ed25519-0.0.5.0/0000755000000000000000000000000012606567661011055 5ustar0000000000000000ed25519-0.0.5.0/AUTHORS.txt0000644000000000000000000000011112606567661012734 0ustar0000000000000000Author, target of blame: Austin Seipp ed25519-0.0.5.0/ed25519.cabal0000644000000000000000000000764112606567661013047 0ustar0000000000000000name: ed25519 version: 0.0.5.0 category: Cryptography license: MIT synopsis: Ed25519 cryptographic signatures homepage: http://thoughtpolice.github.com/hs-ed25519 bug-reports: http://github.com/thoughtpolice/hs-ed25519/issues license-file: LICENSE.txt copyright: Copyright (c) Austin Seipp 2013-2015 author: Austin Seipp maintainer: Austin Seipp build-type: Simple cabal-version: >=1.10 tested-with: GHC == 7.0.1, GHC == 7.0.2, GHC == 7.0.3, GHC == 7.0.4, GHC == 7.2.1, GHC == 7.2.2, GHC == 7.4.1, GHC == 7.4.2, GHC == 7.6.1, GHC == 7.6.2, GHC == 7.6.3, GHC == 7.8.2, GHC == 7.8.3, GHC == 7.8.4, GHC == 7.10.1, GHC == 7.10.2 description: This package provides a simple, fast, self-contained copy of the Ed25519 public-key signature system with a clean interface. It also includes support for detached signatures, and thorough documentation on the design and implementation, including usage guidelines. extra-source-files: .travis.yml AUTHORS.txt README.md CONTRIBUTING.md CHANGELOG.md src/cbits/ref10/*.c src/cbits/ref10/include/*.h source-repository head type: git location: https://github.com/thoughtpolice/hs-ed25519.git ------------------------------------------------------------------------------- -- Flags flag test-properties default: True manual: True flag test-hlint default: True manual: True flag test-doctests default: True manual: True flag no-donna default: True manual: True ------------------------------------------------------------------------------- -- Build pt 1: main project library build-depends: ghc-prim >= 0.1 && < 0.5, base >= 4 && < 5, bytestring >= 0.9 && < 0.11 exposed-modules: Crypto.Sign.Ed25519 ghc-options: -Wall -fwarn-tabs default-language: Haskell2010 hs-source-dirs: src -- Choose the underlying C implementation if flag(no-donna) -- ref10 implementation from SUPERCOP, about 2x slower than the AMD64 -- SUPERCOP implementations, 15x faster than ronald3072 for signing. c-sources: src/cbits/ref10/ed25519.c include-dirs: src/cbits/ref10 src/cbits/ref10/include else -- TODO(aseipp): ed25519-donna import buildable: False ------------------------------------------------------------------------------- -- Build pt 2: Tests test-suite properties type: exitcode-stdio-1.0 main-is: properties.hs ghc-options: -w hs-source-dirs: tests default-language: Haskell2010 if !flag(test-properties) buildable: False else build-depends: base >= 4 && < 5, bytestring >= 0.9 && < 0.11, QuickCheck >= 2.4 && < 2.9, ed25519 -- -- Style/doc tests below -- test-suite hlint type: exitcode-stdio-1.0 main-is: hlint.hs hs-source-dirs: tests default-language: Haskell2010 if !flag(test-hlint) buildable: False else build-depends: base >= 4 && < 5, hlint >= 1.7 && < 1.10 test-suite doctests type: exitcode-stdio-1.0 main-is: doctests.hs hs-source-dirs: tests default-language: Haskell2010 if !flag(test-doctests) buildable: False else build-depends: base >= 4 && < 5, filepath >= 1.0 && < 1.5, directory >= 1.0 && < 1.3, doctest >= 0.10 && < 0.11 ------------------------------------------------------------------------------- -- Build pt 3: benchmarks benchmark bench type: exitcode-stdio-1.0 build-depends: base >= 4 && < 5, bytestring >= 0.9 && < 0.11, criterion >= 0.8 && < 1.2, deepseq >= 1.3 && < 1.5, ed25519 default-language: Haskell2010 hs-source-dirs: benchmarks main-is: bench.hs ed25519-0.0.5.0/Setup.hs0000644000000000000000000000011012606567661012501 0ustar0000000000000000#!/usr/bin/env runhaskell import Distribution.Simple main = defaultMain ed25519-0.0.5.0/.travis.yml0000644000000000000000000001234212606567661013170 0ustar0000000000000000# NB: don't set `language: haskell` here language: c # See also https://github.com/hvr/multi-ghc-travis for more information # The following lines enable several GHC versions and/or HP versions # to be tested; often it's enough to test only against the last # release of a major GHC version. Setting HPVER implictly sets # GHCVER. Omit lines with versions you don't need/want testing for. env: #- CABALVER=1.16 GHCVER=6.12.3 - CABALVER=1.16 GHCVER=7.0.1 - CABALVER=1.16 GHCVER=7.0.2 - CABALVER=1.16 GHCVER=7.0.3 - CABALVER=1.16 GHCVER=7.0.4 - CABALVER=1.16 GHCVER=7.2.1 - CABALVER=1.16 GHCVER=7.2.2 - CABALVER=1.16 GHCVER=7.4.1 - CABALVER=1.16 GHCVER=7.4.2 - CABALVER=1.16 GHCVER=7.6.1 - CABALVER=1.16 GHCVER=7.6.2 - CABALVER=1.18 GHCVER=7.6.3 - CABALVER=1.18 GHCVER=7.8.1 - CABALVER=1.18 GHCVER=7.8.2 - CABALVER=1.18 GHCVER=7.8.3 - CABALVER=1.18 GHCVER=7.8.4 - CABALVER=1.22 GHCVER=7.10.1 - CABALVER=1.22 GHCVER=7.10.2 - CABALVER=head GHCVER=head - HPVER=2013.2.0.0 - HPVER=2012.4.0.0 - HPVER=2012.2.0.0 - HPVER=2011.4.0.0 matrix: allow_failures: - env: CABALVER=head GHCVER=head # Note: the distinction between `before_install` and `install` is not # important. before_install: - case "$HPVER" in "") ;; "2014.2.0.0") export CABALVER=1.18 ; export GHCVER=7.8.3 ; echo "constraints:async==2.0.1.5,attoparsec==0.10.4.0,case-insensitive==1.1.0.3,fgl==5.5.0.1,GLUT==2.5.1.1,GLURaw==1.4.0.1,haskell-src==1.0.1.6,hashable==1.2.2.0,html==1.0.1.2,HTTP==4000.2.10,HUnit==1.2.5.2,mtl==2.1.3.1,network==2.4.2.3,OpenGL==2.9.2.0,OpenGLRaw==1.5.0.0,parallel==3.2.0.4,parsec==3.1.5,primitive==0.5.2.1,QuickCheck==2.6,random==1.0.1.1,regex-base==0.93.2,regex-compat==0.95.1,regex-posix==0.95.2,split==0.2.2,stm==2.4.2,syb==0.4.1,text==1.1.0.0,transformers==0.3.0.0,unordered-containers==0.2.4.0,vector==0.10.9.1,xhtml==3000.2.1,zlib==0.5.4.1" > cabal.config ;; "2013.2.0.0") export CABALVER=1.16 ; export GHCVER=7.6.3 ; echo "constraints:async==2.0.1.4,attoparsec==0.10.4.0,case-insensitive==1.0.0.1,cgi==3001.1.7.5,fgl==5.4.2.4,GLUT==2.4.0.0,GLURaw==1.3.0.0,haskell-src==1.0.1.5,hashable==1.1.2.5,html==1.0.1.2,HTTP==4000.2.8,HUnit==1.2.5.2,mtl==2.1.2,network==2.4.1.2,OpenGL==2.8.0.0,OpenGLRaw==1.3.0.0,parallel==3.2.0.3,parsec==3.1.3,QuickCheck==2.6,random==1.0.1.1,regex-base==0.93.2,regex-compat==0.95.1,regex-posix==0.95.2,split==0.2.2,stm==2.4.2,syb==0.4.0,text==0.11.3.1,transformers==0.3.0.0,unordered-containers==0.2.3.0,vector==0.10.0.1,xhtml==3000.2.1,zlib==0.5.4.1" > cabal.config ;; "2012.4.0.0") export CABALVER=1.16 ; export GHCVER=7.6.2 ; echo "constraints:async==2.0.1.3,cgi==3001.1.7.4,fgl==5.4.2.4,GLUT==2.1.2.1,haskell-src==1.0.1.5,html==1.0.1.2,HTTP==4000.2.5,HUnit==1.2.5.1,mtl==2.1.2,network==2.3.1.0,OpenGL==2.2.3.1,parallel==3.2.0.3,parsec==3.1.3,QuickCheck==2.5.1.1,random==1.0.1.1,regex-base==0.93.2,regex-compat==0.95.1,regex-posix==0.95.2,split==0.2.1.1,stm==2.4,syb==0.3.7,text==0.11.2.3,transformers==0.3.0.0,vector==0.10.0.1,xhtml==3000.2.1,zlib==0.5.4.0" > cabal.config ;; "2012.2.0.0") export CABALVER=1.16 ; export GHCVER=7.4.1 ; echo "constraints:cgi==3001.1.7.4,fgl==5.4.2.4,GLUT==2.1.2.1,haskell-src==1.0.1.5,html==1.0.1.2,HTTP==4000.2.3,HUnit==1.2.4.2,mtl==2.1.1,network==2.3.0.13,OpenGL==2.2.3.1,parallel==3.2.0.2,parsec==3.1.2,QuickCheck==2.4.2,random==1.0.1.1,regex-base==0.93.2,regex-compat==0.95.1,regex-posix==0.95.1,stm==2.3,syb==0.3.6.1,text==0.11.2.0,transformers==0.3.0.0,xhtml==3000.2.1,zlib==0.5.3.3" > cabal.config ;; "2011.4.0.0") export CABALVER=1.16 ; export GHCVER=7.0.4 ; echo "constraints:cgi==3001.1.7.4,fgl==5.4.2.4,GLUT==2.1.2.1,haskell-src==1.0.1.4,html==1.0.1.2,HUnit==1.2.4.2,network==2.3.0.5,OpenGL==2.2.3.0,parallel==3.1.0.1,parsec==3.1.1,QuickCheck==2.4.1.1,regex-base==0.93.2,regex-compat==0.95.1,regex-posix==0.95.1,stm==2.2.0.1,syb==0.3.3,xhtml==3000.2.0.4,zlib==0.5.3.1,HTTP==4000.1.2,deepseq==1.1.0.2" > cabal.config ;; *) export GHCVER=unknown ; echo "unknown/invalid Haskell Platform requested" ; exit 1 ;; esac - travis_retry sudo add-apt-repository -y ppa:hvr/ghc - travis_retry sudo apt-get update - travis_retry sudo apt-get install cabal-install-$CABALVER ghc-$GHCVER - export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$PATH install: - cabal --version - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]" - travis_retry cabal update - cabal install --only-dependencies --enable-tests -f-test-hlint -f-test-doctests # Here starts the actual work to be performed for the package under # test; any command which exits with a non-zero exit code causes the # build to fail. script: - if [ -f configure.ac ]; then autoreconf -i; fi # -v2 provides useful information for debugging - cabal configure --enable-tests -f-test-hlint -f-test-doctests -v2 # this builds all libraries and executables # (including tests/benchmarks) - cabal build - cabal test - cabal check # tests that a source-distribution can be generated - cabal sdist # check that the generated source-distribution can be built & installed - SRC_TGZ=$(cabal info . | awk '{print $2;exit}').tar.gz && (cd dist && cabal install --force-reinstalls "$SRC_TGZ") # EOF ed25519-0.0.5.0/README.md0000644000000000000000000000357512606567661012346 0ustar0000000000000000# Minimal package for ed25519 signatures [![Build Status](https://travis-ci.org/thoughtpolice/hs-ed25519.png?branch=master)](https://travis-ci.org/thoughtpolice/hs-ed25519) [![MIT](http://b.repl.ca/v1/license-MIT-blue.png)](http://en.wikipedia.org/wiki/MIT_License) [![Haskell](http://b.repl.ca/v1/language-haskell-lightgrey.png)](http://www.haskell.org) This package implements minimal bindings to the [ed25519][] signature scheme. It's designed to be small, with no dependencies, and fast. It also comes with extensive guidelines and detailed documentation. It should be relatively easy to both depend on directly with Cabal or even copy into any projects that need it directly. For full details (including notes on the underlying implementation), check out [the docs][]. [ed25519]: http://ed25519.cr.yp.to/ [SUPERCOP]: http://bench.cr.yp.to/supercop.html [the docs]: http://hackage.haskell.org/package/ed25519/docs/Crypto-Sign-Ed25519.html # Installation It's just a `cabal install` away on [Hackage][]: ```bash $ cabal install ed25519 ``` # Join in Be sure to read the [contributing guidelines][contribute]. File bugs in the GitHub [issue tracker][]. Master [git repository][gh]: * `git clone https://github.com/thoughtpolice/hs-ed25519.git` There's also a [BitBucket mirror][bb]: * `git clone https://bitbucket.org/thoughtpolice/hs-ed25519.git` # Authors See [AUTHORS.txt](https://raw.github.com/thoughtpolice/hs-ed25519/master/AUTHORS.txt). # License MIT. See [LICENSE.txt](https://raw.github.com/thoughtpolice/hs-ed25519/master/LICENSE.txt) for terms of copyright and redistribution. [contribute]: https://github.com/thoughtpolice/hs-ed25519/blob/master/CONTRIBUTING.md [issue tracker]: http://github.com/thoughtpolice/hs-ed25519/issues [gh]: http://github.com/thoughtpolice/hs-ed25519 [bb]: http://bitbucket.org/thoughtpolice/hs-ed25519 [Hackage]: http://hackage.haskell.org/package/ed25519 ed25519-0.0.5.0/LICENSE.txt0000644000000000000000000000204512606567661012701 0ustar0000000000000000Copyright (c) 2013-2015 Austin Seipp Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ed25519-0.0.5.0/CHANGELOG.md0000644000000000000000000000250212606567661012665 0ustar00000000000000000.0.5.0 ------- * Added doctests and crash course introduction. * Fixed some bugs in the test harnesses. * Fixed some `hlint` gripes. * Minor touchups elsewhere. 0.0.4.0 ------- * `Crypto.Sign.Ed25519` is now marked `-XTrustworthy`. * There is now a `Generic` instance for `Signature` on GHC 7.2 and above. * **DEPRECATED**: `createKeypairFromSeed` due to unsafety. - Use `createKeypairFromSeed_` instead, which will return a `Maybe`. * **DEPRECATED**: `sign'` and `verify'` for bad naming - Use `dsign` and `dverify` instead. * Improve benchmarks. * Huge overhaul to documentation, including design and implementation notes. 0.0.3.0 ------- * Tighten dependencies everywhere for cleaner builds. * Fix old code (including compatibility with newer `QuickCheck` versions) * New API: `toPublicKey :: SecretKey -> PublicKey` - Used to derive the public key for a given secret key * New API: `createKeypairFromSeed :: ByteString -> (PublicKey, SecretKey)` - Used to create a deterministic Ed25519 keypair from a 32-byte seed. * For GHC 7.2 and above, both `PublicKey` and `SecretKey` are now instances of `Generic`. * Improved documentation. * Various cleanups and some fixes in the tests and benchmarks. 0.0.2.0 ------- * Portability improvements. 0.0.1.0 ------- * Initial release. ed25519-0.0.5.0/CONTRIBUTING.md0000644000000000000000000000326612606567661013315 0ustar0000000000000000# Contributing ## Commits Rules for contribution: * 80-character column maximum. * The first line of a commit message should be 73 columns max. * Try to make commits self contained. One thing at a time. If it's a branch, squash the commits together to make one. * Always run tests. If benchmarks regress, give OS information, and we'll discuss. * Always reference the issue you're working on in the bug tracker in your commit message, and if it fixes the issue, close it. You can use GitHub pull requests OR just email me patches directly (see `git format-patch --help`,) whatever you are more comfortable with. One nice aspect of submitting a pull request is that [travis-ci.org](http://travis-ci.org) bots will automatically merge, build and run tests against your commits, and continue as you update the request, so you can be sure you didn't typo stuff or something before a final merge. For multi-commit requests, I will often squash them into the smallest possible logical changes and commit with author attribution. ### Notes on sign-offs and attributions, etc. When you commit, **please use -s to add a Signed-off-by line**. I manage the `Signed-off-by` line much like Git itself: by adding it, you make clear that the contributed code abides by the source code license. I'm pretty much always going to want you to do this. I normally merge commits manually and give the original author attribution via `git commit --author`. I also sign-off on it, and add an `Acked-by` field which basically states "this commit is not totally ludicrous." Other fields may be added in the same vein for attribution or other purposes (`Suggested-by`, `Reviewed-by`, etc.) ## Hacker notes N/A. ed25519-0.0.5.0/benchmarks/0000755000000000000000000000000012606567661013172 5ustar0000000000000000ed25519-0.0.5.0/benchmarks/bench.hs0000644000000000000000000000253212606567661014607 0ustar0000000000000000{-# LANGUAGE CPP #-} module Main ( main -- :: IO () ) where import Criterion.Main import Crypto.Sign.Ed25519 import Data.Maybe (fromJust) import Control.DeepSeq import qualified Data.ByteString as B -------------------------------------------------------------------------------- #if !MIN_VERSION_bytestring(0,10,0) instance NFData B.ByteString #endif instance NFData SecretKey instance NFData PublicKey -------------------------------------------------------------------------------- main :: IO () main = do -- Don't use `createKeypair`, since that will incur a ton of calls -- to the OS to generate randomness. Simply generate a bogus Ed25519 -- seed instead. let seed = B.pack [0..31] keys@(pk,sk) = fromJust (createKeypairFromSeed_ seed) -- Generate a dummy message to sign, and a signature to verify -- against. dummy = B.pack [0..255] msg = sign sk dummy defaultMain [ bench "deterministic key generation" $ nf createKeypairFromSeed_ seed , bench "signing a 256 byte message" $ nf (sign sk) dummy , bench "verifying a signature" $ nf (verify pk) msg , bench "roundtrip 256-byte sign/verify" $ nf (signBench keys) dummy ] signBench :: (PublicKey, SecretKey) -> B.ByteString -> Bool signBench (pk, sk) xs = verify pk (sign sk xs) ed25519-0.0.5.0/src/0000755000000000000000000000000012606567661011644 5ustar0000000000000000ed25519-0.0.5.0/src/cbits/0000755000000000000000000000000012606567661012750 5ustar0000000000000000ed25519-0.0.5.0/src/cbits/ref10/0000755000000000000000000000000012606567661013665 5ustar0000000000000000ed25519-0.0.5.0/src/cbits/ref10/fe_tobytes.c0000644000000000000000000000620312606567661016175 0ustar0000000000000000#include "fe.h" /* Preconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Write p=2^255-19; q=floor(h/p). Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). Proof: Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). Then 0> 25; q = (h0 + q) >> 26; q = (h1 + q) >> 25; q = (h2 + q) >> 26; q = (h3 + q) >> 25; q = (h4 + q) >> 26; q = (h5 + q) >> 25; q = (h6 + q) >> 26; q = (h7 + q) >> 25; q = (h8 + q) >> 26; q = (h9 + q) >> 25; /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ h0 += 19 * q; /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = h9 >> 25; h9 -= carry9 << 25; /* h10 = carry9 */ /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. Have h0+...+2^230 h9 between 0 and 2^255-1; evidently 2^255 h10-2^255 q = 0. Goal: Output h0+...+2^230 h9. */ s[0] = h0 >> 0; s[1] = h0 >> 8; s[2] = h0 >> 16; s[3] = (h0 >> 24) | (h1 << 2); s[4] = h1 >> 6; s[5] = h1 >> 14; s[6] = (h1 >> 22) | (h2 << 3); s[7] = h2 >> 5; s[8] = h2 >> 13; s[9] = (h2 >> 21) | (h3 << 5); s[10] = h3 >> 3; s[11] = h3 >> 11; s[12] = (h3 >> 19) | (h4 << 6); s[13] = h4 >> 2; s[14] = h4 >> 10; s[15] = h4 >> 18; s[16] = h5 >> 0; s[17] = h5 >> 8; s[18] = h5 >> 16; s[19] = (h5 >> 24) | (h6 << 1); s[20] = h6 >> 7; s[21] = h6 >> 15; s[22] = (h6 >> 23) | (h7 << 3); s[23] = h7 >> 5; s[24] = h7 >> 13; s[25] = (h7 >> 21) | (h8 << 4); s[26] = h8 >> 4; s[27] = h8 >> 12; s[28] = (h8 >> 20) | (h9 << 6); s[29] = h9 >> 2; s[30] = h9 >> 10; s[31] = h9 >> 18; } ed25519-0.0.5.0/src/cbits/ref10/fe_copy.c0000644000000000000000000000072412606567661015460 0ustar0000000000000000#include "fe.h" /* h = f */ static inline void fe_copy(fe h,const fe f) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; h[0] = f0; h[1] = f1; h[2] = f2; h[3] = f3; h[4] = f4; h[5] = f5; h[6] = f6; h[7] = f7; h[8] = f8; h[9] = f9; } ed25519-0.0.5.0/src/cbits/ref10/fe_1.c0000644000000000000000000000027012606567661014642 0ustar0000000000000000#include "fe.h" /* h = 1 */ static inline void fe_1(fe h) { h[0] = 1; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } ed25519-0.0.5.0/src/cbits/ref10/ge_tobytes.c0000644000000000000000000000035712606567661016202 0ustar0000000000000000#include "ge.h" static inline void ge_tobytes(unsigned char *s,const ge_p2 *h) { fe recip; fe x; fe y; fe_invert(recip,h->Z); fe_mul(x,h->X,recip); fe_mul(y,h->Y,recip); fe_tobytes(s,y); s[31] ^= fe_isnegative(x) << 7; } ed25519-0.0.5.0/src/cbits/ref10/sign.c0000644000000000000000000000143512606567661014774 0ustar0000000000000000#include "ed25519.h" #include "sha512.h" #include "ge.h" #include "sc.h" int ed25519_sign( unsigned char *sm,unsigned long long *smlen, const unsigned char *m,unsigned long long mlen, const unsigned char *sk ) { unsigned char az[64]; unsigned char r[64]; unsigned char hram[64]; ge_p3 R; unsigned long long i; crypto_hash_sha512(az,sk,32); az[0] &= 248; az[31] &= 63; az[31] |= 64; *smlen = mlen + 64; for (i = 0;i < mlen;++i) sm[64 + i] = m[i]; for (i = 0;i < 32;++i) sm[32 + i] = az[32 + i]; crypto_hash_sha512(r,sm + 32,mlen + 32); for (i = 0;i < 32;++i) sm[32 + i] = sk[32 + i]; sc_reduce(r); ge_scalarmult_base(&R,r); ge_p3_tobytes(sm,&R); crypto_hash_sha512(hram,sm,mlen + 64); sc_reduce(hram); sc_muladd(sm + 32,hram,az,r); return 0; } ed25519-0.0.5.0/src/cbits/ref10/fe_sq2.c0000644000000000000000000001375012606567661015216 0ustar0000000000000000#include "fe.h" #include "crypto_int64.h" /* h = 2 * f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ static inline void fe_sq2(fe h,const fe f) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; crypto_int32 f0_2 = 2 * f0; crypto_int32 f1_2 = 2 * f1; crypto_int32 f2_2 = 2 * f2; crypto_int32 f3_2 = 2 * f3; crypto_int32 f4_2 = 2 * f4; crypto_int32 f5_2 = 2 * f5; crypto_int32 f6_2 = 2 * f6; crypto_int32 f7_2 = 2 * f7; crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */ crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */ crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */ crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */ crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */ crypto_int64 f0f0 = f0 * (crypto_int64) f0; crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1; crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2; crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3; crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4; crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5; crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6; crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7; crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8; crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9; crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1; crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2; crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2; crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4; crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2; crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6; crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2; crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8; crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38; crypto_int64 f2f2 = f2 * (crypto_int64) f2; crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3; crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4; crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5; crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6; crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7; crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19; crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38; crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3; crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4; crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2; crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6; crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38; crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19; crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38; crypto_int64 f4f4 = f4 * (crypto_int64) f4; crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5; crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19; crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38; crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19; crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38; crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38; crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19; crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38; crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19; crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38; crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19; crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38; crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19; crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38; crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38; crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19; crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38; crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19; crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38; crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38; crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; crypto_int64 carry0; crypto_int64 carry1; crypto_int64 carry2; crypto_int64 carry3; crypto_int64 carry4; crypto_int64 carry5; crypto_int64 carry6; crypto_int64 carry7; crypto_int64 carry8; crypto_int64 carry9; h0 += h0; h1 += h1; h2 += h2; h3 += h3; h4 += h4; h5 += h5; h6 += h6; h7 += h7; h8 += h8; h9 += h9; carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } ed25519-0.0.5.0/src/cbits/ref10/fe_cmov.c0000644000000000000000000000242112606567661015446 0ustar0000000000000000#include "fe.h" /* Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0. Preconditions: b in {0,1}. */ static inline void fe_cmov(fe f,const fe g,unsigned int b) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; crypto_int32 g0 = g[0]; crypto_int32 g1 = g[1]; crypto_int32 g2 = g[2]; crypto_int32 g3 = g[3]; crypto_int32 g4 = g[4]; crypto_int32 g5 = g[5]; crypto_int32 g6 = g[6]; crypto_int32 g7 = g[7]; crypto_int32 g8 = g[8]; crypto_int32 g9 = g[9]; crypto_int32 x0 = f0 ^ g0; crypto_int32 x1 = f1 ^ g1; crypto_int32 x2 = f2 ^ g2; crypto_int32 x3 = f3 ^ g3; crypto_int32 x4 = f4 ^ g4; crypto_int32 x5 = f5 ^ g5; crypto_int32 x6 = f6 ^ g6; crypto_int32 x7 = f7 ^ g7; crypto_int32 x8 = f8 ^ g8; crypto_int32 x9 = f9 ^ g9; b = -b; x0 &= b; x1 &= b; x2 &= b; x3 &= b; x4 &= b; x5 &= b; x6 &= b; x7 &= b; x8 &= b; x9 &= b; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; } ed25519-0.0.5.0/src/cbits/ref10/ge_p1p1_to_p3.c0000644000000000000000000000030612606567661016370 0ustar0000000000000000#include "ge.h" /* r = p */ static inline void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p) { fe_mul(r->X,p->X,p->T); fe_mul(r->Y,p->Y,p->Z); fe_mul(r->Z,p->Z,p->T); fe_mul(r->T,p->X,p->Y); } ed25519-0.0.5.0/src/cbits/ref10/ge_p3_dbl.c0000644000000000000000000000022112606567661015642 0ustar0000000000000000#include "ge.h" /* r = 2 * p */ static inline void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p) { ge_p2 q; ge_p3_to_p2(&q,p); ge_p2_dbl(r,&q); } ed25519-0.0.5.0/src/cbits/ref10/fe_mul.c0000644000000000000000000002500612606567661015303 0ustar0000000000000000#include "fe.h" #include "crypto_int64.h" /* h = f * g Can overlap h with f or g. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* Notes on implementation strategy: Using schoolbook multiplication. Karatsuba would save a little in some cost models. Most multiplications by 2 and 19 are 32-bit precomputations; cheaper than 64-bit postcomputations. There is one remaining multiplication by 19 in the carry chain; one *19 precomputation can be merged into this, but the resulting data flow is considerably less clean. There are 12 carries below. 10 of them are 2-way parallelizable and vectorizable. Can get away with 11 carries, but then data flow is much deeper. With tighter constraints on inputs can squeeze carries into int32. */ static inline void fe_mul(fe h,const fe f,const fe g) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; crypto_int32 g0 = g[0]; crypto_int32 g1 = g[1]; crypto_int32 g2 = g[2]; crypto_int32 g3 = g[3]; crypto_int32 g4 = g[4]; crypto_int32 g5 = g[5]; crypto_int32 g6 = g[6]; crypto_int32 g7 = g[7]; crypto_int32 g8 = g[8]; crypto_int32 g9 = g[9]; crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */ crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ crypto_int32 g3_19 = 19 * g3; crypto_int32 g4_19 = 19 * g4; crypto_int32 g5_19 = 19 * g5; crypto_int32 g6_19 = 19 * g6; crypto_int32 g7_19 = 19 * g7; crypto_int32 g8_19 = 19 * g8; crypto_int32 g9_19 = 19 * g9; crypto_int32 f1_2 = 2 * f1; crypto_int32 f3_2 = 2 * f3; crypto_int32 f5_2 = 2 * f5; crypto_int32 f7_2 = 2 * f7; crypto_int32 f9_2 = 2 * f9; crypto_int64 f0g0 = f0 * (crypto_int64) g0; crypto_int64 f0g1 = f0 * (crypto_int64) g1; crypto_int64 f0g2 = f0 * (crypto_int64) g2; crypto_int64 f0g3 = f0 * (crypto_int64) g3; crypto_int64 f0g4 = f0 * (crypto_int64) g4; crypto_int64 f0g5 = f0 * (crypto_int64) g5; crypto_int64 f0g6 = f0 * (crypto_int64) g6; crypto_int64 f0g7 = f0 * (crypto_int64) g7; crypto_int64 f0g8 = f0 * (crypto_int64) g8; crypto_int64 f0g9 = f0 * (crypto_int64) g9; crypto_int64 f1g0 = f1 * (crypto_int64) g0; crypto_int64 f1g1_2 = f1_2 * (crypto_int64) g1; crypto_int64 f1g2 = f1 * (crypto_int64) g2; crypto_int64 f1g3_2 = f1_2 * (crypto_int64) g3; crypto_int64 f1g4 = f1 * (crypto_int64) g4; crypto_int64 f1g5_2 = f1_2 * (crypto_int64) g5; crypto_int64 f1g6 = f1 * (crypto_int64) g6; crypto_int64 f1g7_2 = f1_2 * (crypto_int64) g7; crypto_int64 f1g8 = f1 * (crypto_int64) g8; crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19; crypto_int64 f2g0 = f2 * (crypto_int64) g0; crypto_int64 f2g1 = f2 * (crypto_int64) g1; crypto_int64 f2g2 = f2 * (crypto_int64) g2; crypto_int64 f2g3 = f2 * (crypto_int64) g3; crypto_int64 f2g4 = f2 * (crypto_int64) g4; crypto_int64 f2g5 = f2 * (crypto_int64) g5; crypto_int64 f2g6 = f2 * (crypto_int64) g6; crypto_int64 f2g7 = f2 * (crypto_int64) g7; crypto_int64 f2g8_19 = f2 * (crypto_int64) g8_19; crypto_int64 f2g9_19 = f2 * (crypto_int64) g9_19; crypto_int64 f3g0 = f3 * (crypto_int64) g0; crypto_int64 f3g1_2 = f3_2 * (crypto_int64) g1; crypto_int64 f3g2 = f3 * (crypto_int64) g2; crypto_int64 f3g3_2 = f3_2 * (crypto_int64) g3; crypto_int64 f3g4 = f3 * (crypto_int64) g4; crypto_int64 f3g5_2 = f3_2 * (crypto_int64) g5; crypto_int64 f3g6 = f3 * (crypto_int64) g6; crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19; crypto_int64 f3g8_19 = f3 * (crypto_int64) g8_19; crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19; crypto_int64 f4g0 = f4 * (crypto_int64) g0; crypto_int64 f4g1 = f4 * (crypto_int64) g1; crypto_int64 f4g2 = f4 * (crypto_int64) g2; crypto_int64 f4g3 = f4 * (crypto_int64) g3; crypto_int64 f4g4 = f4 * (crypto_int64) g4; crypto_int64 f4g5 = f4 * (crypto_int64) g5; crypto_int64 f4g6_19 = f4 * (crypto_int64) g6_19; crypto_int64 f4g7_19 = f4 * (crypto_int64) g7_19; crypto_int64 f4g8_19 = f4 * (crypto_int64) g8_19; crypto_int64 f4g9_19 = f4 * (crypto_int64) g9_19; crypto_int64 f5g0 = f5 * (crypto_int64) g0; crypto_int64 f5g1_2 = f5_2 * (crypto_int64) g1; crypto_int64 f5g2 = f5 * (crypto_int64) g2; crypto_int64 f5g3_2 = f5_2 * (crypto_int64) g3; crypto_int64 f5g4 = f5 * (crypto_int64) g4; crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19; crypto_int64 f5g6_19 = f5 * (crypto_int64) g6_19; crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19; crypto_int64 f5g8_19 = f5 * (crypto_int64) g8_19; crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19; crypto_int64 f6g0 = f6 * (crypto_int64) g0; crypto_int64 f6g1 = f6 * (crypto_int64) g1; crypto_int64 f6g2 = f6 * (crypto_int64) g2; crypto_int64 f6g3 = f6 * (crypto_int64) g3; crypto_int64 f6g4_19 = f6 * (crypto_int64) g4_19; crypto_int64 f6g5_19 = f6 * (crypto_int64) g5_19; crypto_int64 f6g6_19 = f6 * (crypto_int64) g6_19; crypto_int64 f6g7_19 = f6 * (crypto_int64) g7_19; crypto_int64 f6g8_19 = f6 * (crypto_int64) g8_19; crypto_int64 f6g9_19 = f6 * (crypto_int64) g9_19; crypto_int64 f7g0 = f7 * (crypto_int64) g0; crypto_int64 f7g1_2 = f7_2 * (crypto_int64) g1; crypto_int64 f7g2 = f7 * (crypto_int64) g2; crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19; crypto_int64 f7g4_19 = f7 * (crypto_int64) g4_19; crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19; crypto_int64 f7g6_19 = f7 * (crypto_int64) g6_19; crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19; crypto_int64 f7g8_19 = f7 * (crypto_int64) g8_19; crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19; crypto_int64 f8g0 = f8 * (crypto_int64) g0; crypto_int64 f8g1 = f8 * (crypto_int64) g1; crypto_int64 f8g2_19 = f8 * (crypto_int64) g2_19; crypto_int64 f8g3_19 = f8 * (crypto_int64) g3_19; crypto_int64 f8g4_19 = f8 * (crypto_int64) g4_19; crypto_int64 f8g5_19 = f8 * (crypto_int64) g5_19; crypto_int64 f8g6_19 = f8 * (crypto_int64) g6_19; crypto_int64 f8g7_19 = f8 * (crypto_int64) g7_19; crypto_int64 f8g8_19 = f8 * (crypto_int64) g8_19; crypto_int64 f8g9_19 = f8 * (crypto_int64) g9_19; crypto_int64 f9g0 = f9 * (crypto_int64) g0; crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19; crypto_int64 f9g2_19 = f9 * (crypto_int64) g2_19; crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19; crypto_int64 f9g4_19 = f9 * (crypto_int64) g4_19; crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19; crypto_int64 f9g6_19 = f9 * (crypto_int64) g6_19; crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19; crypto_int64 f9g8_19 = f9 * (crypto_int64) g8_19; crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19; crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; crypto_int64 h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; crypto_int64 h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; crypto_int64 h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; crypto_int64 h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; crypto_int64 h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; crypto_int64 h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; crypto_int64 h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; crypto_int64 h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; crypto_int64 h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; crypto_int64 carry0; crypto_int64 carry1; crypto_int64 carry2; crypto_int64 carry3; crypto_int64 carry4; crypto_int64 carry5; crypto_int64 carry6; crypto_int64 carry7; crypto_int64 carry8; crypto_int64 carry9; /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; /* |h0| <= 2^25 */ /* |h4| <= 2^25 */ /* |h1| <= 1.71*2^59 */ /* |h5| <= 1.71*2^59 */ carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; /* |h1| <= 2^24; from now on fits into int32 */ /* |h5| <= 2^24; from now on fits into int32 */ /* |h2| <= 1.41*2^60 */ /* |h6| <= 1.41*2^60 */ carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; /* |h2| <= 2^25; from now on fits into int32 unchanged */ /* |h6| <= 2^25; from now on fits into int32 unchanged */ /* |h3| <= 1.71*2^59 */ /* |h7| <= 1.71*2^59 */ carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; /* |h3| <= 2^24; from now on fits into int32 unchanged */ /* |h7| <= 2^24; from now on fits into int32 unchanged */ /* |h4| <= 1.72*2^34 */ /* |h8| <= 1.41*2^60 */ carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; /* |h4| <= 2^25; from now on fits into int32 unchanged */ /* |h8| <= 2^25; from now on fits into int32 unchanged */ /* |h5| <= 1.01*2^24 */ /* |h9| <= 1.71*2^59 */ carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; /* |h9| <= 2^24; from now on fits into int32 unchanged */ /* |h0| <= 1.1*2^39 */ carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; /* |h0| <= 2^25; from now on fits into int32 unchanged */ /* |h1| <= 1.01*2^24 */ h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } ed25519-0.0.5.0/src/cbits/ref10/ge_p3_to_cached.c0000644000000000000000000000037512606567661017024 0ustar0000000000000000#include "ge.h" /* r = p */ static const fe d2 = { #include "d2.h" } ; static inline void ge_p3_to_cached(ge_cached *r,const ge_p3 *p) { fe_add(r->YplusX,p->Y,p->X); fe_sub(r->YminusX,p->Y,p->X); fe_copy(r->Z,p->Z); fe_mul(r->T2d,p->T,d2); } ed25519-0.0.5.0/src/cbits/ref10/fe_pow22523.c0000644000000000000000000000021512606567661015704 0ustar0000000000000000#include "fe.h" static inline void fe_pow22523(fe out,const fe z) { fe t0; fe t1; fe t2; int i; #include "pow22523.h" return; } ed25519-0.0.5.0/src/cbits/ref10/sha512.c0000644000000000000000000002017612606567661015042 0ustar0000000000000000#include "sha512.h" #include "crypto_uint64.h" static inline crypto_uint64 load_bigendian(const unsigned char *x) { return (crypto_uint64) (x[7]) \ | (((crypto_uint64) (x[6])) << 8) \ | (((crypto_uint64) (x[5])) << 16) \ | (((crypto_uint64) (x[4])) << 24) \ | (((crypto_uint64) (x[3])) << 32) \ | (((crypto_uint64) (x[2])) << 40) \ | (((crypto_uint64) (x[1])) << 48) \ | (((crypto_uint64) (x[0])) << 56) ; } static inline void store_bigendian(unsigned char *x,crypto_uint64 u) { x[7] = u; u >>= 8; x[6] = u; u >>= 8; x[5] = u; u >>= 8; x[4] = u; u >>= 8; x[3] = u; u >>= 8; x[2] = u; u >>= 8; x[1] = u; u >>= 8; x[0] = u; } #define SHR(x,c) ((x) >> (c)) #define ROTR(x,c) (((x) >> (c)) | ((x) << (64 - (c)))) #define Ch(x,y,z) ((x & y) ^ (~x & z)) #define Maj(x,y,z) ((x & y) ^ (x & z) ^ (y & z)) #define Sigma0(x) (ROTR(x,28) ^ ROTR(x,34) ^ ROTR(x,39)) #define Sigma1(x) (ROTR(x,14) ^ ROTR(x,18) ^ ROTR(x,41)) #define sigma0(x) (ROTR(x, 1) ^ ROTR(x, 8) ^ SHR(x,7)) #define sigma1(x) (ROTR(x,19) ^ ROTR(x,61) ^ SHR(x,6)) #define M(w0,w14,w9,w1) w0 = sigma1(w14) + w9 + sigma0(w1) + w0; #define EXPAND \ M(w0 ,w14,w9 ,w1 ) \ M(w1 ,w15,w10,w2 ) \ M(w2 ,w0 ,w11,w3 ) \ M(w3 ,w1 ,w12,w4 ) \ M(w4 ,w2 ,w13,w5 ) \ M(w5 ,w3 ,w14,w6 ) \ M(w6 ,w4 ,w15,w7 ) \ M(w7 ,w5 ,w0 ,w8 ) \ M(w8 ,w6 ,w1 ,w9 ) \ M(w9 ,w7 ,w2 ,w10) \ M(w10,w8 ,w3 ,w11) \ M(w11,w9 ,w4 ,w12) \ M(w12,w10,w5 ,w13) \ M(w13,w11,w6 ,w14) \ M(w14,w12,w7 ,w15) \ M(w15,w13,w8 ,w0 ) #define F(w,k) \ T1 = h + Sigma1(e) + Ch(e,f,g) + k + w; \ T2 = Sigma0(a) + Maj(a,b,c); \ h = g; \ g = f; \ f = e; \ e = d + T1; \ d = c; \ c = b; \ b = a; \ a = T1 + T2; static inline int crypto_hashblocks_sha512(unsigned char *statebytes,const unsigned char *in,unsigned long long inlen) { crypto_uint64 state[8]; crypto_uint64 a; crypto_uint64 b; crypto_uint64 c; crypto_uint64 d; crypto_uint64 e; crypto_uint64 f; crypto_uint64 g; crypto_uint64 h; crypto_uint64 T1; crypto_uint64 T2; a = load_bigendian(statebytes + 0); state[0] = a; b = load_bigendian(statebytes + 8); state[1] = b; c = load_bigendian(statebytes + 16); state[2] = c; d = load_bigendian(statebytes + 24); state[3] = d; e = load_bigendian(statebytes + 32); state[4] = e; f = load_bigendian(statebytes + 40); state[5] = f; g = load_bigendian(statebytes + 48); state[6] = g; h = load_bigendian(statebytes + 56); state[7] = h; while (inlen >= 128) { crypto_uint64 w0 = load_bigendian(in + 0); crypto_uint64 w1 = load_bigendian(in + 8); crypto_uint64 w2 = load_bigendian(in + 16); crypto_uint64 w3 = load_bigendian(in + 24); crypto_uint64 w4 = load_bigendian(in + 32); crypto_uint64 w5 = load_bigendian(in + 40); crypto_uint64 w6 = load_bigendian(in + 48); crypto_uint64 w7 = load_bigendian(in + 56); crypto_uint64 w8 = load_bigendian(in + 64); crypto_uint64 w9 = load_bigendian(in + 72); crypto_uint64 w10 = load_bigendian(in + 80); crypto_uint64 w11 = load_bigendian(in + 88); crypto_uint64 w12 = load_bigendian(in + 96); crypto_uint64 w13 = load_bigendian(in + 104); crypto_uint64 w14 = load_bigendian(in + 112); crypto_uint64 w15 = load_bigendian(in + 120); F(w0 ,0x428a2f98d728ae22ULL) F(w1 ,0x7137449123ef65cdULL) F(w2 ,0xb5c0fbcfec4d3b2fULL) F(w3 ,0xe9b5dba58189dbbcULL) F(w4 ,0x3956c25bf348b538ULL) F(w5 ,0x59f111f1b605d019ULL) F(w6 ,0x923f82a4af194f9bULL) F(w7 ,0xab1c5ed5da6d8118ULL) F(w8 ,0xd807aa98a3030242ULL) F(w9 ,0x12835b0145706fbeULL) F(w10,0x243185be4ee4b28cULL) F(w11,0x550c7dc3d5ffb4e2ULL) F(w12,0x72be5d74f27b896fULL) F(w13,0x80deb1fe3b1696b1ULL) F(w14,0x9bdc06a725c71235ULL) F(w15,0xc19bf174cf692694ULL) EXPAND F(w0 ,0xe49b69c19ef14ad2ULL) F(w1 ,0xefbe4786384f25e3ULL) F(w2 ,0x0fc19dc68b8cd5b5ULL) F(w3 ,0x240ca1cc77ac9c65ULL) F(w4 ,0x2de92c6f592b0275ULL) F(w5 ,0x4a7484aa6ea6e483ULL) F(w6 ,0x5cb0a9dcbd41fbd4ULL) F(w7 ,0x76f988da831153b5ULL) F(w8 ,0x983e5152ee66dfabULL) F(w9 ,0xa831c66d2db43210ULL) F(w10,0xb00327c898fb213fULL) F(w11,0xbf597fc7beef0ee4ULL) F(w12,0xc6e00bf33da88fc2ULL) F(w13,0xd5a79147930aa725ULL) F(w14,0x06ca6351e003826fULL) F(w15,0x142929670a0e6e70ULL) EXPAND F(w0 ,0x27b70a8546d22ffcULL) F(w1 ,0x2e1b21385c26c926ULL) F(w2 ,0x4d2c6dfc5ac42aedULL) F(w3 ,0x53380d139d95b3dfULL) F(w4 ,0x650a73548baf63deULL) F(w5 ,0x766a0abb3c77b2a8ULL) F(w6 ,0x81c2c92e47edaee6ULL) F(w7 ,0x92722c851482353bULL) F(w8 ,0xa2bfe8a14cf10364ULL) F(w9 ,0xa81a664bbc423001ULL) F(w10,0xc24b8b70d0f89791ULL) F(w11,0xc76c51a30654be30ULL) F(w12,0xd192e819d6ef5218ULL) F(w13,0xd69906245565a910ULL) F(w14,0xf40e35855771202aULL) F(w15,0x106aa07032bbd1b8ULL) EXPAND F(w0 ,0x19a4c116b8d2d0c8ULL) F(w1 ,0x1e376c085141ab53ULL) F(w2 ,0x2748774cdf8eeb99ULL) F(w3 ,0x34b0bcb5e19b48a8ULL) F(w4 ,0x391c0cb3c5c95a63ULL) F(w5 ,0x4ed8aa4ae3418acbULL) F(w6 ,0x5b9cca4f7763e373ULL) F(w7 ,0x682e6ff3d6b2b8a3ULL) F(w8 ,0x748f82ee5defb2fcULL) F(w9 ,0x78a5636f43172f60ULL) F(w10,0x84c87814a1f0ab72ULL) F(w11,0x8cc702081a6439ecULL) F(w12,0x90befffa23631e28ULL) F(w13,0xa4506cebde82bde9ULL) F(w14,0xbef9a3f7b2c67915ULL) F(w15,0xc67178f2e372532bULL) EXPAND F(w0 ,0xca273eceea26619cULL) F(w1 ,0xd186b8c721c0c207ULL) F(w2 ,0xeada7dd6cde0eb1eULL) F(w3 ,0xf57d4f7fee6ed178ULL) F(w4 ,0x06f067aa72176fbaULL) F(w5 ,0x0a637dc5a2c898a6ULL) F(w6 ,0x113f9804bef90daeULL) F(w7 ,0x1b710b35131c471bULL) F(w8 ,0x28db77f523047d84ULL) F(w9 ,0x32caab7b40c72493ULL) F(w10,0x3c9ebe0a15c9bebcULL) F(w11,0x431d67c49c100d4cULL) F(w12,0x4cc5d4becb3e42b6ULL) F(w13,0x597f299cfc657e2aULL) F(w14,0x5fcb6fab3ad6faecULL) F(w15,0x6c44198c4a475817ULL) a += state[0]; b += state[1]; c += state[2]; d += state[3]; e += state[4]; f += state[5]; g += state[6]; h += state[7]; state[0] = a; state[1] = b; state[2] = c; state[3] = d; state[4] = e; state[5] = f; state[6] = g; state[7] = h; in += 128; inlen -= 128; } store_bigendian(statebytes + 0,state[0]); store_bigendian(statebytes + 8,state[1]); store_bigendian(statebytes + 16,state[2]); store_bigendian(statebytes + 24,state[3]); store_bigendian(statebytes + 32,state[4]); store_bigendian(statebytes + 40,state[5]); store_bigendian(statebytes + 48,state[6]); store_bigendian(statebytes + 56,state[7]); return 0; } #define blocks crypto_hashblocks_sha512 static const unsigned char iv[64] = { 0x6a,0x09,0xe6,0x67,0xf3,0xbc,0xc9,0x08, 0xbb,0x67,0xae,0x85,0x84,0xca,0xa7,0x3b, 0x3c,0x6e,0xf3,0x72,0xfe,0x94,0xf8,0x2b, 0xa5,0x4f,0xf5,0x3a,0x5f,0x1d,0x36,0xf1, 0x51,0x0e,0x52,0x7f,0xad,0xe6,0x82,0xd1, 0x9b,0x05,0x68,0x8c,0x2b,0x3e,0x6c,0x1f, 0x1f,0x83,0xd9,0xab,0xfb,0x41,0xbd,0x6b, 0x5b,0xe0,0xcd,0x19,0x13,0x7e,0x21,0x79 } ; static inline int crypto_hash_sha512(unsigned char *out,const unsigned char *in,unsigned long long inlen) { unsigned char h[64]; unsigned char padded[256]; int i; unsigned long long bytes = inlen; for (i = 0;i < 64;++i) h[i] = iv[i]; blocks(h,in,inlen); in += inlen; inlen &= 127; in -= inlen; for (i = 0;i < inlen;++i) padded[i] = in[i]; padded[inlen] = 0x80; if (inlen < 112) { for (i = inlen + 1;i < 119;++i) padded[i] = 0; padded[119] = bytes >> 61; padded[120] = bytes >> 53; padded[121] = bytes >> 45; padded[122] = bytes >> 37; padded[123] = bytes >> 29; padded[124] = bytes >> 21; padded[125] = bytes >> 13; padded[126] = bytes >> 5; padded[127] = bytes << 3; blocks(h,padded,128); } else { for (i = inlen + 1;i < 247;++i) padded[i] = 0; padded[247] = bytes >> 61; padded[248] = bytes >> 53; padded[249] = bytes >> 45; padded[250] = bytes >> 37; padded[251] = bytes >> 29; padded[252] = bytes >> 21; padded[253] = bytes >> 13; padded[254] = bytes >> 5; padded[255] = bytes << 3; blocks(h,padded,256); } for (i = 0;i < 64;++i) out[i] = h[i]; return 0; } ed25519-0.0.5.0/src/cbits/ref10/ge_add.c0000644000000000000000000000021312606567661015230 0ustar0000000000000000#include "ge.h" /* r = p + q */ static inline void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) { fe t0; #include "ge_add.h" } ed25519-0.0.5.0/src/cbits/ref10/ge_sub.c0000644000000000000000000000021312606567661015271 0ustar0000000000000000#include "ge.h" /* r = p - q */ static inline void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) { fe t0; #include "ge_sub.h" } ed25519-0.0.5.0/src/cbits/ref10/fe_add.c0000644000000000000000000000236512606567661015241 0ustar0000000000000000#include "fe.h" /* h = f + g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static inline void fe_add(fe h,const fe f,const fe g) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; crypto_int32 g0 = g[0]; crypto_int32 g1 = g[1]; crypto_int32 g2 = g[2]; crypto_int32 g3 = g[3]; crypto_int32 g4 = g[4]; crypto_int32 g5 = g[5]; crypto_int32 g6 = g[6]; crypto_int32 g7 = g[7]; crypto_int32 g8 = g[8]; crypto_int32 g9 = g[9]; crypto_int32 h0 = f0 + g0; crypto_int32 h1 = f1 + g1; crypto_int32 h2 = f2 + g2; crypto_int32 h3 = f3 + g3; crypto_int32 h4 = f4 + g4; crypto_int32 h5 = f5 + g5; crypto_int32 h6 = f6 + g6; crypto_int32 h7 = f7 + g7; crypto_int32 h8 = f8 + g8; crypto_int32 h9 = f9 + g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } ed25519-0.0.5.0/src/cbits/ref10/ge_p2_0.c0000644000000000000000000000014412606567661015243 0ustar0000000000000000#include "ge.h" static inline void ge_p2_0(ge_p2 *h) { fe_0(h->X); fe_1(h->Y); fe_1(h->Z); } ed25519-0.0.5.0/src/cbits/ref10/ge_p3_to_p2.c0000644000000000000000000000023412606567661016130 0ustar0000000000000000#include "ge.h" /* r = p */ static inline void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p) { fe_copy(r->X,p->X); fe_copy(r->Y,p->Y); fe_copy(r->Z,p->Z); } ed25519-0.0.5.0/src/cbits/ref10/fe_invert.c0000644000000000000000000000020712606567661016011 0ustar0000000000000000#include "fe.h" void fe_invert(fe out,const fe z) { fe t0; fe t1; fe t2; fe t3; int i; #include "pow225521.h" return; } ed25519-0.0.5.0/src/cbits/ref10/test.c0000644000000000000000000000123012606567661015004 0ustar0000000000000000#include #include #include "ed25519.h" unsigned char pk[crypto_sign_PUBLICKEYBYTES]; unsigned char sk[crypto_sign_SECRETKEYBYTES]; int main() { int r = 0; ed25519_sign_keypair(pk,sk); printf("Keypair generated.\n"); unsigned char *msg = "Hello"; unsigned char sm[5+crypto_sign_BYTES]; unsigned long long smlen; r = ed25519_sign(sm, &smlen, msg, 5, sk); assert(r == 0); printf("Signed message (length = %u)\n",smlen); unsigned long long mlen; unsigned char m[5+crypto_sign_BYTES]; r = ed25519_sign_open(m, &mlen, sm, smlen, pk); assert(r == 0); printf("Verified message (length = %u)\n",mlen); return 0; } ed25519-0.0.5.0/src/cbits/ref10/open.c0000644000000000000000000000164112606567661014774 0ustar0000000000000000#include "ed25519.h" #include "sha512.h" #include "crypto_verify.h" #include "ge.h" #include "sc.h" int ed25519_sign_open( unsigned char *m,unsigned long long *mlen, const unsigned char *sm,unsigned long long smlen, const unsigned char *pk ) { unsigned char h[64]; unsigned char checkr[32]; ge_p3 A; ge_p2 R; unsigned long long i; *mlen = -1; if (smlen < 64) return -1; if (sm[63] & 224) return -1; if (ge_frombytes_negate_vartime(&A,pk) != 0) return -1; for (i = 0;i < smlen;++i) m[i] = sm[i]; for (i = 0;i < 32;++i) m[32 + i] = pk[i]; crypto_hash_sha512(h,m,smlen); sc_reduce(h); ge_double_scalarmult_vartime(&R,h,&A,sm + 32); ge_tobytes(checkr,&R); if (crypto_verify_32(checkr,sm) != 0) { for (i = 0;i < smlen;++i) m[i] = 0; return -1; } for (i = 0;i < smlen - 64;++i) m[i] = sm[64 + i]; for (i = smlen - 64;i < smlen;++i) m[i] = 0; *mlen = smlen - 64; return 0; } ed25519-0.0.5.0/src/cbits/ref10/ge_msub.c0000644000000000000000000000021612606567661015451 0ustar0000000000000000#include "ge.h" /* r = p - q */ static inline void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) { fe t0; #include "ge_msub.h" } ed25519-0.0.5.0/src/cbits/ref10/fe_0.c0000644000000000000000000000027012606567661014641 0ustar0000000000000000#include "fe.h" /* h = 0 */ static inline void fe_0(fe h) { h[0] = 0; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } ed25519-0.0.5.0/src/cbits/ref10/fe_sub.c0000644000000000000000000000236512606567661015302 0ustar0000000000000000#include "fe.h" /* h = f - g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static inline void fe_sub(fe h,const fe f,const fe g) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; crypto_int32 g0 = g[0]; crypto_int32 g1 = g[1]; crypto_int32 g2 = g[2]; crypto_int32 g3 = g[3]; crypto_int32 g4 = g[4]; crypto_int32 g5 = g[5]; crypto_int32 g6 = g[6]; crypto_int32 g7 = g[7]; crypto_int32 g8 = g[8]; crypto_int32 g9 = g[9]; crypto_int32 h0 = f0 - g0; crypto_int32 h1 = f1 - g1; crypto_int32 h2 = f2 - g2; crypto_int32 h3 = f3 - g3; crypto_int32 h4 = f4 - g4; crypto_int32 h5 = f5 - g5; crypto_int32 h6 = f6 - g6; crypto_int32 h7 = f7 - g7; crypto_int32 h8 = f8 - g8; crypto_int32 h9 = f9 - g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } ed25519-0.0.5.0/src/cbits/ref10/fe_isnonzero.c0000644000000000000000000000050612606567661016532 0ustar0000000000000000#include "fe.h" #include "crypto_verify.h" /* return 1 if f == 0 return 0 if f != 0 Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static const unsigned char zero[32]; static inline int fe_isnonzero(const fe f) { unsigned char s[32]; fe_tobytes(s,f); return crypto_verify_32(s,zero); } ed25519-0.0.5.0/src/cbits/ref10/fe_isnegative.c0000644000000000000000000000043012606567661016636 0ustar0000000000000000#include "fe.h" /* return 1 if f is in {1,3,5,...,q-2} return 0 if f is in {0,2,4,...,q-1} Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static inline int fe_isnegative(const fe f) { unsigned char s[32]; fe_tobytes(s,f); return s[0] & 1; } ed25519-0.0.5.0/src/cbits/ref10/randombytes.c0000644000000000000000000000176312606567661016367 0ustar0000000000000000#ifndef _WIN32 #include #include #include #include /* it's really stupid that there isn't a syscall for this */ static int ed25519_random_fd = -1; static inline void ed25519_randombytes(unsigned char *x,unsigned long long xlen) { int i; if (ed25519_random_fd == -1) { for (;;) { ed25519_random_fd = open("/dev/urandom",O_RDONLY); if (ed25519_random_fd != -1) break; sleep(1); } } while (xlen > 0) { if (xlen < 1048576) i = xlen; else i = 1048576; i = read(ed25519_random_fd,x,i); if (i < 1) { sleep(1); continue; } x += i; xlen -= i; } } #else #include #include static inline void ed25519_randombytes(unsigned char *x,unsigned long long xlen) { HCRYPTPROV prov = 0; CryptAcquireContextW(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT | CRYPT_SILENT); CryptGenRandom(prov, xlen, x); CryptReleaseContext(prov, 0); } #endif /* _WIN32 */ ed25519-0.0.5.0/src/cbits/ref10/fe_neg.c0000644000000000000000000000154512606567661015261 0ustar0000000000000000#include "fe.h" /* h = -f Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ static inline void fe_neg(fe h,const fe f) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; crypto_int32 h0 = -f0; crypto_int32 h1 = -f1; crypto_int32 h2 = -f2; crypto_int32 h3 = -f3; crypto_int32 h4 = -f4; crypto_int32 h5 = -f5; crypto_int32 h6 = -f6; crypto_int32 h7 = -f7; crypto_int32 h8 = -f8; crypto_int32 h9 = -f9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } ed25519-0.0.5.0/src/cbits/ref10/ge_frombytes.c0000644000000000000000000000175112606567661016522 0ustar0000000000000000#include "ge.h" static const fe d = { #include "d.h" } ; static const fe sqrtm1 = { #include "sqrtm1.h" } ; static inline int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s) { fe u; fe v; fe v3; fe vxx; fe check; fe_frombytes(h->Y,s); fe_1(h->Z); fe_sq(u,h->Y); fe_mul(v,u,d); fe_sub(u,u,h->Z); /* u = y^2-1 */ fe_add(v,v,h->Z); /* v = dy^2+1 */ fe_sq(v3,v); fe_mul(v3,v3,v); /* v3 = v^3 */ fe_sq(h->X,v3); fe_mul(h->X,h->X,v); fe_mul(h->X,h->X,u); /* x = uv^7 */ fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */ fe_mul(h->X,h->X,v3); fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */ fe_sq(vxx,h->X); fe_mul(vxx,vxx,v); fe_sub(check,vxx,u); /* vx^2-u */ if (fe_isnonzero(check)) { fe_add(check,vxx,u); /* vx^2+u */ if (fe_isnonzero(check)) return -1; fe_mul(h->X,h->X,sqrtm1); } if (fe_isnegative(h->X) == (s[31] >> 7)) fe_neg(h->X,h->X); fe_mul(h->T,h->X,h->Y); return 0; } ed25519-0.0.5.0/src/cbits/ref10/ge_p3_tobytes.c0000644000000000000000000000036212606567661016600 0ustar0000000000000000#include "ge.h" static inline void ge_p3_tobytes(unsigned char *s,const ge_p3 *h) { fe recip; fe x; fe y; fe_invert(recip,h->Z); fe_mul(x,h->X,recip); fe_mul(y,h->Y,recip); fe_tobytes(s,y); s[31] ^= fe_isnegative(x) << 7; } ed25519-0.0.5.0/src/cbits/ref10/ge_double_scalarmult.c0000644000000000000000000000453012606567661020207 0ustar0000000000000000#include "ge.h" static inline void slide(signed char *r,const unsigned char *a) { int i; int b; int k; for (i = 0;i < 256;++i) r[i] = 1 & (a[i >> 3] >> (i & 7)); for (i = 0;i < 256;++i) if (r[i]) { for (b = 1;b <= 6 && i + b < 256;++b) { if (r[i + b]) { if (r[i] + (r[i + b] << b) <= 15) { r[i] += r[i + b] << b; r[i + b] = 0; } else if (r[i] - (r[i + b] << b) >= -15) { r[i] -= r[i + b] << b; for (k = i + b;k < 256;++k) { if (!r[k]) { r[k] = 1; break; } r[k] = 0; } } else break; } } } } static ge_precomp Bi[8] = { #include "base2.h" } ; /* r = a * A + b * B where a = a[0]+256*a[1]+...