero coefficients // For instance: // // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) // // Yields // // 56, 100, 255, 2, 23, 1 // // Then we pad with zeroes until we have a list of ω items: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 // // Then we finish with a list of the switch-over-indices in this // list between polynomials, so: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 off := uint8(0) for i := 0; i < K; i++ { for j := uint16(0); j < common.N; j++ { if v[i][j] != 0 { buf[off] = uint8(j) off++ } } buf[Omega+i] = off } for ; off < Omega; off++ { buf[off] = 0 } } // Sets v to the vector encoded using VecK.PackHint() // // Returns whether unpacking was successful. func (v *VecK) UnpackHint(buf []byte) bool { // A priori, there would be several reasonable ways to encode the same // hint vector. We take care to only allow only one encoding, to ensure // "strong unforgeability". // // See PackHint() source for description of the encoding. *v = VecK{} // zero v prevSOP := uint8(0) // previous switch-over-point for i := 0; i < K; i++ { SOP := buf[Omega+i] if SOP < prevSOP || SOP > Omega { return false // ensures switch-over-points are increasing } for j := prevSOP; j < SOP; j++ { if j > prevSOP && buf[j] <= buf[j-1] { return false // ensures indices are increasing (within a poly) } v[i][buf[j]] = 1 } prevSOP = SOP } for j := prevSOP; j < Omega; j++ { if buf[j] != 0 { return false // ensures padding indices are zero } } return true } // Sets p to the polynomial packed into buf by PolyPackLeGamma1. // // p will be normalized. func PolyUnpackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0x3) << 16) p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) | (uint32(buf[i+4]&0xf) << 14) p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) | (uint32(buf[i+6]&0x3f) << 12) p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) | (uint32(buf[i+8]) << 10) // coefficients in [0,…,2γ₁) p0 = Gamma1 - p0 // (-γ₁,…,γ₁] p1 = Gamma1 - p1 p2 = Gamma1 - p2 p3 = Gamma1 - p3 p0 += uint32(int32(p0)>>31) & common.Q // normalize p1 += uint32(int32(p1)>>31) & common.Q p2 += uint32(int32(p2)>>31) & common.Q p3 += uint32(int32(p3)>>31) & common.Q p[j] = p0 p[j+1] = p1 p[j+2] = p2 p[j+3] = p3 j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0xf) << 16) p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) | (uint32(buf[i+4]) << 12) p0 = Gamma1 - p0 p1 = Gamma1 - p1 p0 += uint32(int32(p0)>>31) & common.Q p1 += uint32(int32(p1)>>31) & common.Q p[j] = p0 p[j+1] = p1 j += 2 } } else { panic("γ₁ not supported") } } // Writes p whose coefficients are in (-γ₁,γ₁] into buf // which has to be of length PolyLeGamma1Size. // // Assumes p is normalized. func PolyPackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 // coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q) for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := Gamma1 - p[j] // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q) p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁) p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q p2 := Gamma1 - p[j+2] p2 += uint32(int32(p2)>>31) & common.Q p3 := Gamma1 - p[j+3] p3 += uint32(int32(p3)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<2) buf[i+3] = byte(p1 >> 6) buf[i+4] = byte(p1>>14) | byte(p2<<4) buf[i+5] = byte(p2 >> 4) buf[i+6] = byte(p2>>12) | byte(p3<<6) buf[i+7] = byte(p3 >> 2) buf[i+8] = byte(p3 >> 10) j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { // Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q) p0 := Gamma1 - p[j] p0 += uint32(int32(p0)>>31) & common.Q p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<4) buf[i+3] = byte(p1 >> 4) buf[i+4] = byte(p1 >> 12) j += 2 } } else { panic("γ₁ not supported") } } // Pack w₁ into buf, which must be of length PolyW1Size. // // Assumes w₁ is normalized. func PolyPackW1(p *common.Poly, buf []byte) { if Gamma1Bits == 19 { p.PackLe16(buf) } else if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyW1Size; i += 3 { buf[i] = byte(p[j]) | byte(p[j+1]<<6) buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4) buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2) j += 4 } } else { panic("unsupported γ₁") } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/pack_test.go000066400000000000000000000034671454601126700275600ustar00rootroot00000000000000package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestPolyPackLeqEta(t *testing.T) { var p1, p2 common.Poly var seed [64]byte var buf [PolyLeqEtaSize]byte for i := uint16(0); i < 100; i++ { // Note that DeriveUniformLeqEta sets p to the right kind of // unnormalized vector. PolyDeriveUniformLeqEta(&p1, &seed, i) for j := 0; j < PolyLeqEtaSize; j++ { if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { t.Fatalf("DerveUniformLeqEta out of bounds") } } PolyPackLeqEta(&p1, buf[:]) PolyUnpackLeqEta(&p2, buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT1(t *testing.T) { var p1, p2 common.Poly var seed [32]byte var buf [common.PolyT1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p1, &seed, i) p1.Normalize() for j := 0; j < common.N; j++ { p1[j] &= 0x1ff } p1.PackT1(buf[:]) p2.UnpackT1(buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT0(t *testing.T) { var p, p0, p1, p2 common.Poly var seed [32]byte var buf [common.PolyT0Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p, &seed, i) p.Normalize() p.Power2Round(&p0, &p1) p0.PackT0(buf[:]) p2.UnpackT0(buf[:]) if p0 != p2 { t.Fatalf("%v !=\n%v", p0, p2) } } } func BenchmarkUnpackLeGamma1(b *testing.B) { var p common.Poly var buf [PolyLeGamma1Size]byte for i := 0; i < b.N; i++ { PolyUnpackLeGamma1(&p, buf[:]) } } func TestPolyPackLeGamma1(t *testing.T) { var p0, p1 common.Poly var seed [64]byte var buf [PolyLeGamma1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniformLeGamma1(&p0, &seed, i) p0.Normalize() PolyPackLeGamma1(&p0, buf[:]) PolyUnpackLeGamma1(&p1, buf[:]) if p0 != p1 { t.Fatalf("%v != %v", p0, p1) } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/params.go000066400000000000000000000004471454601126700270610ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal const ( Name = "Dilithium3" UseAES = false K = 6 L = 5 Eta = 4 DoubleEtaBits = 4 Omega = 55 Tau = 49 Gamma1Bits = 19 Gamma2 = 261888 ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/params_test.go000066400000000000000000000103621454601126700301150ustar00rootroot00000000000000package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Tests specific to the current mode func TestVectorDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte p2 := common.Poly{ 0, 0, 1, 8380413, 8380416, 8380416, 3, 0, 1, 8380415, 8380416, 8380414, 3, 3, 8380416, 2, 1, 1, 3, 3, 3, 2, 8380414, 2, 3, 8380415, 2, 3, 8380415, 2, 3, 1, 2, 2, 1, 8380416, 2, 8380414, 0, 3, 2, 8380414, 8380415, 8380415, 1, 8380413, 8380414, 3, 0, 8380416, 8380416, 4, 2, 4, 1, 8380414, 8380416, 3, 8380416, 4, 8380413, 8380413, 8380414, 1, 8380416, 0, 8380415, 8380413, 1, 4, 8380414, 2, 0, 8380413, 4, 0, 3, 4, 8380415, 8380416, 8380414, 3, 0, 1, 1, 8380416, 1, 8380414, 8380414, 3, 3, 8380415, 8380413, 8380413, 3, 3, 2, 8380414, 0, 0, 8380414, 2, 8380414, 0, 1, 8380415, 0, 0, 8380415, 3, 8380413, 3, 8380414, 8380415, 8380414, 4, 1, 4, 2, 8380415, 3, 4, 8380413, 1, 0, 0, 1, 3, 8380414, 8380413, 4, 0, 1, 8380414, 8380414, 8380416, 8380415, 8380415, 3, 8380413, 8380414, 0, 0, 4, 0, 8380415, 3, 0, 8380413, 0, 3, 2, 8380416, 3, 2, 4, 0, 0, 8380413, 8380415, 4, 3, 3, 1, 1, 2, 8380415, 8380414, 0, 0, 8380413, 0, 2, 8380415, 4, 0, 8380415, 1, 4, 1, 2, 4, 8380415, 3, 8380414, 4, 1, 8380413, 3, 0, 2, 8380415, 8380416, 4, 8380413, 0, 3, 0, 8380414, 1, 1, 8380415, 8380416, 8380414, 8380416, 8380413, 8380416, 8380413, 8380415, 3, 4, 8380415, 0, 8380413, 8380414, 2, 4, 1, 8380415, 8380413, 3, 3, 8380415, 1, 3, 2, 8380415, 1, 8380414, 0, 2, 0, 1, 1, 3, 0, 8380413, 0, 4, 8380413, 8380413, 8380413, 4, 1, 2, 8380415, 1, 3, 4, 3, 4, 4, 8380416, 0, 2, 1, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeqEta(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestVectorDeriveUniformLeGamma1(t *testing.T) { var p, p2 common.Poly var seed [64]byte p2 = common.Poly{ 8011853, 7949494, 172552, 263871, 8095275, 155369, 311506, 8076900, 8307558, 8139232, 8041607, 448815, 380634, 180526, 8165391, 101857, 8286792, 427645, 8098920, 7860396, 352757, 8179719, 7954627, 7898860, 28800, 8129086, 111121, 8115657, 8211418, 7943538, 259410, 7965184, 8232538, 7864584, 7991749, 23725, 393449, 8344363, 8041712, 196742, 8187277, 230211, 115522, 205750, 8332267, 8020968, 511882, 66518, 8377952, 283731, 276156, 488847, 218386, 24973, 7960226, 8019608, 8163770, 8099393, 8251752, 8055784, 438808, 408276, 245718, 90648, 8179442, 377149, 66371, 8067974, 8165213, 496174, 7959821, 8174846, 416247, 8334586, 8277522, 137692, 8260481, 45327, 8078022, 8223800, 8070188, 8291718, 156021, 516504, 8144827, 361012, 323861, 8315499, 8004848, 7906709, 7913063, 230858, 311998, 8280928, 8347571, 8236825, 120069, 412722, 476656, 372912, 8036734, 465145, 8275725, 8153834, 411759, 412681, 72836, 8378216, 8305773, 8162477, 8293183, 289061, 7900478, 8133091, 100678, 267462, 254283, 242941, 8009771, 364316, 217523, 8026537, 7899325, 7863708, 211663, 339314, 8133229, 8035753, 135557, 8245724, 7988629, 8042510, 8012465, 386933, 8351229, 88508, 274815, 8293482, 216047, 8232256, 8337777, 8305592, 7938394, 378619, 7942432, 7961498, 360341, 265269, 8346169, 514971, 8255059, 406815, 222421, 8344231, 464482, 94984, 8147964, 8242727, 8211462, 7945005, 8167987, 8290153, 8355124, 303031, 180689, 97653, 8032319, 263210, 684, 437628, 7983244, 359393, 8054335, 223796, 8014878, 8066876, 335829, 467349, 105150, 326057, 229928, 7934510, 26854, 8093051, 8162834, 8013975, 8122355, 44783, 7969925, 465863, 8299023, 8155688, 8256445, 7975782, 7892171, 8075999, 412728, 7858411, 480155, 7922893, 254722, 381253, 8307390, 8040031, 280413, 8089206, 7869244, 8050145, 8028110, 8020538, 8158686, 7875907, 7960483, 7998991, 8317674, 52939, 416219, 501681, 231283, 8151233, 8241847, 8224119, 454076, 8171231, 411693, 8324986, 447356, 400055, 490491, 477035, 8055459, 158775, 383762, 8167063, 8076788, 7956883, 309585, 111368, 8312360, 7992502, 8259793, 461240, 7937002, 8198300, 7862862, 302423, 437299, 420919, 8359979, 8191730, 7895992, 75500, 307359, 435102, 7873624, 457428, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeGamma1(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/rounding.go000066400000000000000000000100521454601126700274140ustar00rootroot00000000000000package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2, // except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken // and -α/2 ≤ a₀ < 0. Returns a₀ + q. Note 0 ≤ a₁ < (q-1)/α. // Recall α = 2γ₂. func decompose(a uint32) (a0plusQ, a1 uint32) { // a₁ = ⌈a / 128⌉ a1 = (a + 127) >> 7 if Alpha == 523776 { // 1025/2²² is close enough to 1/4092 so that a₁ // becomes a/α rounded down. a1 = ((a1*1025 + (1 << 21)) >> 22) // For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0. a1 &= 15 } else if Alpha == 190464 { // 1488/2²⁴ is close enough to 1/1488 so that a₁ // becomes a/α rounded down. a1 = ((a1 * 11275) + (1 << 23)) >> 24 // For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0. a1 ^= uint32(int32(43-a1)>>31) & a1 } else { panic("unsupported α") } a0plusQ = a - a1*Alpha // In the corner-case, when we set a₁=0, we will incorrectly // have a₀ > (q-1)/2 and we'll need to subtract q. As we // return a₀ + q, that comes down to adding q if a₀ < (q-1)/2. a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q return } // Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2. Decompose r as r = r1*α + r0 as // computed by decompose(). Write r' := r - f (mod Q). Now, decompose // r'=r-f again as r' = r'1*α + r'0 using decompose(). As f is small, we // have r'1 = r1 + h, where h ∈ {-1, 0, 1}. makeHint() computes |h| // given z0 := r0 - f (mod Q) and r1. With |h|, which is called the hint, // we can reconstruct r1 using only r' = r - f, which is done by useHint(). // To wit: // // useHint( r - f, makeHint( r0 - f, r1 ) ) = r1. // // Assumes 0 ≤ z0 < Q. func makeHint(z0, r1 uint32) uint32 { // If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r' // with the restrictions of decompose() and so r'1 = r1. So the hint // should be 0. This is covered by the first two inequalities. // There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also // a valid decomposition if r1 = 0. In the other cases a one is carried // and the hint should be 1. if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) { return 0 } return 1 } // Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see // documentation of makeHint() for context. // Assumes 0 ≤ r' < Q. func useHint(rp uint32, hint uint32) uint32 { rp0plusQ, rp1 := decompose(rp) if hint == 0 { return rp1 } if rp0plusQ > common.Q { return (rp1 + 1) & 15 } return (rp1 - 1) & 15 } // Sets p to the hint polynomial for p0 the modified low bits and p1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint polynomial. func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) { for i := 0; i < common.N; i++ { h := makeHint(p0[i], p1[i]) pop += h p[i] = h } return } // Computes corrections to the high bits of the polynomial q according // to the hints in h and sets p to the corrected high bits. Returns p. func PolyUseHint(p, q, hint *common.Poly) { var q0PlusQ common.Poly // See useHint() and makeHint() for an explanation. We reimplement it // here so that we can call Poly.Decompose(), which might be way faster // than calling decompose() in a loop (for instance when having AVX2.) PolyDecompose(q, &q0PlusQ, p) for i := 0; i < common.N; i++ { if hint[i] == 0 { continue } if Gamma2 == 261888 { if q0PlusQ[i] > common.Q { p[i] = (p[i] + 1) & 15 } else { p[i] = (p[i] - 1) & 15 } } else if Gamma2 == 95232 { if q0PlusQ[i] > common.Q { if p[i] == 43 { p[i] = 0 } else { p[i]++ } } else { if p[i] == 0 { p[i] = 43 } else { p[i]-- } } } else { panic("unsupported γ₂") } } } // Splits each of the coefficients of p using decompose. func PolyDecompose(p, p0PlusQ, p1 *common.Poly) { for i := 0; i < common.N; i++ { p0PlusQ[i], p1[i] = decompose(p[i]) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/rounding_test.go000066400000000000000000000030321454601126700304530ustar00rootroot00000000000000package internal import ( "flag" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") func TestDecompose(t *testing.T) { for a := uint32(0); a < common.Q; a++ { a0PlusQ, a1 := decompose(a) a0 := int32(a0PlusQ) - int32(common.Q) recombined := a0 + int32(Alpha*a1) if a1 == 0 && recombined < 0 { recombined += common.Q if -(Alpha/2) > a0 || a0 >= 0 { t.Fatalf("decompose(%v): a0 out of bounds", a) } } else { if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) { t.Fatalf("decompose(%v): a0 out of bounds", a) } } if int32(a) != recombined { t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1) } } } func TestMakeHint(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for w := uint32(0); w < common.Q; w++ { w0, w1 := decompose(w) for fn := uint32(0); fn <= Gamma2; fn++ { fsign := false for { var f uint32 if fsign { if fn == 0 { break } f = common.Q - fn } else { f = fn } hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1) w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint) if w1p != w1 { t.Fatal() } if fsign { break } fsign = true } } } } func BenchmarkDecompose(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyDecompose(&p, &p0, &p1) } } func BenchmarkMakeHint(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyMakeHint(&p, &p0, &p1) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/sample.go000066400000000000000000000205631454601126700270600ustar00rootroot00000000000000package internal import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/simd/keccakf1600" ) // DeriveX4Available indicates whether the system supports the quick fourway // sampling variants like PolyDeriveUniformX4. var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES // For each i, sample ps[i] uniformly from the given seed and nonces[i]. // ps[i] may be nil and is ignored in that case. // // Can only be called when DeriveX4Available is true. func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // Absorb the nonces, the SHAKE128 domain separator (0b1111), the // start of the padding (0b...001) and the end of the padding 0b100... // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. for j := 0; j < 4; j++ { state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) state[20*4+j] = 0x80 << 56 } var idx [4]int // indices into ps for j := 0; j < 4; j++ { if ps[j] == nil { idx[j] = common.N // mark nil polynomial as completed } } done := false for !done { // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each // of the four SHAKE128 streams. perm.Permute() done = true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := 0; i < 7; i++ { var t [8]uint32 t[0] = uint32(state[i*3*4+j] & 0x7fffff) t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) t[2] = uint32((state[i*3*4+j] >> 48) | ((state[(i*3+1)*4+j] & 0x7f) << 16)) t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) t[5] = uint32((state[(i*3+1)*4+j] >> 56) | ((state[(i*3+2)*4+j] & 0x7fff) << 8)) t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) for k := 0; k < 8; k++ { if t[k] < common.Q { ps[j][idx[j]] = t[k] idx[j]++ if idx[j] == common.N { continue PolyLoop } } } } done = false } } } // Sample p uniformly from the given seed and nonce. // // p will be normalized. func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { var i, length int var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks if UseAES { length = 12 * 16 } else { length = 168 } sample := func() { // Note that 3 divides into 168 and 12*16, so we use up buf completely. for j := 0; j < length && i < common.N; j += 3 { t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | (uint32(buf[j+2]) << 16)) & 0x7fffff // We use rejection sampling if t < common.Q { p[i] = t i++ } } } if UseAES { h := common.NewAesStream128(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [32 + 2]byte // 32 byte seed + uint16 nonce h := sha3.NewShake128() copy(iv[:32], seed[:]) iv[32] = uint8(nonce) iv[33] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:168]) sample() } } } // Sample p uniformly with coefficients of norm less than or equal η, // using the given seed and nonce. // // p will not be normalized, but will have coefficients in [q-η,q+η]. func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) { // Assumes 2 < η < 8. var i, length int var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks if UseAES { length = 9 * 16 } else { length = 136 } sample := func() { // We use rejection sampling for j := 0; j < length && i < common.N; j++ { t1 := uint32(buf[j]) & 15 t2 := uint32(buf[j]) >> 4 if Eta == 2 { // branch is eliminated by compiler if t1 <= 14 { t1 -= ((205 * t1) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t1 i++ } if t2 <= 14 && i < common.N { t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t2 i++ } } else if Eta == 4 { if t1 <= 2*Eta { p[i] = common.Q + Eta - t1 i++ } if t2 <= 2*Eta && i < common.N { p[i] = common.Q + Eta - t2 i++ } } else { panic("unsupported η") } } } if UseAES { h := common.NewAesStream256(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [64 + 2]byte // 64 byte seed + uint16 nonce h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) // 136 is SHAKE-256 rate _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:136]) sample() } } } // Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁] using the // given seed and nonce+i // // p will be normalized. func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) { for i := 0; i < L; i++ { PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) } } // Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the // given seed and nonce. // // p will be normalized. func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) { var buf [PolyLeGamma1Size]byte if UseAES { h := common.NewAesStream256(seed, nonce) h.SqueezeInto(buf[:]) } else { var iv [66]byte h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) _, _ = h.Read(buf[:]) } PolyUnpackLeGamma1(p, buf[:]) } // For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1} // using the given seed and w1[i]. ps[i] may be nil and is ignored // in that case. ps[i] will be normalized. // // Can only be called when DeriveX4Available is true. // // This function is currently not used (yet). func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // SHAKE256 domain separator and padding for j := 0; j < 4; j++ { state[4*4+j] ^= 0x1f state[16*4+j] ^= 0x80 << 56 } perm.Permute() var signs [4]uint64 var idx [4]uint16 // indices into ps for j := 0; j < 4; j++ { if ps[j] != nil { signs[j] = state[j] *ps[j] = common.Poly{} // zero ps[j] idx[j] = common.N - Tau } else { idx[j] = common.N // mark as completed } } stateOffset := 1 for { done := true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := stateOffset; i < 17; i++ { var bs [8]byte binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) for k := 0; k < 8; k++ { b := uint16(bs[k]) if b > idx[j] { continue } ps[j][idx[j]] = ps[j][b] ps[j][b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) signs[j] >>= 1 idx[j]++ if idx[j] == common.N { continue PolyLoop } } } done = false } if done { break } perm.Permute() stateOffset = 0 } } // Samples p uniformly with τ non-zero coefficients in {q-1,1}. // // The polynomial p will be normalized. func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) { var buf [136]byte // SHAKE-256 rate is 136 h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(buf[:]) // Essentially we generate a sequence of τ ones or minus ones, // prepend 196 zeroes and shuffle the concatenation using the // usual algorithm (Fisher--Yates.) signs := binary.LittleEndian.Uint64(buf[:]) bufOff := 8 // offset into buf *p = common.Poly{} // zero p for i := uint16(common.N - Tau); i < common.N; i++ { var b uint16 // Find location of where to move the new coefficient to using // rejection sampling. for { if bufOff >= 136 { _, _ = h.Read(buf[:]) bufOff = 0 } b = uint16(buf[bufOff]) bufOff++ if b <= i { break } } p[i] = p[b] p[b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) signs >>= 1 } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/sample_test.go000066400000000000000000000203651454601126700301170ustar00rootroot00000000000000package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestVectorDeriveUniform(t *testing.T) { var p, p2 common.Poly var seed [32]byte if UseAES { p2 = common.Poly{ 6724291, 310295, 6949524, 4464039, 1482136, 2522903, 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, 583034, 4971409, 2259140, 7715362, 3975394, 2341624, 5481174, 8150082, 365246, 5491939, 1083120, 7517301, 3104783, 2475292, 184149, 6425226, 4591622, 5964030, 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, 1512596, 5245430, 5517392, 2814840, 932545, 6826733, 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, 4123492, 8124406, 4016949, 5478752, 2750895, 603525, 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, 7990594, 1105530, 7121836, 1170740, 7417431, 633146, 253820, 7235019, 3539504, 6807707, 451390, 5481526, 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, 5311519, 3057534, 5277666, 682843, 2070398, 2874278, 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, 710407, 713806, 175647, 4274571, 2655021, 7319503, 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, 649664, 1720514, 6497260, 2683517, 7672754, 7105190, 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, 4337416, 2202680, 2338714, 557467, 6752058, 2469794, 485071, 1617604, 3590498, 2151466, 2005823, 7727956, 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, 2280717, 2889355, 3233946, 5187812, 978685, 5177364, 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, 816553, 6041174, 8317591, 1459178, 5332455, 1835058, 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, 4310856, 7135453, 3481032, 652626, 1841361, 8126828, 6250018, 300536, 7380070, 8174419, 1418793, 6208185, 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, 4119736, 6584065, 441634, 6941656, } } else { p2 = common.Poly{ 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, 4352830, } } for i := 0; i < 32; i++ { seed[i] = byte(i) } PolyDeriveUniform(&p, &seed, 30000) if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestDeriveUniform(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniform(&p, &seed, uint16(i)) if !PolyNormalized(&p) { t.Fatal() } } } func TestDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if p[j] < common.Q-Eta || p[j] > common.Q+Eta { t.Fatal() } } } } func TestDeriveUniformLeGamma1(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q { t.Fatal() } } } } func TestDeriveUniformBall(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformBall(&p, &seed) nonzero := 0 for j := 0; j < common.N; j++ { if p[j] != 0 { if p[j] != 1 && p[j] != common.Q-1 { t.Fatal() } nonzero++ } } if nonzero != Tau { t.Fatal() } } } func TestDeriveUniformX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte nonces := [4]uint16{12345, 54321, 13532, 37377} for i := 0; i < len(seed); i++ { seed[i] = byte(i) } PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, nonces) for i := 0; i < 4; i++ { PolyDeriveUniform(&p, &seed, nonces[i]) if ps[i] != p { t.Fatal() } } } func TestDeriveUniformBallX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte PolyDeriveUniformBallX4( [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, ) for j := 0; j < 4; j++ { PolyDeriveUniformBall(&p, &seed) if ps[j] != p { t.Fatalf("%d\n%v\n%v", j, ps[j], p) } } } func BenchmarkPolyDeriveUniformBall(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBall(&p, &seed) } } func BenchmarkPolyDeriveUniformBallX4(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBallX4( [4]*common.Poly{&p, &p, &p, &p}, &seed, ) } } func BenchmarkPolyDeriveUniform(b *testing.B) { var seed [32]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniform(&p, &seed, uint16(i)) } } func BenchmarkPolyDeriveUniformX4(b *testing.B) { if !DeriveX4Available { b.SkipNow() } var seed [32]byte var p [4]common.Poly for i := 0; i < b.N; i++ { nonce := uint16(4 * i) PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) } } func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { var seed [64]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3/internal/vec.go000066400000000000000000000140771454601126700263570ustar00rootroot00000000000000package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A vector of L polynomials. type VecL [L]common.Poly // A vector of K polynomials. type VecK [K]common.Poly // Normalize the polynomials in this vector. func (v *VecL) Normalize() { for i := 0; i < L; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecL) NormalizeAssumingLe2Q() { for i := 0; i < L; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecL) Add(w, u *VecL) { for i := 0; i < L; i++ { v[i].Add(&w[i], &u[i]) } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecL) NTT() { for i := 0; i < L; i++ { v[i].NTT() } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecL) Exceeds(bound uint32) bool { for i := 0; i < L; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecL) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecL.PackLeqEta(). func (v *VecL) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sequentially packs each polynomial using PolyPackLeGamma1(). func (v *VecL) PackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). func (v *VecL) UnpackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Normalize the polynomials in this vector. func (v *VecK) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecK) NormalizeAssumingLe2Q() { for i := 0; i < K; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecK) Add(w, u *VecK) { for i := 0; i < K; i++ { v[i].Add(&w[i], &u[i]) } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecK) Exceeds(bound uint32) bool { for i := 0; i < K; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sets v to the hint vector for v0 the modified low bits and v1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint vector. func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { for i := 0; i < K; i++ { pop += PolyMakeHint(&v[i], &v0[i], &v1[i]) } return } // Computes corrections to the high bits of the polynomials in the vector // w using the hints in h and sets v to the corrected high bits. Returns v. // See useHint(). func (v *VecK) UseHint(q, hint *VecK) *VecK { for i := 0; i < K; i++ { PolyUseHint(&v[i], &q[i], &hint[i]) } return v } // Sequentially packs each polynomial using Poly.PackT1(). func (v *VecK) PackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT1(buf[offset:]) offset += common.PolyT1Size } } // Sets v to the vector packed into buf by PackT1(). func (v *VecK) UnpackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT1(buf[offset:]) offset += common.PolyT1Size } } // Sequentially packs each polynomial using Poly.PackT0(). func (v *VecK) PackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT0(buf[offset:]) offset += common.PolyT0Size } } // Sets v to the vector packed into buf by PackT0(). func (v *VecK) UnpackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT0(buf[offset:]) offset += common.PolyT0Size } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecK) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecK.PackLeqEta(). func (v *VecK) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecK) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sequentially packs each polynomial using PolyPackW1(). func (v *VecK) PackW1(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackW1(&v[i], buf[offset:]) offset += PolyW1Size } } // Sets v to a - b. // // Warning: assumes coefficients of the polynomials of b are less than 2q. func (v *VecK) Sub(a, b *VecK) { for i := 0; i < K; i++ { v[i].Sub(&a[i], &b[i]) } } // Sets v to 2ᵈ w without reducing. func (v *VecK) MulBy2toD(w *VecK) { for i := 0; i < K; i++ { v[i].MulBy2toD(&w[i]) } } // Applies InvNTT componentwise. See Poly.InvNTT() for details. func (v *VecK) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies Poly.ReduceLe2Q() componentwise. func (v *VecK) ReduceLe2Q() { for i := 0; i < K; i++ { v[i].ReduceLe2Q() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes.go000066400000000000000000000042261454601126700244520ustar00rootroot00000000000000// Code generated from mode.templ.go. DO NOT EDIT. package dilithium import ( "fmt" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode3aes" ) // implMode3AES implements the mode.Mode interface for Dilithium3-AES. type implMode3AES struct{} // Mode3AES is Dilithium in mode "Dilithium3-AES". var Mode3AES Mode = &implMode3AES{} func (m *implMode3AES) GenerateKey(rand io.Reader) ( PublicKey, PrivateKey, error) { return mode3aes.GenerateKey(rand) } func (m *implMode3AES) NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) { if len(seed) != common.SeedSize { panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) } seedBuf := [common.SeedSize]byte{} copy(seedBuf[:], seed) return mode3aes.NewKeyFromSeed(&seedBuf) } func (m *implMode3AES) Sign(sk PrivateKey, msg []byte) []byte { isk := sk.(*mode3aes.PrivateKey) ret := [mode3aes.SignatureSize]byte{} mode3aes.SignTo(isk, msg, ret[:]) return ret[:] } func (m *implMode3AES) Verify(pk PublicKey, msg []byte, signature []byte) bool { ipk := pk.(*mode3aes.PublicKey) return mode3aes.Verify(ipk, msg, signature) } func (m *implMode3AES) PublicKeyFromBytes(data []byte) PublicKey { var ret mode3aes.PublicKey if len(data) != mode3aes.PublicKeySize { panic("packed public key must be of mode3aes.PublicKeySize bytes") } var buf [mode3aes.PublicKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode3AES) PrivateKeyFromBytes(data []byte) PrivateKey { var ret mode3aes.PrivateKey if len(data) != mode3aes.PrivateKeySize { panic("packed public key must be of mode3aes.PrivateKeySize bytes") } var buf [mode3aes.PrivateKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode3AES) SeedSize() int { return common.SeedSize } func (m *implMode3AES) PublicKeySize() int { return mode3aes.PublicKeySize } func (m *implMode3AES) PrivateKeySize() int { return mode3aes.PrivateKeySize } func (m *implMode3AES) SignatureSize() int { return mode3aes.SignatureSize } func (m *implMode3AES) Name() string { return "Dilithium3-AES" } func init() { modes["Dilithium3-AES"] = Mode3AES } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/000077500000000000000000000000001454601126700241175ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/dilithium.go000066400000000000000000000116741454601126700264470ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // mode3aes implements the CRYSTALS-Dilithium signature scheme Dilithium3-AES // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf package mode3aes import ( "crypto" "errors" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode3aes/internal" ) const ( // Size of seed for NewKeyFromSeed SeedSize = common.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a signature SignatureSize = internal.SignatureSize ) // PublicKey is the type of Dilithium3-AES public key type PublicKey internal.PublicKey // PrivateKey is the type of Dilithium3-AES private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { pk, sk, err := internal.GenerateKey(rand) return (*PublicKey)(pk), (*PrivateKey)(sk), err } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { internal.SignTo( (*internal.PrivateKey)(sk), msg, signature, ) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { return internal.Verify( (*internal.PublicKey)(pk), msg, signature, ) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Unpack(buf) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Unpack(buf) } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Pack(buf) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Pack(buf) } // Packs the public key. func (pk *PublicKey) Bytes() []byte { var buf [PublicKeySize]byte pk.Pack(&buf) return buf[:] } // Packs the private key. func (sk *PrivateKey) Bytes() []byte { var buf [PrivateKeySize]byte sk.Pack(&buf) return buf[:] } // Packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // Packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // Unpacks the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of mode3aes.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // Unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of mode3aes.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("dilithium: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return (*PublicKey)((*internal.PrivateKey)(sk).Public()) } // Equal returns whether the two private keys equal. func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) } // Equal returns whether the two public keys equal. func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/000077500000000000000000000000001454601126700257335ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/dilithium.go000066400000000000000000000260461454601126700302620ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium.go by gen.go package internal import ( cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) const ( // Size of a packed polynomial of norm ≤η. // (Note that the formula is not valid in general.) PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 // β = τη, the maximum size of c s₂. Beta = Tau * Eta // γ₁ range of y Gamma1 = 1 << Gamma1Bits // Size of packed polynomial of norm <γ₁ such as z PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8 // α = 2γ₂ parameter for decompose Alpha = 2 * Gamma2 // Size of a packed private key PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K // Size of a packed public key PublicKeySize = 32 + common.PolyT1Size*K // Size of a packed signature SignatureSize = L*PolyLeGamma1Size + Omega + K + 32 // Size of packed w₁ PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8 ) // PublicKey is the type of Dilithium public keys. type PublicKey struct { rho [32]byte t1 VecK // Cached values t1p [common.PolyT1Size * K]byte A *Mat tr *[32]byte } // PrivateKey is the type of Dilithium private keys. type PrivateKey struct { rho [32]byte key [32]byte s1 VecL s2 VecK t0 VecK tr [32]byte // Cached values A Mat // ExpandA(ρ) s1h VecL // NTT(s₁) s2h VecK // NTT(s₂) t0h VecK // NTT(t₀) } type unpackedSignature struct { z VecL hint VecK c [32]byte } // Packs the signature into buf. func (sig *unpackedSignature) Pack(buf []byte) { copy(buf[:], sig.c[:]) sig.z.PackLeGamma1(buf[32:]) sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:]) } // Sets sig to the signature encoded in the buffer. // // Returns whether buf contains a properly packed signature. func (sig *unpackedSignature) Unpack(buf []byte) bool { if len(buf) < SignatureSize { return false } copy(sig.c[:], buf[:]) sig.z.UnpackLeGamma1(buf[32:]) if sig.z.Exceeds(Gamma1 - Beta) { return false } if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) { return false } return true } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { copy(buf[:32], pk.rho[:]) copy(buf[32:], pk.t1p[:]) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { copy(pk.rho[:], buf[:32]) copy(pk.t1p[:], buf[32:]) pk.t1.UnpackT1(pk.t1p[:]) pk.A = new(Mat) pk.A.Derive(&pk.rho) // tr = CRH(ρ ‖ t1) = CRH(pk) pk.tr = new([32]byte) h := sha3.NewShake256() _, _ = h.Write(buf[:]) _, _ = h.Read(pk.tr[:]) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { copy(buf[:32], sk.rho[:]) copy(buf[32:64], sk.key[:]) copy(buf[64:96], sk.tr[:]) offset := 96 sk.s1.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.PackT0(buf[offset:]) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { copy(sk.rho[:], buf[:32]) copy(sk.key[:], buf[32:64]) copy(sk.tr[:], buf[64:96]) offset := 96 sk.s1.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.UnpackT0(buf[offset:]) // Cached values sk.A.Derive(&sk.rho) sk.t0h = sk.t0 sk.t0h.NTT() sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [32]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { var eSeed [128]byte // expanded seed var pk PublicKey var sk PrivateKey var sSeed [64]byte h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(eSeed[:]) copy(pk.rho[:], eSeed[:32]) copy(sSeed[:], eSeed[32:96]) copy(sk.key[:], eSeed[96:]) copy(sk.rho[:], pk.rho[:]) sk.A.Derive(&pk.rho) for i := uint16(0); i < L; i++ { PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) } for i := uint16(0); i < K; i++ { PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) } sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() sk.computeT0andT1(&sk.t0, &pk.t1) sk.t0h = sk.t0 sk.t0h.NTT() // Complete public key far enough to be packed pk.t1.PackT1(pk.t1p[:]) pk.A = &sk.A // Finish private key var packedPk [PublicKeySize]byte pk.Pack(&packedPk) // tr = CRH(ρ ‖ t1) = CRH(pk) h.Reset() _, _ = h.Write(packedPk[:]) _, _ = h.Read(sk.tr[:]) // Finish cache of public key pk.tr = &sk.tr return &pk, &sk } // Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { var t VecK // Set t to A s₁ + s₂ for i := 0; i < K; i++ { PolyDotHat(&t[i], &sk.A[i], &sk.s1h) t[i].ReduceLe2Q() t[i].InvNTT() } t.Add(&t, &sk.s2) t.Normalize() // Compute t₀, t₁ = Power2Round(t) t.Power2Round(t0, t1) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { var sig unpackedSignature var mu [64]byte var zh VecL var Az, Az2dct1, w1 VecK var ch common.Poly var cp [32]byte var w1Packed [PolyW1Size * K]byte // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β // and ensured that there at most ω ones in pk.hint. if !sig.Unpack(signature) { return false } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(pk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // Compute Az zh = sig.z zh.NTT() for i := 0; i < K; i++ { PolyDotHat(&Az[i], &pk.A[i], &zh) } // Next, we compute Az - 2ᵈ·c·t₁. // Note that the coefficients of t₁ are bounded by 256 = 2⁹, // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, // which is small enough for NTT(). Az2dct1.MulBy2toD(&pk.t1) Az2dct1.NTT() PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() for i := 0; i < K; i++ { Az2dct1[i].MulHat(&Az2dct1[i], &ch) } Az2dct1.Sub(&Az, &Az2dct1) Az2dct1.ReduceLe2Q() Az2dct1.InvNTT() Az2dct1.NormalizeAssumingLe2Q() // UseHint(pk.hint, Az - 2ᵈ·c·t₁) // = UseHint(pk.hint, w - c·s₂ + c·t₀) // = UseHint(pk.hint, r + c·t₀) // = r₁ = w₁. w1.UseHint(&Az2dct1, &sig.hint) w1.PackW1(w1Packed[:]) // c' = H(μ, w₁) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(cp[:]) return sig.c == cp } // SignTo signs the given message and writes the signature into signature. // //nolint:funlen func SignTo(sk *PrivateKey, msg []byte, signature []byte) { var mu, rhop [64]byte var w1Packed [PolyW1Size * K]byte var y, yh VecL var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK var ch common.Poly var yNonce uint16 var sig unpackedSignature if len(signature) < SignatureSize { panic("Signature does not fit in that byteslice") } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(sk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // ρ' = CRH(key ‖ μ) h.Reset() _, _ = h.Write(sk.key[:]) _, _ = h.Write(mu[:]) _, _ = h.Read(rhop[:]) // Main rejection loop attempt := 0 for { attempt++ if attempt >= 576 { // Depending on the mode, one try has a chance between 1/7 and 1/4 // of succeeding. Thus it is safe to say that 576 iterations // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. panic("This should only happen 1 in 2^{128}: something is wrong.") } // y = ExpandMask(ρ', key) VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) yNonce += uint16(L) // Set w to A y yh = y yh.NTT() for i := 0; i < K; i++ { PolyDotHat(&w[i], &sk.A[i], &yh) w[i].ReduceLe2Q() w[i].InvNTT() } // Decompose w into w₀ and w₁ w.NormalizeAssumingLe2Q() w.Decompose(&w0, &w1) // c~ = H(μ ‖ w₁) w1.PackW1(w1Packed[:]) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(sig.c[:]) PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. // // By Lemma 3 of the specification this is equivalent to checking that // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition // w - c·s₂ = r₁ α + r₀ as computed by decompose(). // See also §4.1 of the specification. for i := 0; i < K; i++ { w0mcs2[i].MulHat(&ch, &sk.s2h[i]) w0mcs2[i].InvNTT() } w0mcs2.Sub(&w0, &w0mcs2) w0mcs2.Normalize() if w0mcs2.Exceeds(Gamma2 - Beta) { continue } // z = y + c·s₁ for i := 0; i < L; i++ { sig.z[i].MulHat(&ch, &sk.s1h[i]) sig.z[i].InvNTT() } sig.z.Add(&sig.z, &y) sig.z.Normalize() // Ensure ‖z‖_∞ < γ₁ - β if sig.z.Exceeds(Gamma1 - Beta) { continue } // Compute c·t₀ for i := 0; i < K; i++ { ct0[i].MulHat(&ch, &sk.t0h[i]) ct0[i].InvNTT() } ct0.NormalizeAssumingLe2Q() // Ensure ‖c·t₀‖_∞ < γ₂. if ct0.Exceeds(Gamma2) { continue } // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. // Note that we're not using makeHint() in the obvious way as we // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note // that our makeHint() is actually the same as a makeHint for a // different decomposition: // // Earlier we ensured indirectly with a check that r₁ = w₁ where // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. w0mcs2pct0.Add(&w0mcs2, &ct0) w0mcs2pct0.NormalizeAssumingLe2Q() hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) if hintPop > Omega { continue } break } sig.Pack(signature[:]) } // Computes the public key corresponding to this private key. func (sk *PrivateKey) Public() *PublicKey { var t0 VecK pk := &PublicKey{ rho: sk.rho, A: &sk.A, tr: &sk.tr, } sk.computeT0andT1(&t0, &pk.t1) pk.t1.PackT1(pk.t1p[:]) return pk } // Equal returns whether the two public keys are equal func (pk *PublicKey) Equal(other *PublicKey) bool { return pk.rho == other.rho && pk.t1 == other.t1 } // Equal returns whether the two private keys are equal func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) acc := uint32(0) for i := 0; i < L; i++ { for j := 0; j < common.N; j++ { acc |= sk.s1[i][j] ^ other.s1[i][j] } } for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { acc |= sk.s2[i][j] ^ other.s2[i][j] acc |= sk.t0[i][j] ^ other.t0[i][j] } } return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/dilithium_test.go000066400000000000000000000062731454601126700313210ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Checks whether p is normalized. Only used in tests. func PolyNormalized(p *common.Poly) bool { p2 := *p p2.Normalize() return p2 == *p } func BenchmarkSkUnpack(b *testing.B) { var buf [PrivateKeySize]byte var sk PrivateKey for i := 0; i < b.N; i++ { sk.Unpack(&buf) } } func BenchmarkPkUnpack(b *testing.B) { var buf [PublicKeySize]byte var pk PublicKey for i := 0; i < b.N; i++ { pk.Unpack(&buf) } } func BenchmarkVerify(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of verification (as in the reference // implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte pk, sk := NewKeyFromSeed(&seed) SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of signing (as in the reference implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte _, sk := NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [common.SeedSize]byte var sig [SignatureSize]byte var msg [8]byte var pkb [PublicKeySize]byte var skb [PrivateKeySize]byte var pk2 PublicKey var sk2 PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) if !sk.Equal(sk) { t.Fatal() } for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) SignTo(sk, msg[:], sig[:]) if !Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb) pk2.Unpack(&pkb) if !pk.Equal(&pk2) { t.Fatal() } sk.Pack(&skb) sk2.Unpack(&skb) if !sk.Equal(&sk2) { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [common.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) pk2 := sk.Public() if !pk.Equal(pk2) { t.Fatal() } } } func TestGamma1Size(t *testing.T) { var expected int switch Gamma1Bits { case 17: expected = 576 case 19: expected = 640 } if expected != PolyLeGamma1Size { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/mat.go000066400000000000000000000024411454601126700270440ustar00rootroot00000000000000// Code generated from mode3/internal/mat.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A k by l matrix of polynomials. type Mat [K]VecL // Expands the given seed to a complete matrix. // // This function is called ExpandA in the specification. func (m *Mat) Derive(seed *[32]byte) { if !DeriveX4Available { for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) } } return } idx := 0 var nonces [4]uint16 var ps [4]*common.Poly for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { nonces[idx] = (i << 8) + j ps[idx] = &m[i][j] idx++ if idx == 4 { idx = 0 PolyDeriveUniformX4(ps, seed, nonces) } } } if idx != 0 { for i := idx; i < 4; i++ { ps[i] = nil } PolyDeriveUniformX4(ps, seed, nonces) } } // Set p to the inner product of a and b using pointwise multiplication. // // Assumes a and b are in Montgomery form and their coefficients are // pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting // coefficients are bounded by 2Lq. func PolyDotHat(p *common.Poly, a, b *VecL) { var t common.Poly *p = common.Poly{} // zero p for i := 0; i < L; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/pack.go000066400000000000000000000164511454601126700272070ustar00rootroot00000000000000// Code generated from mode3/internal/pack.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Writes p with norm less than or equal η into buf, which must be of // size PolyLeqEtaSize. // // Assumes coefficients of p are not normalized, but in [q-η,q+η]. func PolyPackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { buf[i] = (byte(common.Q+Eta-p[j]) | byte(common.Q+Eta-p[j+1])<<4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { buf[i] = (byte(common.Q+Eta-p[j]) | (byte(common.Q+Eta-p[j+1]) << 3) | (byte(common.Q+Eta-p[j+2]) << 6)) buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | (byte(common.Q+Eta-p[j+3]) << 1) | (byte(common.Q+Eta-p[j+4]) << 4) | (byte(common.Q+Eta-p[j+5]) << 7)) buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | (byte(common.Q+Eta-p[j+6]) << 2) | (byte(common.Q+Eta-p[j+7]) << 5)) j += 8 } } else { panic("eta not supported") } } // Sets p to the polynomial of norm less than or equal η encoded in the // given buffer of size PolyLeqEtaSize. // // Output coefficients of p are not normalized, but in [q-η,q+η] provided // buf was created using PackLeqEta. // // Beware, for arbitrary buf the coefficients of p might end up in // the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. func PolyUnpackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { p[j] = common.Q + Eta - uint32(buf[i]&15) p[j+1] = common.Q + Eta - uint32(buf[i]>>4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { p[j] = common.Q + Eta - uint32(buf[i]&7) p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) j += 8 } } else { panic("eta not supported") } } // Writes v with coefficients in {0, 1} of which at most ω non-zero // to buf, which must have length ω+k. func (v *VecK) PackHint(buf []byte) { // The packed hint starts with the indices of the non-zero coefficients // For instance: // // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) // // Yields // // 56, 100, 255, 2, 23, 1 // // Then we pad with zeroes until we have a list of ω items: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 // // Then we finish with a list of the switch-over-indices in this // list between polynomials, so: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 off := uint8(0) for i := 0; i < K; i++ { for j := uint16(0); j < common.N; j++ { if v[i][j] != 0 { buf[off] = uint8(j) off++ } } buf[Omega+i] = off } for ; off < Omega; off++ { buf[off] = 0 } } // Sets v to the vector encoded using VecK.PackHint() // // Returns whether unpacking was successful. func (v *VecK) UnpackHint(buf []byte) bool { // A priori, there would be several reasonable ways to encode the same // hint vector. We take care to only allow only one encoding, to ensure // "strong unforgeability". // // See PackHint() source for description of the encoding. *v = VecK{} // zero v prevSOP := uint8(0) // previous switch-over-point for i := 0; i < K; i++ { SOP := buf[Omega+i] if SOP < prevSOP || SOP > Omega { return false // ensures switch-over-points are increasing } for j := prevSOP; j < SOP; j++ { if j > prevSOP && buf[j] <= buf[j-1] { return false // ensures indices are increasing (within a poly) } v[i][buf[j]] = 1 } prevSOP = SOP } for j := prevSOP; j < Omega; j++ { if buf[j] != 0 { return false // ensures padding indices are zero } } return true } // Sets p to the polynomial packed into buf by PolyPackLeGamma1. // // p will be normalized. func PolyUnpackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0x3) << 16) p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) | (uint32(buf[i+4]&0xf) << 14) p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) | (uint32(buf[i+6]&0x3f) << 12) p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) | (uint32(buf[i+8]) << 10) // coefficients in [0,…,2γ₁) p0 = Gamma1 - p0 // (-γ₁,…,γ₁] p1 = Gamma1 - p1 p2 = Gamma1 - p2 p3 = Gamma1 - p3 p0 += uint32(int32(p0)>>31) & common.Q // normalize p1 += uint32(int32(p1)>>31) & common.Q p2 += uint32(int32(p2)>>31) & common.Q p3 += uint32(int32(p3)>>31) & common.Q p[j] = p0 p[j+1] = p1 p[j+2] = p2 p[j+3] = p3 j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0xf) << 16) p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) | (uint32(buf[i+4]) << 12) p0 = Gamma1 - p0 p1 = Gamma1 - p1 p0 += uint32(int32(p0)>>31) & common.Q p1 += uint32(int32(p1)>>31) & common.Q p[j] = p0 p[j+1] = p1 j += 2 } } else { panic("γ₁ not supported") } } // Writes p whose coefficients are in (-γ₁,γ₁] into buf // which has to be of length PolyLeGamma1Size. // // Assumes p is normalized. func PolyPackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 // coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q) for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := Gamma1 - p[j] // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q) p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁) p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q p2 := Gamma1 - p[j+2] p2 += uint32(int32(p2)>>31) & common.Q p3 := Gamma1 - p[j+3] p3 += uint32(int32(p3)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<2) buf[i+3] = byte(p1 >> 6) buf[i+4] = byte(p1>>14) | byte(p2<<4) buf[i+5] = byte(p2 >> 4) buf[i+6] = byte(p2>>12) | byte(p3<<6) buf[i+7] = byte(p3 >> 2) buf[i+8] = byte(p3 >> 10) j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { // Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q) p0 := Gamma1 - p[j] p0 += uint32(int32(p0)>>31) & common.Q p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<4) buf[i+3] = byte(p1 >> 4) buf[i+4] = byte(p1 >> 12) j += 2 } } else { panic("γ₁ not supported") } } // Pack w₁ into buf, which must be of length PolyW1Size. // // Assumes w₁ is normalized. func PolyPackW1(p *common.Poly, buf []byte) { if Gamma1Bits == 19 { p.PackLe16(buf) } else if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyW1Size; i += 3 { buf[i] = byte(p[j]) | byte(p[j+1]<<6) buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4) buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2) j += 4 } } else { panic("unsupported γ₁") } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/pack_test.go000066400000000000000000000035651454601126700302500ustar00rootroot00000000000000// Code generated from mode3/internal/pack_test.go by gen.go package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestPolyPackLeqEta(t *testing.T) { var p1, p2 common.Poly var seed [64]byte var buf [PolyLeqEtaSize]byte for i := uint16(0); i < 100; i++ { // Note that DeriveUniformLeqEta sets p to the right kind of // unnormalized vector. PolyDeriveUniformLeqEta(&p1, &seed, i) for j := 0; j < PolyLeqEtaSize; j++ { if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { t.Fatalf("DerveUniformLeqEta out of bounds") } } PolyPackLeqEta(&p1, buf[:]) PolyUnpackLeqEta(&p2, buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT1(t *testing.T) { var p1, p2 common.Poly var seed [32]byte var buf [common.PolyT1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p1, &seed, i) p1.Normalize() for j := 0; j < common.N; j++ { p1[j] &= 0x1ff } p1.PackT1(buf[:]) p2.UnpackT1(buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT0(t *testing.T) { var p, p0, p1, p2 common.Poly var seed [32]byte var buf [common.PolyT0Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p, &seed, i) p.Normalize() p.Power2Round(&p0, &p1) p0.PackT0(buf[:]) p2.UnpackT0(buf[:]) if p0 != p2 { t.Fatalf("%v !=\n%v", p0, p2) } } } func BenchmarkUnpackLeGamma1(b *testing.B) { var p common.Poly var buf [PolyLeGamma1Size]byte for i := 0; i < b.N; i++ { PolyUnpackLeGamma1(&p, buf[:]) } } func TestPolyPackLeGamma1(t *testing.T) { var p0, p1 common.Poly var seed [64]byte var buf [PolyLeGamma1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniformLeGamma1(&p0, &seed, i) p0.Normalize() PolyPackLeGamma1(&p0, buf[:]) PolyUnpackLeGamma1(&p1, buf[:]) if p0 != p1 { t.Fatalf("%v != %v", p0, p1) } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/params.go000066400000000000000000000004521454601126700275460ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal const ( Name = "Dilithium3-AES" UseAES = true K = 6 L = 5 Eta = 4 DoubleEtaBits = 4 Omega = 55 Tau = 49 Gamma1Bits = 19 Gamma2 = 261888 ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/params_test.go000066400000000000000000000104331454601126700306050ustar00rootroot00000000000000package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Tests specific to the current mode func TestVectorDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte p2 := common.Poly{ 1, 8380415, 8380415, 8380414, 3, 0, 4, 0, 4, 8380415, 8380414, 3, 0, 0, 8380413, 8380415, 3, 8380414, 3, 8380414, 8380415, 1, 3, 1, 8380415, 4, 8380414, 8380416, 2, 8380415, 4, 8380415, 3, 2, 3, 0, 1, 8380415, 2, 4, 8380413, 8380413, 1, 8380416, 3, 0, 8380416, 3, 0, 8380416, 8380414, 3, 8380416, 8380413, 2, 1, 3, 8380414, 8380416, 8380413, 4, 3, 0, 0, 8380413, 8380414, 2, 2, 2, 2, 8380416, 8380414, 2, 8380413, 8380413, 1, 8380415, 2, 1, 8380416, 2, 0, 8380416, 2, 8380416, 8380413, 1, 1, 8380416, 4, 8380415, 8380413, 4, 3, 8380416, 8380414, 0, 2, 4, 4, 8380415, 2, 3, 8380416, 8380416, 2, 8380416, 8380416, 2, 4, 8380413, 4, 2, 8380415, 4, 4, 3, 8380415, 0, 4, 4, 0, 4, 2, 8380413, 0, 0, 8380414, 8380414, 1, 1, 8380413, 8380416, 2, 8380413, 4, 8380416, 3, 8380416, 8380415, 8380415, 2, 0, 1, 8380416, 8380413, 3, 1, 4, 1, 8380416, 0, 8380415, 8380415, 2, 2, 0, 2, 3, 4, 1, 4, 2, 2, 8380414, 1, 8380414, 4, 1, 2, 3, 2, 8380413, 8380416, 0, 8380415, 8380414, 2, 3, 2, 8380416, 8380415, 2, 4, 8380414, 2, 2, 8380413, 8380415, 4, 0, 0, 3, 8380414, 8380415, 4, 4, 8380416, 4, 8380416, 4, 1, 0, 8380413, 8380414, 1, 3, 1, 8380413, 2, 8380413, 8380415, 1, 1, 8380416, 0, 8380416, 2, 8380413, 8380416, 3, 1, 2, 3, 8380415, 8380416, 8380416, 8380414, 8380415, 4, 8380416, 0, 8380415, 1, 8380415, 8380414, 8380414, 8380416, 1, 0, 4, 8380415, 1, 2, 8380416, 8380413, 8380416, 1, 4, 8380414, 8380416, 8380414, 8380416, 8380415, 3, 4, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeqEta(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestVectorDeriveUniformLeGamma1(t *testing.T) { var p, p2 common.Poly var seed [64]byte p2 = common.Poly{ 91453, 8134283, 8211453, 8218977, 8362980, 431655, 98537, 320966, 7892886, 144675, 495826, 7910635, 308711, 8024934, 8314212, 8323958, 8242606, 7947101, 419492, 427692, 354075, 21485, 456475, 213575, 362300, 8142303, 8322444, 7885879, 89158, 181715, 8094655, 8303634, 8060028, 7920325, 192378, 7910586, 7897074, 8097343, 7899868, 8339413, 73206, 237312, 8183555, 348083, 8154041, 8364746, 8078364, 8312790, 105195, 8037823, 8356712, 7994594, 240882, 70742, 8109371, 8176349, 467152, 51422, 340432, 8030176, 342172, 154911, 64858, 97614, 212758, 8285880, 521738, 326395, 296748, 8111442, 8016327, 7953747, 158922, 330421, 8331843, 449771, 168214, 8198309, 8228760, 7940533, 2498, 305217, 475829, 8037995, 8250962, 305070, 8217080, 432779, 213808, 8162729, 381514, 7995827, 7989202, 129047, 246099, 67554, 8233257, 398954, 223629, 444125, 150369, 223365, 159236, 55259, 172419, 163583, 354428, 8263789, 8017325, 8229594, 32340, 490228, 450684, 8069619, 53733, 7932894, 7955848, 8197876, 201557, 8307246, 446889, 8211538, 7889784, 8071108, 496027, 8159198, 8037, 7973907, 248186, 4806, 185437, 457847, 138862, 8124477, 284692, 8255820, 8068729, 8292005, 244272, 8061114, 21475, 8058902, 421466, 8306487, 455649, 8218652, 7634, 148216, 7951766, 394889, 8127579, 366374, 8062903, 8139245, 367068, 8281027, 734, 396374, 7969282, 7977632, 8098596, 343569, 8191282, 223874, 163783, 203572, 109732, 8229113, 8128208, 321529, 296492, 8202474, 50404, 8336017, 8190899, 8191497, 8279167, 336877, 7878526, 7922949, 7974614, 8076047, 8201365, 8334333, 416495, 8090175, 150066, 7947253, 474615, 7937629, 8027358, 356569, 191566, 87441, 8219157, 8375553, 8029697, 8026188, 8193863, 295873, 7906281, 487687, 8363474, 386621, 282726, 8373831, 50680, 8239505, 7912018, 493972, 8335677, 8079840, 251210, 263667, 221541, 41291, 88028, 8373098, 505241, 7981448, 8308113, 299485, 428036, 93865, 90428, 392003, 80833, 7975521, 336649, 7950328, 8049195, 8332757, 8205291, 8178296, 7911197, 7925805, 519154, 60176, 54121, 222738, 464285, 8022604, 8174235, 7856202, 8291898, 473254, 8106411, 7943812, 267650, 7958173, 372387, 409597, 204263, 477847, 83925, 111791, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeGamma1(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/rounding.go000066400000000000000000000101471454601126700301120ustar00rootroot00000000000000// Code generated from mode3/internal/rounding.