+256^31 a[31]. and b = b[0]+256*b[1]+...+256^31 b[31]. B is the Ed25519 base point (x,4/5) with x positive. */ static inline void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b) { signed char aslide[256]; signed char bslide[256]; ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ ge_p1p1 t; ge_p3 u; ge_p3 A2; int i; slide(aslide,a); slide(bslide,b); ge_p3_to_cached(&Ai[0],A); ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t); ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u); ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u); ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u); ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u); ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u); ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u); ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u); ge_p2_0(r); for (i = 255;i >= 0;--i) { if (aslide[i] || bslide[i]) break; } for (;i >= 0;--i) { ge_p2_dbl(&t,r); if (aslide[i] > 0) { ge_p1p1_to_p3(&u,&t); ge_add(&t,&u,&Ai[aslide[i]/2]); } else if (aslide[i] < 0) { ge_p1p1_to_p3(&u,&t); ge_sub(&t,&u,&Ai[(-aslide[i])/2]); } if (bslide[i] > 0) { ge_p1p1_to_p3(&u,&t); ge_madd(&t,&u,&Bi[bslide[i]/2]); } else if (bslide[i] < 0) { ge_p1p1_to_p3(&u,&t); ge_msub(&t,&u,&Bi[(-bslide[i])/2]); } ge_p1p1_to_p2(r,&t); } } ed25519-0.0.5.0/src/cbits/ref10/ge_p1p1_to_p2.c0000644000000000000000000000025412606567661016371 0ustar0000000000000000#include "ge.h" /* r = p */ static inline void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p) { fe_mul(r->X,p->X,p->T); fe_mul(r->Y,p->Y,p->Z); fe_mul(r->Z,p->Z,p->T); } ed25519-0.0.5.0/src/cbits/ref10/fe_sq.c0000644000000000000000000001355212606567661015134 0ustar0000000000000000#include "fe.h" #include "crypto_int64.h" /* h = f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ static inline void fe_sq(fe h,const fe f) { crypto_int32 f0 = f[0]; crypto_int32 f1 = f[1]; crypto_int32 f2 = f[2]; crypto_int32 f3 = f[3]; crypto_int32 f4 = f[4]; crypto_int32 f5 = f[5]; crypto_int32 f6 = f[6]; crypto_int32 f7 = f[7]; crypto_int32 f8 = f[8]; crypto_int32 f9 = f[9]; crypto_int32 f0_2 = 2 * f0; crypto_int32 f1_2 = 2 * f1; crypto_int32 f2_2 = 2 * f2; crypto_int32 f3_2 = 2 * f3; crypto_int32 f4_2 = 2 * f4; crypto_int32 f5_2 = 2 * f5; crypto_int32 f6_2 = 2 * f6; crypto_int32 f7_2 = 2 * f7; crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */ crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */ crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */ crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */ crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */ crypto_int64 f0f0 = f0 * (crypto_int64) f0; crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1; crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2; crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3; crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4; crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5; crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6; crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7; crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8; crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9; crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1; crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2; crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2; crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4; crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2; crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6; crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2; crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8; crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38; crypto_int64 f2f2 = f2 * (crypto_int64) f2; crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3; crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4; crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5; crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6; crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7; crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19; crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38; crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3; crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4; crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2; crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6; crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38; crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19; crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38; crypto_int64 f4f4 = f4 * (crypto_int64) f4; crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5; crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19; crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38; crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19; crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38; crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38; crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19; crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38; crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19; crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38; crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19; crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38; crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19; crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38; crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38; crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19; crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38; crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19; crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38; crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38; crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; crypto_int64 carry0; crypto_int64 carry1; crypto_int64 carry2; crypto_int64 carry3; crypto_int64 carry4; crypto_int64 carry5; crypto_int64 carry6; crypto_int64 carry7; crypto_int64 carry8; crypto_int64 carry9; carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } ed25519-0.0.5.0/src/cbits/ref10/ge_p3_0.c0000644000000000000000000000016212606567661015244 0ustar0000000000000000#include "ge.h" static inline void ge_p3_0(ge_p3 *h) { fe_0(h->X); fe_1(h->Y); fe_1(h->Z); fe_0(h->T); } ed25519-0.0.5.0/src/cbits/ref10/ge_precomp_0.c0000644000000000000000000000017412606567661016372 0ustar0000000000000000#include "ge.h" static inline void ge_precomp_0(ge_precomp *h) { fe_1(h->yplusx); fe_1(h->yminusx); fe_0(h->xy2d); } ed25519-0.0.5.0/src/cbits/ref10/ge_scalarmult_base.c0000644000000000000000000000475712606567661017662 0ustar0000000000000000#include "ge.h" #include "crypto_uint32.h" static inline unsigned char equal(signed char b,signed char c) { unsigned char ub = b; unsigned char uc = c; unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ crypto_uint32 y = x; /* 0: yes; 1..255: no */ y -= 1; /* 4294967295: yes; 0..254: no */ y >>= 31; /* 1: yes; 0: no */ return y; } static inline unsigned char negative(signed char b) { unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ x >>= 63; /* 1: yes; 0: no */ return x; } static inline void cmov(ge_precomp *t,ge_precomp *u,unsigned char b) { fe_cmov(t->yplusx,u->yplusx,b); fe_cmov(t->yminusx,u->yminusx,b); fe_cmov(t->xy2d,u->xy2d,b); } /* base[i][j] = (j+1)*256^i*B */ static ge_precomp base[32][8] = { #include "base.h" } ; static inline void select_ed25519(ge_precomp *t,int pos,signed char b) { ge_precomp minust; unsigned char bnegative = negative(b); unsigned char babs = b - (((-bnegative) & b) << 1); ge_precomp_0(t); cmov(t,&base[pos][0],equal(babs,1)); cmov(t,&base[pos][1],equal(babs,2)); cmov(t,&base[pos][2],equal(babs,3)); cmov(t,&base[pos][3],equal(babs,4)); cmov(t,&base[pos][4],equal(babs,5)); cmov(t,&base[pos][5],equal(babs,6)); cmov(t,&base[pos][6],equal(babs,7)); cmov(t,&base[pos][7],equal(babs,8)); fe_copy(minust.yplusx,t->yminusx); fe_copy(minust.yminusx,t->yplusx); fe_neg(minust.xy2d,t->xy2d); cmov(t,&minust,bnegative); } /* h = a * B where a = a[0]+256*a[1]+...+256^31 a[31] B is the Ed25519 base point (x,4/5) with x positive. Preconditions: a[31] <= 127 */ static inline void ge_scalarmult_base(ge_p3 *h,const unsigned char *a) { signed char e[64]; signed char carry; ge_p1p1 r; ge_p2 s; ge_precomp t; int i; for (i = 0;i < 32;++i) { e[2 * i + 0] = (a[i] >> 0) & 15; e[2 * i + 1] = (a[i] >> 4) & 15; } /* each e[i] is between 0 and 15 */ /* e[63] is between 0 and 7 */ carry = 0; for (i = 0;i < 63;++i) { e[i] += carry; carry = e[i] + 8; carry >>= 4; e[i] -= carry << 4; } e[63] += carry; /* each e[i] is between -8 and 8 */ ge_p3_0(h); for (i = 1;i < 64;i += 2) { select_ed25519(&t,i / 2,e[i]); ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); } ge_p3_dbl(&r,h); ge_p1p1_to_p2(&s,&r); ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r); for (i = 0;i < 64;i += 2) { select_ed25519(&t,i / 2,e[i]); ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); } } ed25519-0.0.5.0/src/cbits/ref10/sc_reduce.c0000644000000000000000000001701412606567661015770 0ustar0000000000000000#include "sc.h" #include "load.h" #include "crypto_int64.h" #include "crypto_uint32.h" #include "crypto_uint64.h" /* Input: s[0]+256*s[1]+...+256^63*s[63] = s Output: s[0]+256*s[1]+...+256^31*s[31] = s mod l where l = 2^252 + 27742317777372353535851937790883648493. Overwrites s in place. */ static inline void sc_reduce(unsigned char *s) { crypto_int64 s0 = 2097151 & load_3(s); crypto_int64 s1 = 2097151 & (load_4(s + 2) >> 5); crypto_int64 s2 = 2097151 & (load_3(s + 5) >> 2); crypto_int64 s3 = 2097151 & (load_4(s + 7) >> 7); crypto_int64 s4 = 2097151 & (load_4(s + 10) >> 4); crypto_int64 s5 = 2097151 & (load_3(s + 13) >> 1); crypto_int64 s6 = 2097151 & (load_4(s + 15) >> 6); crypto_int64 s7 = 2097151 & (load_3(s + 18) >> 3); crypto_int64 s8 = 2097151 & load_3(s + 21); crypto_int64 s9 = 2097151 & (load_4(s + 23) >> 5); crypto_int64 s10 = 2097151 & (load_3(s + 26) >> 2); crypto_int64 s11 = 2097151 & (load_4(s + 28) >> 7); crypto_int64 s12 = 2097151 & (load_4(s + 31) >> 4); crypto_int64 s13 = 2097151 & (load_3(s + 34) >> 1); crypto_int64 s14 = 2097151 & (load_4(s + 36) >> 6); crypto_int64 s15 = 2097151 & (load_3(s + 39) >> 3); crypto_int64 s16 = 2097151 & load_3(s + 42); crypto_int64 s17 = 2097151 & (load_4(s + 44) >> 5); crypto_int64 s18 = 2097151 & (load_3(s + 47) >> 2); crypto_int64 s19 = 2097151 & (load_4(s + 49) >> 7); crypto_int64 s20 = 2097151 & (load_4(s + 52) >> 4); crypto_int64 s21 = 2097151 & (load_3(s + 55) >> 1); crypto_int64 s22 = 2097151 & (load_4(s + 57) >> 6); crypto_int64 s23 = (load_4(s + 60) >> 3); crypto_int64 carry0; crypto_int64 carry1; crypto_int64 carry2; crypto_int64 carry3; crypto_int64 carry4; crypto_int64 carry5; crypto_int64 carry6; crypto_int64 carry7; crypto_int64 carry8; crypto_int64 carry9; crypto_int64 carry10; crypto_int64 carry11; crypto_int64 carry12; crypto_int64 carry13; crypto_int64 carry14; crypto_int64 carry15; crypto_int64 carry16; s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; s23 = 0; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s22 = 0; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s21 = 0; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s20 = 0; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s19 = 0; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; s18 = 0; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; s17 = 0; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s16 = 0; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s15 = 0; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s14 = 0; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; s13 = 0; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 << 5); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 << 2); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 << 7); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 << 4); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 << 1); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 << 6); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 << 3); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 << 5); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 << 2); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 << 7); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } ed25519-0.0.5.0/src/cbits/ref10/keypair.c0000644000000000000000000000133412606567661015476 0ustar0000000000000000#include #include "randombytes.h" #include "ed25519.h" #include "sha512.h" #include "ge.h" int ed25519_sign_seed_keypair(unsigned char *pk, unsigned char *sk, const unsigned char *seed) { ge_p3 A; crypto_hash_sha512(sk,seed,32); sk[0] &= 248; sk[31] &= 63; sk[31] |= 64; ge_scalarmult_base(&A,sk); ge_p3_tobytes(pk,&A); memmove(sk, seed, 32); memmove(sk + 32, pk, 32); return 0; } int ed25519_sign_keypair(unsigned char *pk, unsigned char *sk) { unsigned char seed[32]; int ret; ed25519_randombytes(seed, sizeof seed); ret = ed25519_sign_seed_keypair(pk, sk, seed); memset(seed, 0, sizeof seed); return ret; } ed25519-0.0.5.0/src/cbits/ref10/crypto_verify.c0000644000000000000000000000215312606567661016736 0ustar0000000000000000#include "crypto_verify.h" #define VERIFY_F(i) differentbits |= x[i] ^ y[i]; static inline int crypto_verify_16(const unsigned char *x,const unsigned char *y) { unsigned int differentbits = 0; VERIFY_F(0) VERIFY_F(1) VERIFY_F(2) VERIFY_F(3) VERIFY_F(4) VERIFY_F(5) VERIFY_F(6) VERIFY_F(7) VERIFY_F(8) VERIFY_F(9) VERIFY_F(10) VERIFY_F(11) VERIFY_F(12) VERIFY_F(13) VERIFY_F(14) VERIFY_F(15) return (1 & ((differentbits - 1) >> 8)) - 1; } static inline int crypto_verify_32(const unsigned char *x,const unsigned char *y) { unsigned int differentbits = 0; VERIFY_F(0) VERIFY_F(1) VERIFY_F(2) VERIFY_F(3) VERIFY_F(4) VERIFY_F(5) VERIFY_F(6) VERIFY_F(7) VERIFY_F(8) VERIFY_F(9) VERIFY_F(10) VERIFY_F(11) VERIFY_F(12) VERIFY_F(13) VERIFY_F(14) VERIFY_F(15) VERIFY_F(16) VERIFY_F(17) VERIFY_F(18) VERIFY_F(19) VERIFY_F(20) VERIFY_F(21) VERIFY_F(22) VERIFY_F(23) VERIFY_F(24) VERIFY_F(25) VERIFY_F(26) VERIFY_F(27) VERIFY_F(28) VERIFY_F(29) VERIFY_F(30) VERIFY_F(31) return (1 & ((differentbits - 1) >> 8)) - 1; } #undef VERIFY_F ed25519-0.0.5.0/src/cbits/ref10/fe_frombytes.c0000644000000000000000000000335712606567661016525 0ustar0000000000000000#include "fe.h" #include "load.h" #include "crypto_int64.h" #include "crypto_uint64.h" /* Ignores top bit of h. */ static inline void fe_frombytes(fe h,const unsigned char *s) { crypto_int64 h0 = load_4(s); crypto_int64 h1 = load_3(s + 4) << 6; crypto_int64 h2 = load_3(s + 7) << 5; crypto_int64 h3 = load_3(s + 10) << 3; crypto_int64 h4 = load_3(s + 13) << 2; crypto_int64 h5 = load_4(s + 16); crypto_int64 h6 = load_3(s + 20) << 7; crypto_int64 h7 = load_3(s + 23) << 5; crypto_int64 h8 = load_3(s + 26) << 4; crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2; crypto_int64 carry0; crypto_int64 carry1; crypto_int64 carry2; crypto_int64 carry3; crypto_int64 carry4; crypto_int64 carry5; crypto_int64 carry6; crypto_int64 carry7; crypto_int64 carry8; crypto_int64 carry9; carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } ed25519-0.0.5.0/src/cbits/ref10/sc_muladd.c0000644000000000000000000002741712606567661015777 0ustar0000000000000000#include "sc.h" #include "load.h" #include "crypto_int64.h" #include "crypto_uint32.h" #include "crypto_uint64.h" /* Input: a[0]+256*a[1]+...+256^31*a[31] = a b[0]+256*b[1]+...+256^31*b[31] = b c[0]+256*c[1]+...+256^31*c[31] = c Output: s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l where l = 2^252 + 27742317777372353535851937790883648493. */ static inline void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c) { crypto_int64 a0 = 2097151 & load_3(a); crypto_int64 a1 = 2097151 & (load_4(a + 2) >> 5); crypto_int64 a2 = 2097151 & (load_3(a + 5) >> 2); crypto_int64 a3 = 2097151 & (load_4(a + 7) >> 7); crypto_int64 a4 = 2097151 & (load_4(a + 10) >> 4); crypto_int64 a5 = 2097151 & (load_3(a + 13) >> 1); crypto_int64 a6 = 2097151 & (load_4(a + 15) >> 6); crypto_int64 a7 = 2097151 & (load_3(a + 18) >> 3); crypto_int64 a8 = 2097151 & load_3(a + 21); crypto_int64 a9 = 2097151 & (load_4(a + 23) >> 5); crypto_int64 a10 = 2097151 & (load_3(a + 26) >> 2); crypto_int64 a11 = (load_4(a + 28) >> 7); crypto_int64 b0 = 2097151 & load_3(b); crypto_int64 b1 = 2097151 & (load_4(b + 2) >> 5); crypto_int64 b2 = 2097151 & (load_3(b + 5) >> 2); crypto_int64 b3 = 2097151 & (load_4(b + 7) >> 7); crypto_int64 b4 = 2097151 & (load_4(b + 10) >> 4); crypto_int64 b5 = 2097151 & (load_3(b + 13) >> 1); crypto_int64 b6 = 2097151 & (load_4(b + 15) >> 6); crypto_int64 b7 = 2097151 & (load_3(b + 18) >> 3); crypto_int64 b8 = 2097151 & load_3(b + 21); crypto_int64 b9 = 2097151 & (load_4(b + 23) >> 5); crypto_int64 b10 = 2097151 & (load_3(b + 26) >> 2); crypto_int64 b11 = (load_4(b + 28) >> 7); crypto_int64 c0 = 2097151 & load_3(c); crypto_int64 c1 = 2097151 & (load_4(c + 2) >> 5); crypto_int64 c2 = 2097151 & (load_3(c + 5) >> 2); crypto_int64 c3 = 2097151 & (load_4(c + 7) >> 7); crypto_int64 c4 = 2097151 & (load_4(c + 10) >> 4); crypto_int64 c5 = 2097151 & (load_3(c + 13) >> 1); crypto_int64 c6 = 2097151 & (load_4(c + 15) >> 6); crypto_int64 c7 = 2097151 & (load_3(c + 18) >> 3); crypto_int64 c8 = 2097151 & load_3(c + 21); crypto_int64 c9 = 2097151 & (load_4(c + 23) >> 5); crypto_int64 c10 = 2097151 & (load_3(c + 26) >> 2); crypto_int64 c11 = (load_4(c + 28) >> 7); crypto_int64 s0; crypto_int64 s1; crypto_int64 s2; crypto_int64 s3; crypto_int64 s4; crypto_int64 s5; crypto_int64 s6; crypto_int64 s7; crypto_int64 s8; crypto_int64 s9; crypto_int64 s10; crypto_int64 s11; crypto_int64 s12; crypto_int64 s13; crypto_int64 s14; crypto_int64 s15; crypto_int64 s16; crypto_int64 s17; crypto_int64 s18; crypto_int64 s19; crypto_int64 s20; crypto_int64 s21; crypto_int64 s22; crypto_int64 s23; crypto_int64 carry0; crypto_int64 carry1; crypto_int64 carry2; crypto_int64 carry3; crypto_int64 carry4; crypto_int64 carry5; crypto_int64 carry6; crypto_int64 carry7; crypto_int64 carry8; crypto_int64 carry9; crypto_int64 carry10; crypto_int64 carry11; crypto_int64 carry12; crypto_int64 carry13; crypto_int64 carry14; crypto_int64 carry15; crypto_int64 carry16; crypto_int64 carry17; crypto_int64 carry18; crypto_int64 carry19; crypto_int64 carry20; crypto_int64 carry21; crypto_int64 carry22; s0 = c0 + a0*b0; s1 = c1 + a0*b1 + a1*b0; s2 = c2 + a0*b2 + a1*b1 + a2*b0; s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0; s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0; s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0; s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0; s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0; s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0; s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0; s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0; s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0; s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1; s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2; s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3; s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4; s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5; s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6; s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7; s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8; s20 = a9*b11 + a10*b10 + a11*b9; s21 = a10*b11 + a11*b10; s22 = a11*b11; s23 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; s23 = 0; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s22 = 0; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s21 = 0; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s20 = 0; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s19 = 0; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; s18 = 0; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; s17 = 0; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s16 = 0; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s15 = 0; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s14 = 0; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; s13 = 0; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 << 5); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 << 2); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 << 7); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 << 4); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 << 1); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 << 6); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 << 3); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 << 5); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 << 2); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 << 7); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } ed25519-0.0.5.0/src/cbits/ref10/ge_madd.c0000644000000000000000000000021612606567661015410 0ustar0000000000000000#include "ge.h" /* r = p + q */ static inline void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) { fe t0; #include "ge_madd.h" } ed25519-0.0.5.0/src/cbits/ref10/ge_p2_dbl.c0000644000000000000000000000017612606567661015652 0ustar0000000000000000#include "ge.h" /* r = 2 * p */ static inline void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p) { fe t0; #include "ge_p2_dbl.h" } ed25519-0.0.5.0/src/cbits/ref10/ed25519.c0000644000000000000000000000171212606567661015030 0ustar0000000000000000#include "sha512.c" #include "fe_tobytes.c" #include "fe_copy.c" #include "fe_1.c" #include "ge_tobytes.c" #include "sign.c" #include "fe_sq2.c" #include "fe_cmov.c" #include "ge_p1p1_to_p3.c" #include "ge_p3_dbl.c" #include "fe_mul.c" #include "ge_p3_to_cached.c" #include "fe_pow22523.c" #include "ge_add.c" #include "ge_sub.c" #include "fe_add.c" #include "ge_p2_0.c" #include "ge_p3_to_p2.c" #include "fe_invert.c" #include "open.c" #include "ge_msub.c" #include "fe_0.c" #include "fe_sub.c" #include "fe_isnonzero.c" #include "fe_isnegative.c" #include "fe_neg.c" #include "ge_frombytes.c" #include "ge_p3_tobytes.c" #include "ge_double_scalarmult.c" #include "ge_p1p1_to_p2.c" #include "fe_sq.c" #include "ge_p3_0.c" #include "ge_precomp_0.c" #include "ge_scalarmult_base.c" #include "sc_reduce.c" #include "keypair.c" #include "fe_frombytes.c" #include "sc_muladd.c" #include "ge_madd.c" #include "ge_p2_dbl.c" #include "crypto_verify.c" #include "randombytes.c" ed25519-0.0.5.0/src/cbits/ref10/include/0000755000000000000000000000000012606567661015310 5ustar0000000000000000ed25519-0.0.5.0/src/cbits/ref10/include/crypto_int8.h0000644000000000000000000000014512606567661017743 0ustar0000000000000000#ifndef crypto_int8_h #define crypto_int8_h #include typedef int8_t crypto_int8; #endif ed25519-0.0.5.0/src/cbits/ref10/include/ge_p2_dbl.h0000644000000000000000000000270412606567661017301 0ustar0000000000000000 /* qhasm: enter ge_p2_dbl */ /* qhasm: fe X1 */ /* qhasm: fe Y1 */ /* qhasm: fe Z1 */ /* qhasm: fe A */ /* qhasm: fe AA */ /* qhasm: fe XX */ /* qhasm: fe YY */ /* qhasm: fe B */ /* qhasm: fe X3 */ /* qhasm: fe Y3 */ /* qhasm: fe Z3 */ /* qhasm: fe T3 */ /* qhasm: XX=X1^2 */ /* asm 1: fe_sq(>XX=fe#1,XX=r->X,X); */ fe_sq(r->X,p->X); /* qhasm: YY=Y1^2 */ /* asm 1: fe_sq(>YY=fe#3,YY=r->Z,Y); */ fe_sq(r->Z,p->Y); /* qhasm: B=2*Z1^2 */ /* asm 1: fe_sq2(>B=fe#4,B=r->T,Z); */ fe_sq2(r->T,p->Z); /* qhasm: A=X1+Y1 */ /* asm 1: fe_add(>A=fe#2,A=r->Y,X,Y); */ fe_add(r->Y,p->X,p->Y); /* qhasm: AA=A^2 */ /* asm 1: fe_sq(>AA=fe#5,AA=t0,Y); */ fe_sq(t0,r->Y); /* qhasm: Y3=YY+XX */ /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,X); */ fe_add(r->Y,r->Z,r->X); /* qhasm: Z3=YY-XX */ /* asm 1: fe_sub(>Z3=fe#3,Z3=r->Z,Z,X); */ fe_sub(r->Z,r->Z,r->X); /* qhasm: X3=AA-Y3 */ /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Y); */ fe_sub(r->X,t0,r->Y); /* qhasm: T3=B-Z3 */ /* asm 1: fe_sub(>T3=fe#4,T3=r->T,T,Z); */ fe_sub(r->T,r->T,r->Z); /* qhasm: return */ ed25519-0.0.5.0/src/cbits/ref10/include/crypto_verify.h0000644000000000000000000000034112606567661020363 0ustar0000000000000000#ifndef crypto_verify_16_H #define crypto_verify_16_H static inline int crypto_verify_16(const unsigned char *,const unsigned char *); static inline int crypto_verify_32(const unsigned char *,const unsigned char *); #endif ed25519-0.0.5.0/src/cbits/ref10/include/crypto_uint8.h0000644000000000000000000000015112606567661020125 0ustar0000000000000000#ifndef crypto_uint8_h #define crypto_uint8_h #include typedef uint8_t crypto_uint8; #endif