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2, // except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken // and -α/2 ≤ a₀ < 0. Returns a₀ + q. Note 0 ≤ a₁ < (q-1)/α. // Recall α = 2γ₂. func decompose(a uint32) (a0plusQ, a1 uint32) { // a₁ = ⌈a / 128⌉ a1 = (a + 127) >> 7 if Alpha == 523776 { // 1025/2²² is close enough to 1/4092 so that a₁ // becomes a/α rounded down. a1 = ((a1*1025 + (1 << 21)) >> 22) // For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0. a1 &= 15 } else if Alpha == 190464 { // 1488/2²⁴ is close enough to 1/1488 so that a₁ // becomes a/α rounded down. a1 = ((a1 * 11275) + (1 << 23)) >> 24 // For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0. a1 ^= uint32(int32(43-a1)>>31) & a1 } else { panic("unsupported α") } a0plusQ = a - a1*Alpha // In the corner-case, when we set a₁=0, we will incorrectly // have a₀ > (q-1)/2 and we'll need to subtract q. As we // return a₀ + q, that comes down to adding q if a₀ < (q-1)/2. a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q return } // Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2. Decompose r as r = r1*α + r0 as // computed by decompose(). Write r' := r - f (mod Q). Now, decompose // r'=r-f again as r' = r'1*α + r'0 using decompose(). As f is small, we // have r'1 = r1 + h, where h ∈ {-1, 0, 1}. makeHint() computes |h| // given z0 := r0 - f (mod Q) and r1. With |h|, which is called the hint, // we can reconstruct r1 using only r' = r - f, which is done by useHint(). // To wit: // // useHint( r - f, makeHint( r0 - f, r1 ) ) = r1. // // Assumes 0 ≤ z0 < Q. func makeHint(z0, r1 uint32) uint32 { // If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r' // with the restrictions of decompose() and so r'1 = r1. So the hint // should be 0. This is covered by the first two inequalities. // There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also // a valid decomposition if r1 = 0. In the other cases a one is carried // and the hint should be 1. if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) { return 0 } return 1 } // Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see // documentation of makeHint() for context. // Assumes 0 ≤ r' < Q. func useHint(rp uint32, hint uint32) uint32 { rp0plusQ, rp1 := decompose(rp) if hint == 0 { return rp1 } if rp0plusQ > common.Q { return (rp1 + 1) & 15 } return (rp1 - 1) & 15 } // Sets p to the hint polynomial for p0 the modified low bits and p1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint polynomial. func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) { for i := 0; i < common.N; i++ { h := makeHint(p0[i], p1[i]) pop += h p[i] = h } return } // Computes corrections to the high bits of the polynomial q according // to the hints in h and sets p to the corrected high bits. Returns p. func PolyUseHint(p, q, hint *common.Poly) { var q0PlusQ common.Poly // See useHint() and makeHint() for an explanation. We reimplement it // here so that we can call Poly.Decompose(), which might be way faster // than calling decompose() in a loop (for instance when having AVX2.) PolyDecompose(q, &q0PlusQ, p) for i := 0; i < common.N; i++ { if hint[i] == 0 { continue } if Gamma2 == 261888 { if q0PlusQ[i] > common.Q { p[i] = (p[i] + 1) & 15 } else { p[i] = (p[i] - 1) & 15 } } else if Gamma2 == 95232 { if q0PlusQ[i] > common.Q { if p[i] == 43 { p[i] = 0 } else { p[i]++ } } else { if p[i] == 0 { p[i] = 43 } else { p[i]-- } } } else { panic("unsupported γ₂") } } } // Splits each of the coefficients of p using decompose. func PolyDecompose(p, p0PlusQ, p1 *common.Poly) { for i := 0; i < common.N; i++ { p0PlusQ[i], p1[i] = decompose(p[i]) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/rounding_test.go000066400000000000000000000031341454601126700311470ustar00rootroot00000000000000// Code generated from mode3/internal/rounding_test.go by gen.go package internal import ( "flag" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") func TestDecompose(t *testing.T) { for a := uint32(0); a < common.Q; a++ { a0PlusQ, a1 := decompose(a) a0 := int32(a0PlusQ) - int32(common.Q) recombined := a0 + int32(Alpha*a1) if a1 == 0 && recombined < 0 { recombined += common.Q if -(Alpha/2) > a0 || a0 >= 0 { t.Fatalf("decompose(%v): a0 out of bounds", a) } } else { if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) { t.Fatalf("decompose(%v): a0 out of bounds", a) } } if int32(a) != recombined { t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1) } } } func TestMakeHint(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for w := uint32(0); w < common.Q; w++ { w0, w1 := decompose(w) for fn := uint32(0); fn <= Gamma2; fn++ { fsign := false for { var f uint32 if fsign { if fn == 0 { break } f = common.Q - fn } else { f = fn } hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1) w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint) if w1p != w1 { t.Fatal() } if fsign { break } fsign = true } } } } func BenchmarkDecompose(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyDecompose(&p, &p0, &p1) } } func BenchmarkMakeHint(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyMakeHint(&p, &p0, &p1) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/sample.go000066400000000000000000000206561454601126700275540ustar00rootroot00000000000000// Code generated from mode3/internal/sample.go by gen.go package internal import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/simd/keccakf1600" ) // DeriveX4Available indicates whether the system supports the quick fourway // sampling variants like PolyDeriveUniformX4. var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES // For each i, sample ps[i] uniformly from the given seed and nonces[i]. // ps[i] may be nil and is ignored in that case. // // Can only be called when DeriveX4Available is true. func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // Absorb the nonces, the SHAKE128 domain separator (0b1111), the // start of the padding (0b...001) and the end of the padding 0b100... // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. for j := 0; j < 4; j++ { state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) state[20*4+j] = 0x80 << 56 } var idx [4]int // indices into ps for j := 0; j < 4; j++ { if ps[j] == nil { idx[j] = common.N // mark nil polynomial as completed } } done := false for !done { // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each // of the four SHAKE128 streams. perm.Permute() done = true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := 0; i < 7; i++ { var t [8]uint32 t[0] = uint32(state[i*3*4+j] & 0x7fffff) t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) t[2] = uint32((state[i*3*4+j] >> 48) | ((state[(i*3+1)*4+j] & 0x7f) << 16)) t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) t[5] = uint32((state[(i*3+1)*4+j] >> 56) | ((state[(i*3+2)*4+j] & 0x7fff) << 8)) t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) for k := 0; k < 8; k++ { if t[k] < common.Q { ps[j][idx[j]] = t[k] idx[j]++ if idx[j] == common.N { continue PolyLoop } } } } done = false } } } // Sample p uniformly from the given seed and nonce. // // p will be normalized. func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { var i, length int var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks if UseAES { length = 12 * 16 } else { length = 168 } sample := func() { // Note that 3 divides into 168 and 12*16, so we use up buf completely. for j := 0; j < length && i < common.N; j += 3 { t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | (uint32(buf[j+2]) << 16)) & 0x7fffff // We use rejection sampling if t < common.Q { p[i] = t i++ } } } if UseAES { h := common.NewAesStream128(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [32 + 2]byte // 32 byte seed + uint16 nonce h := sha3.NewShake128() copy(iv[:32], seed[:]) iv[32] = uint8(nonce) iv[33] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:168]) sample() } } } // Sample p uniformly with coefficients of norm less than or equal η, // using the given seed and nonce. // // p will not be normalized, but will have coefficients in [q-η,q+η]. func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) { // Assumes 2 < η < 8. var i, length int var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks if UseAES { length = 9 * 16 } else { length = 136 } sample := func() { // We use rejection sampling for j := 0; j < length && i < common.N; j++ { t1 := uint32(buf[j]) & 15 t2 := uint32(buf[j]) >> 4 if Eta == 2 { // branch is eliminated by compiler if t1 <= 14 { t1 -= ((205 * t1) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t1 i++ } if t2 <= 14 && i < common.N { t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t2 i++ } } else if Eta == 4 { if t1 <= 2*Eta { p[i] = common.Q + Eta - t1 i++ } if t2 <= 2*Eta && i < common.N { p[i] = common.Q + Eta - t2 i++ } } else { panic("unsupported η") } } } if UseAES { h := common.NewAesStream256(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [64 + 2]byte // 64 byte seed + uint16 nonce h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) // 136 is SHAKE-256 rate _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:136]) sample() } } } // Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁] using the // given seed and nonce+i // // p will be normalized. func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) { for i := 0; i < L; i++ { PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) } } // Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the // given seed and nonce. // // p will be normalized. func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) { var buf [PolyLeGamma1Size]byte if UseAES { h := common.NewAesStream256(seed, nonce) h.SqueezeInto(buf[:]) } else { var iv [66]byte h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) _, _ = h.Read(buf[:]) } PolyUnpackLeGamma1(p, buf[:]) } // For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1} // using the given seed and w1[i]. ps[i] may be nil and is ignored // in that case. ps[i] will be normalized. // // Can only be called when DeriveX4Available is true. // // This function is currently not used (yet). func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // SHAKE256 domain separator and padding for j := 0; j < 4; j++ { state[4*4+j] ^= 0x1f state[16*4+j] ^= 0x80 << 56 } perm.Permute() var signs [4]uint64 var idx [4]uint16 // indices into ps for j := 0; j < 4; j++ { if ps[j] != nil { signs[j] = state[j] *ps[j] = common.Poly{} // zero ps[j] idx[j] = common.N - Tau } else { idx[j] = common.N // mark as completed } } stateOffset := 1 for { done := true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := stateOffset; i < 17; i++ { var bs [8]byte binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) for k := 0; k < 8; k++ { b := uint16(bs[k]) if b > idx[j] { continue } ps[j][idx[j]] = ps[j][b] ps[j][b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) signs[j] >>= 1 idx[j]++ if idx[j] == common.N { continue PolyLoop } } } done = false } if done { break } perm.Permute() stateOffset = 0 } } // Samples p uniformly with τ non-zero coefficients in {q-1,1}. // // The polynomial p will be normalized. func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) { var buf [136]byte // SHAKE-256 rate is 136 h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(buf[:]) // Essentially we generate a sequence of τ ones or minus ones, // prepend 196 zeroes and shuffle the concatenation using the // usual algorithm (Fisher--Yates.) signs := binary.LittleEndian.Uint64(buf[:]) bufOff := 8 // offset into buf *p = common.Poly{} // zero p for i := uint16(common.N - Tau); i < common.N; i++ { var b uint16 // Find location of where to move the new coefficient to using // rejection sampling. for { if bufOff >= 136 { _, _ = h.Read(buf[:]) bufOff = 0 } b = uint16(buf[bufOff]) bufOff++ if b <= i { break } } p[i] = p[b] p[b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) signs >>= 1 } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/sample_test.go000066400000000000000000000204651454601126700306110ustar00rootroot00000000000000// Code generated from mode3/internal/sample_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestVectorDeriveUniform(t *testing.T) { var p, p2 common.Poly var seed [32]byte if UseAES { p2 = common.Poly{ 6724291, 310295, 6949524, 4464039, 1482136, 2522903, 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, 583034, 4971409, 2259140, 7715362, 3975394, 2341624, 5481174, 8150082, 365246, 5491939, 1083120, 7517301, 3104783, 2475292, 184149, 6425226, 4591622, 5964030, 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, 1512596, 5245430, 5517392, 2814840, 932545, 6826733, 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, 4123492, 8124406, 4016949, 5478752, 2750895, 603525, 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, 7990594, 1105530, 7121836, 1170740, 7417431, 633146, 253820, 7235019, 3539504, 6807707, 451390, 5481526, 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, 5311519, 3057534, 5277666, 682843, 2070398, 2874278, 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, 710407, 713806, 175647, 4274571, 2655021, 7319503, 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, 649664, 1720514, 6497260, 2683517, 7672754, 7105190, 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, 4337416, 2202680, 2338714, 557467, 6752058, 2469794, 485071, 1617604, 3590498, 2151466, 2005823, 7727956, 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, 2280717, 2889355, 3233946, 5187812, 978685, 5177364, 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, 816553, 6041174, 8317591, 1459178, 5332455, 1835058, 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, 4310856, 7135453, 3481032, 652626, 1841361, 8126828, 6250018, 300536, 7380070, 8174419, 1418793, 6208185, 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, 4119736, 6584065, 441634, 6941656, } } else { p2 = common.Poly{ 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, 4352830, } } for i := 0; i < 32; i++ { seed[i] = byte(i) } PolyDeriveUniform(&p, &seed, 30000) if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestDeriveUniform(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniform(&p, &seed, uint16(i)) if !PolyNormalized(&p) { t.Fatal() } } } func TestDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if p[j] < common.Q-Eta || p[j] > common.Q+Eta { t.Fatal() } } } } func TestDeriveUniformLeGamma1(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q { t.Fatal() } } } } func TestDeriveUniformBall(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformBall(&p, &seed) nonzero := 0 for j := 0; j < common.N; j++ { if p[j] != 0 { if p[j] != 1 && p[j] != common.Q-1 { t.Fatal() } nonzero++ } } if nonzero != Tau { t.Fatal() } } } func TestDeriveUniformX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte nonces := [4]uint16{12345, 54321, 13532, 37377} for i := 0; i < len(seed); i++ { seed[i] = byte(i) } PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, nonces) for i := 0; i < 4; i++ { PolyDeriveUniform(&p, &seed, nonces[i]) if ps[i] != p { t.Fatal() } } } func TestDeriveUniformBallX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte PolyDeriveUniformBallX4( [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, ) for j := 0; j < 4; j++ { PolyDeriveUniformBall(&p, &seed) if ps[j] != p { t.Fatalf("%d\n%v\n%v", j, ps[j], p) } } } func BenchmarkPolyDeriveUniformBall(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBall(&p, &seed) } } func BenchmarkPolyDeriveUniformBallX4(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBallX4( [4]*common.Poly{&p, &p, &p, &p}, &seed, ) } } func BenchmarkPolyDeriveUniform(b *testing.B) { var seed [32]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniform(&p, &seed, uint16(i)) } } func BenchmarkPolyDeriveUniformX4(b *testing.B) { if !DeriveX4Available { b.SkipNow() } var seed [32]byte var p [4]common.Poly for i := 0; i < b.N; i++ { nonce := uint16(4 * i) PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) } } func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { var seed [64]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode3aes/internal/vec.go000066400000000000000000000141671454601126700270500ustar00rootroot00000000000000// Code generated from mode3/internal/vec.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A vector of L polynomials. type VecL [L]common.Poly // A vector of K polynomials. type VecK [K]common.Poly // Normalize the polynomials in this vector. func (v *VecL) Normalize() { for i := 0; i < L; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecL) NormalizeAssumingLe2Q() { for i := 0; i < L; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecL) Add(w, u *VecL) { for i := 0; i < L; i++ { v[i].Add(&w[i], &u[i]) } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecL) NTT() { for i := 0; i < L; i++ { v[i].NTT() } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecL) Exceeds(bound uint32) bool { for i := 0; i < L; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecL) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecL.PackLeqEta(). func (v *VecL) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sequentially packs each polynomial using PolyPackLeGamma1(). func (v *VecL) PackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). func (v *VecL) UnpackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Normalize the polynomials in this vector. func (v *VecK) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecK) NormalizeAssumingLe2Q() { for i := 0; i < K; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecK) Add(w, u *VecK) { for i := 0; i < K; i++ { v[i].Add(&w[i], &u[i]) } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecK) Exceeds(bound uint32) bool { for i := 0; i < K; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sets v to the hint vector for v0 the modified low bits and v1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint vector. func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { for i := 0; i < K; i++ { pop += PolyMakeHint(&v[i], &v0[i], &v1[i]) } return } // Computes corrections to the high bits of the polynomials in the vector // w using the hints in h and sets v to the corrected high bits. Returns v. // See useHint(). func (v *VecK) UseHint(q, hint *VecK) *VecK { for i := 0; i < K; i++ { PolyUseHint(&v[i], &q[i], &hint[i]) } return v } // Sequentially packs each polynomial using Poly.PackT1(). func (v *VecK) PackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT1(buf[offset:]) offset += common.PolyT1Size } } // Sets v to the vector packed into buf by PackT1(). func (v *VecK) UnpackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT1(buf[offset:]) offset += common.PolyT1Size } } // Sequentially packs each polynomial using Poly.PackT0(). func (v *VecK) PackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT0(buf[offset:]) offset += common.PolyT0Size } } // Sets v to the vector packed into buf by PackT0(). func (v *VecK) UnpackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT0(buf[offset:]) offset += common.PolyT0Size } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecK) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecK.PackLeqEta(). func (v *VecK) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecK) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sequentially packs each polynomial using PolyPackW1(). func (v *VecK) PackW1(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackW1(&v[i], buf[offset:]) offset += PolyW1Size } } // Sets v to a - b. // // Warning: assumes coefficients of the polynomials of b are less than 2q. func (v *VecK) Sub(a, b *VecK) { for i := 0; i < K; i++ { v[i].Sub(&a[i], &b[i]) } } // Sets v to 2ᵈ w without reducing. func (v *VecK) MulBy2toD(w *VecK) { for i := 0; i < K; i++ { v[i].MulBy2toD(&w[i]) } } // Applies InvNTT componentwise. See Poly.InvNTT() for details. func (v *VecK) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies Poly.ReduceLe2Q() componentwise. func (v *VecK) ReduceLe2Q() { for i := 0; i < K; i++ { v[i].ReduceLe2Q() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5.go000066400000000000000000000040321454601126700237560ustar00rootroot00000000000000// Code generated from mode.templ.go. DO NOT EDIT. package dilithium import ( "fmt" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode5" ) // implMode5 implements the mode.Mode interface for Dilithium5. type implMode5 struct{} // Mode5 is Dilithium in mode "Dilithium5". var Mode5 Mode = &implMode5{} func (m *implMode5) GenerateKey(rand io.Reader) ( PublicKey, PrivateKey, error) { return mode5.GenerateKey(rand) } func (m *implMode5) NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) { if len(seed) != common.SeedSize { panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) } seedBuf := [common.SeedSize]byte{} copy(seedBuf[:], seed) return mode5.NewKeyFromSeed(&seedBuf) } func (m *implMode5) Sign(sk PrivateKey, msg []byte) []byte { isk := sk.(*mode5.PrivateKey) ret := [mode5.SignatureSize]byte{} mode5.SignTo(isk, msg, ret[:]) return ret[:] } func (m *implMode5) Verify(pk PublicKey, msg []byte, signature []byte) bool { ipk := pk.(*mode5.PublicKey) return mode5.Verify(ipk, msg, signature) } func (m *implMode5) PublicKeyFromBytes(data []byte) PublicKey { var ret mode5.PublicKey if len(data) != mode5.PublicKeySize { panic("packed public key must be of mode5.PublicKeySize bytes") } var buf [mode5.PublicKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode5) PrivateKeyFromBytes(data []byte) PrivateKey { var ret mode5.PrivateKey if len(data) != mode5.PrivateKeySize { panic("packed public key must be of mode5.PrivateKeySize bytes") } var buf [mode5.PrivateKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode5) SeedSize() int { return common.SeedSize } func (m *implMode5) PublicKeySize() int { return mode5.PublicKeySize } func (m *implMode5) PrivateKeySize() int { return mode5.PrivateKeySize } func (m *implMode5) SignatureSize() int { return mode5.SignatureSize } func (m *implMode5) Name() string { return "Dilithium5" } func init() { modes["Dilithium5"] = Mode5 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/000077500000000000000000000000001454601126700234305ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/dilithium.go000066400000000000000000000116411454601126700257520ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // mode5 implements the CRYSTALS-Dilithium signature scheme Dilithium5 // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf package mode5 import ( "crypto" "errors" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode5/internal" ) const ( // Size of seed for NewKeyFromSeed SeedSize = common.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a signature SignatureSize = internal.SignatureSize ) // PublicKey is the type of Dilithium5 public key type PublicKey internal.PublicKey // PrivateKey is the type of Dilithium5 private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { pk, sk, err := internal.GenerateKey(rand) return (*PublicKey)(pk), (*PrivateKey)(sk), err } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { internal.SignTo( (*internal.PrivateKey)(sk), msg, signature, ) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { return internal.Verify( (*internal.PublicKey)(pk), msg, signature, ) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Unpack(buf) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Unpack(buf) } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Pack(buf) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Pack(buf) } // Packs the public key. func (pk *PublicKey) Bytes() []byte { var buf [PublicKeySize]byte pk.Pack(&buf) return buf[:] } // Packs the private key. func (sk *PrivateKey) Bytes() []byte { var buf [PrivateKeySize]byte sk.Pack(&buf) return buf[:] } // Packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // Packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // Unpacks the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of mode5.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // Unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of mode5.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("dilithium: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return (*PublicKey)((*internal.PrivateKey)(sk).Public()) } // Equal returns whether the two private keys equal. func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) } // Equal returns whether the two public keys equal. func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/000077500000000000000000000000001454601126700252445ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/dilithium.go000066400000000000000000000260461454601126700275730ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium.go by gen.go package internal import ( cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) const ( // Size of a packed polynomial of norm ≤η. // (Note that the formula is not valid in general.) PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 // β = τη, the maximum size of c s₂. Beta = Tau * Eta // γ₁ range of y Gamma1 = 1 << Gamma1Bits // Size of packed polynomial of norm <γ₁ such as z PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8 // α = 2γ₂ parameter for decompose Alpha = 2 * Gamma2 // Size of a packed private key PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K // Size of a packed public key PublicKeySize = 32 + common.PolyT1Size*K // Size of a packed signature SignatureSize = L*PolyLeGamma1Size + Omega + K + 32 // Size of packed w₁ PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8 ) // PublicKey is the type of Dilithium public keys. type PublicKey struct { rho [32]byte t1 VecK // Cached values t1p [common.PolyT1Size * K]byte A *Mat tr *[32]byte } // PrivateKey is the type of Dilithium private keys. type PrivateKey struct { rho [32]byte key [32]byte s1 VecL s2 VecK t0 VecK tr [32]byte // Cached values A Mat // ExpandA(ρ) s1h VecL // NTT(s₁) s2h VecK // NTT(s₂) t0h VecK // NTT(t₀) } type unpackedSignature struct { z VecL hint VecK c [32]byte } // Packs the signature into buf. func (sig *unpackedSignature) Pack(buf []byte) { copy(buf[:], sig.c[:]) sig.z.PackLeGamma1(buf[32:]) sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:]) } // Sets sig to the signature encoded in the buffer. // // Returns whether buf contains a properly packed signature. func (sig *unpackedSignature) Unpack(buf []byte) bool { if len(buf) < SignatureSize { return false } copy(sig.c[:], buf[:]) sig.z.UnpackLeGamma1(buf[32:]) if sig.z.Exceeds(Gamma1 - Beta) { return false } if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) { return false } return true } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { copy(buf[:32], pk.rho[:]) copy(buf[32:], pk.t1p[:]) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { copy(pk.rho[:], buf[:32]) copy(pk.t1p[:], buf[32:]) pk.t1.UnpackT1(pk.t1p[:]) pk.A = new(Mat) pk.A.Derive(&pk.rho) // tr = CRH(ρ ‖ t1) = CRH(pk) pk.tr = new([32]byte) h := sha3.NewShake256() _, _ = h.Write(buf[:]) _, _ = h.Read(pk.tr[:]) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { copy(buf[:32], sk.rho[:]) copy(buf[32:64], sk.key[:]) copy(buf[64:96], sk.tr[:]) offset := 96 sk.s1.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.PackT0(buf[offset:]) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { copy(sk.rho[:], buf[:32]) copy(sk.key[:], buf[32:64]) copy(sk.tr[:], buf[64:96]) offset := 96 sk.s1.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.UnpackT0(buf[offset:]) // Cached values sk.A.Derive(&sk.rho) sk.t0h = sk.t0 sk.t0h.NTT() sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [32]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { var eSeed [128]byte // expanded seed var pk PublicKey var sk PrivateKey var sSeed [64]byte h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(eSeed[:]) copy(pk.rho[:], eSeed[:32]) copy(sSeed[:], eSeed[32:96]) copy(sk.key[:], eSeed[96:]) copy(sk.rho[:], pk.rho[:]) sk.A.Derive(&pk.rho) for i := uint16(0); i < L; i++ { PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) } for i := uint16(0); i < K; i++ { PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) } sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() sk.computeT0andT1(&sk.t0, &pk.t1) sk.t0h = sk.t0 sk.t0h.NTT() // Complete public key far enough to be packed pk.t1.PackT1(pk.t1p[:]) pk.A = &sk.A // Finish private key var packedPk [PublicKeySize]byte pk.Pack(&packedPk) // tr = CRH(ρ ‖ t1) = CRH(pk) h.Reset() _, _ = h.Write(packedPk[:]) _, _ = h.Read(sk.tr[:]) // Finish cache of public key pk.tr = &sk.tr return &pk, &sk } // Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { var t VecK // Set t to A s₁ + s₂ for i := 0; i < K; i++ { PolyDotHat(&t[i], &sk.A[i], &sk.s1h) t[i].ReduceLe2Q() t[i].InvNTT() } t.Add(&t, &sk.s2) t.Normalize() // Compute t₀, t₁ = Power2Round(t) t.Power2Round(t0, t1) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { var sig unpackedSignature var mu [64]byte var zh VecL var Az, Az2dct1, w1 VecK var ch common.Poly var cp [32]byte var w1Packed [PolyW1Size * K]byte // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β // and ensured that there at most ω ones in pk.hint. if !sig.Unpack(signature) { return false } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(pk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // Compute Az zh = sig.z zh.NTT() for i := 0; i < K; i++ { PolyDotHat(&Az[i], &pk.A[i], &zh) } // Next, we compute Az - 2ᵈ·c·t₁. // Note that the coefficients of t₁ are bounded by 256 = 2⁹, // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, // which is small enough for NTT(). Az2dct1.MulBy2toD(&pk.t1) Az2dct1.NTT() PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() for i := 0; i < K; i++ { Az2dct1[i].MulHat(&Az2dct1[i], &ch) } Az2dct1.Sub(&Az, &Az2dct1) Az2dct1.ReduceLe2Q() Az2dct1.InvNTT() Az2dct1.NormalizeAssumingLe2Q() // UseHint(pk.hint, Az - 2ᵈ·c·t₁) // = UseHint(pk.hint, w - c·s₂ + c·t₀) // = UseHint(pk.hint, r + c·t₀) // = r₁ = w₁. w1.UseHint(&Az2dct1, &sig.hint) w1.PackW1(w1Packed[:]) // c' = H(μ, w₁) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(cp[:]) return sig.c == cp } // SignTo signs the given message and writes the signature into signature. // //nolint:funlen func SignTo(sk *PrivateKey, msg []byte, signature []byte) { var mu, rhop [64]byte var w1Packed [PolyW1Size * K]byte var y, yh VecL var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK var ch common.Poly var yNonce uint16 var sig unpackedSignature if len(signature) < SignatureSize { panic("Signature does not fit in that byteslice") } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(sk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // ρ' = CRH(key ‖ μ) h.Reset() _, _ = h.Write(sk.key[:]) _, _ = h.Write(mu[:]) _, _ = h.Read(rhop[:]) // Main rejection loop attempt := 0 for { attempt++ if attempt >= 576 { // Depending on the mode, one try has a chance between 1/7 and 1/4 // of succeeding. Thus it is safe to say that 576 iterations // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. panic("This should only happen 1 in 2^{128}: something is wrong.") } // y = ExpandMask(ρ', key) VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) yNonce += uint16(L) // Set w to A y yh = y yh.NTT() for i := 0; i < K; i++ { PolyDotHat(&w[i], &sk.A[i], &yh) w[i].ReduceLe2Q() w[i].InvNTT() } // Decompose w into w₀ and w₁ w.NormalizeAssumingLe2Q() w.Decompose(&w0, &w1) // c~ = H(μ ‖ w₁) w1.PackW1(w1Packed[:]) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(sig.c[:]) PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. // // By Lemma 3 of the specification this is equivalent to checking that // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition // w - c·s₂ = r₁ α + r₀ as computed by decompose(). // See also §4.1 of the specification. for i := 0; i < K; i++ { w0mcs2[i].MulHat(&ch, &sk.s2h[i]) w0mcs2[i].InvNTT() } w0mcs2.Sub(&w0, &w0mcs2) w0mcs2.Normalize() if w0mcs2.Exceeds(Gamma2 - Beta) { continue } // z = y + c·s₁ for i := 0; i < L; i++ { sig.z[i].MulHat(&ch, &sk.s1h[i]) sig.z[i].InvNTT() } sig.z.Add(&sig.z, &y) sig.z.Normalize() // Ensure ‖z‖_∞ < γ₁ - β if sig.z.Exceeds(Gamma1 - Beta) { continue } // Compute c·t₀ for i := 0; i < K; i++ { ct0[i].MulHat(&ch, &sk.t0h[i]) ct0[i].InvNTT() } ct0.NormalizeAssumingLe2Q() // Ensure ‖c·t₀‖_∞ < γ₂. if ct0.Exceeds(Gamma2) { continue } // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. // Note that we're not using makeHint() in the obvious way as we // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note // that our makeHint() is actually the same as a makeHint for a // different decomposition: // // Earlier we ensured indirectly with a check that r₁ = w₁ where // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. w0mcs2pct0.Add(&w0mcs2, &ct0) w0mcs2pct0.NormalizeAssumingLe2Q() hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) if hintPop > Omega { continue } break } sig.Pack(signature[:]) } // Computes the public key corresponding to this private key. func (sk *PrivateKey) Public() *PublicKey { var t0 VecK pk := &PublicKey{ rho: sk.rho, A: &sk.A, tr: &sk.tr, } sk.computeT0andT1(&t0, &pk.t1) pk.t1.PackT1(pk.t1p[:]) return pk } // Equal returns whether the two public keys are equal func (pk *PublicKey) Equal(other *PublicKey) bool { return pk.rho == other.rho && pk.t1 == other.t1 } // Equal returns whether the two private keys are equal func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) acc := uint32(0) for i := 0; i < L; i++ { for j := 0; j < common.N; j++ { acc |= sk.s1[i][j] ^ other.s1[i][j] } } for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { acc |= sk.s2[i][j] ^ other.s2[i][j] acc |= sk.t0[i][j] ^ other.t0[i][j] } } return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/dilithium_test.go000066400000000000000000000062731454601126700306320ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Checks whether p is normalized. Only used in tests. func PolyNormalized(p *common.Poly) bool { p2 := *p p2.Normalize() return p2 == *p } func BenchmarkSkUnpack(b *testing.B) { var buf [PrivateKeySize]byte var sk PrivateKey for i := 0; i < b.N; i++ { sk.Unpack(&buf) } } func BenchmarkPkUnpack(b *testing.B) { var buf [PublicKeySize]byte var pk PublicKey for i := 0; i < b.N; i++ { pk.Unpack(&buf) } } func BenchmarkVerify(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of verification (as in the reference // implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte pk, sk := NewKeyFromSeed(&seed) SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of signing (as in the reference implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte _, sk := NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [common.SeedSize]byte var sig [SignatureSize]byte var msg [8]byte var pkb [PublicKeySize]byte var skb [PrivateKeySize]byte var pk2 PublicKey var sk2 PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) if !sk.Equal(sk) { t.Fatal() } for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) SignTo(sk, msg[:], sig[:]) if !Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb) pk2.Unpack(&pkb) if !pk.Equal(&pk2) { t.Fatal() } sk.Pack(&skb) sk2.Unpack(&skb) if !sk.Equal(&sk2) { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [common.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) pk2 := sk.Public() if !pk.Equal(pk2) { t.Fatal() } } } func TestGamma1Size(t *testing.T) { var expected int switch Gamma1Bits { case 17: expected = 576 case 19: expected = 640 } if expected != PolyLeGamma1Size { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/mat.go000066400000000000000000000024411454601126700263550ustar00rootroot00000000000000// Code generated from mode3/internal/mat.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A k by l matrix of polynomials. type Mat [K]VecL // Expands the given seed to a complete matrix. // // This function is called ExpandA in the specification. func (m *Mat) Derive(seed *[32]byte) { if !DeriveX4Available { for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) } } return } idx := 0 var nonces [4]uint16 var ps [4]*common.Poly for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { nonces[idx] = (i << 8) + j ps[idx] = &m[i][j] idx++ if idx == 4 { idx = 0 PolyDeriveUniformX4(ps, seed, nonces) } } } if idx != 0 { for i := idx; i < 4; i++ { ps[i] = nil } PolyDeriveUniformX4(ps, seed, nonces) } } // Set p to the inner product of a and b using pointwise multiplication. // // Assumes a and b are in Montgomery form and their coefficients are // pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting // coefficients are bounded by 2Lq. func PolyDotHat(p *common.Poly, a, b *VecL) { var t common.Poly *p = common.Poly{} // zero p for i := 0; i < L; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/pack.go000066400000000000000000000164511454601126700265200ustar00rootroot00000000000000// Code generated from mode3/internal/pack.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Writes p with norm less than or equal η into buf, which must be of // size PolyLeqEtaSize. // // Assumes coefficients of p are not normalized, but in [q-η,q+η]. func PolyPackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { buf[i] = (byte(common.Q+Eta-p[j]) | byte(common.Q+Eta-p[j+1])<<4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { buf[i] = (byte(common.Q+Eta-p[j]) | (byte(common.Q+Eta-p[j+1]) << 3) | (byte(common.Q+Eta-p[j+2]) << 6)) buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | (byte(common.Q+Eta-p[j+3]) << 1) | (byte(common.Q+Eta-p[j+4]) << 4) | (byte(common.Q+Eta-p[j+5]) << 7)) buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | (byte(common.Q+Eta-p[j+6]) << 2) | (byte(common.Q+Eta-p[j+7]) << 5)) j += 8 } } else { panic("eta not supported") } } // Sets p to the polynomial of norm less than or equal η encoded in the // given buffer of size PolyLeqEtaSize. // // Output coefficients of p are not normalized, but in [q-η,q+η] provided // buf was created using PackLeqEta. // // Beware, for arbitrary buf the coefficients of p might end up in // the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. func PolyUnpackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { p[j] = common.Q + Eta - uint32(buf[i]&15) p[j+1] = common.Q + Eta - uint32(buf[i]>>4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { p[j] = common.Q + Eta - uint32(buf[i]&7) p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) j += 8 } } else { panic("eta not supported") } } // Writes v with coefficients in {0, 1} of which at most ω non-zero // to buf, which must have length ω+k. func (v *VecK) PackHint(buf []byte) { // The packed hint starts with the indices of the non-zero coefficients // For instance: // // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) // // Yields // // 56, 100, 255, 2, 23, 1 // // Then we pad with zeroes until we have a list of ω items: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 // // Then we finish with a list of the switch-over-indices in this // list between polynomials, so: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 off := uint8(0) for i := 0; i < K; i++ { for j := uint16(0); j < common.N; j++ { if v[i][j] != 0 { buf[off] = uint8(j) off++ } } buf[Omega+i] = off } for ; off < Omega; off++ { buf[off] = 0 } } // Sets v to the vector encoded using VecK.PackHint() // // Returns whether unpacking was successful. func (v *VecK) UnpackHint(buf []byte) bool { // A priori, there would be several reasonable ways to encode the same // hint vector. We take care to only allow only one encoding, to ensure // "strong unforgeability". // // See PackHint() source for description of the encoding. *v = VecK{} // zero v prevSOP := uint8(0) // previous switch-over-point for i := 0; i < K; i++ { SOP := buf[Omega+i] if SOP < prevSOP || SOP > Omega { return false // ensures switch-over-points are increasing } for j := prevSOP; j < SOP; j++ { if j > prevSOP && buf[j] <= buf[j-1] { return false // ensures indices are increasing (within a poly) } v[i][buf[j]] = 1 } prevSOP = SOP } for j := prevSOP; j < Omega; j++ { if buf[j] != 0 { return false // ensures padding indices are zero } } return true } // Sets p to the polynomial packed into buf by PolyPackLeGamma1. // // p will be normalized. func PolyUnpackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0x3) << 16) p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) | (uint32(buf[i+4]&0xf) << 14) p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) | (uint32(buf[i+6]&0x3f) << 12) p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) | (uint32(buf[i+8]) << 10) // coefficients in [0,…,2γ₁) p0 = Gamma1 - p0 // (-γ₁,…,γ₁] p1 = Gamma1 - p1 p2 = Gamma1 - p2 p3 = Gamma1 - p3 p0 += uint32(int32(p0)>>31) & common.Q // normalize p1 += uint32(int32(p1)>>31) & common.Q p2 += uint32(int32(p2)>>31) & common.Q p3 += uint32(int32(p3)>>31) & common.Q p[j] = p0 p[j+1] = p1 p[j+2] = p2 p[j+3] = p3 j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0xf) << 16) p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) | (uint32(buf[i+4]) << 12) p0 = Gamma1 - p0 p1 = Gamma1 - p1 p0 += uint32(int32(p0)>>31) & common.Q p1 += uint32(int32(p1)>>31) & common.Q p[j] = p0 p[j+1] = p1 j += 2 } } else { panic("γ₁ not supported") } } // Writes p whose coefficients are in (-γ₁,γ₁] into buf // which has to be of length PolyLeGamma1Size. // // Assumes p is normalized. func PolyPackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 // coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q) for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := Gamma1 - p[j] // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q) p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁) p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q p2 := Gamma1 - p[j+2] p2 += uint32(int32(p2)>>31) & common.Q p3 := Gamma1 - p[j+3] p3 += uint32(int32(p3)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<2) buf[i+3] = byte(p1 >> 6) buf[i+4] = byte(p1>>14) | byte(p2<<4) buf[i+5] = byte(p2 >> 4) buf[i+6] = byte(p2>>12) | byte(p3<<6) buf[i+7] = byte(p3 >> 2) buf[i+8] = byte(p3 >> 10) j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { // Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q) p0 := Gamma1 - p[j] p0 += uint32(int32(p0)>>31) & common.Q p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<4) buf[i+3] = byte(p1 >> 4) buf[i+4] = byte(p1 >> 12) j += 2 } } else { panic("γ₁ not supported") } } // Pack w₁ into buf, which must be of length PolyW1Size. // // Assumes w₁ is normalized. func PolyPackW1(p *common.Poly, buf []byte) { if Gamma1Bits == 19 { p.PackLe16(buf) } else if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyW1Size; i += 3 { buf[i] = byte(p[j]) | byte(p[j+1]<<6) buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4) buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2) j += 4 } } else { panic("unsupported γ₁") } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/pack_test.go000066400000000000000000000035651454601126700275610ustar00rootroot00000000000000// Code generated from mode3/internal/pack_test.go by gen.go package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestPolyPackLeqEta(t *testing.T) { var p1, p2 common.Poly var seed [64]byte var buf [PolyLeqEtaSize]byte for i := uint16(0); i < 100; i++ { // Note that DeriveUniformLeqEta sets p to the right kind of // unnormalized vector. PolyDeriveUniformLeqEta(&p1, &seed, i) for j := 0; j < PolyLeqEtaSize; j++ { if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { t.Fatalf("DerveUniformLeqEta out of bounds") } } PolyPackLeqEta(&p1, buf[:]) PolyUnpackLeqEta(&p2, buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT1(t *testing.T) { var p1, p2 common.Poly var seed [32]byte var buf [common.PolyT1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p1, &seed, i) p1.Normalize() for j := 0; j < common.N; j++ { p1[j] &= 0x1ff } p1.PackT1(buf[:]) p2.UnpackT1(buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT0(t *testing.T) { var p, p0, p1, p2 common.Poly var seed [32]byte var buf [common.PolyT0Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p, &seed, i) p.Normalize() p.Power2Round(&p0, &p1) p0.PackT0(buf[:]) p2.UnpackT0(buf[:]) if p0 != p2 { t.Fatalf("%v !=\n%v", p0, p2) } } } func BenchmarkUnpackLeGamma1(b *testing.B) { var p common.Poly var buf [PolyLeGamma1Size]byte for i := 0; i < b.N; i++ { PolyUnpackLeGamma1(&p, buf[:]) } } func TestPolyPackLeGamma1(t *testing.T) { var p0, p1 common.Poly var seed [64]byte var buf [PolyLeGamma1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniformLeGamma1(&p0, &seed, i) p0.Normalize() PolyPackLeGamma1(&p0, buf[:]) PolyUnpackLeGamma1(&p1, buf[:]) if p0 != p1 { t.Fatalf("%v != %v", p0, p1) } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/params.go000066400000000000000000000004471454601126700270630ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal const ( Name = "Dilithium5" UseAES = false K = 8 L = 7 Eta = 2 DoubleEtaBits = 3 Omega = 75 Tau = 60 Gamma1Bits = 19 Gamma2 = 261888 ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/params_test.go000066400000000000000000000104601454601126700301160ustar00rootroot00000000000000package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Tests specific to the current mode func TestVectorDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte p2 := common.Poly{ 8380415, 1, 8380415, 8380416, 1, 8380415, 8380416, 8380415, 8380415, 8380416, 8380416, 2, 2, 1, 8380415, 8380415, 8380416, 1, 8380416, 8380415, 2, 0, 0, 1, 1, 2, 2, 8380415, 0, 8380416, 8380416, 8380416, 8380415, 1, 2, 0, 1, 8380415, 0, 1, 8380415, 1, 0, 8380415, 2, 1, 2, 0, 1, 0, 8380416, 1, 8380416, 1, 0, 1, 1, 0, 1, 8380416, 0, 0, 8380416, 8380415, 8380416, 2, 0, 0, 8380415, 1, 1, 0, 0, 1, 8380415, 1, 8380416, 1, 8380415, 8380416, 8380416, 8380415, 0, 1, 8380415, 8380415, 1, 8380415, 0, 2, 2, 8380415, 1, 2, 8380415, 8380415, 0, 2, 2, 1, 8380415, 8380416, 0, 8380415, 2, 1, 8380415, 2, 2, 8380416, 8380416, 0, 8380416, 0, 2, 8380416, 1, 8380415, 8380416, 8380415, 1, 8380416, 8380416, 2, 2, 0, 0, 0, 8380415, 8380415, 2, 8380416, 2, 2, 8380415, 8380415, 2, 2, 2, 8380415, 1, 2, 1, 2, 8380415, 0, 2, 1, 8380415, 2, 8380415, 8380415, 8380416, 0, 8380416, 8380415, 8380415, 8380416, 8380416, 2, 8380416, 2, 0, 0, 1, 1, 1, 8380416, 0, 8380416, 8380416, 1, 1, 1, 0, 8380416, 2, 0, 8380415, 8380415, 0, 0, 2, 8380416, 1, 0, 0, 8380415, 8380415, 1, 0, 8380416, 1, 2, 8380415, 0, 8380416, 8380415, 1, 1, 0, 1, 8380416, 8380415, 1, 0, 0, 8380416, 1, 0, 2, 8380416, 2, 2, 0, 0, 1, 1, 2, 8380415, 2, 8380416, 8380416, 2, 1, 2, 8380416, 8380415, 8380415, 8380415, 0, 8380416, 1, 0, 2, 8380416, 2, 8380415, 8380415, 2, 2, 8380415, 8380416, 0, 8380415, 8380415, 0, 2, 8380415, 1, 8380415, 8380415, 1, 1, 8380416, 8380416, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeqEta(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestVectorDeriveUniformLeGamma1(t *testing.T) { var p, p2 common.Poly var seed [64]byte p2 = common.Poly{ 8011853, 7949494, 172552, 263871, 8095275, 155369, 311506, 8076900, 8307558, 8139232, 8041607, 448815, 380634, 180526, 8165391, 101857, 8286792, 427645, 8098920, 7860396, 352757, 8179719, 7954627, 7898860, 28800, 8129086, 111121, 8115657, 8211418, 7943538, 259410, 7965184, 8232538, 7864584, 7991749, 23725, 393449, 8344363, 8041712, 196742, 8187277, 230211, 115522, 205750, 8332267, 8020968, 511882, 66518, 8377952, 283731, 276156, 488847, 218386, 24973, 7960226, 8019608, 8163770, 8099393, 8251752, 8055784, 438808, 408276, 245718, 90648, 8179442, 377149, 66371, 8067974, 8165213, 496174, 7959821, 8174846, 416247, 8334586, 8277522, 137692, 8260481, 45327, 8078022, 8223800, 8070188, 8291718, 156021, 516504, 8144827, 361012, 323861, 8315499, 8004848, 7906709, 7913063, 230858, 311998, 8280928, 8347571, 8236825, 120069, 412722, 476656, 372912, 8036734, 465145, 8275725, 8153834, 411759, 412681, 72836, 8378216, 8305773, 8162477, 8293183, 289061, 7900478, 8133091, 100678, 267462, 254283, 242941, 8009771, 364316, 217523, 8026537, 7899325, 7863708, 211663, 339314, 8133229, 8035753, 135557, 8245724, 7988629, 8042510, 8012465, 386933, 8351229, 88508, 274815, 8293482, 216047, 8232256, 8337777, 8305592, 7938394, 378619, 7942432, 7961498, 360341, 265269, 8346169, 514971, 8255059, 406815, 222421, 8344231, 464482, 94984, 8147964, 8242727, 8211462, 7945005, 8167987, 8290153, 8355124, 303031, 180689, 97653, 8032319, 263210, 684, 437628, 7983244, 359393, 8054335, 223796, 8014878, 8066876, 335829, 467349, 105150, 326057, 229928, 7934510, 26854, 8093051, 8162834, 8013975, 8122355, 44783, 7969925, 465863, 8299023, 8155688, 8256445, 7975782, 7892171, 8075999, 412728, 7858411, 480155, 7922893, 254722, 381253, 8307390, 8040031, 280413, 8089206, 7869244, 8050145, 8028110, 8020538, 8158686, 7875907, 7960483, 7998991, 8317674, 52939, 416219, 501681, 231283, 8151233, 8241847, 8224119, 454076, 8171231, 411693, 8324986, 447356, 400055, 490491, 477035, 8055459, 158775, 383762, 8167063, 8076788, 7956883, 309585, 111368, 8312360, 7992502, 8259793, 461240, 7937002, 8198300, 7862862, 302423, 437299, 420919, 8359979, 8191730, 7895992, 75500, 307359, 435102, 7873624, 457428, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeGamma1(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/rounding.go000066400000000000000000000101471454601126700274230ustar00rootroot00000000000000// Code generated from mode3/internal/rounding.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2, // except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken // and -α/2 ≤ a₀ < 0. Returns a₀ + q. Note 0 ≤ a₁ < (q-1)/α. // Recall α = 2γ₂. func decompose(a uint32) (a0plusQ, a1 uint32) { // a₁ = ⌈a / 128⌉ a1 = (a + 127) >> 7 if Alpha == 523776 { // 1025/2²² is close enough to 1/4092 so that a₁ // becomes a/α rounded down. a1 = ((a1*1025 + (1 << 21)) >> 22) // For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0. a1 &= 15 } else if Alpha == 190464 { // 1488/2²⁴ is close enough to 1/1488 so that a₁ // becomes a/α rounded down. a1 = ((a1 * 11275) + (1 << 23)) >> 24 // For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0. a1 ^= uint32(int32(43-a1)>>31) & a1 } else { panic("unsupported α") } a0plusQ = a - a1*Alpha // In the corner-case, when we set a₁=0, we will incorrectly // have a₀ > (q-1)/2 and we'll need to subtract q. As we // return a₀ + q, that comes down to adding q if a₀ < (q-1)/2. a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q return } // Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2. Decompose r as r = r1*α + r0 as // computed by decompose(). Write r' := r - f (mod Q). Now, decompose // r'=r-f again as r' = r'1*α + r'0 using decompose(). As f is small, we // have r'1 = r1 + h, where h ∈ {-1, 0, 1}. makeHint() computes |h| // given z0 := r0 - f (mod Q) and r1. With |h|, which is called the hint, // we can reconstruct r1 using only r' = r - f, which is done by useHint(). // To wit: // // useHint( r - f, makeHint( r0 - f, r1 ) ) = r1. // // Assumes 0 ≤ z0 < Q. func makeHint(z0, r1 uint32) uint32 { // If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r' // with the restrictions of decompose() and so r'1 = r1. So the hint // should be 0. This is covered by the first two inequalities. // There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also // a valid decomposition if r1 = 0. In the other cases a one is carried // and the hint should be 1. if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) { return 0 } return 1 } // Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see // documentation of makeHint() for context. // Assumes 0 ≤ r' < Q. func useHint(rp uint32, hint uint32) uint32 { rp0plusQ, rp1 := decompose(rp) if hint == 0 { return rp1 } if rp0plusQ > common.Q { return (rp1 + 1) & 15 } return (rp1 - 1) & 15 } // Sets p to the hint polynomial for p0 the modified low bits and p1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint polynomial. func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) { for i := 0; i < common.N; i++ { h := makeHint(p0[i], p1[i]) pop += h p[i] = h } return } // Computes corrections to the high bits of the polynomial q according // to the hints in h and sets p to the corrected high bits. Returns p. func PolyUseHint(p, q, hint *common.Poly) { var q0PlusQ common.Poly // See useHint() and makeHint() for an explanation. We reimplement it // here so that we can call Poly.Decompose(), which might be way faster // than calling decompose() in a loop (for instance when having AVX2.) PolyDecompose(q, &q0PlusQ, p) for i := 0; i < common.N; i++ { if hint[i] == 0 { continue } if Gamma2 == 261888 { if q0PlusQ[i] > common.Q { p[i] = (p[i] + 1) & 15 } else { p[i] = (p[i] - 1) & 15 } } else if Gamma2 == 95232 { if q0PlusQ[i] > common.Q { if p[i] == 43 { p[i] = 0 } else { p[i]++ } } else { if p[i] == 0 { p[i] = 43 } else { p[i]-- } } } else { panic("unsupported γ₂") } } } // Splits each of the coefficients of p using decompose. func PolyDecompose(p, p0PlusQ, p1 *common.Poly) { for i := 0; i < common.N; i++ { p0PlusQ[i], p1[i] = decompose(p[i]) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/rounding_test.go000066400000000000000000000031341454601126700304600ustar00rootroot00000000000000// Code generated from mode3/internal/rounding_test.go by gen.go package internal import ( "flag" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") func TestDecompose(t *testing.T) { for a := uint32(0); a < common.Q; a++ { a0PlusQ, a1 := decompose(a) a0 := int32(a0PlusQ) - int32(common.Q) recombined := a0 + int32(Alpha*a1) if a1 == 0 && recombined < 0 { recombined += common.Q if -(Alpha/2) > a0 || a0 >= 0 { t.Fatalf("decompose(%v): a0 out of bounds", a) } } else { if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) { t.Fatalf("decompose(%v): a0 out of bounds", a) } } if int32(a) != recombined { t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1) } } } func TestMakeHint(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for w := uint32(0); w < common.Q; w++ { w0, w1 := decompose(w) for fn := uint32(0); fn <= Gamma2; fn++ { fsign := false for { var f uint32 if fsign { if fn == 0 { break } f = common.Q - fn } else { f = fn } hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1) w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint) if w1p != w1 { t.Fatal() } if fsign { break } fsign = true } } } } func BenchmarkDecompose(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyDecompose(&p, &p0, &p1) } } func BenchmarkMakeHint(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyMakeHint(&p, &p0, &p1) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/sample.go000066400000000000000000000206561454601126700270650ustar00rootroot00000000000000// Code generated from mode3/internal/sample.go by gen.go package internal import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/simd/keccakf1600" ) // DeriveX4Available indicates whether the system supports the quick fourway // sampling variants like PolyDeriveUniformX4. var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES // For each i, sample ps[i] uniformly from the given seed and nonces[i]. // ps[i] may be nil and is ignored in that case. // // Can only be called when DeriveX4Available is true. func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // Absorb the nonces, the SHAKE128 domain separator (0b1111), the // start of the padding (0b...001) and the end of the padding 0b100... // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. for j := 0; j < 4; j++ { state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) state[20*4+j] = 0x80 << 56 } var idx [4]int // indices into ps for j := 0; j < 4; j++ { if ps[j] == nil { idx[j] = common.N // mark nil polynomial as completed } } done := false for !done { // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each // of the four SHAKE128 streams. perm.Permute() done = true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := 0; i < 7; i++ { var t [8]uint32 t[0] = uint32(state[i*3*4+j] & 0x7fffff) t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) t[2] = uint32((state[i*3*4+j] >> 48) | ((state[(i*3+1)*4+j] & 0x7f) << 16)) t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) t[5] = uint32((state[(i*3+1)*4+j] >> 56) | ((state[(i*3+2)*4+j] & 0x7fff) << 8)) t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) for k := 0; k < 8; k++ { if t[k] < common.Q { ps[j][idx[j]] = t[k] idx[j]++ if idx[j] == common.N { continue PolyLoop } } } } done = false } } } // Sample p uniformly from the given seed and nonce. // // p will be normalized. func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { var i, length int var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks if UseAES { length = 12 * 16 } else { length = 168 } sample := func() { // Note that 3 divides into 168 and 12*16, so we use up buf completely. for j := 0; j < length && i < common.N; j += 3 { t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | (uint32(buf[j+2]) << 16)) & 0x7fffff // We use rejection sampling if t < common.Q { p[i] = t i++ } } } if UseAES { h := common.NewAesStream128(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [32 + 2]byte // 32 byte seed + uint16 nonce h := sha3.NewShake128() copy(iv[:32], seed[:]) iv[32] = uint8(nonce) iv[33] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:168]) sample() } } } // Sample p uniformly with coefficients of norm less than or equal η, // using the given seed and nonce. // // p will not be normalized, but will have coefficients in [q-η,q+η]. func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) { // Assumes 2 < η < 8. var i, length int var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks if UseAES { length = 9 * 16 } else { length = 136 } sample := func() { // We use rejection sampling for j := 0; j < length && i < common.N; j++ { t1 := uint32(buf[j]) & 15 t2 := uint32(buf[j]) >> 4 if Eta == 2 { // branch is eliminated by compiler if t1 <= 14 { t1 -= ((205 * t1) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t1 i++ } if t2 <= 14 && i < common.N { t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t2 i++ } } else if Eta == 4 { if t1 <= 2*Eta { p[i] = common.Q + Eta - t1 i++ } if t2 <= 2*Eta && i < common.N { p[i] = common.Q + Eta - t2 i++ } } else { panic("unsupported η") } } } if UseAES { h := common.NewAesStream256(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [64 + 2]byte // 64 byte seed + uint16 nonce h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) // 136 is SHAKE-256 rate _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:136]) sample() } } } // Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁] using the // given seed and nonce+i // // p will be normalized. func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) { for i := 0; i < L; i++ { PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) } } // Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the // given seed and nonce. // // p will be normalized. func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) { var buf [PolyLeGamma1Size]byte if UseAES { h := common.NewAesStream256(seed, nonce) h.SqueezeInto(buf[:]) } else { var iv [66]byte h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) _, _ = h.Read(buf[:]) } PolyUnpackLeGamma1(p, buf[:]) } // For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1} // using the given seed and w1[i]. ps[i] may be nil and is ignored // in that case. ps[i] will be normalized. // // Can only be called when DeriveX4Available is true. // // This function is currently not used (yet). func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // SHAKE256 domain separator and padding for j := 0; j < 4; j++ { state[4*4+j] ^= 0x1f state[16*4+j] ^= 0x80 << 56 } perm.Permute() var signs [4]uint64 var idx [4]uint16 // indices into ps for j := 0; j < 4; j++ { if ps[j] != nil { signs[j] = state[j] *ps[j] = common.Poly{} // zero ps[j] idx[j] = common.N - Tau } else { idx[j] = common.N // mark as completed } } stateOffset := 1 for { done := true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := stateOffset; i < 17; i++ { var bs [8]byte binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) for k := 0; k < 8; k++ { b := uint16(bs[k]) if b > idx[j] { continue } ps[j][idx[j]] = ps[j][b] ps[j][b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) signs[j] >>= 1 idx[j]++ if idx[j] == common.N { continue PolyLoop } } } done = false } if done { break } perm.Permute() stateOffset = 0 } } // Samples p uniformly with τ non-zero coefficients in {q-1,1}. // // The polynomial p will be normalized. func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) { var buf [136]byte // SHAKE-256 rate is 136 h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(buf[:]) // Essentially we generate a sequence of τ ones or minus ones, // prepend 196 zeroes and shuffle the concatenation using the // usual algorithm (Fisher--Yates.) signs := binary.LittleEndian.Uint64(buf[:]) bufOff := 8 // offset into buf *p = common.Poly{} // zero p for i := uint16(common.N - Tau); i < common.N; i++ { var b uint16 // Find location of where to move the new coefficient to using // rejection sampling. for { if bufOff >= 136 { _, _ = h.Read(buf[:]) bufOff = 0 } b = uint16(buf[bufOff]) bufOff++ if b <= i { break } } p[i] = p[b] p[b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) signs >>= 1 } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/sample_test.go000066400000000000000000000204651454601126700301220ustar00rootroot00000000000000// Code generated from mode3/internal/sample_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestVectorDeriveUniform(t *testing.T) { var p, p2 common.Poly var seed [32]byte if UseAES { p2 = common.Poly{ 6724291, 310295, 6949524, 4464039, 1482136, 2522903, 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, 583034, 4971409, 2259140, 7715362, 3975394, 2341624, 5481174, 8150082, 365246, 5491939, 1083120, 7517301, 3104783, 2475292, 184149, 6425226, 4591622, 5964030, 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, 1512596, 5245430, 5517392, 2814840, 932545, 6826733, 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, 4123492, 8124406, 4016949, 5478752, 2750895, 603525, 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, 7990594, 1105530, 7121836, 1170740, 7417431, 633146, 253820, 7235019, 3539504, 6807707, 451390, 5481526, 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, 5311519, 3057534, 5277666, 682843, 2070398, 2874278, 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, 710407, 713806, 175647, 4274571, 2655021, 7319503, 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, 649664, 1720514, 6497260, 2683517, 7672754, 7105190, 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, 4337416, 2202680, 2338714, 557467, 6752058, 2469794, 485071, 1617604, 3590498, 2151466, 2005823, 7727956, 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, 2280717, 2889355, 3233946, 5187812, 978685, 5177364, 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, 816553, 6041174, 8317591, 1459178, 5332455, 1835058, 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, 4310856, 7135453, 3481032, 652626, 1841361, 8126828, 6250018, 300536, 7380070, 8174419, 1418793, 6208185, 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, 4119736, 6584065, 441634, 6941656, } } else { p2 = common.Poly{ 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, 4352830, } } for i := 0; i < 32; i++ { seed[i] = byte(i) } PolyDeriveUniform(&p, &seed, 30000) if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestDeriveUniform(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniform(&p, &seed, uint16(i)) if !PolyNormalized(&p) { t.Fatal() } } } func TestDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if p[j] < common.Q-Eta || p[j] > common.Q+Eta { t.Fatal() } } } } func TestDeriveUniformLeGamma1(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q { t.Fatal() } } } } func TestDeriveUniformBall(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformBall(&p, &seed) nonzero := 0 for j := 0; j < common.N; j++ { if p[j] != 0 { if p[j] != 1 && p[j] != common.Q-1 { t.Fatal() } nonzero++ } } if nonzero != Tau { t.Fatal() } } } func TestDeriveUniformX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte nonces := [4]uint16{12345, 54321, 13532, 37377} for i := 0; i < len(seed); i++ { seed[i] = byte(i) } PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, nonces) for i := 0; i < 4; i++ { PolyDeriveUniform(&p, &seed, nonces[i]) if ps[i] != p { t.Fatal() } } } func TestDeriveUniformBallX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte PolyDeriveUniformBallX4( [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, ) for j := 0; j < 4; j++ { PolyDeriveUniformBall(&p, &seed) if ps[j] != p { t.Fatalf("%d\n%v\n%v", j, ps[j], p) } } } func BenchmarkPolyDeriveUniformBall(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBall(&p, &seed) } } func BenchmarkPolyDeriveUniformBallX4(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBallX4( [4]*common.Poly{&p, &p, &p, &p}, &seed, ) } } func BenchmarkPolyDeriveUniform(b *testing.B) { var seed [32]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniform(&p, &seed, uint16(i)) } } func BenchmarkPolyDeriveUniformX4(b *testing.B) { if !DeriveX4Available { b.SkipNow() } var seed [32]byte var p [4]common.Poly for i := 0; i < b.N; i++ { nonce := uint16(4 * i) PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) } } func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { var seed [64]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5/internal/vec.go000066400000000000000000000141671454601126700263610ustar00rootroot00000000000000// Code generated from mode3/internal/vec.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A vector of L polynomials. type VecL [L]common.Poly // A vector of K polynomials. type VecK [K]common.Poly // Normalize the polynomials in this vector. func (v *VecL) Normalize() { for i := 0; i < L; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecL) NormalizeAssumingLe2Q() { for i := 0; i < L; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecL) Add(w, u *VecL) { for i := 0; i < L; i++ { v[i].Add(&w[i], &u[i]) } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecL) NTT() { for i := 0; i < L; i++ { v[i].NTT() } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecL) Exceeds(bound uint32) bool { for i := 0; i < L; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecL) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecL.PackLeqEta(). func (v *VecL) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sequentially packs each polynomial using PolyPackLeGamma1(). func (v *VecL) PackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). func (v *VecL) UnpackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Normalize the polynomials in this vector. func (v *VecK) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecK) NormalizeAssumingLe2Q() { for i := 0; i < K; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecK) Add(w, u *VecK) { for i := 0; i < K; i++ { v[i].Add(&w[i], &u[i]) } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecK) Exceeds(bound uint32) bool { for i := 0; i < K; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sets v to the hint vector for v0 the modified low bits and v1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint vector. func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { for i := 0; i < K; i++ { pop += PolyMakeHint(&v[i], &v0[i], &v1[i]) } return } // Computes corrections to the high bits of the polynomials in the vector // w using the hints in h and sets v to the corrected high bits. Returns v. // See useHint(). func (v *VecK) UseHint(q, hint *VecK) *VecK { for i := 0; i < K; i++ { PolyUseHint(&v[i], &q[i], &hint[i]) } return v } // Sequentially packs each polynomial using Poly.PackT1(). func (v *VecK) PackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT1(buf[offset:]) offset += common.PolyT1Size } } // Sets v to the vector packed into buf by PackT1(). func (v *VecK) UnpackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT1(buf[offset:]) offset += common.PolyT1Size } } // Sequentially packs each polynomial using Poly.PackT0(). func (v *VecK) PackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT0(buf[offset:]) offset += common.PolyT0Size } } // Sets v to the vector packed into buf by PackT0(). func (v *VecK) UnpackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT0(buf[offset:]) offset += common.PolyT0Size } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecK) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecK.PackLeqEta(). func (v *VecK) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecK) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sequentially packs each polynomial using PolyPackW1(). func (v *VecK) PackW1(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackW1(&v[i], buf[offset:]) offset += PolyW1Size } } // Sets v to a - b. // // Warning: assumes coefficients of the polynomials of b are less than 2q. func (v *VecK) Sub(a, b *VecK) { for i := 0; i < K; i++ { v[i].Sub(&a[i], &b[i]) } } // Sets v to 2ᵈ w without reducing. func (v *VecK) MulBy2toD(w *VecK) { for i := 0; i < K; i++ { v[i].MulBy2toD(&w[i]) } } // Applies InvNTT componentwise. See Poly.InvNTT() for details. func (v *VecK) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies Poly.ReduceLe2Q() componentwise. func (v *VecK) ReduceLe2Q() { for i := 0; i < K; i++ { v[i].ReduceLe2Q() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes.go000066400000000000000000000042261454601126700244540ustar00rootroot00000000000000// Code generated from mode.templ.go. DO NOT EDIT. package dilithium import ( "fmt" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode5aes" ) // implMode5AES implements the mode.Mode interface for Dilithium5-AES. type implMode5AES struct{} // Mode5AES is Dilithium in mode "Dilithium5-AES". var Mode5AES Mode = &implMode5AES{} func (m *implMode5AES) GenerateKey(rand io.Reader) ( PublicKey, PrivateKey, error) { return mode5aes.GenerateKey(rand) } func (m *implMode5AES) NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) { if len(seed) != common.SeedSize { panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) } seedBuf := [common.SeedSize]byte{} copy(seedBuf[:], seed) return mode5aes.NewKeyFromSeed(&seedBuf) } func (m *implMode5AES) Sign(sk PrivateKey, msg []byte) []byte { isk := sk.(*mode5aes.PrivateKey) ret := [mode5aes.SignatureSize]byte{} mode5aes.SignTo(isk, msg, ret[:]) return ret[:] } func (m *implMode5AES) Verify(pk PublicKey, msg []byte, signature []byte) bool { ipk := pk.(*mode5aes.PublicKey) return mode5aes.Verify(ipk, msg, signature) } func (m *implMode5AES) PublicKeyFromBytes(data []byte) PublicKey { var ret mode5aes.PublicKey if len(data) != mode5aes.PublicKeySize { panic("packed public key must be of mode5aes.PublicKeySize bytes") } var buf [mode5aes.PublicKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode5AES) PrivateKeyFromBytes(data []byte) PrivateKey { var ret mode5aes.PrivateKey if len(data) != mode5aes.PrivateKeySize { panic("packed public key must be of mode5aes.PrivateKeySize bytes") } var buf [mode5aes.PrivateKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *implMode5AES) SeedSize() int { return common.SeedSize } func (m *implMode5AES) PublicKeySize() int { return mode5aes.PublicKeySize } func (m *implMode5AES) PrivateKeySize() int { return mode5aes.PrivateKeySize } func (m *implMode5AES) SignatureSize() int { return mode5aes.SignatureSize } func (m *implMode5AES) Name() string { return "Dilithium5-AES" } func init() { modes["Dilithium5-AES"] = Mode5AES } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/000077500000000000000000000000001454601126700241215ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/dilithium.go000066400000000000000000000116741454601126700264510ustar00rootroot00000000000000// Code generated from modePkg.templ.go. DO NOT EDIT. // mode5aes implements the CRYSTALS-Dilithium signature scheme Dilithium5-AES // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf package mode5aes import ( "crypto" "errors" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/mode5aes/internal" ) const ( // Size of seed for NewKeyFromSeed SeedSize = common.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a signature SignatureSize = internal.SignatureSize ) // PublicKey is the type of Dilithium5-AES public key type PublicKey internal.PublicKey // PrivateKey is the type of Dilithium5-AES private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { pk, sk, err := internal.GenerateKey(rand) return (*PublicKey)(pk), (*PrivateKey)(sk), err } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { internal.SignTo( (*internal.PrivateKey)(sk), msg, signature, ) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { return internal.Verify( (*internal.PublicKey)(pk), msg, signature, ) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Unpack(buf) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Unpack(buf) } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Pack(buf) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Pack(buf) } // Packs the public key. func (pk *PublicKey) Bytes() []byte { var buf [PublicKeySize]byte pk.Pack(&buf) return buf[:] } // Packs the private key. func (sk *PrivateKey) Bytes() []byte { var buf [PrivateKeySize]byte sk.Pack(&buf) return buf[:] } // Packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // Packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // Unpacks the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of mode5aes.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // Unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of mode5aes.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("dilithium: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return (*PublicKey)((*internal.PrivateKey)(sk).Public()) } // Equal returns whether the two private keys equal. func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) } // Equal returns whether the two public keys equal. func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/000077500000000000000000000000001454601126700257355ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/dilithium.go000066400000000000000000000260461454601126700302640ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium.go by gen.go package internal import ( cryptoRand "crypto/rand" "crypto/subtle" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) const ( // Size of a packed polynomial of norm ≤η. // (Note that the formula is not valid in general.) PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 // β = τη, the maximum size of c s₂. Beta = Tau * Eta // γ₁ range of y Gamma1 = 1 << Gamma1Bits // Size of packed polynomial of norm <γ₁ such as z PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8 // α = 2γ₂ parameter for decompose Alpha = 2 * Gamma2 // Size of a packed private key PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K // Size of a packed public key PublicKeySize = 32 + common.PolyT1Size*K // Size of a packed signature SignatureSize = L*PolyLeGamma1Size + Omega + K + 32 // Size of packed w₁ PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8 ) // PublicKey is the type of Dilithium public keys. type PublicKey struct { rho [32]byte t1 VecK // Cached values t1p [common.PolyT1Size * K]byte A *Mat tr *[32]byte } // PrivateKey is the type of Dilithium private keys. type PrivateKey struct { rho [32]byte key [32]byte s1 VecL s2 VecK t0 VecK tr [32]byte // Cached values A Mat // ExpandA(ρ) s1h VecL // NTT(s₁) s2h VecK // NTT(s₂) t0h VecK // NTT(t₀) } type unpackedSignature struct { z VecL hint VecK c [32]byte } // Packs the signature into buf. func (sig *unpackedSignature) Pack(buf []byte) { copy(buf[:], sig.c[:]) sig.z.PackLeGamma1(buf[32:]) sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:]) } // Sets sig to the signature encoded in the buffer. // // Returns whether buf contains a properly packed signature. func (sig *unpackedSignature) Unpack(buf []byte) bool { if len(buf) < SignatureSize { return false } copy(sig.c[:], buf[:]) sig.z.UnpackLeGamma1(buf[32:]) if sig.z.Exceeds(Gamma1 - Beta) { return false } if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) { return false } return true } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { copy(buf[:32], pk.rho[:]) copy(buf[32:], pk.t1p[:]) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { copy(pk.rho[:], buf[:32]) copy(pk.t1p[:], buf[32:]) pk.t1.UnpackT1(pk.t1p[:]) pk.A = new(Mat) pk.A.Derive(&pk.rho) // tr = CRH(ρ ‖ t1) = CRH(pk) pk.tr = new([32]byte) h := sha3.NewShake256() _, _ = h.Write(buf[:]) _, _ = h.Read(pk.tr[:]) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { copy(buf[:32], sk.rho[:]) copy(buf[32:64], sk.key[:]) copy(buf[64:96], sk.tr[:]) offset := 96 sk.s1.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.PackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.PackT0(buf[offset:]) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { copy(sk.rho[:], buf[:32]) copy(sk.key[:], buf[32:64]) copy(sk.tr[:], buf[64:96]) offset := 96 sk.s1.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * L sk.s2.UnpackLeqEta(buf[offset:]) offset += PolyLeqEtaSize * K sk.t0.UnpackT0(buf[offset:]) // Cached values sk.A.Derive(&sk.rho) sk.t0h = sk.t0 sk.t0h.NTT() sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [32]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { var eSeed [128]byte // expanded seed var pk PublicKey var sk PrivateKey var sSeed [64]byte h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(eSeed[:]) copy(pk.rho[:], eSeed[:32]) copy(sSeed[:], eSeed[32:96]) copy(sk.key[:], eSeed[96:]) copy(sk.rho[:], pk.rho[:]) sk.A.Derive(&pk.rho) for i := uint16(0); i < L; i++ { PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) } for i := uint16(0); i < K; i++ { PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) } sk.s1h = sk.s1 sk.s1h.NTT() sk.s2h = sk.s2 sk.s2h.NTT() sk.computeT0andT1(&sk.t0, &pk.t1) sk.t0h = sk.t0 sk.t0h.NTT() // Complete public key far enough to be packed pk.t1.PackT1(pk.t1p[:]) pk.A = &sk.A // Finish private key var packedPk [PublicKeySize]byte pk.Pack(&packedPk) // tr = CRH(ρ ‖ t1) = CRH(pk) h.Reset() _, _ = h.Write(packedPk[:]) _, _ = h.Read(sk.tr[:]) // Finish cache of public key pk.tr = &sk.tr return &pk, &sk } // Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { var t VecK // Set t to A s₁ + s₂ for i := 0; i < K; i++ { PolyDotHat(&t[i], &sk.A[i], &sk.s1h) t[i].ReduceLe2Q() t[i].InvNTT() } t.Add(&t, &sk.s2) t.Normalize() // Compute t₀, t₁ = Power2Round(t) t.Power2Round(t0, t1) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { var sig unpackedSignature var mu [64]byte var zh VecL var Az, Az2dct1, w1 VecK var ch common.Poly var cp [32]byte var w1Packed [PolyW1Size * K]byte // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β // and ensured that there at most ω ones in pk.hint. if !sig.Unpack(signature) { return false } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(pk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // Compute Az zh = sig.z zh.NTT() for i := 0; i < K; i++ { PolyDotHat(&Az[i], &pk.A[i], &zh) } // Next, we compute Az - 2ᵈ·c·t₁. // Note that the coefficients of t₁ are bounded by 256 = 2⁹, // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, // which is small enough for NTT(). Az2dct1.MulBy2toD(&pk.t1) Az2dct1.NTT() PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() for i := 0; i < K; i++ { Az2dct1[i].MulHat(&Az2dct1[i], &ch) } Az2dct1.Sub(&Az, &Az2dct1) Az2dct1.ReduceLe2Q() Az2dct1.InvNTT() Az2dct1.NormalizeAssumingLe2Q() // UseHint(pk.hint, Az - 2ᵈ·c·t₁) // = UseHint(pk.hint, w - c·s₂ + c·t₀) // = UseHint(pk.hint, r + c·t₀) // = r₁ = w₁. w1.UseHint(&Az2dct1, &sig.hint) w1.PackW1(w1Packed[:]) // c' = H(μ, w₁) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(cp[:]) return sig.c == cp } // SignTo signs the given message and writes the signature into signature. // //nolint:funlen func SignTo(sk *PrivateKey, msg []byte, signature []byte) { var mu, rhop [64]byte var w1Packed [PolyW1Size * K]byte var y, yh VecL var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK var ch common.Poly var yNonce uint16 var sig unpackedSignature if len(signature) < SignatureSize { panic("Signature does not fit in that byteslice") } // μ = CRH(tr ‖ msg) h := sha3.NewShake256() _, _ = h.Write(sk.tr[:]) _, _ = h.Write(msg) _, _ = h.Read(mu[:]) // ρ' = CRH(key ‖ μ) h.Reset() _, _ = h.Write(sk.key[:]) _, _ = h.Write(mu[:]) _, _ = h.Read(rhop[:]) // Main rejection loop attempt := 0 for { attempt++ if attempt >= 576 { // Depending on the mode, one try has a chance between 1/7 and 1/4 // of succeeding. Thus it is safe to say that 576 iterations // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. panic("This should only happen 1 in 2^{128}: something is wrong.") } // y = ExpandMask(ρ', key) VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) yNonce += uint16(L) // Set w to A y yh = y yh.NTT() for i := 0; i < K; i++ { PolyDotHat(&w[i], &sk.A[i], &yh) w[i].ReduceLe2Q() w[i].InvNTT() } // Decompose w into w₀ and w₁ w.NormalizeAssumingLe2Q() w.Decompose(&w0, &w1) // c~ = H(μ ‖ w₁) w1.PackW1(w1Packed[:]) h.Reset() _, _ = h.Write(mu[:]) _, _ = h.Write(w1Packed[:]) _, _ = h.Read(sig.c[:]) PolyDeriveUniformBall(&ch, &sig.c) ch.NTT() // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. // // By Lemma 3 of the specification this is equivalent to checking that // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition // w - c·s₂ = r₁ α + r₀ as computed by decompose(). // See also §4.1 of the specification. for i := 0; i < K; i++ { w0mcs2[i].MulHat(&ch, &sk.s2h[i]) w0mcs2[i].InvNTT() } w0mcs2.Sub(&w0, &w0mcs2) w0mcs2.Normalize() if w0mcs2.Exceeds(Gamma2 - Beta) { continue } // z = y + c·s₁ for i := 0; i < L; i++ { sig.z[i].MulHat(&ch, &sk.s1h[i]) sig.z[i].InvNTT() } sig.z.Add(&sig.z, &y) sig.z.Normalize() // Ensure ‖z‖_∞ < γ₁ - β if sig.z.Exceeds(Gamma1 - Beta) { continue } // Compute c·t₀ for i := 0; i < K; i++ { ct0[i].MulHat(&ch, &sk.t0h[i]) ct0[i].InvNTT() } ct0.NormalizeAssumingLe2Q() // Ensure ‖c·t₀‖_∞ < γ₂. if ct0.Exceeds(Gamma2) { continue } // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. // Note that we're not using makeHint() in the obvious way as we // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note // that our makeHint() is actually the same as a makeHint for a // different decomposition: // // Earlier we ensured indirectly with a check that r₁ = w₁ where // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. w0mcs2pct0.Add(&w0mcs2, &ct0) w0mcs2pct0.NormalizeAssumingLe2Q() hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) if hintPop > Omega { continue } break } sig.Pack(signature[:]) } // Computes the public key corresponding to this private key. func (sk *PrivateKey) Public() *PublicKey { var t0 VecK pk := &PublicKey{ rho: sk.rho, A: &sk.A, tr: &sk.tr, } sk.computeT0andT1(&t0, &pk.t1) pk.t1.PackT1(pk.t1p[:]) return pk } // Equal returns whether the two public keys are equal func (pk *PublicKey) Equal(other *PublicKey) bool { return pk.rho == other.rho && pk.t1 == other.t1 } // Equal returns whether the two private keys are equal func (sk *PrivateKey) Equal(other *PrivateKey) bool { ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) acc := uint32(0) for i := 0; i < L; i++ { for j := 0; j < common.N; j++ { acc |= sk.s1[i][j] ^ other.s1[i][j] } } for i := 0; i < K; i++ { for j := 0; j < common.N; j++ { acc |= sk.s2[i][j] ^ other.s2[i][j] acc |= sk.t0[i][j] ^ other.t0[i][j] } } return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/dilithium_test.go000066400000000000000000000062731454601126700313230ustar00rootroot00000000000000// Code generated from mode3/internal/dilithium_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Checks whether p is normalized. Only used in tests. func PolyNormalized(p *common.Poly) bool { p2 := *p p2.Normalize() return p2 == *p } func BenchmarkSkUnpack(b *testing.B) { var buf [PrivateKeySize]byte var sk PrivateKey for i := 0; i < b.N; i++ { sk.Unpack(&buf) } } func BenchmarkPkUnpack(b *testing.B) { var buf [PublicKeySize]byte var pk PublicKey for i := 0; i < b.N; i++ { pk.Unpack(&buf) } } func BenchmarkVerify(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of verification (as in the reference // implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte pk, sk := NewKeyFromSeed(&seed) SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that the expansion of the matrix A is done at Unpacking/Keygen // instead of at the moment of signing (as in the reference implementation.) var seed [32]byte var msg [8]byte var sig [SignatureSize]byte _, sk := NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [common.SeedSize]byte var sig [SignatureSize]byte var msg [8]byte var pkb [PublicKeySize]byte var skb [PrivateKeySize]byte var pk2 PublicKey var sk2 PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) if !sk.Equal(sk) { t.Fatal() } for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) SignTo(sk, msg[:], sig[:]) if !Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb) pk2.Unpack(&pkb) if !pk.Equal(&pk2) { t.Fatal() } sk.Pack(&skb) sk2.Unpack(&skb) if !sk.Equal(&sk2) { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [common.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := NewKeyFromSeed(&seed) pk2 := sk.Public() if !pk.Equal(pk2) { t.Fatal() } } } func TestGamma1Size(t *testing.T) { var expected int switch Gamma1Bits { case 17: expected = 576 case 19: expected = 640 } if expected != PolyLeGamma1Size { t.Fatal() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/mat.go000066400000000000000000000024411454601126700270460ustar00rootroot00000000000000// Code generated from mode3/internal/mat.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A k by l matrix of polynomials. type Mat [K]VecL // Expands the given seed to a complete matrix. // // This function is called ExpandA in the specification. func (m *Mat) Derive(seed *[32]byte) { if !DeriveX4Available { for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) } } return } idx := 0 var nonces [4]uint16 var ps [4]*common.Poly for i := uint16(0); i < K; i++ { for j := uint16(0); j < L; j++ { nonces[idx] = (i << 8) + j ps[idx] = &m[i][j] idx++ if idx == 4 { idx = 0 PolyDeriveUniformX4(ps, seed, nonces) } } } if idx != 0 { for i := idx; i < 4; i++ { ps[i] = nil } PolyDeriveUniformX4(ps, seed, nonces) } } // Set p to the inner product of a and b using pointwise multiplication. // // Assumes a and b are in Montgomery form and their coefficients are // pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting // coefficients are bounded by 2Lq. func PolyDotHat(p *common.Poly, a, b *VecL) { var t common.Poly *p = common.Poly{} // zero p for i := 0; i < L; i++ { t.MulHat(&a[i], &b[i]) p.Add(&t, p) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/pack.go000066400000000000000000000164511454601126700272110ustar00rootroot00000000000000// Code generated from mode3/internal/pack.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Writes p with norm less than or equal η into buf, which must be of // size PolyLeqEtaSize. // // Assumes coefficients of p are not normalized, but in [q-η,q+η]. func PolyPackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { buf[i] = (byte(common.Q+Eta-p[j]) | byte(common.Q+Eta-p[j+1])<<4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { buf[i] = (byte(common.Q+Eta-p[j]) | (byte(common.Q+Eta-p[j+1]) << 3) | (byte(common.Q+Eta-p[j+2]) << 6)) buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | (byte(common.Q+Eta-p[j+3]) << 1) | (byte(common.Q+Eta-p[j+4]) << 4) | (byte(common.Q+Eta-p[j+5]) << 7)) buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | (byte(common.Q+Eta-p[j+6]) << 2) | (byte(common.Q+Eta-p[j+7]) << 5)) j += 8 } } else { panic("eta not supported") } } // Sets p to the polynomial of norm less than or equal η encoded in the // given buffer of size PolyLeqEtaSize. // // Output coefficients of p are not normalized, but in [q-η,q+η] provided // buf was created using PackLeqEta. // // Beware, for arbitrary buf the coefficients of p might end up in // the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. func PolyUnpackLeqEta(p *common.Poly, buf []byte) { if DoubleEtaBits == 4 { // compiler eliminates branch j := 0 for i := 0; i < PolyLeqEtaSize; i++ { p[j] = common.Q + Eta - uint32(buf[i]&15) p[j+1] = common.Q + Eta - uint32(buf[i]>>4) j += 2 } } else if DoubleEtaBits == 3 { j := 0 for i := 0; i < PolyLeqEtaSize; i += 3 { p[j] = common.Q + Eta - uint32(buf[i]&7) p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) j += 8 } } else { panic("eta not supported") } } // Writes v with coefficients in {0, 1} of which at most ω non-zero // to buf, which must have length ω+k. func (v *VecK) PackHint(buf []byte) { // The packed hint starts with the indices of the non-zero coefficients // For instance: // // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) // // Yields // // 56, 100, 255, 2, 23, 1 // // Then we pad with zeroes until we have a list of ω items: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 // // Then we finish with a list of the switch-over-indices in this // list between polynomials, so: // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 off := uint8(0) for i := 0; i < K; i++ { for j := uint16(0); j < common.N; j++ { if v[i][j] != 0 { buf[off] = uint8(j) off++ } } buf[Omega+i] = off } for ; off < Omega; off++ { buf[off] = 0 } } // Sets v to the vector encoded using VecK.PackHint() // // Returns whether unpacking was successful. func (v *VecK) UnpackHint(buf []byte) bool { // A priori, there would be several reasonable ways to encode the same // hint vector. We take care to only allow only one encoding, to ensure // "strong unforgeability". // // See PackHint() source for description of the encoding. *v = VecK{} // zero v prevSOP := uint8(0) // previous switch-over-point for i := 0; i < K; i++ { SOP := buf[Omega+i] if SOP < prevSOP || SOP > Omega { return false // ensures switch-over-points are increasing } for j := prevSOP; j < SOP; j++ { if j > prevSOP && buf[j] <= buf[j-1] { return false // ensures indices are increasing (within a poly) } v[i][buf[j]] = 1 } prevSOP = SOP } for j := prevSOP; j < Omega; j++ { if buf[j] != 0 { return false // ensures padding indices are zero } } return true } // Sets p to the polynomial packed into buf by PolyPackLeGamma1. // // p will be normalized. func PolyUnpackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0x3) << 16) p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) | (uint32(buf[i+4]&0xf) << 14) p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) | (uint32(buf[i+6]&0x3f) << 12) p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) | (uint32(buf[i+8]) << 10) // coefficients in [0,…,2γ₁) p0 = Gamma1 - p0 // (-γ₁,…,γ₁] p1 = Gamma1 - p1 p2 = Gamma1 - p2 p3 = Gamma1 - p3 p0 += uint32(int32(p0)>>31) & common.Q // normalize p1 += uint32(int32(p1)>>31) & common.Q p2 += uint32(int32(p2)>>31) & common.Q p3 += uint32(int32(p3)>>31) & common.Q p[j] = p0 p[j+1] = p1 p[j+2] = p2 p[j+3] = p3 j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) | (uint32(buf[i+2]&0xf) << 16) p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) | (uint32(buf[i+4]) << 12) p0 = Gamma1 - p0 p1 = Gamma1 - p1 p0 += uint32(int32(p0)>>31) & common.Q p1 += uint32(int32(p1)>>31) & common.Q p[j] = p0 p[j+1] = p1 j += 2 } } else { panic("γ₁ not supported") } } // Writes p whose coefficients are in (-γ₁,γ₁] into buf // which has to be of length PolyLeGamma1Size. // // Assumes p is normalized. func PolyPackLeGamma1(p *common.Poly, buf []byte) { if Gamma1Bits == 17 { j := 0 // coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q) for i := 0; i < PolyLeGamma1Size; i += 9 { p0 := Gamma1 - p[j] // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q) p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁) p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q p2 := Gamma1 - p[j+2] p2 += uint32(int32(p2)>>31) & common.Q p3 := Gamma1 - p[j+3] p3 += uint32(int32(p3)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<2) buf[i+3] = byte(p1 >> 6) buf[i+4] = byte(p1>>14) | byte(p2<<4) buf[i+5] = byte(p2 >> 4) buf[i+6] = byte(p2>>12) | byte(p3<<6) buf[i+7] = byte(p3 >> 2) buf[i+8] = byte(p3 >> 10) j += 4 } } else if Gamma1Bits == 19 { j := 0 for i := 0; i < PolyLeGamma1Size; i += 5 { // Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q) p0 := Gamma1 - p[j] p0 += uint32(int32(p0)>>31) & common.Q p1 := Gamma1 - p[j+1] p1 += uint32(int32(p1)>>31) & common.Q buf[i+0] = byte(p0) buf[i+1] = byte(p0 >> 8) buf[i+2] = byte(p0>>16) | byte(p1<<4) buf[i+3] = byte(p1 >> 4) buf[i+4] = byte(p1 >> 12) j += 2 } } else { panic("γ₁ not supported") } } // Pack w₁ into buf, which must be of length PolyW1Size. // // Assumes w₁ is normalized. func PolyPackW1(p *common.Poly, buf []byte) { if Gamma1Bits == 19 { p.PackLe16(buf) } else if Gamma1Bits == 17 { j := 0 for i := 0; i < PolyW1Size; i += 3 { buf[i] = byte(p[j]) | byte(p[j+1]<<6) buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4) buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2) j += 4 } } else { panic("unsupported γ₁") } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/pack_test.go000066400000000000000000000035651454601126700302520ustar00rootroot00000000000000// Code generated from mode3/internal/pack_test.go by gen.go package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestPolyPackLeqEta(t *testing.T) { var p1, p2 common.Poly var seed [64]byte var buf [PolyLeqEtaSize]byte for i := uint16(0); i < 100; i++ { // Note that DeriveUniformLeqEta sets p to the right kind of // unnormalized vector. PolyDeriveUniformLeqEta(&p1, &seed, i) for j := 0; j < PolyLeqEtaSize; j++ { if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { t.Fatalf("DerveUniformLeqEta out of bounds") } } PolyPackLeqEta(&p1, buf[:]) PolyUnpackLeqEta(&p2, buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT1(t *testing.T) { var p1, p2 common.Poly var seed [32]byte var buf [common.PolyT1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p1, &seed, i) p1.Normalize() for j := 0; j < common.N; j++ { p1[j] &= 0x1ff } p1.PackT1(buf[:]) p2.UnpackT1(buf[:]) if p1 != p2 { t.Fatalf("%v != %v", p1, p2) } } } func TestPolyPackT0(t *testing.T) { var p, p0, p1, p2 common.Poly var seed [32]byte var buf [common.PolyT0Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniform(&p, &seed, i) p.Normalize() p.Power2Round(&p0, &p1) p0.PackT0(buf[:]) p2.UnpackT0(buf[:]) if p0 != p2 { t.Fatalf("%v !=\n%v", p0, p2) } } } func BenchmarkUnpackLeGamma1(b *testing.B) { var p common.Poly var buf [PolyLeGamma1Size]byte for i := 0; i < b.N; i++ { PolyUnpackLeGamma1(&p, buf[:]) } } func TestPolyPackLeGamma1(t *testing.T) { var p0, p1 common.Poly var seed [64]byte var buf [PolyLeGamma1Size]byte for i := uint16(0); i < 100; i++ { PolyDeriveUniformLeGamma1(&p0, &seed, i) p0.Normalize() PolyPackLeGamma1(&p0, buf[:]) PolyUnpackLeGamma1(&p1, buf[:]) if p0 != p1 { t.Fatalf("%v != %v", p0, p1) } } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/params.go000066400000000000000000000004521454601126700275500ustar00rootroot00000000000000// Code generated from params.templ.go. DO NOT EDIT. package internal const ( Name = "Dilithium5-AES" UseAES = true K = 8 L = 7 Eta = 2 DoubleEtaBits = 3 Omega = 75 Tau = 60 Gamma1Bits = 19 Gamma2 = 261888 ) golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/params_test.go000066400000000000000000000102551454601126700306110ustar00rootroot00000000000000package internal import ( "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Tests specific to the current mode func TestVectorDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte p2 := common.Poly{ 8380416, 0, 2, 8380415, 1, 1, 0, 1, 0, 1, 8380415, 2, 8380415, 8380415, 2, 2, 2, 1, 0, 2, 8380416, 1, 8380415, 8380415, 8380416, 8380415, 8380416, 8380415, 1, 1, 0, 1, 0, 1, 2, 8380416, 2, 1, 8380416, 1, 1, 2, 0, 8380416, 8380416, 2, 0, 2, 8380415, 0, 1, 2, 1, 1, 1, 0, 8380415, 1, 2, 8380415, 8380416, 1, 8380415, 0, 1, 8380416, 8380416, 8380415, 0, 2, 8380415, 1, 8380416, 0, 8380416, 8380416, 8380416, 2, 2, 1, 2, 8380415, 2, 0, 8380415, 8380415, 0, 2, 8380415, 8380415, 1, 8380415, 2, 8380415, 0, 1, 2, 8380415, 8380416, 8380415, 0, 8380416, 1, 0, 2, 0, 2, 8380415, 8380416, 2, 1, 8380415, 1, 8380416, 1, 8380415, 8380415, 0, 8380416, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 8380415, 8380416, 2, 0, 1, 8380416, 2, 1, 8380416, 2, 1, 8380416, 0, 2, 8380416, 2, 0, 8380415, 0, 2, 0, 8380415, 1, 0, 8380415, 2, 8380416, 8380416, 8380415, 0, 0, 8380416, 2, 2, 1, 8380416, 2, 1, 2, 0, 8380415, 1, 0, 2, 2, 1, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 8380416, 2, 2, 0, 8380415, 1, 2, 2, 1, 1, 8380415, 8380415, 2, 2, 1, 8380416, 8380415, 2, 1, 0, 8380416, 8380415, 8380415, 0, 1, 0, 8380416, 8380416, 8380416, 8380416, 2, 8380415, 1, 8380415, 0, 1, 0, 8380416, 2, 8380415, 2, 1, 2, 1, 1, 0, 8380415, 2, 8380416, 8380416, 8380415, 8380415, 0, 2, 8380416, 1, 8380416, 8380415, 8380416, 8380415, 2, 8380416, 2, 8380415, 2, 2, 1, 8380415, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeqEta(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestVectorDeriveUniformLeGamma1(t *testing.T) { var p, p2 common.Poly var seed [64]byte p2 = common.Poly{ 91453, 8134283, 8211453, 8218977, 8362980, 431655, 98537, 320966, 7892886, 144675, 495826, 7910635, 308711, 8024934, 8314212, 8323958, 8242606, 7947101, 419492, 427692, 354075, 21485, 456475, 213575, 362300, 8142303, 8322444, 7885879, 89158, 181715, 8094655, 8303634, 8060028, 7920325, 192378, 7910586, 7897074, 8097343, 7899868, 8339413, 73206, 237312, 8183555, 348083, 8154041, 8364746, 8078364, 8312790, 105195, 8037823, 8356712, 7994594, 240882, 70742, 8109371, 8176349, 467152, 51422, 340432, 8030176, 342172, 154911, 64858, 97614, 212758, 8285880, 521738, 326395, 296748, 8111442, 8016327, 7953747, 158922, 330421, 8331843, 449771, 168214, 8198309, 8228760, 7940533, 2498, 305217, 475829, 8037995, 8250962, 305070, 8217080, 432779, 213808, 8162729, 381514, 7995827, 7989202, 129047, 246099, 67554, 8233257, 398954, 223629, 444125, 150369, 223365, 159236, 55259, 172419, 163583, 354428, 8263789, 8017325, 8229594, 32340, 490228, 450684, 8069619, 53733, 7932894, 7955848, 8197876, 201557, 8307246, 446889, 8211538, 7889784, 8071108, 496027, 8159198, 8037, 7973907, 248186, 4806, 185437, 457847, 138862, 8124477, 284692, 8255820, 8068729, 8292005, 244272, 8061114, 21475, 8058902, 421466, 8306487, 455649, 8218652, 7634, 148216, 7951766, 394889, 8127579, 366374, 8062903, 8139245, 367068, 8281027, 734, 396374, 7969282, 7977632, 8098596, 343569, 8191282, 223874, 163783, 203572, 109732, 8229113, 8128208, 321529, 296492, 8202474, 50404, 8336017, 8190899, 8191497, 8279167, 336877, 7878526, 7922949, 7974614, 8076047, 8201365, 8334333, 416495, 8090175, 150066, 7947253, 474615, 7937629, 8027358, 356569, 191566, 87441, 8219157, 8375553, 8029697, 8026188, 8193863, 295873, 7906281, 487687, 8363474, 386621, 282726, 8373831, 50680, 8239505, 7912018, 493972, 8335677, 8079840, 251210, 263667, 221541, 41291, 88028, 8373098, 505241, 7981448, 8308113, 299485, 428036, 93865, 90428, 392003, 80833, 7975521, 336649, 7950328, 8049195, 8332757, 8205291, 8178296, 7911197, 7925805, 519154, 60176, 54121, 222738, 464285, 8022604, 8174235, 7856202, 8291898, 473254, 8106411, 7943812, 267650, 7958173, 372387, 409597, 204263, 477847, 83925, 111791, } for i := 0; i < 64; i++ { seed[i] = byte(i) } PolyDeriveUniformLeGamma1(&p, &seed, 30000) p.Normalize() if p != p2 { t.Fatalf("%v != %v", p, p2) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/rounding.go000066400000000000000000000101471454601126700301140ustar00rootroot00000000000000// Code generated from mode3/internal/rounding.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2, // except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken // and -α/2 ≤ a₀ < 0. Returns a₀ + q. Note 0 ≤ a₁ < (q-1)/α. // Recall α = 2γ₂. func decompose(a uint32) (a0plusQ, a1 uint32) { // a₁ = ⌈a / 128⌉ a1 = (a + 127) >> 7 if Alpha == 523776 { // 1025/2²² is close enough to 1/4092 so that a₁ // becomes a/α rounded down. a1 = ((a1*1025 + (1 << 21)) >> 22) // For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0. a1 &= 15 } else if Alpha == 190464 { // 1488/2²⁴ is close enough to 1/1488 so that a₁ // becomes a/α rounded down. a1 = ((a1 * 11275) + (1 << 23)) >> 24 // For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0. a1 ^= uint32(int32(43-a1)>>31) & a1 } else { panic("unsupported α") } a0plusQ = a - a1*Alpha // In the corner-case, when we set a₁=0, we will incorrectly // have a₀ > (q-1)/2 and we'll need to subtract q. As we // return a₀ + q, that comes down to adding q if a₀ < (q-1)/2. a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q return } // Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2. Decompose r as r = r1*α + r0 as // computed by decompose(). Write r' := r - f (mod Q). Now, decompose // r'=r-f again as r' = r'1*α + r'0 using decompose(). As f is small, we // have r'1 = r1 + h, where h ∈ {-1, 0, 1}. makeHint() computes |h| // given z0 := r0 - f (mod Q) and r1. With |h|, which is called the hint, // we can reconstruct r1 using only r' = r - f, which is done by useHint(). // To wit: // // useHint( r - f, makeHint( r0 - f, r1 ) ) = r1. // // Assumes 0 ≤ z0 < Q. func makeHint(z0, r1 uint32) uint32 { // If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r' // with the restrictions of decompose() and so r'1 = r1. So the hint // should be 0. This is covered by the first two inequalities. // There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also // a valid decomposition if r1 = 0. In the other cases a one is carried // and the hint should be 1. if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) { return 0 } return 1 } // Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see // documentation of makeHint() for context. // Assumes 0 ≤ r' < Q. func useHint(rp uint32, hint uint32) uint32 { rp0plusQ, rp1 := decompose(rp) if hint == 0 { return rp1 } if rp0plusQ > common.Q { return (rp1 + 1) & 15 } return (rp1 - 1) & 15 } // Sets p to the hint polynomial for p0 the modified low bits and p1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint polynomial. func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) { for i := 0; i < common.N; i++ { h := makeHint(p0[i], p1[i]) pop += h p[i] = h } return } // Computes corrections to the high bits of the polynomial q according // to the hints in h and sets p to the corrected high bits. Returns p. func PolyUseHint(p, q, hint *common.Poly) { var q0PlusQ common.Poly // See useHint() and makeHint() for an explanation. We reimplement it // here so that we can call Poly.Decompose(), which might be way faster // than calling decompose() in a loop (for instance when having AVX2.) PolyDecompose(q, &q0PlusQ, p) for i := 0; i < common.N; i++ { if hint[i] == 0 { continue } if Gamma2 == 261888 { if q0PlusQ[i] > common.Q { p[i] = (p[i] + 1) & 15 } else { p[i] = (p[i] - 1) & 15 } } else if Gamma2 == 95232 { if q0PlusQ[i] > common.Q { if p[i] == 43 { p[i] = 0 } else { p[i]++ } } else { if p[i] == 0 { p[i] = 43 } else { p[i]-- } } } else { panic("unsupported γ₂") } } } // Splits each of the coefficients of p using decompose. func PolyDecompose(p, p0PlusQ, p1 *common.Poly) { for i := 0; i < common.N; i++ { p0PlusQ[i], p1[i] = decompose(p[i]) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/rounding_test.go000066400000000000000000000031341454601126700311510ustar00rootroot00000000000000// Code generated from mode3/internal/rounding_test.go by gen.go package internal import ( "flag" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") func TestDecompose(t *testing.T) { for a := uint32(0); a < common.Q; a++ { a0PlusQ, a1 := decompose(a) a0 := int32(a0PlusQ) - int32(common.Q) recombined := a0 + int32(Alpha*a1) if a1 == 0 && recombined < 0 { recombined += common.Q if -(Alpha/2) > a0 || a0 >= 0 { t.Fatalf("decompose(%v): a0 out of bounds", a) } } else { if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) { t.Fatalf("decompose(%v): a0 out of bounds", a) } } if int32(a) != recombined { t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1) } } } func TestMakeHint(t *testing.T) { if !*runVeryLongTest { t.SkipNow() } for w := uint32(0); w < common.Q; w++ { w0, w1 := decompose(w) for fn := uint32(0); fn <= Gamma2; fn++ { fsign := false for { var f uint32 if fsign { if fn == 0 { break } f = common.Q - fn } else { f = fn } hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1) w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint) if w1p != w1 { t.Fatal() } if fsign { break } fsign = true } } } } func BenchmarkDecompose(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyDecompose(&p, &p0, &p1) } } func BenchmarkMakeHint(b *testing.B) { var p, p0, p1 common.Poly for i := 0; i < b.N; i++ { PolyMakeHint(&p, &p0, &p1) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/sample.go000066400000000000000000000206561454601126700275560ustar00rootroot00000000000000// Code generated from mode3/internal/sample.go by gen.go package internal import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/simd/keccakf1600" ) // DeriveX4Available indicates whether the system supports the quick fourway // sampling variants like PolyDeriveUniformX4. var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES // For each i, sample ps[i] uniformly from the given seed and nonces[i]. // ps[i] may be nil and is ignored in that case. // // Can only be called when DeriveX4Available is true. func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // Absorb the nonces, the SHAKE128 domain separator (0b1111), the // start of the padding (0b...001) and the end of the padding 0b100... // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. for j := 0; j < 4; j++ { state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) state[20*4+j] = 0x80 << 56 } var idx [4]int // indices into ps for j := 0; j < 4; j++ { if ps[j] == nil { idx[j] = common.N // mark nil polynomial as completed } } done := false for !done { // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each // of the four SHAKE128 streams. perm.Permute() done = true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := 0; i < 7; i++ { var t [8]uint32 t[0] = uint32(state[i*3*4+j] & 0x7fffff) t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) t[2] = uint32((state[i*3*4+j] >> 48) | ((state[(i*3+1)*4+j] & 0x7f) << 16)) t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) t[5] = uint32((state[(i*3+1)*4+j] >> 56) | ((state[(i*3+2)*4+j] & 0x7fff) << 8)) t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) for k := 0; k < 8; k++ { if t[k] < common.Q { ps[j][idx[j]] = t[k] idx[j]++ if idx[j] == common.N { continue PolyLoop } } } } done = false } } } // Sample p uniformly from the given seed and nonce. // // p will be normalized. func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { var i, length int var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks if UseAES { length = 12 * 16 } else { length = 168 } sample := func() { // Note that 3 divides into 168 and 12*16, so we use up buf completely. for j := 0; j < length && i < common.N; j += 3 { t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | (uint32(buf[j+2]) << 16)) & 0x7fffff // We use rejection sampling if t < common.Q { p[i] = t i++ } } } if UseAES { h := common.NewAesStream128(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [32 + 2]byte // 32 byte seed + uint16 nonce h := sha3.NewShake128() copy(iv[:32], seed[:]) iv[32] = uint8(nonce) iv[33] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:168]) sample() } } } // Sample p uniformly with coefficients of norm less than or equal η, // using the given seed and nonce. // // p will not be normalized, but will have coefficients in [q-η,q+η]. func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) { // Assumes 2 < η < 8. var i, length int var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks if UseAES { length = 9 * 16 } else { length = 136 } sample := func() { // We use rejection sampling for j := 0; j < length && i < common.N; j++ { t1 := uint32(buf[j]) & 15 t2 := uint32(buf[j]) >> 4 if Eta == 2 { // branch is eliminated by compiler if t1 <= 14 { t1 -= ((205 * t1) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t1 i++ } if t2 <= 14 && i < common.N { t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5 p[i] = common.Q + Eta - t2 i++ } } else if Eta == 4 { if t1 <= 2*Eta { p[i] = common.Q + Eta - t1 i++ } if t2 <= 2*Eta && i < common.N { p[i] = common.Q + Eta - t2 i++ } } else { panic("unsupported η") } } } if UseAES { h := common.NewAesStream256(seed, nonce) for i < common.N { h.SqueezeInto(buf[:length]) sample() } } else { var iv [64 + 2]byte // 64 byte seed + uint16 nonce h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) // 136 is SHAKE-256 rate _, _ = h.Write(iv[:]) for i < common.N { _, _ = h.Read(buf[:136]) sample() } } } // Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁] using the // given seed and nonce+i // // p will be normalized. func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) { for i := 0; i < L; i++ { PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) } } // Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the // given seed and nonce. // // p will be normalized. func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) { var buf [PolyLeGamma1Size]byte if UseAES { h := common.NewAesStream256(seed, nonce) h.SqueezeInto(buf[:]) } else { var iv [66]byte h := sha3.NewShake256() copy(iv[:64], seed[:]) iv[64] = uint8(nonce) iv[65] = uint8(nonce >> 8) _, _ = h.Write(iv[:]) _, _ = h.Read(buf[:]) } PolyUnpackLeGamma1(p, buf[:]) } // For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1} // using the given seed and w1[i]. ps[i] may be nil and is ignored // in that case. ps[i] will be normalized. // // Can only be called when DeriveX4Available is true. // // This function is currently not used (yet). func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) { var perm keccakf1600.StateX4 state := perm.Initialize(false) // Absorb the seed in the four states for i := 0; i < 4; i++ { v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) for j := 0; j < 4; j++ { state[i*4+j] = v } } // SHAKE256 domain separator and padding for j := 0; j < 4; j++ { state[4*4+j] ^= 0x1f state[16*4+j] ^= 0x80 << 56 } perm.Permute() var signs [4]uint64 var idx [4]uint16 // indices into ps for j := 0; j < 4; j++ { if ps[j] != nil { signs[j] = state[j] *ps[j] = common.Poly{} // zero ps[j] idx[j] = common.N - Tau } else { idx[j] = common.N // mark as completed } } stateOffset := 1 for { done := true PolyLoop: for j := 0; j < 4; j++ { if idx[j] == common.N { continue } for i := stateOffset; i < 17; i++ { var bs [8]byte binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) for k := 0; k < 8; k++ { b := uint16(bs[k]) if b > idx[j] { continue } ps[j][idx[j]] = ps[j][b] ps[j][b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) signs[j] >>= 1 idx[j]++ if idx[j] == common.N { continue PolyLoop } } } done = false } if done { break } perm.Permute() stateOffset = 0 } } // Samples p uniformly with τ non-zero coefficients in {q-1,1}. // // The polynomial p will be normalized. func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) { var buf [136]byte // SHAKE-256 rate is 136 h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(buf[:]) // Essentially we generate a sequence of τ ones or minus ones, // prepend 196 zeroes and shuffle the concatenation using the // usual algorithm (Fisher--Yates.) signs := binary.LittleEndian.Uint64(buf[:]) bufOff := 8 // offset into buf *p = common.Poly{} // zero p for i := uint16(common.N - Tau); i < common.N; i++ { var b uint16 // Find location of where to move the new coefficient to using // rejection sampling. for { if bufOff >= 136 { _, _ = h.Read(buf[:]) bufOff = 0 } b = uint16(buf[bufOff]) bufOff++ if b <= i { break } } p[i] = p[b] p[b] = 1 // Takes least significant bit of signs and uses it for the sign. // Note 1 ^ (1 | (Q-1)) = Q-1. p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) signs >>= 1 } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/sample_test.go000066400000000000000000000204651454601126700306130ustar00rootroot00000000000000// Code generated from mode3/internal/sample_test.go by gen.go package internal import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/dilithium/internal/common" ) func TestVectorDeriveUniform(t *testing.T) { var p, p2 common.Poly var seed [32]byte if UseAES { p2 = common.Poly{ 6724291, 310295, 6949524, 4464039, 1482136, 2522903, 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, 583034, 4971409, 2259140, 7715362, 3975394, 2341624, 5481174, 8150082, 365246, 5491939, 1083120, 7517301, 3104783, 2475292, 184149, 6425226, 4591622, 5964030, 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, 1512596, 5245430, 5517392, 2814840, 932545, 6826733, 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, 4123492, 8124406, 4016949, 5478752, 2750895, 603525, 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, 7990594, 1105530, 7121836, 1170740, 7417431, 633146, 253820, 7235019, 3539504, 6807707, 451390, 5481526, 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, 5311519, 3057534, 5277666, 682843, 2070398, 2874278, 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, 710407, 713806, 175647, 4274571, 2655021, 7319503, 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, 649664, 1720514, 6497260, 2683517, 7672754, 7105190, 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, 4337416, 2202680, 2338714, 557467, 6752058, 2469794, 485071, 1617604, 3590498, 2151466, 2005823, 7727956, 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, 2280717, 2889355, 3233946, 5187812, 978685, 5177364, 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, 816553, 6041174, 8317591, 1459178, 5332455, 1835058, 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, 4310856, 7135453, 3481032, 652626, 1841361, 8126828, 6250018, 300536, 7380070, 8174419, 1418793, 6208185, 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, 4119736, 6584065, 441634, 6941656, } } else { p2 = common.Poly{ 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, 4352830, } } for i := 0; i < 32; i++ { seed[i] = byte(i) } PolyDeriveUniform(&p, &seed, 30000) if p != p2 { t.Fatalf("%v != %v", p, p2) } } func TestDeriveUniform(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniform(&p, &seed, uint16(i)) if !PolyNormalized(&p) { t.Fatal() } } } func TestDeriveUniformLeqEta(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if p[j] < common.Q-Eta || p[j] > common.Q+Eta { t.Fatal() } } } } func TestDeriveUniformLeGamma1(t *testing.T) { var p common.Poly var seed [64]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) for j := 0; j < common.N; j++ { if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q { t.Fatal() } } } } func TestDeriveUniformBall(t *testing.T) { var p common.Poly var seed [32]byte for i := 0; i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) PolyDeriveUniformBall(&p, &seed) nonzero := 0 for j := 0; j < common.N; j++ { if p[j] != 0 { if p[j] != 1 && p[j] != common.Q-1 { t.Fatal() } nonzero++ } } if nonzero != Tau { t.Fatal() } } } func TestDeriveUniformX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte nonces := [4]uint16{12345, 54321, 13532, 37377} for i := 0; i < len(seed); i++ { seed[i] = byte(i) } PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, nonces) for i := 0; i < 4; i++ { PolyDeriveUniform(&p, &seed, nonces[i]) if ps[i] != p { t.Fatal() } } } func TestDeriveUniformBallX4(t *testing.T) { if !DeriveX4Available { t.SkipNow() } var ps [4]common.Poly var p common.Poly var seed [32]byte PolyDeriveUniformBallX4( [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, ) for j := 0; j < 4; j++ { PolyDeriveUniformBall(&p, &seed) if ps[j] != p { t.Fatalf("%d\n%v\n%v", j, ps[j], p) } } } func BenchmarkPolyDeriveUniformBall(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBall(&p, &seed) } } func BenchmarkPolyDeriveUniformBallX4(b *testing.B) { var seed [32]byte var p common.Poly var w1 VecK for i := 0; i < b.N; i++ { w1[0][0] = uint32(i) PolyDeriveUniformBallX4( [4]*common.Poly{&p, &p, &p, &p}, &seed, ) } } func BenchmarkPolyDeriveUniform(b *testing.B) { var seed [32]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniform(&p, &seed, uint16(i)) } } func BenchmarkPolyDeriveUniformX4(b *testing.B) { if !DeriveX4Available { b.SkipNow() } var seed [32]byte var p [4]common.Poly for i := 0; i < b.N; i++ { nonce := uint16(4 * i) PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) } } func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { var seed [64]byte var p common.Poly for i := 0; i < b.N; i++ { PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/mode5aes/internal/vec.go000066400000000000000000000141671454601126700270520ustar00rootroot00000000000000// Code generated from mode3/internal/vec.go by gen.go package internal import ( "github.com/cloudflare/circl/sign/dilithium/internal/common" ) // A vector of L polynomials. type VecL [L]common.Poly // A vector of K polynomials. type VecK [K]common.Poly // Normalize the polynomials in this vector. func (v *VecL) Normalize() { for i := 0; i < L; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecL) NormalizeAssumingLe2Q() { for i := 0; i < L; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecL) Add(w, u *VecL) { for i := 0; i < L; i++ { v[i].Add(&w[i], &u[i]) } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecL) NTT() { for i := 0; i < L; i++ { v[i].NTT() } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecL) Exceeds(bound uint32) bool { for i := 0; i < L; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { for i := 0; i < L; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecL) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecL.PackLeqEta(). func (v *VecL) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sequentially packs each polynomial using PolyPackLeGamma1(). func (v *VecL) PackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyPackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). func (v *VecL) UnpackLeGamma1(buf []byte) { offset := 0 for i := 0; i < L; i++ { PolyUnpackLeGamma1(&v[i], buf[offset:]) offset += PolyLeGamma1Size } } // Normalize the polynomials in this vector. func (v *VecK) Normalize() { for i := 0; i < K; i++ { v[i].Normalize() } } // Normalize the polynomials in this vector assuming their coefficients // are already bounded by 2q. func (v *VecK) NormalizeAssumingLe2Q() { for i := 0; i < K; i++ { v[i].NormalizeAssumingLe2Q() } } // Sets v to w + u. Does not normalize. func (v *VecK) Add(w, u *VecK) { for i := 0; i < K; i++ { v[i].Add(&w[i], &u[i]) } } // Checks whether any of the coefficients exceeds the given bound in supnorm // // Requires the vector to be normalized. func (v *VecK) Exceeds(bound uint32) bool { for i := 0; i < K; i++ { if v[i].Exceeds(bound) { return true } } return false } // Applies Poly.Power2Round componentwise. // // Requires the vector to be normalized. func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { v[i].Power2Round(&v0PlusQ[i], &v1[i]) } } // Applies Poly.Decompose componentwise. // // Requires the vector to be normalized. func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { for i := 0; i < K; i++ { PolyDecompose(&v[i], &v0PlusQ[i], &v1[i]) } } // Sets v to the hint vector for v0 the modified low bits and v1 // the unmodified high bits --- see makeHint(). // // Returns the number of ones in the hint vector. func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { for i := 0; i < K; i++ { pop += PolyMakeHint(&v[i], &v0[i], &v1[i]) } return } // Computes corrections to the high bits of the polynomials in the vector // w using the hints in h and sets v to the corrected high bits. Returns v. // See useHint(). func (v *VecK) UseHint(q, hint *VecK) *VecK { for i := 0; i < K; i++ { PolyUseHint(&v[i], &q[i], &hint[i]) } return v } // Sequentially packs each polynomial using Poly.PackT1(). func (v *VecK) PackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT1(buf[offset:]) offset += common.PolyT1Size } } // Sets v to the vector packed into buf by PackT1(). func (v *VecK) UnpackT1(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT1(buf[offset:]) offset += common.PolyT1Size } } // Sequentially packs each polynomial using Poly.PackT0(). func (v *VecK) PackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].PackT0(buf[offset:]) offset += common.PolyT0Size } } // Sets v to the vector packed into buf by PackT0(). func (v *VecK) UnpackT0(buf []byte) { offset := 0 for i := 0; i < K; i++ { v[i].UnpackT0(buf[offset:]) offset += common.PolyT0Size } } // Sequentially packs each polynomial using Poly.PackLeqEta(). func (v *VecK) PackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Sets v to the polynomials packed in buf using VecK.PackLeqEta(). func (v *VecK) UnpackLeqEta(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyUnpackLeqEta(&v[i], buf[offset:]) offset += PolyLeqEtaSize } } // Applies NTT componentwise. See Poly.NTT() for details. func (v *VecK) NTT() { for i := 0; i < K; i++ { v[i].NTT() } } // Sequentially packs each polynomial using PolyPackW1(). func (v *VecK) PackW1(buf []byte) { offset := 0 for i := 0; i < K; i++ { PolyPackW1(&v[i], buf[offset:]) offset += PolyW1Size } } // Sets v to a - b. // // Warning: assumes coefficients of the polynomials of b are less than 2q. func (v *VecK) Sub(a, b *VecK) { for i := 0; i < K; i++ { v[i].Sub(&a[i], &b[i]) } } // Sets v to 2ᵈ w without reducing. func (v *VecK) MulBy2toD(w *VecK) { for i := 0; i < K; i++ { v[i].MulBy2toD(&w[i]) } } // Applies InvNTT componentwise. See Poly.InvNTT() for details. func (v *VecK) InvNTT() { for i := 0; i < K; i++ { v[i].InvNTT() } } // Applies Poly.ReduceLe2Q() componentwise. func (v *VecK) ReduceLe2Q() { for i := 0; i < K; i++ { v[i].ReduceLe2Q() } } golang-github-cloudflare-circl-1.3.7/sign/dilithium/templates/000077500000000000000000000000001454601126700244155ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/dilithium/templates/mode.templ.go000066400000000000000000000043221454601126700270110ustar00rootroot00000000000000// +build ignore // The previous line (and this one up to the warning below) is removed by the // template generator. // Code generated from mode.templ.go. DO NOT EDIT. package dilithium import ( "fmt" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/{{.Pkg}}" ) // {{.Impl}} implements the mode.Mode interface for {{.Name}}. type {{.Impl}} struct{} // {{.Mode}} is Dilithium in mode "{{.Name}}". var {{.Mode}} Mode = &{{.Impl}}{} func (m *{{.Impl}}) GenerateKey(rand io.Reader) ( PublicKey, PrivateKey, error) { return {{.Pkg}}.GenerateKey(rand) } func (m *{{.Impl}}) NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) { if len(seed) != common.SeedSize { panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) } seedBuf := [common.SeedSize]byte{} copy(seedBuf[:], seed) return {{.Pkg}}.NewKeyFromSeed(&seedBuf) } func (m *{{.Impl}}) Sign(sk PrivateKey, msg []byte) []byte { isk := sk.(*{{.Pkg}}.PrivateKey) ret := [{{.Pkg}}.SignatureSize]byte{} {{.Pkg}}.SignTo(isk, msg, ret[:]) return ret[:] } func (m *{{.Impl}}) Verify(pk PublicKey, msg []byte, signature []byte) bool { ipk := pk.(*{{.Pkg}}.PublicKey) return {{.Pkg}}.Verify(ipk, msg, signature) } func (m *{{.Impl}}) PublicKeyFromBytes(data []byte) PublicKey { var ret {{.Pkg}}.PublicKey if len(data) != {{.Pkg}}.PublicKeySize { panic("packed public key must be of {{.Pkg}}.PublicKeySize bytes") } var buf [{{.Pkg}}.PublicKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *{{.Impl}}) PrivateKeyFromBytes(data []byte) PrivateKey { var ret {{.Pkg}}.PrivateKey if len(data) != {{.Pkg}}.PrivateKeySize { panic("packed public key must be of {{.Pkg}}.PrivateKeySize bytes") } var buf [{{.Pkg}}.PrivateKeySize]byte copy(buf[:], data) ret.Unpack(&buf) return &ret } func (m *{{.Impl}}) SeedSize() int { return common.SeedSize } func (m *{{.Impl}}) PublicKeySize() int { return {{.Pkg}}.PublicKeySize } func (m *{{.Impl}}) PrivateKeySize() int { return {{.Pkg}}.PrivateKeySize } func (m *{{.Impl}}) SignatureSize() int { return {{.Pkg}}.SignatureSize } func (m *{{.Impl}}) Name() string { return "{{.Name}}" } func init() { modes["{{.Name}}"] = {{.Mode}} } golang-github-cloudflare-circl-1.3.7/sign/dilithium/templates/modePkg.templ.go000066400000000000000000000120441454601126700274530ustar00rootroot00000000000000// +build ignore // The previous line (and this one up to the warning below) is removed by the // template generator. // Code generated from modePkg.templ.go. DO NOT EDIT. // {{.Pkg}} implements the CRYSTALS-Dilithium signature scheme {{.Name}} // as submitted to round3 of the NIST PQC competition and described in // // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf package {{.Pkg}} import ( "crypto" "errors" "io" "github.com/cloudflare/circl/sign/dilithium/internal/common" "github.com/cloudflare/circl/sign/dilithium/{{.Pkg}}/internal" ) const ( // Size of seed for NewKeyFromSeed SeedSize = common.SeedSize // Size of a packed PublicKey PublicKeySize = internal.PublicKeySize // Size of a packed PrivateKey PrivateKeySize = internal.PrivateKeySize // Size of a signature SignatureSize = internal.SignatureSize ) // PublicKey is the type of {{.Name}} public key type PublicKey internal.PublicKey // PrivateKey is the type of {{.Name}} private key type PrivateKey internal.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { pk, sk, err := internal.GenerateKey(rand) return (*PublicKey)(pk), (*PrivateKey)(sk), err } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { pk, sk := internal.NewKeyFromSeed(seed) return (*PublicKey)(pk), (*PrivateKey)(sk) } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { internal.SignTo( (*internal.PrivateKey)(sk), msg, signature, ) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { return internal.Verify( (*internal.PublicKey)(pk), msg, signature, ) } // Sets pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Unpack(buf) } // Sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Unpack(buf) } // Packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { (*internal.PublicKey)(pk).Pack(buf) } // Packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { (*internal.PrivateKey)(sk).Pack(buf) } // Packs the public key. func (pk *PublicKey) Bytes() []byte { var buf [PublicKeySize]byte pk.Pack(&buf) return buf[:] } // Packs the private key. func (sk *PrivateKey) Bytes() []byte { var buf [PrivateKeySize]byte sk.Pack(&buf) return buf[:] } // Packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // Packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // Unpacks the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of {{.Pkg}}.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // Unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of {{.Pkg}}.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("dilithium: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return (*PublicKey)((*internal.PrivateKey)(sk).Public()) } // Equal returns whether the two private keys equal. func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) } // Equal returns whether the two public keys equal. func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) } golang-github-cloudflare-circl-1.3.7/sign/dilithium/templates/params.templ.go000066400000000000000000000007451454601126700273550ustar00rootroot00000000000000// +build ignore // The previous line (and this one up to the warning below) is removed by the // template generator. // Code generated from params.templ.go. DO NOT EDIT. package internal const ( Name = "{{.Name}}" UseAES = {{.UseAES}} K = {{.K}} L = {{.L}} Eta = {{.Eta}} DoubleEtaBits = {{.DoubleEtaBits}} Omega = {{.Omega}} Tau = {{.Tau}} Gamma1Bits = {{.Gamma1Bits}} Gamma2 = {{.Gamma2}} ) golang-github-cloudflare-circl-1.3.7/sign/ed25519/000077500000000000000000000000001454601126700214255ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/ed25519/ed25519.go000066400000000000000000000344771454601126700227710ustar00rootroot00000000000000// Package ed25519 implements Ed25519 signature scheme as described in RFC-8032. // // This package provides optimized implementations of the three signature // variants and maintaining closer compatibility with crypto/ed25519. // // | Scheme Name | Sign Function | Verification | Context | // |-------------|-------------------|---------------|-------------------| // | Ed25519 | Sign | Verify | None | // | Ed25519Ph | SignPh | VerifyPh | Yes, can be empty | // | Ed25519Ctx | SignWithCtx | VerifyWithCtx | Yes, non-empty | // | All above | (PrivateKey).Sign | VerifyAny | As above | // // Specific functions for sign and verify are defined. A generic signing // function for all schemes is available through the crypto.Signer interface, // which is implemented by the PrivateKey type. A correspond all-in-one // verification method is provided by the VerifyAny function. // // Signing with Ed25519Ph or Ed25519Ctx requires a context string for domain // separation. This parameter is passed using a SignerOptions struct defined // in this package. While Ed25519Ph accepts an empty context, Ed25519Ctx // enforces non-empty context strings. // // # Compatibility with crypto.ed25519 // // These functions are compatible with the “Ed25519” function defined in // RFC-8032. However, unlike RFC 8032's formulation, this package's private // key representation includes a public key suffix to make multiple signing // operations with the same key more efficient. This package refers to the // RFC-8032 private key as the “seed”. // // References // // - RFC-8032: https://rfc-editor.org/rfc/rfc8032.txt // - Ed25519: https://ed25519.cr.yp.to/ // - EdDSA: High-speed high-security signatures. https://doi.org/10.1007/s13389-012-0027-1 package ed25519 import ( "bytes" "crypto" cryptoRand "crypto/rand" "crypto/sha512" "crypto/subtle" "errors" "fmt" "io" "strconv" "github.com/cloudflare/circl/sign" ) const ( // ContextMaxSize is the maximum length (in bytes) allowed for context. ContextMaxSize = 255 // PublicKeySize is the size, in bytes, of public keys as used in this package. PublicKeySize = 32 // PrivateKeySize is the size, in bytes, of private keys as used in this package. PrivateKeySize = 64 // SignatureSize is the size, in bytes, of signatures generated and verified by this package. SignatureSize = 64 // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. SeedSize = 32 ) const ( paramB = 256 / 8 // Size of keys in bytes. ) // SignerOptions implements crypto.SignerOpts and augments with parameters // that are specific to the Ed25519 signature schemes. type SignerOptions struct { // Hash must be crypto.Hash(0) for Ed25519/Ed25519ctx, or crypto.SHA512 // for Ed25519ph. crypto.Hash // Context is an optional domain separation string for Ed25519ph and a // must for Ed25519ctx. Its length must be less or equal than 255 bytes. Context string // Scheme is an identifier for choosing a signature scheme. The zero value // is ED25519. Scheme SchemeID } // SchemeID is an identifier for each signature scheme. type SchemeID uint const ( ED25519 SchemeID = iota ED25519Ph ED25519Ctx ) // PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer. type PrivateKey []byte // Equal reports whether priv and x have the same value. func (priv PrivateKey) Equal(x crypto.PrivateKey) bool { xx, ok := x.(PrivateKey) return ok && subtle.ConstantTimeCompare(priv, xx) == 1 } // Public returns the PublicKey corresponding to priv. func (priv PrivateKey) Public() crypto.PublicKey { publicKey := make(PublicKey, PublicKeySize) copy(publicKey, priv[SeedSize:]) return publicKey } // Seed returns the private key seed corresponding to priv. It is provided for // interoperability with RFC 8032. RFC 8032's private keys correspond to seeds // in this package. func (priv PrivateKey) Seed() []byte { seed := make([]byte, SeedSize) copy(seed, priv[:SeedSize]) return seed } func (priv PrivateKey) Scheme() sign.Scheme { return sch } func (pub PublicKey) Scheme() sign.Scheme { return sch } func (priv PrivateKey) MarshalBinary() (data []byte, err error) { privateKey := make(PrivateKey, PrivateKeySize) copy(privateKey, priv) return privateKey, nil } func (pub PublicKey) MarshalBinary() (data []byte, err error) { publicKey := make(PublicKey, PublicKeySize) copy(publicKey, pub) return publicKey, nil } // Equal reports whether pub and x have the same value. func (pub PublicKey) Equal(x crypto.PublicKey) bool { xx, ok := x.(PublicKey) return ok && bytes.Equal(pub, xx) } // Sign creates a signature of a message with priv key. // This function is compatible with crypto.ed25519 and also supports the // three signature variants defined in RFC-8032, namely Ed25519 (or pure // EdDSA), Ed25519Ph, and Ed25519Ctx. // The opts.HashFunc() must return zero to specify either Ed25519 or Ed25519Ctx // variant. This can be achieved by passing crypto.Hash(0) as the value for // opts. // The opts.HashFunc() must return SHA512 to specify the Ed25519Ph variant. // This can be achieved by passing crypto.SHA512 as the value for opts. // Use a SignerOptions struct (defined in this package) to pass a context // string for signing. func (priv PrivateKey) Sign( rand io.Reader, message []byte, opts crypto.SignerOpts, ) (signature []byte, err error) { var ctx string var scheme SchemeID if o, ok := opts.(SignerOptions); ok { ctx = o.Context scheme = o.Scheme } switch true { case scheme == ED25519 && opts.HashFunc() == crypto.Hash(0): return Sign(priv, message), nil case scheme == ED25519Ph && opts.HashFunc() == crypto.SHA512: return SignPh(priv, message, ctx), nil case scheme == ED25519Ctx && opts.HashFunc() == crypto.Hash(0) && len(ctx) > 0: return SignWithCtx(priv, message, ctx), nil default: return nil, errors.New("ed25519: bad hash algorithm") } } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { if rand == nil { rand = cryptoRand.Reader } seed := make([]byte, SeedSize) if _, err := io.ReadFull(rand, seed); err != nil { return nil, nil, err } privateKey := NewKeyFromSeed(seed) publicKey := make(PublicKey, PublicKeySize) copy(publicKey, privateKey[SeedSize:]) return publicKey, privateKey, nil } // NewKeyFromSeed calculates a private key from a seed. It will panic if // len(seed) is not SeedSize. This function is provided for interoperability // with RFC 8032. RFC 8032's private keys correspond to seeds in this // package. func NewKeyFromSeed(seed []byte) PrivateKey { privateKey := make(PrivateKey, PrivateKeySize) newKeyFromSeed(privateKey, seed) return privateKey } func newKeyFromSeed(privateKey, seed []byte) { if l := len(seed); l != SeedSize { panic("ed25519: bad seed length: " + strconv.Itoa(l)) } var P pointR1 k := sha512.Sum512(seed) clamp(k[:]) reduceModOrder(k[:paramB], false) P.fixedMult(k[:paramB]) copy(privateKey[:SeedSize], seed) _ = P.ToBytes(privateKey[SeedSize:]) } func signAll(signature []byte, privateKey PrivateKey, message, ctx []byte, preHash bool) { if l := len(privateKey); l != PrivateKeySize { panic("ed25519: bad private key length: " + strconv.Itoa(l)) } H := sha512.New() var PHM []byte if preHash { _, _ = H.Write(message) PHM = H.Sum(nil) H.Reset() } else { PHM = message } // 1. Hash the 32-byte private key using SHA-512. _, _ = H.Write(privateKey[:SeedSize]) h := H.Sum(nil) clamp(h[:]) prefix, s := h[paramB:], h[:paramB] // 2. Compute SHA-512(dom2(F, C) || prefix || PH(M)) H.Reset() writeDom(H, ctx, preHash) _, _ = H.Write(prefix) _, _ = H.Write(PHM) r := H.Sum(nil) reduceModOrder(r[:], true) // 3. Compute the point [r]B. var P pointR1 P.fixedMult(r[:paramB]) R := (&[paramB]byte{})[:] if err := P.ToBytes(R); err != nil { panic(err) } // 4. Compute SHA512(dom2(F, C) || R || A || PH(M)). H.Reset() writeDom(H, ctx, preHash) _, _ = H.Write(R) _, _ = H.Write(privateKey[SeedSize:]) _, _ = H.Write(PHM) hRAM := H.Sum(nil) reduceModOrder(hRAM[:], true) // 5. Compute S = (r + k * s) mod order. S := (&[paramB]byte{})[:] calculateS(S, r[:paramB], hRAM[:paramB], s) // 6. The signature is the concatenation of R and S. copy(signature[:paramB], R[:]) copy(signature[paramB:], S[:]) } // Sign signs the message with privateKey and returns a signature. // This function supports the signature variant defined in RFC-8032: Ed25519, // also known as the pure version of EdDSA. // It will panic if len(privateKey) is not PrivateKeySize. func Sign(privateKey PrivateKey, message []byte) []byte { signature := make([]byte, SignatureSize) signAll(signature, privateKey, message, []byte(""), false) return signature } // SignPh creates a signature of a message with private key and context. // This function supports the signature variant defined in RFC-8032: Ed25519ph, // meaning it internally hashes the message using SHA-512, and optionally // accepts a context string. // It will panic if len(privateKey) is not PrivateKeySize. // Context could be passed to this function, which length should be no more than // ContextMaxSize=255. It can be empty. func SignPh(privateKey PrivateKey, message []byte, ctx string) []byte { if len(ctx) > ContextMaxSize { panic(fmt.Errorf("ed25519: bad context length: %v", len(ctx))) } signature := make([]byte, SignatureSize) signAll(signature, privateKey, message, []byte(ctx), true) return signature } // SignWithCtx creates a signature of a message with private key and context. // This function supports the signature variant defined in RFC-8032: Ed25519ctx, // meaning it accepts a non-empty context string. // It will panic if len(privateKey) is not PrivateKeySize. // Context must be passed to this function, which length should be no more than // ContextMaxSize=255 and cannot be empty. func SignWithCtx(privateKey PrivateKey, message []byte, ctx string) []byte { if len(ctx) == 0 || len(ctx) > ContextMaxSize { panic(fmt.Errorf("ed25519: bad context length: %v > %v", len(ctx), ContextMaxSize)) } signature := make([]byte, SignatureSize) signAll(signature, privateKey, message, []byte(ctx), false) return signature } func verify(public PublicKey, message, signature, ctx []byte, preHash bool) bool { if len(public) != PublicKeySize || len(signature) != SignatureSize || !isLessThanOrder(signature[paramB:]) { return false } var P pointR1 if ok := P.FromBytes(public); !ok { return false } H := sha512.New() var PHM []byte if preHash { _, _ = H.Write(message) PHM = H.Sum(nil) H.Reset() } else { PHM = message } R := signature[:paramB] writeDom(H, ctx, preHash) _, _ = H.Write(R) _, _ = H.Write(public) _, _ = H.Write(PHM) hRAM := H.Sum(nil) reduceModOrder(hRAM[:], true) var Q pointR1 encR := (&[paramB]byte{})[:] P.neg() Q.doubleMult(&P, signature[paramB:], hRAM[:paramB]) _ = Q.ToBytes(encR) return bytes.Equal(R, encR) } // VerifyAny returns true if the signature is valid. Failure cases are invalid // signature, or when the public key cannot be decoded. // This function supports all the three signature variants defined in RFC-8032, // namely Ed25519 (or pure EdDSA), Ed25519Ph, and Ed25519Ctx. // The opts.HashFunc() must return zero to specify either Ed25519 or Ed25519Ctx // variant. This can be achieved by passing crypto.Hash(0) as the value for opts. // The opts.HashFunc() must return SHA512 to specify the Ed25519Ph variant. // This can be achieved by passing crypto.SHA512 as the value for opts. // Use a SignerOptions struct to pass a context string for signing. func VerifyAny(public PublicKey, message, signature []byte, opts crypto.SignerOpts) bool { var ctx string var scheme SchemeID if o, ok := opts.(SignerOptions); ok { ctx = o.Context scheme = o.Scheme } switch true { case scheme == ED25519 && opts.HashFunc() == crypto.Hash(0): return Verify(public, message, signature) case scheme == ED25519Ph && opts.HashFunc() == crypto.SHA512: return VerifyPh(public, message, signature, ctx) case scheme == ED25519Ctx && opts.HashFunc() == crypto.Hash(0) && len(ctx) > 0: return VerifyWithCtx(public, message, signature, ctx) default: return false } } // Verify returns true if the signature is valid. Failure cases are invalid // signature, or when the public key cannot be decoded. // This function supports the signature variant defined in RFC-8032: Ed25519, // also known as the pure version of EdDSA. func Verify(public PublicKey, message, signature []byte) bool { return verify(public, message, signature, []byte(""), false) } // VerifyPh returns true if the signature is valid. Failure cases are invalid // signature, or when the public key cannot be decoded. // This function supports the signature variant defined in RFC-8032: Ed25519ph, // meaning it internally hashes the message using SHA-512. // Context could be passed to this function, which length should be no more than // 255. It can be empty. func VerifyPh(public PublicKey, message, signature []byte, ctx string) bool { return verify(public, message, signature, []byte(ctx), true) } // VerifyWithCtx returns true if the signature is valid. Failure cases are invalid // signature, or when the public key cannot be decoded, or when context is // not provided. // This function supports the signature variant defined in RFC-8032: Ed25519ctx, // meaning it does not handle prehashed messages. Non-empty context string must be // provided, and must not be more than 255 of length. func VerifyWithCtx(public PublicKey, message, signature []byte, ctx string) bool { if len(ctx) == 0 || len(ctx) > ContextMaxSize { return false } return verify(public, message, signature, []byte(ctx), false) } func clamp(k []byte) { k[0] &= 248 k[paramB-1] = (k[paramB-1] & 127) | 64 } // isLessThanOrder returns true if 0 <= x < order. func isLessThanOrder(x []byte) bool { i := len(order) - 1 for i > 0 && x[i] == order[i] { i-- } return x[i] < order[i] } func writeDom(h io.Writer, ctx []byte, preHash bool) { dom2 := "SigEd25519 no Ed25519 collisions" if len(ctx) > 0 { _, _ = h.Write([]byte(dom2)) if preHash { _, _ = h.Write([]byte{byte(0x01), byte(len(ctx))}) } else { _, _ = h.Write([]byte{byte(0x00), byte(len(ctx))}) } _, _ = h.Write(ctx) } else if preHash { _, _ = h.Write([]byte(dom2)) _, _ = h.Write([]byte{0x01, 0x00}) } } golang-github-cloudflare-circl-1.3.7/sign/ed25519/ed25519_test.go000066400000000000000000000046621454601126700240210ustar00rootroot00000000000000package ed25519_test import ( "testing" "github.com/cloudflare/circl/sign/ed25519" ) type zeroReader struct{} func (zeroReader) Read(buf []byte) (int, error) { for i := range buf { buf[i] = 0 } return len(buf), nil } func TestMalleability(t *testing.T) { // https://tools.ietf.org/html/rfc8032#section-5.1.7 adds an additional test // that s be in [0, order). This prevents someone from adding a multiple of // order to s and obtaining a second valid signature for the same message. msg := []byte{0x54, 0x65, 0x73, 0x74} sig := []byte{ 0x7c, 0x38, 0xe0, 0x26, 0xf2, 0x9e, 0x14, 0xaa, 0xbd, 0x05, 0x9a, 0x0f, 0x2d, 0xb8, 0xb0, 0xcd, 0x78, 0x30, 0x40, 0x60, 0x9a, 0x8b, 0xe6, 0x84, 0xdb, 0x12, 0xf8, 0x2a, 0x27, 0x77, 0x4a, 0xb0, 0x67, 0x65, 0x4b, 0xce, 0x38, 0x32, 0xc2, 0xd7, 0x6f, 0x8f, 0x6f, 0x5d, 0xaf, 0xc0, 0x8d, 0x93, 0x39, 0xd4, 0xee, 0xf6, 0x76, 0x57, 0x33, 0x36, 0xa5, 0xc5, 0x1e, 0xb6, 0xf9, 0x46, 0xb3, 0x1d, } publicKey := []byte{ 0x7d, 0x4d, 0x0e, 0x7f, 0x61, 0x53, 0xa6, 0x9b, 0x62, 0x42, 0xb5, 0x22, 0xab, 0xbe, 0xe6, 0x85, 0xfd, 0xa4, 0x42, 0x0f, 0x88, 0x34, 0xb1, 0x08, 0xc3, 0xbd, 0xae, 0x36, 0x9e, 0xf5, 0x49, 0xfa, } if ed25519.Verify(publicKey, msg, sig) { t.Fatal("non-canonical signature accepted") } } func TestPublic(t *testing.T) { var zero zeroReader pub, priv, err := ed25519.GenerateKey(zero) if err != nil { t.Fatal(err) } if !priv.Equal(priv) { t.FailNow() } if !pub.Equal(pub) { t.FailNow() } pub2 := priv.Public() if !pub.Equal(pub2) { t.FailNow() } } func BenchmarkKeyGeneration(b *testing.B) { var zero zeroReader for i := 0; i < b.N; i++ { if _, _, err := ed25519.GenerateKey(zero); err != nil { b.Fatal(err) } } } func BenchmarkNewKeyFromSeed(b *testing.B) { seed := make([]byte, ed25519.SeedSize) b.ReportAllocs() for i := 0; i < b.N; i++ { _ = ed25519.NewKeyFromSeed(seed) } } func BenchmarkSigning(b *testing.B) { var zero zeroReader _, priv, err := ed25519.GenerateKey(zero) if err != nil { b.Fatal(err) } message := []byte("Hello, world!") b.ReportAllocs() b.ResetTimer() for i := 0; i < b.N; i++ { ed25519.Sign(priv, message) } } func BenchmarkVerification(b *testing.B) { var zero zeroReader pub, priv, err := ed25519.GenerateKey(zero) if err != nil { b.Fatal(err) } message := []byte("Hello, world!") signature := ed25519.Sign(priv, message) b.ResetTimer() for i := 0; i < b.N; i++ { ed25519.Verify(pub, message, signature) } } golang-github-cloudflare-circl-1.3.7/sign/ed25519/extra_test.go000066400000000000000000000146401454601126700241430ustar00rootroot00000000000000package ed25519_test import ( "bytes" "crypto" "crypto/rand" "errors" "fmt" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/sign/ed25519" ) func TestWrongPublicKey(t *testing.T) { wrongPublicKeys := [...][ed25519.PublicKeySize]byte{ { // y = p 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, }, { // y > p 0xed + 1, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, }, { // x^2 = u/v = (y^2-1)/(dy^2+1) is not a quadratic residue 0x9a, 0x0a, 0xbe, 0xc6, 0x23, 0xcb, 0x5a, 0x23, 0x4e, 0x49, 0xd8, 0x92, 0xc2, 0x72, 0xd5, 0xa8, 0x27, 0xff, 0x42, 0x07, 0x7d, 0xe3, 0xf2, 0xb4, 0x74, 0x75, 0x9d, 0x04, 0x34, 0xed, 0xa6, 0x70, }, { // y = 1 and x^2 = u/v = 0, and the sign of X is 1 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 | 0x80, }, { // y = -1 and x^2 = u/v = 0, and the sign of X is 1 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f | 0x80, }, } sig := (&[ed25519.SignatureSize]byte{})[:] for _, public := range wrongPublicKeys { got := ed25519.Verify(public[:], []byte(""), sig) want := false if got != want { test.ReportError(t, got, want, public) } } } func TestSigner(t *testing.T) { seed := (&[ed25519.SeedSize]byte{})[:] _, _ = rand.Read(seed) key := ed25519.NewKeyFromSeed(seed) priv := key.Seed() if !bytes.Equal(seed, priv) { got := priv want := seed test.ReportError(t, got, want) } for _, o := range []ed25519.SignerOptions{ {Scheme: ed25519.ED25519, Hash: crypto.Hash(0), Context: ""}, {Scheme: ed25519.ED25519Ph, Hash: crypto.SHA512, Context: ""}, {Scheme: ed25519.ED25519Ph, Hash: crypto.SHA512, Context: "non-empty"}, {Scheme: ed25519.ED25519Ctx, Hash: crypto.Hash(0), Context: "non-empty"}, } { testSigner(t, key, o) } } func testSigner(t *testing.T, signer crypto.Signer, ops ed25519.SignerOptions) { msg := make([]byte, 64) _, _ = rand.Read(msg) sig, err := signer.Sign(nil, msg, ops) if err != nil { got := err var want error test.ReportError(t, got, want, ops) } if len(sig) != ed25519.SignatureSize { got := len(sig) want := ed25519.SignatureSize test.ReportError(t, got, want, ops) } pubSigner, ok := signer.Public().(ed25519.PublicKey) if !ok { got := ok want := true test.ReportError(t, got, want, ops) } got := ed25519.VerifyAny(pubSigner, msg, sig, ops) want := true if got != want { test.ReportError(t, got, want, ops) } } type badReader struct{} func (badReader) Read([]byte) (int, error) { return 0, errors.New("cannot read") } func TestErrors(t *testing.T) { t.Run("badHash", func(t *testing.T) { var msg [16]byte ops := crypto.SHA224 _, priv, _ := ed25519.GenerateKey(nil) _, got := priv.Sign(nil, msg[:], ops) want := errors.New("ed25519: bad hash algorithm") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) t.Run("badReader", func(t *testing.T) { _, _, got := ed25519.GenerateKey(badReader{}) want := errors.New("cannot read") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) t.Run("wrongSeedSize", func(t *testing.T) { var seed [256]byte var want error got := test.CheckPanic(func() { ed25519.NewKeyFromSeed(seed[:]) }) if got != want { test.ReportError(t, got, want) } }) } func BenchmarkEd25519Ph(b *testing.B) { msg := make([]byte, 128) _, _ = rand.Read(msg) b.Run("Sign", func(b *testing.B) { _, key, _ := ed25519.GenerateKey(rand.Reader) ctx := "" b.ResetTimer() for i := 0; i < b.N; i++ { _ = ed25519.SignPh(key, msg, ctx) } }) b.Run("Verify", func(b *testing.B) { pub, priv, _ := ed25519.GenerateKey(rand.Reader) ctx := "" sig := ed25519.SignPh(priv, msg, ctx) b.ResetTimer() for i := 0; i < b.N; i++ { ed25519.VerifyPh(pub, msg, sig, ctx) } }) } func BenchmarkEd25519Ctx(b *testing.B) { ctx := "a context" msg := make([]byte, 128) _, _ = rand.Read(msg) b.Run("Sign", func(b *testing.B) { _, priv, _ := ed25519.GenerateKey(rand.Reader) b.ResetTimer() for i := 0; i < b.N; i++ { _ = ed25519.SignWithCtx(priv, msg, ctx) } }) b.Run("Verify", func(b *testing.B) { pub, priv, _ := ed25519.GenerateKey(rand.Reader) sig := ed25519.SignWithCtx(priv, msg, ctx) b.ResetTimer() for i := 0; i < b.N; i++ { ed25519.VerifyWithCtx(pub, msg, sig, ctx) } }) } func Example_ed25519() { // import "github.com/cloudflare/circl/sign/ed25519" // import "crypto/rand" // Generating Alice's key pair pub, priv, err := ed25519.GenerateKey(rand.Reader) if err != nil { panic("error on generating keys") } // Alice signs a message. message := []byte("A message to be signed") signature := ed25519.Sign(priv, message) // Anyone can verify the signature using Alice's public key. ok := ed25519.Verify(pub, message, signature) fmt.Println(ok) // Output: true } func ExampleSignPh() { // import "github.com/cloudflare/circl/sign/ed25519" // import "crypto/rand" // Generating Alice's key pair pub, priv, err := ed25519.GenerateKey(rand.Reader) if err != nil { panic("error on generating keys") } // Alice signs a message. message := []byte("A message to be signed") ctx := "an optional context string" signature := ed25519.SignPh(priv, message, ctx) // Anyone can verify the signature using Alice's public key. ok := ed25519.VerifyPh(pub, message, signature, ctx) fmt.Println(ok) // Output: true } func ExampleSignWithCtx() { // import "github.com/cloudflare/circl/sign/ed25519" // import "crypto/rand" // Generating Alice's key pair pub, priv, err := ed25519.GenerateKey(rand.Reader) if err != nil { panic("error on generating keys") } // Alice signs a message. message := []byte("A message to be signed") ctx := "a non-empty context string" signature := ed25519.SignWithCtx(priv, message, ctx) // Anyone can verify the signature using Alice's public key. ok := ed25519.VerifyWithCtx(pub, message, signature, ctx) fmt.Println(ok) // Output: true } golang-github-cloudflare-circl-1.3.7/sign/ed25519/modular.go000066400000000000000000000113251454601126700234210ustar00rootroot00000000000000package ed25519 import ( "encoding/binary" "math/bits" ) var order = [paramB]byte{ 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, } // isLessThan returns true if 0 <= x < y, and assumes that slices have the same length. func isLessThan(x, y []byte) bool { i := len(x) - 1 for i > 0 && x[i] == y[i] { i-- } return x[i] < y[i] } // reduceModOrder calculates k = k mod order of the curve. func reduceModOrder(k []byte, is512Bit bool) { var X [((2 * paramB) * 8) / 64]uint64 numWords := len(k) >> 3 for i := 0; i < numWords; i++ { X[i] = binary.LittleEndian.Uint64(k[i*8 : (i+1)*8]) } red512(&X, is512Bit) for i := 0; i < numWords; i++ { binary.LittleEndian.PutUint64(k[i*8:(i+1)*8], X[i]) } } // red512 calculates x = x mod Order of the curve. func red512(x *[8]uint64, full bool) { // Implementation of Algs.(14.47)+(14.52) of Handbook of Applied // Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone. const ( ell0 = uint64(0x5812631a5cf5d3ed) ell1 = uint64(0x14def9dea2f79cd6) ell160 = uint64(0x812631a5cf5d3ed0) ell161 = uint64(0x4def9dea2f79cd65) ell162 = uint64(0x0000000000000001) ) var c0, c1, c2, c3 uint64 r0, r1, r2, r3, r4 := x[0], x[1], x[2], x[3], uint64(0) if full { q0, q1, q2, q3 := x[4], x[5], x[6], x[7] for i := 0; i < 3; i++ { h0, s0 := bits.Mul64(q0, ell160) h1, s1 := bits.Mul64(q1, ell160) h2, s2 := bits.Mul64(q2, ell160) h3, s3 := bits.Mul64(q3, ell160) s1, c0 = bits.Add64(h0, s1, 0) s2, c1 = bits.Add64(h1, s2, c0) s3, c2 = bits.Add64(h2, s3, c1) s4, _ := bits.Add64(h3, 0, c2) h0, l0 := bits.Mul64(q0, ell161) h1, l1 := bits.Mul64(q1, ell161) h2, l2 := bits.Mul64(q2, ell161) h3, l3 := bits.Mul64(q3, ell161) l1, c0 = bits.Add64(h0, l1, 0) l2, c1 = bits.Add64(h1, l2, c0) l3, c2 = bits.Add64(h2, l3, c1) l4, _ := bits.Add64(h3, 0, c2) s1, c0 = bits.Add64(s1, l0, 0) s2, c1 = bits.Add64(s2, l1, c0) s3, c2 = bits.Add64(s3, l2, c1) s4, c3 = bits.Add64(s4, l3, c2) s5, s6 := bits.Add64(l4, 0, c3) s2, c0 = bits.Add64(s2, q0, 0) s3, c1 = bits.Add64(s3, q1, c0) s4, c2 = bits.Add64(s4, q2, c1) s5, c3 = bits.Add64(s5, q3, c2) s6, s7 := bits.Add64(s6, 0, c3) q := q0 | q1 | q2 | q3 m := -((q | -q) >> 63) // if q=0 then m=0...0 else m=1..1 s0 &= m s1 &= m s2 &= m s3 &= m q0, q1, q2, q3 = s4, s5, s6, s7 if (i+1)%2 == 0 { r0, c0 = bits.Add64(r0, s0, 0) r1, c1 = bits.Add64(r1, s1, c0) r2, c2 = bits.Add64(r2, s2, c1) r3, c3 = bits.Add64(r3, s3, c2) r4, _ = bits.Add64(r4, 0, c3) } else { r0, c0 = bits.Sub64(r0, s0, 0) r1, c1 = bits.Sub64(r1, s1, c0) r2, c2 = bits.Sub64(r2, s2, c1) r3, c3 = bits.Sub64(r3, s3, c2) r4, _ = bits.Sub64(r4, 0, c3) } } m := -(r4 >> 63) r0, c0 = bits.Add64(r0, m&ell160, 0) r1, c1 = bits.Add64(r1, m&ell161, c0) r2, c2 = bits.Add64(r2, m&ell162, c1) r3, c3 = bits.Add64(r3, 0, c2) r4, _ = bits.Add64(r4, m&1, c3) x[4], x[5], x[6], x[7] = 0, 0, 0, 0 } q0 := (r4 << 4) | (r3 >> 60) r3 &= (uint64(1) << 60) - 1 h0, s0 := bits.Mul64(ell0, q0) h1, s1 := bits.Mul64(ell1, q0) s1, c0 = bits.Add64(h0, s1, 0) s2, _ := bits.Add64(h1, 0, c0) r0, c0 = bits.Sub64(r0, s0, 0) r1, c1 = bits.Sub64(r1, s1, c0) r2, c2 = bits.Sub64(r2, s2, c1) r3, _ = bits.Sub64(r3, 0, c2) x[0], x[1], x[2], x[3] = r0, r1, r2, r3 } // calculateS performs s = r+k*a mod Order of the curve. func calculateS(s, r, k, a []byte) { K := [4]uint64{ binary.LittleEndian.Uint64(k[0*8 : 1*8]), binary.LittleEndian.Uint64(k[1*8 : 2*8]), binary.LittleEndian.Uint64(k[2*8 : 3*8]), binary.LittleEndian.Uint64(k[3*8 : 4*8]), } S := [8]uint64{ binary.LittleEndian.Uint64(r[0*8 : 1*8]), binary.LittleEndian.Uint64(r[1*8 : 2*8]), binary.LittleEndian.Uint64(r[2*8 : 3*8]), binary.LittleEndian.Uint64(r[3*8 : 4*8]), } var c3 uint64 for i := range K { ai := binary.LittleEndian.Uint64(a[i*8 : (i+1)*8]) h0, l0 := bits.Mul64(K[0], ai) h1, l1 := bits.Mul64(K[1], ai) h2, l2 := bits.Mul64(K[2], ai) h3, l3 := bits.Mul64(K[3], ai) l1, c0 := bits.Add64(h0, l1, 0) l2, c1 := bits.Add64(h1, l2, c0) l3, c2 := bits.Add64(h2, l3, c1) l4, _ := bits.Add64(h3, 0, c2) S[i+0], c0 = bits.Add64(S[i+0], l0, 0) S[i+1], c1 = bits.Add64(S[i+1], l1, c0) S[i+2], c2 = bits.Add64(S[i+2], l2, c1) S[i+3], c3 = bits.Add64(S[i+3], l3, c2) S[i+4], _ = bits.Add64(S[i+4], l4, c3) } red512(&S, true) binary.LittleEndian.PutUint64(s[0*8:1*8], S[0]) binary.LittleEndian.PutUint64(s[1*8:2*8], S[1]) binary.LittleEndian.PutUint64(s[2*8:3*8], S[2]) binary.LittleEndian.PutUint64(s[3*8:4*8], S[3]) } golang-github-cloudflare-circl-1.3.7/sign/ed25519/modular_test.go000066400000000000000000000042271454601126700244630ustar00rootroot00000000000000package ed25519 import ( "crypto/rand" "testing" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/internal/test" ) func TestCalculateS(t *testing.T) { const testTimes = 1 << 10 s := make([]byte, paramB) k := make([]byte, paramB) r := make([]byte, paramB) a := make([]byte, paramB) orderBig := conv.BytesLe2BigInt(order[:]) for i := 0; i < testTimes; i++ { _, _ = rand.Read(k[:]) _, _ = rand.Read(r[:]) _, _ = rand.Read(a[:]) bigK := conv.BytesLe2BigInt(k[:]) bigR := conv.BytesLe2BigInt(r[:]) bigA := conv.BytesLe2BigInt(a[:]) calculateS(s, r, k, a) got := conv.BytesLe2BigInt(s[:]) bigK.Mul(bigK, bigA).Add(bigK, bigR) want := bigK.Mod(bigK, orderBig) if got.Cmp(want) != 0 { test.ReportError(t, got, want, k, r, a) } } } func TestReduction(t *testing.T) { const testTimes = 1 << 10 var x, y [paramB * 2]byte orderBig := conv.BytesLe2BigInt(order[:]) for i := 0; i < testTimes; i++ { for _, j := range []int{paramB, 2 * paramB} { _, _ = rand.Read(x[:j]) bigX := conv.BytesLe2BigInt(x[:j]) copy(y[:j], x[:j]) reduceModOrder(y[:j], true) got := conv.BytesLe2BigInt(y[:]) want := bigX.Mod(bigX, orderBig) if got.Cmp(want) != 0 { test.ReportError(t, got, want, x) } } } } func TestRangeOrder(t *testing.T) { aboveOrder := [...][paramB]byte{ { // order 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, }, { // order+1 0xed + 1, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, }, { // all-ones 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, }, } for i := range aboveOrder { got := isLessThanOrder(aboveOrder[i][:]) want := false if got != want { test.ReportError(t, got, want, i, aboveOrder[i]) } } } golang-github-cloudflare-circl-1.3.7/sign/ed25519/mult.go000066400000000000000000000102571454601126700227420ustar00rootroot00000000000000package ed25519 import ( "crypto/subtle" "encoding/binary" "math/bits" "github.com/cloudflare/circl/internal/conv" "github.com/cloudflare/circl/math" fp "github.com/cloudflare/circl/math/fp25519" ) var paramD = fp.Elt{ 0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75, 0xab, 0xd8, 0x41, 0x41, 0x4d, 0x0a, 0x70, 0x00, 0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c, 0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52, } // mLSBRecoding parameters. const ( fxT = 257 fxV = 2 fxW = 3 fx2w1 = 1 << (uint(fxW) - 1) numWords64 = (paramB * 8 / 64) ) // mLSBRecoding is the odd-only modified LSB-set. // // Reference: // // "Efficient and secure algorithms for GLV-based scalar multiplication and // their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) // http://doi.org/10.1007/s13389-014-0085-7. func mLSBRecoding(L []int8, k []byte) { const ee = (fxT + fxW*fxV - 1) / (fxW * fxV) const dd = ee * fxV const ll = dd * fxW if len(L) == (ll + 1) { var m [numWords64 + 1]uint64 for i := 0; i < numWords64; i++ { m[i] = binary.LittleEndian.Uint64(k[8*i : 8*i+8]) } condAddOrderN(&m) L[dd-1] = 1 for i := 0; i < dd-1; i++ { kip1 := (m[(i+1)/64] >> (uint(i+1) % 64)) & 0x1 L[i] = int8(kip1<<1) - 1 } { // right-shift by d right := uint(dd % 64) left := uint(64) - right lim := ((numWords64+1)*64 - dd) / 64 j := dd / 64 for i := 0; i < lim; i++ { m[i] = (m[i+j] >> right) | (m[i+j+1] << left) } m[lim] = m[lim+j] >> right } for i := dd; i < ll; i++ { L[i] = L[i%dd] * int8(m[0]&0x1) div2subY(m[:], int64(L[i]>>1), numWords64) } L[ll] = int8(m[0]) } } // absolute returns always a positive value. func absolute(x int32) int32 { mask := x >> 31 return (x + mask) ^ mask } // condAddOrderN updates x = x+order if x is even, otherwise x remains unchanged. func condAddOrderN(x *[numWords64 + 1]uint64) { isOdd := (x[0] & 0x1) - 1 c := uint64(0) for i := 0; i < numWords64; i++ { orderWord := binary.LittleEndian.Uint64(order[8*i : 8*i+8]) o := isOdd & orderWord x0, c0 := bits.Add64(x[i], o, c) x[i] = x0 c = c0 } x[numWords64], _ = bits.Add64(x[numWords64], 0, c) } // div2subY update x = (x/2) - y. func div2subY(x []uint64, y int64, l int) { s := uint64(y >> 63) for i := 0; i < l-1; i++ { x[i] = (x[i] >> 1) | (x[i+1] << 63) } x[l-1] = (x[l-1] >> 1) b := uint64(0) x0, b0 := bits.Sub64(x[0], uint64(y), b) x[0] = x0 b = b0 for i := 1; i < l-1; i++ { x0, b0 := bits.Sub64(x[i], s, b) x[i] = x0 b = b0 } x[l-1], _ = bits.Sub64(x[l-1], s, b) } func (P *pointR1) fixedMult(scalar []byte) { if len(scalar) != paramB { panic("wrong scalar size") } const ee = (fxT + fxW*fxV - 1) / (fxW * fxV) const dd = ee * fxV const ll = dd * fxW L := make([]int8, ll+1) mLSBRecoding(L[:], scalar) S := &pointR3{} P.SetIdentity() for ii := ee - 1; ii >= 0; ii-- { P.double() for j := 0; j < fxV; j++ { dig := L[fxW*dd-j*ee+ii-ee] for i := (fxW-1)*dd - j*ee + ii - ee; i >= (2*dd - j*ee + ii - ee); i = i - dd { dig = 2*dig + L[i] } idx := absolute(int32(dig)) sig := L[dd-j*ee+ii-ee] Tabj := &tabSign[fxV-j-1] for k := 0; k < fx2w1; k++ { S.cmov(&Tabj[k], subtle.ConstantTimeEq(int32(k), idx)) } S.cneg(subtle.ConstantTimeEq(int32(sig), -1)) P.mixAdd(S) } } } const ( omegaFix = 7 omegaVar = 5 ) // doubleMult returns P=mG+nQ. func (P *pointR1) doubleMult(Q *pointR1, m, n []byte) { nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m), omegaFix) nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n), omegaVar) if len(nafFix) > len(nafVar) { nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...) } else if len(nafFix) < len(nafVar) { nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...) } var TabQ [1 << (omegaVar - 2)]pointR2 Q.oddMultiples(TabQ[:]) P.SetIdentity() for i := len(nafFix) - 1; i >= 0; i-- { P.double() // Generator point if nafFix[i] != 0 { idxM := absolute(nafFix[i]) >> 1 R := tabVerif[idxM] if nafFix[i] < 0 { R.neg() } P.mixAdd(&R) } // Variable input point if nafVar[i] != 0 { idxN := absolute(nafVar[i]) >> 1 S := TabQ[idxN] if nafVar[i] < 0 { S.neg() } P.add(&S) } } } golang-github-cloudflare-circl-1.3.7/sign/ed25519/point.go000066400000000000000000000104011454601126700231010ustar00rootroot00000000000000package ed25519 import fp "github.com/cloudflare/circl/math/fp25519" type ( pointR1 struct{ x, y, z, ta, tb fp.Elt } pointR2 struct { pointR3 z2 fp.Elt } ) type pointR3 struct{ addYX, subYX, dt2 fp.Elt } func (P *pointR1) neg() { fp.Neg(&P.x, &P.x) fp.Neg(&P.ta, &P.ta) } func (P *pointR1) SetIdentity() { P.x = fp.Elt{} fp.SetOne(&P.y) fp.SetOne(&P.z) P.ta = fp.Elt{} P.tb = fp.Elt{} } func (P *pointR1) toAffine() { fp.Inv(&P.z, &P.z) fp.Mul(&P.x, &P.x, &P.z) fp.Mul(&P.y, &P.y, &P.z) fp.Modp(&P.x) fp.Modp(&P.y) fp.SetOne(&P.z) P.ta = P.x P.tb = P.y } func (P *pointR1) ToBytes(k []byte) error { P.toAffine() var x [fp.Size]byte err := fp.ToBytes(k[:fp.Size], &P.y) if err != nil { return err } err = fp.ToBytes(x[:], &P.x) if err != nil { return err } b := x[0] & 1 k[paramB-1] = k[paramB-1] | (b << 7) return nil } func (P *pointR1) FromBytes(k []byte) bool { if len(k) != paramB { panic("wrong size") } signX := k[paramB-1] >> 7 copy(P.y[:], k[:fp.Size]) P.y[fp.Size-1] &= 0x7F p := fp.P() if !isLessThan(P.y[:], p[:]) { return false } one, u, v := &fp.Elt{}, &fp.Elt{}, &fp.Elt{} fp.SetOne(one) fp.Sqr(u, &P.y) // u = y^2 fp.Mul(v, u, ¶mD) // v = dy^2 fp.Sub(u, u, one) // u = y^2-1 fp.Add(v, v, one) // v = dy^2+1 isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v) if !isQR { return false } fp.Modp(&P.x) // x = x mod p if fp.IsZero(&P.x) && signX == 1 { return false } if signX != (P.x[0] & 1) { fp.Neg(&P.x, &P.x) } P.ta = P.x P.tb = P.y fp.SetOne(&P.z) return true } // double calculates 2P for curves with A=-1. func (P *pointR1) double() { Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb fp.Add(e, Px, Py) // x+y fp.Sqr(a, Px) // A = x^2 fp.Sqr(b, Py) // B = y^2 fp.Sqr(c, Pz) // z^2 fp.Add(c, c, c) // C = 2*z^2 fp.Add(h, a, b) // H = A+B fp.Sqr(e, e) // (x+y)^2 fp.Sub(e, e, h) // E = (x+y)^2-A-B fp.Sub(g, b, a) // G = B-A fp.Sub(f, c, g) // F = C-G fp.Mul(Pz, f, g) // Z = F * G fp.Mul(Px, e, f) // X = E * F fp.Mul(Py, g, h) // Y = G * H, T = E * H } func (P *pointR1) mixAdd(Q *pointR3) { fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 P.coreAddition(Q) } func (P *pointR1) add(Q *pointR2) { fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2 P.coreAddition(&Q.pointR3) } // coreAddition calculates P=P+Q for curves with A=-1. func (P *pointR1) coreAddition(Q *pointR3) { Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2 a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb fp.Mul(c, Pta, Ptb) // t1 = ta*tb fp.Sub(h, Py, Px) // y1-x1 fp.Add(b, Py, Px) // y1+x1 fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2) fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2) fp.Mul(c, c, dt2) // C = 2*D*t1*t2 fp.Sub(e, b, a) // E = B-A fp.Add(h, b, a) // H = B+A fp.Sub(f, d, c) // F = D-C fp.Add(g, d, c) // G = D+C fp.Mul(Pz, f, g) // Z = F * G fp.Mul(Px, e, f) // X = E * F fp.Mul(Py, g, h) // Y = G * H, T = E * H } func (P *pointR1) oddMultiples(T []pointR2) { var R pointR2 n := len(T) T[0].fromR1(P) _2P := *P _2P.double() R.fromR1(&_2P) for i := 1; i < n; i++ { P.add(&R) T[i].fromR1(P) } } func (P *pointR1) isEqual(Q *pointR1) bool { l, r := &fp.Elt{}, &fp.Elt{} fp.Mul(l, &P.x, &Q.z) fp.Mul(r, &Q.x, &P.z) fp.Sub(l, l, r) b := fp.IsZero(l) fp.Mul(l, &P.y, &Q.z) fp.Mul(r, &Q.y, &P.z) fp.Sub(l, l, r) b = b && fp.IsZero(l) fp.Mul(l, &P.ta, &P.tb) fp.Mul(l, l, &Q.z) fp.Mul(r, &Q.ta, &Q.tb) fp.Mul(r, r, &P.z) fp.Sub(l, l, r) b = b && fp.IsZero(l) return b } func (P *pointR3) neg() { P.addYX, P.subYX = P.subYX, P.addYX fp.Neg(&P.dt2, &P.dt2) } func (P *pointR2) fromR1(Q *pointR1) { fp.Add(&P.addYX, &Q.y, &Q.x) fp.Sub(&P.subYX, &Q.y, &Q.x) fp.Mul(&P.dt2, &Q.ta, &Q.tb) fp.Mul(&P.dt2, &P.dt2, ¶mD) fp.Add(&P.dt2, &P.dt2, &P.dt2) fp.Add(&P.z2, &Q.z, &Q.z) } func (P *pointR3) cneg(b int) { t := &fp.Elt{} fp.Cswap(&P.addYX, &P.subYX, uint(b)) fp.Neg(t, &P.dt2) fp.Cmov(&P.dt2, t, uint(b)) } func (P *pointR3) cmov(Q *pointR3, b int) { fp.Cmov(&P.addYX, &Q.addYX, uint(b)) fp.Cmov(&P.subYX, &Q.subYX, uint(b)) fp.Cmov(&P.dt2, &Q.dt2, uint(b)) } golang-github-cloudflare-circl-1.3.7/sign/ed25519/point_test.go000066400000000000000000000037471454601126700241570ustar00rootroot00000000000000package ed25519 import ( "crypto/rand" "flag" "testing" "github.com/cloudflare/circl/internal/test" ) func randomPoint(P *pointR1) { k := make([]byte, paramB) _, _ = rand.Read(k[:]) P.fixedMult(k) } func TestPoint(t *testing.T) { const testTimes = 1 << 10 t.Run("add", func(t *testing.T) { var P pointR1 var Q pointR1 var R pointR2 for i := 0; i < testTimes; i++ { randomPoint(&P) _16P := P R.fromR1(&P) // 16P = 2^4P for j := 0; j < 4; j++ { _16P.double() } // 16P = P+P...+P Q.SetIdentity() for j := 0; j < 16; j++ { Q.add(&R) } got := _16P.isEqual(&Q) want := true if got != want { test.ReportError(t, got, want, P) } } }) t.Run("fixed", func(t *testing.T) { var P, Q, R pointR1 k := make([]byte, paramB) l := make([]byte, paramB) for i := 0; i < testTimes; i++ { randomPoint(&P) _, _ = rand.Read(k[:]) Q.fixedMult(k[:]) R.doubleMult(&P, k[:], l[:]) got := Q.isEqual(&R) want := true if got != want { test.ReportError(t, got, want, P, k) } } }) } var runLongBench = flag.Bool("long", false, "runs longer benchmark") func BenchmarkPoint(b *testing.B) { if !*runLongBench { b.Log("Skipped one long bench, add -long flag to run longer bench") b.SkipNow() } k := make([]byte, paramB) l := make([]byte, paramB) _, _ = rand.Read(k) _, _ = rand.Read(l) var P pointR1 var Q pointR2 var R pointR3 randomPoint(&P) Q.fromR1(&P) b.Run("toAffine", func(b *testing.B) { for i := 0; i < b.N; i++ { P.toAffine() } }) b.Run("double", func(b *testing.B) { for i := 0; i < b.N; i++ { P.double() } }) b.Run("mixadd", func(b *testing.B) { for i := 0; i < b.N; i++ { P.mixAdd(&R) } }) b.Run("add", func(b *testing.B) { for i := 0; i < b.N; i++ { P.add(&Q) } }) b.Run("fixedMult", func(b *testing.B) { for i := 0; i < b.N; i++ { P.fixedMult(k) } }) b.Run("doubleMult", func(b *testing.B) { for i := 0; i < b.N; i++ { P.doubleMult(&P, k, l) } }) } golang-github-cloudflare-circl-1.3.7/sign/ed25519/pubkey.go000066400000000000000000000002641454601126700232550ustar00rootroot00000000000000//go:build go1.13 // +build go1.13 package ed25519 import cryptoEd25519 "crypto/ed25519" // PublicKey is the type of Ed25519 public keys. type PublicKey cryptoEd25519.PublicKey golang-github-cloudflare-circl-1.3.7/sign/ed25519/pubkey112.go000066400000000000000000000001761454601126700235030ustar00rootroot00000000000000//go:build !go1.13 // +build !go1.13 package ed25519 // PublicKey is the type of Ed25519 public keys. type PublicKey []byte golang-github-cloudflare-circl-1.3.7/sign/ed25519/rfc8032_test.go000066400000000000000000000505311454601126700241060ustar00rootroot00000000000000package ed25519_test import ( "archive/zip" "bufio" "bytes" "encoding/hex" "fmt" "strings" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/sign/ed25519" ) type rfc8032Vector struct { private ed25519.PrivateKey public ed25519.PublicKey message []byte signature []byte } func (v *rfc8032Vector) fetch(line string) { values := strings.Split(line, ":") if len(values) != 5 { panic(fmt.Errorf("len: %v %v", len(values), values)) } v.private, _ = hex.DecodeString(values[0]) v.public, _ = hex.DecodeString(values[1]) v.message, _ = hex.DecodeString(values[2]) v.signature, _ = hex.DecodeString(values[3]) v.private = v.private[:ed25519.SeedSize] v.signature = v.signature[:ed25519.SignatureSize] } func (v *rfc8032Vector) test(t *testing.T, lineNum int) { key := ed25519.NewKeyFromSeed(v.private) { got := key.Public().(ed25519.PublicKey) want := v.public if !bytes.Equal(got, want) { test.ReportError(t, got, want, lineNum, v) } got = ed25519.Sign(key, v.message) want = v.signature if !bytes.Equal(got, want) { test.ReportError(t, got, want, lineNum, v) } } { got := ed25519.Verify(key.Public().(ed25519.PublicKey), v.message, v.signature) want := true if got != want { test.ReportError(t, got, want, lineNum, v) } } } func TestRFC8032(t *testing.T) { const nameFile = "testdata/sign.input.zip" zipFile, err := zip.OpenReader(nameFile) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) } defer zipFile.Close() for _, f := range zipFile.File { unzipped, err := f.Open() if err != nil { t.Fatalf("File %v can not be opened. Error: %v", f.Name, err) } defer unzipped.Close() fScanner := bufio.NewScanner(unzipped) var v rfc8032Vector for i := 1; fScanner.Scan(); i++ { v.fetch(fScanner.Text()) v.test(t, i) } } } type vector struct { name string scheme string sk []byte pk []byte sig []byte msg []byte msgLen uint ph bool ctx []byte ctxLen uint } var vectorsEd25519 = [...]vector{ { name: "-----TEST 1", scheme: "Ed25519Pure", sk: []byte{ 0x9d, 0x61, 0xb1, 0x9d, 0xef, 0xfd, 0x5a, 0x60, 0xba, 0x84, 0x4a, 0xf4, 0x92, 0xec, 0x2c, 0xc4, 0x44, 0x49, 0xc5, 0x69, 0x7b, 0x32, 0x69, 0x19, 0x70, 0x3b, 0xac, 0x03, 0x1c, 0xae, 0x7f, 0x60, }, pk: []byte{ 0xd7, 0x5a, 0x98, 0x01, 0x82, 0xb1, 0x0a, 0xb7, 0xd5, 0x4b, 0xfe, 0xd3, 0xc9, 0x64, 0x07, 0x3a, 0x0e, 0xe1, 0x72, 0xf3, 0xda, 0xa6, 0x23, 0x25, 0xaf, 0x02, 0x1a, 0x68, 0xf7, 0x07, 0x51, 0x1a, }, msg: []byte{}, msgLen: 0, sig: []byte{ 0xe5, 0x56, 0x43, 0x00, 0xc3, 0x60, 0xac, 0x72, 0x90, 0x86, 0xe2, 0xcc, 0x80, 0x6e, 0x82, 0x8a, 0x84, 0x87, 0x7f, 0x1e, 0xb8, 0xe5, 0xd9, 0x74, 0xd8, 0x73, 0xe0, 0x65, 0x22, 0x49, 0x01, 0x55, 0x5f, 0xb8, 0x82, 0x15, 0x90, 0xa3, 0x3b, 0xac, 0xc6, 0x1e, 0x39, 0x70, 0x1c, 0xf9, 0xb4, 0x6b, 0xd2, 0x5b, 0xf5, 0xf0, 0x59, 0x5b, 0xbe, 0x24, 0x65, 0x51, 0x41, 0x43, 0x8e, 0x7a, 0x10, 0x0b, }, ph: false, ctx: []byte{}, ctxLen: 0, }, { name: "-----TEST 2", scheme: "Ed25519Pure", sk: []byte{ 0x4c, 0xcd, 0x08, 0x9b, 0x28, 0xff, 0x96, 0xda, 0x9d, 0xb6, 0xc3, 0x46, 0xec, 0x11, 0x4e, 0x0f, 0x5b, 0x8a, 0x31, 0x9f, 0x35, 0xab, 0xa6, 0x24, 0xda, 0x8c, 0xf6, 0xed, 0x4f, 0xb8, 0xa6, 0xfb, }, pk: []byte{ 0x3d, 0x40, 0x17, 0xc3, 0xe8, 0x43, 0x89, 0x5a, 0x92, 0xb7, 0x0a, 0xa7, 0x4d, 0x1b, 0x7e, 0xbc, 0x9c, 0x98, 0x2c, 0xcf, 0x2e, 0xc4, 0x96, 0x8c, 0xc0, 0xcd, 0x55, 0xf1, 0x2a, 0xf4, 0x66, 0x0c, }, msg: []byte{ 0x72, }, msgLen: 1, sig: []byte{ 0x92, 0xa0, 0x09, 0xa9, 0xf0, 0xd4, 0xca, 0xb8, 0x72, 0x0e, 0x82, 0x0b, 0x5f, 0x64, 0x25, 0x40, 0xa2, 0xb2, 0x7b, 0x54, 0x16, 0x50, 0x3f, 0x8f, 0xb3, 0x76, 0x22, 0x23, 0xeb, 0xdb, 0x69, 0xda, 0x08, 0x5a, 0xc1, 0xe4, 0x3e, 0x15, 0x99, 0x6e, 0x45, 0x8f, 0x36, 0x13, 0xd0, 0xf1, 0x1d, 0x8c, 0x38, 0x7b, 0x2e, 0xae, 0xb4, 0x30, 0x2a, 0xee, 0xb0, 0x0d, 0x29, 0x16, 0x12, 0xbb, 0x0c, 0x00, }, ph: false, ctx: []byte{}, ctxLen: 0, }, { name: "-----TEST 3", scheme: "Ed25519Pure", sk: []byte{ 0xc5, 0xaa, 0x8d, 0xf4, 0x3f, 0x9f, 0x83, 0x7b, 0xed, 0xb7, 0x44, 0x2f, 0x31, 0xdc, 0xb7, 0xb1, 0x66, 0xd3, 0x85, 0x35, 0x07, 0x6f, 0x09, 0x4b, 0x85, 0xce, 0x3a, 0x2e, 0x0b, 0x44, 0x58, 0xf7, }, pk: []byte{ 0xfc, 0x51, 0xcd, 0x8e, 0x62, 0x18, 0xa1, 0xa3, 0x8d, 0xa4, 0x7e, 0xd0, 0x02, 0x30, 0xf0, 0x58, 0x08, 0x16, 0xed, 0x13, 0xba, 0x33, 0x03, 0xac, 0x5d, 0xeb, 0x91, 0x15, 0x48, 0x90, 0x80, 0x25, }, msg: []byte{ 0xaf, 0x82, }, msgLen: 2, sig: []byte{ 0x62, 0x91, 0xd6, 0x57, 0xde, 0xec, 0x24, 0x02, 0x48, 0x27, 0xe6, 0x9c, 0x3a, 0xbe, 0x01, 0xa3, 0x0c, 0xe5, 0x48, 0xa2, 0x84, 0x74, 0x3a, 0x44, 0x5e, 0x36, 0x80, 0xd7, 0xdb, 0x5a, 0xc3, 0xac, 0x18, 0xff, 0x9b, 0x53, 0x8d, 0x16, 0xf2, 0x90, 0xae, 0x67, 0xf7, 0x60, 0x98, 0x4d, 0xc6, 0x59, 0x4a, 0x7c, 0x15, 0xe9, 0x71, 0x6e, 0xd2, 0x8d, 0xc0, 0x27, 0xbe, 0xce, 0xea, 0x1e, 0xc4, 0x0a, }, ph: false, ctx: []byte{}, ctxLen: 0, }, { name: "-----TEST 1024", scheme: "Ed25519Pure", sk: []byte{ 0xf5, 0xe5, 0x76, 0x7c, 0xf1, 0x53, 0x31, 0x95, 0x17, 0x63, 0x0f, 0x22, 0x68, 0x76, 0xb8, 0x6c, 0x81, 0x60, 0xcc, 0x58, 0x3b, 0xc0, 0x13, 0x74, 0x4c, 0x6b, 0xf2, 0x55, 0xf5, 0xcc, 0x0e, 0xe5, }, pk: []byte{ 0x27, 0x81, 0x17, 0xfc, 0x14, 0x4c, 0x72, 0x34, 0x0f, 0x67, 0xd0, 0xf2, 0x31, 0x6e, 0x83, 0x86, 0xce, 0xff, 0xbf, 0x2b, 0x24, 0x28, 0xc9, 0xc5, 0x1f, 0xef, 0x7c, 0x59, 0x7f, 0x1d, 0x42, 0x6e, }, msg: []byte{ 0x08, 0xb8, 0xb2, 0xb7, 0x33, 0x42, 0x42, 0x43, 0x76, 0x0f, 0xe4, 0x26, 0xa4, 0xb5, 0x49, 0x08, 0x63, 0x21, 0x10, 0xa6, 0x6c, 0x2f, 0x65, 0x91, 0xea, 0xbd, 0x33, 0x45, 0xe3, 0xe4, 0xeb, 0x98, 0xfa, 0x6e, 0x26, 0x4b, 0xf0, 0x9e, 0xfe, 0x12, 0xee, 0x50, 0xf8, 0xf5, 0x4e, 0x9f, 0x77, 0xb1, 0xe3, 0x55, 0xf6, 0xc5, 0x05, 0x44, 0xe2, 0x3f, 0xb1, 0x43, 0x3d, 0xdf, 0x73, 0xbe, 0x84, 0xd8, 0x79, 0xde, 0x7c, 0x00, 0x46, 0xdc, 0x49, 0x96, 0xd9, 0xe7, 0x73, 0xf4, 0xbc, 0x9e, 0xfe, 0x57, 0x38, 0x82, 0x9a, 0xdb, 0x26, 0xc8, 0x1b, 0x37, 0xc9, 0x3a, 0x1b, 0x27, 0x0b, 0x20, 0x32, 0x9d, 0x65, 0x86, 0x75, 0xfc, 0x6e, 0xa5, 0x34, 0xe0, 0x81, 0x0a, 0x44, 0x32, 0x82, 0x6b, 0xf5, 0x8c, 0x94, 0x1e, 0xfb, 0x65, 0xd5, 0x7a, 0x33, 0x8b, 0xbd, 0x2e, 0x26, 0x64, 0x0f, 0x89, 0xff, 0xbc, 0x1a, 0x85, 0x8e, 0xfc, 0xb8, 0x55, 0x0e, 0xe3, 0xa5, 0xe1, 0x99, 0x8b, 0xd1, 0x77, 0xe9, 0x3a, 0x73, 0x63, 0xc3, 0x44, 0xfe, 0x6b, 0x19, 0x9e, 0xe5, 0xd0, 0x2e, 0x82, 0xd5, 0x22, 0xc4, 0xfe, 0xba, 0x15, 0x45, 0x2f, 0x80, 0x28, 0x8a, 0x82, 0x1a, 0x57, 0x91, 0x16, 0xec, 0x6d, 0xad, 0x2b, 0x3b, 0x31, 0x0d, 0xa9, 0x03, 0x40, 0x1a, 0xa6, 0x21, 0x00, 0xab, 0x5d, 0x1a, 0x36, 0x55, 0x3e, 0x06, 0x20, 0x3b, 0x33, 0x89, 0x0c, 0xc9, 0xb8, 0x32, 0xf7, 0x9e, 0xf8, 0x05, 0x60, 0xcc, 0xb9, 0xa3, 0x9c, 0xe7, 0x67, 0x96, 0x7e, 0xd6, 0x28, 0xc6, 0xad, 0x57, 0x3c, 0xb1, 0x16, 0xdb, 0xef, 0xef, 0xd7, 0x54, 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0x45, 0x98, 0x67, 0x80, 0xfc, 0x0b, 0x16, 0xac, 0x45, 0x16, 0x49, 0xde, 0x61, 0x88, 0xa7, 0xdb, 0xdf, 0x19, 0x1f, 0x64, 0xb5, 0xfc, 0x5e, 0x2a, 0xb4, 0x7b, 0x57, 0xf7, 0xf7, 0x27, 0x6c, 0xd4, 0x19, 0xc1, 0x7a, 0x3c, 0xa8, 0xe1, 0xb9, 0x39, 0xae, 0x49, 0xe4, 0x88, 0xac, 0xba, 0x6b, 0x96, 0x56, 0x10, 0xb5, 0x48, 0x01, 0x09, 0xc8, 0xb1, 0x7b, 0x80, 0xe1, 0xb7, 0xb7, 0x50, 0xdf, 0xc7, 0x59, 0x8d, 0x5d, 0x50, 0x11, 0xfd, 0x2d, 0xcc, 0x56, 0x00, 0xa3, 0x2e, 0xf5, 0xb5, 0x2a, 0x1e, 0xcc, 0x82, 0x0e, 0x30, 0x8a, 0xa3, 0x42, 0x72, 0x1a, 0xac, 0x09, 0x43, 0xbf, 0x66, 0x86, 0xb6, 0x4b, 0x25, 0x79, 0x37, 0x65, 0x04, 0xcc, 0xc4, 0x93, 0xd9, 0x7e, 0x6a, 0xed, 0x3f, 0xb0, 0xf9, 0xcd, 0x71, 0xa4, 0x3d, 0xd4, 0x97, 0xf0, 0x1f, 0x17, 0xc0, 0xe2, 0xcb, 0x37, 0x97, 0xaa, 0x2a, 0x2f, 0x25, 0x66, 0x56, 0x16, 0x8e, 0x6c, 0x49, 0x6a, 0xfc, 0x5f, 0xb9, 0x32, 0x46, 0xf6, 0xb1, 0x11, 0x63, 0x98, 0xa3, 0x46, 0xf1, 0xa6, 0x41, 0xf3, 0xb0, 0x41, 0xe9, 0x89, 0xf7, 0x91, 0x4f, 0x90, 0xcc, 0x2c, 0x7f, 0xff, 0x35, 0x78, 0x76, 0xe5, 0x06, 0xb5, 0x0d, 0x33, 0x4b, 0xa7, 0x7c, 0x22, 0x5b, 0xc3, 0x07, 0xba, 0x53, 0x71, 0x52, 0xf3, 0xf1, 0x61, 0x0e, 0x4e, 0xaf, 0xe5, 0x95, 0xf6, 0xd9, 0xd9, 0x0d, 0x11, 0xfa, 0xa9, 0x33, 0xa1, 0x5e, 0xf1, 0x36, 0x95, 0x46, 0x86, 0x8a, 0x7f, 0x3a, 0x45, 0xa9, 0x67, 0x68, 0xd4, 0x0f, 0xd9, 0xd0, 0x34, 0x12, 0xc0, 0x91, 0xc6, 0x31, 0x5c, 0xf4, 0xfd, 0xe7, 0xcb, 0x68, 0x60, 0x69, 0x37, 0x38, 0x0d, 0xb2, 0xea, 0xaa, 0x70, 0x7b, 0x4c, 0x41, 0x85, 0xc3, 0x2e, 0xdd, 0xcd, 0xd3, 0x06, 0x70, 0x5e, 0x4d, 0xc1, 0xff, 0xc8, 0x72, 0xee, 0xee, 0x47, 0x5a, 0x64, 0xdf, 0xac, 0x86, 0xab, 0xa4, 0x1c, 0x06, 0x18, 0x98, 0x3f, 0x87, 0x41, 0xc5, 0xef, 0x68, 0xd3, 0xa1, 0x01, 0xe8, 0xa3, 0xb8, 0xca, 0xc6, 0x0c, 0x90, 0x5c, 0x15, 0xfc, 0x91, 0x08, 0x40, 0xb9, 0x4c, 0x00, 0xa0, 0xb9, 0xd0, }, msgLen: 1023, sig: []byte{ 0x0a, 0xab, 0x4c, 0x90, 0x05, 0x01, 0xb3, 0xe2, 0x4d, 0x7c, 0xdf, 0x46, 0x63, 0x32, 0x6a, 0x3a, 0x87, 0xdf, 0x5e, 0x48, 0x43, 0xb2, 0xcb, 0xdb, 0x67, 0xcb, 0xf6, 0xe4, 0x60, 0xfe, 0xc3, 0x50, 0xaa, 0x53, 0x71, 0xb1, 0x50, 0x8f, 0x9f, 0x45, 0x28, 0xec, 0xea, 0x23, 0xc4, 0x36, 0xd9, 0x4b, 0x5e, 0x8f, 0xcd, 0x4f, 0x68, 0x1e, 0x30, 0xa6, 0xac, 0x00, 0xa9, 0x70, 0x4a, 0x18, 0x8a, 0x03, }, ph: false, ctx: []byte{}, ctxLen: 0, }, { name: "-----TEST sha(abc)", scheme: "Ed25519Pure", sk: []byte{ 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, }, pk: []byte{ 0xec, 0x17, 0x2b, 0x93, 0xad, 0x5e, 0x56, 0x3b, 0xf4, 0x93, 0x2c, 0x70, 0xe1, 0x24, 0x50, 0x34, 0xc3, 0x54, 0x67, 0xef, 0x2e, 0xfd, 0x4d, 0x64, 0xeb, 0xf8, 0x19, 0x68, 0x34, 0x67, 0xe2, 0xbf, }, msg: []byte{ 0xdd, 0xaf, 0x35, 0xa1, 0x93, 0x61, 0x7a, 0xba, 0xcc, 0x41, 0x73, 0x49, 0xae, 0x20, 0x41, 0x31, 0x12, 0xe6, 0xfa, 0x4e, 0x89, 0xa9, 0x7e, 0xa2, 0x0a, 0x9e, 0xee, 0xe6, 0x4b, 0x55, 0xd3, 0x9a, 0x21, 0x92, 0x99, 0x2a, 0x27, 0x4f, 0xc1, 0xa8, 0x36, 0xba, 0x3c, 0x23, 0xa3, 0xfe, 0xeb, 0xbd, 0x45, 0x4d, 0x44, 0x23, 0x64, 0x3c, 0xe8, 0x0e, 0x2a, 0x9a, 0xc9, 0x4f, 0xa5, 0x4c, 0xa4, 0x9f, }, msgLen: 64, sig: []byte{ 0xdc, 0x2a, 0x44, 0x59, 0xe7, 0x36, 0x96, 0x33, 0xa5, 0x2b, 0x1b, 0xf2, 0x77, 0x83, 0x9a, 0x00, 0x20, 0x10, 0x09, 0xa3, 0xef, 0xbf, 0x3e, 0xcb, 0x69, 0xbe, 0xa2, 0x18, 0x6c, 0x26, 0xb5, 0x89, 0x09, 0x35, 0x1f, 0xc9, 0xac, 0x90, 0xb3, 0xec, 0xfd, 0xfb, 0xc7, 0xc6, 0x64, 0x31, 0xe0, 0x30, 0x3d, 0xca, 0x17, 0x9c, 0x13, 0x8a, 0xc1, 0x7a, 0xd9, 0xbe, 0xf1, 0x17, 0x73, 0x31, 0xa7, 0x04, }, ph: false, ctx: []byte{}, ctxLen: 0, }, { name: "-----TEST abc", scheme: "Ed25519Ph", sk: []byte{ 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, }, pk: []byte{ 0xec, 0x17, 0x2b, 0x93, 0xad, 0x5e, 0x56, 0x3b, 0xf4, 0x93, 0x2c, 0x70, 0xe1, 0x24, 0x50, 0x34, 0xc3, 0x54, 0x67, 0xef, 0x2e, 0xfd, 0x4d, 0x64, 0xeb, 0xf8, 0x19, 0x68, 0x34, 0x67, 0xe2, 0xbf, }, msg: []byte{ 0x61, 0x62, 0x63, }, msgLen: 3, sig: []byte{ 0x98, 0xa7, 0x02, 0x22, 0xf0, 0xb8, 0x12, 0x1a, 0xa9, 0xd3, 0x0f, 0x81, 0x3d, 0x68, 0x3f, 0x80, 0x9e, 0x46, 0x2b, 0x46, 0x9c, 0x7f, 0xf8, 0x76, 0x39, 0x49, 0x9b, 0xb9, 0x4e, 0x6d, 0xae, 0x41, 0x31, 0xf8, 0x50, 0x42, 0x46, 0x3c, 0x2a, 0x35, 0x5a, 0x20, 0x03, 0xd0, 0x62, 0xad, 0xf5, 0xaa, 0xa1, 0x0b, 0x8c, 0x61, 0xe6, 0x36, 0x06, 0x2a, 0xaa, 0xd1, 0x1c, 0x2a, 0x26, 0x08, 0x34, 0x06, }, ph: true, ctx: []byte{}, ctxLen: 0, }, { name: "-----foo", scheme: "Ed25519Ctx", sk: []byte{ 0x03, 0x05, 0x33, 0x4e, 0x38, 0x1a, 0xf7, 0x8f, 0x14, 0x1c, 0xb6, 0x66, 0xf6, 0x19, 0x9f, 0x57, 0xbc, 0x34, 0x95, 0x33, 0x5a, 0x25, 0x6a, 0x95, 0xbd, 0x2a, 0x55, 0xbf, 0x54, 0x66, 0x63, 0xf6, }, pk: []byte{ 0xdf, 0xc9, 0x42, 0x5e, 0x4f, 0x96, 0x8f, 0x7f, 0x0c, 0x29, 0xf0, 0x25, 0x9c, 0xf5, 0xf9, 0xae, 0xd6, 0x85, 0x1c, 0x2b, 0xb4, 0xad, 0x8b, 0xfb, 0x86, 0x0c, 0xfe, 0xe0, 0xab, 0x24, 0x82, 0x92, }, msg: []byte{ 0xf7, 0x26, 0x93, 0x6d, 0x19, 0xc8, 0x00, 0x49, 0x4e, 0x3f, 0xda, 0xff, 0x20, 0xb2, 0x76, 0xa8, }, msgLen: 16, sig: []byte{ 0x55, 0xa4, 0xcc, 0x2f, 0x70, 0xa5, 0x4e, 0x04, 0x28, 0x8c, 0x5f, 0x4c, 0xd1, 0xe4, 0x5a, 0x7b, 0xb5, 0x20, 0xb3, 0x62, 0x92, 0x91, 0x18, 0x76, 0xca, 0xda, 0x73, 0x23, 0x19, 0x8d, 0xd8, 0x7a, 0x8b, 0x36, 0x95, 0x0b, 0x95, 0x13, 0x00, 0x22, 0x90, 0x7a, 0x7f, 0xb7, 0xc4, 0xe9, 0xb2, 0xd5, 0xf6, 0xcc, 0xa6, 0x85, 0xa5, 0x87, 0xb4, 0xb2, 0x1f, 0x4b, 0x88, 0x8e, 0x4e, 0x7e, 0xdb, 0x0d, }, ph: false, ctx: []byte{ 0x66, 0x6f, 0x6f, }, ctxLen: 3, }, { name: "-----bar", scheme: "Ed25519Ctx", sk: []byte{ 0x03, 0x05, 0x33, 0x4e, 0x38, 0x1a, 0xf7, 0x8f, 0x14, 0x1c, 0xb6, 0x66, 0xf6, 0x19, 0x9f, 0x57, 0xbc, 0x34, 0x95, 0x33, 0x5a, 0x25, 0x6a, 0x95, 0xbd, 0x2a, 0x55, 0xbf, 0x54, 0x66, 0x63, 0xf6, }, pk: []byte{ 0xdf, 0xc9, 0x42, 0x5e, 0x4f, 0x96, 0x8f, 0x7f, 0x0c, 0x29, 0xf0, 0x25, 0x9c, 0xf5, 0xf9, 0xae, 0xd6, 0x85, 0x1c, 0x2b, 0xb4, 0xad, 0x8b, 0xfb, 0x86, 0x0c, 0xfe, 0xe0, 0xab, 0x24, 0x82, 0x92, }, msg: []byte{ 0xf7, 0x26, 0x93, 0x6d, 0x19, 0xc8, 0x00, 0x49, 0x4e, 0x3f, 0xda, 0xff, 0x20, 0xb2, 0x76, 0xa8, }, msgLen: 16, sig: []byte{ 0xfc, 0x60, 0xd5, 0x87, 0x2f, 0xc4, 0x6b, 0x3a, 0xa6, 0x9f, 0x8b, 0x5b, 0x43, 0x51, 0xd5, 0x80, 0x8f, 0x92, 0xbc, 0xc0, 0x44, 0x60, 0x6d, 0xb0, 0x97, 0xab, 0xab, 0x6d, 0xbc, 0xb1, 0xae, 0xe3, 0x21, 0x6c, 0x48, 0xe8, 0xb3, 0xb6, 0x64, 0x31, 0xb5, 0xb1, 0x86, 0xd1, 0xd2, 0x8f, 0x8e, 0xe1, 0x5a, 0x5c, 0xa2, 0xdf, 0x66, 0x68, 0x34, 0x62, 0x91, 0xc2, 0x04, 0x3d, 0x4e, 0xb3, 0xe9, 0x0d, }, ph: false, ctx: []byte{ 0x62, 0x61, 0x72, }, ctxLen: 3, }, { name: "-----foo2", scheme: "Ed25519Ctx", sk: []byte{ 0x03, 0x05, 0x33, 0x4e, 0x38, 0x1a, 0xf7, 0x8f, 0x14, 0x1c, 0xb6, 0x66, 0xf6, 0x19, 0x9f, 0x57, 0xbc, 0x34, 0x95, 0x33, 0x5a, 0x25, 0x6a, 0x95, 0xbd, 0x2a, 0x55, 0xbf, 0x54, 0x66, 0x63, 0xf6, }, pk: []byte{ 0xdf, 0xc9, 0x42, 0x5e, 0x4f, 0x96, 0x8f, 0x7f, 0x0c, 0x29, 0xf0, 0x25, 0x9c, 0xf5, 0xf9, 0xae, 0xd6, 0x85, 0x1c, 0x2b, 0xb4, 0xad, 0x8b, 0xfb, 0x86, 0x0c, 0xfe, 0xe0, 0xab, 0x24, 0x82, 0x92, }, msg: []byte{ 0x50, 0x8e, 0x9e, 0x68, 0x82, 0xb9, 0x79, 0xfe, 0xa9, 0x00, 0xf6, 0x2a, 0xdc, 0xea, 0xca, 0x35, }, msgLen: 16, sig: []byte{ 0x8b, 0x70, 0xc1, 0xcc, 0x83, 0x10, 0xe1, 0xde, 0x20, 0xac, 0x53, 0xce, 0x28, 0xae, 0x6e, 0x72, 0x07, 0xf3, 0x3c, 0x32, 0x95, 0xe0, 0x3b, 0xb5, 0xc0, 0x73, 0x2a, 0x1d, 0x20, 0xdc, 0x64, 0x90, 0x89, 0x22, 0xa8, 0xb0, 0x52, 0xcf, 0x99, 0xb7, 0xc4, 0xfe, 0x10, 0x7a, 0x5a, 0xbb, 0x5b, 0x2c, 0x40, 0x85, 0xae, 0x75, 0x89, 0x0d, 0x02, 0xdf, 0x26, 0x26, 0x9d, 0x89, 0x45, 0xf8, 0x4b, 0x0b, }, ph: false, ctx: []byte{ 0x66, 0x6f, 0x6f, }, ctxLen: 3, }, { name: "-----foo3", scheme: "Ed25519Ctx", sk: []byte{ 0xab, 0x9c, 0x28, 0x53, 0xce, 0x29, 0x7d, 0xda, 0xb8, 0x5c, 0x99, 0x3b, 0x3a, 0xe1, 0x4b, 0xca, 0xd3, 0x9b, 0x2c, 0x68, 0x2b, 0xea, 0xbc, 0x27, 0xd6, 0xd4, 0xeb, 0x20, 0x71, 0x1d, 0x65, 0x60, }, pk: []byte{ 0x0f, 0x1d, 0x12, 0x74, 0x94, 0x3b, 0x91, 0x41, 0x58, 0x89, 0x15, 0x2e, 0x89, 0x3d, 0x80, 0xe9, 0x32, 0x75, 0xa1, 0xfc, 0x0b, 0x65, 0xfd, 0x71, 0xb4, 0xb0, 0xdd, 0xa1, 0x0a, 0xd7, 0xd7, 0x72, }, msg: []byte{ 0xf7, 0x26, 0x93, 0x6d, 0x19, 0xc8, 0x00, 0x49, 0x4e, 0x3f, 0xda, 0xff, 0x20, 0xb2, 0x76, 0xa8, }, msgLen: 16, sig: []byte{ 0x21, 0x65, 0x5b, 0x5f, 0x1a, 0xa9, 0x65, 0x99, 0x6b, 0x3f, 0x97, 0xb3, 0xc8, 0x49, 0xea, 0xfb, 0xa9, 0x22, 0xa0, 0xa6, 0x29, 0x92, 0xf7, 0x3b, 0x3d, 0x1b, 0x73, 0x10, 0x6a, 0x84, 0xad, 0x85, 0xe9, 0xb8, 0x6a, 0x7b, 0x60, 0x05, 0xea, 0x86, 0x83, 0x37, 0xff, 0x2d, 0x20, 0xa7, 0xf5, 0xfb, 0xd4, 0xcd, 0x10, 0xb0, 0xbe, 0x49, 0xa6, 0x8d, 0xa2, 0xb2, 0xe0, 0xdc, 0x0a, 0xd8, 0x96, 0x0f, }, ph: false, ctx: []byte{ 0x66, 0x6f, 0x6f, }, ctxLen: 3, }, } func (v vector) isPure() bool { return v.scheme == "Ed25519Pure" } func (v vector) isPreHashed() bool { return v.scheme == "Ed25519Ph" } func (v vector) hasContext() bool { return v.scheme == "Ed25519Ctx" } func (v vector) matchMsgLen() bool { return uint(len(v.msg)) == v.msgLen } func (v vector) matchCtxLen() bool { return uint(len(v.ctx)) == v.ctxLen } func (v vector) testPublicKey(t *testing.T) { keys := ed25519.NewKeyFromSeed(v.sk) got := keys.Public().(ed25519.PublicKey) want := v.pk if !bytes.Equal(got, want) { test.ReportError(t, got, want, v.name) } } func (v vector) testSign(t *testing.T) { key := ed25519.NewKeyFromSeed(v.sk) var got []byte if v.ph { got = ed25519.SignPh(key, v.msg, "") } else if v.ctxLen > 0 { got = ed25519.SignWithCtx(key, v.msg, string(v.ctx)) } else { got = ed25519.Sign(key, v.msg) } want := v.sig if !bytes.Equal(got, want) { test.ReportError(t, got, want, v.name) } } func (v vector) testVerify(t *testing.T) { var got bool if v.ph { got = ed25519.VerifyPh(v.pk, v.msg, v.sig, "") } else if v.ctxLen > 0 { got = ed25519.VerifyWithCtx(v.pk, v.msg, v.sig, string(v.ctx)) } else { got = ed25519.Verify(v.pk, v.msg, v.sig) } want := true if got != want { test.ReportError(t, got, want, v.name) } } func TestEd25519(t *testing.T) { for _, v := range vectorsEd25519 { got := (v.isPure() || v.isPreHashed() || v.hasContext()) && v.matchMsgLen() && v.matchCtxLen() want := true if got != want { test.ReportError(t, got, want, v.sk) } v.testPublicKey(t) v.testSign(t) v.testVerify(t) } } golang-github-cloudflare-circl-1.3.7/sign/ed25519/signapi.go000066400000000000000000000041521454601126700234100ustar00rootroot00000000000000package ed25519 import ( "crypto/rand" "encoding/asn1" "github.com/cloudflare/circl/sign" ) var sch sign.Scheme = &scheme{} // Scheme returns a signature interface. func Scheme() sign.Scheme { return sch } type scheme struct{} func (*scheme) Name() string { return "Ed25519" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SignatureSize() int { return SignatureSize } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) TLSIdentifier() uint { return 0x0807 } func (*scheme) SupportsContext() bool { return false } func (*scheme) Oid() asn1.ObjectIdentifier { return asn1.ObjectIdentifier{1, 3, 101, 112} } func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { return GenerateKey(rand.Reader) } func (*scheme) Sign( sk sign.PrivateKey, message []byte, opts *sign.SignatureOpts, ) []byte { priv, ok := sk.(PrivateKey) if !ok { panic(sign.ErrTypeMismatch) } if opts != nil && opts.Context != "" { panic(sign.ErrContextNotSupported) } return Sign(priv, message) } func (*scheme) Verify( pk sign.PublicKey, message, signature []byte, opts *sign.SignatureOpts, ) bool { pub, ok := pk.(PublicKey) if !ok { panic(sign.ErrTypeMismatch) } if opts != nil { if opts.Context != "" { panic(sign.ErrContextNotSupported) } } return Verify(pub, message, signature) } func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { privateKey := NewKeyFromSeed(seed) publicKey := make(PublicKey, PublicKeySize) copy(publicKey, privateKey[SeedSize:]) return publicKey, privateKey } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { if len(buf) < PublicKeySize { return nil, sign.ErrPubKeySize } pub := make(PublicKey, PublicKeySize) copy(pub, buf[:PublicKeySize]) return pub, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { if len(buf) < PrivateKeySize { return nil, sign.ErrPrivKeySize } priv := make(PrivateKey, PrivateKeySize) copy(priv, buf[:PrivateKeySize]) return priv, nil } golang-github-cloudflare-circl-1.3.7/sign/ed25519/tables.go000066400000000000000000000624361454601126700232410ustar00rootroot00000000000000package ed25519 import fp "github.com/cloudflare/circl/math/fp25519" var tabSign = [fxV][fx2w1]pointR3{ { pointR3{ addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07}, subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44}, dt2: fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f}, }, { addYX: fp.Elt{0x7c, 0xb0, 0x9e, 0xe6, 0xc5, 0xbf, 0xfa, 0x13, 0x8e, 0x0d, 0x22, 0xde, 0xc8, 0xd1, 0xce, 0x52, 0x02, 0xd5, 0x62, 0x31, 0x71, 0x0e, 0x8e, 0x9d, 0xb0, 0xd6, 0x00, 0xa5, 0x5a, 0x0e, 0xce, 0x72}, subYX: fp.Elt{0x1a, 0x8e, 0x5c, 0xdc, 0xa4, 0xb3, 0x6c, 0x51, 0x18, 0xa0, 0x09, 0x80, 0x9a, 0x46, 0x33, 0xd5, 0xe0, 0x3c, 0x4d, 0x3b, 0xfc, 0x49, 0xa2, 0x43, 0x29, 0xe1, 0x29, 0xa9, 0x93, 0xea, 0x7c, 0x35}, dt2: fp.Elt{0x08, 0x46, 0x6f, 0x68, 0x7f, 0x0b, 0x7c, 0x9e, 0xad, 0xba, 0x07, 0x61, 0x74, 0x83, 0x2f, 0xfc, 0x26, 0xd6, 0x09, 0xb9, 0x00, 0x34, 0x36, 0x4f, 0x01, 0xf3, 0x48, 0xdb, 0x43, 0xba, 0x04, 0x44}, }, { addYX: fp.Elt{0x4c, 0xda, 0x0d, 0x13, 0x66, 0xfd, 0x82, 0x84, 0x9f, 0x75, 0x5b, 0xa2, 0x17, 0xfe, 0x34, 0xbf, 0x1f, 0xcb, 0xba, 0x90, 0x55, 0x80, 0x83, 0xfd, 0x63, 0xb9, 0x18, 0xf8, 0x5b, 0x5d, 0x94, 0x1e}, subYX: fp.Elt{0xb9, 0xdb, 0x6c, 0x04, 0x88, 0x22, 0xd8, 0x79, 0x83, 0x2f, 0x8d, 0x65, 0x6b, 0xd2, 0xab, 0x1b, 0xdd, 0x65, 0xe5, 0x93, 0x63, 0xf8, 0xa2, 0xd8, 0x3c, 0xf1, 0x4b, 0xc5, 0x99, 0xd1, 0xf2, 0x12}, dt2: fp.Elt{0x05, 0x4c, 0xb8, 0x3b, 0xfe, 0xf5, 0x9f, 0x2e, 0xd1, 0xb2, 0xb8, 0xff, 0xfe, 0x6d, 0xd9, 0x37, 0xe0, 0xae, 0xb4, 0x5a, 0x51, 0x80, 0x7e, 0x9b, 0x1d, 0xd1, 0x8d, 0x8c, 0x56, 0xb1, 0x84, 0x35}, }, { addYX: fp.Elt{0x39, 0x71, 0x43, 0x34, 0xe3, 0x42, 0x45, 0xa1, 0xf2, 0x68, 0x71, 0xa7, 0xe8, 0x23, 0xfd, 0x9f, 0x86, 0x48, 0xff, 0xe5, 0x96, 0x74, 0xcf, 0x05, 0x49, 0xe2, 0xb3, 0x6c, 0x17, 0x77, 0x2f, 0x6d}, subYX: fp.Elt{0x73, 0x3f, 0xc1, 0xc7, 0x6a, 0x66, 0xa1, 0x20, 0xdd, 0x11, 0xfb, 0x7a, 0x6e, 0xa8, 0x51, 0xb8, 0x3f, 0x9d, 0xa2, 0x97, 0x84, 0xb5, 0xc7, 0x90, 0x7c, 0xab, 0x48, 0xd6, 0x84, 0xa3, 0xd5, 0x1a}, dt2: fp.Elt{0x63, 0x27, 0x3c, 0x49, 0x4b, 0xfc, 0x22, 0xf2, 0x0b, 0x50, 0xc2, 0x0f, 0xb4, 0x1f, 0x31, 0x0c, 0x2f, 0x53, 0xab, 0xaa, 0x75, 0x6f, 0xe0, 0x69, 0x39, 0x56, 0xe0, 0x3b, 0xb7, 0xa8, 0xbf, 0x45}, }, }, { { addYX: fp.Elt{0x00, 0x45, 0xd9, 0x0d, 0x58, 0x03, 0xfc, 0x29, 0x93, 0xec, 0xbb, 0x6f, 0xa4, 0x7a, 0xd2, 0xec, 0xf8, 0xa7, 0xe2, 0xc2, 0x5f, 0x15, 0x0a, 0x13, 0xd5, 0xa1, 0x06, 0xb7, 0x1a, 0x15, 0x6b, 0x41}, subYX: fp.Elt{0x85, 0x8c, 0xb2, 0x17, 0xd6, 0x3b, 0x0a, 0xd3, 0xea, 0x3b, 0x77, 0x39, 0xb7, 0x77, 0xd3, 0xc5, 0xbf, 0x5c, 0x6a, 0x1e, 0x8c, 0xe7, 0xc6, 0xc6, 0xc4, 0xb7, 0x2a, 0x8b, 0xf7, 0xb8, 0x61, 0x0d}, dt2: fp.Elt{0xb0, 0x36, 0xc1, 0xe9, 0xef, 0xd7, 0xa8, 0x56, 0x20, 0x4b, 0xe4, 0x58, 0xcd, 0xe5, 0x07, 0xbd, 0xab, 0xe0, 0x57, 0x1b, 0xda, 0x2f, 0xe6, 0xaf, 0xd2, 0xe8, 0x77, 0x42, 0xf7, 0x2a, 0x1a, 0x19}, }, { addYX: fp.Elt{0x6a, 0x6d, 0x6d, 0xd1, 0xfa, 0xf5, 0x03, 0x30, 0xbd, 0x6d, 0xc2, 0xc8, 0xf5, 0x38, 0x80, 0x4f, 0xb2, 0xbe, 0xa1, 0x76, 0x50, 0x1a, 0x73, 0xf2, 0x78, 0x2b, 0x8e, 0x3a, 0x1e, 0x34, 0x47, 0x7b}, subYX: fp.Elt{0xc3, 0x2c, 0x36, 0xdc, 0xc5, 0x45, 0xbc, 0xef, 0x1b, 0x64, 0xd6, 0x65, 0x28, 0xe9, 0xda, 0x84, 0x13, 0xbe, 0x27, 0x8e, 0x3f, 0x98, 0x2a, 0x37, 0xee, 0x78, 0x97, 0xd6, 0xc0, 0x6f, 0xb4, 0x53}, dt2: fp.Elt{0x58, 0x5d, 0xa7, 0xa3, 0x68, 0xbb, 0x20, 0x30, 0x2e, 0x03, 0xe9, 0xb1, 0xd4, 0x90, 0x72, 0xe3, 0x71, 0xb2, 0x36, 0x3e, 0x73, 0xa0, 0x2e, 0x3d, 0xd1, 0x85, 0x33, 0x62, 0x4e, 0xa7, 0x7b, 0x31}, }, { addYX: fp.Elt{0xbf, 0xc4, 0x38, 0x53, 0xfb, 0x68, 0xa9, 0x77, 0xce, 0x55, 0xf9, 0x05, 0xcb, 0xeb, 0xfb, 0x8c, 0x46, 0xc2, 0x32, 0x7c, 0xf0, 0xdb, 0xd7, 0x2c, 0x62, 0x8e, 0xdd, 0x54, 0x75, 0xcf, 0x3f, 0x33}, subYX: fp.Elt{0x49, 0x50, 0x1f, 0x4e, 0x6e, 0x55, 0x55, 0xde, 0x8c, 0x4e, 0x77, 0x96, 0x38, 0x3b, 0xfe, 0xb6, 0x43, 0x3c, 0x86, 0x69, 0xc2, 0x72, 0x66, 0x1f, 0x6b, 0xf9, 0x87, 0xbc, 0x4f, 0x37, 0x3e, 0x3c}, dt2: fp.Elt{0xd2, 0x2f, 0x06, 0x6b, 0x08, 0x07, 0x69, 0x77, 0xc0, 0x94, 0xcc, 0xae, 0x43, 0x00, 0x59, 0x6e, 0xa3, 0x63, 0xa8, 0xdd, 0xfa, 0x24, 0x18, 0xd0, 0x35, 0xc7, 0x78, 0xf7, 0x0d, 0xd4, 0x5a, 0x1e}, }, { addYX: fp.Elt{0x45, 0xc1, 0x17, 0x51, 0xf8, 0xed, 0x7e, 0xc7, 0xa9, 0x1a, 0x11, 0x6e, 0x2d, 0xef, 0x0b, 0xd5, 0x3f, 0x98, 0xb0, 0xa3, 0x9d, 0x65, 0xf1, 0xcd, 0x53, 0x4a, 0x8a, 0x18, 0x70, 0x0a, 0x7f, 0x23}, subYX: fp.Elt{0xdd, 0xef, 0xbe, 0x3a, 0x31, 0xe0, 0xbc, 0xbe, 0x6d, 0x5d, 0x79, 0x87, 0xd6, 0xbe, 0x68, 0xe3, 0x59, 0x76, 0x8c, 0x86, 0x0e, 0x7a, 0x92, 0x13, 0x14, 0x8f, 0x67, 0xb3, 0xcb, 0x1a, 0x76, 0x76}, dt2: fp.Elt{0x56, 0x7a, 0x1c, 0x9d, 0xca, 0x96, 0xf9, 0xf9, 0x03, 0x21, 0xd4, 0xe8, 0xb3, 0xd5, 0xe9, 0x52, 0xc8, 0x54, 0x1e, 0x1b, 0x13, 0xb6, 0xfd, 0x47, 0x7d, 0x02, 0x32, 0x33, 0x27, 0xe2, 0x1f, 0x19}, }, }, } var tabVerif = [1 << (omegaFix - 2)]pointR3{ { /* 1P */ addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07}, subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44}, dt2: fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f}, }, { /* 3P */ addYX: fp.Elt{0x30, 0x97, 0xee, 0x4c, 0xa8, 0xb0, 0x25, 0xaf, 0x8a, 0x4b, 0x86, 0xe8, 0x30, 0x84, 0x5a, 0x02, 0x32, 0x67, 0x01, 0x9f, 0x02, 0x50, 0x1b, 0xc1, 0xf4, 0xf8, 0x80, 0x9a, 0x1b, 0x4e, 0x16, 0x7a}, subYX: fp.Elt{0x65, 0xd2, 0xfc, 0xa4, 0xe8, 0x1f, 0x61, 0x56, 0x7d, 0xba, 0xc1, 0xe5, 0xfd, 0x53, 0xd3, 0x3b, 0xbd, 0xd6, 0x4b, 0x21, 0x1a, 0xf3, 0x31, 0x81, 0x62, 0xda, 0x5b, 0x55, 0x87, 0x15, 0xb9, 0x2a}, dt2: fp.Elt{0x89, 0xd8, 0xd0, 0x0d, 0x3f, 0x93, 0xae, 0x14, 0x62, 0xda, 0x35, 0x1c, 0x22, 0x23, 0x94, 0x58, 0x4c, 0xdb, 0xf2, 0x8c, 0x45, 0xe5, 0x70, 0xd1, 0xc6, 0xb4, 0xb9, 0x12, 0xaf, 0x26, 0x28, 0x5a}, }, { /* 5P */ addYX: fp.Elt{0x33, 0xbb, 0xa5, 0x08, 0x44, 0xbc, 0x12, 0xa2, 0x02, 0xed, 0x5e, 0xc7, 0xc3, 0x48, 0x50, 0x8d, 0x44, 0xec, 0xbf, 0x5a, 0x0c, 0xeb, 0x1b, 0xdd, 0xeb, 0x06, 0xe2, 0x46, 0xf1, 0xcc, 0x45, 0x29}, subYX: fp.Elt{0xba, 0xd6, 0x47, 0xa4, 0xc3, 0x82, 0x91, 0x7f, 0xb7, 0x29, 0x27, 0x4b, 0xd1, 0x14, 0x00, 0xd5, 0x87, 0xa0, 0x64, 0xb8, 0x1c, 0xf1, 0x3c, 0xe3, 0xf3, 0x55, 0x1b, 0xeb, 0x73, 0x7e, 0x4a, 0x15}, dt2: fp.Elt{0x85, 0x82, 0x2a, 0x81, 0xf1, 0xdb, 0xbb, 0xbc, 0xfc, 0xd1, 0xbd, 0xd0, 0x07, 0x08, 0x0e, 0x27, 0x2d, 0xa7, 0xbd, 0x1b, 0x0b, 0x67, 0x1b, 0xb4, 0x9a, 0xb6, 0x3b, 0x6b, 0x69, 0xbe, 0xaa, 0x43}, }, { /* 7P */ addYX: fp.Elt{0xbf, 0xa3, 0x4e, 0x94, 0xd0, 0x5c, 0x1a, 0x6b, 0xd2, 0xc0, 0x9d, 0xb3, 0x3a, 0x35, 0x70, 0x74, 0x49, 0x2e, 0x54, 0x28, 0x82, 0x52, 0xb2, 0x71, 0x7e, 0x92, 0x3c, 0x28, 0x69, 0xea, 0x1b, 0x46}, subYX: fp.Elt{0xb1, 0x21, 0x32, 0xaa, 0x9a, 0x2c, 0x6f, 0xba, 0xa7, 0x23, 0xba, 0x3b, 0x53, 0x21, 0xa0, 0x6c, 0x3a, 0x2c, 0x19, 0x92, 0x4f, 0x76, 0xea, 0x9d, 0xe0, 0x17, 0x53, 0x2e, 0x5d, 0xdd, 0x6e, 0x1d}, dt2: fp.Elt{0xa2, 0xb3, 0xb8, 0x01, 0xc8, 0x6d, 0x83, 0xf1, 0x9a, 0xa4, 0x3e, 0x05, 0x47, 0x5f, 0x03, 0xb3, 0xf3, 0xad, 0x77, 0x58, 0xba, 0x41, 0x9c, 0x52, 0xa7, 0x90, 0x0f, 0x6a, 0x1c, 0xbb, 0x9f, 0x7a}, }, { /* 9P */ addYX: fp.Elt{0x2f, 0x63, 0xa8, 0xa6, 0x8a, 0x67, 0x2e, 0x9b, 0xc5, 0x46, 0xbc, 0x51, 0x6f, 0x9e, 0x50, 0xa6, 0xb5, 0xf5, 0x86, 0xc6, 0xc9, 0x33, 0xb2, 0xce, 0x59, 0x7f, 0xdd, 0x8a, 0x33, 0xed, 0xb9, 0x34}, subYX: fp.Elt{0x64, 0x80, 0x9d, 0x03, 0x7e, 0x21, 0x6e, 0xf3, 0x9b, 0x41, 0x20, 0xf5, 0xb6, 0x81, 0xa0, 0x98, 0x44, 0xb0, 0x5e, 0xe7, 0x08, 0xc6, 0xcb, 0x96, 0x8f, 0x9c, 0xdc, 0xfa, 0x51, 0x5a, 0xc0, 0x49}, dt2: fp.Elt{0x1b, 0xaf, 0x45, 0x90, 0xbf, 0xe8, 0xb4, 0x06, 0x2f, 0xd2, 0x19, 0xa7, 0xe8, 0x83, 0xff, 0xe2, 0x16, 0xcf, 0xd4, 0x93, 0x29, 0xfc, 0xf6, 0xaa, 0x06, 0x8b, 0x00, 0x1b, 0x02, 0x72, 0xc1, 0x73}, }, { /* 11P */ addYX: fp.Elt{0xde, 0x2a, 0x80, 0x8a, 0x84, 0x00, 0xbf, 0x2f, 0x27, 0x2e, 0x30, 0x02, 0xcf, 0xfe, 0xd9, 0xe5, 0x06, 0x34, 0x70, 0x17, 0x71, 0x84, 0x3e, 0x11, 0xaf, 0x8f, 0x6d, 0x54, 0xe2, 0xaa, 0x75, 0x42}, subYX: fp.Elt{0x48, 0x43, 0x86, 0x49, 0x02, 0x5b, 0x5f, 0x31, 0x81, 0x83, 0x08, 0x77, 0x69, 0xb3, 0xd6, 0x3e, 0x95, 0xeb, 0x8d, 0x6a, 0x55, 0x75, 0xa0, 0xa3, 0x7f, 0xc7, 0xd5, 0x29, 0x80, 0x59, 0xab, 0x18}, dt2: fp.Elt{0xe9, 0x89, 0x60, 0xfd, 0xc5, 0x2c, 0x2b, 0xd8, 0xa4, 0xe4, 0x82, 0x32, 0xa1, 0xb4, 0x1e, 0x03, 0x22, 0x86, 0x1a, 0xb5, 0x99, 0x11, 0x31, 0x44, 0x48, 0xf9, 0x3d, 0xb5, 0x22, 0x55, 0xc6, 0x3d}, }, { /* 13P */ addYX: fp.Elt{0x6d, 0x7f, 0x00, 0xa2, 0x22, 0xc2, 0x70, 0xbf, 0xdb, 0xde, 0xbc, 0xb5, 0x9a, 0xb3, 0x84, 0xbf, 0x07, 0xba, 0x07, 0xfb, 0x12, 0x0e, 0x7a, 0x53, 0x41, 0xf2, 0x46, 0xc3, 0xee, 0xd7, 0x4f, 0x23}, subYX: fp.Elt{0x93, 0xbf, 0x7f, 0x32, 0x3b, 0x01, 0x6f, 0x50, 0x6b, 0x6f, 0x77, 0x9b, 0xc9, 0xeb, 0xfc, 0xae, 0x68, 0x59, 0xad, 0xaa, 0x32, 0xb2, 0x12, 0x9d, 0xa7, 0x24, 0x60, 0x17, 0x2d, 0x88, 0x67, 0x02}, dt2: fp.Elt{0x78, 0xa3, 0x2e, 0x73, 0x19, 0xa1, 0x60, 0x53, 0x71, 0xd4, 0x8d, 0xdf, 0xb1, 0xe6, 0x37, 0x24, 0x33, 0xe5, 0xa7, 0x91, 0xf8, 0x37, 0xef, 0xa2, 0x63, 0x78, 0x09, 0xaa, 0xfd, 0xa6, 0x7b, 0x49}, }, { /* 15P */ addYX: fp.Elt{0xa0, 0xea, 0xcf, 0x13, 0x03, 0xcc, 0xce, 0x24, 0x6d, 0x24, 0x9c, 0x18, 0x8d, 0xc2, 0x48, 0x86, 0xd0, 0xd4, 0xf2, 0xc1, 0xfa, 0xbd, 0xbd, 0x2d, 0x2b, 0xe7, 0x2d, 0xf1, 0x17, 0x29, 0xe2, 0x61}, subYX: fp.Elt{0x0b, 0xcf, 0x8c, 0x46, 0x86, 0xcd, 0x0b, 0x04, 0xd6, 0x10, 0x99, 0x2a, 0xa4, 0x9b, 0x82, 0xd3, 0x92, 0x51, 0xb2, 0x07, 0x08, 0x30, 0x08, 0x75, 0xbf, 0x5e, 0xd0, 0x18, 0x42, 0xcd, 0xb5, 0x43}, dt2: fp.Elt{0x16, 0xb5, 0xd0, 0x9b, 0x2f, 0x76, 0x9a, 0x5d, 0xee, 0xde, 0x3f, 0x37, 0x4e, 0xaf, 0x38, 0xeb, 0x70, 0x42, 0xd6, 0x93, 0x7d, 0x5a, 0x2e, 0x03, 0x42, 0xd8, 0xe4, 0x0a, 0x21, 0x61, 0x1d, 0x51}, }, { /* 17P */ addYX: fp.Elt{0x81, 0x9d, 0x0e, 0x95, 0xef, 0x76, 0xc6, 0x92, 0x4f, 0x04, 0xd7, 0xc0, 0xcd, 0x20, 0x46, 0xa5, 0x48, 0x12, 0x8f, 0x6f, 0x64, 0x36, 0x9b, 0xaa, 0xe3, 0x55, 0xb8, 0xdd, 0x24, 0x59, 0x32, 0x6d}, subYX: fp.Elt{0x87, 0xde, 0x20, 0x44, 0x48, 0x86, 0x13, 0x08, 0xb4, 0xed, 0x92, 0xb5, 0x16, 0xf0, 0x1c, 0x8a, 0x25, 0x2d, 0x94, 0x29, 0x27, 0x4e, 0xfa, 0x39, 0x10, 0x28, 0x48, 0xe2, 0x6f, 0xfe, 0xa7, 0x71}, dt2: fp.Elt{0x54, 0xc8, 0xc8, 0xa5, 0xb8, 0x82, 0x71, 0x6c, 0x03, 0x2a, 0x5f, 0xfe, 0x79, 0x14, 0xfd, 0x33, 0x0c, 0x8d, 0x77, 0x83, 0x18, 0x59, 0xcf, 0x72, 0xa9, 0xea, 0x9e, 0x55, 0xb6, 0xc4, 0x46, 0x47}, }, { /* 19P */ addYX: fp.Elt{0x2b, 0x9a, 0xc6, 0x6d, 0x3c, 0x7b, 0x77, 0xd3, 0x17, 0xf6, 0x89, 0x6f, 0x27, 0xb2, 0xfa, 0xde, 0xb5, 0x16, 0x3a, 0xb5, 0xf7, 0x1c, 0x65, 0x45, 0xb7, 0x9f, 0xfe, 0x34, 0xde, 0x51, 0x9a, 0x5c}, subYX: fp.Elt{0x47, 0x11, 0x74, 0x64, 0xc8, 0x46, 0x85, 0x34, 0x49, 0xc8, 0xfc, 0x0e, 0xdd, 0xae, 0x35, 0x7d, 0x32, 0xa3, 0x72, 0x06, 0x76, 0x9a, 0x93, 0xff, 0xd6, 0xe6, 0xb5, 0x7d, 0x49, 0x63, 0x96, 0x21}, dt2: fp.Elt{0x67, 0x0e, 0xf1, 0x79, 0xcf, 0xf1, 0x10, 0xf5, 0x5b, 0x51, 0x58, 0xe6, 0xa1, 0xda, 0xdd, 0xff, 0x77, 0x22, 0x14, 0x10, 0x17, 0xa7, 0xc3, 0x09, 0xbb, 0x23, 0x82, 0x60, 0x3c, 0x50, 0x04, 0x48}, }, { /* 21P */ addYX: fp.Elt{0xc7, 0x7f, 0xa3, 0x2c, 0xd0, 0x9e, 0x24, 0xc4, 0xab, 0xac, 0x15, 0xa6, 0xe3, 0xa0, 0x59, 0xa0, 0x23, 0x0e, 0x6e, 0xc9, 0xd7, 0x6e, 0xa9, 0x88, 0x6d, 0x69, 0x50, 0x16, 0xa5, 0x98, 0x33, 0x55}, subYX: fp.Elt{0x75, 0xd1, 0x36, 0x3a, 0xd2, 0x21, 0x68, 0x3b, 0x32, 0x9e, 0x9b, 0xe9, 0xa7, 0x0a, 0xb4, 0xbb, 0x47, 0x8a, 0x83, 0x20, 0xe4, 0x5c, 0x9e, 0x5d, 0x5e, 0x4c, 0xde, 0x58, 0x88, 0x09, 0x1e, 0x77}, dt2: fp.Elt{0xdf, 0x1e, 0x45, 0x78, 0xd2, 0xf5, 0x12, 0x9a, 0xcb, 0x9c, 0x89, 0x85, 0x79, 0x5d, 0xda, 0x3a, 0x08, 0x95, 0xa5, 0x9f, 0x2d, 0x4a, 0x7f, 0x47, 0x11, 0xa6, 0xf5, 0x8f, 0xd6, 0xd1, 0x5e, 0x5a}, }, { /* 23P */ addYX: fp.Elt{0x83, 0x0e, 0x15, 0xfe, 0x2a, 0x12, 0x95, 0x11, 0xd8, 0x35, 0x4b, 0x7e, 0x25, 0x9a, 0x20, 0xcf, 0x20, 0x1e, 0x71, 0x1e, 0x29, 0xf8, 0x87, 0x73, 0xf0, 0x92, 0xbf, 0xd8, 0x97, 0xb8, 0xac, 0x44}, subYX: fp.Elt{0x59, 0x73, 0x52, 0x58, 0xc5, 0xe0, 0xe5, 0xba, 0x7e, 0x9d, 0xdb, 0xca, 0x19, 0x5c, 0x2e, 0x39, 0xe9, 0xab, 0x1c, 0xda, 0x1e, 0x3c, 0x65, 0x28, 0x44, 0xdc, 0xef, 0x5f, 0x13, 0x60, 0x9b, 0x01}, dt2: fp.Elt{0x83, 0x4b, 0x13, 0x5e, 0x14, 0x68, 0x60, 0x1e, 0x16, 0x4c, 0x30, 0x24, 0x4f, 0xe6, 0xf5, 0xc4, 0xd7, 0x3e, 0x1a, 0xfc, 0xa8, 0x88, 0x6e, 0x50, 0x92, 0x2f, 0xad, 0xe6, 0xfd, 0x49, 0x0c, 0x15}, }, { /* 25P */ addYX: fp.Elt{0x38, 0x11, 0x47, 0x09, 0x95, 0xf2, 0x7b, 0x8e, 0x51, 0xa6, 0x75, 0x4f, 0x39, 0xef, 0x6f, 0x5d, 0xad, 0x08, 0xa7, 0x25, 0xc4, 0x79, 0xaf, 0x10, 0x22, 0x99, 0xb9, 0x5b, 0x07, 0x5a, 0x2b, 0x6b}, subYX: fp.Elt{0x68, 0xa8, 0xdc, 0x9c, 0x3c, 0x86, 0x49, 0xb8, 0xd0, 0x4a, 0x71, 0xb8, 0xdb, 0x44, 0x3f, 0xc8, 0x8d, 0x16, 0x36, 0x0c, 0x56, 0xe3, 0x3e, 0xfe, 0xc1, 0xfb, 0x05, 0x1e, 0x79, 0xd7, 0xa6, 0x78}, dt2: fp.Elt{0x76, 0xb9, 0xa0, 0x47, 0x4b, 0x70, 0xbf, 0x58, 0xd5, 0x48, 0x17, 0x74, 0x55, 0xb3, 0x01, 0xa6, 0x90, 0xf5, 0x42, 0xd5, 0xb1, 0x1f, 0x2b, 0xaa, 0x00, 0x5d, 0xd5, 0x4a, 0xfc, 0x7f, 0x5c, 0x72}, }, { /* 27P */ addYX: fp.Elt{0xb2, 0x99, 0xcf, 0xd1, 0x15, 0x67, 0x42, 0xe4, 0x34, 0x0d, 0xa2, 0x02, 0x11, 0xd5, 0x52, 0x73, 0x9f, 0x10, 0x12, 0x8b, 0x7b, 0x15, 0xd1, 0x23, 0xa3, 0xf3, 0xb1, 0x7c, 0x27, 0xc9, 0x4c, 0x79}, subYX: fp.Elt{0xc0, 0x98, 0xd0, 0x1c, 0xf7, 0x2b, 0x80, 0x91, 0x66, 0x63, 0x5e, 0xed, 0xa4, 0x6c, 0x41, 0xfe, 0x4c, 0x99, 0x02, 0x49, 0x71, 0x5d, 0x58, 0xdf, 0xe7, 0xfa, 0x55, 0xf8, 0x25, 0x46, 0xd5, 0x4c}, dt2: fp.Elt{0x53, 0x50, 0xac, 0xc2, 0x26, 0xc4, 0xf6, 0x4a, 0x58, 0x72, 0xf6, 0x32, 0xad, 0xed, 0x9a, 0xbc, 0x21, 0x10, 0x31, 0x0a, 0xf1, 0x32, 0xd0, 0x2a, 0x85, 0x8e, 0xcc, 0x6f, 0x7b, 0x35, 0x08, 0x70}, }, { /* 29P */ addYX: fp.Elt{0x01, 0x3f, 0x77, 0x38, 0x27, 0x67, 0x88, 0x0b, 0xfb, 0xcc, 0xfb, 0x95, 0xfa, 0xc8, 0xcc, 0xb8, 0xb6, 0x29, 0xad, 0xb9, 0xa3, 0xd5, 0x2d, 0x8d, 0x6a, 0x0f, 0xad, 0x51, 0x98, 0x7e, 0xef, 0x06}, subYX: fp.Elt{0x34, 0x4a, 0x58, 0x82, 0xbb, 0x9f, 0x1b, 0xd0, 0x2b, 0x79, 0xb4, 0xd2, 0x63, 0x64, 0xab, 0x47, 0x02, 0x62, 0x53, 0x48, 0x9c, 0x63, 0x31, 0xb6, 0x28, 0xd4, 0xd6, 0x69, 0x36, 0x2a, 0xa9, 0x13}, dt2: fp.Elt{0xe5, 0x7d, 0x57, 0xc0, 0x1c, 0x77, 0x93, 0xca, 0x5c, 0xdc, 0x35, 0x50, 0x1e, 0xe4, 0x40, 0x75, 0x71, 0xe0, 0x02, 0xd8, 0x01, 0x0f, 0x68, 0x24, 0x6a, 0xf8, 0x2a, 0x8a, 0xdf, 0x6d, 0x29, 0x3c}, }, { /* 31P */ addYX: fp.Elt{0x13, 0xa7, 0x14, 0xd9, 0xf9, 0x15, 0xad, 0xae, 0x12, 0xf9, 0x8f, 0x8c, 0xf9, 0x7b, 0x2f, 0xa9, 0x30, 0xd7, 0x53, 0x9f, 0x17, 0x23, 0xf8, 0xaf, 0xba, 0x77, 0x0c, 0x49, 0x93, 0xd3, 0x99, 0x7a}, subYX: fp.Elt{0x41, 0x25, 0x1f, 0xbb, 0x2e, 0x4d, 0xeb, 0xfc, 0x1f, 0xb9, 0xad, 0x40, 0xc7, 0x10, 0x95, 0xb8, 0x05, 0xad, 0xa1, 0xd0, 0x7d, 0xa3, 0x71, 0xfc, 0x7b, 0x71, 0x47, 0x07, 0x70, 0x2c, 0x89, 0x0a}, dt2: fp.Elt{0xe8, 0xa3, 0xbd, 0x36, 0x24, 0xed, 0x52, 0x8f, 0x94, 0x07, 0xe8, 0x57, 0x41, 0xc8, 0xa8, 0x77, 0xe0, 0x9c, 0x2f, 0x26, 0x63, 0x65, 0xa9, 0xa5, 0xd2, 0xf7, 0x02, 0x83, 0xd2, 0x62, 0x67, 0x28}, }, { /* 33P */ addYX: fp.Elt{0x25, 0x5b, 0xe3, 0x3c, 0x09, 0x36, 0x78, 0x4e, 0x97, 0xaa, 0x6b, 0xb2, 0x1d, 0x18, 0xe1, 0x82, 0x3f, 0xb8, 0xc7, 0xcb, 0xd3, 0x92, 0xc1, 0x0c, 0x3a, 0x9d, 0x9d, 0x6a, 0x04, 0xda, 0xf1, 0x32}, subYX: fp.Elt{0xbd, 0xf5, 0x2e, 0xce, 0x2b, 0x8e, 0x55, 0x7c, 0x63, 0xbc, 0x47, 0x67, 0xb4, 0x6c, 0x98, 0xe4, 0xb8, 0x89, 0xbb, 0x3b, 0x9f, 0x17, 0x4a, 0x15, 0x7a, 0x76, 0xf1, 0xd6, 0xa3, 0xf2, 0x86, 0x76}, dt2: fp.Elt{0x6a, 0x7c, 0x59, 0x6d, 0xa6, 0x12, 0x8d, 0xaa, 0x2b, 0x85, 0xd3, 0x04, 0x03, 0x93, 0x11, 0x8f, 0x22, 0xb0, 0x09, 0xc2, 0x73, 0xdc, 0x91, 0x3f, 0xa6, 0x28, 0xad, 0xa9, 0xf8, 0x05, 0x13, 0x56}, }, { /* 35P */ addYX: fp.Elt{0xd1, 0xae, 0x92, 0xec, 0x8d, 0x97, 0x0c, 0x10, 0xe5, 0x73, 0x6d, 0x4d, 0x43, 0xd5, 0x43, 0xca, 0x48, 0xba, 0x47, 0xd8, 0x22, 0x1b, 0x13, 0x83, 0x2c, 0x4d, 0x5d, 0xe3, 0x53, 0xec, 0xaa}, subYX: fp.Elt{0xd5, 0xc0, 0xb0, 0xe7, 0x28, 0xcc, 0x22, 0x67, 0x53, 0x5c, 0x07, 0xdb, 0xbb, 0xe9, 0x9d, 0x70, 0x61, 0x0a, 0x01, 0xd7, 0xa7, 0x8d, 0xf6, 0xca, 0x6c, 0xcc, 0x57, 0x2c, 0xef, 0x1a, 0x0a, 0x03}, dt2: fp.Elt{0xaa, 0xd2, 0x3a, 0x00, 0x73, 0xf7, 0xb1, 0x7b, 0x08, 0x66, 0x21, 0x2b, 0x80, 0x29, 0x3f, 0x0b, 0x3e, 0xd2, 0x0e, 0x52, 0x86, 0xdc, 0x21, 0x78, 0x80, 0x54, 0x06, 0x24, 0x1c, 0x9c, 0xbe, 0x20}, }, { /* 37P */ addYX: fp.Elt{0xa6, 0x73, 0x96, 0x24, 0xd8, 0x87, 0x53, 0xe1, 0x93, 0xe4, 0x46, 0xf5, 0x2d, 0xbc, 0x43, 0x59, 0xb5, 0x63, 0x6f, 0xc3, 0x81, 0x9a, 0x7f, 0x1c, 0xde, 0xc1, 0x0a, 0x1f, 0x36, 0xb3, 0x0a, 0x75}, subYX: fp.Elt{0x60, 0x5e, 0x02, 0xe2, 0x4a, 0xe4, 0xe0, 0x20, 0x38, 0xb9, 0xdc, 0xcb, 0x2f, 0x3b, 0x3b, 0xb0, 0x1c, 0x0d, 0x5a, 0xf9, 0x9c, 0x63, 0x5d, 0x10, 0x11, 0xe3, 0x67, 0x50, 0x54, 0x4c, 0x76, 0x69}, dt2: fp.Elt{0x37, 0x10, 0xf8, 0xa2, 0x83, 0x32, 0x8a, 0x1e, 0xf1, 0xcb, 0x7f, 0xbd, 0x23, 0xda, 0x2e, 0x6f, 0x63, 0x25, 0x2e, 0xac, 0x5b, 0xd1, 0x2f, 0xb7, 0x40, 0x50, 0x07, 0xb7, 0x3f, 0x6b, 0xf9, 0x54}, }, { /* 39P */ addYX: fp.Elt{0x79, 0x92, 0x66, 0x29, 0x04, 0xf2, 0xad, 0x0f, 0x4a, 0x72, 0x7d, 0x7d, 0x04, 0xa2, 0xdd, 0x3a, 0xf1, 0x60, 0x57, 0x8c, 0x82, 0x94, 0x3d, 0x6f, 0x9e, 0x53, 0xb7, 0x2b, 0xc5, 0xe9, 0x7f, 0x3d}, subYX: fp.Elt{0xcd, 0x1e, 0xb1, 0x16, 0xc6, 0xaf, 0x7d, 0x17, 0x79, 0x64, 0x57, 0xfa, 0x9c, 0x4b, 0x76, 0x89, 0x85, 0xe7, 0xec, 0xe6, 0x10, 0xa1, 0xa8, 0xb7, 0xf0, 0xdb, 0x85, 0xbe, 0x9f, 0x83, 0xe6, 0x78}, dt2: fp.Elt{0x6b, 0x85, 0xb8, 0x37, 0xf7, 0x2d, 0x33, 0x70, 0x8a, 0x17, 0x1a, 0x04, 0x43, 0x5d, 0xd0, 0x75, 0x22, 0x9e, 0xe5, 0xa0, 0x4a, 0xf7, 0x0f, 0x32, 0x42, 0x82, 0x08, 0x50, 0xf3, 0x68, 0xf2, 0x70}, }, { /* 41P */ addYX: fp.Elt{0x47, 0x5f, 0x80, 0xb1, 0x83, 0x45, 0x86, 0x66, 0x19, 0x7c, 0xdd, 0x60, 0xd1, 0xc5, 0x35, 0xf5, 0x06, 0xb0, 0x4c, 0x1e, 0xb7, 0x4e, 0x87, 0xe9, 0xd9, 0x89, 0xd8, 0xfa, 0x5c, 0x34, 0x0d, 0x7c}, subYX: fp.Elt{0x55, 0xf3, 0xdc, 0x70, 0x20, 0x11, 0x24, 0x23, 0x17, 0xe1, 0xfc, 0xe7, 0x7e, 0xc9, 0x0c, 0x38, 0x98, 0xb6, 0x52, 0x35, 0xed, 0xde, 0x1d, 0xb3, 0xb9, 0xc4, 0xb8, 0x39, 0xc0, 0x56, 0x4e, 0x40}, dt2: fp.Elt{0x8a, 0x33, 0x78, 0x8c, 0x4b, 0x1f, 0x1f, 0x59, 0xe1, 0xb5, 0xe0, 0x67, 0xb1, 0x6a, 0x36, 0xa0, 0x44, 0x3d, 0x5f, 0xb4, 0x52, 0x41, 0xbc, 0x5c, 0x77, 0xc7, 0xae, 0x2a, 0x76, 0x54, 0xd7, 0x20}, }, { /* 43P */ addYX: fp.Elt{0x58, 0xb7, 0x3b, 0xc7, 0x6f, 0xc3, 0x8f, 0x5e, 0x9a, 0xbb, 0x3c, 0x36, 0xa5, 0x43, 0xe5, 0xac, 0x22, 0xc9, 0x3b, 0x90, 0x7d, 0x4a, 0x93, 0xa9, 0x62, 0xec, 0xce, 0xf3, 0x46, 0x1e, 0x8f, 0x2b}, subYX: fp.Elt{0x43, 0xf5, 0xb9, 0x35, 0xb1, 0xfe, 0x74, 0x9d, 0x6c, 0x95, 0x8c, 0xde, 0xf1, 0x7d, 0xb3, 0x84, 0xa9, 0x8b, 0x13, 0x57, 0x07, 0x2b, 0x32, 0xe9, 0xe1, 0x4c, 0x0b, 0x79, 0xa8, 0xad, 0xb8, 0x38}, dt2: fp.Elt{0x5d, 0xf9, 0x51, 0xdf, 0x9c, 0x4a, 0xc0, 0xb5, 0xac, 0xde, 0x1f, 0xcb, 0xae, 0x52, 0x39, 0x2b, 0xda, 0x66, 0x8b, 0x32, 0x8b, 0x6d, 0x10, 0x1d, 0x53, 0x19, 0xba, 0xce, 0x32, 0xeb, 0x9a, 0x04}, }, { /* 45P */ addYX: fp.Elt{0x31, 0x79, 0xfc, 0x75, 0x0b, 0x7d, 0x50, 0xaa, 0xd3, 0x25, 0x67, 0x7a, 0x4b, 0x92, 0xef, 0x0f, 0x30, 0x39, 0x6b, 0x39, 0x2b, 0x54, 0x82, 0x1d, 0xfc, 0x74, 0xf6, 0x30, 0x75, 0xe1, 0x5e, 0x79}, subYX: fp.Elt{0x7e, 0xfe, 0xdc, 0x63, 0x3c, 0x7d, 0x76, 0xd7, 0x40, 0x6e, 0x85, 0x97, 0x48, 0x59, 0x9c, 0x20, 0x13, 0x7c, 0x4f, 0xe1, 0x61, 0x68, 0x67, 0xb6, 0xfc, 0x25, 0xd6, 0xc8, 0xe0, 0x65, 0xc6, 0x51}, dt2: fp.Elt{0x81, 0xbd, 0xec, 0x52, 0x0a, 0x5b, 0x4a, 0x25, 0xe7, 0xaf, 0x34, 0xe0, 0x6e, 0x1f, 0x41, 0x5d, 0x31, 0x4a, 0xee, 0xca, 0x0d, 0x4d, 0xa2, 0xe6, 0x77, 0x44, 0xc5, 0x9d, 0xf4, 0x9b, 0xd1, 0x6c}, }, { /* 47P */ addYX: fp.Elt{0x86, 0xc3, 0xaf, 0x65, 0x21, 0x61, 0xfe, 0x1f, 0x10, 0x1b, 0xd5, 0xb8, 0x88, 0x2a, 0x2a, 0x08, 0xaa, 0x0b, 0x99, 0x20, 0x7e, 0x62, 0xf6, 0x76, 0xe7, 0x43, 0x9e, 0x42, 0xa7, 0xb3, 0x01, 0x5e}, subYX: fp.Elt{0xa3, 0x9c, 0x17, 0x52, 0x90, 0x61, 0x87, 0x7e, 0x85, 0x9f, 0x2c, 0x0b, 0x06, 0x0a, 0x1d, 0x57, 0x1e, 0x71, 0x99, 0x84, 0xa8, 0xba, 0xa2, 0x80, 0x38, 0xe6, 0xb2, 0x40, 0xdb, 0xf3, 0x20, 0x75}, dt2: fp.Elt{0xa1, 0x57, 0x93, 0xd3, 0xe3, 0x0b, 0xb5, 0x3d, 0xa5, 0x94, 0x9e, 0x59, 0xdd, 0x6c, 0x7b, 0x96, 0x6e, 0x1e, 0x31, 0xdf, 0x64, 0x9a, 0x30, 0x1a, 0x86, 0xc9, 0xf3, 0xce, 0x9c, 0x2c, 0x09, 0x71}, }, { /* 49P */ addYX: fp.Elt{0xcf, 0x1d, 0x05, 0x74, 0xac, 0xd8, 0x6b, 0x85, 0x1e, 0xaa, 0xb7, 0x55, 0x08, 0xa4, 0xf6, 0x03, 0xeb, 0x3c, 0x74, 0xc9, 0xcb, 0xe7, 0x4a, 0x3a, 0xde, 0xab, 0x37, 0x71, 0xbb, 0xa5, 0x73, 0x41}, subYX: fp.Elt{0x8c, 0x91, 0x64, 0x03, 0x3f, 0x52, 0xd8, 0x53, 0x1c, 0x6b, 0xab, 0x3f, 0xf4, 0x04, 0xb4, 0xa2, 0xa4, 0xe5, 0x81, 0x66, 0x9e, 0x4a, 0x0b, 0x08, 0xa7, 0x7b, 0x25, 0xd0, 0x03, 0x5b, 0xa1, 0x0e}, dt2: fp.Elt{0x8a, 0x21, 0xf9, 0xf0, 0x31, 0x6e, 0xc5, 0x17, 0x08, 0x47, 0xfc, 0x1a, 0x2b, 0x6e, 0x69, 0x5a, 0x76, 0xf1, 0xb2, 0xf4, 0x68, 0x16, 0x93, 0xf7, 0x67, 0x3a, 0x4e, 0x4a, 0x61, 0x65, 0xc5, 0x5f}, }, { /* 51P */ addYX: fp.Elt{0x8e, 0x98, 0x90, 0x77, 0xe6, 0xe1, 0x92, 0x48, 0x22, 0xd7, 0x5c, 0x1c, 0x0f, 0x95, 0xd5, 0x01, 0xed, 0x3e, 0x92, 0xe5, 0x9a, 0x81, 0xb0, 0xe3, 0x1b, 0x65, 0x46, 0x9d, 0x40, 0xc7, 0x14, 0x32}, subYX: fp.Elt{0xe5, 0x7a, 0x6d, 0xc4, 0x0d, 0x57, 0x6e, 0x13, 0x8f, 0xdc, 0xf8, 0x54, 0xcc, 0xaa, 0xd0, 0x0f, 0x86, 0xad, 0x0d, 0x31, 0x03, 0x9f, 0x54, 0x59, 0xa1, 0x4a, 0x45, 0x4c, 0x41, 0x1c, 0x71, 0x62}, dt2: fp.Elt{0x70, 0x17, 0x65, 0x06, 0x74, 0x82, 0x29, 0x13, 0x36, 0x94, 0x27, 0x8a, 0x66, 0xa0, 0xa4, 0x3b, 0x3c, 0x22, 0x5d, 0x18, 0xec, 0xb8, 0xb6, 0xd9, 0x3c, 0x83, 0xcb, 0x3e, 0x07, 0x94, 0xea, 0x5b}, }, { /* 53P */ addYX: fp.Elt{0xf8, 0xd2, 0x43, 0xf3, 0x63, 0xce, 0x70, 0xb4, 0xf1, 0xe8, 0x43, 0x05, 0x8f, 0xba, 0x67, 0x00, 0x6f, 0x7b, 0x11, 0xa2, 0xa1, 0x51, 0xda, 0x35, 0x2f, 0xbd, 0xf1, 0x44, 0x59, 0x78, 0xd0, 0x4a}, subYX: fp.Elt{0xe4, 0x9b, 0xc8, 0x12, 0x09, 0xbf, 0x1d, 0x64, 0x9c, 0x57, 0x6e, 0x7d, 0x31, 0x8b, 0xf3, 0xac, 0x65, 0xb0, 0x97, 0xf6, 0x02, 0x9e, 0xfe, 0xab, 0xec, 0x1e, 0xf6, 0x48, 0xc1, 0xd5, 0xac, 0x3a}, dt2: fp.Elt{0x01, 0x83, 0x31, 0xc3, 0x34, 0x3b, 0x8e, 0x85, 0x26, 0x68, 0x31, 0x07, 0x47, 0xc0, 0x99, 0xdc, 0x8c, 0xa8, 0x9d, 0xd3, 0x2e, 0x5b, 0x08, 0x34, 0x3d, 0x85, 0x02, 0xd9, 0xb1, 0x0c, 0xff, 0x3a}, }, { /* 55P */ addYX: fp.Elt{0x05, 0x35, 0xc5, 0xf4, 0x0b, 0x43, 0x26, 0x92, 0x83, 0x22, 0x1f, 0x26, 0x13, 0x9c, 0xe4, 0x68, 0xc6, 0x27, 0xd3, 0x8f, 0x78, 0x33, 0xef, 0x09, 0x7f, 0x9e, 0xd9, 0x2b, 0x73, 0x9f, 0xcf, 0x2c}, subYX: fp.Elt{0x5e, 0x40, 0x20, 0x3a, 0xeb, 0xc7, 0xc5, 0x87, 0xc9, 0x56, 0xad, 0xed, 0xef, 0x11, 0xe3, 0x8e, 0xf9, 0xd5, 0x29, 0xad, 0x48, 0x2e, 0x25, 0x29, 0x1d, 0x25, 0xcd, 0xf4, 0x86, 0x7e, 0x0e, 0x11}, dt2: fp.Elt{0xe4, 0xf5, 0x03, 0xd6, 0x9e, 0xd8, 0xc0, 0x57, 0x0c, 0x20, 0xb0, 0xf0, 0x28, 0x86, 0x88, 0x12, 0xb7, 0x3b, 0x2e, 0xa0, 0x09, 0x27, 0x17, 0x53, 0x37, 0x3a, 0x69, 0xb9, 0xe0, 0x57, 0xc5, 0x05}, }, { /* 57P */ addYX: fp.Elt{0xb0, 0x0e, 0xc2, 0x89, 0xb0, 0xbb, 0x76, 0xf7, 0x5c, 0xd8, 0x0f, 0xfa, 0xf6, 0x5b, 0xf8, 0x61, 0xfb, 0x21, 0x44, 0x63, 0x4e, 0x3f, 0xb9, 0xb6, 0x05, 0x12, 0x86, 0x41, 0x08, 0xef, 0x9f, 0x28}, subYX: fp.Elt{0x6f, 0x7e, 0xc9, 0x1f, 0x31, 0xce, 0xf9, 0xd8, 0xae, 0xfd, 0xf9, 0x11, 0x30, 0x26, 0x3f, 0x7a, 0xdd, 0x25, 0xed, 0x8b, 0xa0, 0x7e, 0x5b, 0xe1, 0x5a, 0x87, 0xe9, 0x8f, 0x17, 0x4c, 0x15, 0x6e}, dt2: fp.Elt{0xbf, 0x9a, 0xd6, 0xfe, 0x36, 0x63, 0x61, 0xcf, 0x4f, 0xc9, 0x35, 0x83, 0xe7, 0xe4, 0x16, 0x9b, 0xe7, 0x7f, 0x3a, 0x75, 0x65, 0x97, 0x78, 0x13, 0x19, 0xa3, 0x5c, 0xa9, 0x42, 0xf6, 0xfb, 0x6a}, }, { /* 59P */ addYX: fp.Elt{0xcc, 0xa8, 0x13, 0xf9, 0x70, 0x50, 0xe5, 0x5d, 0x61, 0xf5, 0x0c, 0x2b, 0x7b, 0x16, 0x1d, 0x7d, 0x89, 0xd4, 0xea, 0x90, 0xb6, 0x56, 0x29, 0xda, 0xd9, 0x1e, 0x80, 0xdb, 0xce, 0x93, 0xc0, 0x12}, subYX: fp.Elt{0xc1, 0xd2, 0xf5, 0x62, 0x0c, 0xde, 0xa8, 0x7d, 0x9a, 0x7b, 0x0e, 0xb0, 0xa4, 0x3d, 0xfc, 0x98, 0xe0, 0x70, 0xad, 0x0d, 0xda, 0x6a, 0xeb, 0x7d, 0xc4, 0x38, 0x50, 0xb9, 0x51, 0xb8, 0xb4, 0x0d}, dt2: fp.Elt{0x0f, 0x19, 0xb8, 0x08, 0x93, 0x7f, 0x14, 0xfc, 0x10, 0xe3, 0x1a, 0xa1, 0xa0, 0x9d, 0x96, 0x06, 0xfd, 0xd7, 0xc7, 0xda, 0x72, 0x55, 0xe7, 0xce, 0xe6, 0x5c, 0x63, 0xc6, 0x99, 0x87, 0xaa, 0x33}, }, { /* 61P */ addYX: fp.Elt{0xb1, 0x6c, 0x15, 0xfc, 0x88, 0xf5, 0x48, 0x83, 0x27, 0x6d, 0x0a, 0x1a, 0x9b, 0xba, 0xa2, 0x6d, 0xb6, 0x5a, 0xca, 0x87, 0x5c, 0x2d, 0x26, 0xe2, 0xa6, 0x89, 0xd5, 0xc8, 0xc1, 0xd0, 0x2c, 0x21}, subYX: fp.Elt{0xf2, 0x5c, 0x08, 0xbd, 0x1e, 0xf5, 0x0f, 0xaf, 0x1f, 0x3f, 0xd3, 0x67, 0x89, 0x1a, 0xf5, 0x78, 0x3c, 0x03, 0x60, 0x50, 0xe1, 0xbf, 0xc2, 0x6e, 0x86, 0x1a, 0xe2, 0xe8, 0x29, 0x6f, 0x3c, 0x23}, dt2: fp.Elt{0x81, 0xc7, 0x18, 0x7f, 0x10, 0xd5, 0xf4, 0xd2, 0x28, 0x9d, 0x7e, 0x52, 0xf2, 0xcd, 0x2e, 0x12, 0x41, 0x33, 0x3d, 0x3d, 0x2a, 0x86, 0x0a, 0xa7, 0xe3, 0x4c, 0x91, 0x11, 0x89, 0x77, 0xb7, 0x1d}, }, { /* 63P */ addYX: fp.Elt{0xb6, 0x1a, 0x70, 0xdd, 0x69, 0x47, 0x39, 0xb3, 0xa5, 0x8d, 0xcf, 0x19, 0xd4, 0xde, 0xb8, 0xe2, 0x52, 0xc8, 0x2a, 0xfd, 0x61, 0x41, 0xdf, 0x15, 0xbe, 0x24, 0x7d, 0x01, 0x8a, 0xca, 0xe2, 0x7a}, subYX: fp.Elt{0x6f, 0xc2, 0x6b, 0x7c, 0x39, 0x52, 0xf3, 0xdd, 0x13, 0x01, 0xd5, 0x53, 0xcc, 0xe2, 0x97, 0x7a, 0x30, 0xa3, 0x79, 0xbf, 0x3a, 0xf4, 0x74, 0x7c, 0xfc, 0xad, 0xe2, 0x26, 0xad, 0x97, 0xad, 0x31}, dt2: fp.Elt{0x62, 0xb9, 0x20, 0x09, 0xed, 0x17, 0xe8, 0xb7, 0x9d, 0xda, 0x19, 0x3f, 0xcc, 0x18, 0x85, 0x1e, 0x64, 0x0a, 0x56, 0x25, 0x4f, 0xc1, 0x91, 0xe4, 0x83, 0x2c, 0x62, 0xa6, 0x53, 0xfc, 0xd1, 0x1e}, }, } golang-github-cloudflare-circl-1.3.7/sign/ed25519/testdata/000077500000000000000000000000001454601126700232365ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/ed25519/testdata/sign.input.zip000066400000000000000000027746571454601126700261140ustar00rootroot00000000000000PKN % sign.input.txtUT \W\ux ܽ[,7eC `C赌%-%UB2In0Ug>2kX?ϼHM:ʩ8Zk!wvkحCi0WYg8't󞳦ʼ!Ym|N)!4Bg:/[~ٽjI!R=2̾[ɼh|XO];u eNzj)OL yϙf}q0fyr=\؟x )I[TZi-B9XI?8c/=7El=b%iqBi_𮷵٣׾Kzb/reѿxtsbVZ?hL5`جXqa|v>%>Ù+]72k1<9kK΄aaN{qli7l6)9GA}rgNl΂`!U/OyzߺÄ%ZȎvl /x`g ʾX㜡Pˠ`bVŠ3>K:lyq-5yelY\w_<Zg{<-c0opyrk6[ `p!M;[Nz鴃{=0\,TeKޙ%A06Syz|C-ˍϊ=䋛m~WkaspyG̓AS/7L%T.M ;Ë58ɛ<|b*:6xPQt]PdbN`73?'񥳼=wxNʋ9;[X\ScȐ zAzrKy,yAs|K`D`pQ0.#Q=yiy0+/ hxײn^:&߈d rj*{hB ˎcOx'n(UcEXA^+ <7(Ì ၫ#<~cEI_Gm:78g3Δ |Ȉ]xxJU8h11uF|x7.^:~WFg@ (d#Hݙ2TPVN0|NnHy)1P$Y2\MM2{{F=C('}CE*)VU<#P4 Yfߝ8Fn8ī]Ե<8 )t$&e+;%Cz"0QOkqTW9l(T: 6{A%.e2']y/1:͑ | g* #CTZj~ KX?YX4X)(79FDW{3%Oa/({:KRD(F ]4\>8~|}.i_3ݮrl F(Zk|D[= 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y$7p$jpP i8K"n S7'0XmUn3>M$ӥ(gq?:|4X8u {C7مUate9@z}! 9KmfiV؛g %M!&/vhVj&jH@-rgW&}'uoXW69j7%/[<)ZcP2e쩈&$1d3AL떆A9:&2%@|DdwWDr{ژ6 Ԭ^تd `xeX+[@x*,EPGFPAG e L҇q|n/K|fʿTA: |.vM$|`6U/nPWoz$1SR"7{Aϟe wf^g[=?zb `T(6u`#m^(((NmbcP/_WJ?W^E E}6=~=~=~ z3X|W馴XH(gaSeC9)_r2*e@Y W4֠ Ǐ{T~fmO "|?b'v$ДΟ˃耏WN S{HwWe5zE)7"Abɜڔ&%ey9YOض1FWF|%-TNV9uJy8)fv3#p9# #Q.8i &i3"vt>%͍Ϯ N6X͉v]tg,K$a8CH)U={僈8 D:,h¯̄l{yMNǣ*Պޟ6UV$,$WRgj'YlP4*3 rE1CVAo~x|CVz){etDt`(ɖ8*u5C$q {X 2CXM̓D ]IRn˪Y&V""%d;) ]2HYm:5#{ 7h gDs+P:iY'+PU6FYsu uZ7m~||||XĚ;U>g) p*DbbYϼJהyg u>ku[-Y8B1+[ڐ)e'Mc2v M.Z`z+m^Kk]߸S Ox͘k)vb^r9S'U î QW& P+Vncx&#$kN"ijzlQrz,1[插4ߣ(YBb&ԋ54fvWyj2GN;0=}Qҳ$:Ap(7ӧwlj> 'LɬUGaIB.,MN+pYF o880nC v浤&.$V#6D[ LDcN+580Z2?Qy>Gi\."}x;4f{]w}G{,8B7տS/[< )Ѳ950$9,u^Tú|YUe@bl8iLEv֌ wDhgc|~-!@_{gp$1EccpـCn8~z,Bh9kpG0n)1-e,x,5OL? y7($*jVwXt<SV[SQ[o*!=Hyw'Aܩ|FXpB-4z# ŚLQhJZt[yNL\?7`ʑ쟡i# mV6STHkk]/6u[]fg}##A>D#ܨ8Xn,wܯZۉ4_i^B O;ٸ)3N<^Y_Xi*ۡhFHTxH/pEe=V\;b}ϓx'/5M p< J~F$ʪIMQ<*st N./͝>ɠ4pPMT{J f]';VtoiE;=H}XݮDK#NN`v%4ۍ(N{XZ?~8qPK^gN %PKN^gN % sign.input.txtUT \W\ux PK\= golang-github-cloudflare-circl-1.3.7/sign/ed25519/testdata/wycheproof_Ed25519.json000066400000000000000000002720021454601126700273370ustar00rootroot00000000000000{ "algorithm" : "EDDSA", "generatorVersion" : "0.8rc16", "numberOfTests" : 145, "header" : [ "Test vectors of type EddsaVerify are intended for testing", "the verification of Eddsa signatures." ], "notes" : { "SignatureMalleability" : "EdDSA signatures are non-malleable, if implemented accordingly. Failing to check the range of S allows to modify signatures. See RFC 8032, Section 5.2.7 and Section 8.4." }, "schema" : "eddsa_verify_schema.json", "testGroups" : [ { "jwk" : { "crv" : "Ed25519", "d" : "rdS7gQN4W6-axTQljoqvZfXxrbXvXz3xm7gKuYnE1ks", "kid" : "none", "kty" : "OKP", "x" : "fU0Of2FTpptiQrUiq77mhf2kQg-INLEIw72uNp71Sfo" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "7d4d0e7f6153a69b6242b522abbee685fda4420f8834b108c3bdae369ef549fa", "sk" : "add4bb8103785baf9ac534258e8aaf65f5f1adb5ef5f3df19bb80ab989c4d64b", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b65700321007d4d0e7f6153a69b6242b522abbee685fda4420f8834b108c3bdae369ef549fa", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAfU0Of2FTpptiQrUiq77mhf2kQg+INLEIw72uNp71Sfo=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 1, "comment" : "", "msg" : "", "sig" : "d4fbdb52bfa726b44d1786a8c0d171c3e62ca83c9e5bbe63de0bb2483f8fd6cc1429ab72cafc41ab56af02ff8fcc43b99bfe4c7ae940f60f38ebaa9d311c4007", "result" : "valid", "flags" : [] }, { "tcId" : 2, "comment" : "", "msg" : "78", "sig" : "d80737358ede548acb173ef7e0399f83392fe8125b2ce877de7975d8b726ef5b1e76632280ee38afad12125ea44b961bf92f1178c9fa819d020869975bcbe109", "result" : "valid", "flags" : [] }, { "tcId" : 3, "comment" : "", "msg" : "54657374", "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab07a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946b30d", "result" : "valid", "flags" : [] }, { "tcId" : 4, "comment" : "", "msg" : "48656c6c6f", "sig" : "1c1ad976cbaae3b31dee07971cf92c928ce2091a85f5899f5e11ecec90fc9f8e93df18c5037ec9b29c07195ad284e63d548cd0a6fe358cc775bd6c1608d2c905", "result" : "valid", "flags" : [] }, { "tcId" : 5, "comment" : "", "msg" : "313233343030", "sig" : "657c1492402ab5ce03e2c3a7f0384d051b9cf3570f1207fc78c1bcc98c281c2bf0cf5b3a289976458a1be6277a5055545253b45b07dcc1abd96c8b989c00f301", "result" : "valid", "flags" : [] }, { "tcId" : 6, "comment" : "", "msg" : "000000000000000000000000", "sig" : 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"7b64a28c50ec7678a90e3e1a21522e30ac9db7b5215aea2bfb33bea037eab987", "sk" : "a89ea18476b9ad90cb14b8b1ff24777e4ebd015bc810a60785a9154dacf3be52", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b65700321007b64a28c50ec7678a90e3e1a21522e30ac9db7b5215aea2bfb33bea037eab987", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAe2SijFDsdnipDj4aIVIuMKydt7UhWuor+zO+oDfquYc=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 136, "comment" : "regression test for arithmetic error", "msg" : "6e911edb27a170b983d4dee1110554f804330f41", "sig" : "4204d620cde0c3008c0b2901f5d6b44f88f0e3cb4f4d62252bf6f3cb37c1fb150a9ccb296afe5e7c75f65b5c8edd13dc4910ffe1e1265b3707c59042cf9a5902", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "abHaVs3o0WdsKowOf5XH0L9gc579EwTdLMsCcp0Xoiw", "kid" : "none", "kty" : "OKP", "x" : "ckRSIQqeTJlIGSKb8Sv4TpV2ijqXwI2Nj1-TmkytNMU" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "724452210a9e4c994819229bf12bf84e95768a3a97c08d8d8f5f939a4cad34c5", "sk" : "69b1da56cde8d1676c2a8c0e7f95c7d0bf60739efd1304dd2ccb02729d17a22c", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b6570032100724452210a9e4c994819229bf12bf84e95768a3a97c08d8d8f5f939a4cad34c5", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAckRSIQqeTJlIGSKb8Sv4TpV2ijqXwI2Nj1+TmkytNMU=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 137, "comment" : "regression test for arithmetic error", "msg" : "b8cf807eea809aaf739aa091f3b7a3f2fd39fb51", "sig" : "f8a69d3fd8c2ff0a9dec41e4c6b43675ce08366a35e220b1185ffc246c339e22c20ac661e866f52054015efd04f42eca2adcee6834c4df923b4a62576e4dff0e", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "szImXPlVlfDJAiFZO1orPFdNYNxjTd_2GG8O7XmAo4M", "kid" : "none", "kty" : "OKP", "x" : "utJlspTtL0IstqFBaUCGI4-_6YdXGqdl2LTzokEFqgE" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "bad265b294ed2f422cb6a141694086238fbfe987571aa765d8b4f3a24105aa01", "sk" : "b332265cf95595f0c90221593b5a2b3c574d60dc634ddff6186f0eed7980a383", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b6570032100bad265b294ed2f422cb6a141694086238fbfe987571aa765d8b4f3a24105aa01", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAutJlspTtL0IstqFBaUCGI4+/6YdXGqdl2LTzokEFqgE=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 138, "comment" : "regression test for arithmetic error", "msg" : "01a2b5f7fee813b4e9bd7fc25137648004795010", "sig" : "61792c9442bc6338ac41fd42a40bee9b02ec1836503d60ff725128c63d72808880c36e6190b7da525cbee5d12900aa043547dd14a2709ef9e49d628f37f6b70c", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "-uyXZLNp3w7xCJDdAixQLlUaMiK0PoQpRVSWx2_upF0", "kid" : "none", "kty" : "OKP", "x" : "Cq7ktyPbm1G6fSLrI-uKdqWsAvT8ndBvd76kLh037Fo" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "0aaee4b723db9b51ba7d22eb23eb8a76a5ac02f4fc9dd06f77bea42e1d37ec5a", "sk" : "faec9764b369df0ef10890dd022c502e551a3222b43e8429455496c76feea45d", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b65700321000aaee4b723db9b51ba7d22eb23eb8a76a5ac02f4fc9dd06f77bea42e1d37ec5a", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEACq7ktyPbm1G6fSLrI+uKdqWsAvT8ndBvd76kLh037Fo=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 139, "comment" : "regression test for arithmetic error", "msg" : "0fbf5d47cb5d498feace8f98f1896208da38a885", "sig" : "fa3cd41e3a8c00b19eecd404a63c3cb787cd30de0dfc936966cff2117f5aff18db6bef80fcfd8856f3fb2e9c3dc47593e9471103032af918feee638a33d40505", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "TrGeJ496MKBqfVXkLER3X0qBt6RcBRKq4CYmLnF3Daw", "kid" : "none", "kty" : "OKP", "x" : "gSNErxWpG6g8LJHpbxcnrA88TEE4W5-oTvo5mtpRaL4" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "812344af15a91ba83c2c91e96f1727ac0f3c4c41385b9fa84efa399ada5168be", "sk" : "4eb19e278f7a30a06a7d55e42c44775f4a81b7a45c0512aae026262e71770dac", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b6570032100812344af15a91ba83c2c91e96f1727ac0f3c4c41385b9fa84efa399ada5168be", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAgSNErxWpG6g8LJHpbxcnrA88TEE4W5+oTvo5mtpRaL4=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 140, "comment" : "regression test for arithmetic error", "msg" : "36e67c1939750bffb3e4ba6cb85562612275e862", "sig" : "97fbbcd7a1d0eb42d2f8c42448ef35a2c2472740556b645547865330d6c57068af377fced08aaf810c08cd3c43d296f1975710312e9334c98b485f831efa4103", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "GZjVlJyrNloA-Cjn0XsGxwjTP-8AMdNTpOFb9yIqc7A", "kid" : "none", "kty" : "OKP", "x" : "DuXLVZf7343MxIsBSF45szqhM7UtMNI3QCdyZ8_sPj4" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "0ee5cb5597fbdf8dccc48b01485e39b33aa133b52d30d23740277267cfec3e3e", "sk" : "1998d5949cab365a00f828e7d17b06c708d33fef0031d353a4e15bf7222a73b0", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b65700321000ee5cb5597fbdf8dccc48b01485e39b33aa133b52d30d23740277267cfec3e3e", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEADuXLVZf7343MxIsBSF45szqhM7UtMNI3QCdyZ8/sPj4=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 141, "comment" : "regression test for arithmetic error", "msg" : "13945c894c1d3fe8562e8b20e5f0efaa26ade8e3", "sig" : "d7dbaa337ffd2a5fd8d5fd8ad5aeccc0c0f83795c2c59fe62a40b87903b1ae62ed748a8df5af4d32f9f822a65d0e498b6f40eaf369a9342a1164ee7d08b58103", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "YWRnYRTGa9mIfaw0HGYgncWHzPDMXNm6_9-skpWgDEo", "kid" : "none", "kty" : "OKP", "x" : "n7od6StgtbRwMIl2PQ1vkSXk3X765B8IoiiCrvloksQ" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "9fba1de92b60b5b4703089763d0d6f9125e4dd7efae41f08a22882aef96892c4", "sk" : "6164676114c66bd9887dac341c66209dc587ccf0cc5cd9baffdfac9295a00c4a", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b65700321009fba1de92b60b5b4703089763d0d6f9125e4dd7efae41f08a22882aef96892c4", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAn7od6StgtbRwMIl2PQ1vkSXk3X765B8IoiiCrvloksQ=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 142, "comment" : "regression test for arithmetic error", "msg" : "4de142af4b8402f80a47fa812df84f42e283cee7", "sig" : "09a2ed303a2fa7027a1dd7c3b0d25121eeed2b644a2fbc17aa0c8aea4524071ede7e7dd7a536d5497f8165d29e4e1b63200f74bbae39fbbbccb29889c62c1f09", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "SwvQOgOyAGnMvMIUp0SEc_TnpJH6fOtI3b4kyDxKpLs", "kid" : "none", "kty" : "OKP", "x" : "dYKrG1LhMW5cE2cfQ7Oco2soEzzQgygxvN3QsPIzmMs" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "7582ab1b52e1316e5c13671f43b39ca36b28133cd0832831bcddd0b0f23398cb", "sk" : "4b0bd03a03b20069ccbcc214a7448473f4e7a491fa7ceb48ddbe24c83c4aa4bb", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b65700321007582ab1b52e1316e5c13671f43b39ca36b28133cd0832831bcddd0b0f23398cb", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAdYKrG1LhMW5cE2cfQ7Oco2soEzzQgygxvN3QsPIzmMs=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 143, "comment" : "regression test for arithmetic error", "msg" : "563357f41b8b23b1d83f19f5667177a67da20b18", "sig" : "e6884a6e6b2e60a0b5862251c001e7c79d581d777d6fc11d218d0aecd79f26a30e2ca22cc7c4674f8b72655bc4ee5cb5494ca07c05177656142ac55cc9d33e02", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "L854cL4fOS0h-x0jUOx4d9uKqZs1n-W91TOP81p5HRw", "kid" : "none", "kty" : "OKP", "x" : "3S1ni64iLz-26CePCMyeGmYznJJsKawKFvlxf17hjNg" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "dd2d678bae222f3fb6e8278f08cc9e1a66339c926c29ac0a16f9717f5ee18cd8", "sk" : "2fce7870be1f392d21fb1d2350ec7877db8aa99b359fe5bdd5338ff35a791d1c", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b6570032100dd2d678bae222f3fb6e8278f08cc9e1a66339c926c29ac0a16f9717f5ee18cd8", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEA3S1ni64iLz+26CePCMyeGmYznJJsKawKFvlxf17hjNg=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 144, "comment" : "regression test for arithmetic error", "msg" : "931bbf9c877a6571cf7d4609fc3eb867edd43f51", "sig" : "6124c206d864507ea5d984b363b4cf583314db6856a45ded5e61eebff4d5e337e0b4c82b445ae2e52d549d2d961eace2ea01f81158e09a9686baa040db65ad08", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed25519", "d" : "qazkIZXduzoW82ayTdnTeooEPtLmAB9UZSKWdQN5Nn0", "kid" : "none", "kty" : "OKP", "x" : "zL58suS8IVzuL4heHSL34NWCsru9eCwQTlSLFS0m_Gk" }, "key" : { "curve" : "edwards25519", "keySize" : 255, "pk" : "ccbe7cb2e4bc215cee2f885e1d22f7e0d582b2bbbd782c104e548b152d26fc69", "sk" : "a9ace42195ddbb3a16f366b24dd9d37a8a043ed2e6001f54652296750379367d", "type" : "EDDSAKeyPair" }, "keyDer" : "302a300506032b6570032100ccbe7cb2e4bc215cee2f885e1d22f7e0d582b2bbbd782c104e548b152d26fc69", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAzL58suS8IVzuL4heHSL34NWCsru9eCwQTlSLFS0m/Gk=\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 145, "comment" : "regression test for arithmetic error", "msg" : "44530b0b34f598767a7b875b0caee3c7b9c502d1", "sig" : "cfbd450a2c83cb8436c348822fe3ee347d4ee937b7f2ea11ed755cc52852407c9eec2c1fa30d2f9aef90e89b2cc3bcef2b1b9ca59f712110d19894a9cf6a2802", "result" : "valid", "flags" : [] } ] } ] } golang-github-cloudflare-circl-1.3.7/sign/ed25519/wycheproof_test.go000066400000000000000000000053631454601126700252070ustar00rootroot00000000000000package ed25519_test import ( "bytes" "encoding/hex" "encoding/json" "io" "os" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/sign/ed25519" ) type group struct { Key struct { Curve string `json:"curve"` Size int `json:"keySize"` Pk string `json:"pk"` Sk string `json:"sk"` Type string `json:"type"` } `json:"key"` Type string `json:"type"` Tests []struct { TcID int `json:"tcId"` Comment string `json:"comment"` Msg string `json:"msg"` Sig string `json:"sig"` Result string `json:"result"` Flags []string `json:"flags"` } `json:"tests"` } type Wycheproof struct { Alg string `json:"algorithm"` Version string `json:"generatorVersion"` Num int `json:"numberOfTests"` Groups []group `json:"testGroups"` } func (kat *Wycheproof) readFile(t *testing.T, fileName string) { jsonFile, err := os.Open(fileName) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", fileName, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", fileName, err) } err = json.Unmarshal(input, &kat) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) } } func (kat *Wycheproof) keyPair(t *testing.T) { for i, g := range kat.Groups { if g.Key.Curve != "edwards25519" { t.Errorf("Curve not expected %v", g.Key.Curve) } private, _ := hex.DecodeString(g.Key.Sk) public, _ := hex.DecodeString(g.Key.Pk) keys := ed25519.NewKeyFromSeed(private) got := keys.Public().(ed25519.PublicKey) want := public if !bytes.Equal(got, want) { test.ReportError(t, got, want, i, g.Key.Sk) } } } func (kat *Wycheproof) verify(t *testing.T) { for i, g := range kat.Groups { for _, gT := range g.Tests { isValid := gT.Result == "valid" private, _ := hex.DecodeString(g.Key.Sk) public, _ := hex.DecodeString(g.Key.Pk) sig, _ := hex.DecodeString(gT.Sig) msg, _ := hex.DecodeString(gT.Msg) priv := ed25519.NewKeyFromSeed(private) got := priv.Public().(ed25519.PublicKey) want := public if !bytes.Equal(got, want) { test.ReportError(t, got, want, i, gT.TcID) } if isValid { got := ed25519.Sign(priv, msg) want := sig if !bytes.Equal(got, want) { test.ReportError(t, got, want, i, gT.TcID) } } { got := ed25519.Verify(priv.Public().(ed25519.PublicKey), msg, sig) want := isValid if got != want { test.ReportError(t, got, want, i, gT.TcID) } } } } } func TestWycheproof(t *testing.T) { // Test vectors from Wycheproof v0.4.12 var kat Wycheproof kat.readFile(t, "testdata/wycheproof_Ed25519.json") t.Run("EDDSAKeyPair", kat.keyPair) t.Run("EDDSAVerify", kat.verify) } golang-github-cloudflare-circl-1.3.7/sign/ed448/000077500000000000000000000000001454601126700212575ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/ed448/ed448.go000066400000000000000000000302111454601126700224330ustar00rootroot00000000000000// Package ed448 implements Ed448 signature scheme as described in RFC-8032. // // This package implements two signature variants. // // | Scheme Name | Sign Function | Verification | Context | // |-------------|-------------------|---------------|-------------------| // | Ed448 | Sign | Verify | Yes, can be empty | // | Ed448Ph | SignPh | VerifyPh | Yes, can be empty | // | All above | (PrivateKey).Sign | VerifyAny | As above | // // Specific functions for sign and verify are defined. A generic signing // function for all schemes is available through the crypto.Signer interface, // which is implemented by the PrivateKey type. A correspond all-in-one // verification method is provided by the VerifyAny function. // // Both schemes require a context string for domain separation. This parameter // is passed using a SignerOptions struct defined in this package. // // References: // // - RFC8032: https://rfc-editor.org/rfc/rfc8032.txt // - EdDSA for more curves: https://eprint.iacr.org/2015/677 // - High-speed high-security signatures: https://doi.org/10.1007/s13389-012-0027-1 package ed448 import ( "bytes" "crypto" cryptoRand "crypto/rand" "crypto/subtle" "errors" "fmt" "io" "strconv" "github.com/cloudflare/circl/ecc/goldilocks" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign" ) const ( // ContextMaxSize is the maximum length (in bytes) allowed for context. ContextMaxSize = 255 // PublicKeySize is the length in bytes of Ed448 public keys. PublicKeySize = 57 // PrivateKeySize is the length in bytes of Ed448 private keys. PrivateKeySize = 114 // SignatureSize is the length in bytes of signatures. SignatureSize = 114 // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. SeedSize = 57 ) const ( paramB = 456 / 8 // Size of keys in bytes. hashSize = 2 * paramB // Size of the hash function's output. ) // SignerOptions implements crypto.SignerOpts and augments with parameters // that are specific to the Ed448 signature schemes. type SignerOptions struct { // Hash must be crypto.Hash(0) for both Ed448 and Ed448Ph. crypto.Hash // Context is an optional domain separation string for signing. // Its length must be less or equal than 255 bytes. Context string // Scheme is an identifier for choosing a signature scheme. Scheme SchemeID } // SchemeID is an identifier for each signature scheme. type SchemeID uint const ( ED448 SchemeID = iota ED448Ph ) // PublicKey is the type of Ed448 public keys. type PublicKey []byte // Equal reports whether pub and x have the same value. func (pub PublicKey) Equal(x crypto.PublicKey) bool { xx, ok := x.(PublicKey) return ok && bytes.Equal(pub, xx) } // PrivateKey is the type of Ed448 private keys. It implements crypto.Signer. type PrivateKey []byte // Equal reports whether priv and x have the same value. func (priv PrivateKey) Equal(x crypto.PrivateKey) bool { xx, ok := x.(PrivateKey) return ok && subtle.ConstantTimeCompare(priv, xx) == 1 } // Public returns the PublicKey corresponding to priv. func (priv PrivateKey) Public() crypto.PublicKey { publicKey := make([]byte, PublicKeySize) copy(publicKey, priv[SeedSize:]) return PublicKey(publicKey) } // Seed returns the private key seed corresponding to priv. It is provided for // interoperability with RFC 8032. RFC 8032's private keys correspond to seeds // in this package. func (priv PrivateKey) Seed() []byte { seed := make([]byte, SeedSize) copy(seed, priv[:SeedSize]) return seed } func (priv PrivateKey) Scheme() sign.Scheme { return sch } func (pub PublicKey) Scheme() sign.Scheme { return sch } func (priv PrivateKey) MarshalBinary() (data []byte, err error) { privateKey := make(PrivateKey, PrivateKeySize) copy(privateKey, priv) return privateKey, nil } func (pub PublicKey) MarshalBinary() (data []byte, err error) { publicKey := make(PublicKey, PublicKeySize) copy(publicKey, pub) return publicKey, nil } // Sign creates a signature of a message given a key pair. // This function supports all the two signature variants defined in RFC-8032, // namely Ed448 (or pure EdDSA) and Ed448Ph. // The opts.HashFunc() must return zero to the specify Ed448 variant. This can // be achieved by passing crypto.Hash(0) as the value for opts. // Use an Options struct to pass a bool indicating that the ed448Ph variant // should be used. // The struct can also be optionally used to pass a context string for signing. func (priv PrivateKey) Sign( rand io.Reader, message []byte, opts crypto.SignerOpts, ) (signature []byte, err error) { var ctx string var scheme SchemeID if o, ok := opts.(SignerOptions); ok { ctx = o.Context scheme = o.Scheme } switch true { case scheme == ED448 && opts.HashFunc() == crypto.Hash(0): return Sign(priv, message, ctx), nil case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0): return SignPh(priv, message, ctx), nil default: return nil, errors.New("ed448: bad hash algorithm") } } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { if rand == nil { rand = cryptoRand.Reader } seed := make(PrivateKey, SeedSize) if _, err := io.ReadFull(rand, seed); err != nil { return nil, nil, err } privateKey := NewKeyFromSeed(seed) publicKey := make([]byte, PublicKeySize) copy(publicKey, privateKey[SeedSize:]) return publicKey, privateKey, nil } // NewKeyFromSeed calculates a private key from a seed. It will panic if // len(seed) is not SeedSize. This function is provided for interoperability // with RFC 8032. RFC 8032's private keys correspond to seeds in this // package. func NewKeyFromSeed(seed []byte) PrivateKey { privateKey := make([]byte, PrivateKeySize) newKeyFromSeed(privateKey, seed) return privateKey } func newKeyFromSeed(privateKey, seed []byte) { if l := len(seed); l != SeedSize { panic("ed448: bad seed length: " + strconv.Itoa(l)) } var h [hashSize]byte H := sha3.NewShake256() _, _ = H.Write(seed) _, _ = H.Read(h[:]) s := &goldilocks.Scalar{} deriveSecretScalar(s, h[:paramB]) copy(privateKey[:SeedSize], seed) _ = goldilocks.Curve{}.ScalarBaseMult(s).ToBytes(privateKey[SeedSize:]) } func signAll(signature []byte, privateKey PrivateKey, message, ctx []byte, preHash bool) { if len(ctx) > ContextMaxSize { panic(fmt.Errorf("ed448: bad context length: " + strconv.Itoa(len(ctx)))) } H := sha3.NewShake256() var PHM []byte if preHash { var h [64]byte _, _ = H.Write(message) _, _ = H.Read(h[:]) PHM = h[:] H.Reset() } else { PHM = message } // 1. Hash the 57-byte private key using SHAKE256(x, 114). var h [hashSize]byte _, _ = H.Write(privateKey[:SeedSize]) _, _ = H.Read(h[:]) s := &goldilocks.Scalar{} deriveSecretScalar(s, h[:paramB]) prefix := h[paramB:] // 2. Compute SHAKE256(dom4(F, C) || prefix || PH(M), 114). var rPM [hashSize]byte H.Reset() writeDom(&H, ctx, preHash) _, _ = H.Write(prefix) _, _ = H.Write(PHM) _, _ = H.Read(rPM[:]) // 3. Compute the point [r]B. r := &goldilocks.Scalar{} r.FromBytes(rPM[:]) R := (&[paramB]byte{})[:] if err := (goldilocks.Curve{}.ScalarBaseMult(r).ToBytes(R)); err != nil { panic(err) } // 4. Compute SHAKE256(dom4(F, C) || R || A || PH(M), 114) var hRAM [hashSize]byte H.Reset() writeDom(&H, ctx, preHash) _, _ = H.Write(R) _, _ = H.Write(privateKey[SeedSize:]) _, _ = H.Write(PHM) _, _ = H.Read(hRAM[:]) // 5. Compute S = (r + k * s) mod order. k := &goldilocks.Scalar{} k.FromBytes(hRAM[:]) S := &goldilocks.Scalar{} S.Mul(k, s) S.Add(S, r) // 6. The signature is the concatenation of R and S. copy(signature[:paramB], R[:]) copy(signature[paramB:], S[:]) } // Sign signs the message with privateKey and returns a signature. // This function supports the signature variant defined in RFC-8032: Ed448, // also known as the pure version of EdDSA. // It will panic if len(privateKey) is not PrivateKeySize. func Sign(priv PrivateKey, message []byte, ctx string) []byte { signature := make([]byte, SignatureSize) signAll(signature, priv, message, []byte(ctx), false) return signature } // SignPh creates a signature of a message given a keypair. // This function supports the signature variant defined in RFC-8032: Ed448ph, // meaning it internally hashes the message using SHAKE-256. // Context could be passed to this function, which length should be no more than // 255. It can be empty. func SignPh(priv PrivateKey, message []byte, ctx string) []byte { signature := make([]byte, SignatureSize) signAll(signature, priv, message, []byte(ctx), true) return signature } func verify(public PublicKey, message, signature, ctx []byte, preHash bool) bool { if len(public) != PublicKeySize || len(signature) != SignatureSize || len(ctx) > ContextMaxSize || !isLessThanOrder(signature[paramB:]) { return false } P, err := goldilocks.FromBytes(public) if err != nil { return false } H := sha3.NewShake256() var PHM []byte if preHash { var h [64]byte _, _ = H.Write(message) _, _ = H.Read(h[:]) PHM = h[:] H.Reset() } else { PHM = message } var hRAM [hashSize]byte R := signature[:paramB] writeDom(&H, ctx, preHash) _, _ = H.Write(R) _, _ = H.Write(public) _, _ = H.Write(PHM) _, _ = H.Read(hRAM[:]) k := &goldilocks.Scalar{} k.FromBytes(hRAM[:]) S := &goldilocks.Scalar{} S.FromBytes(signature[paramB:]) encR := (&[paramB]byte{})[:] P.Neg() _ = goldilocks.Curve{}.CombinedMult(S, k, P).ToBytes(encR) return bytes.Equal(R, encR) } // VerifyAny returns true if the signature is valid. Failure cases are invalid // signature, or when the public key cannot be decoded. // This function supports all the two signature variants defined in RFC-8032, // namely Ed448 (or pure EdDSA) and Ed448Ph. // The opts.HashFunc() must return zero, this can be achieved by passing // crypto.Hash(0) as the value for opts. // Use a SignerOptions struct to pass a context string for signing. func VerifyAny(public PublicKey, message, signature []byte, opts crypto.SignerOpts) bool { var ctx string var scheme SchemeID if o, ok := opts.(SignerOptions); ok { ctx = o.Context scheme = o.Scheme } switch true { case scheme == ED448 && opts.HashFunc() == crypto.Hash(0): return Verify(public, message, signature, ctx) case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0): return VerifyPh(public, message, signature, ctx) default: return false } } // Verify returns true if the signature is valid. Failure cases are invalid // signature, or when the public key cannot be decoded. // This function supports the signature variant defined in RFC-8032: Ed448, // also known as the pure version of EdDSA. func Verify(public PublicKey, message, signature []byte, ctx string) bool { return verify(public, message, signature, []byte(ctx), false) } // VerifyPh returns true if the signature is valid. Failure cases are invalid // signature, or when the public key cannot be decoded. // This function supports the signature variant defined in RFC-8032: Ed448ph, // meaning it internally hashes the message using SHAKE-256. // Context could be passed to this function, which length should be no more than // 255. It can be empty. func VerifyPh(public PublicKey, message, signature []byte, ctx string) bool { return verify(public, message, signature, []byte(ctx), true) } func deriveSecretScalar(s *goldilocks.Scalar, h []byte) { h[0] &= 0xFC // The two least significant bits of the first octet are cleared, h[paramB-1] = 0x00 // all eight bits the last octet are cleared, and h[paramB-2] |= 0x80 // the highest bit of the second to last octet is set. s.FromBytes(h[:paramB]) } // isLessThanOrder returns true if 0 <= x < order and if the last byte of x is zero. func isLessThanOrder(x []byte) bool { order := goldilocks.Curve{}.Order() i := len(order) - 1 for i > 0 && x[i] == order[i] { i-- } return x[paramB-1] == 0 && x[i] < order[i] } func writeDom(h io.Writer, ctx []byte, preHash bool) { dom4 := "SigEd448" _, _ = h.Write([]byte(dom4)) if preHash { _, _ = h.Write([]byte{byte(0x01), byte(len(ctx))}) } else { _, _ = h.Write([]byte{byte(0x00), byte(len(ctx))}) } _, _ = h.Write(ctx) } golang-github-cloudflare-circl-1.3.7/sign/ed448/ed448_test.go000066400000000000000000000205521454601126700235010ustar00rootroot00000000000000package ed448_test import ( "bytes" "crypto" "crypto/rand" "errors" "fmt" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/sign/ed448" ) type zeroReader struct{} func (zeroReader) Read(buf []byte) (int, error) { for i := range buf { buf[i] = 0 } return len(buf), nil } func TestEqual(t *testing.T) { public, private, _ := ed448.GenerateKey(rand.Reader) if !public.Equal(public) { t.Errorf("public key is not equal to itself: %q", public) } if !public.Equal(crypto.Signer(private).Public()) { t.Errorf("private.Public() is not Equal to public: %q", public) } if !private.Equal(private) { t.Errorf("private key is not equal to itself: %q", private) } otherPub, otherPriv, _ := ed448.GenerateKey(rand.Reader) if public.Equal(otherPub) { t.Errorf("different public keys are Equal") } if private.Equal(otherPriv) { t.Errorf("different private keys are Equal") } } func TestWrongPublicKey(t *testing.T) { wrongPublicKeys := [...][ed448.PublicKeySize]byte{ { // y = p 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, }, { // y > p 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, }, { // x^2 = u/v = (y^2-1)/(dy^2-1) is not a quadratic residue 0xa4, 0x8b, 0xae, 0x31, 0x1b, 0x3a, 0xe5, 0x62, 0x3d, 0x6f, 0x2d, 0xbe, 0x8b, 0xb4, 0xd3, 0x21, 0x0f, 0x04, 0x0a, 0x7e, 0xf2, 0x25, 0x87, 0xc3, 0xc0, 0x1e, 0xe1, 0xf4, 0x6d, 0xc7, 0x28, 0x8f, 0x8b, 0xb9, 0x9f, 0x3d, 0x02, 0xb0, 0xc0, 0xa8, 0xe7, 0xe3, 0x4f, 0xb2, 0x82, 0x64, 0x98, 0x4a, 0x84, 0x73, 0xd7, 0x57, 0x6a, 0x39, 0x90, 0xa3, }, { // y = 1 and x^2 = u/v = 0, and the sign of X is 1 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, }, { // y = -1 and x^2 = u/v = 0, and the sign of X is 1 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x80, }, } sig := (&[ed448.SignatureSize]byte{})[:] for _, public := range wrongPublicKeys { got := ed448.Verify(public[:], []byte(""), sig, "") want := false if got != want { test.ReportError(t, got, want, public) } } } func TestSigner(t *testing.T) { seed := (&[ed448.SeedSize]byte{})[:] _, _ = rand.Read(seed) key := ed448.NewKeyFromSeed(seed) priv := key.Seed() if !bytes.Equal(seed, priv) { got := priv want := seed test.ReportError(t, got, want) } signer := crypto.Signer(key) ops := crypto.Hash(0) msg := make([]byte, 16) _, _ = rand.Read(msg) sig, err := signer.Sign(nil, msg, ops) if err != nil { got := err var want error test.ReportError(t, got, want) } if len(sig) != ed448.SignatureSize { got := len(sig) want := ed448.SignatureSize test.ReportError(t, got, want) } for _, o := range []ed448.SignerOptions{ {Scheme: ed448.ED448, Hash: crypto.Hash(0), Context: ""}, {Scheme: ed448.ED448, Hash: crypto.Hash(0), Context: "non-empty"}, {Scheme: ed448.ED448Ph, Hash: crypto.Hash(0), Context: ""}, {Scheme: ed448.ED448Ph, Hash: crypto.Hash(0), Context: "non-empty"}, } { testSigner(t, key, o) } } func testSigner(t *testing.T, signer crypto.Signer, ops ed448.SignerOptions) { msg := make([]byte, 64) _, _ = rand.Read(msg) sig, err := signer.Sign(nil, msg, ops) if err != nil { got := err var want error test.ReportError(t, got, want, ops) } if len(sig) != ed448.SignatureSize { got := len(sig) want := ed448.SignatureSize test.ReportError(t, got, want, ops) } pubSigner, ok := signer.Public().(ed448.PublicKey) if !ok { got := ok want := true test.ReportError(t, got, want, ops) } got := ed448.VerifyAny(pubSigner, msg, sig, ops) want := true if got != want { test.ReportError(t, got, want, ops) } } type badReader struct{} func (badReader) Read([]byte) (n int, err error) { return 0, errors.New("cannot read") } func TestErrors(t *testing.T) { t.Run("badHash", func(t *testing.T) { var msg [16]byte ops := crypto.SHA224 _, priv, _ := ed448.GenerateKey(nil) _, got := priv.Sign(nil, msg[:], ops) want := errors.New("ed448: bad hash algorithm") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) t.Run("badReader", func(t *testing.T) { _, _, got := ed448.GenerateKey(badReader{}) want := errors.New("cannot read") if got.Error() != want.Error() { test.ReportError(t, got, want) } }) t.Run("wrongSeedSize", func(t *testing.T) { var seed [256]byte var want error got := test.CheckPanic(func() { ed448.NewKeyFromSeed(seed[:]) }) if got != want { test.ReportError(t, got, want) } }) t.Run("bigContext", func(t *testing.T) { var msg [16]byte var ctx [256]byte var want error _, priv, _ := ed448.GenerateKey(nil) got := test.CheckPanic(func() { ed448.Sign(priv, msg[:], string(ctx[:])) }) if got != want { test.ReportError(t, got, want) } }) } func BenchmarkKeyGeneration(b *testing.B) { var zero zeroReader for i := 0; i < b.N; i++ { if _, _, err := ed448.GenerateKey(zero); err != nil { b.Fatal(err) } } } func BenchmarkNewKeyFromSeed(b *testing.B) { seed := make([]byte, ed448.SeedSize) b.ReportAllocs() for i := 0; i < b.N; i++ { _ = ed448.NewKeyFromSeed(seed) } } func BenchmarkSigning(b *testing.B) { var zero zeroReader _, priv, err := ed448.GenerateKey(zero) if err != nil { b.Fatal(err) } message := []byte("Hello, world!") ctx := "a context string" b.ReportAllocs() b.ResetTimer() for i := 0; i < b.N; i++ { ed448.Sign(priv, message, ctx) } } func BenchmarkVerification(b *testing.B) { var zero zeroReader pub, priv, err := ed448.GenerateKey(zero) if err != nil { b.Fatal(err) } message := []byte("Hello, world!") ctx := "a context string" signature := ed448.Sign(priv, message, ctx) b.ResetTimer() for i := 0; i < b.N; i++ { ed448.Verify(pub, message, signature, ctx) } } func BenchmarkEd448Ph(b *testing.B) { msg := make([]byte, 128) _, _ = rand.Read(msg) b.Run("Sign", func(b *testing.B) { _, key, _ := ed448.GenerateKey(rand.Reader) ctx := "" b.ResetTimer() for i := 0; i < b.N; i++ { _ = ed448.SignPh(key, msg, ctx) } }) b.Run("Verify", func(b *testing.B) { pub, priv, _ := ed448.GenerateKey(rand.Reader) ctx := "" sig := ed448.SignPh(priv, msg, ctx) b.ResetTimer() for i := 0; i < b.N; i++ { ed448.VerifyPh(pub, msg, sig, ctx) } }) } func Example_ed448() { // import "github.com/cloudflare/circl/sign/ed448" // import "crypto/rand" // Generating Alice's key pair pub, priv, err := ed448.GenerateKey(rand.Reader) if err != nil { panic("error on generating keys") } // Alice signs a message. message := []byte("A message to be signed") ctx := "This is a context string" signature := ed448.Sign(priv, message, ctx) // Anyone can verify the signature using Alice's public key. ok := ed448.Verify(pub, message, signature, ctx) fmt.Println(ok) // Output: true } func ExampleSignPh() { // import "github.com/cloudflare/circl/sign/ed448" // import "crypto/rand" // Generating Alice's key pair pub, priv, err := ed448.GenerateKey(rand.Reader) if err != nil { panic("error on generating keys") } // Alice signs a message. message := []byte("A message to be signed") ctx := "This is a context string" signature := ed448.SignPh(priv, message, ctx) // Anyone can verify the signature using Alice's public key. ok := ed448.VerifyPh(pub, message, signature, ctx) fmt.Println(ok) // Output: true } golang-github-cloudflare-circl-1.3.7/sign/ed448/rfc8032_test.go000066400000000000000000000667661454601126700237610ustar00rootroot00000000000000package ed448_test import ( "bytes" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/sign/ed448" ) type vector struct { name string scheme string sk []byte pk []byte sig []byte msg []byte msgLen uint ph bool ctx []byte ctxLen uint } var vectorsEd448 = [...]vector{ { name: "-----Blank", scheme: "Ed448Pure", sk: []byte{ 0x6c, 0x82, 0xa5, 0x62, 0xcb, 0x80, 0x8d, 0x10, 0xd6, 0x32, 0xbe, 0x89, 0xc8, 0x51, 0x3e, 0xbf, 0x6c, 0x92, 0x9f, 0x34, 0xdd, 0xfa, 0x8c, 0x9f, 0x63, 0xc9, 0x96, 0x0e, 0xf6, 0xe3, 0x48, 0xa3, 0x52, 0x8c, 0x8a, 0x3f, 0xcc, 0x2f, 0x04, 0x4e, 0x39, 0xa3, 0xfc, 0x5b, 0x94, 0x49, 0x2f, 0x8f, 0x03, 0x2e, 0x75, 0x49, 0xa2, 0x00, 0x98, 0xf9, 0x5b, }, pk: []byte{ 0x5f, 0xd7, 0x44, 0x9b, 0x59, 0xb4, 0x61, 0xfd, 0x2c, 0xe7, 0x87, 0xec, 0x61, 0x6a, 0xd4, 0x6a, 0x1d, 0xa1, 0x34, 0x24, 0x85, 0xa7, 0x0e, 0x1f, 0x8a, 0x0e, 0xa7, 0x5d, 0x80, 0xe9, 0x67, 0x78, 0xed, 0xf1, 0x24, 0x76, 0x9b, 0x46, 0xc7, 0x06, 0x1b, 0xd6, 0x78, 0x3d, 0xf1, 0xe5, 0x0f, 0x6c, 0xd1, 0xfa, 0x1a, 0xbe, 0xaf, 0xe8, 0x25, 0x61, 0x80, }, msg: []byte{}, msgLen: 0, ph: false, sig: []byte{ 0x53, 0x3a, 0x37, 0xf6, 0xbb, 0xe4, 0x57, 0x25, 0x1f, 0x02, 0x3c, 0x0d, 0x88, 0xf9, 0x76, 0xae, 0x2d, 0xfb, 0x50, 0x4a, 0x84, 0x3e, 0x34, 0xd2, 0x07, 0x4f, 0xd8, 0x23, 0xd4, 0x1a, 0x59, 0x1f, 0x2b, 0x23, 0x3f, 0x03, 0x4f, 0x62, 0x82, 0x81, 0xf2, 0xfd, 0x7a, 0x22, 0xdd, 0xd4, 0x7d, 0x78, 0x28, 0xc5, 0x9b, 0xd0, 0xa2, 0x1b, 0xfd, 0x39, 0x80, 0xff, 0x0d, 0x20, 0x28, 0xd4, 0xb1, 0x8a, 0x9d, 0xf6, 0x3e, 0x00, 0x6c, 0x5d, 0x1c, 0x2d, 0x34, 0x5b, 0x92, 0x5d, 0x8d, 0xc0, 0x0b, 0x41, 0x04, 0x85, 0x2d, 0xb9, 0x9a, 0xc5, 0xc7, 0xcd, 0xda, 0x85, 0x30, 0xa1, 0x13, 0xa0, 0xf4, 0xdb, 0xb6, 0x11, 0x49, 0xf0, 0x5a, 0x73, 0x63, 0x26, 0x8c, 0x71, 0xd9, 0x58, 0x08, 0xff, 0x2e, 0x65, 0x26, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----1 octet", scheme: "Ed448Pure", sk: []byte{ 0xc4, 0xea, 0xb0, 0x5d, 0x35, 0x70, 0x07, 0xc6, 0x32, 0xf3, 0xdb, 0xb4, 0x84, 0x89, 0x92, 0x4d, 0x55, 0x2b, 0x08, 0xfe, 0x0c, 0x35, 0x3a, 0x0d, 0x4a, 0x1f, 0x00, 0xac, 0xda, 0x2c, 0x46, 0x3a, 0xfb, 0xea, 0x67, 0xc5, 0xe8, 0xd2, 0x87, 0x7c, 0x5e, 0x3b, 0xc3, 0x97, 0xa6, 0x59, 0x94, 0x9e, 0xf8, 0x02, 0x1e, 0x95, 0x4e, 0x0a, 0x12, 0x27, 0x4e, }, pk: []byte{ 0x43, 0xba, 0x28, 0xf4, 0x30, 0xcd, 0xff, 0x45, 0x6a, 0xe5, 0x31, 0x54, 0x5f, 0x7e, 0xcd, 0x0a, 0xc8, 0x34, 0xa5, 0x5d, 0x93, 0x58, 0xc0, 0x37, 0x2b, 0xfa, 0x0c, 0x6c, 0x67, 0x98, 0xc0, 0x86, 0x6a, 0xea, 0x01, 0xeb, 0x00, 0x74, 0x28, 0x02, 0xb8, 0x43, 0x8e, 0xa4, 0xcb, 0x82, 0x16, 0x9c, 0x23, 0x51, 0x60, 0x62, 0x7b, 0x4c, 0x3a, 0x94, 0x80, }, msg: []byte{ 0x03, }, msgLen: 1, ph: false, sig: []byte{ 0x26, 0xb8, 0xf9, 0x17, 0x27, 0xbd, 0x62, 0x89, 0x7a, 0xf1, 0x5e, 0x41, 0xeb, 0x43, 0xc3, 0x77, 0xef, 0xb9, 0xc6, 0x10, 0xd4, 0x8f, 0x23, 0x35, 0xcb, 0x0b, 0xd0, 0x08, 0x78, 0x10, 0xf4, 0x35, 0x25, 0x41, 0xb1, 0x43, 0xc4, 0xb9, 0x81, 0xb7, 0xe1, 0x8f, 0x62, 0xde, 0x8c, 0xcd, 0xf6, 0x33, 0xfc, 0x1b, 0xf0, 0x37, 0xab, 0x7c, 0xd7, 0x79, 0x80, 0x5e, 0x0d, 0xbc, 0xc0, 0xaa, 0xe1, 0xcb, 0xce, 0xe1, 0xaf, 0xb2, 0xe0, 0x27, 0xdf, 0x36, 0xbc, 0x04, 0xdc, 0xec, 0xbf, 0x15, 0x43, 0x36, 0xc1, 0x9f, 0x0a, 0xf7, 0xe0, 0xa6, 0x47, 0x29, 0x05, 0xe7, 0x99, 0xf1, 0x95, 0x3d, 0x2a, 0x0f, 0xf3, 0x34, 0x8a, 0xb2, 0x1a, 0xa4, 0xad, 0xaf, 0xd1, 0xd2, 0x34, 0x44, 0x1c, 0xf8, 0x07, 0xc0, 0x3a, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----1 octet (with context)", scheme: "Ed448Pure", sk: []byte{ 0xc4, 0xea, 0xb0, 0x5d, 0x35, 0x70, 0x07, 0xc6, 0x32, 0xf3, 0xdb, 0xb4, 0x84, 0x89, 0x92, 0x4d, 0x55, 0x2b, 0x08, 0xfe, 0x0c, 0x35, 0x3a, 0x0d, 0x4a, 0x1f, 0x00, 0xac, 0xda, 0x2c, 0x46, 0x3a, 0xfb, 0xea, 0x67, 0xc5, 0xe8, 0xd2, 0x87, 0x7c, 0x5e, 0x3b, 0xc3, 0x97, 0xa6, 0x59, 0x94, 0x9e, 0xf8, 0x02, 0x1e, 0x95, 0x4e, 0x0a, 0x12, 0x27, 0x4e, }, pk: []byte{ 0x43, 0xba, 0x28, 0xf4, 0x30, 0xcd, 0xff, 0x45, 0x6a, 0xe5, 0x31, 0x54, 0x5f, 0x7e, 0xcd, 0x0a, 0xc8, 0x34, 0xa5, 0x5d, 0x93, 0x58, 0xc0, 0x37, 0x2b, 0xfa, 0x0c, 0x6c, 0x67, 0x98, 0xc0, 0x86, 0x6a, 0xea, 0x01, 0xeb, 0x00, 0x74, 0x28, 0x02, 0xb8, 0x43, 0x8e, 0xa4, 0xcb, 0x82, 0x16, 0x9c, 0x23, 0x51, 0x60, 0x62, 0x7b, 0x4c, 0x3a, 0x94, 0x80, }, msg: []byte{ 0x03, }, msgLen: 1, ph: false, sig: []byte{ 0xd4, 0xf8, 0xf6, 0x13, 0x17, 0x70, 0xdd, 0x46, 0xf4, 0x08, 0x67, 0xd6, 0xfd, 0x5d, 0x50, 0x55, 0xde, 0x43, 0x54, 0x1f, 0x8c, 0x5e, 0x35, 0xab, 0xbc, 0xd0, 0x01, 0xb3, 0x2a, 0x89, 0xf7, 0xd2, 0x15, 0x1f, 0x76, 0x47, 0xf1, 0x1d, 0x8c, 0xa2, 0xae, 0x27, 0x9f, 0xb8, 0x42, 0xd6, 0x07, 0x21, 0x7f, 0xce, 0x6e, 0x04, 0x2f, 0x68, 0x15, 0xea, 0x00, 0x0c, 0x85, 0x74, 0x1d, 0xe5, 0xc8, 0xda, 0x11, 0x44, 0xa6, 0xa1, 0xab, 0xa7, 0xf9, 0x6d, 0xe4, 0x25, 0x05, 0xd7, 0xa7, 0x29, 0x85, 0x24, 0xfd, 0xa5, 0x38, 0xfc, 0xcb, 0xbb, 0x75, 0x4f, 0x57, 0x8c, 0x1c, 0xad, 0x10, 0xd5, 0x4d, 0x0d, 0x54, 0x28, 0x40, 0x7e, 0x85, 0xdc, 0xbc, 0x98, 0xa4, 0x91, 0x55, 0xc1, 0x37, 0x64, 0xe6, 0x6c, 0x3c, 0x00, }, ctx: []byte{ 0x66, 0x6f, 0x6f, }, ctxLen: 3, }, { name: "-----11 octets", scheme: "Ed448Pure", sk: []byte{ 0xcd, 0x23, 0xd2, 0x4f, 0x71, 0x42, 0x74, 0xe7, 0x44, 0x34, 0x32, 0x37, 0xb9, 0x32, 0x90, 0xf5, 0x11, 0xf6, 0x42, 0x5f, 0x98, 0xe6, 0x44, 0x59, 0xff, 0x20, 0x3e, 0x89, 0x85, 0x08, 0x3f, 0xfd, 0xf6, 0x05, 0x00, 0x55, 0x3a, 0xbc, 0x0e, 0x05, 0xcd, 0x02, 0x18, 0x4b, 0xdb, 0x89, 0xc4, 0xcc, 0xd6, 0x7e, 0x18, 0x79, 0x51, 0x26, 0x7e, 0xb3, 0x28, }, pk: []byte{ 0xdc, 0xea, 0x9e, 0x78, 0xf3, 0x5a, 0x1b, 0xf3, 0x49, 0x9a, 0x83, 0x1b, 0x10, 0xb8, 0x6c, 0x90, 0xaa, 0xc0, 0x1c, 0xd8, 0x4b, 0x67, 0xa0, 0x10, 0x9b, 0x55, 0xa3, 0x6e, 0x93, 0x28, 0xb1, 0xe3, 0x65, 0xfc, 0xe1, 0x61, 0xd7, 0x1c, 0xe7, 0x13, 0x1a, 0x54, 0x3e, 0xa4, 0xcb, 0x5f, 0x7e, 0x9f, 0x1d, 0x8b, 0x00, 0x69, 0x64, 0x47, 0x00, 0x14, 0x00, }, msg: []byte{ 0x0c, 0x3e, 0x54, 0x40, 0x74, 0xec, 0x63, 0xb0, 0x26, 0x5e, 0x0c, }, msgLen: 11, ph: false, sig: []byte{ 0x1f, 0x0a, 0x88, 0x88, 0xce, 0x25, 0xe8, 0xd4, 0x58, 0xa2, 0x11, 0x30, 0x87, 0x9b, 0x84, 0x0a, 0x90, 0x89, 0xd9, 0x99, 0xaa, 0xba, 0x03, 0x9e, 0xaf, 0x3e, 0x3a, 0xfa, 0x09, 0x0a, 0x09, 0xd3, 0x89, 0xdb, 0xa8, 0x2c, 0x4f, 0xf2, 0xae, 0x8a, 0xc5, 0xcd, 0xfb, 0x7c, 0x55, 0xe9, 0x4d, 0x5d, 0x96, 0x1a, 0x29, 0xfe, 0x01, 0x09, 0x94, 0x1e, 0x00, 0xb8, 0xdb, 0xde, 0xea, 0x6d, 0x3b, 0x05, 0x10, 0x68, 0xdf, 0x72, 0x54, 0xc0, 0xcd, 0xc1, 0x29, 0xcb, 0xe6, 0x2d, 0xb2, 0xdc, 0x95, 0x7d, 0xbb, 0x47, 0xb5, 0x1f, 0xd3, 0xf2, 0x13, 0xfb, 0x86, 0x98, 0xf0, 0x64, 0x77, 0x42, 0x50, 0xa5, 0x02, 0x89, 0x61, 0xc9, 0xbf, 0x8f, 0xfd, 0x97, 0x3f, 0xe5, 0xd5, 0xc2, 0x06, 0x49, 0x2b, 0x14, 0x0e, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----12 octets", scheme: "Ed448Pure", sk: []byte{ 0x25, 0x8c, 0xdd, 0x4a, 0xda, 0x32, 0xed, 0x9c, 0x9f, 0xf5, 0x4e, 0x63, 0x75, 0x6a, 0xe5, 0x82, 0xfb, 0x8f, 0xab, 0x2a, 0xc7, 0x21, 0xf2, 0xc8, 0xe6, 0x76, 0xa7, 0x27, 0x68, 0x51, 0x3d, 0x93, 0x9f, 0x63, 0xdd, 0xdb, 0x55, 0x60, 0x91, 0x33, 0xf2, 0x9a, 0xdf, 0x86, 0xec, 0x99, 0x29, 0xdc, 0xcb, 0x52, 0xc1, 0xc5, 0xfd, 0x2f, 0xf7, 0xe2, 0x1b, }, pk: []byte{ 0x3b, 0xa1, 0x6d, 0xa0, 0xc6, 0xf2, 0xcc, 0x1f, 0x30, 0x18, 0x77, 0x40, 0x75, 0x6f, 0x5e, 0x79, 0x8d, 0x6b, 0xc5, 0xfc, 0x01, 0x5d, 0x7c, 0x63, 0xcc, 0x95, 0x10, 0xee, 0x3f, 0xd4, 0x4a, 0xdc, 0x24, 0xd8, 0xe9, 0x68, 0xb6, 0xe4, 0x6e, 0x6f, 0x94, 0xd1, 0x9b, 0x94, 0x53, 0x61, 0x72, 0x6b, 0xd7, 0x5e, 0x14, 0x9e, 0xf0, 0x98, 0x17, 0xf5, 0x80, }, msg: []byte{ 0x64, 0xa6, 0x5f, 0x3c, 0xde, 0xdc, 0xdd, 0x66, 0x81, 0x1e, 0x29, 0x15, }, msgLen: 12, ph: false, sig: []byte{ 0x7e, 0xee, 0xab, 0x7c, 0x4e, 0x50, 0xfb, 0x79, 0x9b, 0x41, 0x8e, 0xe5, 0xe3, 0x19, 0x7f, 0xf6, 0xbf, 0x15, 0xd4, 0x3a, 0x14, 0xc3, 0x43, 0x89, 0xb5, 0x9d, 0xd1, 0xa7, 0xb1, 0xb8, 0x5b, 0x4a, 0xe9, 0x04, 0x38, 0xac, 0xa6, 0x34, 0xbe, 0xa4, 0x5e, 0x3a, 0x26, 0x95, 0xf1, 0x27, 0x0f, 0x07, 0xfd, 0xcd, 0xf7, 0xc6, 0x2b, 0x8e, 0xfe, 0xaf, 0x00, 0xb4, 0x5c, 0x2c, 0x96, 0xba, 0x45, 0x7e, 0xb1, 0xa8, 0xbf, 0x07, 0x5a, 0x3d, 0xb2, 0x8e, 0x5c, 0x24, 0xf6, 0xb9, 0x23, 0xed, 0x4a, 0xd7, 0x47, 0xc3, 0xc9, 0xe0, 0x3c, 0x70, 0x79, 0xef, 0xb8, 0x7c, 0xb1, 0x10, 0xd3, 0xa9, 0x98, 0x61, 0xe7, 0x20, 0x03, 0xcb, 0xae, 0x6d, 0x6b, 0x8b, 0x82, 0x7e, 0x4e, 0x6c, 0x14, 0x30, 0x64, 0xff, 0x3c, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----13 octets", scheme: "Ed448Pure", sk: []byte{ 0x7e, 0xf4, 0xe8, 0x45, 0x44, 0x23, 0x67, 0x52, 0xfb, 0xb5, 0x6b, 0x8f, 0x31, 0xa2, 0x3a, 0x10, 0xe4, 0x28, 0x14, 0xf5, 0xf5, 0x5c, 0xa0, 0x37, 0xcd, 0xcc, 0x11, 0xc6, 0x4c, 0x9a, 0x3b, 0x29, 0x49, 0xc1, 0xbb, 0x60, 0x70, 0x03, 0x14, 0x61, 0x17, 0x32, 0xa6, 0xc2, 0xfe, 0xa9, 0x8e, 0xeb, 0xc0, 0x26, 0x6a, 0x11, 0xa9, 0x39, 0x70, 0x10, 0x0e, }, pk: []byte{ 0xb3, 0xda, 0x07, 0x9b, 0x0a, 0xa4, 0x93, 0xa5, 0x77, 0x20, 0x29, 0xf0, 0x46, 0x7b, 0xae, 0xbe, 0xe5, 0xa8, 0x11, 0x2d, 0x9d, 0x3a, 0x22, 0x53, 0x23, 0x61, 0xda, 0x29, 0x4f, 0x7b, 0xb3, 0x81, 0x5c, 0x5d, 0xc5, 0x9e, 0x17, 0x6b, 0x4d, 0x9f, 0x38, 0x1c, 0xa0, 0x93, 0x8e, 0x13, 0xc6, 0xc0, 0x7b, 0x17, 0x4b, 0xe6, 0x5d, 0xfa, 0x57, 0x8e, 0x80, }, msg: []byte{ 0x64, 0xa6, 0x5f, 0x3c, 0xde, 0xdc, 0xdd, 0x66, 0x81, 0x1e, 0x29, 0x15, 0xe7, }, msgLen: 13, ph: false, sig: []byte{ 0x6a, 0x12, 0x06, 0x6f, 0x55, 0x33, 0x1b, 0x6c, 0x22, 0xac, 0xd5, 0xd5, 0xbf, 0xc5, 0xd7, 0x12, 0x28, 0xfb, 0xda, 0x80, 0xae, 0x8d, 0xec, 0x26, 0xbd, 0xd3, 0x06, 0x74, 0x3c, 0x50, 0x27, 0xcb, 0x48, 0x90, 0x81, 0x0c, 0x16, 0x2c, 0x02, 0x74, 0x68, 0x67, 0x5e, 0xcf, 0x64, 0x5a, 0x83, 0x17, 0x6c, 0x0d, 0x73, 0x23, 0xa2, 0xcc, 0xde, 0x2d, 0x80, 0xef, 0xe5, 0xa1, 0x26, 0x8e, 0x8a, 0xca, 0x1d, 0x6f, 0xbc, 0x19, 0x4d, 0x3f, 0x77, 0xc4, 0x49, 0x86, 0xeb, 0x4a, 0xb4, 0x17, 0x79, 0x19, 0xad, 0x8b, 0xec, 0x33, 0xeb, 0x47, 0xbb, 0xb5, 0xfc, 0x6e, 0x28, 0x19, 0x6f, 0xd1, 0xca, 0xf5, 0x6b, 0x4e, 0x7e, 0x0b, 0xa5, 0x51, 0x92, 0x34, 0xd0, 0x47, 0x15, 0x5a, 0xc7, 0x27, 0xa1, 0x05, 0x31, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----64 octets", scheme: "Ed448Pure", sk: []byte{ 0xd6, 0x5d, 0xf3, 0x41, 0xad, 0x13, 0xe0, 0x08, 0x56, 0x76, 0x88, 0xba, 0xed, 0xda, 0x8e, 0x9d, 0xcd, 0xc1, 0x7d, 0xc0, 0x24, 0x97, 0x4e, 0xa5, 0xb4, 0x22, 0x7b, 0x65, 0x30, 0xe3, 0x39, 0xbf, 0xf2, 0x1f, 0x99, 0xe6, 0x8c, 0xa6, 0x96, 0x8f, 0x3c, 0xca, 0x6d, 0xfe, 0x0f, 0xb9, 0xf4, 0xfa, 0xb4, 0xfa, 0x13, 0x5d, 0x55, 0x42, 0xea, 0x3f, 0x01, }, pk: []byte{ 0xdf, 0x97, 0x05, 0xf5, 0x8e, 0xdb, 0xab, 0x80, 0x2c, 0x7f, 0x83, 0x63, 0xcf, 0xe5, 0x56, 0x0a, 0xb1, 0xc6, 0x13, 0x2c, 0x20, 0xa9, 0xf1, 0xdd, 0x16, 0x34, 0x83, 0xa2, 0x6f, 0x8a, 0xc5, 0x3a, 0x39, 0xd6, 0x80, 0x8b, 0xf4, 0xa1, 0xdf, 0xbd, 0x26, 0x1b, 0x09, 0x9b, 0xb0, 0x3b, 0x3f, 0xb5, 0x09, 0x06, 0xcb, 0x28, 0xbd, 0x8a, 0x08, 0x1f, 0x00, }, msg: []byte{ 0xbd, 0x0f, 0x6a, 0x37, 0x47, 0xcd, 0x56, 0x1b, 0xdd, 0xdf, 0x46, 0x40, 0xa3, 0x32, 0x46, 0x1a, 0x4a, 0x30, 0xa1, 0x2a, 0x43, 0x4c, 0xd0, 0xbf, 0x40, 0xd7, 0x66, 0xd9, 0xc6, 0xd4, 0x58, 0xe5, 0x51, 0x22, 0x04, 0xa3, 0x0c, 0x17, 0xd1, 0xf5, 0x0b, 0x50, 0x79, 0x63, 0x1f, 0x64, 0xeb, 0x31, 0x12, 0x18, 0x2d, 0xa3, 0x00, 0x58, 0x35, 0x46, 0x11, 0x13, 0x71, 0x8d, 0x1a, 0x5e, 0xf9, 0x44, }, msgLen: 64, ph: false, sig: []byte{ 0x55, 0x4b, 0xc2, 0x48, 0x08, 0x60, 0xb4, 0x9e, 0xab, 0x85, 0x32, 0xd2, 0xa5, 0x33, 0xb7, 0xd5, 0x78, 0xef, 0x47, 0x3e, 0xeb, 0x58, 0xc9, 0x8b, 0xb2, 0xd0, 0xe1, 0xce, 0x48, 0x8a, 0x98, 0xb1, 0x8d, 0xfd, 0xe9, 0xb9, 0xb9, 0x07, 0x75, 0xe6, 0x7f, 0x47, 0xd4, 0xa1, 0xc3, 0x48, 0x20, 0x58, 0xef, 0xc9, 0xf4, 0x0d, 0x2c, 0xa0, 0x33, 0xa0, 0x80, 0x1b, 0x63, 0xd4, 0x5b, 0x3b, 0x72, 0x2e, 0xf5, 0x52, 0xba, 0xd3, 0xb4, 0xcc, 0xb6, 0x67, 0xda, 0x35, 0x01, 0x92, 0xb6, 0x1c, 0x50, 0x8c, 0xf7, 0xb6, 0xb5, 0xad, 0xad, 0xc2, 0xc8, 0xd9, 0xa4, 0x46, 0xef, 0x00, 0x3f, 0xb0, 0x5c, 0xba, 0x5f, 0x30, 0xe8, 0x8e, 0x36, 0xec, 0x27, 0x03, 0xb3, 0x49, 0xca, 0x22, 0x9c, 0x26, 0x70, 0x83, 0x39, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----256 octets", scheme: "Ed448Pure", sk: []byte{ 0x2e, 0xc5, 0xfe, 0x3c, 0x17, 0x04, 0x5a, 0xbd, 0xb1, 0x36, 0xa5, 0xe6, 0xa9, 0x13, 0xe3, 0x2a, 0xb7, 0x5a, 0xe6, 0x8b, 0x53, 0xd2, 0xfc, 0x14, 0x9b, 0x77, 0xe5, 0x04, 0x13, 0x2d, 0x37, 0x56, 0x9b, 0x7e, 0x76, 0x6b, 0xa7, 0x4a, 0x19, 0xbd, 0x61, 0x62, 0x34, 0x3a, 0x21, 0xc8, 0x59, 0x0a, 0xa9, 0xce, 0xbc, 0xa9, 0x01, 0x4c, 0x63, 0x6d, 0xf5, }, pk: []byte{ 0x79, 0x75, 0x6f, 0x01, 0x4d, 0xcf, 0xe2, 0x07, 0x9f, 0x5d, 0xd9, 0xe7, 0x18, 0xbe, 0x41, 0x71, 0xe2, 0xef, 0x24, 0x86, 0xa0, 0x8f, 0x25, 0x18, 0x6f, 0x6b, 0xff, 0x43, 0xa9, 0x93, 0x6b, 0x9b, 0xfe, 0x12, 0x40, 0x2b, 0x08, 0xae, 0x65, 0x79, 0x8a, 0x3d, 0x81, 0xe2, 0x2e, 0x9e, 0xc8, 0x0e, 0x76, 0x90, 0x86, 0x2e, 0xf3, 0xd4, 0xed, 0x3a, 0x00, }, msg: []byte{ 0x15, 0x77, 0x75, 0x32, 0xb0, 0xbd, 0xd0, 0xd1, 0x38, 0x9f, 0x63, 0x6c, 0x5f, 0x6b, 0x9b, 0xa7, 0x34, 0xc9, 0x0a, 0xf5, 0x72, 0x87, 0x7e, 0x2d, 0x27, 0x2d, 0xd0, 0x78, 0xaa, 0x1e, 0x56, 0x7c, 0xfa, 0x80, 0xe1, 0x29, 0x28, 0xbb, 0x54, 0x23, 0x30, 0xe8, 0x40, 0x9f, 0x31, 0x74, 0x50, 0x41, 0x07, 0xec, 0xd5, 0xef, 0xac, 0x61, 0xae, 0x75, 0x04, 0xda, 0xbe, 0x2a, 0x60, 0x2e, 0xde, 0x89, 0xe5, 0xcc, 0xa6, 0x25, 0x7a, 0x7c, 0x77, 0xe2, 0x7a, 0x70, 0x2b, 0x3a, 0xe3, 0x9f, 0xc7, 0x69, 0xfc, 0x54, 0xf2, 0x39, 0x5a, 0xe6, 0xa1, 0x17, 0x8c, 0xab, 0x47, 0x38, 0xe5, 0x43, 0x07, 0x2f, 0xc1, 0xc1, 0x77, 0xfe, 0x71, 0xe9, 0x2e, 0x25, 0xbf, 0x03, 0xe4, 0xec, 0xb7, 0x2f, 0x47, 0xb6, 0x4d, 0x04, 0x65, 0xaa, 0xea, 0x4c, 0x7f, 0xad, 0x37, 0x25, 0x36, 0xc8, 0xba, 0x51, 0x6a, 0x60, 0x39, 0xc3, 0xc2, 0xa3, 0x9f, 0x0e, 0x4d, 0x83, 0x2b, 0xe4, 0x32, 0xdf, 0xa9, 0xa7, 0x06, 0xa6, 0xe5, 0xc7, 0xe1, 0x9f, 0x39, 0x79, 0x64, 0xca, 0x42, 0x58, 0x00, 0x2f, 0x7c, 0x05, 0x41, 0xb5, 0x90, 0x31, 0x6d, 0xbc, 0x56, 0x22, 0xb6, 0xb2, 0xa6, 0xfe, 0x7a, 0x4a, 0xbf, 0xfd, 0x96, 0x10, 0x5e, 0xca, 0x76, 0xea, 0x7b, 0x98, 0x81, 0x6a, 0xf0, 0x74, 0x8c, 0x10, 0xdf, 0x04, 0x8c, 0xe0, 0x12, 0xd9, 0x01, 0x01, 0x5a, 0x51, 0xf1, 0x89, 0xf3, 0x88, 0x81, 0x45, 0xc0, 0x36, 0x50, 0xaa, 0x23, 0xce, 0x89, 0x4c, 0x3b, 0xd8, 0x89, 0xe0, 0x30, 0xd5, 0x65, 0x07, 0x1c, 0x59, 0xf4, 0x09, 0xa9, 0x98, 0x1b, 0x51, 0x87, 0x8f, 0xd6, 0xfc, 0x11, 0x06, 0x24, 0xdc, 0xbc, 0xde, 0x0b, 0xf7, 0xa6, 0x9c, 0xcc, 0xe3, 0x8f, 0xab, 0xdf, 0x86, 0xf3, 0xbe, 0xf6, 0x04, 0x48, 0x19, 0xde, 0x11, }, msgLen: 256, ph: false, sig: []byte{ 0xc6, 0x50, 0xdd, 0xbb, 0x06, 0x01, 0xc1, 0x9c, 0xa1, 0x14, 0x39, 0xe1, 0x64, 0x0d, 0xd9, 0x31, 0xf4, 0x3c, 0x51, 0x8e, 0xa5, 0xbe, 0xa7, 0x0d, 0x3d, 0xcd, 0xe5, 0xf4, 0x19, 0x1f, 0xe5, 0x3f, 0x00, 0xcf, 0x96, 0x65, 0x46, 0xb7, 0x2b, 0xcc, 0x7d, 0x58, 0xbe, 0x2b, 0x9b, 0xad, 0xef, 0x28, 0x74, 0x39, 0x54, 0xe3, 0xa4, 0x4a, 0x23, 0xf8, 0x80, 0xe8, 0xd4, 0xf1, 0xcf, 0xce, 0x2d, 0x7a, 0x61, 0x45, 0x2d, 0x26, 0xda, 0x05, 0x89, 0x6f, 0x0a, 0x50, 0xda, 0x66, 0xa2, 0x39, 0xa8, 0xa1, 0x88, 0xb6, 0xd8, 0x25, 0xb3, 0x30, 0x5a, 0xd7, 0x7b, 0x73, 0xfb, 0xac, 0x08, 0x36, 0xec, 0xc6, 0x09, 0x87, 0xfd, 0x08, 0x52, 0x7c, 0x1a, 0x8e, 0x80, 0xd5, 0x82, 0x3e, 0x65, 0xca, 0xfe, 0x2a, 0x3d, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----1023 octets", scheme: "Ed448Pure", sk: []byte{ 0x87, 0x2d, 0x09, 0x37, 0x80, 0xf5, 0xd3, 0x73, 0x0d, 0xf7, 0xc2, 0x12, 0x66, 0x4b, 0x37, 0xb8, 0xa0, 0xf2, 0x4f, 0x56, 0x81, 0x0d, 0xaa, 0x83, 0x82, 0xcd, 0x4f, 0xa3, 0xf7, 0x76, 0x34, 0xec, 0x44, 0xdc, 0x54, 0xf1, 0xc2, 0xed, 0x9b, 0xea, 0x86, 0xfa, 0xfb, 0x76, 0x32, 0xd8, 0xbe, 0x19, 0x9e, 0xa1, 0x65, 0xf5, 0xad, 0x55, 0xdd, 0x9c, 0xe8, }, pk: []byte{ 0xa8, 0x1b, 0x2e, 0x8a, 0x70, 0xa5, 0xac, 0x94, 0xff, 0xdb, 0xcc, 0x9b, 0xad, 0xfc, 0x3f, 0xeb, 0x08, 0x01, 0xf2, 0x58, 0x57, 0x8b, 0xb1, 0x14, 0xad, 0x44, 0xec, 0xe1, 0xec, 0x0e, 0x79, 0x9d, 0xa0, 0x8e, 0xff, 0xb8, 0x1c, 0x5d, 0x68, 0x5c, 0x0c, 0x56, 0xf6, 0x4e, 0xec, 0xae, 0xf8, 0xcd, 0xf1, 0x1c, 0xc3, 0x87, 0x37, 0x83, 0x8c, 0xf4, 0x00, }, msg: []byte{ 0x6d, 0xdf, 0x80, 0x2e, 0x1a, 0xae, 0x49, 0x86, 0x93, 0x5f, 0x7f, 0x98, 0x1b, 0xa3, 0xf0, 0x35, 0x1d, 0x62, 0x73, 0xc0, 0xa0, 0xc2, 0x2c, 0x9c, 0x0e, 0x83, 0x39, 0x16, 0x8e, 0x67, 0x54, 0x12, 0xa3, 0xde, 0xbf, 0xaf, 0x43, 0x5e, 0xd6, 0x51, 0x55, 0x80, 0x07, 0xdb, 0x43, 0x84, 0xb6, 0x50, 0xfc, 0xc0, 0x7e, 0x3b, 0x58, 0x6a, 0x27, 0xa4, 0xf7, 0xa0, 0x0a, 0xc8, 0xa6, 0xfe, 0xc2, 0xcd, 0x86, 0xae, 0x4b, 0xf1, 0x57, 0x0c, 0x41, 0xe6, 0xa4, 0x0c, 0x93, 0x1d, 0xb2, 0x7b, 0x2f, 0xaa, 0x15, 0xa8, 0xce, 0xdd, 0x52, 0xcf, 0xf7, 0x36, 0x2c, 0x4e, 0x6e, 0x23, 0xda, 0xec, 0x0f, 0xbc, 0x3a, 0x79, 0xb6, 0x80, 0x6e, 0x31, 0x6e, 0xfc, 0xc7, 0xb6, 0x81, 0x19, 0xbf, 0x46, 0xbc, 0x76, 0xa2, 0x60, 0x67, 0xa5, 0x3f, 0x29, 0x6d, 0xaf, 0xdb, 0xdc, 0x11, 0xc7, 0x7f, 0x77, 0x77, 0xe9, 0x72, 0x66, 0x0c, 0xf4, 0xb6, 0xa9, 0xb3, 0x69, 0xa6, 0x66, 0x5f, 0x02, 0xe0, 0xcc, 0x9b, 0x6e, 0xdf, 0xad, 0x13, 0x6b, 0x4f, 0xab, 0xe7, 0x23, 0xd2, 0x81, 0x3d, 0xb3, 0x13, 0x6c, 0xfd, 0xe9, 0xb6, 0xd0, 0x44, 0x32, 0x2f, 0xee, 0x29, 0x47, 0x95, 0x2e, 0x03, 0x1b, 0x73, 0xab, 0x5c, 0x60, 0x33, 0x49, 0xb3, 0x07, 0xbd, 0xc2, 0x7b, 0xc6, 0xcb, 0x8b, 0x8b, 0xbd, 0x7b, 0xd3, 0x23, 0x21, 0x9b, 0x80, 0x33, 0xa5, 0x81, 0xb5, 0x9e, 0xad, 0xeb, 0xb0, 0x9b, 0x3c, 0x4f, 0x3d, 0x22, 0x77, 0xd4, 0xf0, 0x34, 0x36, 0x24, 0xac, 0xc8, 0x17, 0x80, 0x47, 0x28, 0xb2, 0x5a, 0xb7, 0x97, 0x17, 0x2b, 0x4c, 0x5c, 0x21, 0xa2, 0x2f, 0x9c, 0x78, 0x39, 0xd6, 0x43, 0x00, 0x23, 0x2e, 0xb6, 0x6e, 0x53, 0xf3, 0x1c, 0x72, 0x3f, 0xa3, 0x7f, 0xe3, 0x87, 0xc7, 0xd3, 0xe5, 0x0b, 0xdf, 0x98, 0x13, 0xa3, 0x0e, 0x5b, 0xb1, 0x2c, 0xf4, 0xcd, 0x93, 0x0c, 0x40, 0xcf, 0xb4, 0xe1, 0xfc, 0x62, 0x25, 0x92, 0xa4, 0x95, 0x88, 0x79, 0x44, 0x94, 0xd5, 0x6d, 0x24, 0xea, 0x4b, 0x40, 0xc8, 0x9f, 0xc0, 0x59, 0x6c, 0xc9, 0xeb, 0xb9, 0x61, 0xc8, 0xcb, 0x10, 0xad, 0xde, 0x97, 0x6a, 0x5d, 0x60, 0x2b, 0x1c, 0x3f, 0x85, 0xb9, 0xb9, 0xa0, 0x01, 0xed, 0x3c, 0x6a, 0x4d, 0x3b, 0x14, 0x37, 0xf5, 0x20, 0x96, 0xcd, 0x19, 0x56, 0xd0, 0x42, 0xa5, 0x97, 0xd5, 0x61, 0xa5, 0x96, 0xec, 0xd3, 0xd1, 0x73, 0x5a, 0x8d, 0x57, 0x0e, 0xa0, 0xec, 0x27, 0x22, 0x5a, 0x2c, 0x4a, 0xaf, 0xf2, 0x63, 0x06, 0xd1, 0x52, 0x6c, 0x1a, 0xf3, 0xca, 0x6d, 0x9c, 0xf5, 0xa2, 0xc9, 0x8f, 0x47, 0xe1, 0xc4, 0x6d, 0xb9, 0xa3, 0x32, 0x34, 0xcf, 0xd4, 0xd8, 0x1f, 0x2c, 0x98, 0x53, 0x8a, 0x09, 0xeb, 0xe7, 0x69, 0x98, 0xd0, 0xd8, 0xfd, 0x25, 0x99, 0x7c, 0x7d, 0x25, 0x5c, 0x6d, 0x66, 0xec, 0xe6, 0xfa, 0x56, 0xf1, 0x11, 0x44, 0x95, 0x0f, 0x02, 0x77, 0x95, 0xe6, 0x53, 0x00, 0x8f, 0x4b, 0xd7, 0xca, 0x2d, 0xee, 0x85, 0xd8, 0xe9, 0x0f, 0x3d, 0xc3, 0x15, 0x13, 0x0c, 0xe2, 0xa0, 0x03, 0x75, 0xa3, 0x18, 0xc7, 0xc3, 0xd9, 0x7b, 0xe2, 0xc8, 0xce, 0x5b, 0x6d, 0xb4, 0x1a, 0x62, 0x54, 0xff, 0x26, 0x4f, 0xa6, 0x15, 0x5b, 0xae, 0xe3, 0xb0, 0x77, 0x3c, 0x0f, 0x49, 0x7c, 0x57, 0x3f, 0x19, 0xbb, 0x4f, 0x42, 0x40, 0x28, 0x1f, 0x0b, 0x1f, 0x4f, 0x7b, 0xe8, 0x57, 0xa4, 0xe5, 0x9d, 0x41, 0x6c, 0x06, 0xb4, 0xc5, 0x0f, 0xa0, 0x9e, 0x18, 0x10, 0xdd, 0xc6, 0xb1, 0x46, 0x7b, 0xae, 0xac, 0x5a, 0x36, 0x68, 0xd1, 0x1b, 0x6e, 0xca, 0xa9, 0x01, 0x44, 0x00, 0x16, 0xf3, 0x89, 0xf8, 0x0a, 0xcc, 0x4d, 0xb9, 0x77, 0x02, 0x5e, 0x7f, 0x59, 0x24, 0x38, 0x8c, 0x7e, 0x34, 0x0a, 0x73, 0x2e, 0x55, 0x44, 0x40, 0xe7, 0x65, 0x70, 0xf8, 0xdd, 0x71, 0xb7, 0xd6, 0x40, 0xb3, 0x45, 0x0d, 0x1f, 0xd5, 0xf0, 0x41, 0x0a, 0x18, 0xf9, 0xa3, 0x49, 0x4f, 0x70, 0x7c, 0x71, 0x7b, 0x79, 0xb4, 0xbf, 0x75, 0xc9, 0x84, 0x00, 0xb0, 0x96, 0xb2, 0x16, 0x53, 0xb5, 0xd2, 0x17, 0xcf, 0x35, 0x65, 0xc9, 0x59, 0x74, 0x56, 0xf7, 0x07, 0x03, 0x49, 0x7a, 0x07, 0x87, 0x63, 0x82, 0x9b, 0xc0, 0x1b, 0xb1, 0xcb, 0xc8, 0xfa, 0x04, 0xea, 0xdc, 0x9a, 0x6e, 0x3f, 0x66, 0x99, 0x58, 0x7a, 0x9e, 0x75, 0xc9, 0x4e, 0x5b, 0xab, 0x00, 0x36, 0xe0, 0xb2, 0xe7, 0x11, 0x39, 0x2c, 0xff, 0x00, 0x47, 0xd0, 0xd6, 0xb0, 0x5b, 0xd2, 0xa5, 0x88, 0xbc, 0x10, 0x97, 0x18, 0x95, 0x42, 0x59, 0xf1, 0xd8, 0x66, 0x78, 0xa5, 0x79, 0xa3, 0x12, 0x0f, 0x19, 0xcf, 0xb2, 0x96, 0x3f, 0x17, 0x7a, 0xeb, 0x70, 0xf2, 0xd4, 0x84, 0x48, 0x26, 0x26, 0x2e, 0x51, 0xb8, 0x02, 0x71, 0x27, 0x20, 0x68, 0xef, 0x5b, 0x38, 0x56, 0xfa, 0x85, 0x35, 0xaa, 0x2a, 0x88, 0xb2, 0xd4, 0x1f, 0x2a, 0x0e, 0x2f, 0xda, 0x76, 0x24, 0xc2, 0x85, 0x02, 0x72, 0xac, 0x4a, 0x2f, 0x56, 0x1f, 0x8f, 0x2f, 0x7a, 0x31, 0x8b, 0xfd, 0x5c, 0xaf, 0x96, 0x96, 0x14, 0x9e, 0x4a, 0xc8, 0x24, 0xad, 0x34, 0x60, 0x53, 0x8f, 0xdc, 0x25, 0x42, 0x1b, 0xee, 0xc2, 0xcc, 0x68, 0x18, 0x16, 0x2d, 0x06, 0xbb, 0xed, 0x0c, 0x40, 0xa3, 0x87, 0x19, 0x23, 0x49, 0xdb, 0x67, 0xa1, 0x18, 0xba, 0xda, 0x6c, 0xd5, 0xab, 0x01, 0x40, 0xee, 0x27, 0x32, 0x04, 0xf6, 0x28, 0xaa, 0xd1, 0xc1, 0x35, 0xf7, 0x70, 0x27, 0x9a, 0x65, 0x1e, 0x24, 0xd8, 0xc1, 0x4d, 0x75, 0xa6, 0x05, 0x9d, 0x76, 0xb9, 0x6a, 0x6f, 0xd8, 0x57, 0xde, 0xf5, 0xe0, 0xb3, 0x54, 0xb2, 0x7a, 0xb9, 0x37, 0xa5, 0x81, 0x5d, 0x16, 0xb5, 0xfa, 0xe4, 0x07, 0xff, 0x18, 0x22, 0x2c, 0x6d, 0x1e, 0xd2, 0x63, 0xbe, 0x68, 0xc9, 0x5f, 0x32, 0xd9, 0x08, 0xbd, 0x89, 0x5c, 0xd7, 0x62, 0x07, 0xae, 0x72, 0x64, 0x87, 0x56, 0x7f, 0x9a, 0x67, 0xda, 0xd7, 0x9a, 0xbe, 0xc3, 0x16, 0xf6, 0x83, 0xb1, 0x7f, 0x2d, 0x02, 0xbf, 0x07, 0xe0, 0xac, 0x8b, 0x5b, 0xc6, 0x16, 0x2c, 0xf9, 0x46, 0x97, 0xb3, 0xc2, 0x7c, 0xd1, 0xfe, 0xa4, 0x9b, 0x27, 0xf2, 0x3b, 0xa2, 0x90, 0x18, 0x71, 0x96, 0x25, 0x06, 0x52, 0x0c, 0x39, 0x2d, 0xa8, 0xb6, 0xad, 0x0d, 0x99, 0xf7, 0x01, 0x3f, 0xbc, 0x06, 0xc2, 0xc1, 0x7a, 0x56, 0x95, 0x00, 0xc8, 0xa7, 0x69, 0x64, 0x81, 0xc1, 0xcd, 0x33, 0xe9, 0xb1, 0x4e, 0x40, 0xb8, 0x2e, 0x79, 0xa5, 0xf5, 0xdb, 0x82, 0x57, 0x1b, 0xa9, 0x7b, 0xae, 0x3a, 0xd3, 0xe0, 0x47, 0x95, 0x15, 0xbb, 0x0e, 0x2b, 0x0f, 0x3b, 0xfc, 0xd1, 0xfd, 0x33, 0x03, 0x4e, 0xfc, 0x62, 0x45, 0xed, 0xdd, 0x7e, 0xe2, 0x08, 0x6d, 0xda, 0xe2, 0x60, 0x0d, 0x8c, 0xa7, 0x3e, 0x21, 0x4e, 0x8c, 0x2b, 0x0b, 0xdb, 0x2b, 0x04, 0x7c, 0x6a, 0x46, 0x4a, 0x56, 0x2e, 0xd7, 0x7b, 0x73, 0xd2, 0xd8, 0x41, 0xc4, 0xb3, 0x49, 0x73, 0x55, 0x12, 0x57, 0x71, 0x3b, 0x75, 0x36, 0x32, 0xef, 0xba, 0x34, 0x81, 0x69, 0xab, 0xc9, 0x0a, 0x68, 0xf4, 0x26, 0x11, 0xa4, 0x01, 0x26, 0xd7, 0xcb, 0x21, 0xb5, 0x86, 0x95, 0x56, 0x81, 0x86, 0xf7, 0xe5, 0x69, 0xd2, 0xff, 0x0f, 0x9e, 0x74, 0x5d, 0x04, 0x87, 0xdd, 0x2e, 0xb9, 0x97, 0xca, 0xfc, 0x5a, 0xbf, 0x9d, 0xd1, 0x02, 0xe6, 0x2f, 0xf6, 0x6c, 0xba, 0x87, }, msgLen: 1023, ph: false, sig: []byte{ 0xe3, 0x01, 0x34, 0x5a, 0x41, 0xa3, 0x9a, 0x4d, 0x72, 0xff, 0xf8, 0xdf, 0x69, 0xc9, 0x80, 0x75, 0xa0, 0xcc, 0x08, 0x2b, 0x80, 0x2f, 0xc9, 0xb2, 0xb6, 0xbc, 0x50, 0x3f, 0x92, 0x6b, 0x65, 0xbd, 0xdf, 0x7f, 0x4c, 0x8f, 0x1c, 0xb4, 0x9f, 0x63, 0x96, 0xaf, 0xc8, 0xa7, 0x0a, 0xbe, 0x6d, 0x8a, 0xef, 0x0d, 0xb4, 0x78, 0xd4, 0xc6, 0xb2, 0x97, 0x00, 0x76, 0xc6, 0xa0, 0x48, 0x4f, 0xe7, 0x6d, 0x76, 0xb3, 0xa9, 0x76, 0x25, 0xd7, 0x9f, 0x1c, 0xe2, 0x40, 0xe7, 0xc5, 0x76, 0x75, 0x0d, 0x29, 0x55, 0x28, 0x28, 0x6f, 0x71, 0x9b, 0x41, 0x3d, 0xe9, 0xad, 0xa3, 0xe8, 0xeb, 0x78, 0xed, 0x57, 0x36, 0x03, 0xce, 0x30, 0xd8, 0xbb, 0x76, 0x17, 0x85, 0xdc, 0x30, 0xdb, 0xc3, 0x20, 0x86, 0x9e, 0x1a, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----TEST abc", scheme: "Ed448Ph", sk: []byte{ 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, 0xef, 0x78, 0x22, 0xe0, 0xd5, 0x10, 0x41, 0x27, 0xdc, 0x05, 0xd6, 0xdb, 0xef, 0xde, 0x69, 0xe3, 0xab, 0x2c, 0xec, 0x7c, 0x86, 0x7c, 0x6e, 0x2c, 0x49, }, pk: []byte{ 0x25, 0x9b, 0x71, 0xc1, 0x9f, 0x83, 0xef, 0x77, 0xa7, 0xab, 0xd2, 0x65, 0x24, 0xcb, 0xdb, 0x31, 0x61, 0xb5, 0x90, 0xa4, 0x8f, 0x7d, 0x17, 0xde, 0x3e, 0xe0, 0xba, 0x9c, 0x52, 0xbe, 0xb7, 0x43, 0xc0, 0x94, 0x28, 0xa1, 0x31, 0xd6, 0xb1, 0xb5, 0x73, 0x03, 0xd9, 0x0d, 0x81, 0x32, 0xc2, 0x76, 0xd5, 0xed, 0x3d, 0x5d, 0x01, 0xc0, 0xf5, 0x38, 0x80, }, msg: []byte{ 0x61, 0x62, 0x63, }, msgLen: 3, ph: true, sig: []byte{ 0x82, 0x2f, 0x69, 0x01, 0xf7, 0x48, 0x0f, 0x3d, 0x5f, 0x56, 0x2c, 0x59, 0x29, 0x94, 0xd9, 0x69, 0x36, 0x02, 0x87, 0x56, 0x14, 0x48, 0x32, 0x56, 0x50, 0x56, 0x00, 0xbb, 0xc2, 0x81, 0xae, 0x38, 0x1f, 0x54, 0xd6, 0xbc, 0xe2, 0xea, 0x91, 0x15, 0x74, 0x93, 0x2f, 0x52, 0xa4, 0xe6, 0xca, 0xdd, 0x78, 0x76, 0x93, 0x75, 0xec, 0x3f, 0xfd, 0x1b, 0x80, 0x1a, 0x0d, 0x9b, 0x3f, 0x40, 0x30, 0xcd, 0x43, 0x39, 0x64, 0xb6, 0x45, 0x7e, 0xa3, 0x94, 0x76, 0x51, 0x12, 0x14, 0xf9, 0x74, 0x69, 0xb5, 0x7d, 0xd3, 0x2d, 0xbc, 0x56, 0x0a, 0x9a, 0x94, 0xd0, 0x0b, 0xff, 0x07, 0x62, 0x04, 0x64, 0xa3, 0xad, 0x20, 0x3d, 0xf7, 0xdc, 0x7c, 0xe3, 0x60, 0xc3, 0xcd, 0x36, 0x96, 0xd9, 0xd9, 0xfa, 0xb9, 0x0f, 0x00, }, ctx: []byte{}, ctxLen: 0, }, { name: "-----TEST abc (with context)", scheme: "Ed448Ph", sk: []byte{ 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, 0xef, 0x78, 0x22, 0xe0, 0xd5, 0x10, 0x41, 0x27, 0xdc, 0x05, 0xd6, 0xdb, 0xef, 0xde, 0x69, 0xe3, 0xab, 0x2c, 0xec, 0x7c, 0x86, 0x7c, 0x6e, 0x2c, 0x49, }, pk: []byte{ 0x25, 0x9b, 0x71, 0xc1, 0x9f, 0x83, 0xef, 0x77, 0xa7, 0xab, 0xd2, 0x65, 0x24, 0xcb, 0xdb, 0x31, 0x61, 0xb5, 0x90, 0xa4, 0x8f, 0x7d, 0x17, 0xde, 0x3e, 0xe0, 0xba, 0x9c, 0x52, 0xbe, 0xb7, 0x43, 0xc0, 0x94, 0x28, 0xa1, 0x31, 0xd6, 0xb1, 0xb5, 0x73, 0x03, 0xd9, 0x0d, 0x81, 0x32, 0xc2, 0x76, 0xd5, 0xed, 0x3d, 0x5d, 0x01, 0xc0, 0xf5, 0x38, 0x80, }, msg: []byte{ 0x61, 0x62, 0x63, }, msgLen: 3, ph: true, sig: []byte{ 0xc3, 0x22, 0x99, 0xd4, 0x6e, 0xc8, 0xff, 0x02, 0xb5, 0x45, 0x40, 0x98, 0x28, 0x14, 0xdc, 0xe9, 0xa0, 0x58, 0x12, 0xf8, 0x19, 0x62, 0xb6, 0x49, 0xd5, 0x28, 0x09, 0x59, 0x16, 0xa2, 0xaa, 0x48, 0x10, 0x65, 0xb1, 0x58, 0x04, 0x23, 0xef, 0x92, 0x7e, 0xcf, 0x0a, 0xf5, 0x88, 0x8f, 0x90, 0xda, 0x0f, 0x6a, 0x9a, 0x85, 0xad, 0x5d, 0xc3, 0xf2, 0x80, 0xd9, 0x12, 0x24, 0xba, 0x99, 0x11, 0xa3, 0x65, 0x3d, 0x00, 0xe4, 0x84, 0xe2, 0xce, 0x23, 0x25, 0x21, 0x48, 0x1c, 0x86, 0x58, 0xdf, 0x30, 0x4b, 0xb7, 0x74, 0x5a, 0x73, 0x51, 0x4c, 0xdb, 0x9b, 0xf3, 0xe1, 0x57, 0x84, 0xab, 0x71, 0x28, 0x4f, 0x8d, 0x07, 0x04, 0xa6, 0x08, 0xc5, 0x4a, 0x6b, 0x62, 0xd9, 0x7b, 0xeb, 0x51, 0x1d, 0x13, 0x21, 0x00, }, ctx: []byte{ 0x66, 0x6f, 0x6f, }, ctxLen: 3, }, } func (v vector) isPure() bool { return v.scheme == "Ed448Pure" } func (v vector) isPreHashed() bool { return v.scheme == "Ed448Ph" } func (v vector) matchMsgLen() bool { return uint(len(v.msg)) == v.msgLen } func (v vector) matchCtxLen() bool { return uint(len(v.ctx)) == v.ctxLen } func (v vector) testPublicKey(t *testing.T) { keys := ed448.NewKeyFromSeed(v.sk) got := keys.Public().(ed448.PublicKey) want := v.pk if !bytes.Equal(got, want) { test.ReportError(t, got, want, v.name) } } func (v vector) testSign(t *testing.T) { private := ed448.NewKeyFromSeed(v.sk) var got []byte if v.ph { got = ed448.SignPh(private, v.msg, string(v.ctx)) } else { got = ed448.Sign(private, v.msg, string(v.ctx)) } want := v.sig if !bytes.Equal(got, want) { test.ReportError(t, got, want, v.name) } } func (v vector) testVerify(t *testing.T) { var got bool if v.ph { got = ed448.VerifyPh(v.pk, v.msg, v.sig, string(v.ctx)) } else { got = ed448.Verify(v.pk, v.msg, v.sig, string(v.ctx)) } want := true if got != want { test.ReportError(t, got, want, v.name) } } func TestEd448(t *testing.T) { for _, v := range vectorsEd448 { got := (v.isPure() || v.isPreHashed()) && v.matchMsgLen() && v.matchCtxLen() want := true if got != want { test.ReportError(t, got, want, v.sk) } v.testPublicKey(t) v.testSign(t) v.testVerify(t) } } golang-github-cloudflare-circl-1.3.7/sign/ed448/signapi.go000066400000000000000000000040601454601126700232400ustar00rootroot00000000000000package ed448 import ( "crypto/rand" "encoding/asn1" "github.com/cloudflare/circl/sign" ) var sch sign.Scheme = &scheme{} // Scheme returns a signature interface. func Scheme() sign.Scheme { return sch } type scheme struct{} func (*scheme) Name() string { return "Ed448" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SignatureSize() int { return SignatureSize } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) TLSIdentifier() uint { return 0x0808 } func (*scheme) SupportsContext() bool { return true } func (*scheme) Oid() asn1.ObjectIdentifier { return asn1.ObjectIdentifier{1, 3, 101, 113} } func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { return GenerateKey(rand.Reader) } func (*scheme) Sign( sk sign.PrivateKey, message []byte, opts *sign.SignatureOpts, ) []byte { priv, ok := sk.(PrivateKey) if !ok { panic(sign.ErrTypeMismatch) } ctx := "" if opts != nil { ctx = opts.Context } return Sign(priv, message, ctx) } func (*scheme) Verify( pk sign.PublicKey, message, signature []byte, opts *sign.SignatureOpts, ) bool { pub, ok := pk.(PublicKey) if !ok { panic(sign.ErrTypeMismatch) } ctx := "" if opts != nil { ctx = opts.Context } return Verify(pub, message, signature, ctx) } func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { privateKey := NewKeyFromSeed(seed) publicKey := make(PublicKey, PublicKeySize) copy(publicKey, privateKey[SeedSize:]) return publicKey, privateKey } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { if len(buf) < PublicKeySize { return nil, sign.ErrPubKeySize } pub := make(PublicKey, PublicKeySize) copy(pub, buf[:PublicKeySize]) return pub, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { if len(buf) < PrivateKeySize { return nil, sign.ErrPrivKeySize } priv := make(PrivateKey, PrivateKeySize) copy(priv, buf[:PrivateKeySize]) return priv, nil } golang-github-cloudflare-circl-1.3.7/sign/ed448/testdata/000077500000000000000000000000001454601126700230705ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/ed448/testdata/wycheproof_Ed448.json000066400000000000000000001405221454601126700270240ustar00rootroot00000000000000{ "algorithm" : "EDDSA", "generatorVersion" : "0.8r12", "numberOfTests" : 86, "header" : [ "Test vectors of type EddsaVerify are intended for testing", "the verification of Eddsa signatures." ], "notes" : { "SignatureMalleability" : "EdDSA signatures are non-malleable, if implemented accordingly. Failing to check the range of S allows to modify signatures. See RFC 8032, Section 5.2.7 and Section 8.4." }, "schema" : "eddsa_verify_schema.json", "testGroups" : [ { "jwk" : { "crv" : "Ed448", "d" : "iDAeB2UY01N_kwLuD1Ij5LY-HwFgB9PC69_sX3CZfoEZxrrQrnuAP0h5HKjsVJqiobhi96UVkLnV", "kid" : "none", "kty" : "OKP", "x" : "QZYQpTSvEn9YOwSBjNt_D_MAsCXy4BaCvK4z_Wkc7gOVEd8M3caQ7peEJuizjlDOWvfc-6UPcEwA" }, "key" : { "curve" : "edwards448", "keySize" : 448, "pk" : "419610a534af127f583b04818cdb7f0ff300b025f2e01682bcae33fd691cee039511df0cddc690ee978426e8b38e50ce5af7dcfba50f704c00", "sk" : "88301e076518d3537f9302ee0f5223e4b63e1f016007d3c2ebdfec5f70997e8119c6bad0ae7b803f48791ca8ec549aa2a1b862f7a51590b9d5", "type" : "EDDSAKeyPair" }, "keyDer" : "3043300506032b6571033a00419610a534af127f583b04818cdb7f0ff300b025f2e01682bcae33fd691cee039511df0cddc690ee978426e8b38e50ce5af7dcfba50f704c00", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAQZYQpTSvEn9YOwSBjNt/D/MAsCXy4BaCvK4z/Wkc7gOVEd8M3caQ7peEJuizjlDOWvfc+6UPcEwA\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 1, "comment" : "", "msg" : "", "sig" : "cf7953007666e12f73af9ec92e3e018da5ee5a8d5b17f5100a354c58f1d5f4bb37ab835c52f72374c72d612689149cf6d36a70db6dc5a6c400b597348e0e31e51e65bb144e63c892a367b4c055c036aa6cd7e728cdd2a098963bda863903e6dd025b5a5d891209f4e28537694804e50b0800", "result" : "valid", "flags" : [] }, { "tcId" : 2, "comment" : "", "msg" : "78", "sig" : "c56e94d5c9ca860c244f33db556bf6b3cec38b024b77604a35d6a07211b1316b9a027133c374b86f72665cc45ce01583a2e0f2775c6172da801acef168717cab1196cddfb149359dfef589756257cc2d6b02fc516d8d41b4adaa3f11428f41410ef0dc3c1b008d3d052173d4389508ed0100", "result" : "valid", "flags" : [] }, { "tcId" : 3, "comment" : "", "msg" : "54657374", "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f28031d67d699a188a9ca46b4eabe2107aef237ca609cb462e24c91d25d286402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd982600", "result" : "valid", "flags" : [] }, { "tcId" : 4, "comment" : "", "msg" : "48656c6c6f", "sig" : "442e33780f199dd7bc71d1335f74df7f3a0ec789e21a175c1bffddb6e50091998d969ac8194b3acefb7702f6c222f84f7eeca3b80406f1fe80687915e7925bf52deb47b6b779e26d30eec7c5fef03580f280a089eefd0bacc9fbbb6a4d73a591d1671d192e6bbcfdb79ad3db5673a1263000", "result" : "valid", "flags" : [] }, { "tcId" : 5, "comment" : "", "msg" : "313233343030", "sig" : "5db94c53101f521f6c1f43b60ea4d7e06fbd49c2e8afaf4fcc289e645e0880a87b8e55858df4cf2291a7303ffda446b82a117b4dd408cff28060a05236fc9c1682b0e55b60a082c9a57bffe61ef4dda5ce65df539805122b3a09a05976d41ad68ab52df85428152c57da93531e5d16920e00", "result" : "valid", "flags" : [] }, { "tcId" : 6, "comment" : "", "msg" : "000000000000000000000000", "sig" : "a8ca64d1ab00eae77fd2854d8422db3ae12fca91c14f274f30a44df98590786ec4cbb96a9564fc1b9b16c22d2bd00aa65f0876323729f5ac809fb0b89a4d3f27afbabb596851d835173d60ea34e0875359f3d6adb13cef1395b7eaa5f9147583ff38b4deb183062874915bf194ae61072300", "result" : "valid", "flags" : [] }, { "tcId" : 7, "comment" : "", "msg" : "6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161", "sig" : "b205d3e24ccef64c1e86f15f48ddfa682453503489475188b04a8f55860b3c8a9c01e6de820bb7d9b15daff8de25a4a870e987157a115ec1802da0d0606da12842ea7eab658b5eea6dd1f3a641a5174425578003cd318b8d6b8dcb4de954b5078d1912c578ad8281515d6df3672b94173f00", "result" : "valid", "flags" : [] }, { "tcId" : 8, "comment" : "", "msg" : "202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f60", "sig" : "3492ef66e5fdf1503e9e206c5c2f0d4b7891aad793575527d2251e0df1b97c2feac188bc382ce3c92c4bc36ba2695f32bedadd480eaa932300d0db1f9a9c60844d2ea5aea64933c7be46c4f9d21cb48b39eae23d08496de7ce9501197185cc5d4ff8aa4b018ce7ad321f6a7d778c4a070400", "result" : "valid", "flags" : [] }, { "tcId" : 9, "comment" : "", "msg" : "ffffffffffffffffffffffffffffffff", "sig" : "545e1905af1b5886552eaf78e17304c6f83fcfb3444df2d1ea056486db615e3bb29131bb0c1fd295364dc515dae581967148eb23c6c9012e806d3623baff00548c648e3cb3756aaaaf659f2fb7dd2e71c7611448593ca63f2a98913ab7f182e6820eaf1334e2745e0e7bc0dccab98de71600", "result" : "valid", "flags" : [] }, { "tcId" : 10, "comment" : "special values for r and s", "msg" : "3f", "sig" : "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "result" : "invalid", "flags" : [] }, { "tcId" : 11, "comment" : "special values for r and s", "msg" : "3f", "sig" : "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "result" : "invalid", "flags" : [] }, { "tcId" : 12, "comment" : "special values for r and s", "msg" : "3f", "sig" : "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000f24458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result" : "invalid", "flags" : [] }, { "tcId" : 13, "comment" : "special values for r and s", "msg" : "3f", "sig" : "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000f34458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result" : "invalid", "flags" : [] }, { "tcId" : 14, "comment" : "special values for r and s", "msg" : "3f", "sig" : "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff", "result" : "invalid", "flags" : [] }, { "tcId" : 15, "comment" : "special values for r and s", "msg" : "3f", "sig" : "01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "result" : "invalid", "flags" : [] }, { "tcId" : 16, "comment" : "special values for r and s", "msg" : "3f", "sig" : "01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "result" : "invalid", "flags" : [] }, { "tcId" : 17, "comment" : "special values for r and s", "msg" : "3f", "sig" : "0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000f24458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result" : "invalid", "flags" : [] }, { "tcId" : 18, "comment" : "special values for r and s", "msg" : "3f", "sig" : "0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000f34458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result" : "invalid", "flags" : [] }, { "tcId" : 19, "comment" : "special values for r and s", "msg" : "3f", "sig" : "0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff", "result" : "invalid", "flags" : [] }, { "tcId" : 20, "comment" : "special values for r and s", "msg" : "3f", "sig" : "f34458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "result" : "invalid", "flags" : [] }, { "tcId" : 21, "comment" : "special values for r and s", "msg" : "3f", "sig" : "f34458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3f0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "result" : "invalid", "flags" : [] }, { "tcId" : 22, "comment" : "special values for r and s", "msg" : "3f", "sig" : "f34458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3ff24458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", "result" : "invalid", "flags" : [] }, { "tcId" : 23, "comment" : "special values 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: "313233343030", "sig" : "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd11bae33a0999fd3fd2bed6fa5577685e8fd595e79c006e58fd35f69f91b1d853553fb4006019a07725aa37773883dbe12253812887ac828", "result" : "invalid", "flags" : [] }, { "tcId" : 69, "comment" : "all bits flipped in R", "msg" : "313233343030", "sig" : "a246b3acefe0ade093e0bc49f15b281f9042b63d175050b033d7619ba1f77f578471aa7a720b30dd6e58cfc0025bb947d5ee84b22bf7300d7f334e48141af0fade1469f5dedb851c9e725d27bd65012bada05e70cde641aad9ce0bea4983164f73816b6f13095e6b93eb03e850cad0cf0d", "result" : "invalid", "flags" : [] }, { "tcId" : 70, "comment" : "checking malleability ", "msg" : "54657374", "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f280241bd6142ddb02c0f9fa133955d3e610b4b27cb814227de8b241ef4e86402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd9866", "result" : "invalid", "flags" : [ "SignatureMalleability" ] }, { "tcId" : 71, "comment" : "checking malleability ", "msg" : "54657374", "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f28017602ec0bf9d7be34e8ad9c6c795533244e952675efdcbac9c65b9cb85402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd98a6", "result" : "invalid", "flags" : [ "SignatureMalleability" ] }, { "tcId" : 72, "comment" : "checking malleability ", "msg" : "54657374", "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f280fde9de16e5226d2af9a864e2ac1a2d756456ffc4f1b3693570ad4dc584402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd9826", "result" : "invalid", "flags" : [ "SignatureMalleability" ] }, { "tcId" : 73, "comment" : "checking malleability ", "msg" : "54657374", "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f280c9fd3fc42f2d50b84de67a197724e0faa43058801821a546173d76b882402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd9826", "result" : "invalid", "flags" : [ "SignatureMalleability" ] }, { "tcId" : 74, "comment" : "checking malleability ", "msg" : "54657374", "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f28031d67d699a188a9ca46b4eabe2107aef237ca609cb462e24c91d25d286402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd9866", "result" : "invalid", "flags" : [ "SignatureMalleability" ] }, { "tcId" : 75, "comment" : "checking malleability ", "msg" : "54657374", "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f28031d67d699a188a9ca46b4eabe2107aef237ca609cb462e24c91d25d286402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd98a6", "result" : "invalid", 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"554bc2480860b49eab8532d2a533b7d578ef473eeb58c98bb2d0e1ce488a98b18dfde9b9b90775e67f47d4a1c3482058efc9f40d2ca033a0801b63d45b3b722ef552bad3b4ccb667da350192b61c508cf7b6b5adadc2c8d9a446ef003fb05cba5f30e88e36ec2703b349ca229c2670833900", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed448", "d" : "LsX-PBcEWr2xNqXmqRPjKrda5otT0vwUm3flBBMtN1abfnZrp0oZvWFiNDohyFkKqc68qQFMY231", "kid" : "none", "kty" : "OKP", "x" : "eXVvAU3P4gefXdnnGL5BceLvJIagjyUYb2v_Q6mTa5v-EkArCK5leYo9geIunsgOdpCGLvPU7ToA" }, "key" : { "curve" : "edwards448", "keySize" : 448, "pk" : "79756f014dcfe2079f5dd9e718be4171e2ef2486a08f25186f6bff43a9936b9bfe12402b08ae65798a3d81e22e9ec80e7690862ef3d4ed3a00", "sk" : "2ec5fe3c17045abdb136a5e6a913e32ab75ae68b53d2fc149b77e504132d37569b7e766ba74a19bd6162343a21c8590aa9cebca9014c636df5", "type" : "EDDSAKeyPair" }, "keyDer" : "3043300506032b6571033a0079756f014dcfe2079f5dd9e718be4171e2ef2486a08f25186f6bff43a9936b9bfe12402b08ae65798a3d81e22e9ec80e7690862ef3d4ed3a00", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAeXVvAU3P4gefXdnnGL5BceLvJIagjyUYb2v/Q6mTa5v+EkArCK5leYo9geIunsgOdpCGLvPU7ToA\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 85, "comment" : "RFC 8032: 256 bytes", "msg" : "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", "sig" : "c650ddbb0601c19ca11439e1640dd931f43c518ea5bea70d3dcde5f4191fe53f00cf966546b72bcc7d58be2b9badef28743954e3a44a23f880e8d4f1cfce2d7a61452d26da05896f0a50da66a239a8a188b6d825b3305ad77b73fbac0836ecc60987fd08527c1a8e80d5823e65cafe2a3d00", "result" : "valid", "flags" : [] } ] }, { "jwk" : { "crv" : "Ed448", "d" : "hy0JN4D103MN98ISZks3uKDyT1aBDaqDgs1Po_d2NOxE3FTxwu2b6ob6-3Yy2L4ZnqFl9a1V3Zzo", "kid" : "none", "kty" : "OKP", "x" : "qBsuinClrJT_28ybrfw_6wgB8lhXi7EUrUTs4ewOeZ2gjv-4HF1oXAxW9k7srvjN8RzDhzeDjPQA" }, "key" : { "curve" : "edwards448", "keySize" : 448, "pk" : "a81b2e8a70a5ac94ffdbcc9badfc3feb0801f258578bb114ad44ece1ec0e799da08effb81c5d685c0c56f64eecaef8cdf11cc38737838cf400", "sk" : "872d093780f5d3730df7c212664b37b8a0f24f56810daa8382cd4fa3f77634ec44dc54f1c2ed9bea86fafb7632d8be199ea165f5ad55dd9ce8", "type" : "EDDSAKeyPair" }, "keyDer" : "3043300506032b6571033a00a81b2e8a70a5ac94ffdbcc9badfc3feb0801f258578bb114ad44ece1ec0e799da08effb81c5d685c0c56f64eecaef8cdf11cc38737838cf400", "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAqBsuinClrJT/28ybrfw/6wgB8lhXi7EUrUTs4ewOeZ2gjv+4HF1oXAxW9k7srvjN8RzDhzeDjPQA\n-----END PUBLIC KEY-----\n", "type" : "EddsaVerify", "tests" : [ { "tcId" : 86, "comment" : "RFC 8032: 1023 bytes", "msg" : "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", "sig" : "e301345a41a39a4d72fff8df69c98075a0cc082b802fc9b2b6bc503f926b65bddf7f4c8f1cb49f6396afc8a70abe6d8aef0db478d4c6b2970076c6a0484fe76d76b3a97625d79f1ce240e7c576750d295528286f719b413de9ada3e8eb78ed573603ce30d8bb761785dc30dbc320869e1a00", "result" : "valid", "flags" : [] } ] } ] } golang-github-cloudflare-circl-1.3.7/sign/ed448/wycheproof_test.go000066400000000000000000000054111454601126700250330ustar00rootroot00000000000000package ed448_test import ( "bytes" "encoding/hex" "encoding/json" "io" "os" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/sign/ed448" ) type group struct { Key struct { Curve string `json:"curve"` Size int `json:"keySize"` Pk string `json:"pk"` Sk string `json:"sk"` Type string `json:"type"` } `json:"key"` Type string `json:"type"` Tests []struct { TcID int `json:"tcId"` Comment string `json:"comment"` Msg string `json:"msg"` Sig string `json:"sig"` Result string `json:"result"` Flags []string `json:"flags"` } `json:"tests"` } type Wycheproof struct { Alg string `json:"algorithm"` Version string `json:"generatorVersion"` Num int `json:"numberOfTests"` Groups []group `json:"testGroups"` } func (kat *Wycheproof) readFile(t *testing.T, fileName string) { jsonFile, err := os.Open(fileName) if err != nil { t.Fatalf("File %v can not be opened. Error: %v", fileName, err) } defer jsonFile.Close() input, err := io.ReadAll(jsonFile) if err != nil { t.Fatalf("File %v can not be read. Error: %v", fileName, err) } err = json.Unmarshal(input, &kat) if err != nil { t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) } } func (kat *Wycheproof) keyPair(t *testing.T) { for i, g := range kat.Groups { if g.Key.Curve != "edwards448" { t.Errorf("Curve not expected %v", g.Key.Curve) } private, _ := hex.DecodeString(g.Key.Sk) public, _ := hex.DecodeString(g.Key.Pk) keys := ed448.NewKeyFromSeed(private) got := keys.Public().(ed448.PublicKey) want := public if !bytes.Equal(got, want) { test.ReportError(t, got, want, i, g.Key.Sk) } } } func (kat *Wycheproof) verify(t *testing.T) { ctx := []byte{} for i, g := range kat.Groups { for _, gT := range g.Tests { isValid := gT.Result == "valid" private, _ := hex.DecodeString(g.Key.Sk) public, _ := hex.DecodeString(g.Key.Pk) sig, _ := hex.DecodeString(gT.Sig) msg, _ := hex.DecodeString(gT.Msg) priv := ed448.NewKeyFromSeed(private) got := priv.Public().(ed448.PublicKey) want := public if !bytes.Equal(got, want) { test.ReportError(t, got, want, i, gT.TcID) } if isValid { got := ed448.Sign(priv, msg, string(ctx)) want := sig if !bytes.Equal(got, want) { test.ReportError(t, got, want, i, gT.TcID) } } { got := ed448.Verify(priv.Public().(ed448.PublicKey), msg, sig, string(ctx)) want := isValid if got != want { test.ReportError(t, got, want, i, gT.TcID) } } } } } func TestWycheproof(t *testing.T) { // Test vectors from Wycheproof v0.4.12 var kat Wycheproof kat.readFile(t, "testdata/wycheproof_Ed448.json") t.Run("EDDSAKeyPair", kat.keyPair) t.Run("EDDSAVerify", kat.verify) } golang-github-cloudflare-circl-1.3.7/sign/eddilithium2/000077500000000000000000000000001454601126700230125ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/eddilithium2/eddilithium.go000066400000000000000000000150601454601126700256440ustar00rootroot00000000000000// Package eddilithium2 implements the hybrid signature scheme Ed25519-Dilithium2. package eddilithium2 import ( "crypto" cryptoRand "crypto/rand" "errors" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign" "github.com/cloudflare/circl/sign/dilithium/mode2" "github.com/cloudflare/circl/sign/ed25519" ) const ( // SeedSize is the length of the seed for NewKeyFromSeed SeedSize = mode2.SeedSize // = ed25519.SeedSize = 32 // PublicKeySize is the length in bytes of the packed public key. PublicKeySize = mode2.PublicKeySize + ed25519.PublicKeySize // PrivateKeySize is the length in bytes of the packed public key. PrivateKeySize = mode2.PrivateKeySize + ed25519.SeedSize // SignatureSize is the length in bytes of the signatures. SignatureSize = mode2.SignatureSize + ed25519.SignatureSize ) // PublicKey is the type of an EdDilithium2 public key. type PublicKey struct { e ed25519.PublicKey d mode2.PublicKey } // PrivateKey is the type of an EdDilithium2 private key. type PrivateKey struct { e ed25519.PrivateKey d mode2.PrivateKey } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [SeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { var seed1 [32]byte var seed2 [ed25519.SeedSize]byte // Internally, Ed25519 and Dilithium hash the seeds they are passed again // with different hash functions, so it would be safe to use exactly the // same seed for Ed25519 and Dilithium here. However, in general, when // combining any two signature schemes it might not be the case that this // is safe. Setting a bad example here isn't worth the tiny gain in // performance. h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(seed1[:]) _, _ = h.Read(seed2[:]) dpk, dsk := mode2.NewKeyFromSeed(&seed1) esk := ed25519.NewKeyFromSeed(seed2[:]) return &PublicKey{esk.Public().(ed25519.PublicKey), *dpk}, &PrivateKey{esk, *dsk} } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { mode2.SignTo( &sk.d, msg, signature[:mode2.SignatureSize], ) esig := ed25519.Sign( sk.e, msg, ) copy(signature[mode2.SignatureSize:], esig[:]) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { if !mode2.Verify( &pk.d, msg, signature[:mode2.SignatureSize], ) { return false } if !ed25519.Verify( pk.e, msg, signature[mode2.SignatureSize:], ) { return false } return true } // Unpack unpacks pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { var tmp [mode2.PublicKeySize]byte copy(tmp[:], buf[:mode2.PublicKeySize]) pk.d.Unpack(&tmp) pk.e = make([]byte, ed25519.PublicKeySize) copy(pk.e, buf[mode2.PublicKeySize:]) } // Unpack sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { var tmp [mode2.PrivateKeySize]byte copy(tmp[:], buf[:mode2.PrivateKeySize]) sk.d.Unpack(&tmp) sk.e = ed25519.NewKeyFromSeed(buf[mode2.PrivateKeySize:]) } // Pack packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { var tmp [mode2.PublicKeySize]byte pk.d.Pack(&tmp) copy(buf[:mode2.PublicKeySize], tmp[:]) copy(buf[mode2.PublicKeySize:], pk.e) } // Pack packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { var tmp [mode2.PrivateKeySize]byte sk.d.Pack(&tmp) copy(buf[:mode2.PrivateKeySize], tmp[:]) copy(buf[mode2.PrivateKeySize:], sk.e.Seed()) } // Bytes packs the public key. func (pk *PublicKey) Bytes() []byte { return append(pk.d.Bytes(), pk.e...) } // Bytes packs the private key. func (sk *PrivateKey) Bytes() []byte { return append(sk.d.Bytes(), sk.e.Seed()...) } // MarshalBinary packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // MarshalBinary packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // UnmarshalBinary the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of eddilithium2.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // UnmarshalBinary unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of eddilithium2.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } func (sk *PrivateKey) Scheme() sign.Scheme { return sch } func (pk *PublicKey) Scheme() sign.Scheme { return sch } func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return castOther.e.Equal(sk.e) && castOther.d.Equal(&sk.d) } func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return castOther.e.Equal(pk.e) && castOther.d.Equal(&pk.d) } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign( rand io.Reader, msg []byte, opts crypto.SignerOpts, ) (signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("eddilithium2: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Public computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return &PublicKey{ sk.e.Public().(ed25519.PublicKey), *sk.d.Public().(*mode2.PublicKey), } } golang-github-cloudflare-circl-1.3.7/sign/eddilithium2/eddilithium_test.go000066400000000000000000000057771454601126700267210ustar00rootroot00000000000000package eddilithium2_test import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/eddilithium2" ) func BenchmarkVerify(b *testing.B) { // Note that Dilithium precomputes quite a bit during Unpacking/Keygen // instead of at the moment of verification (as compared to the reference // implementation. A fair comparison thus should sum verification // times with unpacking times.) var seed [32]byte var msg [8]byte var sig [eddilithium2.SignatureSize]byte pk, sk := eddilithium2.NewKeyFromSeed(&seed) eddilithium2.SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. eddilithium2.Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that Dilithium precomputes quite a bit during Unpacking/Keygen // instead of at the moment of signing (as compared to the reference // implementation. A fair comparison thus should sum sign times with // unpacking times.) var seed [32]byte var msg [8]byte var sig [eddilithium2.SignatureSize]byte _, sk := eddilithium2.NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) eddilithium2.SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) eddilithium2.NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [32]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := eddilithium2.NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [eddilithium2.SeedSize]byte var sig [eddilithium2.SignatureSize]byte var msg [8]byte var pkb [eddilithium2.PublicKeySize]byte var skb [eddilithium2.PrivateKeySize]byte var pk2 eddilithium2.PublicKey var sk2 eddilithium2.PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := eddilithium2.NewKeyFromSeed(&seed) for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) eddilithium2.SignTo(sk, msg[:], sig[:]) if !eddilithium2.Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb) pk2.Unpack(&pkb) if !pk.Equal(&pk2) { t.Fatal() } sk.Pack(&skb) sk2.Unpack(&skb) if !sk.Equal(&sk2) { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [eddilithium2.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := eddilithium2.NewKeyFromSeed(&seed) pk2 := sk.Public().(*eddilithium2.PublicKey) var pkb1, pkb2 [eddilithium2.PublicKeySize]byte pk.Pack(&pkb1) pk2.Pack(&pkb2) if pkb1 != pkb2 { t.Fatal() } } } golang-github-cloudflare-circl-1.3.7/sign/eddilithium2/example_test.go000066400000000000000000000017141454601126700260360ustar00rootroot00000000000000package eddilithium2_test import ( "fmt" "github.com/cloudflare/circl/sign/eddilithium2" ) func Example() { // Generates a keypair. pk, sk, err := eddilithium2.GenerateKey(nil) if err != nil { panic(err) } // (Alternatively one can derive a keypair from a seed, // see NewKeyFromSeed().) // Packs public and private key var packedSk [eddilithium2.PrivateKeySize]byte var packedPk [eddilithium2.PublicKeySize]byte sk.Pack(&packedSk) pk.Pack(&packedPk) // Load it again var sk2 eddilithium2.PrivateKey var pk2 eddilithium2.PublicKey sk2.Unpack(&packedSk) pk2.Unpack(&packedPk) // Creates a signature on our message with the generated private key. msg := []byte("Some message") var signature [eddilithium2.SignatureSize]byte eddilithium2.SignTo(&sk2, msg, signature[:]) // Checks whether a signature is correct if !eddilithium2.Verify(&pk2, msg, signature[:]) { panic("incorrect signature") } fmt.Printf("O.K.") // Output: // O.K. } golang-github-cloudflare-circl-1.3.7/sign/eddilithium2/signapi.go000066400000000000000000000043031454601126700247730ustar00rootroot00000000000000package eddilithium2 import ( "crypto/rand" "encoding/asn1" "github.com/cloudflare/circl/sign" ) var sch sign.Scheme = &scheme{} // Scheme returns a signature interface. func Scheme() sign.Scheme { return sch } type scheme struct{} func (*scheme) Name() string { return "Ed25519-Dilithium2" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SignatureSize() int { return SignatureSize } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) TLSIdentifier() uint { return 0xfe61 /* temp*/ } func (*scheme) SupportsContext() bool { return false } func (*scheme) Oid() asn1.ObjectIdentifier { return asn1.ObjectIdentifier{1, 3, 6, 1, 4, 1, 44363, 45, 9} } func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { return GenerateKey(rand.Reader) } func (*scheme) Sign( sk sign.PrivateKey, message []byte, opts *sign.SignatureOpts, ) []byte { priv, ok := sk.(*PrivateKey) if !ok { panic(sign.ErrTypeMismatch) } if opts != nil && opts.Context != "" { panic(sign.ErrContextNotSupported) } var sig [SignatureSize]byte SignTo(priv, message, sig[:]) return sig[:] } func (*scheme) Verify( pk sign.PublicKey, message, signature []byte, opts *sign.SignatureOpts, ) bool { pub, ok := pk.(*PublicKey) if !ok { panic(sign.ErrTypeMismatch) } if opts != nil && opts.Context != "" { panic(sign.ErrContextNotSupported) } return Verify(pub, message, signature) } func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { if len(seed) != SeedSize { panic(sign.ErrSeedSize) } var tmp [SeedSize]byte copy(tmp[:], seed) return NewKeyFromSeed(&tmp) } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { if len(buf) != PublicKeySize { return nil, sign.ErrPubKeySize } var tmp [PublicKeySize]byte copy(tmp[:], buf) var ret PublicKey ret.Unpack(&tmp) return &ret, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { if len(buf) != PrivateKeySize { return nil, sign.ErrPrivKeySize } var tmp [PrivateKeySize]byte copy(tmp[:], buf) var ret PrivateKey ret.Unpack(&tmp) return &ret, nil } golang-github-cloudflare-circl-1.3.7/sign/eddilithium3/000077500000000000000000000000001454601126700230135ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/eddilithium3/eddilithium.go000066400000000000000000000142261454601126700256500ustar00rootroot00000000000000// Package eddilithium3 implements the hybrid signature scheme Ed448-Dilithium3. package eddilithium3 import ( "crypto" cryptoRand "crypto/rand" "errors" "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/sign" "github.com/cloudflare/circl/sign/dilithium/mode3" "github.com/cloudflare/circl/sign/ed448" ) const ( // SeedSize is the length of the seed for NewKeyFromSeed SeedSize = ed448.SeedSize // > mode3.SeedSize // PublicKeySize is the length in bytes of the packed public key. PublicKeySize = mode3.PublicKeySize + ed448.PublicKeySize // PrivateKeySize is the length in bytes of the packed public key. PrivateKeySize = mode3.PrivateKeySize + ed448.SeedSize // SignatureSize is the length in bytes of the signatures. SignatureSize = mode3.SignatureSize + ed448.SignatureSize ) // PublicKey is the type of an EdDilithium3 public key. type PublicKey struct { e ed448.PublicKey d mode3.PublicKey } // PrivateKey is the type of an EdDilithium3 private key. type PrivateKey struct { e ed448.PrivateKey d mode3.PrivateKey } // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { var seed [SeedSize]byte if rand == nil { rand = cryptoRand.Reader } _, err := io.ReadFull(rand, seed[:]) if err != nil { return nil, nil, err } pk, sk := NewKeyFromSeed(&seed) return pk, sk, nil } // NewKeyFromSeed derives a public/private key pair using the given seed. func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { var seed1 [32]byte var seed2 [ed448.SeedSize]byte h := sha3.NewShake256() _, _ = h.Write(seed[:]) _, _ = h.Read(seed1[:]) _, _ = h.Read(seed2[:]) dpk, dsk := mode3.NewKeyFromSeed(&seed1) esk := ed448.NewKeyFromSeed(seed2[:]) return &PublicKey{esk.Public().(ed448.PublicKey), *dpk}, &PrivateKey{esk, *dsk} } // SignTo signs the given message and writes the signature into signature. // It will panic if signature is not of length at least SignatureSize. func SignTo(sk *PrivateKey, msg []byte, signature []byte) { mode3.SignTo( &sk.d, msg, signature[:mode3.SignatureSize], ) esig := ed448.Sign( sk.e, msg, "", ) copy(signature[mode3.SignatureSize:], esig[:]) } // Verify checks whether the given signature by pk on msg is valid. func Verify(pk *PublicKey, msg []byte, signature []byte) bool { if !mode3.Verify( &pk.d, msg, signature[:mode3.SignatureSize], ) { return false } if !ed448.Verify( pk.e, msg, signature[mode3.SignatureSize:], "", ) { return false } return true } // Unpack unpacks pk to the public key encoded in buf. func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { var tmp [mode3.PublicKeySize]byte copy(tmp[:], buf[:mode3.PublicKeySize]) pk.d.Unpack(&tmp) pk.e = make([]byte, ed448.PublicKeySize) copy(pk.e, buf[mode3.PublicKeySize:]) } // Unpack sets sk to the private key encoded in buf. func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { var tmp [mode3.PrivateKeySize]byte copy(tmp[:], buf[:mode3.PrivateKeySize]) sk.d.Unpack(&tmp) sk.e = ed448.NewKeyFromSeed(buf[mode3.PrivateKeySize:]) } // Pack packs the public key into buf. func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { var tmp [mode3.PublicKeySize]byte pk.d.Pack(&tmp) copy(buf[:mode3.PublicKeySize], tmp[:]) copy(buf[mode3.PublicKeySize:], pk.e) } // Pack packs the private key into buf. func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { var tmp [mode3.PrivateKeySize]byte sk.d.Pack(&tmp) copy(buf[:mode3.PrivateKeySize], tmp[:]) copy(buf[mode3.PrivateKeySize:], sk.e.Seed()) } // Bytes packs the public key. func (pk *PublicKey) Bytes() []byte { return append(pk.d.Bytes(), pk.e...) } // Bytes packs the private key. func (sk *PrivateKey) Bytes() []byte { return append(sk.d.Bytes(), sk.e.Seed()...) } // MarshalBinary packs the public key. func (pk *PublicKey) MarshalBinary() ([]byte, error) { return pk.Bytes(), nil } // MarshalBinary packs the private key. func (sk *PrivateKey) MarshalBinary() ([]byte, error) { return sk.Bytes(), nil } // UnmarshalBinary the public key from data. func (pk *PublicKey) UnmarshalBinary(data []byte) error { if len(data) != PublicKeySize { return errors.New("packed public key must be of eddilithium4.PublicKeySize bytes") } var buf [PublicKeySize]byte copy(buf[:], data) pk.Unpack(&buf) return nil } // UnmarshalBinary unpacks the private key from data. func (sk *PrivateKey) UnmarshalBinary(data []byte) error { if len(data) != PrivateKeySize { return errors.New("packed private key must be of eddilithium4.PrivateKeySize bytes") } var buf [PrivateKeySize]byte copy(buf[:], data) sk.Unpack(&buf) return nil } func (sk *PrivateKey) Scheme() sign.Scheme { return sch } func (pk *PublicKey) Scheme() sign.Scheme { return sch } func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { castOther, ok := other.(*PrivateKey) if !ok { return false } return castOther.e.Equal(sk.e) && castOther.d.Equal(&sk.d) } func (pk *PublicKey) Equal(other crypto.PublicKey) bool { castOther, ok := other.(*PublicKey) if !ok { return false } return castOther.e.Equal(pk.e) && castOther.d.Equal(&pk.d) } // Sign signs the given message. // // opts.HashFunc() must return zero, which can be achieved by passing // crypto.Hash(0) for opts. rand is ignored. Will only return an error // if opts.HashFunc() is non-zero. // // This function is used to make PrivateKey implement the crypto.Signer // interface. The package-level SignTo function might be more convenient // to use. func (sk *PrivateKey) Sign( rand io.Reader, msg []byte, opts crypto.SignerOpts, ) (signature []byte, err error) { var sig [SignatureSize]byte if opts.HashFunc() != crypto.Hash(0) { return nil, errors.New("eddilithium4: cannot sign hashed message") } SignTo(sk, msg, sig[:]) return sig[:], nil } // Public computes the public key corresponding to this private key. // // Returns a *PublicKey. The type crypto.PublicKey is used to make // PrivateKey implement the crypto.Signer interface. func (sk *PrivateKey) Public() crypto.PublicKey { return &PublicKey{ sk.e.Public().(ed448.PublicKey), *sk.d.Public().(*mode3.PublicKey), } } golang-github-cloudflare-circl-1.3.7/sign/eddilithium3/eddilithium_test.go000066400000000000000000000060571454601126700267120ustar00rootroot00000000000000package eddilithium3_test import ( "encoding/binary" "testing" "github.com/cloudflare/circl/sign/eddilithium3" ) func BenchmarkVerify(b *testing.B) { // Note that Dilithium precomputes quite a bit during Unpacking/Keygen // instead of at the moment of verification (as compared to the reference // implementation. A fair comparison thus should sum verification // times with unpacking times.) var seed [57]byte var msg [8]byte var sig [eddilithium3.SignatureSize]byte pk, sk := eddilithium3.NewKeyFromSeed(&seed) eddilithium3.SignTo(sk, msg[:], sig[:]) b.ResetTimer() for i := 0; i < b.N; i++ { // We should generate a new signature for every verify attempt, // as this influences the time a little bit. This difference, however, // is small and generating a new signature in between creates a lot // pressure on the allocator which makes an accurate measurement hard. eddilithium3.Verify(pk, msg[:], sig[:]) } } func BenchmarkSign(b *testing.B) { // Note that Dilithium precomputes quite a bit during Unpacking/Keygen // instead of at the moment of signing (as compared to the reference // implementation. A fair comparison thus should sum sign times with // unpacking times.) var seed [57]byte var msg [8]byte var sig [eddilithium3.SignatureSize]byte _, sk := eddilithium3.NewKeyFromSeed(&seed) b.ResetTimer() for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(msg[:], uint64(i)) eddilithium3.SignTo(sk, msg[:], sig[:]) } } func BenchmarkGenerateKey(b *testing.B) { var seed [57]byte for i := 0; i < b.N; i++ { binary.LittleEndian.PutUint64(seed[:], uint64(i)) eddilithium3.NewKeyFromSeed(&seed) } } func BenchmarkPublicFromPrivate(b *testing.B) { var seed [57]byte for i := 0; i < b.N; i++ { b.StopTimer() binary.LittleEndian.PutUint64(seed[:], uint64(i)) _, sk := eddilithium3.NewKeyFromSeed(&seed) b.StartTimer() sk.Public() } } func TestSignThenVerifyAndPkSkPacking(t *testing.T) { var seed [eddilithium3.SeedSize]byte var sig [eddilithium3.SignatureSize]byte var msg [8]byte var pkb1, pkb2 [eddilithium3.PublicKeySize]byte var skb1, skb2 [eddilithium3.PrivateKeySize]byte var pk2 eddilithium3.PublicKey var sk2 eddilithium3.PrivateKey for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := eddilithium3.NewKeyFromSeed(&seed) for j := uint64(0); j < 10; j++ { binary.LittleEndian.PutUint64(msg[:], j) eddilithium3.SignTo(sk, msg[:], sig[:]) if !eddilithium3.Verify(pk, msg[:], sig[:]) { t.Fatal() } } pk.Pack(&pkb1) pk2.Unpack(&pkb1) pk2.Pack(&pkb2) if pkb1 != pkb2 { t.Fatal() } sk.Pack(&skb1) sk2.Unpack(&skb1) sk2.Pack(&skb2) if skb1 != skb2 { t.Fatal() } } } func TestPublicFromPrivate(t *testing.T) { var seed [eddilithium3.SeedSize]byte for i := uint64(0); i < 100; i++ { binary.LittleEndian.PutUint64(seed[:], i) pk, sk := eddilithium3.NewKeyFromSeed(&seed) pk2 := sk.Public().(*eddilithium3.PublicKey) var pkb1, pkb2 [eddilithium3.PublicKeySize]byte pk.Pack(&pkb1) pk2.Pack(&pkb2) if pkb1 != pkb2 { t.Fatal() } } } golang-github-cloudflare-circl-1.3.7/sign/eddilithium3/example_test.go000066400000000000000000000017141454601126700260370ustar00rootroot00000000000000package eddilithium3_test import ( "fmt" "github.com/cloudflare/circl/sign/eddilithium3" ) func Example() { // Generates a keypair. pk, sk, err := eddilithium3.GenerateKey(nil) if err != nil { panic(err) } // (Alternatively one can derive a keypair from a seed, // see NewKeyFromSeed().) // Packs public and private key var packedSk [eddilithium3.PrivateKeySize]byte var packedPk [eddilithium3.PublicKeySize]byte sk.Pack(&packedSk) pk.Pack(&packedPk) // Load it again var sk2 eddilithium3.PrivateKey var pk2 eddilithium3.PublicKey sk2.Unpack(&packedSk) pk2.Unpack(&packedPk) // Creates a signature on our message with the generated private key. msg := []byte("Some message") var signature [eddilithium3.SignatureSize]byte eddilithium3.SignTo(&sk2, msg, signature[:]) // Checks whether a signature is correct if !eddilithium3.Verify(&pk2, msg, signature[:]) { panic("incorrect signature") } fmt.Printf("O.K.") // Output: // O.K. } golang-github-cloudflare-circl-1.3.7/sign/eddilithium3/signapi.go000066400000000000000000000043031454601126700247740ustar00rootroot00000000000000package eddilithium3 import ( "crypto/rand" "encoding/asn1" "github.com/cloudflare/circl/sign" ) var sch sign.Scheme = &scheme{} // Scheme returns a signature interface. func Scheme() sign.Scheme { return sch } type scheme struct{} func (*scheme) Name() string { return "Ed448-Dilithium3" } func (*scheme) PublicKeySize() int { return PublicKeySize } func (*scheme) PrivateKeySize() int { return PrivateKeySize } func (*scheme) SignatureSize() int { return SignatureSize } func (*scheme) SeedSize() int { return SeedSize } func (*scheme) TLSIdentifier() uint { return 0xfe62 /* temp */ } func (*scheme) SupportsContext() bool { return false } func (*scheme) Oid() asn1.ObjectIdentifier { return asn1.ObjectIdentifier{1, 3, 6, 1, 4, 1, 44363, 45, 10} } func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { return GenerateKey(rand.Reader) } func (*scheme) Sign( sk sign.PrivateKey, message []byte, opts *sign.SignatureOpts, ) []byte { priv, ok := sk.(*PrivateKey) if !ok { panic(sign.ErrTypeMismatch) } if opts != nil && opts.Context != "" { panic(sign.ErrContextNotSupported) } var sig [SignatureSize]byte SignTo(priv, message, sig[:]) return sig[:] } func (*scheme) Verify( pk sign.PublicKey, message, signature []byte, opts *sign.SignatureOpts, ) bool { pub, ok := pk.(*PublicKey) if !ok { panic(sign.ErrTypeMismatch) } if opts != nil && opts.Context != "" { panic(sign.ErrContextNotSupported) } return Verify(pub, message, signature) } func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { if len(seed) != SeedSize { panic(sign.ErrSeedSize) } var tmp [SeedSize]byte copy(tmp[:], seed) return NewKeyFromSeed(&tmp) } func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { if len(buf) != PublicKeySize { return nil, sign.ErrPubKeySize } var tmp [PublicKeySize]byte copy(tmp[:], buf) var ret PublicKey ret.Unpack(&tmp) return &ret, nil } func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { if len(buf) != PrivateKeySize { return nil, sign.ErrPrivKeySize } var tmp [PrivateKeySize]byte copy(tmp[:], buf) var ret PrivateKey ret.Unpack(&tmp) return &ret, nil } golang-github-cloudflare-circl-1.3.7/sign/schemes/000077500000000000000000000000001454601126700220565ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/sign/schemes/schemes.go000066400000000000000000000020401454601126700240300ustar00rootroot00000000000000// Package schemes contains a register of signature algorithms. // // Implemented schemes: // // Ed25519 // Ed448 // Ed25519-Dilithium2 // Ed448-Dilithium3 package schemes import ( "strings" "github.com/cloudflare/circl/sign" "github.com/cloudflare/circl/sign/ed25519" "github.com/cloudflare/circl/sign/ed448" "github.com/cloudflare/circl/sign/eddilithium2" "github.com/cloudflare/circl/sign/eddilithium3" ) var allSchemes = [...]sign.Scheme{ ed25519.Scheme(), ed448.Scheme(), eddilithium2.Scheme(), eddilithium3.Scheme(), } var allSchemeNames map[string]sign.Scheme func init() { allSchemeNames = make(map[string]sign.Scheme) for _, scheme := range allSchemes { allSchemeNames[strings.ToLower(scheme.Name())] = scheme } } // ByName returns the scheme with the given name and nil if it is not // supported. // // Names are case insensitive. func ByName(name string) sign.Scheme { return allSchemeNames[strings.ToLower(name)] } // All returns all signature schemes supported. func All() []sign.Scheme { a := allSchemes; return a[:] } golang-github-cloudflare-circl-1.3.7/sign/schemes/schemes_test.go000066400000000000000000000060441454601126700250770ustar00rootroot00000000000000package schemes_test import ( "fmt" "testing" "github.com/cloudflare/circl/sign" "github.com/cloudflare/circl/sign/schemes" ) func TestCaseSensitivity(t *testing.T) { if schemes.ByName("ed25519") != schemes.ByName("Ed25519") { t.Fatal() } } func TestApi(t *testing.T) { allSchemes := schemes.All() for _, scheme := range allSchemes { scheme := scheme t.Run(scheme.Name(), func(t *testing.T) { if scheme == nil { t.Fatal() } pk, sk, err := scheme.GenerateKey() if err != nil { t.Fatal() } packedPk, err := pk.MarshalBinary() if err != nil { t.Fatal() } if len(packedPk) != scheme.PublicKeySize() { t.Fatal() } packedSk, err := sk.MarshalBinary() if err != nil { t.Fatal(err) } if len(packedSk) != scheme.PrivateKeySize() { t.Fatal() } pk2, err := scheme.UnmarshalBinaryPublicKey(packedPk) if err != nil { t.Fatal(err) } sk2, err := scheme.UnmarshalBinaryPrivateKey(packedSk) if err != nil { t.Fatal(err) } if !sk.Equal(sk2) { t.Fatal() } if !pk.Equal(pk2) { t.Fatal() } msg := []byte(fmt.Sprintf("Signing with %s", scheme.Name())) opts := &sign.SignatureOpts{} if scheme.SupportsContext() { opts.Context = "A context" } sig := scheme.Sign(sk, msg, opts) if scheme.SignatureSize() != len(sig) { t.Fatal() } if !scheme.Verify(pk2, msg, sig, opts) { t.Fatal() } if scheme.SupportsContext() { opts2 := opts opts2.Context = "Wrong context" if scheme.Verify(pk2, msg, sig, opts2) { t.Fatal() } } sig[0]++ if scheme.Verify(pk2, msg, sig, opts) { t.Fatal() } scheme2 := schemes.ByName(scheme.Name()) if scheme2 == nil || scheme2 != scheme { t.Fatal() } if pk.Scheme() != scheme { t.Fatal() } if sk.Scheme() != scheme { t.Fatal() } }) } } func Example() { for _, sch := range schemes.All() { fmt.Println(sch.Name()) } // Output: // Ed25519 // Ed448 // Ed25519-Dilithium2 // Ed448-Dilithium3 } func BenchmarkGenerateKeyPair(b *testing.B) { allSchemes := schemes.All() for _, scheme := range allSchemes { scheme := scheme b.Run(scheme.Name(), func(b *testing.B) { for i := 0; i < b.N; i++ { _, _, _ = scheme.GenerateKey() } }) } } func BenchmarkSign(b *testing.B) { allSchemes := schemes.All() opts := &sign.SignatureOpts{} for _, scheme := range allSchemes { msg := []byte(fmt.Sprintf("Signing with %s", scheme.Name())) scheme := scheme _, sk, _ := scheme.GenerateKey() b.Run(scheme.Name(), func(b *testing.B) { for i := 0; i < b.N; i++ { _ = scheme.Sign(sk, msg, opts) } }) } } func BenchmarkVerify(b *testing.B) { allSchemes := schemes.All() opts := &sign.SignatureOpts{} for _, scheme := range allSchemes { msg := []byte(fmt.Sprintf("Signing with %s", scheme.Name())) scheme := scheme pk, sk, _ := scheme.GenerateKey() sig := scheme.Sign(sk, msg, opts) b.Run(scheme.Name(), func(b *testing.B) { for i := 0; i < b.N; i++ { _ = scheme.Verify(pk, msg, sig, opts) } }) } } golang-github-cloudflare-circl-1.3.7/sign/sign.go000066400000000000000000000062761454601126700217310ustar00rootroot00000000000000// Package sign provides unified interfaces for signature schemes. // // A register of schemes is available in the package // // github.com/cloudflare/circl/sign/schemes package sign import ( "crypto" "encoding" "errors" ) type SignatureOpts struct { // If non-empty, includes the given context in the signature if supported // and will cause an error during signing otherwise. Context string } // A public key is used to verify a signature set by the corresponding private // key. type PublicKey interface { // Returns the signature scheme for this public key. Scheme() Scheme Equal(crypto.PublicKey) bool encoding.BinaryMarshaler crypto.PublicKey } // A private key allows one to create signatures. type PrivateKey interface { // Returns the signature scheme for this private key. Scheme() Scheme Equal(crypto.PrivateKey) bool // For compatibility with Go standard library crypto.Signer crypto.PrivateKey encoding.BinaryMarshaler } // A Scheme represents a specific instance of a signature scheme. type Scheme interface { // Name of the scheme. Name() string // GenerateKey creates a new key-pair. GenerateKey() (PublicKey, PrivateKey, error) // Creates a signature using the PrivateKey on the given message and // returns the signature. opts are additional options which can be nil. // // Panics if key is nil or wrong type or opts context is not supported. Sign(sk PrivateKey, message []byte, opts *SignatureOpts) []byte // Checks whether the given signature is a valid signature set by // the private key corresponding to the given public key on the // given message. opts are additional options which can be nil. // // Panics if key is nil or wrong type or opts context is not supported. Verify(pk PublicKey, message []byte, signature []byte, opts *SignatureOpts) bool // Deterministically derives a keypair from a seed. If you're unsure, // you're better off using GenerateKey(). // // Panics if seed is not of length SeedSize(). DeriveKey(seed []byte) (PublicKey, PrivateKey) // Unmarshals a PublicKey from the provided buffer. UnmarshalBinaryPublicKey([]byte) (PublicKey, error) // Unmarshals a PublicKey from the provided buffer. UnmarshalBinaryPrivateKey([]byte) (PrivateKey, error) // Size of binary marshalled public keys. PublicKeySize() int // Size of binary marshalled public keys. PrivateKeySize() int // Size of signatures. SignatureSize() int // Size of seeds. SeedSize() int // Returns whether contexts are supported. SupportsContext() bool } var ( // ErrTypeMismatch is the error used if types of, for instance, private // and public keys don't match. ErrTypeMismatch = errors.New("types mismatch") // ErrSeedSize is the error used if the provided seed is of the wrong // size. ErrSeedSize = errors.New("wrong seed size") // ErrPubKeySize is the error used if the provided public key is of // the wrong size. ErrPubKeySize = errors.New("wrong size for public key") // ErrPrivKeySize is the error used if the provided private key is of // the wrong size. ErrPrivKeySize = errors.New("wrong size for private key") // ErrContextNotSupported is the error used if a context is not // supported. ErrContextNotSupported = errors.New("context not supported") ) golang-github-cloudflare-circl-1.3.7/simd/000077500000000000000000000000001454601126700204235ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/simd/doc.go000066400000000000000000000001231454601126700215130ustar00rootroot00000000000000// Package simd provides parallel implementations of some primitives. package simd golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/000077500000000000000000000000001454601126700223215ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/example_test.go000066400000000000000000000051571454601126700253520ustar00rootroot00000000000000package keccakf1600_test import ( "encoding/binary" "fmt" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/simd/keccakf1600" ) func Example() { // As an example, computes the (first 32 bytes of a) SHAKE-256 stream of // four short strings at the same time. msgs := [4][]byte{ []byte("These are some short"), []byte("strings of the same "), []byte("length that fit in a"), []byte("single block. "), } var hashes [4][32]byte // The user could branch to a fast non-SIMD implementation if this function // returns false. if !keccakf1600.IsEnabledX4() { // Compute hashes separately using golang.org/x/crypto/sha3 instead // when a fast four-way implementation is not available. A generic // keccakf1600 implementation is quite a bit slower than using // the non-interleaved hashes because of the need to interleave and // deinterleave the state. for i := 0; i < 4; i++ { h := sha3.NewShake256() _, _ = h.Write(msgs[i]) _, _ = h.Read(hashes[i][:]) } } else { // f1600 acts on 1600 bits arranged as 25 uint64s. Our fourway f1600 // acts on four interleaved states; that is a [100]uint64. (A separate // type is used to ensure that the encapsulated [100]uint64 is aligned // properly to be used efficiently with vector instructions.) var perm keccakf1600.StateX4 state := perm.Initialize(false) // state is initialized with zeroes. As the messages fit within one // block, we only need to write the messages, domain separators // and padding. for i := 0; i < 4; i++ { // The messages. state[i] = binary.LittleEndian.Uint64(msgs[i][:8]) state[4+i] = binary.LittleEndian.Uint64(msgs[i][8:16]) // Final bit of the message together with the SHAKE-256 domain // separator (0b1111) and the start of the padding (0b10....) state[8+i] = uint64(binary.LittleEndian.Uint32(msgs[i][16:])) | (uint64(0x1f) << 32) state[16*4+i] = 0x80 << 56 // end of padding (0b...01) } // Executes the permutation on state. perm.Permute() // As our desired output fits within one block, we can read it without // repeating the permutation. for i := 0; i < 4; i++ { for j := 0; j < 4; j++ { binary.LittleEndian.PutUint64( hashes[i][8*j:8*(j+1)], state[4*j+i], ) } } } fmt.Printf("\n%x\n%x\n%x\n%x\n", hashes[0], hashes[1], hashes[2], hashes[3]) // Output: // 9b48efc4f4e562fe28c510b2ad3966b101ac20066dc88117d85a595cc965f7e4 // 19333d8bb71edce81f0630e4154abea83bf7d2f7e709d62fda878b6e9db9c9c1 // 28f31cc0b8d95185fbba5c4ed5cd94ed7dba0e13c21ca830d1325a212defdfc5 // 51392299d6b10e62b98eb02c9540784046cc9c83e46eddd2ce57cddc2037f917 } golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/f1600x.go000066400000000000000000000121171454601126700235760ustar00rootroot00000000000000// Package keccakf1600 provides a two and four-way Keccak-f[1600] permutation in parallel. // // Keccak-f[1600] is the permutation underlying several algorithms such as // Keccak, SHA3 and SHAKE. Running two or four permutations in parallel is // useful in some scenarios like in hash-based signatures. // // # Limitations // // Note that not all the architectures support SIMD instructions. This package // uses AVX2 instructions that are available in some AMD64 architectures // and NEON instructions that are available in some ARM64 architectures. // // For those systems not supporting these, the package still provides the // expected functionality by means of a generic and slow implementation. // The recommendation is to beforehand verify IsEnabledX4() and IsEnabledX2() // to determine if the current system supports the SIMD implementation. package keccakf1600 import ( "runtime" "unsafe" "github.com/cloudflare/circl/internal/sha3" "golang.org/x/sys/cpu" ) // StateX4 contains state for the four-way permutation including the four // interleaved [25]uint64 buffers. Call Initialize() before use to initialize // and get a pointer to the interleaved buffer. type StateX4 struct { // Go guarantees a to be aligned on 8 bytes, whereas we need it to be // aligned on 32 bytes for bet performance. Thus we leave some headroom // to be able to move the start of the state. // 4 x 25 uint64s for the interleaved states and three uint64s headroom // to fix alignment. a [103]uint64 // Offset into a that is 32 byte aligned. offset int // If true, permute will use 12-round keccak instead of 24-round keccak turbo bool } // StateX2 contains state for the two-way permutation including the two // interleaved [25]uint64 buffers. Call Initialize() before use to initialize // and get a pointer to the interleaved buffer. type StateX2 struct { // Go guarantees a to be aligned on 8 bytes, whereas we need it to be // aligned on 32 bytes for bet performance. Thus we leave some headroom // to be able to move the start of the state. // 2 x 25 uint64s for the interleaved states and three uint64s headroom // to fix alignment. a [53]uint64 // Offset into a that is 32 byte aligned. offset int // If true, permute will use 12-round keccak instead of 24-round keccak turbo bool } // IsEnabledX4 returns true if the architecture supports a four-way SIMD // implementation provided in this package. func IsEnabledX4() bool { return cpu.X86.HasAVX2 } // IsEnabledX2 returns true if the architecture supports a two-way SIMD // implementation provided in this package. func IsEnabledX2() bool { return enabledX2 } // Initialize the state and returns the buffer on which the four permutations // will act: a uint64 slice of length 100. The first permutation will act // on {a[0], a[4], ..., a[96]}, the second on {a[1], a[5], ..., a[97]}, etc. // If turbo is true, applies 12-round variant instead of the usual 24. func (s *StateX4) Initialize(turbo bool) []uint64 { s.turbo = turbo rp := unsafe.Pointer(&s.a[0]) // uint64s are always aligned by a multiple of 8. Compute the remainder // of the address modulo 32 divided by 8. rem := (int(uintptr(rp)&31) >> 3) if rem != 0 { s.offset = 4 - rem } // The slice we return will be aligned on 32 byte boundary. return s.a[s.offset : s.offset+100] } // Initialize the state and returns the buffer on which the two permutations // will act: a uint64 slice of length 50. The first permutation will act // on {a[0], a[2], ..., a[48]} and the second on {a[1], a[3], ..., a[49]}. // If turbo is true, applies 12-round variant instead of the usual 24. func (s *StateX2) Initialize(turbo bool) []uint64 { s.turbo = turbo rp := unsafe.Pointer(&s.a[0]) // uint64s are always aligned by a multiple of 8. Compute the remainder // of the address modulo 32 divided by 8. rem := (int(uintptr(rp)&31) >> 3) if rem != 0 { s.offset = 4 - rem } // The slice we return will be aligned on 32 byte boundary. return s.a[s.offset : s.offset+50] } // Permute performs the four parallel Keccak-f[1600]s interleaved on the slice // returned from Initialize(). func (s *StateX4) Permute() { if IsEnabledX4() { permuteSIMDx4(s.a[s.offset:], s.turbo) } else { permuteScalarX4(s.a[s.offset:], s.turbo) // A slower generic implementation. } } // Permute performs the two parallel Keccak-f[1600]s interleaved on the slice // returned from Initialize(). func (s *StateX2) Permute() { if IsEnabledX2() { permuteSIMDx2(s.a[s.offset:], s.turbo) } else { permuteScalarX2(s.a[s.offset:], s.turbo) // A slower generic implementation. } } func permuteScalarX4(a []uint64, turbo bool) { var buf [25]uint64 for i := 0; i < 4; i++ { for j := 0; j < 25; j++ { buf[j] = a[4*j+i] } sha3.KeccakF1600(&buf, turbo) for j := 0; j < 25; j++ { a[4*j+i] = buf[j] } } } func permuteScalarX2(a []uint64, turbo bool) { var buf [25]uint64 for i := 0; i < 2; i++ { for j := 0; j < 25; j++ { buf[j] = a[2*j+i] } sha3.KeccakF1600(&buf, turbo) for j := 0; j < 25; j++ { a[2*j+i] = buf[j] } } } var enabledX2 bool func init() { enabledX2 = runtime.GOARCH == "arm64" && runtime.GOOS == "darwin" } golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/f1600x2_arm64.go000066400000000000000000000005621454601126700246720ustar00rootroot00000000000000//go:build arm64 && go1.16 // +build arm64,go1.16 package keccakf1600 import "github.com/cloudflare/circl/internal/sha3" func permuteSIMDx2(state []uint64, turbo bool) { f1600x2ARM(&state[0], &sha3.RC, turbo) } func permuteSIMDx4(state []uint64, turbo bool) { permuteScalarX4(state, turbo) } //go:noescape func f1600x2ARM(state *uint64, rc *[24]uint64, turbo bool) golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/f1600x2_arm64.s000066400000000000000000000104451454601126700245300ustar00rootroot00000000000000// +build arm64,go1.16 // Taken from https://github.com/bwesterb/armed-keccak #include "textflag.h" // func f1600x2ARM(state *uint64, rc *[24]uint64, turbo bool) TEXT ·f1600x2ARM(SB), NOSPLIT, $0-17 MOVD state+0(FP), R0 MOVD rc+8(FP), R1 MOVD R0, R2 MOVD $24, R3 VLD1.P 64(R0), [ V0.B16, V1.B16, V2.B16, V3.B16] VLD1.P 64(R0), [ V4.B16, V5.B16, V6.B16, V7.B16] VLD1.P 64(R0), [ V8.B16, V9.B16, V10.B16, V11.B16] VLD1.P 64(R0), [V12.B16, V13.B16, V14.B16, V15.B16] VLD1.P 64(R0), [V16.B16, V17.B16, V18.B16, V19.B16] VLD1.P 64(R0), [V20.B16, V21.B16, V22.B16, V23.B16] VLD1.P (R0), [V24.B16] MOVBU turbo+16(FP), R4 CBZ R4, loop SUB $12, R3, R3 ADD $96, R1, R1 loop: // Execute theta but without xorring into the state yet. VEOR3 V10.B16, V5.B16, V0.B16, V25.B16 VEOR3 V11.B16, V6.B16, V1.B16, V26.B16 VEOR3 V12.B16, V7.B16, V2.B16, V27.B16 VEOR3 V13.B16, V8.B16, V3.B16, V28.B16 VEOR3 V14.B16, V9.B16, V4.B16, V29.B16 VEOR3 V20.B16, V15.B16, V25.B16, V25.B16 VEOR3 V21.B16, V16.B16, V26.B16, V26.B16 VEOR3 V22.B16, V17.B16, V27.B16, V27.B16 VEOR3 V23.B16, V18.B16, V28.B16, V28.B16 VEOR3 V24.B16, V19.B16, V29.B16, V29.B16 // Xor parities from step theta into the state at the same time as // exeuting rho and pi. VRAX1 V26.D2, V29.D2, V30.D2 VRAX1 V29.D2, V27.D2, V29.D2 VRAX1 V27.D2, V25.D2, V27.D2 VRAX1 V25.D2, V28.D2, V25.D2 VRAX1 V28.D2, V26.D2, V28.D2 VEOR V30.B16, V0.B16, V0.B16 VMOV V1.B16, V31.B16 VXAR $20, V27.D2, V6.D2, V1.D2 VXAR $44, V25.D2, V9.D2, V6.D2 VXAR $3 , V28.D2, V22.D2, V9.D2 VXAR $25, V25.D2, V14.D2, V22.D2 VXAR $46, V30.D2, V20.D2, V14.D2 VXAR $2 , V28.D2, V2.D2, V20.D2 VXAR $21, V28.D2, V12.D2, V2.D2 VXAR $39, V29.D2, V13.D2, V12.D2 VXAR $56, V25.D2, V19.D2, V13.D2 VXAR $8 , V29.D2, V23.D2, V19.D2 VXAR $23, V30.D2, V15.D2, V23.D2 VXAR $37, V25.D2, V4.D2, V15.D2 VXAR $50, V25.D2, V24.D2, V4.D2 VXAR $62, V27.D2, V21.D2, V24.D2 VXAR $9 , V29.D2, V8.D2, V21.D2 VXAR $19, V27.D2, V16.D2, V8.D2 VXAR $28, V30.D2, V5.D2, V16.D2 VXAR $36, V29.D2, V3.D2, V5.D2 VXAR $43, V29.D2, V18.D2, V3.D2 VXAR $49, V28.D2, V17.D2, V18.D2 VXAR $54, V27.D2, V11.D2, V17.D2 VXAR $58, V28.D2, V7.D2, V11.D2 VXAR $61, V30.D2, V10.D2, V7.D2 VXAR $63, V27.D2, V31.D2, V10.D2 // Chi VBCAX V1.B16, V2.B16, V0.B16, V25.B16 VBCAX V2.B16, V3.B16, V1.B16, V26.B16 VBCAX V3.B16, V4.B16, V2.B16, V2.B16 VBCAX V4.B16, V0.B16, V3.B16, V3.B16 VBCAX V0.B16, V1.B16, V4.B16, V4.B16 VMOV V25.B16, V0.B16 VMOV V26.B16, V1.B16 VBCAX V6.B16, V7.B16, V5.B16, V25.B16 VBCAX V7.B16, V8.B16, V6.B16, V26.B16 VBCAX V8.B16, V9.B16, V7.B16, V7.B16 VBCAX V9.B16, V5.B16, V8.B16, V8.B16 VBCAX V5.B16, V6.B16, V9.B16, V9.B16 VMOV V25.B16, V5.B16 VMOV V26.B16, V6.B16 VBCAX V11.B16, V12.B16, V10.B16, V25.B16 VBCAX V12.B16, V13.B16, V11.B16, V26.B16 VBCAX V13.B16, V14.B16, V12.B16, V12.B16 VBCAX V14.B16, V10.B16, V13.B16, V13.B16 VBCAX V10.B16, V11.B16, V14.B16, V14.B16 VMOV V25.B16, V10.B16 VMOV V26.B16, V11.B16 VBCAX V16.B16, V17.B16, V15.B16, V25.B16 VBCAX V17.B16, V18.B16, V16.B16, V26.B16 VBCAX V18.B16, V19.B16, V17.B16, V17.B16 VBCAX V19.B16, V15.B16, V18.B16, V18.B16 VBCAX V15.B16, V16.B16, V19.B16, V19.B16 VMOV V25.B16, V15.B16 VMOV V26.B16, V16.B16 VBCAX V21.B16, V22.B16, V20.B16, V25.B16 VBCAX V22.B16, V23.B16, V21.B16, V26.B16 VBCAX V23.B16, V24.B16, V22.B16, V22.B16 VBCAX V24.B16, V20.B16, V23.B16, V23.B16 VBCAX V20.B16, V21.B16, V24.B16, V24.B16 VMOV V25.B16, V20.B16 VMOV V26.B16, V21.B16 // Iota VLD1R.P 8(R1), [V25.D2] VEOR V25.B16, V0.B16, V0.B16 SUBS $1, R3, R3 CBNZ R3, loop MOVD R2, R0 VST1.P [ V0.B16, V1.B16, V2.B16, V3.B16], 64(R0) VST1.P [ V4.B16, V5.B16, V6.B16, V7.B16], 64(R0) VST1.P [ V8.B16, V9.B16, V10.B16, V11.B16], 64(R0) VST1.P [V12.B16, V13.B16, V14.B16, V15.B16], 64(R0) VST1.P [V16.B16, V17.B16, V18.B16, V19.B16], 64(R0) VST1.P [V20.B16, V21.B16, V22.B16, V23.B16], 64(R0) VST1.P [V24.B16], (R0) RET golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/f1600x4_amd64.go000066400000000000000000000003661454601126700246600ustar00rootroot00000000000000package keccakf1600 import "github.com/cloudflare/circl/internal/sha3" func permuteSIMDx4(state []uint64, turbo bool) { f1600x4AVX2(&state[0], &sha3.RC, turbo) } func permuteSIMDx2(state []uint64, turbo bool) { permuteScalarX2(state, turbo) } golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/f1600x4_amd64.s000066400000000000000000000573761454601126700245320ustar00rootroot00000000000000// Code generated by command: go run src.go -out ../../f1600x4_amd64.s -stubs ../../f1600x4stubs_amd64.go -pkg keccakf1600. DO NOT EDIT. //go:build amd64 #include "textflag.h" // func f1600x4AVX2(state *uint64, rc *[24]uint64, turbo bool) // Requires: AVX, AVX2 TEXT ·f1600x4AVX2(SB), NOSPLIT, $0-17 MOVQ state+0(FP), AX MOVQ rc+8(FP), CX MOVQ $0x0000000000000006, DX MOVBQZX turbo+16(FP), BX TESTQ BX, BX JZ loop MOVQ $0x0000000000000003, DX ADDQ $0x60, CX loop: VMOVDQA (AX), Y0 VMOVDQA 32(AX), Y1 VMOVDQA 64(AX), Y2 VMOVDQA 96(AX), Y3 VMOVDQA 128(AX), Y4 VPXOR 160(AX), Y0, Y0 VPXOR 192(AX), Y1, Y1 VPXOR 224(AX), Y2, Y2 VPXOR 256(AX), Y3, Y3 VPXOR 288(AX), Y4, Y4 VPXOR 320(AX), Y0, Y0 VPXOR 352(AX), Y1, Y1 VPXOR 384(AX), Y2, Y2 VPXOR 416(AX), Y3, Y3 VPXOR 448(AX), Y4, Y4 VPXOR 480(AX), Y0, Y0 VPXOR 512(AX), Y1, Y1 VPXOR 544(AX), Y2, Y2 VPXOR 576(AX), Y3, Y3 VPXOR 608(AX), Y4, Y4 VPXOR 640(AX), Y0, Y0 VPXOR 672(AX), Y1, Y1 VPXOR 704(AX), Y2, Y2 VPXOR 736(AX), Y3, Y3 VPXOR 768(AX), Y4, Y4 VPSLLQ $0x01, Y1, Y5 VPSLLQ $0x01, Y2, Y6 VPSLLQ $0x01, Y3, Y7 VPSLLQ $0x01, Y4, Y8 VPSLLQ $0x01, Y0, Y9 VPSRLQ $0x3f, Y1, Y10 VPSRLQ $0x3f, Y2, Y11 VPSRLQ $0x3f, Y3, Y12 VPSRLQ $0x3f, Y4, Y13 VPSRLQ $0x3f, Y0, Y14 VPOR Y5, Y10, Y10 VPOR Y6, Y11, Y11 VPOR Y7, Y12, Y12 VPOR Y8, Y13, Y13 VPOR Y9, Y14, Y14 VPXOR Y10, Y4, Y10 VPXOR Y11, Y0, Y11 VPXOR Y12, Y1, Y12 VPXOR Y13, Y2, Y13 VPXOR Y14, Y3, Y14 VPXOR (AX), Y10, Y0 VPXOR 192(AX), Y11, Y1 VPXOR 384(AX), Y12, Y2 VPXOR 576(AX), Y13, Y3 VPXOR 768(AX), Y14, Y4 VPSLLQ $0x2c, Y1, Y6 VPSLLQ $0x2b, Y2, Y7 VPSLLQ $0x15, Y3, Y8 VPSLLQ $0x0e, Y4, Y9 VPSRLQ $0x14, Y1, Y1 VPSRLQ $0x15, Y2, Y2 VPSRLQ $0x2b, Y3, Y3 VPSRLQ $0x32, Y4, Y4 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VPBROADCASTQ (CX), Y0 VPXOR Y0, Y5, Y5 VMOVDQA Y5, (AX) VMOVDQA Y6, 192(AX) VMOVDQA Y7, 384(AX) VMOVDQA Y8, 576(AX) VMOVDQA Y9, 768(AX) VPXOR 96(AX), Y13, Y0 VPXOR 288(AX), Y14, Y1 VPXOR 320(AX), Y10, Y2 VPXOR 512(AX), Y11, Y3 VPXOR 704(AX), Y12, Y4 VPSLLQ $0x1c, Y0, Y5 VPSLLQ $0x14, Y1, Y6 VPSLLQ $0x03, Y2, Y7 VPSLLQ $0x2d, Y3, Y8 VPSLLQ $0x3d, Y4, Y9 VPSRLQ $0x24, Y0, Y0 VPSRLQ $0x2c, Y1, Y1 VPSRLQ $0x3d, Y2, Y2 VPSRLQ $0x13, Y3, Y3 VPSRLQ $0x03, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 320(AX) VMOVDQA Y6, 512(AX) VMOVDQA Y7, 704(AX) VMOVDQA Y8, 96(AX) VMOVDQA Y9, 288(AX) VPXOR 32(AX), Y11, Y0 VPXOR 224(AX), Y12, Y1 VPXOR 416(AX), Y13, Y2 VPXOR 608(AX), Y14, Y3 VPXOR 640(AX), Y10, Y4 VPSLLQ $0x01, Y0, Y5 VPSLLQ $0x06, Y1, Y6 VPSLLQ $0x19, Y2, Y7 VPSLLQ $0x08, Y3, Y8 VPSLLQ $0x12, Y4, Y9 VPSRLQ $0x3f, Y0, Y0 VPSRLQ $0x3a, Y1, Y1 VPSRLQ $0x27, Y2, Y2 VPSRLQ $0x38, Y3, Y3 VPSRLQ $0x2e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 640(AX) VMOVDQA Y6, 32(AX) VMOVDQA Y7, 224(AX) VMOVDQA Y8, 416(AX) VMOVDQA Y9, 608(AX) VPXOR 128(AX), Y14, Y0 VPXOR 160(AX), Y10, Y1 VPXOR 352(AX), Y11, Y2 VPXOR 544(AX), Y12, Y3 VPXOR 736(AX), Y13, Y4 VPSLLQ $0x1b, Y0, Y5 VPSLLQ $0x24, Y1, Y6 VPSLLQ $0x0a, Y2, Y7 VPSLLQ $0x0f, Y3, Y8 VPSLLQ $0x38, Y4, Y9 VPSRLQ $0x25, Y0, Y0 VPSRLQ $0x1c, Y1, Y1 VPSRLQ $0x36, Y2, Y2 VPSRLQ $0x31, Y3, Y3 VPSRLQ $0x08, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 160(AX) VMOVDQA Y6, 352(AX) VMOVDQA Y7, 544(AX) VMOVDQA Y8, 736(AX) VMOVDQA Y9, 128(AX) VPXOR 64(AX), Y12, Y0 VPXOR 256(AX), Y13, Y1 VPXOR 448(AX), Y14, Y2 VPXOR 480(AX), Y10, Y3 VPXOR 672(AX), Y11, Y4 VPSLLQ $0x3e, Y0, Y5 VPSLLQ $0x37, Y1, Y6 VPSLLQ $0x27, Y2, Y7 VPSLLQ $0x29, Y3, Y8 VPSLLQ $0x02, Y4, Y9 VPSRLQ $0x02, Y0, Y0 VPSRLQ $0x09, Y1, Y1 VPSRLQ $0x19, Y2, Y2 VPSRLQ $0x17, Y3, Y3 VPSRLQ $0x3e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 480(AX) VMOVDQA Y6, 672(AX) VMOVDQA Y7, 64(AX) VMOVDQA Y8, 256(AX) VMOVDQA Y9, 448(AX) VMOVDQA (AX), Y0 VMOVDQA 32(AX), Y1 VMOVDQA 64(AX), Y2 VMOVDQA 96(AX), Y3 VMOVDQA 128(AX), Y4 VPXOR 160(AX), Y0, Y0 VPXOR 192(AX), Y1, Y1 VPXOR 224(AX), Y2, Y2 VPXOR 256(AX), Y3, Y3 VPXOR 288(AX), Y4, Y4 VPXOR 320(AX), Y0, Y0 VPXOR 352(AX), Y1, Y1 VPXOR 384(AX), Y2, Y2 VPXOR 416(AX), Y3, Y3 VPXOR 448(AX), Y4, Y4 VPXOR 480(AX), Y0, Y0 VPXOR 512(AX), Y1, Y1 VPXOR 544(AX), Y2, Y2 VPXOR 576(AX), Y3, Y3 VPXOR 608(AX), Y4, Y4 VPXOR 640(AX), Y0, Y0 VPXOR 672(AX), Y1, Y1 VPXOR 704(AX), Y2, Y2 VPXOR 736(AX), Y3, Y3 VPXOR 768(AX), Y4, Y4 VPSLLQ $0x01, Y1, Y5 VPSLLQ $0x01, Y2, Y6 VPSLLQ $0x01, Y3, Y7 VPSLLQ $0x01, Y4, Y8 VPSLLQ $0x01, Y0, Y9 VPSRLQ $0x3f, Y1, Y10 VPSRLQ $0x3f, Y2, Y11 VPSRLQ $0x3f, Y3, Y12 VPSRLQ $0x3f, Y4, Y13 VPSRLQ $0x3f, Y0, Y14 VPOR Y5, Y10, Y10 VPOR Y6, Y11, Y11 VPOR Y7, Y12, Y12 VPOR Y8, Y13, Y13 VPOR Y9, Y14, Y14 VPXOR Y10, Y4, Y10 VPXOR Y11, Y0, Y11 VPXOR Y12, Y1, Y12 VPXOR Y13, Y2, Y13 VPXOR Y14, Y3, Y14 VPXOR (AX), Y10, Y0 VPXOR 512(AX), Y11, Y1 VPXOR 224(AX), Y12, Y2 VPXOR 736(AX), Y13, Y3 VPXOR 448(AX), Y14, Y4 VPSLLQ $0x2c, Y1, Y6 VPSLLQ $0x2b, Y2, Y7 VPSLLQ $0x15, Y3, Y8 VPSLLQ $0x0e, Y4, Y9 VPSRLQ $0x14, Y1, Y1 VPSRLQ $0x15, Y2, Y2 VPSRLQ $0x2b, Y3, Y3 VPSRLQ $0x32, Y4, Y4 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VPBROADCASTQ 8(CX), Y0 VPXOR Y0, Y5, Y5 VMOVDQA Y5, (AX) VMOVDQA Y6, 512(AX) VMOVDQA Y7, 224(AX) VMOVDQA Y8, 736(AX) VMOVDQA Y9, 448(AX) VPXOR 576(AX), Y13, Y0 VPXOR 288(AX), Y14, Y1 VPXOR 640(AX), Y10, Y2 VPXOR 352(AX), Y11, Y3 VPXOR 64(AX), Y12, Y4 VPSLLQ $0x1c, Y0, Y5 VPSLLQ $0x14, Y1, Y6 VPSLLQ $0x03, Y2, Y7 VPSLLQ $0x2d, Y3, Y8 VPSLLQ $0x3d, Y4, Y9 VPSRLQ $0x24, Y0, Y0 VPSRLQ $0x2c, Y1, Y1 VPSRLQ $0x3d, Y2, Y2 VPSRLQ $0x13, Y3, Y3 VPSRLQ $0x03, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 640(AX) VMOVDQA Y6, 352(AX) VMOVDQA Y7, 64(AX) VMOVDQA Y8, 576(AX) VMOVDQA Y9, 288(AX) VPXOR 192(AX), Y11, Y0 VPXOR 704(AX), Y12, Y1 VPXOR 416(AX), Y13, Y2 VPXOR 128(AX), Y14, Y3 VPXOR 480(AX), Y10, Y4 VPSLLQ $0x01, Y0, Y5 VPSLLQ $0x06, Y1, Y6 VPSLLQ $0x19, Y2, Y7 VPSLLQ $0x08, Y3, Y8 VPSLLQ $0x12, Y4, Y9 VPSRLQ $0x3f, Y0, Y0 VPSRLQ $0x3a, Y1, Y1 VPSRLQ $0x27, Y2, Y2 VPSRLQ $0x38, Y3, Y3 VPSRLQ $0x2e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 480(AX) VMOVDQA Y6, 192(AX) VMOVDQA Y7, 704(AX) VMOVDQA Y8, 416(AX) VMOVDQA Y9, 128(AX) VPXOR 768(AX), Y14, Y0 VPXOR 320(AX), Y10, Y1 VPXOR 32(AX), Y11, Y2 VPXOR 544(AX), Y12, Y3 VPXOR 256(AX), Y13, Y4 VPSLLQ $0x1b, Y0, Y5 VPSLLQ $0x24, Y1, Y6 VPSLLQ $0x0a, Y2, Y7 VPSLLQ $0x0f, Y3, Y8 VPSLLQ $0x38, Y4, Y9 VPSRLQ $0x25, Y0, Y0 VPSRLQ $0x1c, Y1, Y1 VPSRLQ $0x36, Y2, Y2 VPSRLQ $0x31, Y3, Y3 VPSRLQ $0x08, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 320(AX) VMOVDQA Y6, 32(AX) VMOVDQA Y7, 544(AX) VMOVDQA Y8, 256(AX) VMOVDQA Y9, 768(AX) VPXOR 384(AX), Y12, Y0 VPXOR 96(AX), Y13, Y1 VPXOR 608(AX), Y14, Y2 VPXOR 160(AX), Y10, Y3 VPXOR 672(AX), Y11, Y4 VPSLLQ $0x3e, Y0, Y5 VPSLLQ $0x37, Y1, Y6 VPSLLQ $0x27, Y2, Y7 VPSLLQ $0x29, Y3, Y8 VPSLLQ $0x02, Y4, Y9 VPSRLQ $0x02, Y0, Y0 VPSRLQ $0x09, Y1, Y1 VPSRLQ $0x19, Y2, Y2 VPSRLQ $0x17, Y3, Y3 VPSRLQ $0x3e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 160(AX) VMOVDQA Y6, 672(AX) VMOVDQA Y7, 384(AX) VMOVDQA Y8, 96(AX) VMOVDQA Y9, 608(AX) VMOVDQA (AX), Y0 VMOVDQA 32(AX), Y1 VMOVDQA 64(AX), Y2 VMOVDQA 96(AX), Y3 VMOVDQA 128(AX), Y4 VPXOR 160(AX), Y0, Y0 VPXOR 192(AX), Y1, Y1 VPXOR 224(AX), Y2, Y2 VPXOR 256(AX), Y3, Y3 VPXOR 288(AX), Y4, Y4 VPXOR 320(AX), Y0, Y0 VPXOR 352(AX), Y1, Y1 VPXOR 384(AX), Y2, Y2 VPXOR 416(AX), Y3, Y3 VPXOR 448(AX), Y4, Y4 VPXOR 480(AX), Y0, Y0 VPXOR 512(AX), Y1, Y1 VPXOR 544(AX), Y2, Y2 VPXOR 576(AX), Y3, Y3 VPXOR 608(AX), Y4, Y4 VPXOR 640(AX), Y0, Y0 VPXOR 672(AX), Y1, Y1 VPXOR 704(AX), Y2, Y2 VPXOR 736(AX), Y3, Y3 VPXOR 768(AX), Y4, Y4 VPSLLQ $0x01, Y1, Y5 VPSLLQ $0x01, Y2, Y6 VPSLLQ $0x01, Y3, Y7 VPSLLQ $0x01, Y4, Y8 VPSLLQ $0x01, Y0, Y9 VPSRLQ $0x3f, Y1, Y10 VPSRLQ $0x3f, Y2, Y11 VPSRLQ $0x3f, Y3, Y12 VPSRLQ $0x3f, Y4, Y13 VPSRLQ $0x3f, Y0, Y14 VPOR Y5, Y10, Y10 VPOR Y6, Y11, Y11 VPOR Y7, Y12, Y12 VPOR Y8, Y13, Y13 VPOR Y9, Y14, Y14 VPXOR Y10, Y4, Y10 VPXOR Y11, Y0, Y11 VPXOR Y12, Y1, Y12 VPXOR Y13, Y2, Y13 VPXOR Y14, Y3, Y14 VPXOR (AX), Y10, Y0 VPXOR 352(AX), Y11, Y1 VPXOR 704(AX), Y12, Y2 VPXOR 256(AX), Y13, Y3 VPXOR 608(AX), Y14, Y4 VPSLLQ $0x2c, Y1, Y6 VPSLLQ $0x2b, Y2, Y7 VPSLLQ $0x15, Y3, Y8 VPSLLQ $0x0e, Y4, Y9 VPSRLQ $0x14, Y1, Y1 VPSRLQ $0x15, Y2, Y2 VPSRLQ $0x2b, Y3, Y3 VPSRLQ $0x32, Y4, Y4 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VPBROADCASTQ 16(CX), Y0 VPXOR Y0, Y5, Y5 VMOVDQA Y5, (AX) VMOVDQA Y6, 352(AX) VMOVDQA Y7, 704(AX) VMOVDQA Y8, 256(AX) VMOVDQA Y9, 608(AX) VPXOR 736(AX), Y13, Y0 VPXOR 288(AX), Y14, Y1 VPXOR 480(AX), Y10, Y2 VPXOR 32(AX), Y11, Y3 VPXOR 384(AX), Y12, Y4 VPSLLQ $0x1c, Y0, Y5 VPSLLQ $0x14, Y1, Y6 VPSLLQ $0x03, Y2, Y7 VPSLLQ $0x2d, Y3, Y8 VPSLLQ $0x3d, Y4, Y9 VPSRLQ $0x24, Y0, Y0 VPSRLQ $0x2c, Y1, Y1 VPSRLQ $0x3d, Y2, Y2 VPSRLQ $0x13, Y3, Y3 VPSRLQ $0x03, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 480(AX) VMOVDQA Y6, 32(AX) VMOVDQA Y7, 384(AX) VMOVDQA Y8, 736(AX) VMOVDQA Y9, 288(AX) VPXOR 512(AX), Y11, Y0 VPXOR 64(AX), Y12, Y1 VPXOR 416(AX), Y13, Y2 VPXOR 768(AX), Y14, Y3 VPXOR 160(AX), Y10, Y4 VPSLLQ $0x01, Y0, Y5 VPSLLQ $0x06, Y1, Y6 VPSLLQ $0x19, Y2, Y7 VPSLLQ $0x08, Y3, Y8 VPSLLQ $0x12, Y4, Y9 VPSRLQ $0x3f, Y0, Y0 VPSRLQ $0x3a, Y1, Y1 VPSRLQ $0x27, Y2, Y2 VPSRLQ $0x38, Y3, Y3 VPSRLQ $0x2e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 160(AX) VMOVDQA Y6, 512(AX) VMOVDQA Y7, 64(AX) VMOVDQA Y8, 416(AX) VMOVDQA Y9, 768(AX) VPXOR 448(AX), Y14, Y0 VPXOR 640(AX), Y10, Y1 VPXOR 192(AX), Y11, Y2 VPXOR 544(AX), Y12, Y3 VPXOR 96(AX), Y13, Y4 VPSLLQ $0x1b, Y0, Y5 VPSLLQ $0x24, Y1, Y6 VPSLLQ $0x0a, Y2, Y7 VPSLLQ $0x0f, Y3, Y8 VPSLLQ $0x38, Y4, Y9 VPSRLQ $0x25, Y0, Y0 VPSRLQ $0x1c, Y1, Y1 VPSRLQ $0x36, Y2, Y2 VPSRLQ $0x31, Y3, Y3 VPSRLQ $0x08, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 640(AX) VMOVDQA Y6, 192(AX) VMOVDQA Y7, 544(AX) VMOVDQA Y8, 96(AX) VMOVDQA Y9, 448(AX) VPXOR 224(AX), Y12, Y0 VPXOR 576(AX), Y13, Y1 VPXOR 128(AX), Y14, Y2 VPXOR 320(AX), Y10, Y3 VPXOR 672(AX), Y11, Y4 VPSLLQ $0x3e, Y0, Y5 VPSLLQ $0x37, Y1, Y6 VPSLLQ $0x27, Y2, Y7 VPSLLQ $0x29, Y3, Y8 VPSLLQ $0x02, Y4, Y9 VPSRLQ $0x02, Y0, Y0 VPSRLQ $0x09, Y1, Y1 VPSRLQ $0x19, Y2, Y2 VPSRLQ $0x17, Y3, Y3 VPSRLQ $0x3e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 320(AX) VMOVDQA Y6, 672(AX) VMOVDQA Y7, 224(AX) VMOVDQA Y8, 576(AX) VMOVDQA Y9, 128(AX) VMOVDQA (AX), Y0 VMOVDQA 32(AX), Y1 VMOVDQA 64(AX), Y2 VMOVDQA 96(AX), Y3 VMOVDQA 128(AX), Y4 VPXOR 160(AX), Y0, Y0 VPXOR 192(AX), Y1, Y1 VPXOR 224(AX), Y2, Y2 VPXOR 256(AX), Y3, Y3 VPXOR 288(AX), Y4, Y4 VPXOR 320(AX), Y0, Y0 VPXOR 352(AX), Y1, Y1 VPXOR 384(AX), Y2, Y2 VPXOR 416(AX), Y3, Y3 VPXOR 448(AX), Y4, Y4 VPXOR 480(AX), Y0, Y0 VPXOR 512(AX), Y1, Y1 VPXOR 544(AX), Y2, Y2 VPXOR 576(AX), Y3, Y3 VPXOR 608(AX), Y4, Y4 VPXOR 640(AX), Y0, Y0 VPXOR 672(AX), Y1, Y1 VPXOR 704(AX), Y2, Y2 VPXOR 736(AX), Y3, Y3 VPXOR 768(AX), Y4, Y4 VPSLLQ $0x01, Y1, Y5 VPSLLQ $0x01, Y2, Y6 VPSLLQ $0x01, Y3, Y7 VPSLLQ $0x01, Y4, Y8 VPSLLQ $0x01, Y0, Y9 VPSRLQ $0x3f, Y1, Y10 VPSRLQ $0x3f, Y2, Y11 VPSRLQ $0x3f, Y3, Y12 VPSRLQ $0x3f, Y4, Y13 VPSRLQ $0x3f, Y0, Y14 VPOR Y5, Y10, Y10 VPOR Y6, Y11, Y11 VPOR Y7, Y12, Y12 VPOR Y8, Y13, Y13 VPOR Y9, Y14, Y14 VPXOR Y10, Y4, Y10 VPXOR Y11, Y0, Y11 VPXOR Y12, Y1, Y12 VPXOR Y13, Y2, Y13 VPXOR Y14, Y3, Y14 VPXOR (AX), Y10, Y0 VPXOR 32(AX), Y11, Y1 VPXOR 64(AX), Y12, Y2 VPXOR 96(AX), Y13, Y3 VPXOR 128(AX), Y14, Y4 VPSLLQ $0x2c, Y1, Y6 VPSLLQ $0x2b, Y2, Y7 VPSLLQ $0x15, Y3, Y8 VPSLLQ $0x0e, Y4, Y9 VPSRLQ $0x14, Y1, Y1 VPSRLQ $0x15, Y2, Y2 VPSRLQ $0x2b, Y3, Y3 VPSRLQ $0x32, Y4, Y4 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VPBROADCASTQ 24(CX), Y0 VPXOR Y0, Y5, Y5 VMOVDQA Y5, (AX) VMOVDQA Y6, 32(AX) VMOVDQA Y7, 64(AX) VMOVDQA Y8, 96(AX) VMOVDQA Y9, 128(AX) VPXOR 256(AX), Y13, Y0 VPXOR 288(AX), Y14, Y1 VPXOR 160(AX), Y10, Y2 VPXOR 192(AX), Y11, Y3 VPXOR 224(AX), Y12, Y4 VPSLLQ $0x1c, Y0, Y5 VPSLLQ $0x14, Y1, Y6 VPSLLQ $0x03, Y2, Y7 VPSLLQ $0x2d, Y3, Y8 VPSLLQ $0x3d, Y4, Y9 VPSRLQ $0x24, Y0, Y0 VPSRLQ $0x2c, Y1, Y1 VPSRLQ $0x3d, Y2, Y2 VPSRLQ $0x13, Y3, Y3 VPSRLQ $0x03, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 160(AX) VMOVDQA Y6, 192(AX) VMOVDQA Y7, 224(AX) VMOVDQA Y8, 256(AX) VMOVDQA Y9, 288(AX) VPXOR 352(AX), Y11, Y0 VPXOR 384(AX), Y12, Y1 VPXOR 416(AX), Y13, Y2 VPXOR 448(AX), Y14, Y3 VPXOR 320(AX), Y10, Y4 VPSLLQ $0x01, Y0, Y5 VPSLLQ $0x06, Y1, Y6 VPSLLQ $0x19, Y2, Y7 VPSLLQ $0x08, Y3, Y8 VPSLLQ $0x12, Y4, Y9 VPSRLQ $0x3f, Y0, Y0 VPSRLQ $0x3a, Y1, Y1 VPSRLQ $0x27, Y2, Y2 VPSRLQ $0x38, Y3, Y3 VPSRLQ $0x2e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 320(AX) VMOVDQA Y6, 352(AX) VMOVDQA Y7, 384(AX) VMOVDQA Y8, 416(AX) VMOVDQA Y9, 448(AX) VPXOR 608(AX), Y14, Y0 VPXOR 480(AX), Y10, Y1 VPXOR 512(AX), Y11, Y2 VPXOR 544(AX), Y12, Y3 VPXOR 576(AX), Y13, Y4 VPSLLQ $0x1b, Y0, Y5 VPSLLQ $0x24, Y1, Y6 VPSLLQ $0x0a, Y2, Y7 VPSLLQ $0x0f, Y3, Y8 VPSLLQ $0x38, Y4, Y9 VPSRLQ $0x25, Y0, Y0 VPSRLQ $0x1c, Y1, Y1 VPSRLQ $0x36, Y2, Y2 VPSRLQ $0x31, Y3, Y3 VPSRLQ $0x08, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 480(AX) VMOVDQA Y6, 512(AX) VMOVDQA Y7, 544(AX) VMOVDQA Y8, 576(AX) VMOVDQA Y9, 608(AX) VPXOR 704(AX), Y12, Y0 VPXOR 736(AX), Y13, Y1 VPXOR 768(AX), Y14, Y2 VPXOR 640(AX), Y10, Y3 VPXOR 672(AX), Y11, Y4 VPSLLQ $0x3e, Y0, Y5 VPSLLQ $0x37, Y1, Y6 VPSLLQ $0x27, Y2, Y7 VPSLLQ $0x29, Y3, Y8 VPSLLQ $0x02, Y4, Y9 VPSRLQ $0x02, Y0, Y0 VPSRLQ $0x09, Y1, Y1 VPSRLQ $0x19, Y2, Y2 VPSRLQ $0x17, Y3, Y3 VPSRLQ $0x3e, Y4, Y4 VPOR Y5, Y0, Y0 VPOR Y6, Y1, Y1 VPOR Y7, Y2, Y2 VPOR Y8, Y3, Y3 VPOR Y9, Y4, Y4 VPANDN Y2, Y1, Y5 VPANDN Y3, Y2, Y6 VPANDN Y4, Y3, Y7 VPANDN Y0, Y4, Y8 VPANDN Y1, Y0, Y9 VPXOR Y0, Y5, Y5 VPXOR Y1, Y6, Y6 VPXOR Y2, Y7, Y7 VPXOR Y3, Y8, Y8 VPXOR Y4, Y9, Y9 VMOVDQA Y5, 640(AX) VMOVDQA Y6, 672(AX) VMOVDQA Y7, 704(AX) VMOVDQA Y8, 736(AX) VMOVDQA Y9, 768(AX) ADDQ $0x20, CX SUBQ $0x00000001, DX JNZ loop RET golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/f1600x4stubs_amd64.go000066400000000000000000000003731454601126700257370ustar00rootroot00000000000000// Code generated by command: go run src.go -out ../../f1600x4_amd64.s -stubs ../../f1600x4stubs_amd64.go -pkg keccakf1600. DO NOT EDIT. //go:build amd64 package keccakf1600 //go:noescape func f1600x4AVX2(state *uint64, rc *[24]uint64, turbo bool) golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/f1600x_test.go000066400000000000000000000065611454601126700246430ustar00rootroot00000000000000package keccakf1600 import ( "reflect" "testing" ) // From the Keccak code package. var permutationOfZeroes = [25]uint64{ 0xF1258F7940E1DDE7, 0x84D5CCF933C0478A, 0xD598261EA65AA9EE, 0xBD1547306F80494D, 0x8B284E056253D057, 0xFF97A42D7F8E6FD4, 0x90FEE5A0A44647C4, 0x8C5BDA0CD6192E76, 0xAD30A6F71B19059C, 0x30935AB7D08FFC64, 0xEB5AA93F2317D635, 0xA9A6E6260D712103, 0x81A57C16DBCF555F, 0x43B831CD0347C826, 0x01F22F1A11A5569F, 0x05E5635A21D9AE61, 0x64BEFEF28CC970F2, 0x613670957BC46611, 0xB87C5A554FD00ECB, 0x8C3EE88A1CCF32C8, 0x940C7922AE3A2614, 0x1841F924A2C509E4, 0x16F53526E70465C2, 0x75F644E97F30A13B, 0xEAF1FF7B5CECA249, } func TestKeccakF1600x2(t *testing.T) { test := func(t *testing.T, turbo bool, f func(s *StateX2, a []uint64)) { t.Helper() var state StateX2 a := state.Initialize(turbo) f(&state, a) for i := 0; i < 25; i++ { for j := 0; j < 2; j++ { if a[2*i+j] != permutationOfZeroes[i] { t.Fatalf("%X", a) } } } } t.Run("Generic", func(t *testing.T) { test(t, false, func(s *StateX2, a []uint64) { permuteScalarX2(a, false) }) }) t.Run("SIMD", func(t *testing.T) { test(t, false, func(s *StateX2, a []uint64) { s.Permute() }) }) } func TestKeccakF1600x4(t *testing.T) { test := func(t *testing.T, turbo bool, f func(s *StateX4, a []uint64)) { t.Helper() var state StateX4 a := state.Initialize(turbo) f(&state, a) for i := 0; i < 25; i++ { for j := 0; j < 4; j++ { if a[4*i+j] != permutationOfZeroes[i] { t.Fatal() } } } } t.Run("Generic", func(t *testing.T) { test(t, false, func(s *StateX4, a []uint64) { permuteScalarX4(a, false) }) }) t.Run("SIMD", func(t *testing.T) { test(t, false, func(s *StateX4, a []uint64) { s.Permute() }) }) } func TestTurboX2(t *testing.T) { var state1, state2 StateX2 a1 := state1.Initialize(true) a2 := state2.Initialize(true) permuteScalarX2(a1, true) state2.Permute() if !reflect.DeepEqual(a1, a2) { t.Fatal() } } func TestTurboX4(t *testing.T) { var state1, state2 StateX4 a1 := state1.Initialize(true) a2 := state2.Initialize(true) permuteScalarX4(a1, true) state2.Permute() if !reflect.DeepEqual(a1, a2) { t.Fatal() } } func BenchmarkF1600x2(b *testing.B) { benchmark := func(b *testing.B, turbo bool, f func(s *StateX2, a []uint64)) { var state StateX2 a := state.Initialize(turbo) for i := 0; i < b.N; i++ { f(&state, a) } } bench2 := func(b *testing.B, turbo bool) { b.Run("Generic", func(b *testing.B) { benchmark(b, turbo, func(s *StateX2, a []uint64) { permuteScalarX2(a, turbo) }) }) b.Run("SIMD", func(b *testing.B) { benchmark(b, turbo, func(s *StateX2, a []uint64) { s.Permute() }) }) } b.Run("Regular", func(b *testing.B) { bench2(b, false) }) b.Run("Turbo", func(b *testing.B) { bench2(b, true) }) } func BenchmarkF1600x4(b *testing.B) { benchmark := func(b *testing.B, turbo bool, f func(s *StateX4, a []uint64)) { var state StateX4 a := state.Initialize(turbo) for i := 0; i < b.N; i++ { f(&state, a) } } bench2 := func(b *testing.B, turbo bool) { b.Run("Generic", func(b *testing.B) { benchmark(b, turbo, func(s *StateX4, a []uint64) { permuteScalarX4(a, turbo) }) }) b.Run("SIMD", func(b *testing.B) { benchmark(b, turbo, func(s *StateX4, a []uint64) { s.Permute() }) }) } b.Run("Regular", func(b *testing.B) { bench2(b, false) }) b.Run("Turbo", func(b *testing.B) { bench2(b, true) }) } golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/fallback.go000066400000000000000000000004231454601126700244060ustar00rootroot00000000000000//go:build (!amd64 && !arm64) || (arm64 && !go1.16) // +build !amd64,!arm64 arm64,!go1.16 package keccakf1600 func permuteSIMDx2(state []uint64, turbo bool) { permuteScalarX2(state, turbo) } func permuteSIMDx4(state []uint64, turbo bool) { permuteScalarX4(state, turbo) } golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/internal/000077500000000000000000000000001454601126700241355ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/internal/asm/000077500000000000000000000000001454601126700247155ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/internal/asm/go.mod000066400000000000000000000002411454601126700260200ustar00rootroot00000000000000module github.com/cloudflare/circl/simd/keccakf1600/internal/asm go 1.12 require ( github.com/mmcloughlin/avo v0.5.0 golang.org/x/tools v0.8.0 // indirect ) golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/internal/asm/go.sum000066400000000000000000000107351454601126700260560ustar00rootroot00000000000000github.com/mmcloughlin/avo v0.5.0 h1:nAco9/aI9Lg2kiuROBY6BhCI/z0t5jEvJfjWbL8qXLU= github.com/mmcloughlin/avo v0.5.0/go.mod h1:ChHFdoV7ql95Wi7vuq2YT1bwCJqiWdZrQ1im3VujLYM= github.com/yuin/goldmark v1.4.13/go.mod h1:6yULJ656Px+3vBD8DxQVa3kxgyrAnzto9xy5taEt/CY= golang.org/x/arch v0.1.0/go.mod h1:5om86z9Hs0C8fWVUuoMHwpExlXzs5Tkyp9hOrfG7pp8= golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w= golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= golang.org/x/crypto v0.1.0/go.mod h1:RecgLatLF4+eUMCP1PoPZQb+cVrJcOPbHkTkbkB9sbw= golang.org/x/mod v0.6.0-dev.0.20220419223038-86c51ed26bb4/go.mod h1:jJ57K6gSWd91VN4djpZkiMVwK6gcyfeH4XE8wZrZaV4= golang.org/x/mod v0.6.0/go.mod h1:4mET923SAdbXp2ki8ey+zGs1SLqsuM2Y0uvdZR/fUNI= golang.org/x/mod v0.8.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs= golang.org/x/mod v0.10.0 h1:lFO9qtOdlre5W1jxS3r/4szv2/6iXxScdzjoBMXNhYk= golang.org/x/mod v0.10.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs= golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg= golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c= golang.org/x/net v0.1.0/go.mod h1:Cx3nUiGt4eDBEyega/BKRp+/AlGL8hYe7U9odMt2Cco= golang.org/x/net v0.6.0/go.mod h1:2Tu9+aMcznHK/AK1HMvgo6xiTLG5rD5rZLDS+rp2Bjs= golang.org/x/net v0.9.0/go.mod h1:d48xBJpPfHeWQsugry2m+kC02ZBRGRgulfHnEXEuWns= golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sync v0.1.0 h1:wsuoTGHzEhffawBOhz5CYhcrV4IdKZbEyZjBMuTp12o= golang.org/x/sync v0.1.0/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY= golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.1.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.5.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.7.0 h1:3jlCCIQZPdOYu1h8BkNvLz8Kgwtae2cagcG/VamtZRU= golang.org/x/sys v0.7.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo= golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= golang.org/x/term v0.1.0/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= golang.org/x/term 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h1:y4OqIKeOV/fWJetJ8bXPU1sEVniLMIyDAZWeHdV+NTA= golang.org/x/tools v0.6.0/go.mod h1:Xwgl3UAJ/d3gWutnCtw505GrjyAbvKui8lOU390QaIU= golang.org/x/tools v0.8.0 h1:vSDcovVPld282ceKgDimkRSC8kpaH1dgyc9UMzlt84Y= golang.org/x/tools v0.8.0/go.mod h1:JxBZ99ISMI5ViVkT1tr6tdNmXeTrcpVSD3vZ1RsRdN4= golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= rsc.io/pdf v0.1.1/go.mod h1:n8OzWcQ6Sp37PL01nO98y4iUCRdTGarVfzxY20ICaU4= golang-github-cloudflare-circl-1.3.7/simd/keccakf1600/internal/asm/src.go000066400000000000000000000071541454601126700260420ustar00rootroot00000000000000//go:generate go run src.go -out ../../f1600x4_amd64.s -stubs ../../f1600x4stubs_amd64.go -pkg keccakf1600 // AVX2 fourway parallelized Keccak-f[1600]. package main import ( . "github.com/mmcloughlin/avo/build" // nolint:stylecheck,golint . "github.com/mmcloughlin/avo/operand" // nolint:stylecheck,golint ) // nolint:funlen func main() { ConstraintExpr("amd64") // Must be called on 32 byte aligned memory. TEXT("f1600x4AVX2", NOSPLIT, "func(state *uint64, rc *[24]uint64, turbo bool)") Pragma("noescape") statePtr := Load(Param("state"), GP64()) state := func(offset int) Op { return Mem{Base: statePtr, Disp: 32 * offset} } rcPtr := Load(Param("rc"), GP64()) // We use the same approach as the normal Keccak-f[1600] implementation // (in the internal/sha3 package): we group four rounds together into a // super round. Thus we have six super rounds. superRound := GP64() MOVQ(U64(6), superRound) // count down. turbo := Load(Param("turbo"), GP64()) TESTQ(turbo, turbo) JZ(LabelRef("loop")) MOVQ(U64(3), superRound) // Skip 3 * 4 = 12 rounds ADDQ(Imm(8*12), rcPtr) // XXX Because our AVX2 is significantly larger, it might better not // to group four rounds together, but simply loop over the rounds // themselves. Label("loop") for r := 0; r < 4; r++ { // Compute parities: p[i] = a[i] ^ a[i + 5] ^ ... ^ a[i + 20]. p := []Op{YMM(), YMM(), YMM(), YMM(), YMM()} for i := 0; i < 5; i++ { VMOVDQA(state(i), p[i]) } for j := 1; j < 5; j++ { for i := 0; i < 5; i++ { VPXOR(state(5*j+i), p[i], p[i]) } } // Rotate and xor parities: d[i] = rotate_left(p[i+1], 1) ^ p[i-1] t := []Op{YMM(), YMM(), YMM(), YMM(), YMM()} d := []Op{YMM(), YMM(), YMM(), YMM(), YMM()} for i := 0; i < 5; i++ { VPSLLQ(U8(1), p[(i+1)%5], t[i]) } for i := 0; i < 5; i++ { VPSRLQ(U8(63), p[(i+1)%5], d[i]) } for i := 0; i < 5; i++ { VPOR(t[i], d[i], d[i]) } for i := 0; i < 5; i++ { VPXOR(d[i], p[(i+4)%5], d[i]) } // Rotation to use rot := func(i, g int) int { table := [][]int{ {0, 24, 18, 6, 12}, {7, 23, 2, 9, 22}, {1, 3, 17, 16, 20}, {13, 8, 4, 5, 15}, {19, 10, 21, 14, 11}, } t := table[g][i] return ((t + 1) * t / 2) % 64 // t'th triangle number } // Index into d to use di := func(i, g int) int { return (3*g + i) % 5 } // Index into state to use si := func(i, g, r int) int { n := []int{6, 16, 11, 1}[r] m := []int{10, 20, 15, 5}[r] return (i*n + m*g) % 25 } for g := 0; g < 5; g++ { s := []Op{YMM(), YMM(), YMM(), YMM(), YMM()} // Load the right five words from the state and XOR d into them. for i := 0; i < 5; i++ { VPXOR(state(si(di(i, g), g, r)), d[di(i, g)], s[i]) } // Rotate each s[i] by the appropriate amount for i := 0; i < 5; i++ { if rot(i, g) != 0 { VPSLLQ(U8(rot(i, g)), s[i], t[i]) } } for i := 0; i < 5; i++ { if rot(i, g) != 0 { VPSRLQ(U8(64-rot(i, g)), s[i], s[i]) } } for i := 0; i < 5; i++ { if rot(i, g) != 0 { VPOR(t[i], s[i], s[i]) } } // Compute the new words s[i] ^ (s[i+2] & ~s[i+1]) for i := 0; i < 5; i++ { VPANDN(s[(i+2)%5], s[(i+1)%5], t[i]) } for i := 0; i < 5; i++ { VPXOR(s[i], t[i], t[i]) } // Round constant if g == 0 { // Note that we move rcPtr by 8*4 bytes after each superround. rc := YMM() VPBROADCASTQ(Mem{Base: rcPtr, Disp: r * 8}, rc) VPXOR(rc, t[0], t[0]) } // Store back into state for i := 0; i < 5; i++ { VMOVDQA(t[i], state(si(i, g, r))) } } } ADDQ(Imm(8*4), rcPtr) SUBQ(U32(1), superRound) JNZ(LabelRef("loop")) RET() Generate() } golang-github-cloudflare-circl-1.3.7/tss/000077500000000000000000000000001454601126700203005ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/tss/doc.go000066400000000000000000000001011454601126700213640ustar00rootroot00000000000000// Package tss provides threshold signature schemes. package tss golang-github-cloudflare-circl-1.3.7/tss/rsa/000077500000000000000000000000001454601126700210655ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/tss/rsa/README.md000066400000000000000000000020401454601126700223400ustar00rootroot00000000000000# RSA Threshold Signatures This is an implementation of ["Practical Threshold Signatures" by Victor Shoup](https://www.iacr.org/archive/eurocrypt2000/1807/18070209-new.pdf). Protocol 1 is implemented. ## Threshold Primer Let *l* be the total number of players, *t* be the number of corrupted players, and *k* be the threshold. The idea of threshold signatures is that at least *k* players need to participate to form a valid signature. Setup consists of a dealer generating *l* key shares from a key pair and "dealing" them to the players. In this implementation the dealer is trusted. During the signing phase, at least *k* players use their key share and the message to generate a signature share. Finally, the *k* signature shares are combined to form a valid signature for the message. ## Modifications 1. Our implementation is not robust. That is, the corrupted players can prevent a valid signature from being formed by the non-corrupted players. As such, we remove all verification. 2. The paper requires p and q to be safe primes. We do not.golang-github-cloudflare-circl-1.3.7/tss/rsa/internal/000077500000000000000000000000001454601126700227015ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/tss/rsa/internal/pkcs1v15.go000066400000000000000000000075371454601126700246210ustar00rootroot00000000000000// https://cs.opensource.google/go/go/+/refs/tags/go1.18.3:src/crypto/rsa/pkcs1v15.go // Copyright (c) 2009 The Go Authors. All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following disclaimer // in the documentation and/or other materials provided with the // distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived from // this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // Copyright 2009 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package internal import ( "crypto" "crypto/rsa" "errors" "fmt" ) var hashPrefixes = map[crypto.Hash][]byte{ crypto.MD5: { 0x30, 0x20, 0x30, 0x0c, 0x06, 0x08, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x02, 0x05, 0x05, 0x00, 0x04, 0x10, }, crypto.SHA1: {0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2b, 0x0e, 0x03, 0x02, 0x1a, 0x05, 0x00, 0x04, 0x14}, crypto.SHA224: { 0x30, 0x2d, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x04, 0x05, 0x00, 0x04, 0x1c, }, crypto.SHA256: { 0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20, }, crypto.SHA384: { 0x30, 0x41, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x05, 0x00, 0x04, 0x30, }, crypto.SHA512: { 0x30, 0x51, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x05, 0x00, 0x04, 0x40, }, crypto.MD5SHA1: {}, // A special TLS case which doesn't use an ASN1 prefix. crypto.RIPEMD160: {0x30, 0x20, 0x30, 0x08, 0x06, 0x06, 0x28, 0xcf, 0x06, 0x03, 0x00, 0x31, 0x04, 0x14}, } func PadPKCS1v15(pub *rsa.PublicKey, hash crypto.Hash, hashed []byte) ([]byte, error) { hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed)) if err != nil { return nil, err } tLen := len(prefix) + hashLen k := pub.Size() if k < tLen+11 { return nil, fmt.Errorf("message too long") } // EM = 0x00 || 0x01 || PS || 0x00 || T em := make([]byte, k) em[1] = 1 for i := 2; i < k-tLen-1; i++ { em[i] = 0xff } copy(em[k-tLen:k-hashLen], prefix) copy(em[k-hashLen:k], hashed) return em, nil } func pkcs1v15HashInfo(hash crypto.Hash, inLen int) (hashLen int, prefix []byte, err error) { // Special case: crypto.Hash(0) is used to indicate that the data is // signed directly. if hash == 0 { return inLen, nil, nil } hashLen = hash.Size() if inLen != hashLen { return 0, nil, errors.New("threshold_internal: crypto/rsa: input must be hashed message") } prefix, ok := hashPrefixes[hash] if !ok { return 0, nil, errors.New("threshold_internal: crypto/rsa: unsupported hash function") } return } golang-github-cloudflare-circl-1.3.7/tss/rsa/internal/pss/000077500000000000000000000000001454601126700235065ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/tss/rsa/internal/pss/pss.go000066400000000000000000000116311454601126700246440ustar00rootroot00000000000000// https://cs.opensource.google/go/go/+/refs/tags/go1.18.3:src/crypto/rsa/pss.go // Copyright (c) 2009 The Go Authors. All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following disclaimer // in the documentation and/or other materials provided with the // distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived from // this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // Copyright 2013 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package pss // This file implements the RSASSA-PSS signature scheme according to RFC 8017. import ( "crypto" "crypto/rsa" "errors" "hash" "io" ) // Per RFC 8017, Section 9.1 // // EM = MGF1 xor DB || H( 8*0x00 || mHash || salt ) || 0xbc // // where // // DB = PS || 0x01 || salt // // and PS can be empty so // // emLen = dbLen + hLen + 1 = psLen + sLen + hLen + 2 // func emsaPSSEncode(mHash []byte, emBits int, salt []byte, hash hash.Hash) ([]byte, error) { // See RFC 8017, Section 9.1.1. hLen := hash.Size() sLen := len(salt) emLen := (emBits + 7) / 8 // 1. If the length of M is greater than the input limitation for the // hash function (2^61 - 1 octets for SHA-1), output "message too // long" and stop. // // 2. Let mHash = Hash(M), an octet string of length hLen. if len(mHash) != hLen { return nil, errors.New("crypto/rsa: input must be hashed with given hash") } // 3. If emLen < hLen + sLen + 2, output "encoding error" and stop. if emLen < hLen+sLen+2 { return nil, errors.New("crypto/rsa: key size too small for PSS signature") } em := make([]byte, emLen) psLen := emLen - sLen - hLen - 2 db := em[:psLen+1+sLen] h := em[psLen+1+sLen : emLen-1] // 4. Generate a random octet string salt of length sLen; if sLen = 0, // then salt is the empty string. // // 5. Let // M' = (0x)00 00 00 00 00 00 00 00 || mHash || salt; // // M' is an octet string of length 8 + hLen + sLen with eight // initial zero octets. // // 6. Let H = Hash(M'), an octet string of length hLen. var prefix [8]byte hash.Write(prefix[:]) hash.Write(mHash) hash.Write(salt) h = hash.Sum(h[:0]) hash.Reset() // 7. Generate an octet string PS consisting of emLen - sLen - hLen - 2 // zero octets. The length of PS may be 0. // // 8. Let DB = PS || 0x01 || salt; DB is an octet string of length // emLen - hLen - 1. db[psLen] = 0x01 copy(db[psLen+1:], salt) // 9. Let dbMask = MGF(H, emLen - hLen - 1). // // 10. Let maskedDB = DB \xor dbMask. mgf1XOR(db, hash, h) // 11. Set the leftmost 8 * emLen - emBits bits of the leftmost octet in // maskedDB to zero. db[0] &= 0xff >> (8*emLen - emBits) // 12. Let EM = maskedDB || H || 0xbc. em[emLen-1] = 0xbc // 13. Output EM. return em, nil } func padPSSWithSalt(pub *rsa.PublicKey, hash crypto.Hash, hashed, salt []byte) ([]byte, error) { emBits := pub.N.BitLen() - 1 em, err := emsaPSSEncode(hashed, emBits, salt, hash.New()) if err != nil { return nil, err } return em, nil } func saltLength(opts *rsa.PSSOptions) int { if opts == nil { return rsa.PSSSaltLengthAuto } return opts.SaltLength } func PadPSS(rand io.Reader, pub *rsa.PublicKey, hash crypto.Hash, digest []byte, opts *rsa.PSSOptions) ([]byte, error) { if opts != nil && opts.Hash != 0 { hash = opts.Hash } saltLength := saltLength(opts) switch saltLength { case rsa.PSSSaltLengthAuto: saltLength = (pub.N.BitLen()-1+7)/8 - 2 - hash.Size() case rsa.PSSSaltLengthEqualsHash: saltLength = hash.Size() } salt := make([]byte, saltLength) if _, err := io.ReadFull(rand, salt); err != nil { return nil, err } return padPSSWithSalt(pub, hash, digest, salt) } golang-github-cloudflare-circl-1.3.7/tss/rsa/internal/pss/rsa.go000066400000000000000000000044421454601126700246260ustar00rootroot00000000000000// https://cs.opensource.google/go/go/+/refs/tags/go1.18.3:src/crypto/rsa/rsa.go // Copyright (c) 2009 The Go Authors. All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following disclaimer // in the documentation and/or other materials provided with the // distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived from // this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. package pss import ( "hash" ) // incCounter increments a four byte, big-endian counter. func incCounter(c *[4]byte) { if c[3]++; c[3] != 0 { return } if c[2]++; c[2] != 0 { return } if c[1]++; c[1] != 0 { return } c[0]++ } // mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function // specified in PKCS #1 v2.1. func mgf1XOR(out []byte, hash hash.Hash, seed []byte) { var counter [4]byte var digest []byte done := 0 for done < len(out) { hash.Write(seed) hash.Write(counter[0:4]) digest = hash.Sum(digest[:0]) hash.Reset() for i := 0; i < len(digest) && done < len(out); i++ { out[done] ^= digest[i] done++ } incCounter(&counter) } } golang-github-cloudflare-circl-1.3.7/tss/rsa/keyshare.go000066400000000000000000000175261454601126700232420ustar00rootroot00000000000000package rsa import ( "crypto/rand" "crypto/rsa" "encoding/binary" "errors" "fmt" "io" "math" "math/big" "sync" ) // KeyShare represents a portion of the key. It can only be used to generate SignShare's. During the dealing phase (when Deal is called), one KeyShare is generated per player. type KeyShare struct { si *big.Int twoDeltaSi *big.Int // optional cached value, this value is used to marginally speed up SignShare generation in Sign. If nil, it will be generated when needed and then cached. Index uint // When KeyShare's are generated they are each assigned an index sequentially Players uint Threshold uint } func (kshare KeyShare) String() string { return fmt.Sprintf("(t,n): (%v,%v) index: %v si: 0x%v", kshare.Threshold, kshare.Players, kshare.Index, kshare.si.Text(16)) } // MarshalBinary encodes a KeyShare into a byte array in a format readable by UnmarshalBinary. // Note: Only Index's up to math.MaxUint16 are supported func (kshare *KeyShare) MarshalBinary() ([]byte, error) { // The encoding format is // | Players: uint16 | Threshold: uint16 | Index: uint16 | siLen: uint16 | si: []byte | twoDeltaSiNil: bool | twoDeltaSiLen: uint16 | twoDeltaSi: []byte | // with all values in big-endian. if kshare.Players > math.MaxUint16 { return nil, fmt.Errorf("rsa_threshold: keyshare marshall: Players is too big to fit in a uint16") } if kshare.Threshold > math.MaxUint16 { return nil, fmt.Errorf("rsa_threshold: keyshare marshall: Threshold is too big to fit in a uint16") } if kshare.Index > math.MaxUint16 { return nil, fmt.Errorf("rsa_threshold: keyshare marshall: Index is too big to fit in a uint16") } players := uint16(kshare.Players) threshold := uint16(kshare.Threshold) index := uint16(kshare.Index) twoDeltaSiBytes := []byte(nil) if kshare.twoDeltaSi != nil { twoDeltaSiBytes = kshare.twoDeltaSi.Bytes() } twoDeltaSiLen := len(twoDeltaSiBytes) if twoDeltaSiLen > math.MaxInt16 { return nil, fmt.Errorf("rsa_threshold: keyshare marshall: twoDeltaSiBytes is too big to fit it's length in a uint16") } siBytes := kshare.si.Bytes() siLength := len(siBytes) if siLength == 0 { siLength = 1 siBytes = []byte{0} } if siLength > math.MaxInt16 { return nil, fmt.Errorf("rsa_threshold: keyshare marshall: siBytes is too big to fit it's length in a uint16") } blen := 2 + 2 + 2 + 2 + 2 + 1 + siLength + twoDeltaSiLen out := make([]byte, blen) binary.BigEndian.PutUint16(out[0:2], players) binary.BigEndian.PutUint16(out[2:4], threshold) binary.BigEndian.PutUint16(out[4:6], index) binary.BigEndian.PutUint16(out[6:8], uint16(siLength)) // okay because of conditions checked above copy(out[8:8+siLength], siBytes) if twoDeltaSiBytes != nil { out[8+siLength] = 1 // twoDeltaSiNil } binary.BigEndian.PutUint16(out[8+siLength+1:8+siLength+3], uint16(twoDeltaSiLen)) if twoDeltaSiBytes != nil { copy(out[8+siLength+3:8+siLength+3+twoDeltaSiLen], twoDeltaSiBytes) } return out, nil } // UnmarshalBinary recovers a KeyShare from a slice of bytes, or returns an error if the encoding is invalid. func (kshare *KeyShare) UnmarshalBinary(data []byte) error { // The encoding format is // | Players: uint16 | Threshold: uint16 | Index: uint16 | siLen: uint16 | si: []byte | twoDeltaSiNil: bool | twoDeltaSiLen: uint16 | twoDeltaSi: []byte | // with all values in big-endian. if len(data) < 6 { return fmt.Errorf("rsa_threshold: keyshare unmarshalKeyShareTest failed: data length was too short for reading Players, Threshold, Index") } players := binary.BigEndian.Uint16(data[0:2]) threshold := binary.BigEndian.Uint16(data[2:4]) index := binary.BigEndian.Uint16(data[4:6]) if len(data[6:]) < 2 { return fmt.Errorf("rsa_threshold: keyshare unmarshalKeyShareTest failed: data length was too short for reading siLen length") } siLen := binary.BigEndian.Uint16(data[6:8]) if siLen == 0 { return fmt.Errorf("rsa_threshold: keyshare unmarshalKeyShareTest failed: si is a required field but siLen was 0") } if uint16(len(data[8:])) < siLen { return fmt.Errorf("rsa_threshold: keyshare unmarshalKeyShareTest failed: data length was too short for reading si, needed: %d found: %d", siLen, len(data[8:])) } si := new(big.Int).SetBytes(data[8 : 8+siLen]) if len(data[8+siLen:]) < 1 { return fmt.Errorf("rsa_threshold: keyshare unmarshalKeyShareTest failed: data length was too short for reading twoDeltaSiNil") } isNil := data[8+siLen] var twoDeltaSi *big.Int if isNil != 0 { if len(data[8+siLen+1:]) < 2 { return fmt.Errorf("rsa_threshold: keyshare unmarshalKeyShareTest failed: data length was too short for reading twoDeltaSiLen length") } twoDeltaSiLen := binary.BigEndian.Uint16(data[8+siLen+1 : 8+siLen+3]) if uint16(len(data[8+siLen+3:])) < twoDeltaSiLen { return fmt.Errorf("rsa_threshold: keyshare unmarshalKeyShareTest failed: data length was too short for reading twoDeltaSi, needed: %d found: %d", twoDeltaSiLen, len(data[8+siLen+2:])) } twoDeltaSi = new(big.Int).SetBytes(data[8+siLen+3 : 8+siLen+3+twoDeltaSiLen]) } kshare.Players = uint(players) kshare.Threshold = uint(threshold) kshare.Index = uint(index) kshare.si = si kshare.twoDeltaSi = twoDeltaSi return nil } // Returns the cached value in twoDeltaSi or if nil, generates 2∆s_i, stores it in twoDeltaSi, and returns it func (kshare *KeyShare) get2DeltaSi(players int64) *big.Int { // use the cached value if it exists if kshare.twoDeltaSi != nil { return kshare.twoDeltaSi } delta := calculateDelta(players) // 2∆s_i // delta << 1 == delta * 2 delta.Lsh(delta, 1).Mul(delta, kshare.si) kshare.twoDeltaSi = delta return delta } // Sign msg using a KeyShare. msg MUST be padded and hashed. Call PadHash before this method. // // If rand is not nil then blinding will be used to avoid timing // side-channel attacks. // // parallel indicates whether the blinding operations should use go routines to operate in parallel. // If parallel is false, blinding will take about 2x longer than nonbinding, otherwise it will take about the same time // (see benchmarks). If randSource is nil, parallel has no effect. parallel should almost always be set to true. func (kshare *KeyShare) Sign(randSource io.Reader, pub *rsa.PublicKey, digest []byte, parallel bool) (SignShare, error) { x := &big.Int{} x.SetBytes(digest) exp := kshare.get2DeltaSi(int64(kshare.Players)) var signShare SignShare signShare.Players = kshare.Players signShare.Threshold = kshare.Threshold signShare.Index = kshare.Index signShare.xi = &big.Int{} if randSource != nil { // Let's blind. // We can't use traditional RSA blinding (as used in rsa.go) because we are exponentiating by exp and not d. // As such, Euler's theorem doesn't apply ( exp * d != 0 (mod ϕ(n)) ). // Instead, we will choose a random r and compute x^{exp+r} * x^{-r} = x^{exp}. // This should (hopefully) prevent revealing information of the true value of exp, since with exp you can derive // s_i, the secret key share. r, err := rand.Int(randSource, pub.N) if err != nil { return SignShare{}, errors.New("rsa_threshold: unable to get random value for blinding") } expPlusr := big.Int{} // exp + r expPlusr.Add(exp, r) var wg *sync.WaitGroup // x^{|2∆s_i+r|} if parallel { wg = &sync.WaitGroup{} wg.Add(1) go func() { signShare.xi.Exp(x, &expPlusr, pub.N) wg.Done() }() } else { signShare.xi.Exp(x, &expPlusr, pub.N) } xExpr := big.Int{} // x^r xExpr.Exp(x, r, pub.N) // x^{-r} res := xExpr.ModInverse(&xExpr, pub.N) if res == nil { // extremely unlikely, somehow x^r is p or q return SignShare{}, errors.New("rsa_threshold: no mod inverse") } if wg != nil { wg.Wait() } // x^{|2∆s_i+r|} * x^{-r} = x^{2∆s_i} signShare.xi.Mul(signShare.xi, &xExpr) signShare.xi.Mod(signShare.xi, pub.N) } else { // x^{2∆s_i} signShare.xi = &big.Int{} signShare.xi.Exp(x, exp, pub.N) } return signShare, nil } golang-github-cloudflare-circl-1.3.7/tss/rsa/keyshare_test.go000066400000000000000000000076361454601126700243020ustar00rootroot00000000000000package rsa import ( "crypto/rand" "crypto/rsa" "math/big" "testing" ) func TestKeyShare_Sign(t *testing.T) { // delta = 3! = 6 // n = 253 // Players = 3 // kshare = { si: 15, Index: 1 } // x = { 150 } // x_i = x^{2∆kshare.si} = 150^{2 * 6 * 15} = 150^180 = 243 kshare := KeyShare{ si: big.NewInt(15), Index: 1, Players: 3, } pub := rsa.PublicKey{N: big.NewInt(253)} share, err := kshare.Sign(nil, &pub, []byte{150}, false) if err != nil { t.Fatal(err) } if share.xi.Cmp(big.NewInt(243)) != 0 { t.Fatalf("share.xi should be 243 but was %d", share.xi) } } func testSignBlind(parallel bool, t *testing.T) { // delta = 3! = 6 // n = 253 // Players = 3 // kshare = { si: 15, i: 1 } // x = { 150 } // x_i = x^{2∆kshare.si} = 150^{2 * 6 * 15} = 150^180 = 243 kshare := KeyShare{ si: big.NewInt(15), Index: 1, Players: 3, } pub := rsa.PublicKey{N: big.NewInt(253)} share, err := kshare.Sign(rand.Reader, &pub, []byte{150}, parallel) if err != nil { t.Fatal(err) } if share.xi.Cmp(big.NewInt(243)) != 0 { t.Fatalf("share.xi should be 243 but was %d", share.xi) } } func TestKeyShare_SignBlind(t *testing.T) { testSignBlind(false, t) } func TestKeyShare_SignBlindParallel(t *testing.T) { testSignBlind(true, t) } func marshalTestKeyShare(share KeyShare, t *testing.T) { marshall, err := share.MarshalBinary() if err != nil { t.Fatal(err) } share2 := KeyShare{} err = share2.UnmarshalBinary(marshall) if err != nil { t.Fatal(err) } if share.Players != share2.Players { t.Fatalf("Players did not match, expected %d, found %d", share.Players, share2.Players) } if share.Threshold != share2.Threshold { t.Fatalf("Threshold did not match, expected %d, found %d", share.Threshold, share2.Threshold) } if share.Index != share2.Index { t.Fatalf("Index did not match, expected %d, found %d", share.Index, share2.Index) } if (share.twoDeltaSi == nil || share2.twoDeltaSi == nil) && share.twoDeltaSi != share2.twoDeltaSi { t.Fatalf("twoDeltaSi did not match, expected %v, found %v", share.twoDeltaSi, share2.twoDeltaSi) } if !(share.twoDeltaSi == nil && share2.twoDeltaSi == nil) && share.twoDeltaSi.Cmp(share2.twoDeltaSi) != 0 { t.Fatalf("twoDeltaSi did not match, expected %v, found %v", share.twoDeltaSi.Bytes(), share2.twoDeltaSi.Bytes()) } if share.si.Cmp(share2.si) != 0 { t.Fatalf("si did not match, expected %v, found %v", share.si.Bytes(), share2.si.Bytes()) } } func unmarshalKeyShareTest(t *testing.T, input []byte) { share := KeyShare{} err := share.UnmarshalBinary(input) if err == nil { t.Fatalf("unmarshall succeeded when it shouldn't have") } } func TestMarshallKeyShare(t *testing.T) { marshalTestKeyShare(KeyShare{ si: big.NewInt(10), twoDeltaSi: big.NewInt(20), Index: 30, Threshold: 10, Players: 2, }, t) marshalTestKeyShare(KeyShare{ si: big.NewInt(10), twoDeltaSi: nil, Index: 30, Threshold: 0, Players: 200, }, t) marshalTestKeyShare(KeyShare{ si: big.NewInt(0), twoDeltaSi: big.NewInt(0), Index: 0, Threshold: 0, Players: 0, }, t) unmarshalKeyShareTest(t, []byte{}) unmarshalKeyShareTest(t, []byte{1, 0, 1}) unmarshalKeyShareTest(t, []byte{1, 0, 1}) unmarshalKeyShareTest(t, []byte{0, 1, 0, 1, 0, 1}) unmarshalKeyShareTest(t, []byte{0, 1, 0, 1, 0, 1, 0, 1}) unmarshalKeyShareTest(t, []byte{0, 1, 0, 1, 0, 1, 0}) unmarshalKeyShareTest(t, []byte{0, 1, 0, 1, 0, 1, 0, 2, 1}) unmarshalKeyShareTest(t, []byte{0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0}) unmarshalKeyShareTest(t, []byte{0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1}) } func TestMarshallKeyShareFull(t *testing.T) { const players = 3 const threshold = 2 const bits = 4096 key, err := rsa.GenerateKey(rand.Reader, bits) if err != nil { t.Fatal(err) } keys, err := Deal(rand.Reader, players, threshold, key, false) if err != nil { t.Fatal(err) } for _, share := range keys { marshalTestKeyShare(share, t) } } golang-github-cloudflare-circl-1.3.7/tss/rsa/padding.go000066400000000000000000000024571454601126700230320ustar00rootroot00000000000000package rsa import ( "crypto" "crypto/rsa" "io" "github.com/cloudflare/circl/tss/rsa/internal" pss2 "github.com/cloudflare/circl/tss/rsa/internal/pss" ) type Padder interface { Pad(pub *rsa.PublicKey, hash crypto.Hash, hashed []byte) ([]byte, error) } type PKCS1v15Padder struct{} func (PKCS1v15Padder) Pad(pub *rsa.PublicKey, hash crypto.Hash, hashed []byte) ([]byte, error) { return internal.PadPKCS1v15(pub, hash, hashed) } // PSSPadder is a padder for RSA Probabilistic Padding Scheme (RSA-PSS) used in TLS 1.3 // // Note: If the salt length is non-zero, PSS padding is not deterministic. // TLS 1.3 mandates that the salt length is the same as the hash output length. As such, each player cannot // pad the message individually, otherwise they will produce unique messages and the signature will not be valid. // Instead, one party should generate a random saltLen byte string. When requesting signatures from the rest of the // parties they should send along the same random string to be used as `rand` here. // // For TLS, rsa.PSSOptions.SaltLength should be PSSSaltLengthEqualsHash. type PSSPadder struct { Rand io.Reader Opts *rsa.PSSOptions } func (pss *PSSPadder) Pad(pub *rsa.PublicKey, hash crypto.Hash, hashed []byte) ([]byte, error) { return pss2.PadPSS(pss.Rand, pub, hash, hashed, pss.Opts) } golang-github-cloudflare-circl-1.3.7/tss/rsa/rsa_threshold.go000066400000000000000000000201621454601126700242560ustar00rootroot00000000000000// Package rsa provides RSA threshold signature scheme. // // This package implements the Protocol 1 of "Practical Threshold Signatures" // by Victor Shoup [1]. // // # References // // [1] https://www.iacr.org/archive/eurocrypt2000/1807/18070209-new.pdf package rsa import ( "crypto" "crypto/rand" "crypto/rsa" "errors" "fmt" "io" "math" "math/big" cmath "github.com/cloudflare/circl/math" ) // GenerateKey generates a RSA keypair for its use in RSA threshold signatures. // Internally, the modulus is the product of two safe primes. The time // consumed by this function is relatively longer than the regular // GenerateKey function from the crypto/rsa package. func GenerateKey(random io.Reader, bits int) (*rsa.PrivateKey, error) { p, err := cmath.SafePrime(random, bits/2) if err != nil { return nil, err } var q *big.Int n := new(big.Int) found := false for !found { q, err = cmath.SafePrime(random, bits-p.BitLen()) if err != nil { return nil, err } // check for different primes. if p.Cmp(q) != 0 { n.Mul(p, q) // check n has the desired bitlength. if n.BitLen() == bits { found = true } } } one := big.NewInt(1) pminus1 := new(big.Int).Sub(p, one) qminus1 := new(big.Int).Sub(q, one) totient := new(big.Int).Mul(pminus1, qminus1) priv := new(rsa.PrivateKey) priv.Primes = []*big.Int{p, q} priv.N = n priv.E = 65537 priv.D = new(big.Int) e := big.NewInt(int64(priv.E)) ok := priv.D.ModInverse(e, totient) if ok == nil { return nil, errors.New("public key is not coprime to phi(n)") } priv.Precompute() return priv, nil } // l or `Players`, the total number of Players. // t, the number of corrupted Players. // k=t+1 or `Threshold`, the number of signature shares needed to obtain a signature. func validateParams(players, threshold uint) error { if players <= 1 { return errors.New("rsa_threshold: Players (l) invalid: should be > 1") } if threshold < 1 || threshold > players { return fmt.Errorf("rsa_threshold: Threshold (k) invalid: %d < 1 || %d > %d", threshold, threshold, players) } return nil } // Deal takes in an existing RSA private key generated elsewhere. If cache is true, cached values are stored in KeyShare taking up more memory by reducing Sign time. // See KeyShare documentation. Multi-prime RSA keys are unsupported. func Deal(randSource io.Reader, players, threshold uint, key *rsa.PrivateKey, cache bool) ([]KeyShare, error) { err := validateParams(players, threshold) ONE := big.NewInt(1) if err != nil { return nil, err } if len(key.Primes) != 2 { return nil, errors.New("multiprime rsa keys are unsupported") } p := key.Primes[0] q := key.Primes[1] e := int64(key.E) // p = 2p' + 1 // q = 2q' + 1 // p' = (p - 1)/2 // q' = (q - 1)/2 // m = p'q' = (p - 1)(q - 1)/4 var pprime big.Int // p - 1 pprime.Sub(p, ONE) // q - 1 var m big.Int m.Sub(q, ONE) // (p - 1)(q - 1) m.Mul(&m, &pprime) // >> 2 == / 4 m.Rsh(&m, 2) // de ≡ 1 var d big.Int _d := d.ModInverse(big.NewInt(e), &m) if _d == nil { return nil, errors.New("rsa_threshold: no ModInverse for e in Z/Zm") } // a_0...a_{k-1} a := make([]*big.Int, threshold) // a_0 = d a[0] = &d // a_0...a_{k-1} = rand from {0, ..., m - 1} for i := uint(1); i <= threshold-1; i++ { a[i], err = rand.Int(randSource, &m) if err != nil { return nil, errors.New("rsa_threshold: unable to generate an int within [0, m)") } } shares := make([]KeyShare, players) // 1 <= i <= l for i := uint(1); i <= players; i++ { shares[i-1].Players = players shares[i-1].Threshold = threshold // Σ^{k-1}_{i=0} | a_i * X^i (mod m) poly := computePolynomial(threshold, a, i, &m) shares[i-1].si = poly shares[i-1].Index = i if cache { shares[i-1].get2DeltaSi(int64(players)) } } return shares, nil } func calcN(p, q *big.Int) big.Int { // n = pq var n big.Int n.Mul(p, q) return n } // f(X) = Σ^{k-1}_{i=0} | a_i * X^i (mod m) func computePolynomial(k uint, a []*big.Int, x uint, m *big.Int) *big.Int { // TODO: use Horner's method here. sum := big.NewInt(0) // Σ^{k-1}_{i=0} for i := uint(0); i <= k-1; i++ { // X^i // TODO optimize: we can compute x^{n+1} from the previous x^n xi := int64(math.Pow(float64(x), float64(i))) // a_i * X^i prod := big.Int{} prod.Mul(a[i], big.NewInt(xi)) // (mod m) prod.Mod(&prod, m) // while not in the spec, we are eventually modding m, so we can mod here for efficiency // Σ sum.Add(sum, &prod) } sum.Mod(sum, m) return sum } // PadHash MUST be called before signing a message func PadHash(padder Padder, hash crypto.Hash, pub *rsa.PublicKey, msg []byte) ([]byte, error) { // Sign(Pad(Hash(M))) hasher := hash.New() hasher.Write(msg) digest := hasher.Sum(nil) return padder.Pad(pub, hash, digest) } type Signature = []byte // CombineSignShares combines t SignShare's to produce a valid signature func CombineSignShares(pub *rsa.PublicKey, shares []SignShare, msg []byte) (Signature, error) { players := shares[0].Players threshold := shares[0].Threshold for i := range shares { if shares[i].Players != players { return nil, errors.New("rsa_threshold: shares didn't have consistent players") } if shares[i].Threshold != threshold { return nil, errors.New("rsa_threshold: shares didn't have consistent threshold") } } if uint(len(shares)) < threshold { return nil, errors.New("rsa_threshold: insufficient shares for the threshold") } w := big.NewInt(1) delta := calculateDelta(int64(players)) // i_1 ... i_k for _, share := range shares { // λ(S, 0, i) lambda, err := computeLambda(delta, shares, 0, int64(share.Index)) if err != nil { return nil, err } // 2λ var exp big.Int exp.Add(lambda, lambda) // faster than TWO * lambda // we need to handle negative λ's (aka inverse), so abs it, compare, and if necessary modinverse abslam := big.Int{} abslam.Abs(&exp) var tmp big.Int // x_i^{|2λ|} tmp.Exp(share.xi, &abslam, pub.N) if abslam.Cmp(&exp) == 1 { tmp.ModInverse(&tmp, pub.N) } // TODO first compute all the powers for the negative exponents (but don't invert yet); multiply these together and then invert all at once. This is ok since (ab)^-1 = a^-1 b^-1 w.Mul(w, &tmp).Mod(w, pub.N) } w.Mod(w, pub.N) // e′ = 4∆^2 eprime := big.Int{} eprime.Mul(delta, delta) // faster than delta^TWO eprime.Add(&eprime, &eprime) // faster than FOUR * eprime eprime.Add(&eprime, &eprime) // e′a + eb = 1 a := big.Int{} b := big.Int{} e := big.NewInt(int64(pub.E)) tmp := big.Int{} tmp.GCD(&a, &b, &eprime, e) // TODO You can compute a earlier and multiply a into the exponents used when computing w. // w^a wa := big.Int{} wa.Exp(w, &a, pub.N) // TODO justification // x^b x := big.Int{} x.SetBytes(msg) xb := big.Int{} xb.Exp(&x, &b, pub.N) // TODO justification // y = w^a * x^b y := big.Int{} y.Mul(&wa, &xb).Mod(&y, pub.N) // verify that signature is valid by checking x == y^e. ye := big.Int{} ye.Exp(&y, e, pub.N) if ye.Cmp(&x) != 0 { return nil, errors.New("rsa: internal error") } // ensure signature has the right size. sig := y.FillBytes(make([]byte, pub.Size())) return sig, nil } // computes lagrange Interpolation for the shares // i must be an id 0..l but not in S // j must be in S func computeLambda(delta *big.Int, S []SignShare, i, j int64) (*big.Int, error) { if i == j { return nil, errors.New("rsa_threshold: i and j can't be equal by precondition") } // these are just to check preconditions foundi := false foundj := false // λ(s, i, j) = ∆( ( π{j'∈S\{j}} (i - j') ) / ( π{j'∈S\{j}} (j - j') ) ) num := int64(1) den := int64(1) // ∈ S for _, s := range S { // j' jprime := int64(s.Index) // S\{j} if jprime == j { foundj = true continue } if jprime == i { foundi = false break } // (i - j') num *= i - jprime // (j - j') den *= j - jprime } // ∆ * (num/den) var lambda big.Int // (num/den) lambda.Div(big.NewInt(num), big.NewInt(den)) // ∆ * (num/den) lambda.Mul(delta, &lambda) if foundi { return nil, fmt.Errorf("rsa_threshold: i: %d should not be in S", i) } if !foundj { return nil, fmt.Errorf("rsa_threshold: j: %d should be in S", j) } return &lambda, nil } golang-github-cloudflare-circl-1.3.7/tss/rsa/rsa_threshold_test.go000066400000000000000000000227741454601126700253300ustar00rootroot00000000000000package rsa import ( "bytes" "crypto" "crypto/rand" "crypto/rsa" _ "crypto/sha256" "errors" "fmt" "io" "math/big" "testing" "github.com/cloudflare/circl/internal/test" ) var ONE = big.NewInt(1) func TestGenerateKey(t *testing.T) { // [Warning]: this is only for tests, use a secure bitlen above 2048 bits. bitlen := 128 key, err := GenerateKey(rand.Reader, bitlen) test.CheckNoErr(t, err, "failed to create key") test.CheckOk(key.Validate() == nil, fmt.Sprintf("key is not valid: %v", key), t) } func createPrivateKey(p, q *big.Int, e int) *rsa.PrivateKey { return &rsa.PrivateKey{ PublicKey: rsa.PublicKey{ E: e, }, D: nil, Primes: []*big.Int{p, q}, Precomputed: rsa.PrecomputedValues{}, } } func TestCalcN(t *testing.T) { TWO := big.NewInt(2) n := calcN(ONE, TWO) if n.Cmp(TWO) != 0 { t.Fatal("calcN failed: (1, 2)") } n = calcN(TWO, big.NewInt(4)) if n.Cmp(big.NewInt(8)) != 0 { t.Fatal("calcN failed: (2, 4)") } } func TestComputePolynomial(t *testing.T) { m := big.NewInt(11) const k = 5 a := make([]*big.Int, k) for i := 0; i < k; i++ { a[i] = big.NewInt(int64(i + 1)) } // a = {1, 2, 3, 4, 5} x := uint(3) out := computePolynomial(k, a, x, m) // 1 * 3^0 = 1 = 1 // 2 * 3^1 = 6 = 6 // 3 * 3^2 = 27 = 5 // 4 * 3^3 = 108 = 9 // 5 * 3^4 = 405 = 9 // 1 + 6 + 5 + 9 + 9 = 30 = 8 if out.Cmp(big.NewInt(8)) != 0 { t.Fatal("compute polynomial failed") } } func TestComputeLambda(t *testing.T) { // shares = {1, 2, 3, 4, 5} // i = 0 // ∆ = 5! = 120 // j = 3 // // num = (0 - 1) * (0 - 2) * (0 - 4) * (0 - 5) = 40 // dem = (3 - 1) * (3 - 2) * (3 - 4) * (3 - 5) = 4 // num/dev = 40/4 = 10 // ∆ * 10 = 120 * 10 = 1200 shares := make([]SignShare, 5) for i := uint(1); i <= 5; i++ { shares[i-1].Index = i } i := int64(0) delta := int64(120) j := int64(3) lambda, err := computeLambda(big.NewInt(delta), shares, i, j) if err != nil || lambda.Cmp(big.NewInt(1200)) != 0 { t.Fatal("computeLambda failed") } } func TestDeal(t *testing.T) { // Players = 3 // Threshold = 2 // e = 3 // p' = 11 // q' = 5 // p = 2(11) + 1 = 23 // q = 2(5) + 1 = 11 // n = 253 // m = 55 // d = 37 // // a[0] = 37 // a[1] = 33 // // // Index = 1 // computePolynomial(k: 2, a: {37, 33}, x: 1, m: 55) : // 37 * 1^0 = 37 * 1 = 37 // 33 * 1^1 = 33 * 1 = 33 // 37 + 33 = 70 = 15 // // shares[0].si = 15 // shares[0].Index = 1 // // Index = 2 // computePolynomial(k: 2, a: {37, 33}, x: 2, m: 55) : // 37 * 2^0 = 37 * 1 = 37 // 33 * 2^1 = 33 * 2 = 66 = 11 // 37 + 11 = 48 // // shares[1].si = 48 // shares[1].Index = 2 // // // Index = 3 // computePolynomial(k: 2, a: {37, 33}, x: 3, m: 55) : // 37 * 3^0 = 37 * 1 = 37 // 33 * 3^1 = 33 * 3 = 99 = 44 // 37 + 44 = 81 = 26 // // shares[2].si = 26 // shares[2].Index = 3 // // // r := bytes.NewReader([]byte{33, 17}) players := uint(3) threshold := uint(2) p := int64(23) q := int64(11) e := 3 key := createPrivateKey(big.NewInt(p), big.NewInt(q), e) share, err := Deal(r, players, threshold, key, false) if err != nil { t.Fatal(err) } if share[0].si.Cmp(big.NewInt(15)) != 0 { t.Fatalf("share[0].si should have been 15 but was %d", share[0].si) } if share[1].si.Cmp(big.NewInt(48)) != 0 { t.Fatalf("share[1].si should have been 48 but was %d", share[1].si) } if share[2].si.Cmp(big.NewInt(26)) != 0 { t.Fatalf("share[2].si should have been 26 but was %d", share[2].si) } } const ( PKS1v15 = 0 PSS = 1 ) func testIntegration(t *testing.T, algo crypto.Hash, priv *rsa.PrivateKey, threshold uint, keys []KeyShare, padScheme int) { msg := []byte("hello") pub := &priv.PublicKey var padder Padder if padScheme == PKS1v15 { padder = &PKCS1v15Padder{} } else if padScheme == PSS { padder = &PSSPadder{ Rand: rand.Reader, Opts: nil, } } else { t.Fatal(errors.New("unknown padScheme")) } msgPH, err := PadHash(padder, algo, pub, msg) if err != nil { t.Fatal(err) } signshares := make([]SignShare, threshold) for i := uint(0); i < threshold; i++ { signshares[i], err = keys[i].Sign(rand.Reader, pub, msgPH, true) if err != nil { t.Fatal(err) } } sig, err := CombineSignShares(pub, signshares, msgPH) if err != nil { t.Fatal(err) } if len(sig) != pub.Size() { t.Fatal("bad signature size") } h := algo.New() h.Write(msg) hashed := h.Sum(nil) if padScheme == PKS1v15 { err = rsa.VerifyPKCS1v15(pub, algo, hashed, sig) } else if padScheme == PSS { err = rsa.VerifyPSS(pub, algo, hashed, sig, padder.(*PSSPadder).Opts) } else { panic("logical error") } if err != nil { t.Logf("d: %v p: %v q: %v\n", priv.D.Text(16), priv.Primes[0].Text(16), priv.Primes[1].Text(16)) for i, k := range keys { t.Logf("keys[%v]: %v\n", i, k) } for i, s := range signshares { t.Logf("signShares[%v]: %v\n", i, s) } t.Logf("sig: %x\n", sig) t.Fatal(err) } } func TestIntegrationStdRsaKeyGenerationPKS1v15(t *testing.T) { const players = 3 const threshold = 2 const bits = 2048 const algo = crypto.SHA256 key, err := rsa.GenerateKey(rand.Reader, bits) if err != nil { t.Fatal(err) } keys, err := Deal(rand.Reader, players, threshold, key, false) if err != nil { t.Fatal(err) } testIntegration(t, algo, key, threshold, keys, PKS1v15) } func TestIntegrationStdRsaKeyGenerationPSS(t *testing.T) { const players = 3 const threshold = 2 const bits = 2048 const algo = crypto.SHA256 key, err := rsa.GenerateKey(rand.Reader, bits) if err != nil { t.Fatal(err) } keys, err := Deal(rand.Reader, players, threshold, key, false) if err != nil { t.Fatal(err) } testIntegration(t, algo, key, threshold, keys, PSS) } // nolint: unparam func benchmarkSignCombineHelper(randSource io.Reader, parallel bool, b *testing.B, players, threshold uint, bits int, algo crypto.Hash, padScheme int) { key, err := rsa.GenerateKey(rand.Reader, bits) pub := key.PublicKey if err != nil { panic(err) } keys, err := Deal(rand.Reader, players, threshold, key, true) if err != nil { b.Fatal(err) } msg := []byte("hello") var padder Padder if padScheme == PKS1v15 { padder = &PKCS1v15Padder{} } else if padScheme == PSS { padder = &PSSPadder{ Rand: rand.Reader, Opts: nil, } } else { b.Fatal(errors.New("unknown padScheme")) } msgPH, err := PadHash(padder, algo, &pub, msg) if err != nil { b.Fatal(err) } signshares := make([]SignShare, threshold) b.ResetTimer() for i := 0; i < b.N; i++ { for i := uint(0); i < threshold; i++ { signshares[i], err = keys[i].Sign(randSource, &pub, msgPH, parallel) if err != nil { b.Fatal(err) } } _, err = CombineSignShares(&pub, signshares, msgPH) if err != nil { b.Fatal(err) } } b.StopTimer() } func BenchmarkBaselineRSA_SHA256_4096(b *testing.B) { const bits = 4096 const algo = crypto.SHA256 key, err := rsa.GenerateKey(rand.Reader, bits) if err != nil { b.Fatal(err) } h := algo.New() msg := []byte("hello") h.Write(msg) d := h.Sum(nil) b.ResetTimer() for i := 0; i < b.N; i++ { _, err = rsa.SignPKCS1v15(rand.Reader, key, algo, d) if err != nil { b.Fatal(err) } } b.StopTimer() } func BenchmarkBaselineRSA_SHA256_2048(b *testing.B) { const bits = 2048 const algo = crypto.SHA256 key, err := rsa.GenerateKey(rand.Reader, bits) if err != nil { b.Fatal(err) } h := algo.New() msg := []byte("hello") h.Write(msg) d := h.Sum(nil) b.ResetTimer() for i := 0; i < b.N; i++ { _, err = rsa.SignPKCS1v15(rand.Reader, key, algo, d) if err != nil { b.Fatal(err) } } b.StopTimer() } func BenchmarkSignCombine_SHA256_4096_3_2_Scheme(b *testing.B) { const players = 3 const threshold = 2 const bits = 4096 const algo = crypto.SHA256 benchmarkSignCombineHelper(nil, false, b, players, threshold, bits, algo, PKS1v15) } func BenchmarkSignCombine_SHA256_4096_3_2_Scheme_Blind(b *testing.B) { const players = 3 const threshold = 2 const bits = 4096 const algo = crypto.SHA256 benchmarkSignCombineHelper(rand.Reader, false, b, players, threshold, bits, algo, PKS1v15) } func BenchmarkSignCombine_SHA256_4096_3_2_Scheme_BlindParallel(b *testing.B) { const players = 3 const threshold = 2 const bits = 4096 const algo = crypto.SHA256 benchmarkSignCombineHelper(rand.Reader, true, b, players, threshold, bits, algo, PKS1v15) } func BenchmarkSignCombine_SHA256_2048_3_2_Scheme(b *testing.B) { const players = 3 const threshold = 2 const bits = 2048 const algo = crypto.SHA256 benchmarkSignCombineHelper(nil, false, b, players, threshold, bits, algo, PKS1v15) } func BenchmarkSignCombine_SHA256_2048_3_2_Scheme_Blind(b *testing.B) { const players = 3 const threshold = 2 const bits = 2048 const algo = crypto.SHA256 benchmarkSignCombineHelper(rand.Reader, false, b, players, threshold, bits, algo, PKS1v15) } func BenchmarkSignCombine_SHA256_2048_3_2_Scheme_BlindParallel(b *testing.B) { const players = 3 const threshold = 2 const bits = 2048 const algo = crypto.SHA256 benchmarkSignCombineHelper(rand.Reader, true, b, players, threshold, bits, algo, PKS1v15) } func BenchmarkSignCombine_SHA256_1024_3_2_Scheme(b *testing.B) { const players = 3 const threshold = 2 const bits = 1024 const algo = crypto.SHA256 benchmarkSignCombineHelper(nil, false, b, players, threshold, bits, algo, PKS1v15) } func BenchmarkDealGeneration(b *testing.B) { const players = 3 const threshold = 2 const bits = 2048 key, err := rsa.GenerateKey(rand.Reader, bits) if err != nil { b.Fatal("could not generate key") } b.ResetTimer() for i := 0; i < b.N; i++ { _, err := Deal(rand.Reader, players, threshold, key, false) if err != nil { b.Fatal(err) } } } golang-github-cloudflare-circl-1.3.7/tss/rsa/signShare.go000066400000000000000000000057351454601126700233510ustar00rootroot00000000000000package rsa import ( "encoding/binary" "fmt" "math" "math/big" ) // SignShare represents a portion of a signature. It is generated when a message is signed by a KeyShare. t SignShare's are then combined by calling CombineSignShares, where t is the Threshold. type SignShare struct { xi *big.Int Index uint Players uint Threshold uint } func (s SignShare) String() string { return fmt.Sprintf("(t,n): (%v,%v) index: %v xi: 0x%v", s.Threshold, s.Players, s.Index, s.xi.Text(16)) } // MarshalBinary encodes SignShare into a byte array in a format readable by UnmarshalBinary. // Note: Only Index's up to math.MaxUint16 are supported func (s *SignShare) MarshalBinary() ([]byte, error) { // | Players: uint16 | Threshold: uint16 | Index: uint16 | xiLen: uint16 | xi: []byte | if s.Players > math.MaxUint16 { return nil, fmt.Errorf("rsa_threshold: signshare marshall: Players is too big to fit in a uint16") } if s.Threshold > math.MaxUint16 { return nil, fmt.Errorf("rsa_threshold: signshare marshall: Threshold is too big to fit in a uint16") } if s.Index > math.MaxUint16 { return nil, fmt.Errorf("rsa_threshold: signshare marshall: Index is too big to fit in a uint16") } players := uint16(s.Players) threshold := uint16(s.Threshold) index := uint16(s.Index) xiBytes := s.xi.Bytes() xiLen := len(xiBytes) if xiLen > math.MaxInt16 { return nil, fmt.Errorf("rsa_threshold: signshare marshall: xiBytes is too big to fit it's length in a uint16") } if xiLen == 0 { xiLen = 1 xiBytes = []byte{0} } blen := 2 + 2 + 2 + 2 + xiLen out := make([]byte, blen) binary.BigEndian.PutUint16(out[0:2], players) binary.BigEndian.PutUint16(out[2:4], threshold) binary.BigEndian.PutUint16(out[4:6], index) binary.BigEndian.PutUint16(out[6:8], uint16(xiLen)) copy(out[8:8+xiLen], xiBytes) return out, nil } // UnmarshalBinary converts a byte array outputted from Marshall into a SignShare or returns an error if the value is invalid func (s *SignShare) UnmarshalBinary(data []byte) error { // | Players: uint16 | Threshold: uint16 | Index: uint16 | xiLen: uint16 | xi: []byte | if len(data) < 8 { return fmt.Errorf("rsa_threshold: signshare unmarshalKeyShareTest failed: data length was too short for reading Players, Threshold, Index, and xiLen") } players := binary.BigEndian.Uint16(data[0:2]) threshold := binary.BigEndian.Uint16(data[2:4]) index := binary.BigEndian.Uint16(data[4:6]) xiLen := binary.BigEndian.Uint16(data[6:8]) if xiLen == 0 { return fmt.Errorf("rsa_threshold: signshare unmarshalKeyShareTest failed: xi is a required field but xiLen was 0") } if uint16(len(data[8:])) < xiLen { return fmt.Errorf("rsa_threshold: signshare unmarshalKeyShareTest failed: data length was too short for reading xi, needed: %d found: %d", xiLen, len(data[6:])) } xi := big.Int{} bytes := make([]byte, xiLen) copy(bytes, data[8:8+xiLen]) xi.SetBytes(bytes) s.Players = uint(players) s.Threshold = uint(threshold) s.Index = uint(index) s.xi = &xi return nil } golang-github-cloudflare-circl-1.3.7/tss/rsa/signShare_test.go000066400000000000000000000040721454601126700244010ustar00rootroot00000000000000package rsa import ( "crypto/rand" "crypto/rsa" "math/big" "testing" ) func marshalTestSignShare(share SignShare, t *testing.T) { marshall, err := share.MarshalBinary() if err != nil { t.Fatal(err) } share2 := SignShare{} err = share2.UnmarshalBinary(marshall) if err != nil { t.Fatal(err) } if share.Players != share2.Players { t.Fatalf("Players did not match, expected %d, found %d", share.Players, share2.Players) } if share.Threshold != share2.Threshold { t.Fatalf("Threshold did not match, expected %d, found %d", share.Threshold, share2.Threshold) } if share.Index != share2.Index { t.Fatalf("Index did not match, expected %d, found %d", share.Index, share2.Index) } if share.xi.Cmp(share2.xi) != 0 { t.Fatalf("si did not match, expected %v, found %v", share.xi.Bytes(), share2.xi.Bytes()) } } func unmarshalSignShareTest(t *testing.T, input []byte) { share := SignShare{} err := share.UnmarshalBinary(input) if err == nil { t.Fatalf("unmarshall succeeded when it shouldn't have") } } func TestMarshallSignShare(t *testing.T) { marshalTestSignShare(SignShare{ xi: big.NewInt(10), Index: 30, Players: 16, Threshold: 18, }, t) marshalTestSignShare(SignShare{ xi: big.NewInt(0), Index: 0, Players: 0, Threshold: 0, }, t) unmarshalSignShareTest(t, []byte{}) unmarshalSignShareTest(t, []byte{0, 0, 0}) unmarshalSignShareTest(t, []byte{0, 0, 0, 0, 0, 0, 0, 0}) unmarshalSignShareTest(t, []byte{0, 0, 0, 0, 0, 0, 0, 1}) unmarshalSignShareTest(t, []byte{0, 0, 0, 0, 0, 0, 0, 2, 1}) } func TestMarshallFullSignShare(t *testing.T) { const players = 3 const threshold = 2 const bits = 4096 key, err := rsa.GenerateKey(rand.Reader, bits) if err != nil { t.Fatal(err) } keys, err := Deal(rand.Reader, players, threshold, key, false) if err != nil { t.Fatal(err) } for _, share := range keys { keyshare, err := share.Sign(rand.Reader, &key.PublicKey, []byte("Cloudflare!"), true) if err != nil { t.Fatal(err) } _, err = keyshare.MarshalBinary() if err != nil { t.Fatal(err) } } } golang-github-cloudflare-circl-1.3.7/tss/rsa/util.go000066400000000000000000000002251454601126700223700ustar00rootroot00000000000000package rsa import ( "math/big" ) func calculateDelta(l int64) *big.Int { // ∆ = l! delta := big.Int{} delta.MulRange(1, l) return &delta } golang-github-cloudflare-circl-1.3.7/tss/rsa/util_test.go000066400000000000000000000005611454601126700234320ustar00rootroot00000000000000package rsa import ( "math/big" "testing" ) func TestCalculateDelta(t *testing.T) { ONE := big.NewInt(1) if calculateDelta(0).Cmp(ONE) != 0 { t.Fatal("calculateDelta failed on 0") } if calculateDelta(1).Cmp(ONE) != 0 { t.Fatal("calculateDelta failed on 1") } if calculateDelta(5).Cmp(big.NewInt(120)) != 0 { t.Fatal("calculateDelta failed on 5") } } golang-github-cloudflare-circl-1.3.7/xof/000077500000000000000000000000001454601126700202635ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/xof/k12/000077500000000000000000000000001454601126700206605ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/xof/k12/k12.go000066400000000000000000000220311454601126700216020ustar00rootroot00000000000000// k12 implements the KangarooTwelve XOF. // // KangarooTwelve is being standardised at the CFRG working group // of the IRTF. This package implements draft 10. // // https://datatracker.ietf.org/doc/draft-irtf-cfrg-kangarootwelve/10/ package k12 import ( "encoding/binary" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/simd/keccakf1600" ) const chunkSize = 8192 // aka B // KangarooTwelve splits the message into chunks of 8192 bytes each. // The first chunk is absorbed directly in a TurboSHAKE128 instance, which // we call the stalk. The subsequent chunks aren't absorbed directly, but // instead their hash is absorbed: they're like leafs on a stalk. // If we have a fast TurboSHAKE128 available, we buffer chunks until we have // enough to do the parallel TurboSHAKE128. If not, we absorb directly into // a separate TurboSHAKE128 state. type State struct { initialTodo int // Bytes left to absorb for the first chunk. stalk sha3.State context []byte // context string "C" provided by the user // buffer of incoming data so we can do parallel TurboSHAKE128: // nil when we haven't absorbed the first chunk yet; // empty if we have, but we do not have a fast parallel TurboSHAKE128; // and chunkSize*lanes in length if we have. buf []byte offset int // offset in buf or bytes written to leaf // Number of chunk hashes ("CV_i") absorbed into the stalk. chunk uint // TurboSHAKE128 instance to compute the leaf in case we don't have // a fast parallel TurboSHAKE128, viz when lanes == 1. leaf *sha3.State lanes uint8 // number of TurboSHAKE128s to compute in parallel } // NewDraft10 creates a new instance of Kangaroo12 draft version -10. func NewDraft10(c []byte) State { var lanes byte = 1 if keccakf1600.IsEnabledX4() { lanes = 4 } else if keccakf1600.IsEnabledX2() { lanes = 2 } return newDraft10(c, lanes) } func newDraft10(c []byte, lanes byte) State { return State{ initialTodo: chunkSize, stalk: sha3.NewTurboShake128(0x07), context: c, lanes: lanes, } } func (s *State) Reset() { s.initialTodo = chunkSize s.stalk.Reset() s.stalk.SwitchDS(0x07) s.buf = nil s.offset = 0 s.chunk = 0 } func (s *State) Clone() State { stalk := s.stalk.Clone().(*sha3.State) ret := State{ initialTodo: s.initialTodo, stalk: *stalk, context: s.context, offset: s.offset, chunk: s.chunk, lanes: s.lanes, } if s.leaf != nil { ret.leaf = s.leaf.Clone().(*sha3.State) } if s.buf != nil { ret.buf = make([]byte, len(s.buf)) copy(ret.buf, s.buf) } return ret } func Draft10Sum(hash []byte, msg []byte, c []byte) { // TODO Tweak number of lanes depending on the length of the message s := NewDraft10(c) _, _ = s.Write(msg) _, _ = s.Read(hash) } func (s *State) Write(p []byte) (int, error) { written := len(p) // The first chunk is written directly to the stalk. if s.initialTodo > 0 { taken := s.initialTodo if len(p) < taken { taken = len(p) } headP := p[:taken] _, _ = s.stalk.Write(headP) s.initialTodo -= taken p = p[taken:] } if len(p) == 0 { return written, nil } // If this is the first bit of data written after the initial chunk, // we're out of the fast-path and allocate some buffers. if s.buf == nil { if s.lanes != 1 { s.buf = make([]byte, int(s.lanes)*chunkSize) } else { // We create the buffer to signal we're past the first chunk, // but do not use it. s.buf = make([]byte, 0) h := sha3.NewTurboShake128(0x0B) s.leaf = &h } _, _ = s.stalk.Write([]byte{0x03, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}) s.stalk.SwitchDS(0x06) } // If we're just using one lane, we don't need to cache in a buffer // for parallel hashing. Instead, we feed directly to TurboSHAKE. if s.lanes == 1 { for len(p) > 0 { // Write to current leaf. to := chunkSize - s.offset if len(p) < to { to = len(p) } _, _ = s.leaf.Write(p[:to]) p = p[to:] s.offset += to // Did we fill the chunk? if s.offset == chunkSize { var cv [32]byte _, _ = s.leaf.Read(cv[:]) _, _ = s.stalk.Write(cv[:]) s.leaf.Reset() s.offset = 0 s.chunk++ } } return written, nil } // If we can't fill all our lanes or the buffer isn't empty, we write the // data to the buffer. if s.offset != 0 || len(p) < len(s.buf) { to := len(s.buf) - s.offset if len(p) < to { to = len(p) } p2 := p[:to] p = p[to:] copy(s.buf[s.offset:], p2) s.offset += to } // Absorb the buffer if we filled it if s.offset == len(s.buf) { s.writeX(s.buf) s.offset = 0 } // Note that at this point we may assume that s.offset = 0 if len(p) != 0 if len(p) != 0 && s.offset != 0 { panic("shouldn't happen") } // Absorb a bunch of chunks at the same time. if len(p) >= int(s.lanes)*chunkSize { p = s.writeX(p) } // Put the remainder in the buffer. if len(p) > 0 { copy(s.buf, p) s.offset = len(p) } return written, nil } // Absorb a multiple of a multiple of lanes * chunkSize. // Returns the remainder. func (s *State) writeX(p []byte) []byte { switch s.lanes { case 4: return s.writeX4(p) default: return s.writeX2(p) } } func (s *State) writeX4(p []byte) []byte { for len(p) >= 4*chunkSize { var x4 keccakf1600.StateX4 a := x4.Initialize(true) for offset := 0; offset < 48*168; offset += 168 { for i := 0; i < 21; i++ { a[i*4] ^= binary.LittleEndian.Uint64( p[8*i+offset:], ) a[i*4+1] ^= binary.LittleEndian.Uint64( p[chunkSize+8*i+offset:], ) a[i*4+2] ^= binary.LittleEndian.Uint64( p[chunkSize*2+8*i+offset:], ) a[i*4+3] ^= binary.LittleEndian.Uint64( p[chunkSize*3+8*i+offset:], ) } x4.Permute() } for i := 0; i < 16; i++ { a[i*4] ^= binary.LittleEndian.Uint64( p[8*i+48*168:], ) a[i*4+1] ^= binary.LittleEndian.Uint64( p[chunkSize+8*i+48*168:], ) a[i*4+2] ^= binary.LittleEndian.Uint64( p[chunkSize*2+8*i+48*168:], ) a[i*4+3] ^= binary.LittleEndian.Uint64( p[chunkSize*3+8*i+48*168:], ) } a[16*4] ^= 0x0b a[16*4+1] ^= 0x0b a[16*4+2] ^= 0x0b a[16*4+3] ^= 0x0b a[20*4] ^= 0x80 << 56 a[20*4+1] ^= 0x80 << 56 a[20*4+2] ^= 0x80 << 56 a[20*4+3] ^= 0x80 << 56 x4.Permute() var buf [32 * 4]byte for i := 0; i < 4; i++ { binary.LittleEndian.PutUint64(buf[8*i:], a[4*i]) binary.LittleEndian.PutUint64(buf[32+8*i:], a[4*i+1]) binary.LittleEndian.PutUint64(buf[32*2+8*i:], a[4*i+2]) binary.LittleEndian.PutUint64(buf[32*3+8*i:], a[4*i+3]) } _, _ = s.stalk.Write(buf[:]) p = p[chunkSize*4:] s.chunk += 4 } return p } func (s *State) writeX2(p []byte) []byte { // TODO On M2 Pro, 1/3 of the time is spent on this function // and LittleEndian.Uint64 excluding the actual permutation. // Rewriting in assembler might be worthwhile. for len(p) >= 2*chunkSize { var x2 keccakf1600.StateX2 a := x2.Initialize(true) for offset := 0; offset < 48*168; offset += 168 { for i := 0; i < 21; i++ { a[i*2] ^= binary.LittleEndian.Uint64( p[8*i+offset:], ) a[i*2+1] ^= binary.LittleEndian.Uint64( p[chunkSize+8*i+offset:], ) } x2.Permute() } for i := 0; i < 16; i++ { a[i*2] ^= binary.LittleEndian.Uint64( p[8*i+48*168:], ) a[i*2+1] ^= binary.LittleEndian.Uint64( p[chunkSize+8*i+48*168:], ) } a[16*2] ^= 0x0b a[16*2+1] ^= 0x0b a[20*2] ^= 0x80 << 56 a[20*2+1] ^= 0x80 << 56 x2.Permute() var buf [32 * 2]byte for i := 0; i < 4; i++ { binary.LittleEndian.PutUint64(buf[8*i:], a[2*i]) binary.LittleEndian.PutUint64(buf[32+8*i:], a[2*i+1]) } _, _ = s.stalk.Write(buf[:]) p = p[chunkSize*2:] s.chunk += 2 } return p } func (s *State) Read(p []byte) (int, error) { if s.stalk.IsAbsorbing() { // Write context string C _, _ = s.Write(s.context) // Write length_encode( |C| ) var buf [9]byte binary.BigEndian.PutUint64(buf[:8], uint64(len(s.context))) // Find first non-zero digit in big endian encoding of context length i := 0 for buf[i] == 0 && i < 8 { i++ } buf[8] = byte(8 - i) // number of bytes to represent |C| _, _ = s.Write(buf[i:]) // We need to write the chunk number if we're past the first chunk. if s.buf != nil { // Write last remaining chunk(s) var cv [32]byte if s.lanes == 1 { if s.offset != 0 { _, _ = s.leaf.Read(cv[:]) _, _ = s.stalk.Write(cv[:]) s.chunk++ } } else { remainingBuf := s.buf[:s.offset] for len(remainingBuf) > 0 { h := sha3.NewTurboShake128(0x0B) to := chunkSize if len(remainingBuf) < to { to = len(remainingBuf) } _, _ = h.Write(remainingBuf[:to]) _, _ = h.Read(cv[:]) _, _ = s.stalk.Write(cv[:]) s.chunk++ remainingBuf = remainingBuf[to:] } } // Write length_encode( chunk ) binary.BigEndian.PutUint64(buf[:8], uint64(s.chunk)) // Find first non-zero digit in big endian encoding of number of chunks i = 0 for buf[i] == 0 && i < 8 { i++ } buf[8] = byte(8 - i) // number of bytes to represent number of chunks. _, _ = s.stalk.Write(buf[i:]) _, _ = s.stalk.Write([]byte{0xff, 0xff}) } } return s.stalk.Read(p) } golang-github-cloudflare-circl-1.3.7/xof/k12/k12_test.go000066400000000000000000000064331454601126700226510ustar00rootroot00000000000000package k12 import ( "encoding/hex" "testing" ) // See draft-irtf-cfrg-kangarootwelve-10 §4. // https://datatracker.ietf.org/doc/draft-irtf-cfrg-kangarootwelve/10/ func ptn(n int) []byte { buf := make([]byte, n) for i := 0; i < n; i++ { buf[i] = byte(i % 0xfb) } return buf } func testK12(t *testing.T, msg []byte, c []byte, l int, want string) { do := func(lanes byte, writeSize int) { h := newDraft10(c, lanes) msg2 := msg for len(msg2) > 0 { to := writeSize if len(msg2) < to { to = len(msg2) } _, _ = h.Write(msg2[:to]) msg2 = msg2[to:] } buf := make([]byte, l) _, _ = h.Read(buf) got := hex.EncodeToString(buf) if want != got { t.Fatalf("%s != %s (lanes=%d, writeSize=%d )", want, got, lanes, writeSize) } } for _, lanes := range []byte{1, 2, 4} { for _, writeSize := range []int{7919, 1024, 8 * 1024} { do(lanes, writeSize) } } } func TestK12(t *testing.T) { // I-D test vectors testK12(t, []byte{}, []byte{}, 32, "1ac2d450fc3b4205d19da7bfca1b37513c0803577ac7167f06fe2ce1f0ef39e5") i := 17 testK12(t, ptn(i), []byte{}, 32, "6bf75fa2239198db4772e36478f8e19b0f371205f6a9a93a273f51df37122888") i *= 17 testK12(t, ptn(i), []byte{}, 32, "0c315ebcdedbf61426de7dcf8fb725d1e74675d7f5327a5067f367b108ecb67c") i *= 17 testK12(t, ptn(i), []byte{}, 32, "cb552e2ec77d9910701d578b457ddf772c12e322e4ee7fe417f92c758f0d59d0") i *= 17 testK12(t, ptn(i), []byte{}, 32, "8701045e22205345ff4dda05555cbb5c3af1a771c2b89baef37db43d9998b9fe") i *= 17 testK12(t, ptn(i), []byte{}, 32, "844d610933b1b9963cbdeb5ae3b6b05cc7cbd67ceedf883eb678a0a8e0371682") i *= 17 testK12(t, ptn(i), []byte{}, 32, "3c390782a8a4e89fa6367f72feaaf13255c8d95878481d3cd8ce85f58e880af8") testK12(t, []byte{}, ptn(1), 32, "fab658db63e94a246188bf7af69a133045f46ee984c56e3c3328caaf1aa1a583") testK12(t, []byte{0xff}, ptn(41), 32, "d848c5068ced736f4462159b9867fd4c20b808acc3d5bc48e0b06ba0a3762ec4") testK12(t, []byte{0xff, 0xff, 0xff}, ptn(41*41), 32, "c389e5009ae57120854c2e8c64670ac01358cf4c1baf89447a724234dc7ced74") testK12(t, []byte{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, ptn(41*41*41), 32, "75d2f86a2e644566726b4fbcfc5657b9dbcf070c7b0dca06450ab291d7443bcf") // Cornercases testK12(t, ptn(chunkSize), []byte{}, 16, "48f256f6772f9edfb6a8b661ec92dc93") testK12(t, ptn(chunkSize+1), []byte{}, 16, "bb66fe72eaea5179418d5295ee134485") testK12(t, ptn(2*chunkSize), []byte{}, 16, "82778f7f7234c83352e76837b721fbdb") testK12(t, ptn(2*chunkSize+1), []byte{}, 16, "5f8d2b943922b451842b4e82740d0236") testK12(t, ptn(3*chunkSize), []byte{}, 16, "f4082a8fe7d1635aa042cd1da63bf235") testK12(t, ptn(3*chunkSize+1), []byte{}, 16, "38cb940999aca742d69dd79298c6051c") } func BenchmarkK12_100B(b *testing.B) { benchmarkK12(b, 100, 1) } func BenchmarkK12_10K(b *testing.B) { benchmarkK12(b, 10000, 1) } func BenchmarkK12_100K(b *testing.B) { benchmarkK12(b, 10000, 10) } func BenchmarkK12_1M(b *testing.B) { benchmarkK12(b, 10000, 100) } func BenchmarkK12_10M(b *testing.B) { benchmarkK12(b, 10000, 1000) } func benchmarkK12(b *testing.B, size, num int) { b.StopTimer() h := NewDraft10([]byte{}) data := make([]byte, size) d := make([]byte, 32) b.SetBytes(int64(size * num)) b.StartTimer() for i := 0; i < b.N; i++ { h.Reset() for j := 0; j < num; j++ { _, _ = h.Write(data) } _, _ = h.Read(d) } } golang-github-cloudflare-circl-1.3.7/xof/xof.go000066400000000000000000000036421454601126700214130ustar00rootroot00000000000000// Package xof provides an interface for eXtendable-Output Functions. // // # Available Functions // // SHAKE functions are defined in FIPS-202, see https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf. // BLAKE2Xb and BLAKE2Xs are defined in https://www.blake2.net/blake2x.pdf. package xof import ( "io" "github.com/cloudflare/circl/internal/sha3" "github.com/cloudflare/circl/xof/k12" "golang.org/x/crypto/blake2b" "golang.org/x/crypto/blake2s" ) // XOF defines the interface to hash functions that support arbitrary-length output. type XOF interface { // Write absorbs more data into the XOF's state. It panics if called // after Read. io.Writer // Read reads more output from the XOF. It returns io.EOF if the limit // has been reached. io.Reader // Clone returns a copy of the XOF in its current state. Clone() XOF // Reset restores the XOF to its initial state and discards all data appended by Write. Reset() } type ID uint const ( SHAKE128 ID = iota + 1 SHAKE256 BLAKE2XB BLAKE2XS K12D10 ) func (x ID) New() XOF { switch x { case SHAKE128: s := sha3.NewShake128() return shakeBody{&s} case SHAKE256: s := sha3.NewShake256() return shakeBody{&s} case BLAKE2XB: x, _ := blake2b.NewXOF(blake2b.OutputLengthUnknown, nil) return blake2xb{x} case BLAKE2XS: x, _ := blake2s.NewXOF(blake2s.OutputLengthUnknown, nil) return blake2xs{x} case K12D10: x := k12.NewDraft10([]byte{}) return k12d10{&x} default: panic("crypto: requested unavailable XOF function") } } type shakeBody struct{ sha3.ShakeHash } func (s shakeBody) Clone() XOF { return shakeBody{s.ShakeHash.Clone()} } type blake2xb struct{ blake2b.XOF } func (s blake2xb) Clone() XOF { return blake2xb{s.XOF.Clone()} } type blake2xs struct{ blake2s.XOF } func (s blake2xs) Clone() XOF { return blake2xs{s.XOF.Clone()} } type k12d10 struct{ *k12.State } func (s k12d10) Clone() XOF { x := s.State.Clone() return k12d10{&x} } golang-github-cloudflare-circl-1.3.7/xof/xof_test.go000066400000000000000000000040121454601126700224420ustar00rootroot00000000000000package xof_test import ( "bytes" "encoding/hex" "io" "testing" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/xof" ) type vector struct { id xof.ID in, out string outLen int } var allVectors = []vector{ { id: xof.SHAKE128, in: "", out: "7f9c2ba4e88f827d616045507605853ed73b8093f6efbc88eb1a6eacfa66ef26", outLen: 32, }, { id: xof.SHAKE256, in: "", out: "46b9dd2b0ba88d13233b3feb743eeb243fcd52ea62b81b82b50c27646ed5762fd75dc4ddd8c0f200cb05019d67b592f6fc821c49479ab48640292eacb3b7c4be", outLen: 64, }, { id: xof.SHAKE128, in: "The quick brown fox jumps over the lazy dog", out: "f4202e3c5852f9182a0430fd8144f0a74b95e7417ecae17db0f8cfeed0e3e66e", outLen: 32, }, { id: xof.SHAKE128, in: "The quick brown fox jumps over the lazy dof", out: "853f4538be0db9621a6cea659a06c1107b1f83f02b13d18297bd39d7411cf10c", outLen: 32, }, { id: xof.BLAKE2XB, in: "The quick brown fox jumps over the lazy dog", out: "364e84ca4c103df292306c93ebba6f6633d5e9cc8a95e040498e9a012d5ca534", outLen: 32, }, { id: xof.BLAKE2XS, in: "The quick brown fox jumps over the lazy dog", out: "0650cde4df888a06eada0f0fecb3c17594304b4a03fdd678182f27db1238b174", outLen: 32, }, { id: xof.K12D10, in: "The quick brown fox jumps over the lazy dog", out: "b4f249b4f77c58df170aa4d1723db1127d82f1d98d25ddda561ada459cd11a48", outLen: 32, }, } func TestXof(t *testing.T) { for i, v := range allVectors { X := v.id.New() _, err := X.Write([]byte(v.in)) test.CheckNoErr(t, err, "error on xof.Write") got := make([]byte, v.outLen) want, _ := hex.DecodeString(v.out) for _, x := range []io.Reader{X, X.Clone()} { n, err := x.Read(got) test.CheckNoErr(t, err, "error on xof.Read") if n != v.outLen || !bytes.Equal(got, want) { test.ReportError(t, got, want, i, v.id) } } } err := test.CheckPanic(func() { var nonID xof.ID nonID.New() }) test.CheckNoErr(t, err, "must panic") } golang-github-cloudflare-circl-1.3.7/zk/000077500000000000000000000000001454601126700201135ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/zk/dl/000077500000000000000000000000001454601126700205125ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/zk/dl/dl.go000066400000000000000000000045301454601126700214420ustar00rootroot00000000000000// Package dl provides a Schnorr NIZK discrete-log proof. // // This package implements a Schnorr NIZK discrete-log proof obtained from the // interactive Schnorr identification scheme through a Fiat-Shamir transformation. // // Given (k,G,kG) the Prove function returns a Proof struct attesting that // kG = [k]G, which can be validated using the Verify function. // // The userID label is a unique identifier for the prover. // // The otherInfo label is defined to allow flexible inclusion of contextual // information in the Schnorr NIZK proof. // The otherInfo is also used as a domain separation tag (dst) for the hash // to scalar function. // // Reference: https://datatracker.ietf.org/doc/html/rfc8235 package dl import ( "encoding/binary" "io" "github.com/cloudflare/circl/group" ) type Proof struct { V group.Element R group.Scalar } func calcChallenge(myGroup group.Group, G, V, A group.Element, userID, otherInfo []byte) group.Scalar { // Hash transcript (G | V | A | UserID | OtherInfo) to get the random coin. GByte, errByte := G.MarshalBinary() if errByte != nil { panic(errByte) } VByte, errByte := V.MarshalBinary() if errByte != nil { panic(errByte) } AByte, errByte := A.MarshalBinary() if errByte != nil { panic(errByte) } uPrefix := [4]byte{} binary.BigEndian.PutUint32(uPrefix[:], uint32(len(userID))) oPrefix := [4]byte{} binary.BigEndian.PutUint32(oPrefix[:], uint32(len(otherInfo))) hashByte := append(append(append(append(append(append( GByte, VByte...), AByte...), uPrefix[:]...), userID...), oPrefix[:]...), otherInfo...) return myGroup.HashToScalar(hashByte, otherInfo) } // Prove returns a proof attesting that kG = [k]G. func Prove(myGroup group.Group, G, kG group.Element, k group.Scalar, userID, otherInfo []byte, rnd io.Reader) Proof { v := myGroup.RandomNonZeroScalar(rnd) V := myGroup.NewElement() V.Mul(G, v) c := calcChallenge(myGroup, G, V, kG, userID, otherInfo) r := myGroup.NewScalar() r.Sub(v, myGroup.NewScalar().Mul(k, c)) return Proof{V, r} } // Verify checks whether the proof attests that kG = [k]G. func Verify(myGroup group.Group, G, kG group.Element, p Proof, userID, otherInfo []byte) bool { c := calcChallenge(myGroup, G, p.V, kG, userID, otherInfo) rG := myGroup.NewElement() rG.Mul(G, p.R) ckG := myGroup.NewElement() ckG.Mul(kG, c) rG.Add(rG, ckG) return p.V.IsEqual(rG) } golang-github-cloudflare-circl-1.3.7/zk/dl/dl_test.go000066400000000000000000000025521454601126700225030ustar00rootroot00000000000000package dl_test import ( "crypto/rand" "testing" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/zk/dl" ) const testzkDLCount = 1 << 8 func testzkDL(t *testing.T, myGroup group.Group) { kA := myGroup.RandomNonZeroScalar(rand.Reader) DB := myGroup.RandomElement(rand.Reader) R := myGroup.NewElement() R.Mul(DB, kA) dst := "zeroknowledge" rnd := rand.Reader proof := dl.Prove(myGroup, DB, R, kA, []byte("Prover"), []byte(dst), rnd) verify := dl.Verify(myGroup, DB, R, proof, []byte("Prover"), []byte(dst)) if verify == false { t.Error("zk/dl verification failed") } } func testzkDLNegative(t *testing.T, myGroup group.Group) { kA := myGroup.RandomNonZeroScalar(rand.Reader) DB := myGroup.RandomElement(rand.Reader) R := myGroup.RandomElement(rand.Reader) dst := "zeroknowledge" rnd := rand.Reader proof := dl.Prove(myGroup, DB, R, kA, []byte("Prover"), []byte(dst), rnd) verify := dl.Verify(myGroup, DB, R, proof, []byte("Prover"), []byte(dst)) if verify == true { t.Error("zk/dl verification should fail") } } func TestZKDL(t *testing.T) { t.Run("zkDL", func(t *testing.T) { for i := 0; i < testzkDLCount; i++ { currGroup := group.P256 testzkDL(t, currGroup) } }) t.Run("zkDLNegative", func(t *testing.T) { for i := 0; i < testzkDLCount; i++ { currGroup := group.P256 testzkDLNegative(t, currGroup) } }) } golang-github-cloudflare-circl-1.3.7/zk/dleq/000077500000000000000000000000001454601126700210405ustar00rootroot00000000000000golang-github-cloudflare-circl-1.3.7/zk/dleq/dleq.go000066400000000000000000000141331454601126700223160ustar00rootroot00000000000000// Package dleq provides zero-knowledge proofs of Discrete-Logarithm Equivalence (DLEQ). // // This implementation is compatible with the one used for VOPRFs [1]. // It supports batching proofs to amortize the cost of the proof generation and // verification. // // References: // // [1] draft-irtf-cfrg-voprf: https://datatracker.ietf.org/doc/draft-irtf-cfrg-voprf package dleq import ( "crypto" "encoding/binary" "io" "github.com/cloudflare/circl/group" ) const ( labelSeed = "Seed-" labelChallenge = "Challenge" labelComposite = "Composite" labelHashToScalar = "HashToScalar-" ) type Params struct { G group.Group H crypto.Hash DST []byte } type Proof struct { c, s group.Scalar } type Prover struct{ Params } func (p Prover) Prove(k group.Scalar, a, ka, b, kb group.Element, rnd io.Reader) (*Proof, error) { return p.ProveBatch(k, a, ka, []group.Element{b}, []group.Element{kb}, rnd) } func (p Prover) ProveWithRandomness(k group.Scalar, a, ka, b, kb group.Element, rnd group.Scalar) (*Proof, error) { return p.ProveBatchWithRandomness(k, a, ka, []group.Element{b}, []group.Element{kb}, rnd) } func (p Prover) ProveBatch(k group.Scalar, a, ka group.Element, bi, kbi []group.Element, rnd io.Reader) (*Proof, error) { return p.ProveBatchWithRandomness(k, a, ka, bi, kbi, p.Params.G.RandomScalar(rnd)) } func (p Prover) ProveBatchWithRandomness( k group.Scalar, a, ka group.Element, bi, kbi []group.Element, rnd group.Scalar, ) (*Proof, error) { M, Z, err := p.computeComposites(k, ka, bi, kbi) if err != nil { return nil, err } kAm, err := ka.MarshalBinaryCompress() if err != nil { return nil, err } a0, err := M.MarshalBinaryCompress() if err != nil { return nil, err } a1, err := Z.MarshalBinaryCompress() if err != nil { return nil, err } t2 := p.G.NewElement().Mul(a, rnd) a2, err := t2.MarshalBinaryCompress() if err != nil { return nil, err } t3 := p.G.NewElement().Mul(M, rnd) a3, err := t3.MarshalBinaryCompress() if err != nil { return nil, err } cc := p.doChallenge([5][]byte{kAm, a0, a1, a2, a3}) ss := p.G.NewScalar() ss.Mul(cc, k) ss.Sub(rnd, ss) return &Proof{cc, ss}, nil } func (p Params) computeComposites( k group.Scalar, ka group.Element, bi []group.Element, kbi []group.Element, ) (m, z group.Element, err error) { kAm, err := ka.MarshalBinaryCompress() if err != nil { return nil, nil, err } lenBuf := []byte{0, 0} H := p.H.New() binary.BigEndian.PutUint16(lenBuf, uint16(len(kAm))) mustWrite(H, lenBuf) mustWrite(H, kAm) seedDST := append(append([]byte{}, labelSeed...), p.DST...) binary.BigEndian.PutUint16(lenBuf, uint16(len(seedDST))) mustWrite(H, lenBuf) mustWrite(H, seedDST) seed := H.Sum(nil) m = p.G.Identity() z = p.G.Identity() h2sDST := append(append([]byte{}, labelHashToScalar...), p.DST...) for j := range bi { h2Input := []byte{} Bij, err := bi[j].MarshalBinaryCompress() if err != nil { return nil, nil, err } kBij, err := kbi[j].MarshalBinaryCompress() if err != nil { return nil, nil, err } binary.BigEndian.PutUint16(lenBuf, uint16(len(seed))) h2Input = append(append(h2Input, lenBuf...), seed...) binary.BigEndian.PutUint16(lenBuf, uint16(j)) h2Input = append(h2Input, lenBuf...) binary.BigEndian.PutUint16(lenBuf, uint16(len(Bij))) h2Input = append(append(h2Input, lenBuf...), Bij...) binary.BigEndian.PutUint16(lenBuf, uint16(len(kBij))) h2Input = append(append(h2Input, lenBuf...), kBij...) h2Input = append(h2Input, labelComposite...) dj := p.G.HashToScalar(h2Input, h2sDST) Mj := p.G.NewElement() Mj.Mul(bi[j], dj) m.Add(m, Mj) if k == nil { Zj := p.G.NewElement() Zj.Mul(kbi[j], dj) z.Add(z, Zj) } } if k != nil { z.Mul(m, k) } return m, z, nil } func (p Params) doChallenge(a [5][]byte) group.Scalar { h2Input := []byte{} lenBuf := []byte{0, 0} for i := range a { binary.BigEndian.PutUint16(lenBuf, uint16(len(a[i]))) h2Input = append(append(h2Input, lenBuf...), a[i]...) } h2Input = append(h2Input, labelChallenge...) dst := append(append([]byte{}, labelHashToScalar...), p.DST...) return p.G.HashToScalar(h2Input, dst) } type Verifier struct{ Params } func (v Verifier) Verify(a, ka, b, kb group.Element, p *Proof) bool { return v.VerifyBatch(a, ka, []group.Element{b}, []group.Element{kb}, p) } func (v Verifier) VerifyBatch(a, ka group.Element, bi, kbi []group.Element, p *Proof) bool { g := v.Params.G M, Z, err := v.Params.computeComposites(nil, ka, bi, kbi) if err != nil { return false } sA := g.NewElement().Mul(a, p.s) ckA := g.NewElement().Mul(ka, p.c) t2 := g.NewElement().Add(sA, ckA) sM := g.NewElement().Mul(M, p.s) cZ := g.NewElement().Mul(Z, p.c) t3 := g.NewElement().Add(sM, cZ) kAm, err := ka.MarshalBinaryCompress() if err != nil { return false } a0, err := M.MarshalBinaryCompress() if err != nil { return false } a1, err := Z.MarshalBinaryCompress() if err != nil { return false } a2, err := t2.MarshalBinaryCompress() if err != nil { return false } a3, err := t3.MarshalBinaryCompress() if err != nil { return false } gotC := v.Params.doChallenge([5][]byte{kAm, a0, a1, a2, a3}) return gotC.IsEqual(p.c) } func (p *Proof) MarshalBinary() ([]byte, error) { g := p.c.Group() scalarSize := int(g.Params().ScalarLength) output := make([]byte, 0, 2*scalarSize) serC, err := p.c.MarshalBinary() if err != nil { return nil, err } output = append(output, serC...) serS, err := p.s.MarshalBinary() if err != nil { return nil, err } output = append(output, serS...) return output, nil } func (p *Proof) UnmarshalBinary(g group.Group, data []byte) error { scalarSize := int(g.Params().ScalarLength) if len(data) < 2*scalarSize { return io.ErrShortBuffer } c := g.NewScalar() err := c.UnmarshalBinary(data[:scalarSize]) if err != nil { return err } s := g.NewScalar() err = s.UnmarshalBinary(data[scalarSize : 2*scalarSize]) if err != nil { return err } p.c = c p.s = s return nil } func mustWrite(h io.Writer, bytes []byte) { bytesLen, err := h.Write(bytes) if err != nil { panic(err) } if len(bytes) != bytesLen { panic("dleq: failed to write on hash") } } golang-github-cloudflare-circl-1.3.7/zk/dleq/dleq_test.go000066400000000000000000000111131454601126700233500ustar00rootroot00000000000000package dleq_test import ( "bytes" "crypto" "crypto/rand" "fmt" "testing" "github.com/cloudflare/circl/group" "github.com/cloudflare/circl/internal/test" "github.com/cloudflare/circl/zk/dleq" ) func TestDLEQ(t *testing.T) { for _, g := range []group.Group{ group.P256, group.P384, group.P521, group.Ristretto255, } { t.Run(g.(fmt.Stringer).String(), func(t *testing.T) { params := dleq.Params{g, crypto.SHA256, []byte("domain_sep_string")} Peggy := dleq.Prover{params} Victor := dleq.Verifier{params} k := g.RandomScalar(rand.Reader) A := g.RandomElement(rand.Reader) kA := g.NewElement().Mul(A, k) B := g.RandomElement(rand.Reader) kB := g.NewElement().Mul(B, k) proof, err := Peggy.Prove(k, A, kA, B, kB, rand.Reader) test.CheckNoErr(t, err, "wrong proof generation") test.CheckOk(Victor.Verify(A, kA, B, kB, proof), "proof must verify", t) rr := g.RandomScalar(rand.Reader) proof, err = Peggy.ProveWithRandomness(k, A, kA, B, kB, rr) test.CheckNoErr(t, err, "wrong proof generation") test.CheckOk(Victor.Verify(A, kA, B, kB, proof), "proof must verify", t) const N = 4 C := make([]group.Element, N) kC := make([]group.Element, N) for i := 0; i < N; i++ { C[i] = g.RandomElement(rand.Reader) kC[i] = g.NewElement().Mul(C[i], k) } proof, err = Peggy.ProveBatch(k, A, kA, C, kC, rand.Reader) test.CheckNoErr(t, err, "wrong proof generation") test.CheckOk(Victor.VerifyBatch(A, kA, C, kC, proof), "proof must verify", t) testMarshal(t, g, proof) testErrors(t, &Peggy, &Victor, g, k, A, kA, B, kB) }) } } func testMarshal(t *testing.T, g group.Group, proof *dleq.Proof) { t.Helper() wantProofBytes, err := proof.MarshalBinary() test.CheckNoErr(t, err, "error on marshaling proof") gotProof := new(dleq.Proof) err = gotProof.UnmarshalBinary(g, wantProofBytes) test.CheckNoErr(t, err, "error on unmarshaling proof") gotProofBytes, err := gotProof.MarshalBinary() test.CheckNoErr(t, err, "error on marshaling proof") if !bytes.Equal(gotProofBytes, wantProofBytes) { test.ReportError(t, gotProofBytes, wantProofBytes) } } func testErrors( t *testing.T, Peggy *dleq.Prover, Victor *dleq.Verifier, g group.Group, k group.Scalar, a, ka, b, kb group.Element, ) { goodProof, err := Peggy.Prove(k, a, ka, b, kb, rand.Reader) test.CheckNoErr(t, err, "wrong proof generation") proofBytes, err := goodProof.MarshalBinary() test.CheckNoErr(t, err, "error on marshaling proof") // Tamper proof (in transit) _, _ = rand.Read(proofBytes) tamperedProof := new(dleq.Proof) err = tamperedProof.UnmarshalBinary(g, proofBytes[:5]) test.CheckIsErr(t, err, "unmarshal must fail") err = tamperedProof.UnmarshalBinary(g, proofBytes) test.CheckNoErr(t, err, "proof must be unmarshaled") test.CheckOk(false == Victor.Verify(a, ka, b, kb, tamperedProof), "proof must not verify", t) // Tamper elements bada := g.NewElement().Neg(a) test.CheckOk(false == Victor.Verify(bada, ka, b, kb, goodProof), "proof must not verify", t) badka := g.NewElement().Neg(ka) test.CheckOk(false == Victor.Verify(a, badka, b, kb, goodProof), "proof must not verify", t) badb := g.NewElement().Neg(b) test.CheckOk(false == Victor.Verify(a, ka, badb, kb, goodProof), "proof must not verify", t) badkb := g.NewElement().Neg(kb) test.CheckOk(false == Victor.Verify(a, ka, b, badkb, goodProof), "proof must not verify", t) } func BenchmarkDLEQ(b *testing.B) { g := group.P256 params := dleq.Params{g, crypto.SHA256, []byte("domain_sep_string")} Peggy := dleq.Prover{params} Victor := dleq.Verifier{params} k := g.RandomScalar(rand.Reader) A := g.Generator() kA := g.NewElement().MulGen(k) B := g.RandomElement(rand.Reader) kB := g.NewElement().Mul(B, k) rr := g.RandomScalar(rand.Reader) proof, _ := Peggy.ProveWithRandomness(k, A, kA, B, kB, rr) const N = 4 C := make([]group.Element, N) kC := make([]group.Element, N) for i := 0; i < N; i++ { C[i] = g.RandomElement(rand.Reader) kC[i] = g.NewElement().Mul(C[i], k) } proofBatched, _ := Peggy.ProveBatchWithRandomness(k, A, kA, C, kC, rr) b.Run("Prove", func(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = Peggy.ProveWithRandomness(k, A, kA, B, kB, rr) } }) b.Run("Verify", func(b *testing.B) { for i := 0; i < b.N; i++ { _ = Victor.Verify(A, kA, B, kB, proof) } }) b.Run(fmt.Sprint("ProveBatch=", N), func(b *testing.B) { for i := 0; i < b.N; i++ { _, _ = Peggy.ProveBatchWithRandomness(k, A, kA, C, kC, rr) } }) b.Run(fmt.Sprint("VerifyBatch=", N), func(b *testing.B) { for i := 0; i < b.N; i++ { _ = Victor.VerifyBatch(A, kA, C, kC, proofBatched) } }) } golang-github-cloudflare-circl-1.3.7/zk/doc.go000066400000000000000000000001251454601126700212050ustar00rootroot00000000000000// Package zk provides primitives for zero-knowledge proofs of knowledge. package zk

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