ed25519-0.0.5.0/src/cbits/ref10/include/sqrtm1.h0000644000000000000000000000012712606567661016710 0ustar0000000000000000-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482 ed25519-0.0.5.0/src/cbits/ref10/include/ge_sub.h0000644000000000000000000000404012606567661016723 0ustar0000000000000000 /* qhasm: enter ge_sub */ /* qhasm: fe X1 */ /* qhasm: fe Y1 */ /* qhasm: fe Z1 */ /* qhasm: fe Z2 */ /* qhasm: fe T1 */ /* qhasm: fe ZZ */ /* qhasm: fe YpX2 */ /* qhasm: fe YmX2 */ /* qhasm: fe T2d2 */ /* qhasm: fe X3 */ /* qhasm: fe Y3 */ /* qhasm: fe Z3 */ /* qhasm: fe T3 */ /* qhasm: fe YpX1 */ /* qhasm: fe YmX1 */ /* qhasm: fe A */ /* qhasm: fe B */ /* qhasm: fe C */ /* qhasm: fe D */ /* qhasm: YpX1 = Y1+X1 */ /* asm 1: fe_add(>YpX1=fe#1,YpX1=r->X,Y,X); */ fe_add(r->X,p->Y,p->X); /* qhasm: YmX1 = Y1-X1 */ /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */ fe_sub(r->Y,p->Y,p->X); /* qhasm: A = YpX1*YmX2 */ /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,YminusX); */ fe_mul(r->Z,r->X,q->YminusX); /* qhasm: B = YmX1*YpX2 */ /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,YplusX); */ fe_mul(r->Y,r->Y,q->YplusX); /* qhasm: C = T2d2*T1 */ /* asm 1: fe_mul(>C=fe#4,C=r->T,T2d,T); */ fe_mul(r->T,q->T2d,p->T); /* qhasm: ZZ = Z1*Z2 */ /* asm 1: fe_mul(>ZZ=fe#1,ZZ=r->X,Z,Z); */ fe_mul(r->X,p->Z,q->Z); /* qhasm: D = 2*ZZ */ /* asm 1: fe_add(>D=fe#5,D=t0,X,X); */ fe_add(t0,r->X,r->X); /* qhasm: X3 = A-B */ /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */ fe_sub(r->X,r->Z,r->Y); /* qhasm: Y3 = A+B */ /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */ fe_add(r->Y,r->Z,r->Y); /* qhasm: Z3 = D-C */ /* asm 1: fe_sub(>Z3=fe#3,Z3=r->Z,T); */ fe_sub(r->Z,t0,r->T); /* qhasm: T3 = D+C */ /* asm 1: fe_add(>T3=fe#4,T3=r->T,T); */ fe_add(r->T,t0,r->T); /* qhasm: return */ ed25519-0.0.5.0/src/cbits/ref10/include/crypto_uint32.h0000644000000000000000000000015512606567661020206 0ustar0000000000000000#ifndef crypto_uint32_h #define crypto_uint32_h #include typedef uint32_t crypto_uint32; #endif ed25519-0.0.5.0/src/cbits/ref10/include/randombytes.h0000644000000000000000000000026412606567661020012 0ustar0000000000000000#ifndef _ED25519_RANDOMBYTES_H_ #define _ED25519_RANDOMBYTES_H_ static inline void ed25519_randombytes(unsigned char *, unsigned long long); #endif /* _ED25519_RANDOMBYTES_H_ */ ed25519-0.0.5.0/src/cbits/ref10/include/d.h0000644000000000000000000000013312606567661015701 0ustar0000000000000000-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116 ed25519-0.0.5.0/src/cbits/ref10/include/pow22523.h0000644000000000000000000001261612606567661016672 0ustar0000000000000000 /* qhasm: fe z1 */ /* qhasm: fe z2 */ /* qhasm: fe z8 */ /* qhasm: fe z9 */ /* qhasm: fe z11 */ /* qhasm: fe z22 */ /* qhasm: fe z_5_0 */ /* qhasm: fe z_10_5 */ /* qhasm: fe z_10_0 */ /* qhasm: fe z_20_10 */ /* qhasm: fe z_20_0 */ /* qhasm: fe z_40_20 */ /* qhasm: fe z_40_0 */ /* qhasm: fe z_50_10 */ /* qhasm: fe z_50_0 */ /* qhasm: fe z_100_50 */ /* qhasm: fe z_100_0 */ /* qhasm: fe z_200_100 */ /* qhasm: fe z_200_0 */ /* qhasm: fe z_250_50 */ /* qhasm: fe z_250_0 */ /* qhasm: fe z_252_2 */ /* qhasm: fe z_252_3 */ /* qhasm: enter pow22523 */ /* qhasm: z2 = z1^2^1 */ /* asm 1: fe_sq(>z2=fe#1,z2=fe#1,>z2=fe#1); */ /* asm 2: fe_sq(>z2=t0,z2=t0,>z2=t0); */ fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0); /* qhasm: z8 = z2^2^2 */ /* asm 1: fe_sq(>z8=fe#2,z8=fe#2,>z8=fe#2); */ /* asm 2: fe_sq(>z8=t1,z8=t1,>z8=t1); */ fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1); /* qhasm: z9 = z1*z8 */ /* asm 1: fe_mul(>z9=fe#2,z9=t1,z11=fe#1,z11=t0,z22=fe#1,z22=fe#1,>z22=fe#1); */ /* asm 2: fe_sq(>z22=t0,z22=t0,>z22=t0); */ fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0); /* qhasm: z_5_0 = z9*z22 */ /* asm 1: fe_mul(>z_5_0=fe#1,z_5_0=t0,z_10_5=fe#2,z_10_5=fe#2,>z_10_5=fe#2); */ /* asm 2: fe_sq(>z_10_5=t1,z_10_5=t1,>z_10_5=t1); */ fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1); /* qhasm: z_10_0 = z_10_5*z_5_0 */ /* asm 1: fe_mul(>z_10_0=fe#1,z_10_0=t0,z_20_10=fe#2,z_20_10=fe#2,>z_20_10=fe#2); */ /* asm 2: fe_sq(>z_20_10=t1,z_20_10=t1,>z_20_10=t1); */ fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1); /* qhasm: z_20_0 = z_20_10*z_10_0 */ /* asm 1: fe_mul(>z_20_0=fe#2,z_20_0=t1,z_40_20=fe#3,z_40_20=fe#3,>z_40_20=fe#3); */ /* asm 2: fe_sq(>z_40_20=t2,z_40_20=t2,>z_40_20=t2); */ fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2); /* qhasm: z_40_0 = z_40_20*z_20_0 */ /* asm 1: fe_mul(>z_40_0=fe#2,z_40_0=t1,z_50_10=fe#2,z_50_10=fe#2,>z_50_10=fe#2); */ /* asm 2: fe_sq(>z_50_10=t1,z_50_10=t1,>z_50_10=t1); */ fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1); /* qhasm: z_50_0 = z_50_10*z_10_0 */ /* asm 1: fe_mul(>z_50_0=fe#1,z_50_0=t0,z_100_50=fe#2,z_100_50=fe#2,>z_100_50=fe#2); */ /* asm 2: fe_sq(>z_100_50=t1,z_100_50=t1,>z_100_50=t1); */ fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1); /* qhasm: z_100_0 = z_100_50*z_50_0 */ /* asm 1: fe_mul(>z_100_0=fe#2,z_100_0=t1,z_200_100=fe#3,z_200_100=fe#3,>z_200_100=fe#3); */ /* asm 2: fe_sq(>z_200_100=t2,z_200_100=t2,>z_200_100=t2); */ fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2); /* qhasm: z_200_0 = z_200_100*z_100_0 */ /* asm 1: fe_mul(>z_200_0=fe#2,z_200_0=t1,z_250_50=fe#2,z_250_50=fe#2,>z_250_50=fe#2); */ /* asm 2: fe_sq(>z_250_50=t1,z_250_50=t1,>z_250_50=t1); */ fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1); /* qhasm: z_250_0 = z_250_50*z_50_0 */ /* asm 1: fe_mul(>z_250_0=fe#1,z_250_0=t0,z_252_2=fe#1,z_252_2=fe#1,>z_252_2=fe#1); */ /* asm 2: fe_sq(>z_252_2=t0,z_252_2=t0,>z_252_2=t0); */ fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0); /* qhasm: z_252_3 = z_252_2*z1 */ /* asm 1: fe_mul(>z_252_3=fe#12,z_252_3=out, typedef int16_t crypto_int16; #endif ed25519-0.0.5.0/src/cbits/ref10/include/crypto_uint64.h0000644000000000000000000000015512606567661020213 0ustar0000000000000000#ifndef crypto_uint64_h #define crypto_uint64_h #include typedef uint64_t crypto_uint64; #endif ed25519-0.0.5.0/src/cbits/ref10/include/crypto_uint16.h0000644000000000000000000000015512606567661020210 0ustar0000000000000000#ifndef crypto_uint16_h #define crypto_uint16_h #include typedef uint16_t crypto_uint16; #endif ed25519-0.0.5.0/src/cbits/ref10/include/sha512.h0000644000000000000000000000053112606567661016463 0ustar0000000000000000#ifndef SHA512_H #define SHA512_H #define crypto_hash_BYTES 64 #define crypto_hash_STATEBYTES 64 #define crypto_hash_BLOCKBYTES 128 static inline int crypto_hash_sha512(unsigned char *out, const unsigned char *in, unsigned long long inlen); #endif /* SHA512_H */ ed25519-0.0.5.0/src/cbits/ref10/include/sc.h0000644000000000000000000000061412606567661016067 0ustar0000000000000000#ifndef SC_H #define SC_H /* The set of scalars is \Z/l where l = 2^252 + 27742317777372353535851937790883648493. */ #define sc_reduce crypto_sign_ed25519_ref10_sc_reduce #define sc_muladd crypto_sign_ed25519_ref10_sc_muladd static inline void sc_reduce(unsigned char *); static inline void sc_muladd(unsigned char *,const unsigned char *,const unsigned char *,const unsigned char *); #endif ed25519-0.0.5.0/src/cbits/ref10/include/base2.h0000644000000000000000000000452412606567661016462 0ustar0000000000000000 { { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 }, { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 }, { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 }, }, { { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 }, { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 }, { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 }, }, { { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 }, { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 }, { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 }, }, { { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 }, { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 }, { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 }, }, { { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 }, { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 }, { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 }, }, { { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 }, { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 }, { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 }, }, { { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 }, { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 }, { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 }, }, { { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 }, { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 }, { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 }, }, ed25519-0.0.5.0/src/cbits/ref10/include/crypto_int64.h0000644000000000000000000000015112606567661020022 0ustar0000000000000000#ifndef crypto_int64_h #define crypto_int64_h #include typedef int64_t crypto_int64; #endif ed25519-0.0.5.0/src/cbits/ref10/include/pow225521.h0000644000000000000000000001262712606567661016757 0ustar0000000000000000 /* qhasm: fe z1 */ /* qhasm: fe z2 */ /* qhasm: fe z8 */ /* qhasm: fe z9 */ /* qhasm: fe z11 */ /* qhasm: fe z22 */ /* qhasm: fe z_5_0 */ /* qhasm: fe z_10_5 */ /* qhasm: fe z_10_0 */ /* qhasm: fe z_20_10 */ /* qhasm: fe z_20_0 */ /* qhasm: fe z_40_20 */ /* qhasm: fe z_40_0 */ /* qhasm: fe z_50_10 */ /* qhasm: fe z_50_0 */ /* qhasm: fe z_100_50 */ /* qhasm: fe z_100_0 */ /* qhasm: fe z_200_100 */ /* qhasm: fe z_200_0 */ /* qhasm: fe z_250_50 */ /* qhasm: fe z_250_0 */ /* qhasm: fe z_255_5 */ /* qhasm: fe z_255_21 */ /* qhasm: enter pow225521 */ /* qhasm: z2 = z1^2^1 */ /* asm 1: fe_sq(>z2=fe#1,z2=fe#1,>z2=fe#1); */ /* asm 2: fe_sq(>z2=t0,z2=t0,>z2=t0); */ fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0); /* qhasm: z8 = z2^2^2 */ /* asm 1: fe_sq(>z8=fe#2,z8=fe#2,>z8=fe#2); */ /* asm 2: fe_sq(>z8=t1,z8=t1,>z8=t1); */ fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1); /* qhasm: z9 = z1*z8 */ /* asm 1: fe_mul(>z9=fe#2,z9=t1,z11=fe#1,z11=t0,z22=fe#3,z22=fe#3,>z22=fe#3); */ /* asm 2: fe_sq(>z22=t2,z22=t2,>z22=t2); */ fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2); /* qhasm: z_5_0 = z9*z22 */ /* asm 1: fe_mul(>z_5_0=fe#2,z_5_0=t1,z_10_5=fe#3,z_10_5=fe#3,>z_10_5=fe#3); */ /* asm 2: fe_sq(>z_10_5=t2,z_10_5=t2,>z_10_5=t2); */ fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2); /* qhasm: z_10_0 = z_10_5*z_5_0 */ /* asm 1: fe_mul(>z_10_0=fe#2,z_10_0=t1,z_20_10=fe#3,z_20_10=fe#3,>z_20_10=fe#3); */ /* asm 2: fe_sq(>z_20_10=t2,z_20_10=t2,>z_20_10=t2); */ fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2); /* qhasm: z_20_0 = z_20_10*z_10_0 */ /* asm 1: fe_mul(>z_20_0=fe#3,z_20_0=t2,z_40_20=fe#4,z_40_20=fe#4,>z_40_20=fe#4); */ /* asm 2: fe_sq(>z_40_20=t3,z_40_20=t3,>z_40_20=t3); */ fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3); /* qhasm: z_40_0 = z_40_20*z_20_0 */ /* asm 1: fe_mul(>z_40_0=fe#3,z_40_0=t2,z_50_10=fe#3,z_50_10=fe#3,>z_50_10=fe#3); */ /* asm 2: fe_sq(>z_50_10=t2,z_50_10=t2,>z_50_10=t2); */ fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2); /* qhasm: z_50_0 = z_50_10*z_10_0 */ /* asm 1: fe_mul(>z_50_0=fe#2,z_50_0=t1,z_100_50=fe#3,z_100_50=fe#3,>z_100_50=fe#3); */ /* asm 2: fe_sq(>z_100_50=t2,z_100_50=t2,>z_100_50=t2); */ fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2); /* qhasm: z_100_0 = z_100_50*z_50_0 */ /* asm 1: fe_mul(>z_100_0=fe#3,z_100_0=t2,z_200_100=fe#4,z_200_100=fe#4,>z_200_100=fe#4); */ /* asm 2: fe_sq(>z_200_100=t3,z_200_100=t3,>z_200_100=t3); */ fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3); /* qhasm: z_200_0 = z_200_100*z_100_0 */ /* asm 1: fe_mul(>z_200_0=fe#3,z_200_0=t2,z_250_50=fe#3,z_250_50=fe#3,>z_250_50=fe#3); */ /* asm 2: fe_sq(>z_250_50=t2,z_250_50=t2,>z_250_50=t2); */ fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2); /* qhasm: z_250_0 = z_250_50*z_50_0 */ /* asm 1: fe_mul(>z_250_0=fe#2,z_250_0=t1,z_255_5=fe#2,z_255_5=fe#2,>z_255_5=fe#2); */ /* asm 2: fe_sq(>z_255_5=t1,z_255_5=t1,>z_255_5=t1); */ fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1); /* qhasm: z_255_21 = z_255_5*z11 */ /* asm 1: fe_mul(>z_255_21=fe#12,z_255_21=out,YpX1=fe#1,YpX1=r->X,Y,X); */ fe_add(r->X,p->Y,p->X); /* qhasm: YmX1 = Y1-X1 */ /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */ fe_sub(r->Y,p->Y,p->X); /* qhasm: A = YpX1*ymx2 */ /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,yminusx); */ fe_mul(r->Z,r->X,q->yminusx); /* qhasm: B = YmX1*ypx2 */ /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,yplusx); */ fe_mul(r->Y,r->Y,q->yplusx); /* qhasm: C = xy2d2*T1 */ /* asm 1: fe_mul(>C=fe#4,C=r->T,xy2d,T); */ fe_mul(r->T,q->xy2d,p->T); /* qhasm: D = 2*Z1 */ /* asm 1: fe_add(>D=fe#5,D=t0,Z,Z); */ fe_add(t0,p->Z,p->Z); /* qhasm: X3 = A-B */ /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */ fe_sub(r->X,r->Z,r->Y); /* qhasm: Y3 = A+B */ /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */ fe_add(r->Y,r->Z,r->Y); /* qhasm: Z3 = D-C */ /* asm 1: fe_sub(>Z3=fe#3,Z3=r->Z,T); */ fe_sub(r->Z,t0,r->T); /* qhasm: T3 = D+C */ /* asm 1: fe_add(>T3=fe#4,T3=r->T,T); */ fe_add(r->T,t0,r->T); /* qhasm: return */ ed25519-0.0.5.0/src/cbits/ref10/include/api.h0000644000000000000000000000013212606567661016226 0ustar0000000000000000#define CRYPTO_SECRETKEYBYTES 64 #define CRYPTO_PUBLICKEYBYTES 32 #define CRYPTO_BYTES 64 ed25519-0.0.5.0/src/cbits/ref10/include/ge_madd.h0000644000000000000000000000355412606567661017050 0ustar0000000000000000 /* qhasm: enter ge_madd */ /* qhasm: fe X1 */ /* qhasm: fe Y1 */ /* qhasm: fe Z1 */ /* qhasm: fe T1 */ /* qhasm: fe ypx2 */ /* qhasm: fe ymx2 */ /* qhasm: fe xy2d2 */ /* qhasm: fe X3 */ /* qhasm: fe Y3 */ /* qhasm: fe Z3 */ /* qhasm: fe T3 */ /* qhasm: fe YpX1 */ /* qhasm: fe YmX1 */ /* qhasm: fe A */ /* qhasm: fe B */ /* qhasm: fe C */ /* qhasm: fe D */ /* qhasm: YpX1 = Y1+X1 */ /* asm 1: fe_add(>YpX1=fe#1,YpX1=r->X,Y,X); */ fe_add(r->X,p->Y,p->X); /* qhasm: YmX1 = Y1-X1 */ /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */ fe_sub(r->Y,p->Y,p->X); /* qhasm: A = YpX1*ypx2 */ /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,yplusx); */ fe_mul(r->Z,r->X,q->yplusx); /* qhasm: B = YmX1*ymx2 */ /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,yminusx); */ fe_mul(r->Y,r->Y,q->yminusx); /* qhasm: C = xy2d2*T1 */ /* asm 1: fe_mul(>C=fe#4,C=r->T,xy2d,T); */ fe_mul(r->T,q->xy2d,p->T); /* qhasm: D = 2*Z1 */ /* asm 1: fe_add(>D=fe#5,D=t0,Z,Z); */ fe_add(t0,p->Z,p->Z); /* qhasm: X3 = A-B */ /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */ fe_sub(r->X,r->Z,r->Y); /* qhasm: Y3 = A+B */ /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */ fe_add(r->Y,r->Z,r->Y); /* qhasm: Z3 = D+C */ /* asm 1: fe_add(>Z3=fe#3,Z3=r->Z,T); */ fe_add(r->Z,t0,r->T); /* qhasm: T3 = D-C */ /* asm 1: fe_sub(>T3=fe#4,T3=r->T,T); */ fe_sub(r->T,t0,r->T); /* qhasm: return */ ed25519-0.0.5.0/src/cbits/ref10/include/ge.h0000644000000000000000000000566412606567661016067 0ustar0000000000000000#ifndef GE_H #define GE_H /* ge means group element. Here the group is the set of pairs (x,y) of field elements (see fe.h) satisfying -x^2 + y^2 = 1 + d x^2y^2 where d = -121665/121666. Representations: ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T ge_precomp (Duif): (y+x,y-x,2dxy) */ #include "fe.h" typedef struct { fe X; fe Y; fe Z; } ge_p2; typedef struct { fe X; fe Y; fe Z; fe T; } ge_p3; typedef struct { fe X; fe Y; fe Z; fe T; } ge_p1p1; typedef struct { fe yplusx; fe yminusx; fe xy2d; } ge_precomp; typedef struct { fe YplusX; fe YminusX; fe Z; fe T2d; } ge_cached; #define ge_frombytes_negate_vartime crypto_sign_ed25519_ref10_ge_frombytes_negate_vartime #define ge_tobytes crypto_sign_ed25519_ref10_ge_tobytes #define ge_p3_tobytes crypto_sign_ed25519_ref10_ge_p3_tobytes #define ge_p2_0 crypto_sign_ed25519_ref10_ge_p2_0 #define ge_p3_0 crypto_sign_ed25519_ref10_ge_p3_0 #define ge_precomp_0 crypto_sign_ed25519_ref10_ge_precomp_0 #define ge_p3_to_p2 crypto_sign_ed25519_ref10_ge_p3_to_p2 #define ge_p3_to_cached crypto_sign_ed25519_ref10_ge_p3_to_cached #define ge_p1p1_to_p2 crypto_sign_ed25519_ref10_ge_p1p1_to_p2 #define ge_p1p1_to_p3 crypto_sign_ed25519_ref10_ge_p1p1_to_p3 #define ge_p2_dbl crypto_sign_ed25519_ref10_ge_p2_dbl #define ge_p3_dbl crypto_sign_ed25519_ref10_ge_p3_dbl #define ge_madd crypto_sign_ed25519_ref10_ge_madd #define ge_msub crypto_sign_ed25519_ref10_ge_msub #define ge_add crypto_sign_ed25519_ref10_ge_add #define ge_sub crypto_sign_ed25519_ref10_ge_sub #define ge_scalarmult_base crypto_sign_ed25519_ref10_ge_scalarmult_base #define ge_double_scalarmult_vartime crypto_sign_ed25519_ref10_ge_double_scalarmult_vartime static inline void ge_tobytes(unsigned char *,const ge_p2 *); static inline void ge_p3_tobytes(unsigned char *,const ge_p3 *); static inline int ge_frombytes_negate_vartime(ge_p3 *,const unsigned char *); static inline void ge_p2_0(ge_p2 *); static inline void ge_p3_0(ge_p3 *); static inline void ge_precomp_0(ge_precomp *); static inline void ge_p3_to_p2(ge_p2 *,const ge_p3 *); static inline void ge_p3_to_cached(ge_cached *,const ge_p3 *); static inline void ge_p1p1_to_p2(ge_p2 *,const ge_p1p1 *); static inline void ge_p1p1_to_p3(ge_p3 *,const ge_p1p1 *); static inline void ge_p2_dbl(ge_p1p1 *,const ge_p2 *); static inline void ge_p3_dbl(ge_p1p1 *,const ge_p3 *); static inline void ge_madd(ge_p1p1 *,const ge_p3 *,const ge_precomp *); static inline void ge_msub(ge_p1p1 *,const ge_p3 *,const ge_precomp *); static inline void ge_add(ge_p1p1 *,const ge_p3 *,const ge_cached *); static inline void ge_sub(ge_p1p1 *,const ge_p3 *,const ge_cached *); static inline void ge_scalarmult_base(ge_p3 *,const unsigned char *); static inline void ge_double_scalarmult_vartime(ge_p2 *,const unsigned char *,const ge_p3 *,const unsigned char *); #endif ed25519-0.0.5.0/src/cbits/ref10/include/load.h0000644000000000000000000000106512606567661016402 0ustar0000000000000000#ifndef CRYPTO_LOAD_H #define CRYPTO_LOAD_H static inline crypto_uint64 load_3(const unsigned char *in) { crypto_uint64 result; result = (crypto_uint64) in[0]; result |= ((crypto_uint64) in[1]) << 8; result |= ((crypto_uint64) in[2]) << 16; return result; } static inline crypto_uint64 load_4(const unsigned char *in) { crypto_uint64 result; result = (crypto_uint64) in[0]; result |= ((crypto_uint64) in[1]) << 8; result |= ((crypto_uint64) in[2]) << 16; result |= ((crypto_uint64) in[3]) << 24; return result; } #endif /* CRYPTO_LOAD_H */ ed25519-0.0.5.0/src/cbits/ref10/include/d2.h0000644000000000000000000000013212606567661015762 0ustar0000000000000000-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199 ed25519-0.0.5.0/src/cbits/ref10/include/crypto_int32.h0000644000000000000000000000015112606567661020015 0ustar0000000000000000#ifndef crypto_int32_h #define crypto_int32_h #include typedef int32_t crypto_int32; #endif ed25519-0.0.5.0/src/cbits/ref10/include/fe.h0000644000000000000000000000350412606567661016055 0ustar0000000000000000#ifndef FE_H #define FE_H #include "crypto_int32.h" typedef crypto_int32 fe[10]; /* fe means field element. Here the field is \Z/(2^255-19). An element t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on context. */ #define fe_frombytes crypto_sign_ed25519_ref10_fe_frombytes #define fe_tobytes crypto_sign_ed25519_ref10_fe_tobytes #define fe_copy crypto_sign_ed25519_ref10_fe_copy #define fe_isnonzero crypto_sign_ed25519_ref10_fe_isnonzero #define fe_isnegative crypto_sign_ed25519_ref10_fe_isnegative #define fe_0 crypto_sign_ed25519_ref10_fe_0 #define fe_1 crypto_sign_ed25519_ref10_fe_1 #define fe_cmov crypto_sign_ed25519_ref10_fe_cmov #define fe_add crypto_sign_ed25519_ref10_fe_add #define fe_sub crypto_sign_ed25519_ref10_fe_sub #define fe_neg crypto_sign_ed25519_ref10_fe_neg #define fe_mul crypto_sign_ed25519_ref10_fe_mul #define fe_sq crypto_sign_ed25519_ref10_fe_sq #define fe_sq2 crypto_sign_ed25519_ref10_fe_sq2 #define fe_invert crypto_sign_ed25519_ref10_fe_invert #define fe_pow22523 crypto_sign_ed25519_ref10_fe_pow22523 static inline void fe_frombytes(fe,const unsigned char *); static inline void fe_tobytes(unsigned char *,const fe); static inline void fe_copy(fe,const fe); static inline int fe_isnonzero(const fe); static inline int fe_isnegative(const fe); static inline void fe_0(fe); static inline void fe_1(fe); static inline void fe_cmov(fe,const fe,unsigned int); static inline void fe_add(fe,const fe,const fe); static inline void fe_sub(fe,const fe,const fe); static inline void fe_neg(fe,const fe); static inline void fe_mul(fe,const fe,const fe); static inline void fe_sq(fe,const fe); static inline void fe_sq2(fe,const fe); static inline void fe_invert(fe,const fe); static inline void fe_pow22523(fe,const fe); #endif ed25519-0.0.5.0/src/cbits/ref10/include/base.h0000644000000000000000000022525112606567661016402 0ustar0000000000000000{ { { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 }, { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 }, { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 }, }, { { -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 }, { -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 }, { 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 }, }, { { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 }, { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 }, { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 }, }, { { -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 }, { 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 }, { 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 }, }, { { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 }, { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 }, { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 }, }, { { -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 }, { -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 }, { -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 }, }, { { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 }, { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 }, { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 }, }, { { 14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726 }, { -7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955 }, { 27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425 }, }, }, { { { -13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171 }, { 27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510 }, { 17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660 }, }, { { -10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639 }, { 29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963 }, { 5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950 }, }, { { -27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568 }, { 12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335 }, { 25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628 }, }, { { -26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007 }, { -2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772 }, { -22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653 }, }, { { 2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567 }, { 13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686 }, { 21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372 }, }, { { -13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887 }, { -23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954 }, { -29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953 }, }, { { 24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833 }, { -16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532 }, { -22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876 }, }, { { 2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268 }, { 33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214 }, { 1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038 }, }, }, { { { 6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800 }, { 4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645 }, { -4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664 }, }, { { 1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933 }, { -25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182 }, { -17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222 }, }, { { -18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991 }, { 20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880 }, { 9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092 }, }, { { -16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295 }, { 19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788 }, { 8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553 }, }, { { -15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026 }, { 11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347 }, { -18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033 }, }, { { -23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395 }, { -27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278 }, { 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 }, }, { { 32173121,-16129311,24896207,3921497,22579056,-3410854,19270449,12217473,17789017,-3395995 }, { -30552961,-2228401,-15578829,-10147201,13243889,517024,15479401,-3853233,30460520,1052596 }, { -11614875,13323618,32618793,8175907,-15230173,12596687,27491595,-4612359,3179268,-9478891 }, }, { { 31947069,-14366651,-4640583,-15339921,-15125977,-6039709,-14756777,-16411740,19072640,-9511060 }, { 11685058,11822410,3158003,-13952594,33402194,-4165066,5977896,-5215017,473099,5040608 }, { -20290863,8198642,-27410132,11602123,1290375,-2799760,28326862,1721092,-19558642,-3131606 }, }, }, { { { 7881532,10687937,7578723,7738378,-18951012,-2553952,21820786,8076149,-27868496,11538389 }, { -19935666,3899861,18283497,-6801568,-15728660,-11249211,8754525,7446702,-5676054,5797016 }, { -11295600,-3793569,-15782110,-7964573,12708869,-8456199,2014099,-9050574,-2369172,-5877341 }, }, { { -22472376,-11568741,-27682020,1146375,18956691,16640559,1192730,-3714199,15123619,10811505 }, { 14352098,-3419715,-18942044,10822655,32750596,4699007,-70363,15776356,-28886779,-11974553 }, { -28241164,-8072475,-4978962,-5315317,29416931,1847569,-20654173,-16484855,4714547,-9600655 }, }, { { 15200332,8368572,19679101,15970074,-31872674,1959451,24611599,-4543832,-11745876,12340220 }, { 12876937,-10480056,33134381,6590940,-6307776,14872440,9613953,8241152,15370987,9608631 }, { -4143277,-12014408,8446281,-391603,4407738,13629032,-7724868,15866074,-28210621,-8814099 }, }, { { 26660628,-15677655,8393734,358047,-7401291,992988,-23904233,858697,20571223,8420556 }, { 14620715,13067227,-15447274,8264467,14106269,15080814,33531827,12516406,-21574435,-12476749 }, { 236881,10476226,57258,-14677024,6472998,2466984,17258519,7256740,8791136,15069930 }, }, { { 1276410,-9371918,22949635,-16322807,-23493039,-5702186,14711875,4874229,-30663140,-2331391 }, { 5855666,4990204,-13711848,7294284,-7804282,1924647,-1423175,-7912378,-33069337,9234253 }, { 20590503,-9018988,31529744,-7352666,-2706834,10650548,31559055,-11609587,18979186,13396066 }, }, { { 24474287,4968103,22267082,4407354,24063882,-8325180,-18816887,13594782,33514650,7021958 }, { -11566906,-6565505,-21365085,15928892,-26158305,4315421,-25948728,-3916677,-21480480,12868082 }, { -28635013,13504661,19988037,-2132761,21078225,6443208,-21446107,2244500,-12455797,-8089383 }, }, { { -30595528,13793479,-5852820,319136,-25723172,-6263899,33086546,8957937,-15233648,5540521 }, { -11630176,-11503902,-8119500,-7643073,2620056,1022908,-23710744,-1568984,-16128528,-14962807 }, { 23152971,775386,27395463,14006635,-9701118,4649512,1689819,892185,-11513277,-15205948 }, }, { { 9770129,9586738,26496094,4324120,1556511,-3550024,27453819,4763127,-19179614,5867134 }, { -32765025,1927590,31726409,-4753295,23962434,-16019500,27846559,5931263,-29749703,-16108455 }, { 27461885,-2977536,22380810,1815854,-23033753,-3031938,7283490,-15148073,-19526700,7734629 }, }, }, { { { -8010264,-9590817,-11120403,6196038,29344158,-13430885,7585295,-3176626,18549497,15302069 }, { -32658337,-6171222,-7672793,-11051681,6258878,13504381,10458790,-6418461,-8872242,8424746 }, { 24687205,8613276,-30667046,-3233545,1863892,-1830544,19206234,7134917,-11284482,-828919 }, }, { { 11334899,-9218022,8025293,12707519,17523892,-10476071,10243738,-14685461,-5066034,16498837 }, { 8911542,6887158,-9584260,-6958590,11145641,-9543680,17303925,-14124238,6536641,10543906 }, { -28946384,15479763,-17466835,568876,-1497683,11223454,-2669190,-16625574,-27235709,8876771 }, }, { { -25742899,-12566864,-15649966,-846607,-33026686,-796288,-33481822,15824474,-604426,-9039817 }, { 10330056,70051,7957388,-9002667,9764902,15609756,27698697,-4890037,1657394,3084098 }, { 10477963,-7470260,12119566,-13250805,29016247,-5365589,31280319,14396151,-30233575,15272409 }, }, { { -12288309,3169463,28813183,16658753,25116432,-5630466,-25173957,-12636138,-25014757,1950504 }, { -26180358,9489187,11053416,-14746161,-31053720,5825630,-8384306,-8767532,15341279,8373727 }, { 28685821,7759505,-14378516,-12002860,-31971820,4079242,298136,-10232602,-2878207,15190420 }, }, { { -32932876,13806336,-14337485,-15794431,-24004620,10940928,8669718,2742393,-26033313,-6875003 }, { -1580388,-11729417,-25979658,-11445023,-17411874,-10912854,9291594,-16247779,-12154742,6048605 }, { -30305315,14843444,1539301,11864366,20201677,1900163,13934231,5128323,11213262,9168384 }, }, { { -26280513,11007847,19408960,-940758,-18592965,-4328580,-5088060,-11105150,20470157,-16398701 }, { -23136053,9282192,14855179,-15390078,-7362815,-14408560,-22783952,14461608,14042978,5230683 }, { 29969567,-2741594,-16711867,-8552442,9175486,-2468974,21556951,3506042,-5933891,-12449708 }, }, { { -3144746,8744661,19704003,4581278,-20430686,6830683,-21284170,8971513,-28539189,15326563 }, { -19464629,10110288,-17262528,-3503892,-23500387,1355669,-15523050,15300988,-20514118,9168260 }, { -5353335,4488613,-23803248,16314347,7780487,-15638939,-28948358,9601605,33087103,-9011387 }, }, { { -19443170,-15512900,-20797467,-12445323,-29824447,10229461,-27444329,-15000531,-5996870,15664672 }, { 23294591,-16632613,-22650781,-8470978,27844204,11461195,13099750,-2460356,18151676,13417686 }, { -24722913,-4176517,-31150679,5988919,-26858785,6685065,1661597,-12551441,15271676,-15452665 }, }, }, { { { 11433042,-13228665,8239631,-5279517,-1985436,-725718,-18698764,2167544,-6921301,-13440182 }, { -31436171,15575146,30436815,12192228,-22463353,9395379,-9917708,-8638997,12215110,12028277 }, { 14098400,6555944,23007258,5757252,-15427832,-12950502,30123440,4617780,-16900089,-655628 }, }, { { -4026201,-15240835,11893168,13718664,-14809462,1847385,-15819999,10154009,23973261,-12684474 }, { -26531820,-3695990,-1908898,2534301,-31870557,-16550355,18341390,-11419951,32013174,-10103539 }, { -25479301,10876443,-11771086,-14625140,-12369567,1838104,21911214,6354752,4425632,-837822 }, }, { { -10433389,-14612966,22229858,-3091047,-13191166,776729,-17415375,-12020462,4725005,14044970 }, { 19268650,-7304421,1555349,8692754,-21474059,-9910664,6347390,-1411784,-19522291,-16109756 }, { -24864089,12986008,-10898878,-5558584,-11312371,-148526,19541418,8180106,9282262,10282508 }, }, { { -26205082,4428547,-8661196,-13194263,4098402,-14165257,15522535,8372215,5542595,-10702683 }, { -10562541,14895633,26814552,-16673850,-17480754,-2489360,-2781891,6993761,-18093885,10114655 }, { -20107055,-929418,31422704,10427861,-7110749,6150669,-29091755,-11529146,25953725,-106158 }, }, { { -4234397,-8039292,-9119125,3046000,2101609,-12607294,19390020,6094296,-3315279,12831125 }, { -15998678,7578152,5310217,14408357,-33548620,-224739,31575954,6326196,7381791,-2421839 }, { -20902779,3296811,24736065,-16328389,18374254,7318640,6295303,8082724,-15362489,12339664 }, }, { { 27724736,2291157,6088201,-14184798,1792727,5857634,13848414,15768922,25091167,14856294 }, { -18866652,8331043,24373479,8541013,-701998,-9269457,12927300,-12695493,-22182473,-9012899 }, { -11423429,-5421590,11632845,3405020,30536730,-11674039,-27260765,13866390,30146206,9142070 }, }, { { 3924129,-15307516,-13817122,-10054960,12291820,-668366,-27702774,9326384,-8237858,4171294 }, { -15921940,16037937,6713787,16606682,-21612135,2790944,26396185,3731949,345228,-5462949 }, { -21327538,13448259,25284571,1143661,20614966,-8849387,2031539,-12391231,-16253183,-13582083 }, }, { { 31016211,-16722429,26371392,-14451233,-5027349,14854137,17477601,3842657,28012650,-16405420 }, { -5075835,9368966,-8562079,-4600902,-15249953,6970560,-9189873,16292057,-8867157,3507940 }, { 29439664,3537914,23333589,6997794,-17555561,-11018068,-15209202,-15051267,-9164929,6580396 }, }, }, { { { -12185861,-7679788,16438269,10826160,-8696817,-6235611,17860444,-9273846,-2095802,9304567 }, { 20714564,-4336911,29088195,7406487,11426967,-5095705,14792667,-14608617,5289421,-477127 }, { -16665533,-10650790,-6160345,-13305760,9192020,-1802462,17271490,12349094,26939669,-3752294 }, }, { { -12889898,9373458,31595848,16374215,21471720,13221525,-27283495,-12348559,-3698806,117887 }, { 22263325,-6560050,3984570,-11174646,-15114008,-566785,28311253,5358056,-23319780,541964 }, { 16259219,3261970,2309254,-15534474,-16885711,-4581916,24134070,-16705829,-13337066,-13552195 }, }, { { 9378160,-13140186,-22845982,-12745264,28198281,-7244098,-2399684,-717351,690426,14876244 }, { 24977353,-314384,-8223969,-13465086,28432343,-1176353,-13068804,-12297348,-22380984,6618999 }, { -1538174,11685646,12944378,13682314,-24389511,-14413193,8044829,-13817328,32239829,-5652762 }, }, { { -18603066,4762990,-926250,8885304,-28412480,-3187315,9781647,-10350059,32779359,5095274 }, { -33008130,-5214506,-32264887,-3685216,9460461,-9327423,-24601656,14506724,21639561,-2630236 }, { -16400943,-13112215,25239338,15531969,3987758,-4499318,-1289502,-6863535,17874574,558605 }, }, { { -13600129,10240081,9171883,16131053,-20869254,9599700,33499487,5080151,2085892,5119761 }, { -22205145,-2519528,-16381601,414691,-25019550,2170430,30634760,-8363614,-31999993,-5759884 }, { -6845704,15791202,8550074,-1312654,29928809,-12092256,27534430,-7192145,-22351378,12961482 }, }, { { -24492060,-9570771,10368194,11582341,-23397293,-2245287,16533930,8206996,-30194652,-5159638 }, { -11121496,-3382234,2307366,6362031,-135455,8868177,-16835630,7031275,7589640,8945490 }, { -32152748,8917967,6661220,-11677616,-1192060,-15793393,7251489,-11182180,24099109,-14456170 }, }, { { 5019558,-7907470,4244127,-14714356,-26933272,6453165,-19118182,-13289025,-6231896,-10280736 }, { 10853594,10721687,26480089,5861829,-22995819,1972175,-1866647,-10557898,-3363451,-6441124 }, { -17002408,5906790,221599,-6563147,7828208,-13248918,24362661,-2008168,-13866408,7421392 }, }, { { 8139927,-6546497,32257646,-5890546,30375719,1886181,-21175108,15441252,28826358,-4123029 }, { 6267086,9695052,7709135,-16603597,-32869068,-1886135,14795160,-7840124,13746021,-1742048 }, { 28584902,7787108,-6732942,-15050729,22846041,-7571236,-3181936,-363524,4771362,-8419958 }, }, }, { { { 24949256,6376279,-27466481,-8174608,-18646154,-9930606,33543569,-12141695,3569627,11342593 }, { 26514989,4740088,27912651,3697550,19331575,-11472339,6809886,4608608,7325975,-14801071 }, { -11618399,-14554430,-24321212,7655128,-1369274,5214312,-27400540,10258390,-17646694,-8186692 }, }, { { 11431204,15823007,26570245,14329124,18029990,4796082,-31446179,15580664,9280358,-3973687 }, { -160783,-10326257,-22855316,-4304997,-20861367,-13621002,-32810901,-11181622,-15545091,4387441 }, { -20799378,12194512,3937617,-5805892,-27154820,9340370,-24513992,8548137,20617071,-7482001 }, }, { { -938825,-3930586,-8714311,16124718,24603125,-6225393,-13775352,-11875822,24345683,10325460 }, { -19855277,-1568885,-22202708,8714034,14007766,6928528,16318175,-1010689,4766743,3552007 }, { -21751364,-16730916,1351763,-803421,-4009670,3950935,3217514,14481909,10988822,-3994762 }, }, { { 15564307,-14311570,3101243,5684148,30446780,-8051356,12677127,-6505343,-8295852,13296005 }, { -9442290,6624296,-30298964,-11913677,-4670981,-2057379,31521204,9614054,-30000824,12074674 }, { 4771191,-135239,14290749,-13089852,27992298,14998318,-1413936,-1556716,29832613,-16391035 }, }, { { 7064884,-7541174,-19161962,-5067537,-18891269,-2912736,25825242,5293297,-27122660,13101590 }, { -2298563,2439670,-7466610,1719965,-27267541,-16328445,32512469,-5317593,-30356070,-4190957 }, { -30006540,10162316,-33180176,3981723,-16482138,-13070044,14413974,9515896,19568978,9628812 }, }, { { 33053803,199357,15894591,1583059,27380243,-4580435,-17838894,-6106839,-6291786,3437740 }, { -18978877,3884493,19469877,12726490,15913552,13614290,-22961733,70104,7463304,4176122 }, { -27124001,10659917,11482427,-16070381,12771467,-6635117,-32719404,-5322751,24216882,5944158 }, }, { { 8894125,7450974,-2664149,-9765752,-28080517,-12389115,19345746,14680796,11632993,5847885 }, { 26942781,-2315317,9129564,-4906607,26024105,11769399,-11518837,6367194,-9727230,4782140 }, { 19916461,-4828410,-22910704,-11414391,25606324,-5972441,33253853,8220911,6358847,-1873857 }, }, { { 801428,-2081702,16569428,11065167,29875704,96627,7908388,-4480480,-13538503,1387155 }, { 19646058,5720633,-11416706,12814209,11607948,12749789,14147075,15156355,-21866831,11835260 }, { 19299512,1155910,28703737,14890794,2925026,7269399,26121523,15467869,-26560550,5052483 }, }, }, { { { -3017432,10058206,1980837,3964243,22160966,12322533,-6431123,-12618185,12228557,-7003677 }, { 32944382,14922211,-22844894,5188528,21913450,-8719943,4001465,13238564,-6114803,8653815 }, { 22865569,-4652735,27603668,-12545395,14348958,8234005,24808405,5719875,28483275,2841751 }, }, { { -16420968,-1113305,-327719,-12107856,21886282,-15552774,-1887966,-315658,19932058,-12739203 }, { -11656086,10087521,-8864888,-5536143,-19278573,-3055912,3999228,13239134,-4777469,-13910208 }, { 1382174,-11694719,17266790,9194690,-13324356,9720081,20403944,11284705,-14013818,3093230 }, }, { { 16650921,-11037932,-1064178,1570629,-8329746,7352753,-302424,16271225,-24049421,-6691850 }, { -21911077,-5927941,-4611316,-5560156,-31744103,-10785293,24123614,15193618,-21652117,-16739389 }, { -9935934,-4289447,-25279823,4372842,2087473,10399484,31870908,14690798,17361620,11864968 }, }, { { -11307610,6210372,13206574,5806320,-29017692,-13967200,-12331205,-7486601,-25578460,-16240689 }, { 14668462,-12270235,26039039,15305210,25515617,4542480,10453892,6577524,9145645,-6443880 }, { 5974874,3053895,-9433049,-10385191,-31865124,3225009,-7972642,3936128,-5652273,-3050304 }, }, { { 30625386,-4729400,-25555961,-12792866,-20484575,7695099,17097188,-16303496,-27999779,1803632 }, { -3553091,9865099,-5228566,4272701,-5673832,-16689700,14911344,12196514,-21405489,7047412 }, { 20093277,9920966,-11138194,-5343857,13161587,12044805,-32856851,4124601,-32343828,-10257566 }, }, { { -20788824,14084654,-13531713,7842147,19119038,-13822605,4752377,-8714640,-21679658,2288038 }, { -26819236,-3283715,29965059,3039786,-14473765,2540457,29457502,14625692,-24819617,12570232 }, { -1063558,-11551823,16920318,12494842,1278292,-5869109,-21159943,-3498680,-11974704,4724943 }, }, { { 17960970,-11775534,-4140968,-9702530,-8876562,-1410617,-12907383,-8659932,-29576300,1903856 }, { 23134274,-14279132,-10681997,-1611936,20684485,15770816,-12989750,3190296,26955097,14109738 }, { 15308788,5320727,-30113809,-14318877,22902008,7767164,29425325,-11277562,31960942,11934971 }, }, { { -27395711,8435796,4109644,12222639,-24627868,14818669,20638173,4875028,10491392,1379718 }, { -13159415,9197841,3875503,-8936108,-1383712,-5879801,33518459,16176658,21432314,12180697 }, { -11787308,11500838,13787581,-13832590,-22430679,10140205,1465425,12689540,-10301319,-13872883 }, }, }, { { { 5414091,-15386041,-21007664,9643570,12834970,1186149,-2622916,-1342231,26128231,6032912 }, { -26337395,-13766162,32496025,-13653919,17847801,-12669156,3604025,8316894,-25875034,-10437358 }, { 3296484,6223048,24680646,-12246460,-23052020,5903205,-8862297,-4639164,12376617,3188849 }, }, { { 29190488,-14659046,27549113,-1183516,3520066,-10697301,32049515,-7309113,-16109234,-9852307 }, { -14744486,-9309156,735818,-598978,-20407687,-5057904,25246078,-15795669,18640741,-960977 }, { -6928835,-16430795,10361374,5642961,4910474,12345252,-31638386,-494430,10530747,1053335 }, }, { { -29265967,-14186805,-13538216,-12117373,-19457059,-10655384,-31462369,-2948985,24018831,15026644 }, { -22592535,-3145277,-2289276,5953843,-13440189,9425631,25310643,13003497,-2314791,-15145616 }, { -27419985,-603321,-8043984,-1669117,-26092265,13987819,-27297622,187899,-23166419,-2531735 }, }, { { -21744398,-13810475,1844840,5021428,-10434399,-15911473,9716667,16266922,-5070217,726099 }, { 29370922,-6053998,7334071,-15342259,9385287,2247707,-13661962,-4839461,30007388,-15823341 }, { -936379,16086691,23751945,-543318,-1167538,-5189036,9137109,730663,9835848,4555336 }, }, { { -23376435,1410446,-22253753,-12899614,30867635,15826977,17693930,544696,-11985298,12422646 }, { 31117226,-12215734,-13502838,6561947,-9876867,-12757670,-5118685,-4096706,29120153,13924425 }, { -17400879,-14233209,19675799,-2734756,-11006962,-5858820,-9383939,-11317700,7240931,-237388 }, }, { { -31361739,-11346780,-15007447,-5856218,-22453340,-12152771,1222336,4389483,3293637,-15551743 }, { -16684801,-14444245,11038544,11054958,-13801175,-3338533,-24319580,7733547,12796905,-6335822 }, { -8759414,-10817836,-25418864,10783769,-30615557,-9746811,-28253339,3647836,3222231,-11160462 }, }, { { 18606113,1693100,-25448386,-15170272,4112353,10045021,23603893,-2048234,-7550776,2484985 }, { 9255317,-3131197,-12156162,-1004256,13098013,-9214866,16377220,-2102812,-19802075,-3034702 }, { -22729289,7496160,-5742199,11329249,19991973,-3347502,-31718148,9936966,-30097688,-10618797 }, }, { { 21878590,-5001297,4338336,13643897,-3036865,13160960,19708896,5415497,-7360503,-4109293 }, { 27736861,10103576,12500508,8502413,-3413016,-9633558,10436918,-1550276,-23659143,-8132100 }, { 19492550,-12104365,-29681976,-852630,-3208171,12403437,30066266,8367329,13243957,8709688 }, }, }, { { { 12015105,2801261,28198131,10151021,24818120,-4743133,-11194191,-5645734,5150968,7274186 }, { 2831366,-12492146,1478975,6122054,23825128,-12733586,31097299,6083058,31021603,-9793610 }, { -2529932,-2229646,445613,10720828,-13849527,-11505937,-23507731,16354465,15067285,-14147707 }, }, { { 7840942,14037873,-33364863,15934016,-728213,-3642706,21403988,1057586,-19379462,-12403220 }, { 915865,-16469274,15608285,-8789130,-24357026,6060030,-17371319,8410997,-7220461,16527025 }, { 32922597,-556987,20336074,-16184568,10903705,-5384487,16957574,52992,23834301,6588044 }, }, { { 32752030,11232950,3381995,-8714866,22652988,-10744103,17159699,16689107,-20314580,-1305992 }, { -4689649,9166776,-25710296,-10847306,11576752,12733943,7924251,-2752281,1976123,-7249027 }, { 21251222,16309901,-2983015,-6783122,30810597,12967303,156041,-3371252,12331345,-8237197 }, }, { { 8651614,-4477032,-16085636,-4996994,13002507,2950805,29054427,-5106970,10008136,-4667901 }, { 31486080,15114593,-14261250,12951354,14369431,-7387845,16347321,-13662089,8684155,-10532952 }, { 19443825,11385320,24468943,-9659068,-23919258,2187569,-26263207,-6086921,31316348,14219878 }, }, { { -28594490,1193785,32245219,11392485,31092169,15722801,27146014,6992409,29126555,9207390 }, { 32382935,1110093,18477781,11028262,-27411763,-7548111,-4980517,10843782,-7957600,-14435730 }, { 2814918,7836403,27519878,-7868156,-20894015,-11553689,-21494559,8550130,28346258,1994730 }, }, { { -19578299,8085545,-14000519,-3948622,2785838,-16231307,-19516951,7174894,22628102,8115180 }, { -30405132,955511,-11133838,-15078069,-32447087,-13278079,-25651578,3317160,-9943017,930272 }, { -15303681,-6833769,28856490,1357446,23421993,1057177,24091212,-1388970,-22765376,-10650715 }, }, { { -22751231,-5303997,-12907607,-12768866,-15811511,-7797053,-14839018,-16554220,-1867018,8398970 }, { -31969310,2106403,-4736360,1362501,12813763,16200670,22981545,-6291273,18009408,-15772772 }, { -17220923,-9545221,-27784654,14166835,29815394,7444469,29551787,-3727419,19288549,1325865 }, }, { { 15100157,-15835752,-23923978,-1005098,-26450192,15509408,12376730,-3479146,33166107,-8042750 }, { 20909231,13023121,-9209752,16251778,-5778415,-8094914,12412151,10018715,2213263,-13878373 }, { 32529814,-11074689,30361439,-16689753,-9135940,1513226,22922121,6382134,-5766928,8371348 }, }, }, { { { 9923462,11271500,12616794,3544722,-29998368,-1721626,12891687,-8193132,-26442943,10486144 }, { -22597207,-7012665,8587003,-8257861,4084309,-12970062,361726,2610596,-23921530,-11455195 }, { 5408411,-1136691,-4969122,10561668,24145918,14240566,31319731,-4235541,19985175,-3436086 }, }, { { -13994457,16616821,14549246,3341099,32155958,13648976,-17577068,8849297,65030,8370684 }, { -8320926,-12049626,31204563,5839400,-20627288,-1057277,-19442942,6922164,12743482,-9800518 }, { -2361371,12678785,28815050,4759974,-23893047,4884717,23783145,11038569,18800704,255233 }, }, { { -5269658,-1773886,13957886,7990715,23132995,728773,13393847,9066957,19258688,-14753793 }, { -2936654,-10827535,-10432089,14516793,-3640786,4372541,-31934921,2209390,-1524053,2055794 }, { 580882,16705327,5468415,-2683018,-30926419,-14696000,-7203346,-8994389,-30021019,7394435 }, }, { { 23838809,1822728,-15738443,15242727,8318092,-3733104,-21672180,-3492205,-4821741,14799921 }, { 13345610,9759151,3371034,-16137791,16353039,8577942,31129804,13496856,-9056018,7402518 }, { 2286874,-4435931,-20042458,-2008336,-13696227,5038122,11006906,-15760352,8205061,1607563 }, }, { { 14414086,-8002132,3331830,-3208217,22249151,-5594188,18364661,-2906958,30019587,-9029278 }, { -27688051,1585953,-10775053,931069,-29120221,-11002319,-14410829,12029093,9944378,8024 }, { 4368715,-3709630,29874200,-15022983,-20230386,-11410704,-16114594,-999085,-8142388,5640030 }, }, { { 10299610,13746483,11661824,16234854,7630238,5998374,9809887,-16694564,15219798,-14327783 }, { 27425505,-5719081,3055006,10660664,23458024,595578,-15398605,-1173195,-18342183,9742717 }, { 6744077,2427284,26042789,2720740,-847906,1118974,32324614,7406442,12420155,1994844 }, }, { { 14012521,-5024720,-18384453,-9578469,-26485342,-3936439,-13033478,-10909803,24319929,-6446333 }, { 16412690,-4507367,10772641,15929391,-17068788,-4658621,10555945,-10484049,-30102368,-4739048 }, { 22397382,-7767684,-9293161,-12792868,17166287,-9755136,-27333065,6199366,21880021,-12250760 }, }, { { -4283307,5368523,-31117018,8163389,-30323063,3209128,16557151,8890729,8840445,4957760 }, { -15447727,709327,-6919446,-10870178,-29777922,6522332,-21720181,12130072,-14796503,5005757 }, { -2114751,-14308128,23019042,15765735,-25269683,6002752,10183197,-13239326,-16395286,-2176112 }, }, }, { { { -19025756,1632005,13466291,-7995100,-23640451,16573537,-32013908,-3057104,22208662,2000468 }, { 3065073,-1412761,-25598674,-361432,-17683065,-5703415,-8164212,11248527,-3691214,-7414184 }, { 10379208,-6045554,8877319,1473647,-29291284,-12507580,16690915,2553332,-3132688,16400289 }, }, { { 15716668,1254266,-18472690,7446274,-8448918,6344164,-22097271,-7285580,26894937,9132066 }, { 24158887,12938817,11085297,-8177598,-28063478,-4457083,-30576463,64452,-6817084,-2692882 }, { 13488534,7794716,22236231,5989356,25426474,-12578208,2350710,-3418511,-4688006,2364226 }, }, { { 16335052,9132434,25640582,6678888,1725628,8517937,-11807024,-11697457,15445875,-7798101 }, { 29004207,-7867081,28661402,-640412,-12794003,-7943086,31863255,-4135540,-278050,-15759279 }, { -6122061,-14866665,-28614905,14569919,-10857999,-3591829,10343412,-6976290,-29828287,-10815811 }, }, { { 27081650,3463984,14099042,-4517604,1616303,-6205604,29542636,15372179,17293797,960709 }, { 20263915,11434237,-5765435,11236810,13505955,-10857102,-16111345,6493122,-19384511,7639714 }, { -2830798,-14839232,25403038,-8215196,-8317012,-16173699,18006287,-16043750,29994677,-15808121 }, }, { { 9769828,5202651,-24157398,-13631392,-28051003,-11561624,-24613141,-13860782,-31184575,709464 }, { 12286395,13076066,-21775189,-1176622,-25003198,4057652,-32018128,-8890874,16102007,13205847 }, { 13733362,5599946,10557076,3195751,-5557991,8536970,-25540170,8525972,10151379,10394400 }, }, { { 4024660,-16137551,22436262,12276534,-9099015,-2686099,19698229,11743039,-33302334,8934414 }, { -15879800,-4525240,-8580747,-2934061,14634845,-698278,-9449077,3137094,-11536886,11721158 }, { 17555939,-5013938,8268606,2331751,-22738815,9761013,9319229,8835153,-9205489,-1280045 }, }, { { -461409,-7830014,20614118,16688288,-7514766,-4807119,22300304,505429,6108462,-6183415 }, { -5070281,12367917,-30663534,3234473,32617080,-8422642,29880583,-13483331,-26898490,-7867459 }, { -31975283,5726539,26934134,10237677,-3173717,-605053,24199304,3795095,7592688,-14992079 }, }, { { 21594432,-14964228,17466408,-4077222,32537084,2739898,6407723,12018833,-28256052,4298412 }, { -20650503,-11961496,-27236275,570498,3767144,-1717540,13891942,-1569194,13717174,10805743 }, { -14676630,-15644296,15287174,11927123,24177847,-8175568,-796431,14860609,-26938930,-5863836 }, }, }, { { { 12962541,5311799,-10060768,11658280,18855286,-7954201,13286263,-12808704,-4381056,9882022 }, { 18512079,11319350,-20123124,15090309,18818594,5271736,-22727904,3666879,-23967430,-3299429 }, { -6789020,-3146043,16192429,13241070,15898607,-14206114,-10084880,-6661110,-2403099,5276065 }, }, { { 30169808,-5317648,26306206,-11750859,27814964,7069267,7152851,3684982,1449224,13082861 }, { 10342826,3098505,2119311,193222,25702612,12233820,23697382,15056736,-21016438,-8202000 }, { -33150110,3261608,22745853,7948688,19370557,-15177665,-26171976,6482814,-10300080,-11060101 }, }, { { 32869458,-5408545,25609743,15678670,-10687769,-15471071,26112421,2521008,-22664288,6904815 }, { 29506923,4457497,3377935,-9796444,-30510046,12935080,1561737,3841096,-29003639,-6657642 }, { 10340844,-6630377,-18656632,-2278430,12621151,-13339055,30878497,-11824370,-25584551,5181966 }, }, { { 25940115,-12658025,17324188,-10307374,-8671468,15029094,24396252,-16450922,-2322852,-12388574 }, { -21765684,9916823,-1300409,4079498,-1028346,11909559,1782390,12641087,20603771,-6561742 }, { -18882287,-11673380,24849422,11501709,13161720,-4768874,1925523,11914390,4662781,7820689 }, }, { { 12241050,-425982,8132691,9393934,32846760,-1599620,29749456,12172924,16136752,15264020 }, { -10349955,-14680563,-8211979,2330220,-17662549,-14545780,10658213,6671822,19012087,3772772 }, { 3753511,-3421066,10617074,2028709,14841030,-6721664,28718732,-15762884,20527771,12988982 }, }, { { -14822485,-5797269,-3707987,12689773,-898983,-10914866,-24183046,-10564943,3299665,-12424953 }, { -16777703,-15253301,-9642417,4978983,3308785,8755439,6943197,6461331,-25583147,8991218 }, { -17226263,1816362,-1673288,-6086439,31783888,-8175991,-32948145,7417950,-30242287,1507265 }, }, { { 29692663,6829891,-10498800,4334896,20945975,-11906496,-28887608,8209391,14606362,-10647073 }, { -3481570,8707081,32188102,5672294,22096700,1711240,-33020695,9761487,4170404,-2085325 }, { -11587470,14855945,-4127778,-1531857,-26649089,15084046,22186522,16002000,-14276837,-8400798 }, }, { { -4811456,13761029,-31703877,-2483919,-3312471,7869047,-7113572,-9620092,13240845,10965870 }, { -7742563,-8256762,-14768334,-13656260,-23232383,12387166,4498947,14147411,29514390,4302863 }, { -13413405,-12407859,20757302,-13801832,14785143,8976368,-5061276,-2144373,17846988,-13971927 }, }, }, { { { -2244452,-754728,-4597030,-1066309,-6247172,1455299,-21647728,-9214789,-5222701,12650267 }, { -9906797,-16070310,21134160,12198166,-27064575,708126,387813,13770293,-19134326,10958663 }, { 22470984,12369526,23446014,-5441109,-21520802,-9698723,-11772496,-11574455,-25083830,4271862 }, }, { { -25169565,-10053642,-19909332,15361595,-5984358,2159192,75375,-4278529,-32526221,8469673 }, { 15854970,4148314,-8893890,7259002,11666551,13824734,-30531198,2697372,24154791,-9460943 }, { 15446137,-15806644,29759747,14019369,30811221,-9610191,-31582008,12840104,24913809,9815020 }, }, { { -4709286,-5614269,-31841498,-12288893,-14443537,10799414,-9103676,13438769,18735128,9466238 }, { 11933045,9281483,5081055,-5183824,-2628162,-4905629,-7727821,-10896103,-22728655,16199064 }, { 14576810,379472,-26786533,-8317236,-29426508,-10812974,-102766,1876699,30801119,2164795 }, }, { { 15995086,3199873,13672555,13712240,-19378835,-4647646,-13081610,-15496269,-13492807,1268052 }, { -10290614,-3659039,-3286592,10948818,23037027,3794475,-3470338,-12600221,-17055369,3565904 }, { 29210088,-9419337,-5919792,-4952785,10834811,-13327726,-16512102,-10820713,-27162222,-14030531 }, }, { { -13161890,15508588,16663704,-8156150,-28349942,9019123,-29183421,-3769423,2244111,-14001979 }, { -5152875,-3800936,-9306475,-6071583,16243069,14684434,-25673088,-16180800,13491506,4641841 }, { 10813417,643330,-19188515,-728916,30292062,-16600078,27548447,-7721242,14476989,-12767431 }, }, { { 10292079,9984945,6481436,8279905,-7251514,7032743,27282937,-1644259,-27912810,12651324 }, { -31185513,-813383,22271204,11835308,10201545,15351028,17099662,3988035,21721536,-3148940 }, { 10202177,-6545839,-31373232,-9574638,-32150642,-8119683,-12906320,3852694,13216206,14842320 }, }, { { -15815640,-10601066,-6538952,-7258995,-6984659,-6581778,-31500847,13765824,-27434397,9900184 }, { 14465505,-13833331,-32133984,-14738873,-27443187,12990492,33046193,15796406,-7051866,-8040114 }, { 30924417,-8279620,6359016,-12816335,16508377,9071735,-25488601,15413635,9524356,-7018878 }, }, { { 12274201,-13175547,32627641,-1785326,6736625,13267305,5237659,-5109483,15663516,4035784 }, { -2951309,8903985,17349946,601635,-16432815,-4612556,-13732739,-15889334,-22258478,4659091 }, { -16916263,-4952973,-30393711,-15158821,20774812,15897498,5736189,15026997,-2178256,-13455585 }, }, }, { { { -8858980,-2219056,28571666,-10155518,-474467,-10105698,-3801496,278095,23440562,-290208 }, { 10226241,-5928702,15139956,120818,-14867693,5218603,32937275,11551483,-16571960,-7442864 }, { 17932739,-12437276,-24039557,10749060,11316803,7535897,22503767,5561594,-3646624,3898661 }, }, { { 7749907,-969567,-16339731,-16464,-25018111,15122143,-1573531,7152530,21831162,1245233 }, { 26958459,-14658026,4314586,8346991,-5677764,11960072,-32589295,-620035,-30402091,-16716212 }, { -12165896,9166947,33491384,13673479,29787085,13096535,6280834,14587357,-22338025,13987525 }, }, { { -24349909,7778775,21116000,15572597,-4833266,-5357778,-4300898,-5124639,-7469781,-2858068 }, { 9681908,-6737123,-31951644,13591838,-6883821,386950,31622781,6439245,-14581012,4091397 }, { -8426427,1470727,-28109679,-1596990,3978627,-5123623,-19622683,12092163,29077877,-14741988 }, }, { { 5269168,-6859726,-13230211,-8020715,25932563,1763552,-5606110,-5505881,-20017847,2357889 }, { 32264008,-15407652,-5387735,-1160093,-2091322,-3946900,23104804,-12869908,5727338,189038 }, { 14609123,-8954470,-6000566,-16622781,-14577387,-7743898,-26745169,10942115,-25888931,-14884697 }, }, { { 20513500,5557931,-15604613,7829531,26413943,-2019404,-21378968,7471781,13913677,-5137875 }, { -25574376,11967826,29233242,12948236,-6754465,4713227,-8940970,14059180,12878652,8511905 }, { -25656801,3393631,-2955415,-7075526,-2250709,9366908,-30223418,6812974,5568676,-3127656 }, }, { { 11630004,12144454,2116339,13606037,27378885,15676917,-17408753,-13504373,-14395196,8070818 }, { 27117696,-10007378,-31282771,-5570088,1127282,12772488,-29845906,10483306,-11552749,-1028714 }, { 10637467,-5688064,5674781,1072708,-26343588,-6982302,-1683975,9177853,-27493162,15431203 }, }, { { 20525145,10892566,-12742472,12779443,-29493034,16150075,-28240519,14943142,-15056790,-7935931 }, { -30024462,5626926,-551567,-9981087,753598,11981191,25244767,-3239766,-3356550,9594024 }, { -23752644,2636870,-5163910,-10103818,585134,7877383,11345683,-6492290,13352335,-10977084 }, }, { { -1931799,-5407458,3304649,-12884869,17015806,-4877091,-29783850,-7752482,-13215537,-319204 }, { 20239939,6607058,6203985,3483793,-18386976,-779229,-20723742,15077870,-22750759,14523817 }, { 27406042,-6041657,27423596,-4497394,4996214,10002360,-28842031,-4545494,-30172742,-4805667 }, }, }, { { { 11374242,12660715,17861383,-12540833,10935568,1099227,-13886076,-9091740,-27727044,11358504 }, { -12730809,10311867,1510375,10778093,-2119455,-9145702,32676003,11149336,-26123651,4985768 }, { -19096303,341147,-6197485,-239033,15756973,-8796662,-983043,13794114,-19414307,-15621255 }, }, { { 6490081,11940286,25495923,-7726360,8668373,-8751316,3367603,6970005,-1691065,-9004790 }, { 1656497,13457317,15370807,6364910,13605745,8362338,-19174622,-5475723,-16796596,-5031438 }, { -22273315,-13524424,-64685,-4334223,-18605636,-10921968,-20571065,-7007978,-99853,-10237333 }, }, { { 17747465,10039260,19368299,-4050591,-20630635,-16041286,31992683,-15857976,-29260363,-5511971 }, { 31932027,-4986141,-19612382,16366580,22023614,88450,11371999,-3744247,4882242,-10626905 }, { 29796507,37186,19818052,10115756,-11829032,3352736,18551198,3272828,-5190932,-4162409 }, }, { { 12501286,4044383,-8612957,-13392385,-32430052,5136599,-19230378,-3529697,330070,-3659409 }, { 6384877,2899513,17807477,7663917,-2358888,12363165,25366522,-8573892,-271295,12071499 }, { -8365515,-4042521,25133448,-4517355,-6211027,2265927,-32769618,1936675,-5159697,3829363 }, }, { { 28425966,-5835433,-577090,-4697198,-14217555,6870930,7921550,-6567787,26333140,14267664 }, { -11067219,11871231,27385719,-10559544,-4585914,-11189312,10004786,-8709488,-21761224,8930324 }, { -21197785,-16396035,25654216,-1725397,12282012,11008919,1541940,4757911,-26491501,-16408940 }, }, { { 13537262,-7759490,-20604840,10961927,-5922820,-13218065,-13156584,6217254,-15943699,13814990 }, { -17422573,15157790,18705543,29619,24409717,-260476,27361681,9257833,-1956526,-1776914 }, { -25045300,-10191966,15366585,15166509,-13105086,8423556,-29171540,12361135,-18685978,4578290 }, }, { { 24579768,3711570,1342322,-11180126,-27005135,14124956,-22544529,14074919,21964432,8235257 }, { -6528613,-2411497,9442966,-5925588,12025640,-1487420,-2981514,-1669206,13006806,2355433 }, { -16304899,-13605259,-6632427,-5142349,16974359,-10911083,27202044,1719366,1141648,-12796236 }, }, { { -12863944,-13219986,-8318266,-11018091,-6810145,-4843894,13475066,-3133972,32674895,13715045 }, { 11423335,-5468059,32344216,8962751,24989809,9241752,-13265253,16086212,-28740881,-15642093 }, { -1409668,12530728,-6368726,10847387,19531186,-14132160,-11709148,7791794,-27245943,4383347 }, }, }, { { { -28970898,5271447,-1266009,-9736989,-12455236,16732599,-4862407,-4906449,27193557,6245191 }, { -15193956,5362278,-1783893,2695834,4960227,12840725,23061898,3260492,22510453,8577507 }, { -12632451,11257346,-32692994,13548177,-721004,10879011,31168030,13952092,-29571492,-3635906 }, }, { { 3877321,-9572739,32416692,5405324,-11004407,-13656635,3759769,11935320,5611860,8164018 }, { -16275802,14667797,15906460,12155291,-22111149,-9039718,32003002,-8832289,5773085,-8422109 }, { -23788118,-8254300,1950875,8937633,18686727,16459170,-905725,12376320,31632953,190926 }, }, { { -24593607,-16138885,-8423991,13378746,14162407,6901328,-8288749,4508564,-25341555,-3627528 }, { 8884438,-5884009,6023974,10104341,-6881569,-4941533,18722941,-14786005,-1672488,827625 }, { -32720583,-16289296,-32503547,7101210,13354605,2659080,-1800575,-14108036,-24878478,1541286 }, }, { { 2901347,-1117687,3880376,-10059388,-17620940,-3612781,-21802117,-3567481,20456845,-1885033 }, { 27019610,12299467,-13658288,-1603234,-12861660,-4861471,-19540150,-5016058,29439641,15138866 }, { 21536104,-6626420,-32447818,-10690208,-22408077,5175814,-5420040,-16361163,7779328,109896 }, }, { { 30279744,14648750,-8044871,6425558,13639621,-743509,28698390,12180118,23177719,-554075 }, { 26572847,3405927,-31701700,12890905,-19265668,5335866,-6493768,2378492,4439158,-13279347 }, { -22716706,3489070,-9225266,-332753,18875722,-1140095,14819434,-12731527,-17717757,-5461437 }, }, { { -5056483,16566551,15953661,3767752,-10436499,15627060,-820954,2177225,8550082,-15114165 }, { -18473302,16596775,-381660,15663611,22860960,15585581,-27844109,-3582739,-23260460,-8428588 }, { -32480551,15707275,-8205912,-5652081,29464558,2713815,-22725137,15860482,-21902570,1494193 }, }, { { -19562091,-14087393,-25583872,-9299552,13127842,759709,21923482,16529112,8742704,12967017 }, { -28464899,1553205,32536856,-10473729,-24691605,-406174,-8914625,-2933896,-29903758,15553883 }, { 21877909,3230008,9881174,10539357,-4797115,2841332,11543572,14513274,19375923,-12647961 }, }, { { 8832269,-14495485,13253511,5137575,5037871,4078777,24880818,-6222716,2862653,9455043 }, { 29306751,5123106,20245049,-14149889,9592566,8447059,-2077124,-2990080,15511449,4789663 }, { -20679756,7004547,8824831,-9434977,-4045704,-3750736,-5754762,108893,23513200,16652362 }, }, }, { { { -33256173,4144782,-4476029,-6579123,10770039,-7155542,-6650416,-12936300,-18319198,10212860 }, { 2756081,8598110,7383731,-6859892,22312759,-1105012,21179801,2600940,-9988298,-12506466 }, { -24645692,13317462,-30449259,-15653928,21365574,-10869657,11344424,864440,-2499677,-16710063 }, }, { { -26432803,6148329,-17184412,-14474154,18782929,-275997,-22561534,211300,2719757,4940997 }, { -1323882,3911313,-6948744,14759765,-30027150,7851207,21690126,8518463,26699843,5276295 }, { -13149873,-6429067,9396249,365013,24703301,-10488939,1321586,149635,-15452774,7159369 }, }, { { 9987780,-3404759,17507962,9505530,9731535,-2165514,22356009,8312176,22477218,-8403385 }, { 18155857,-16504990,19744716,9006923,15154154,-10538976,24256460,-4864995,-22548173,9334109 }, { 2986088,-4911893,10776628,-3473844,10620590,-7083203,-21413845,14253545,-22587149,536906 }, }, { { 4377756,8115836,24567078,15495314,11625074,13064599,7390551,10589625,10838060,-15420424 }, { -19342404,867880,9277171,-3218459,-14431572,-1986443,19295826,-15796950,6378260,699185 }, { 7895026,4057113,-7081772,-13077756,-17886831,-323126,-716039,15693155,-5045064,-13373962 }, }, { { -7737563,-5869402,-14566319,-7406919,11385654,13201616,31730678,-10962840,-3918636,-9669325 }, { 10188286,-15770834,-7336361,13427543,22223443,14896287,30743455,7116568,-21786507,5427593 }, { 696102,13206899,27047647,-10632082,15285305,-9853179,10798490,-4578720,19236243,12477404 }, }, { { -11229439,11243796,-17054270,-8040865,-788228,-8167967,-3897669,11180504,-23169516,7733644 }, { 17800790,-14036179,-27000429,-11766671,23887827,3149671,23466177,-10538171,10322027,15313801 }, { 26246234,11968874,32263343,-5468728,6830755,-13323031,-15794704,-101982,-24449242,10890804 }, }, { { -31365647,10271363,-12660625,-6267268,16690207,-13062544,-14982212,16484931,25180797,-5334884 }, { -586574,10376444,-32586414,-11286356,19801893,10997610,2276632,9482883,316878,13820577 }, { -9882808,-4510367,-2115506,16457136,-11100081,11674996,30756178,-7515054,30696930,-3712849 }, }, { { 32988917,-9603412,12499366,7910787,-10617257,-11931514,-7342816,-9985397,-32349517,7392473 }, { -8855661,15927861,9866406,-3649411,-2396914,-16655781,-30409476,-9134995,25112947,-2926644 }, { -2504044,-436966,25621774,-5678772,15085042,-5479877,-24884878,-13526194,5537438,-13914319 }, }, }, { { { -11225584,2320285,-9584280,10149187,-33444663,5808648,-14876251,-1729667,31234590,6090599 }, { -9633316,116426,26083934,2897444,-6364437,-2688086,609721,15878753,-6970405,-9034768 }, { -27757857,247744,-15194774,-9002551,23288161,-10011936,-23869595,6503646,20650474,1804084 }, }, { { -27589786,15456424,8972517,8469608,15640622,4439847,3121995,-10329713,27842616,-202328 }, { -15306973,2839644,22530074,10026331,4602058,5048462,28248656,5031932,-11375082,12714369 }, { 20807691,-7270825,29286141,11421711,-27876523,-13868230,-21227475,1035546,-19733229,12796920 }, }, { { 12076899,-14301286,-8785001,-11848922,-25012791,16400684,-17591495,-12899438,3480665,-15182815 }, { -32361549,5457597,28548107,7833186,7303070,-11953545,-24363064,-15921875,-33374054,2771025 }, { -21389266,421932,26597266,6860826,22486084,-6737172,-17137485,-4210226,-24552282,15673397 }, }, { { -20184622,2338216,19788685,-9620956,-4001265,-8740893,-20271184,4733254,3727144,-12934448 }, { 6120119,814863,-11794402,-622716,6812205,-15747771,2019594,7975683,31123697,-10958981 }, { 30069250,-11435332,30434654,2958439,18399564,-976289,12296869,9204260,-16432438,9648165 }, }, { { 32705432,-1550977,30705658,7451065,-11805606,9631813,3305266,5248604,-26008332,-11377501 }, { 17219865,2375039,-31570947,-5575615,-19459679,9219903,294711,15298639,2662509,-16297073 }, { -1172927,-7558695,-4366770,-4287744,-21346413,-8434326,32087529,-1222777,32247248,-14389861 }, }, { { 14312628,1221556,17395390,-8700143,-4945741,-8684635,-28197744,-9637817,-16027623,-13378845 }, { -1428825,-9678990,-9235681,6549687,-7383069,-468664,23046502,9803137,17597934,2346211 }, { 18510800,15337574,26171504,981392,-22241552,7827556,-23491134,-11323352,3059833,-11782870 }, }, { { 10141598,6082907,17829293,-1947643,9830092,13613136,-25556636,-5544586,-33502212,3592096 }, { 33114168,-15889352,-26525686,-13343397,33076705,8716171,1151462,1521897,-982665,-6837803 }, { -32939165,-4255815,23947181,-324178,-33072974,-12305637,-16637686,3891704,26353178,693168 }, }, { { 30374239,1595580,-16884039,13186931,4600344,406904,9585294,-400668,31375464,14369965 }, { -14370654,-7772529,1510301,6434173,-18784789,-6262728,32732230,-13108839,17901441,16011505 }, { 18171223,-11934626,-12500402,15197122,-11038147,-15230035,-19172240,-16046376,8764035,12309598 }, }, }, { { { 5975908,-5243188,-19459362,-9681747,-11541277,14015782,-23665757,1228319,17544096,-10593782 }, { 5811932,-1715293,3442887,-2269310,-18367348,-8359541,-18044043,-15410127,-5565381,12348900 }, { -31399660,11407555,25755363,6891399,-3256938,14872274,-24849353,8141295,-10632534,-585479 }, }, { { -12675304,694026,-5076145,13300344,14015258,-14451394,-9698672,-11329050,30944593,1130208 }, { 8247766,-6710942,-26562381,-7709309,-14401939,-14648910,4652152,2488540,23550156,-271232 }, { 17294316,-3788438,7026748,15626851,22990044,113481,2267737,-5908146,-408818,-137719 }, }, { { 16091085,-16253926,18599252,7340678,2137637,-1221657,-3364161,14550936,3260525,-7166271 }, { -4910104,-13332887,18550887,10864893,-16459325,-7291596,-23028869,-13204905,-12748722,2701326 }, { -8574695,16099415,4629974,-16340524,-20786213,-6005432,-10018363,9276971,11329923,1862132 }, }, { { 14763076,-15903608,-30918270,3689867,3511892,10313526,-21951088,12219231,-9037963,-940300 }, { 8894987,-3446094,6150753,3013931,301220,15693451,-31981216,-2909717,-15438168,11595570 }, { 15214962,3537601,-26238722,-14058872,4418657,-15230761,13947276,10730794,-13489462,-4363670 }, }, { { -2538306,7682793,32759013,263109,-29984731,-7955452,-22332124,-10188635,977108,699994 }, { -12466472,4195084,-9211532,550904,-15565337,12917920,19118110,-439841,-30534533,-14337913 }, { 31788461,-14507657,4799989,7372237,8808585,-14747943,9408237,-10051775,12493932,-5409317 }, }, { { -25680606,5260744,-19235809,-6284470,-3695942,16566087,27218280,2607121,29375955,6024730 }, { 842132,-2794693,-4763381,-8722815,26332018,-12405641,11831880,6985184,-9940361,2854096 }, { -4847262,-7969331,2516242,-5847713,9695691,-7221186,16512645,960770,12121869,16648078 }, }, { { -15218652,14667096,-13336229,2013717,30598287,-464137,-31504922,-7882064,20237806,2838411 }, { -19288047,4453152,15298546,-16178388,22115043,-15972604,12544294,-13470457,1068881,-12499905 }, { -9558883,-16518835,33238498,13506958,30505848,-1114596,-8486907,-2630053,12521378,4845654 }, }, { { -28198521,10744108,-2958380,10199664,7759311,-13088600,3409348,-873400,-6482306,-12885870 }, { -23561822,6230156,-20382013,10655314,-24040585,-11621172,10477734,-1240216,-3113227,13974498 }, { 12966261,15550616,-32038948,-1615346,21025980,-629444,5642325,7188737,18895762,12629579 }, }, }, { { { 14741879,-14946887,22177208,-11721237,1279741,8058600,11758140,789443,32195181,3895677 }, { 10758205,15755439,-4509950,9243698,-4879422,6879879,-2204575,-3566119,-8982069,4429647 }, { -2453894,15725973,-20436342,-10410672,-5803908,-11040220,-7135870,-11642895,18047436,-15281743 }, }, { { -25173001,-11307165,29759956,11776784,-22262383,-15820455,10993114,-12850837,-17620701,-9408468 }, { 21987233,700364,-24505048,14972008,-7774265,-5718395,32155026,2581431,-29958985,8773375 }, { -25568350,454463,-13211935,16126715,25240068,8594567,20656846,12017935,-7874389,-13920155 }, }, { { 6028182,6263078,-31011806,-11301710,-818919,2461772,-31841174,-5468042,-1721788,-2776725 }, { -12278994,16624277,987579,-5922598,32908203,1248608,7719845,-4166698,28408820,6816612 }, { -10358094,-8237829,19549651,-12169222,22082623,16147817,20613181,13982702,-10339570,5067943 }, }, { { -30505967,-3821767,12074681,13582412,-19877972,2443951,-19719286,12746132,5331210,-10105944 }, { 30528811,3601899,-1957090,4619785,-27361822,-15436388,24180793,-12570394,27679908,-1648928 }, { 9402404,-13957065,32834043,10838634,-26580150,-13237195,26653274,-8685565,22611444,-12715406 }, }, { { 22190590,1118029,22736441,15130463,-30460692,-5991321,19189625,-4648942,4854859,6622139 }, { -8310738,-2953450,-8262579,-3388049,-10401731,-271929,13424426,-3567227,26404409,13001963 }, { -31241838,-15415700,-2994250,8939346,11562230,-12840670,-26064365,-11621720,-15405155,11020693 }, }, { { 1866042,-7949489,-7898649,-10301010,12483315,13477547,3175636,-12424163,28761762,1406734 }, { -448555,-1777666,13018551,3194501,-9580420,-11161737,24760585,-4347088,25577411,-13378680 }, { -24290378,4759345,-690653,-1852816,2066747,10693769,-29595790,9884936,-9368926,4745410 }, }, { { -9141284,6049714,-19531061,-4341411,-31260798,9944276,-15462008,-11311852,10931924,-11931931 }, { -16561513,14112680,-8012645,4817318,-8040464,-11414606,-22853429,10856641,-20470770,13434654 }, { 22759489,-10073434,-16766264,-1871422,13637442,-10168091,1765144,-12654326,28445307,-5364710 }, }, { { 29875063,12493613,2795536,-3786330,1710620,15181182,-10195717,-8788675,9074234,1167180 }, { -26205683,11014233,-9842651,-2635485,-26908120,7532294,-18716888,-9535498,3843903,9367684 }, { -10969595,-6403711,9591134,9582310,11349256,108879,16235123,8601684,-139197,4242895 }, }, }, { { { 22092954,-13191123,-2042793,-11968512,32186753,-11517388,-6574341,2470660,-27417366,16625501 }, { -11057722,3042016,13770083,-9257922,584236,-544855,-7770857,2602725,-27351616,14247413 }, { 6314175,-10264892,-32772502,15957557,-10157730,168750,-8618807,14290061,27108877,-1180880 }, }, { { -8586597,-7170966,13241782,10960156,-32991015,-13794596,33547976,-11058889,-27148451,981874 }, { 22833440,9293594,-32649448,-13618667,-9136966,14756819,-22928859,-13970780,-10479804,-16197962 }, { -7768587,3326786,-28111797,10783824,19178761,14905060,22680049,13906969,-15933690,3797899 }, }, { { 21721356,-4212746,-12206123,9310182,-3882239,-13653110,23740224,-2709232,20491983,-8042152 }, { 9209270,-15135055,-13256557,-6167798,-731016,15289673,25947805,15286587,30997318,-6703063 }, { 7392032,16618386,23946583,-8039892,-13265164,-1533858,-14197445,-2321576,17649998,-250080 }, }, { { -9301088,-14193827,30609526,-3049543,-25175069,-1283752,-15241566,-9525724,-2233253,7662146 }, { -17558673,1763594,-33114336,15908610,-30040870,-12174295,7335080,-8472199,-3174674,3440183 }, { -19889700,-5977008,-24111293,-9688870,10799743,-16571957,40450,-4431835,4862400,1133 }, }, { { -32856209,-7873957,-5422389,14860950,-16319031,7956142,7258061,311861,-30594991,-7379421 }, { -3773428,-1565936,28985340,7499440,24445838,9325937,29727763,16527196,18278453,15405622 }, { -4381906,8508652,-19898366,-3674424,-5984453,15149970,-13313598,843523,-21875062,13626197 }, }, { { 2281448,-13487055,-10915418,-2609910,1879358,16164207,-10783882,3953792,13340839,15928663 }, { 31727126,-7179855,-18437503,-8283652,2875793,-16390330,-25269894,-7014826,-23452306,5964753 }, { 4100420,-5959452,-17179337,6017714,-18705837,12227141,-26684835,11344144,2538215,-7570755 }, }, { { -9433605,6123113,11159803,-2156608,30016280,14966241,-20474983,1485421,-629256,-15958862 }, { -26804558,4260919,11851389,9658551,-32017107,16367492,-20205425,-13191288,11659922,-11115118 }, { 26180396,10015009,-30844224,-8581293,5418197,9480663,2231568,-10170080,33100372,-1306171 }, }, { { 15121113,-5201871,-10389905,15427821,-27509937,-15992507,21670947,4486675,-5931810,-14466380 }, { 16166486,-9483733,-11104130,6023908,-31926798,-1364923,2340060,-16254968,-10735770,-10039824 }, { 28042865,-3557089,-12126526,12259706,-3717498,-6945899,6766453,-8689599,18036436,5803270 }, }, }, { { { -817581,6763912,11803561,1585585,10958447,-2671165,23855391,4598332,-6159431,-14117438 }, { -31031306,-14256194,17332029,-2383520,31312682,-5967183,696309,50292,-20095739,11763584 }, { -594563,-2514283,-32234153,12643980,12650761,14811489,665117,-12613632,-19773211,-10713562 }, }, { { 30464590,-11262872,-4127476,-12734478,19835327,-7105613,-24396175,2075773,-17020157,992471 }, { 18357185,-6994433,7766382,16342475,-29324918,411174,14578841,8080033,-11574335,-10601610 }, { 19598397,10334610,12555054,2555664,18821899,-10339780,21873263,16014234,26224780,16452269 }, }, { { -30223925,5145196,5944548,16385966,3976735,2009897,-11377804,-7618186,-20533829,3698650 }, { 14187449,3448569,-10636236,-10810935,-22663880,-3433596,7268410,-10890444,27394301,12015369 }, { 19695761,16087646,28032085,12999827,6817792,11427614,20244189,-1312777,-13259127,-3402461 }, }, { { 30860103,12735208,-1888245,-4699734,-16974906,2256940,-8166013,12298312,-8550524,-10393462 }, { -5719826,-11245325,-1910649,15569035,26642876,-7587760,-5789354,-15118654,-4976164,12651793 }, { -2848395,9953421,11531313,-5282879,26895123,-12697089,-13118820,-16517902,9768698,-2533218 }, }, { { -24719459,1894651,-287698,-4704085,15348719,-8156530,32767513,12765450,4940095,10678226 }, { 18860224,15980149,-18987240,-1562570,-26233012,-11071856,-7843882,13944024,-24372348,16582019 }, { -15504260,4970268,-29893044,4175593,-20993212,-2199756,-11704054,15444560,-11003761,7989037 }, }, { { 31490452,5568061,-2412803,2182383,-32336847,4531686,-32078269,6200206,-19686113,-14800171 }, { -17308668,-15879940,-31522777,-2831,-32887382,16375549,8680158,-16371713,28550068,-6857132 }, { -28126887,-5688091,16837845,-1820458,-6850681,12700016,-30039981,4364038,1155602,5988841 }, }, { { 21890435,-13272907,-12624011,12154349,-7831873,15300496,23148983,-4470481,24618407,8283181 }, { -33136107,-10512751,9975416,6841041,-31559793,16356536,3070187,-7025928,1466169,10740210 }, { -1509399,-15488185,-13503385,-10655916,32799044,909394,-13938903,-5779719,-32164649,-15327040 }, }, { { 3960823,-14267803,-28026090,-15918051,-19404858,13146868,15567327,951507,-3260321,-573935 }, { 24740841,5052253,-30094131,8961361,25877428,6165135,-24368180,14397372,-7380369,-6144105 }, { -28888365,3510803,-28103278,-1158478,-11238128,-10631454,-15441463,-14453128,-1625486,-6494814 }, }, }, { { { 793299,-9230478,8836302,-6235707,-27360908,-2369593,33152843,-4885251,-9906200,-621852 }, { 5666233,525582,20782575,-8038419,-24538499,14657740,16099374,1468826,-6171428,-15186581 }, { -4859255,-3779343,-2917758,-6748019,7778750,11688288,-30404353,-9871238,-1558923,-9863646 }, }, { { 10896332,-7719704,824275,472601,-19460308,3009587,25248958,14783338,-30581476,-15757844 }, { 10566929,12612572,-31944212,11118703,-12633376,12362879,21752402,8822496,24003793,14264025 }, { 27713862,-7355973,-11008240,9227530,27050101,2504721,23886875,-13117525,13958495,-5732453 }, }, { { -23481610,4867226,-27247128,3900521,29838369,-8212291,-31889399,-10041781,7340521,-15410068 }, { 4646514,-8011124,-22766023,-11532654,23184553,8566613,31366726,-1381061,-15066784,-10375192 }, { -17270517,12723032,-16993061,14878794,21619651,-6197576,27584817,3093888,-8843694,3849921 }, }, { { -9064912,2103172,25561640,-15125738,-5239824,9582958,32477045,-9017955,5002294,-15550259 }, { -12057553,-11177906,21115585,-13365155,8808712,-12030708,16489530,13378448,-25845716,12741426 }, { -5946367,10645103,-30911586,15390284,-3286982,-7118677,24306472,15852464,28834118,-7646072 }, }, { { -17335748,-9107057,-24531279,9434953,-8472084,-583362,-13090771,455841,20461858,5491305 }, { 13669248,-16095482,-12481974,-10203039,-14569770,-11893198,-24995986,11293807,-28588204,-9421832 }, { 28497928,6272777,-33022994,14470570,8906179,-1225630,18504674,-14165166,29867745,-8795943 }, }, { { -16207023,13517196,-27799630,-13697798,24009064,-6373891,-6367600,-13175392,22853429,-4012011 }, { 24191378,16712145,-13931797,15217831,14542237,1646131,18603514,-11037887,12876623,-2112447 }, { 17902668,4518229,-411702,-2829247,26878217,5258055,-12860753,608397,16031844,3723494 }, }, { { -28632773,12763728,-20446446,7577504,33001348,-13017745,17558842,-7872890,23896954,-4314245 }, { -20005381,-12011952,31520464,605201,2543521,5991821,-2945064,7229064,-9919646,-8826859 }, { 28816045,298879,-28165016,-15920938,19000928,-1665890,-12680833,-2949325,-18051778,-2082915 }, }, { { 16000882,-344896,3493092,-11447198,-29504595,-13159789,12577740,16041268,-19715240,7847707 }, { 10151868,10572098,27312476,7922682,14825339,4723128,-32855931,-6519018,-10020567,3852848 }, { -11430470,15697596,-21121557,-4420647,5386314,15063598,16514493,-15932110,29330899,-15076224 }, }, }, { { { -25499735,-4378794,-15222908,-6901211,16615731,2051784,3303702,15490,-27548796,12314391 }, { 15683520,-6003043,18109120,-9980648,15337968,-5997823,-16717435,15921866,16103996,-3731215 }, { -23169824,-10781249,13588192,-1628807,-3798557,-1074929,-19273607,5402699,-29815713,-9841101 }, }, { { 23190676,2384583,-32714340,3462154,-29903655,-1529132,-11266856,8911517,-25205859,2739713 }, { 21374101,-3554250,-33524649,9874411,15377179,11831242,-33529904,6134907,4931255,11987849 }, { -7732,-2978858,-16223486,7277597,105524,-322051,-31480539,13861388,-30076310,10117930 }, }, { { -29501170,-10744872,-26163768,13051539,-25625564,5089643,-6325503,6704079,12890019,15728940 }, { -21972360,-11771379,-951059,-4418840,14704840,2695116,903376,-10428139,12885167,8311031 }, { -17516482,5352194,10384213,-13811658,7506451,13453191,26423267,4384730,1888765,-5435404 }, }, { { -25817338,-3107312,-13494599,-3182506,30896459,-13921729,-32251644,-12707869,-19464434,-3340243 }, { -23607977,-2665774,-526091,4651136,5765089,4618330,6092245,14845197,17151279,-9854116 }, { -24830458,-12733720,-15165978,10367250,-29530908,-265356,22825805,-7087279,-16866484,16176525 }, }, { { -23583256,6564961,20063689,3798228,-4740178,7359225,2006182,-10363426,-28746253,-10197509 }, { -10626600,-4486402,-13320562,-5125317,3432136,-6393229,23632037,-1940610,32808310,1099883 }, { 15030977,5768825,-27451236,-2887299,-6427378,-15361371,-15277896,-6809350,2051441,-15225865 }, }, { { -3362323,-7239372,7517890,9824992,23555850,295369,5148398,-14154188,-22686354,16633660 }, { 4577086,-16752288,13249841,-15304328,19958763,-14537274,18559670,-10759549,8402478,-9864273 }, { -28406330,-1051581,-26790155,-907698,-17212414,-11030789,9453451,-14980072,17983010,9967138 }, }, { { -25762494,6524722,26585488,9969270,24709298,1220360,-1677990,7806337,17507396,3651560 }, { -10420457,-4118111,14584639,15971087,-15768321,8861010,26556809,-5574557,-18553322,-11357135 }, { 2839101,14284142,4029895,3472686,14402957,12689363,-26642121,8459447,-5605463,-7621941 }, }, { { -4839289,-3535444,9744961,2871048,25113978,3187018,-25110813,-849066,17258084,-7977739 }, { 18164541,-10595176,-17154882,-1542417,19237078,-9745295,23357533,-15217008,26908270,12150756 }, { -30264870,-7647865,5112249,-7036672,-1499807,-6974257,43168,-5537701,-32302074,16215819 }, }, }, { { { -6898905,9824394,-12304779,-4401089,-31397141,-6276835,32574489,12532905,-7503072,-8675347 }, { -27343522,-16515468,-27151524,-10722951,946346,16291093,254968,7168080,21676107,-1943028 }, { 21260961,-8424752,-16831886,-11920822,-23677961,3968121,-3651949,-6215466,-3556191,-7913075 }, }, { { 16544754,13250366,-16804428,15546242,-4583003,12757258,-2462308,-8680336,-18907032,-9662799 }, { -2415239,-15577728,18312303,4964443,-15272530,-12653564,26820651,16690659,25459437,-4564609 }, { -25144690,11425020,28423002,-11020557,-6144921,-15826224,9142795,-2391602,-6432418,-1644817 }, }, { { -23104652,6253476,16964147,-3768872,-25113972,-12296437,-27457225,-16344658,6335692,7249989 }, { -30333227,13979675,7503222,-12368314,-11956721,-4621693,-30272269,2682242,25993170,-12478523 }, { 4364628,5930691,32304656,-10044554,-8054781,15091131,22857016,-10598955,31820368,15075278 }, }, { { 31879134,-8918693,17258761,90626,-8041836,-4917709,24162788,-9650886,-17970238,12833045 }, { 19073683,14851414,-24403169,-11860168,7625278,11091125,-19619190,2074449,-9413939,14905377 }, { 24483667,-11935567,-2518866,-11547418,-1553130,15355506,-25282080,9253129,27628530,-7555480 }, }, { { 17597607,8340603,19355617,552187,26198470,-3176583,4593324,-9157582,-14110875,15297016 }, { 510886,14337390,-31785257,16638632,6328095,2713355,-20217417,-11864220,8683221,2921426 }, { 18606791,11874196,27155355,-5281482,-24031742,6265446,-25178240,-1278924,4674690,13890525 }, }, { { 13609624,13069022,-27372361,-13055908,24360586,9592974,14977157,9835105,4389687,288396 }, { 9922506,-519394,13613107,5883594,-18758345,-434263,-12304062,8317628,23388070,16052080 }, { 12720016,11937594,-31970060,-5028689,26900120,8561328,-20155687,-11632979,-14754271,-10812892 }, }, { { 15961858,14150409,26716931,-665832,-22794328,13603569,11829573,7467844,-28822128,929275 }, { 11038231,-11582396,-27310482,-7316562,-10498527,-16307831,-23479533,-9371869,-21393143,2465074 }, { 20017163,-4323226,27915242,1529148,12396362,15675764,13817261,-9658066,2463391,-4622140 }, }, { { -16358878,-12663911,-12065183,4996454,-1256422,1073572,9583558,12851107,4003896,12673717 }, { -1731589,-15155870,-3262930,16143082,19294135,13385325,14741514,-9103726,7903886,2348101 }, { 24536016,-16515207,12715592,-3862155,1511293,10047386,-3842346,-7129159,-28377538,10048127 }, }, }, { { { -12622226,-6204820,30718825,2591312,-10617028,12192840,18873298,-7297090,-32297756,15221632 }, { -26478122,-11103864,11546244,-1852483,9180880,7656409,-21343950,2095755,29769758,6593415 }, { -31994208,-2907461,4176912,3264766,12538965,-868111,26312345,-6118678,30958054,8292160 }, }, { { 31429822,-13959116,29173532,15632448,12174511,-2760094,32808831,3977186,26143136,-3148876 }, { 22648901,1402143,-22799984,13746059,7936347,365344,-8668633,-1674433,-3758243,-2304625 }, { -15491917,8012313,-2514730,-12702462,-23965846,-10254029,-1612713,-1535569,-16664475,8194478 }, }, { { 27338066,-7507420,-7414224,10140405,-19026427,-6589889,27277191,8855376,28572286,3005164 }, { 26287124,4821776,25476601,-4145903,-3764513,-15788984,-18008582,1182479,-26094821,-13079595 }, { -7171154,3178080,23970071,6201893,-17195577,-4489192,-21876275,-13982627,32208683,-1198248 }, }, { { -16657702,2817643,-10286362,14811298,6024667,13349505,-27315504,-10497842,-27672585,-11539858 }, { 15941029,-9405932,-21367050,8062055,31876073,-238629,-15278393,-1444429,15397331,-4130193 }, { 8934485,-13485467,-23286397,-13423241,-32446090,14047986,31170398,-1441021,-27505566,15087184 }, }, { { -18357243,-2156491,24524913,-16677868,15520427,-6360776,-15502406,11461896,16788528,-5868942 }, { -1947386,16013773,21750665,3714552,-17401782,-16055433,-3770287,-10323320,31322514,-11615635 }, { 21426655,-5650218,-13648287,-5347537,-28812189,-4920970,-18275391,-14621414,13040862,-12112948 }, }, { { 11293895,12478086,-27136401,15083750,-29307421,14748872,14555558,-13417103,1613711,4896935 }, { -25894883,15323294,-8489791,-8057900,25967126,-13425460,2825960,-4897045,-23971776,-11267415 }, { -15924766,-5229880,-17443532,6410664,3622847,10243618,20615400,12405433,-23753030,-8436416 }, }, { { -7091295,12556208,-20191352,9025187,-17072479,4333801,4378436,2432030,23097949,-566018 }, { 4565804,-16025654,20084412,-7842817,1724999,189254,24767264,10103221,-18512313,2424778 }, { 366633,-11976806,8173090,-6890119,30788634,5745705,-7168678,1344109,-3642553,12412659 }, }, { { -24001791,7690286,14929416,-168257,-32210835,-13412986,24162697,-15326504,-3141501,11179385 }, { 18289522,-14724954,8056945,16430056,-21729724,7842514,-6001441,-1486897,-18684645,-11443503 }, { 476239,6601091,-6152790,-9723375,17503545,-4863900,27672959,13403813,11052904,5219329 }, }, }, { { { 20678546,-8375738,-32671898,8849123,-5009758,14574752,31186971,-3973730,9014762,-8579056 }, { -13644050,-10350239,-15962508,5075808,-1514661,-11534600,-33102500,9160280,8473550,-3256838 }, { 24900749,14435722,17209120,-15292541,-22592275,9878983,-7689309,-16335821,-24568481,11788948 }, }, { { -3118155,-11395194,-13802089,14797441,9652448,-6845904,-20037437,10410733,-24568470,-1458691 }, { -15659161,16736706,-22467150,10215878,-9097177,7563911,11871841,-12505194,-18513325,8464118 }, { -23400612,8348507,-14585951,-861714,-3950205,-6373419,14325289,8628612,33313881,-8370517 }, }, { { -20186973,-4967935,22367356,5271547,-1097117,-4788838,-24805667,-10236854,-8940735,-5818269 }, { -6948785,-1795212,-32625683,-16021179,32635414,-7374245,15989197,-12838188,28358192,-4253904 }, { -23561781,-2799059,-32351682,-1661963,-9147719,10429267,-16637684,4072016,-5351664,5596589 }, }, { { -28236598,-3390048,12312896,6213178,3117142,16078565,29266239,2557221,1768301,15373193 }, { -7243358,-3246960,-4593467,-7553353,-127927,-912245,-1090902,-4504991,-24660491,3442910 }, { -30210571,5124043,14181784,8197961,18964734,-11939093,22597931,7176455,-18585478,13365930 }, }, { { -7877390,-1499958,8324673,4690079,6261860,890446,24538107,-8570186,-9689599,-3031667 }, { 25008904,-10771599,-4305031,-9638010,16265036,15721635,683793,-11823784,15723479,-15163481 }, { -9660625,12374379,-27006999,-7026148,-7724114,-12314514,11879682,5400171,519526,-1235876 }, }, { { 22258397,-16332233,-7869817,14613016,-22520255,-2950923,-20353881,7315967,16648397,7605640 }, { -8081308,-8464597,-8223311,9719710,19259459,-15348212,23994942,-5281555,-9468848,4763278 }, { -21699244,9220969,-15730624,1084137,-25476107,-2852390,31088447,-7764523,-11356529,728112 }, }, { { 26047220,-11751471,-6900323,-16521798,24092068,9158119,-4273545,-12555558,-29365436,-5498272 }, { 17510331,-322857,5854289,8403524,17133918,-3112612,-28111007,12327945,10750447,10014012 }, { -10312768,3936952,9156313,-8897683,16498692,-994647,-27481051,-666732,3424691,7540221 }, }, { { 30322361,-6964110,11361005,-4143317,7433304,4989748,-7071422,-16317219,-9244265,15258046 }, { 13054562,-2779497,19155474,469045,-12482797,4566042,5631406,2711395,1062915,-5136345 }, { -19240248,-11254599,-29509029,-7499965,-5835763,13005411,-6066489,12194497,32960380,1459310 }, }, }, { { { 19852034,7027924,23669353,10020366,8586503,-6657907,394197,-6101885,18638003,-11174937 }, { 31395534,15098109,26581030,8030562,-16527914,-5007134,9012486,-7584354,-6643087,-5442636 }, { -9192165,-2347377,-1997099,4529534,25766844,607986,-13222,9677543,-32294889,-6456008 }, }, { { -2444496,-149937,29348902,8186665,1873760,12489863,-30934579,-7839692,-7852844,-8138429 }, { -15236356,-15433509,7766470,746860,26346930,-10221762,-27333451,10754588,-9431476,5203576 }, { 31834314,14135496,-770007,5159118,20917671,-16768096,-7467973,-7337524,31809243,7347066 }, }, { { -9606723,-11874240,20414459,13033986,13716524,-11691881,19797970,-12211255,15192876,-2087490 }, { -12663563,-2181719,1168162,-3804809,26747877,-14138091,10609330,12694420,33473243,-13382104 }, { 33184999,11180355,15832085,-11385430,-1633671,225884,15089336,-11023903,-6135662,14480053 }, }, { { 31308717,-5619998,31030840,-1897099,15674547,-6582883,5496208,13685227,27595050,8737275 }, { -20318852,-15150239,10933843,-16178022,8335352,-7546022,-31008351,-12610604,26498114,66511 }, { 22644454,-8761729,-16671776,4884562,-3105614,-13559366,30540766,-4286747,-13327787,-7515095 }, }, { { -28017847,9834845,18617207,-2681312,-3401956,-13307506,8205540,13585437,-17127465,15115439 }, { 23711543,-672915,31206561,-8362711,6164647,-9709987,-33535882,-1426096,8236921,16492939 }, { -23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424 }, }, { { 2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310 }, { 3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608 }, { -32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079 }, }, { { -23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101 }, { 21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418 }, { 18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576 }, }, { { 30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356 }, { 9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996 }, { -26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099 }, }, }, { { { -26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728 }, { -13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658 }, { -10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242 }, }, { { -21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001 }, { -4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766 }, { 18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373 }, }, { { 26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458 }, { -17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628 }, { -13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657 }, }, { { -23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062 }, { 25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616 }, { 31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014 }, }, { { 24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383 }, { -25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814 }, { -20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718 }, }, { { 30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417 }, { 2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222 }, { 33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444 }, }, { { -20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597 }, { 23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970 }, { 1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799 }, }, { { -5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647 }, { 13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511 }, { -29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032 }, }, }, { { { 9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834 }, { -23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461 }, { 29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062 }, }, { { -25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516 }, { -20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547 }, { -24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240 }, }, { { -17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038 }, { -33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741 }, { 16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103 }, }, { { -19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747 }, { -1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323 }, { 31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016 }, }, { { -14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373 }, { 15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228 }, { -2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141 }, }, { { 16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399 }, { 11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831 }, { -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 }, }, { { -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 }, { -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 }, { -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 }, }, { { -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 }, { 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 }, { -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 }, }, }, ed25519-0.0.5.0/src/cbits/ref10/include/ge_add.h0000644000000000000000000000404012606567661016662 0ustar0000000000000000 /* qhasm: enter ge_add */ /* qhasm: fe X1 */ /* qhasm: fe Y1 */ /* qhasm: fe Z1 */ /* qhasm: fe Z2 */ /* qhasm: fe T1 */ /* qhasm: fe ZZ */ /* qhasm: fe YpX2 */ /* qhasm: fe YmX2 */ /* qhasm: fe T2d2 */ /* qhasm: fe X3 */ /* qhasm: fe Y3 */ /* qhasm: fe Z3 */ /* qhasm: fe T3 */ /* qhasm: fe YpX1 */ /* qhasm: fe YmX1 */ /* qhasm: fe A */ /* qhasm: fe B */ /* qhasm: fe C */ /* qhasm: fe D */ /* qhasm: YpX1 = Y1+X1 */ /* asm 1: fe_add(>YpX1=fe#1,YpX1=r->X,Y,X); */ fe_add(r->X,p->Y,p->X); /* qhasm: YmX1 = Y1-X1 */ /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */ fe_sub(r->Y,p->Y,p->X); /* qhasm: A = YpX1*YpX2 */ /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,YplusX); */ fe_mul(r->Z,r->X,q->YplusX); /* qhasm: B = YmX1*YmX2 */ /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,YminusX); */ fe_mul(r->Y,r->Y,q->YminusX); /* qhasm: C = T2d2*T1 */ /* asm 1: fe_mul(>C=fe#4,C=r->T,T2d,T); */ fe_mul(r->T,q->T2d,p->T); /* qhasm: ZZ = Z1*Z2 */ /* asm 1: fe_mul(>ZZ=fe#1,ZZ=r->X,Z,Z); */ fe_mul(r->X,p->Z,q->Z); /* qhasm: D = 2*ZZ */ /* asm 1: fe_add(>D=fe#5,D=t0,X,X); */ fe_add(t0,r->X,r->X); /* qhasm: X3 = A-B */ /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */ fe_sub(r->X,r->Z,r->Y); /* qhasm: Y3 = A+B */ /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */ fe_add(r->Y,r->Z,r->Y); /* qhasm: Z3 = D+C */ /* asm 1: fe_add(>Z3=fe#3,Z3=r->Z,T); */ fe_add(r->Z,t0,r->T); /* qhasm: T3 = D-C */ /* asm 1: fe_sub(>T3=fe#4,T3=r->T,T); */ fe_sub(r->T,t0,r->T); /* qhasm: return */ ed25519-0.0.5.0/src/Crypto/0000755000000000000000000000000012606567661013124 5ustar0000000000000000ed25519-0.0.5.0/src/Crypto/Sign/0000755000000000000000000000000012606567661014024 5ustar0000000000000000ed25519-0.0.5.0/src/Crypto/Sign/Ed25519.hs0000644000000000000000000010456712606567661015333 0ustar0000000000000000{-# LANGUAGE CPP #-} {-# LANGUAGE ForeignFunctionInterface #-} #if __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE StandaloneDeriving #-} {-# LANGUAGE DeriveGeneric #-} #endif -- | -- Module : Crypto.Sign.Ed25519 -- Copyright : (c) Austin Seipp 2013-2015 -- License : MIT -- -- Maintainer : aseipp@pobox.com -- Stability : experimental -- Portability : portable -- -- This module provides bindings to the Ed25519 public-key signature -- system, including detached signatures. The documentation should be -- self explanatory with complete examples. -- -- Below the basic documentation you'll find API, performance and -- security notes, which you may want to read carefully before -- continuing. (Nonetheless, @Ed25519@ is one of the easiest-to-use -- signature systems around, and is simple to get started with for -- building more complex protocols. But the below details are highly -- educational and should help adjust your expectations properly.) -- -- For more reading on the underlying implementation and theory -- (including how to get a copy of the Ed25519 software), -- visit . There are two papers that discuss -- the design of EdDSA/Ed25519 in detail: -- -- * - -- The original specification by Bernstein, Duif, Lange, Schwabe, -- and Yang. -- -- * - -- An extension of the original EdDSA specification allowing it to -- be used with more curves (such as Ed41417, or Ed488), as well as -- defining the support for __message prehashing__. The original -- EdDSA is easily derived from the extended version through a few -- parameter defaults. (This package won't consider non-Ed25519 -- EdDSA systems any further.) -- module Crypto.Sign.Ed25519 ( -- * A crash course introduction -- $intro -- * Keypair creation -- $creatingkeys PublicKey(..) -- :: * , SecretKey(..) -- :: * , createKeypair -- :: IO (PublicKey, SecretKey) , createKeypairFromSeed_ -- :: ByteString -> Maybe (PublicKey, SecretKey) , createKeypairFromSeed -- :: ByteString -> (PublicKey, SecretKey) , toPublicKey -- :: SecretKey -> PublicKey -- * Signing and verifying messages -- $signatures , sign -- :: SecretKey -> ByteString -> ByteString , verify -- :: PublicKey -> ByteString -> Bool -- * Detached signatures -- $detachedsigs , Signature(..) -- :: * , dsign -- :: SecretKey -> ByteString -> Signature , dverify -- :: PublicKey -> ByteString -> Signature -> Bool -- ** Deprecated interface -- | The below interface is deprecated but functionally -- equivalent to the above; it simply has \"worse\" naming and will -- eventually be removed. , sign' -- :: SecretKey -> ByteString -> Signature , verify' -- :: PublicKey -> ByteString -> Signature -> Bool -- * Security, design and implementation notes -- $security -- ** EdDSA background and properties -- $background -- *** Generation of psuedo-random seeds -- $seedgen -- ** Performance and implementation -- $performance -- ** Secure @'SecretKey'@ storage -- $keystorage -- ** Prehashing and large input messages -- $prehashing ) where import Foreign.C.Types import Foreign.ForeignPtr (withForeignPtr) import Foreign.Marshal.Alloc (alloca) import Foreign.Ptr import Foreign.Storable import System.IO.Unsafe (unsafePerformIO) import Data.Maybe (fromMaybe) import Data.ByteString as S import Data.ByteString.Internal as SI import Data.ByteString.Unsafe as SU import Data.Word #if __GLASGOW_HASKELL__ >= 702 import GHC.Generics (Generic) #endif -- Doctest setup with some examples -- $setup -- >>> :set -XOverloadedStrings -- >>> import Data.ByteString.Char8 -- >>> let hash x = x -- >>> let readBigFile x = return x -------------------------------------------------------------------------------- -- Key creation -- $creatingkeys -- -- Ed25519 signatures start off life by having a keypair created, -- using @'createKeypair'@ or @'createKeypairFromSeed_'@, which gives -- you back a @'SecretKey'@ you can use for signing messages, and a -- @'PublicKey'@ your users can use to verify you in fact authored the -- messages. -- -- Ed25519 is a /deterministic signature system/, meaning that you may -- always recompute a @'PublicKey'@ and a @'SecretKey'@ from an -- initial, 32-byte input seed. Despite that, the default interface -- almost all clients will wish to use is simply @'createKeypair'@, -- which uses an Operating System provided source of secure randomness -- to seed key creation. (For more information, see the security notes -- at the bottom of this page.) -- | A @'PublicKey'@ created by @'createKeypair'@. -- -- @since 0.0.1.0 newtype PublicKey = PublicKey { unPublicKey :: ByteString -- ^ Unwrapper for getting the raw -- @'ByteString'@ in a -- @'PublicKey'@. In general you -- should not make any assumptions -- about the underlying blob; this is -- only provided for interoperability. } deriving (Eq, Show, Ord) -- | A @'SecretKey'@ created by @'createKeypair'@. __Be sure to keep this__ -- __safe!__ -- -- @since 0.0.1.0 newtype SecretKey = SecretKey { unSecretKey :: ByteString -- ^ Unwrapper for getting the raw -- @'ByteString'@ in a -- @'SecretKey'@. In general you -- should not make any assumptions -- about the underlying blob; this is -- only provided for interoperability. } deriving (Eq, Show, Ord) #if __GLASGOW_HASKELL__ >= 702 deriving instance Generic PublicKey deriving instance Generic SecretKey #endif -- | Randomly generate a @'SecretKey'@ and @'PublicKey'@ for doing -- authenticated signing and verification. This essentically calls -- @'createKeypairFromSeed_'@ with a randomly generated 32-byte seed, -- the source of which is operating-system dependent (see security -- notes below). However, internally it is implemented more -- efficiently (with less allocations and copies). -- -- If you wish to use your own seed (for design purposes so you may -- recreate keys, due to high paranoia, or because you have your own -- source of randomness), please use @'createKeypairFromSeed_'@ -- instead. -- -- @since 0.0.1.0 createKeypair :: IO (PublicKey, SecretKey) createKeypair = do pk <- SI.mallocByteString cryptoSignPUBLICKEYBYTES sk <- SI.mallocByteString cryptoSignSECRETKEYBYTES _ <- withForeignPtr pk $ \ppk -> do _ <- withForeignPtr sk $ \psk -> do _ <- c_crypto_sign_keypair ppk psk return () return () return (PublicKey $ SI.fromForeignPtr pk 0 cryptoSignPUBLICKEYBYTES, SecretKey $ SI.fromForeignPtr sk 0 cryptoSignSECRETKEYBYTES) -- | Generate a deterministic @'PublicKey'@ and @'SecretKey'@ from a -- given 32-byte seed, allowing you to recreate a keypair at any point -- in time, providing you have the seed available. -- -- If the input seed is not 32 bytes in length, -- @'createKeypairFromSeed_'@ returns @'Nothing'@. Otherwise, it -- always returns @'Just' (pk, sk)@ for the given seed. -- -- __/NOTE/__: This function will replace @'createKeypairFromSeed'@ in -- the future. -- -- @since 0.0.4.0 createKeypairFromSeed_ :: ByteString -- ^ 32-byte seed -> Maybe (PublicKey, SecretKey) -- ^ Resulting keypair createKeypairFromSeed_ seed | S.length seed /= cryptoSignSEEDBYTES = Nothing | otherwise = unsafePerformIO $ do pk <- SI.mallocByteString cryptoSignPUBLICKEYBYTES sk <- SI.mallocByteString cryptoSignSECRETKEYBYTES _ <- SU.unsafeUseAsCString seed $ \pseed -> do _ <- withForeignPtr pk $ \ppk -> do _ <- withForeignPtr sk $ \psk -> do _ <- c_crypto_sign_seed_keypair ppk psk pseed return () return () return () return $ Just (PublicKey $ SI.fromForeignPtr pk 0 cryptoSignPUBLICKEYBYTES, SecretKey $ SI.fromForeignPtr sk 0 cryptoSignSECRETKEYBYTES) -- | Generate a deterministic @'PublicKey'@ and @'SecretKey'@ from a -- given 32-byte seed, allowing you to recreate a keypair at any point -- in time, providing you have the seed available. -- -- Note that this will @'error'@ if the given input is not 32 bytes in -- length, so you must be careful with this input. -- -- @since 0.0.3.0 createKeypairFromSeed :: ByteString -- ^ 32-byte seed -> (PublicKey, SecretKey) -- ^ Resulting keypair createKeypairFromSeed seed = fromMaybe (error "seed has incorrect length") (createKeypairFromSeed_ seed) {-# DEPRECATED createKeypairFromSeed "This function is unsafe as it can @'fail'@ with an invalid input. Use @'createKeypairWithSeed_'@ instead." #-} -- | Derive the @'PublicKey'@ for a given @'SecretKey'@. This is a -- convenience which allows (for example) using @'createKeypair'@ and -- only ever storing the returned @'SecretKey'@ for any future -- operations. -- -- @since 0.0.3.0 toPublicKey :: SecretKey -- ^ Any valid @'SecretKey'@ -> PublicKey -- ^ Corresponding @'PublicKey'@ toPublicKey = PublicKey . S.drop prefixBytes . unSecretKey where prefixBytes = cryptoSignSECRETKEYBYTES - cryptoSignPUBLICKEYBYTES -------------------------------------------------------------------------------- -- Default, non-detached API -- $signatures -- -- By default, the Ed25519 interface computes a /signed message/ given -- a @'SecretKey'@ and an input message. A /signed message/ consists -- of an Ed25519 signature (of unspecified format), followed by the -- input message. This means that given an input message of @M@ -- bytes, you get back a message of @M+N@ bytes where @N@ is a -- constant (the size of the Ed25519 signature blob). -- -- The default interface in this package reflects that. As a result, -- any time you use @'sign'@ or @'verify'@ you will be given back the -- full input, and then some. -- -- | Sign a message with a particular @'SecretKey'@. Note that the resulting -- signed message contains both the message itself, and the signature -- attached. If you only want the signature of a given input string, -- please see @'dsign'@. -- -- @since 0.0.1.0 sign :: SecretKey -- ^ Signers @'SecretKey'@ -> ByteString -- ^ Input message -> ByteString -- ^ Resulting signed message sign (SecretKey sk) xs = unsafePerformIO . SU.unsafeUseAsCStringLen xs $ \(mstr,mlen) -> SU.unsafeUseAsCString sk $ \psk -> SI.createAndTrim (mlen+cryptoSignBYTES) $ \out -> alloca $ \smlen -> do _ <- c_crypto_sign out smlen mstr (fromIntegral mlen) psk fromIntegral `fmap` peek smlen {-# INLINE sign #-} -- | Verifies a signed message against a @'PublicKey'@. Note that the input -- message must be generated by @'sign'@ (that is, it is the message -- itself plus its signature). If you want to verify an arbitrary -- signature against an arbitrary message, please see @'dverify'@. -- -- @since 0.0.1.0 verify :: PublicKey -- ^ Signers @'PublicKey'@ -> ByteString -- ^ Signed message -> Bool -- ^ Verification result verify (PublicKey pk) xs = unsafePerformIO . SU.unsafeUseAsCStringLen xs $ \(smstr,smlen) -> SU.unsafeUseAsCString pk $ \ppk -> alloca $ \pmlen -> do out <- SI.mallocByteString smlen r <- withForeignPtr out $ \pout -> c_crypto_sign_open pout pmlen smstr (fromIntegral smlen) ppk return (r == 0) {-# INLINE verify #-} -------------------------------------------------------------------------------- -- Detached signature support -- $detachedsigs -- -- This package also provides an alternative interface for /detached/ -- /signatures/, which is more in-line with what you might -- traditionally expect from a signing API. In this mode, the -- @'dsign'@ and @'dverify'@ interfaces simply return a constant-sized -- blob, representing the Ed25519 signature of the input message. -- -- This allows users to independently download, verify or attach -- signatures to messages in any way they see fit - for example, by -- providing a tarball file to download, with a corresponding @.sig@ -- file containing the Ed25519 signature from the author. -- | A @'Signature'@ which is detached from the message it signed. -- -- @since 0.0.1.0 newtype Signature = Signature { unSignature :: ByteString -- ^ Unwrapper for getting the raw -- @'ByteString'@ in a -- @'Signature'@. In general you -- should not make any assumptions -- about the underlying blob; this is -- only provided for interoperability. } deriving (Eq, Show, Ord) #if __GLASGOW_HASKELL__ >= 702 deriving instance Generic Signature #endif -- | Sign a message with a particular @'SecretKey'@, only returning the -- @'Signature'@ without the message. -- -- @since 0.0.4.0 dsign :: SecretKey -- ^ Signers @'SecretKey'@ -> ByteString -- ^ Input message -> Signature -- ^ Message @'Signature'@, without the message dsign sk xs = let sm = sign sk xs l = S.length sm in Signature $! S.take (l - S.length xs) sm {-# INLINE dsign #-} -- | Verify a message with a detached @'Signature'@ against a given -- @'PublicKey'@. -- -- @since 0.0.4.0 dverify :: PublicKey -- ^ Signers @'PublicKey'@ -> ByteString -- ^ Raw input message -> Signature -- ^ Message @'Signature'@ -> Bool -- ^ Verification result dverify pk xs (Signature sig) = verify pk (sig `S.append` xs) {-# INLINE dverify #-} -- | Sign a message with a particular @'SecretKey'@, only returning the -- @'Signature'@ without the message. Simply an alias for @'dsign'@. -- -- @since 0.0.1.0 sign' :: SecretKey -- ^ Signers @'SecretKey'@ -> ByteString -- ^ Input message -> Signature -- ^ Message @'Signature'@, without the message sign' sk xs = dsign sk xs {-# DEPRECATED sign' "@'sign''@ will be removed in a future release; use @'dsign'@ instead." #-} -- | Verify a message with a detached @'Signature'@ against a given -- @'PublicKey'@. Simply an alias for @'dverify'@. -- -- @since 0.0.1.0 verify' :: PublicKey -- ^ Signers @'PublicKey'@ -> ByteString -- ^ Raw input message -> Signature -- ^ Message @'Signature'@ -> Bool -- ^ Verification result verify' pk xs sig = dverify pk xs sig {-# DEPRECATED verify' "@'verify''@ will be removed in a future release; use @'dverify'@ instead." #-} -------------------------------------------------------------------------------- -- FFI binding cryptoSignSECRETKEYBYTES :: Int cryptoSignSECRETKEYBYTES = 64 cryptoSignPUBLICKEYBYTES :: Int cryptoSignPUBLICKEYBYTES = 32 cryptoSignBYTES :: Int cryptoSignBYTES = 64 cryptoSignSEEDBYTES :: Int cryptoSignSEEDBYTES = 32 foreign import ccall unsafe "ed25519_sign_seed_keypair" c_crypto_sign_seed_keypair :: Ptr Word8 -> Ptr Word8 -> Ptr CChar -> IO CInt foreign import ccall unsafe "ed25519_sign_keypair" c_crypto_sign_keypair :: Ptr Word8 -> Ptr Word8 -> IO CInt foreign import ccall unsafe "ed25519_sign" c_crypto_sign :: Ptr Word8 -> Ptr CULLong -> Ptr CChar -> CULLong -> Ptr CChar -> IO CULLong foreign import ccall unsafe "ed25519_sign_open" c_crypto_sign_open :: Ptr Word8 -> Ptr CULLong -> Ptr CChar -> CULLong -> Ptr CChar -> IO CInt -------------------------------------------------------------------------------- -- Documentation and notes -- $intro -- -- The simplest use of this library is one where you probably need to -- sign short messages, so they can be verified independently. That's -- easily done by first creating a keypair with @'createKeypair'@, and -- using @'sign'@ to create a signed message. Then, you can distribute -- your public key and the signed message, and any recipient can -- verify that message: -- -- >>> (pk, sk) <- createKeypair -- >>> let msg = sign sk "Hello world" -- >>> verify pk msg -- True -- -- This interface is fine if your messages are small and simple binary -- blobs you want to verify in an opaque manner, but internally it -- creates a copy of the input message. Often, you'll want the -- signature independently of the message, and that can be done with -- @'dsign'@ and @'dverify'@. Naturally, verification fails if the -- message is incorrect: -- -- >>> (pk, sk) <- createKeypair -- >>> let msg = "Hello world" :: ByteString -- >>> let sig = dsign sk msg -- >>> dverify pk msg sig -- True -- >>> dverify pk "Hello world" sig -- True -- >>> dverify pk "Goodbye world" sig -- False -- -- Finally, it's worth keeping in mind this package doesn't expose any -- kind of incremental interface, and signing/verification can be -- expensive. So, if you're dealing with __large inputs__, you can -- hash the input with a robust, fast cryptographic hash, and then -- sign that (for example, the @hash@ function below could be -- __SHA-512__ or __BLAKE2b__): -- -- >>> (pk, sk) <- createKeypair -- >>> msg <- readBigFile "blob.tar.gz" :: IO ByteString -- >>> let sig = dsign sk (hash msg) -- >>> dverify pk (hash msg) sig -- True -- -- See the notes at the bottom of this module for more on message -- prehashing (as it acts slightly differently in an EdDSA system). -- $security -- -- Included below are some notes on the security aspects of the -- Ed25519 signature system, its implementation and design, this -- package, and suggestions for how you might use it properly. -- $background -- -- Ed25519 is a specific instantiation of the __EdDSA__ digital -- signature scheme - a high performance, secure-by-design variant of -- Schnorr signatures based on "Twisted Edwards Curves" (hence the -- name __Ed__DSA). The (__extended__) EdDSA system is defined by an -- elliptic curve: -- -- > ax^2 + y^2 = 1 + d*x^2*y^2 -- -- along with several other parameters, chosen by the implementation -- in question. These parameters include @a@, @d@, and a field @GF(p)@ -- where @p@ is prime. Ed25519 specifically uses @d = -121665/121666@, -- @a = -1@, and the finite field @GF((2^155)-19)@, where @(2^155)-19@ -- is a prime number (which is also the namesake of the algorithm in -- question, as Ed__25519__). This yields the equation: -- -- > -x^2 + y^2 = 1 - (121665/121666)*x^2*y^2 -- -- This curve is \'birationally equivalent\' to the well-known -- Montgomery curve \'Curve25519\', which means that EdDSA shares the -- same the difficult problem as Curve25519: that of the Elliptic -- Curve Discrete Logarithm Problem (ECDLP). Ed25519 is currently -- still the recommended EdDSA curve for most deployments. -- -- As Ed25519 is an elliptic curve algorithm, the security level -- (i.e. number of computations taken to find a solution to the ECDLP -- with the fastest known attacks) is roughly half the key size in -- bits, as it stands. As Ed25519 features 32-byte keys, the security -- level of Ed25519 is thus @2^((32*8)/2) = 2^128@, far beyond any -- attacker capability (modulo major breakthroughs for the ECDLP, -- which would likely catastrophically be applicable to other systems -- too). -- -- Ed25519 designed to meet the standard notion of unforgeability for -- a public-key signature scheme under chosen-message attacks. This -- means that even should the attacker be able to request someone sign -- any arbitrary message of their choice (hence /chosen-message/), -- they are still not capable of any forgery what-so-ever, even the -- weakest kind of \'existential forgery\'. -- $seedgen -- -- Seed generation as done by @'createKeypair'@ uses Operating System -- provided APIs for generating cryptographically secure psuedo-random -- data to be used as an Ed25519 key seed. Your own deterministic keys -- may be generated using @'createKeypairFromSeed_'@, provided you have -- your own cryptographically secure psuedo-random data from -- somewhere. -- -- On __Linux__, __OS X__ and __other Unix__ machines, the -- @\/dev\/urandom@ device is consulted internally in order to generate -- random data. In the current implementation, a global file -- descriptor is used through the lifetime of the program to -- periodically get psuedo-random data. -- -- On __Windows__, the @CryptGenRandom@ API is used internally. This -- does not require file handles of any kind, and should work on all -- versions of Windows. (Windows may instead use @RtlGenRandom@ in the -- future for even less overhead.) -- -- In the future, there are plans for this package to internally take -- advantage of better APIs when they are available; for example, on -- Linux 3.17 and above, @getrandom(2)@ provides psuedo-random data -- directly through the internal pool provided by @\/dev\/urandom@, -- without a file descriptor. Similarly, OpenBSD provides the -- @arc4random(3)@ family of functions, which internally uses a data -- generator based on ChaCha20. These should offer somewhat better -- efficiency, and also avoid file-descriptor exhaustion attacks which -- could lead to denial of service in some scenarios. -- $performance -- -- Ed25519 is exceptionally fast, although the implementation provided -- by this package is not the fastest possible implementation. Indeed, -- it is rather slow, even by non-handwritten-assembly standards of -- speed. That said, it should still be competitive with most other -- signature schemes: the underlying implementation is @ref10@ from -- , authored by Daniel J. Bernstein, -- which is within the -- -- against some assembly implementations (only 2x slower), and much -- faster than the slow reference implementation (25x slower). When up -- -- signatures (ronald3072) on a modern Intel machine, it is still __15x__ -- faster at signing messages /at the same 128-bit security level/. -- -- On the author's Sandy Bridge i5-2520M 2.50GHz CPU, the benchmarking -- code included with the library reports the following numbers for -- the Haskell interface: -- -- @ -- benchmarking deterministic key generation -- time 250.0 μs (249.8 μs .. 250.3 μs) -- 1.000 R² (1.000 R² .. 1.000 R²) -- mean 250.0 μs (249.9 μs .. 250.2 μs) -- std dev 467.0 ns (331.7 ns .. 627.9 ns) -- -- benchmarking signing a 256 byte message -- time 273.2 μs (273.0 μs .. 273.4 μs) -- 1.000 R² (1.000 R² .. 1.000 R²) -- mean 273.3 μs (273.1 μs .. 273.5 μs) -- std dev 616.2 ns (374.1 ns .. 998.8 ns) -- -- benchmarking verifying a signature -- time 635.7 μs (634.6 μs .. 637.3 μs) -- 1.000 R² (1.000 R² .. 1.000 R²) -- mean 635.4 μs (635.0 μs .. 636.0 μs) -- std dev 1.687 μs (999.3 ns .. 2.487 μs) -- -- benchmarking roundtrip 256-byte sign/verify -- time 923.6 μs (910.0 μs .. 950.6 μs) -- 0.998 R² (0.996 R² .. 1.000 R²) -- mean 913.2 μs (910.6 μs .. 923.0 μs) -- std dev 15.93 μs (1.820 μs .. 33.72 μs) -- @ -- -- In the future, this package will hopefully provide an opt-in (or -- possibly default) implementation of -- , which -- should dramatically increase speed at no cost for many/all -- platforms. -- $keystorage -- -- By default, keys are not encrypted in any meaningful manner with -- any mechanism, and this package does not provide any means of doing -- so. As a result, your secret keys are only as secure as the -- computing environment housing them - a server alone out on the -- hostile internet, or a USB stick that's susceptable to theft. -- -- If you wish to add some security to your keys, a very simple and -- effective way is __to add a password to your @'SecretKey'@ with a__ -- __KDF and a hash__. How does this work? -- -- * First, hash the secret key you have generated. Use this as a -- __checksum__ of the original key. Truncating this hash to save -- space is acceptable; see below for more details and boring -- hemming and hawing. -- -- * Given an input password, use a KDF to stretch it to the length -- of a @'SecretKey'@. -- -- * XOR the @'SecretKey'@ bytewise, directly with the output of -- your chosen KDF. -- -- * Attach the checksum you generated to the resulting encrypted -- key, and store it as you like. -- -- In this mode, your key is XOR'd with the psuedo-random result of a -- KDF, which will stretch simple passwords like "I am the robot" into -- a suitable amount of psuedo-random data for a given secret key to -- be encrypted with. Decryption is simply the act of taking the -- password, generating the psuedo-random stream again, XORing the key -- bytewise, and validating the checksum. In this sense, you are -- simply using a KDF as a short stream cipher. -- -- __Recommendation__: Encrypt keys by stretching a password with -- __scrypt__ (or __yescrypt__), using better-than-default parameters. -- (These being @N = 2^14@, @r = 8@, @p = 1@; the default results in -- 16mb of memory per invocation, and this is the recommended default -- for 'interactive systems'; signing keys may be loaded on-startup -- for some things however, so it may be profitable to increase -- security as well as memory use in these cases. For example, at @N = -- 2^18@, @r = 10@ and @p = 2@, you'll get 320mb of memory per use, -- which may be acceptable for dramatic security increases. See -- elsewhere for exact memory use.) Checksums may be computed with an -- exceptionally fast hash such as __BLAKE2b__. -- -- __Bonus points__: Print that resulting checksum + key out on a -- piece of paper (~100 bytes, tops), and put /that/ somewhere safe. -- -- __Q__: What is the hash needed for? __A__: A simple file integrity -- check. Rather than invoke complicated methods of verifying if an -- ed25519 keypair is valid (as it is simply an opaque binary blob, -- for all intents and purposes), especially after 'streaming -- decryption', it's far easier to simply compute and compare against -- a checksum of the original to determine if decryption with your -- password worked. -- -- __Q__: Wait, why is it OK to truncate the hash here? That sounds -- scary. Won't that open up collisions or something like that if they -- stole my encrypted key? __A__: No. The hash in this case is only -- used as a checksum to see if the password is legitimate after -- running the KDF and XORing with the result. Think about how the -- \'challenge\' itself is chosen: if you know @H(m)@, do you want to -- find @m@ itself, or simply find @m'@ where @H(m') = H(m)@? To -- forge a signature, you want the original key, @m@. Suppose given an -- input of 256-bits, we hashed it and truncated to one bit. Finding -- collisions would be easy: you would only need to try a few times to -- find a collision or preimage. But you probably found @m'@ such that -- @H(m') = H(m)@ - you didn't necessarily find @m@ itself. In this -- sense, finding collisions or preimages of the hash is not useful to -- the attacker, because you must find the unique @m@. -- -- __Q__: Okay, why use hashes at all? Why not CRC32? __A__: You could -- do that, it wouldn't change much. You can really use any kind of -- error detecting code you want. The thing is, some hashes such as -- __BLAKE2__ are very fast in things like software (not every CPU has -- CRC instructions, not all software uses CRC instructions), and -- you're likely to already have a fast, modern hash function sitting -- around anyway if you're signing stuff with Ed25519. Why not use it? -- $prehashing -- -- __Message prehashing__ (although not an official term in any right) -- is the idea of first taking an input @x@, using a -- __cryptographically secure__ hash function @H@ to calculate @y = -- H(x)@, and then generating a signature via @Sign(secretKey, -- y)@. The idea is that signing is often expensive, while hashing is -- often extremely fast. As a result, signing the hash of a message -- (which should be indistinguishable from a truly random function) is -- often faster than simply signing the full message alone, and in -- larger cases can save a significant amount of CPU cycles. However, -- internally Ed25519 uses a hash function @H@ already to hash the -- input message for computing the signature. Thus, there is a -- question - is it appropriate or desireable to hash the input -- already if this is the case? -- -- Generally speaking, it's OK to prehash messages before giving them -- to Ed25519. However, there is a caveat. In the paper -- , -- the authors of the original EdDSA enhance the specification by -- extending it with a message prehash function, @H'@, along with an -- internal hash @H@. Here, the prehash @H'@ is simply applied to the -- original message first before anything else. The original EdDSA -- specification (and the implementation in /this package/) was a -- trivial case of this enhancement: it was implicit that @H'@ is -- simply the identity function. We call the case where @H'@ is the -- identity function __PureEdDSA__, while the case where @H'@ is a -- cryptographic hash function is known as __HashEdDSA__. (Thus, the -- interfaces @'sign'@ and @'dsign'@ implement PureEdDSA - while they can -- be converted to HashEdDSA by simply hashing the @'ByteString'@ -- first with some other function.) -- -- However, the authors note that HashEdDSA suffers from a weakness -- that PureEdDSA does not - PureEdDSA is resiliant to collision -- attacks in the underlying hash function @H@, while HashEdDSA is -- vulnerable to collisions in @H'@. This is an important -- distinction. Assume that the attacker finds a collision such that -- @H'(x) = H'(y)@, and then gets convinces a signer to HashEdDSA-sign -- @x@ - the attacker may then forge this signature and use it as the -- same signature as for the message @y@. For a hash function of -- @N@-bits of output, a collision attack takes roughly @2^(N/2)@ -- operations. -- -- Ed25519 internally sets @H = SHA-512@ anyway, which has no known -- collision attacks or weaknesses in any meaningful sense. It is -- however slower compared to other, more modern hash functions, and -- is used on the input message in its entirety (and there are no -- plans to switch the internal implementation of this package, or the -- standard Ed25519 away from @H = SHA-512@). -- -- But note: /all other hash-then-sign constructions suffer from/ -- /this/, in the sense they are all vulnerable to collision attacks -- in @H'@, should you prehash the message. In fact, PureEdDSA is -- unique (as far as I am aware) in that it is immune to collision -- attacks in @H@ - should a collision be found, it would not suffer -- from these forgeries. By this view, it's arguable that /depending/ -- on the HashEdDSA construction (for efficiency or size purposes) -- when using EdDSA is somewhat less robust, even if SHA-512 or -- whatever is not very fast. Despite that, just about any /modern/ -- /hash/ you pick is going to be collision resistant to a fine degree -- (say, 256 bits of output, therefore collisions 'at best' happen in -- @2^128@ operations), so in practice this robustness issue may not -- be that big of a deal. -- -- However, the more pertinent issue is that due to the current design -- of the API which requires the entire blob to sign up front, using -- the HashEdDSA construction is often much more convenient, faster -- and sometimes /necessary/ too. For example, when signing very large -- messages (such as creating a very large @tar.gz@ file which you -- wish to sign after creation), it is often convenient and possible -- to use \'incremental\' hashing APIs to incrementally consume data -- blocks from the input in a constant amount of memory. At the end of -- consumption, you can \'finalize\' the data blocks and get back a -- final N-bit hash, and sign this hash all in a constant amount of -- memory. With the current API, using PureDSA would require you -- loading the entire file up front to either sign, or verify it. This -- is especially unoptimal for possibly smaller, low-memory systems -- (where decompression, hashing or verification are all best done in -- constant space if possible). -- -- Beware however, that if you do this sort of incremental hashing for -- large blobs, you are __taking untrusted data__ and hashing it -- __before checking the signature__ - be __exceptionally careful__ -- with data from a possibly untrustworthy source until you can verify -- the signature. -- -- So, __some basic guidelines are__: -- -- - If you are simply not worried about efficiency very much, just -- use __PureEdDSA__ (i.e. just use @'sign'@ and @'verify'@ -- directly). -- -- - If you have __lots of small messages__, use __PureEdDSA__ (i.e. -- just use @'sign'@ and @'verify'@ directly). -- -- - If you have to sign/verify __large messages__, possibly __in__ -- __an incremental fashion__, use __HashEdDSA__ with __a fast__ -- __hash__ (i.e. just hash a message before using @'sign'@ or -- @'verify'@ on it). -- -- - A hash like __BLAKE2b__ is recommended. Fast and very secure. -- -- - Remember: __never touch input data in any form until you__ -- __are done hashing it and verifying the signature__. -- -- As a result, you should be safe hashing your input before passing -- it to @'sign'@ or @'dsign'@ in this library if you desire, and it may -- save you CPU cycles for large inputs. It should be no different -- than the typical /hash-then-sign/ construction you see elsewhere, -- with the same downfalls. Should you do this, an extremely -- fast-yet-secure hash such as __BLAKE2b__ is recommended, which is -- even faster than MD5 or SHA-1 (and __do not ever use MD5 or__ -- __SHA-1__, on that note - they suffer from collision attacks). ed25519-0.0.5.0/tests/0000755000000000000000000000000012606567661012217 5ustar0000000000000000ed25519-0.0.5.0/tests/doctests.hs0000644000000000000000000000164612606567661014412 0ustar0000000000000000module Main ( main -- :: IO () ) where import Control.Applicative import Control.Monad import Data.List import System.Directory import System.FilePath import Test.DocTest main :: IO () main = allSources >>= \sources -> doctest ("-isrc":sources) allSources :: IO [FilePath] allSources = liftM2 (++) (getFiles ".hs" "src") (getFiles ".o" "dist/build/src/cbits") getFiles :: String -> FilePath -> IO [FilePath] getFiles ext root = filter (isSuffixOf ext) <$> go root where go dir = do (dirs, files) <- getFilesAndDirectories dir (files ++) . concat <$> mapM go dirs getFilesAndDirectories :: FilePath -> IO ([FilePath], [FilePath]) getFilesAndDirectories dir = do c <- fmap (dir ) . filter (`notElem` ["..", "."]) <$> getDirectoryContents dir (,) <$> filterM doesDirectoryExist c <*> filterM doesFileExist c ed25519-0.0.5.0/tests/hlint.hs0000644000000000000000000000076712606567661013703 0ustar0000000000000000module Main ( main -- :: IO () ) where import Control.Monad import Data.Monoid import Language.Haskell.HLint import System.Environment import System.Exit main :: IO () main = do args <- getArgs hints <- hlint $ [ "src", "benchmarks", "tests" , "--cpp-define=HLINT" , "--cpp-file=dist/build/autogen/cabal_macros.h" ] `mappend` args unless (null hints) exitFailure ed25519-0.0.5.0/tests/properties.hs0000644000000000000000000000617112606567661014754 0ustar0000000000000000{-# OPTIONS_GHC -fno-warn-orphans #-} {-# LANGUAGE CPP #-} module Main ( main -- :: IO () ) where import Control.Monad import Data.ByteString (ByteString) import qualified Data.ByteString as S import Crypto.Sign.Ed25519 import System.Environment (getArgs) import Test.QuickCheck import Test.QuickCheck.Property (morallyDubiousIOProperty) import Text.Printf -------------------------------------------------------------------------------- -- Orphans instance Arbitrary ByteString where arbitrary = S.pack `liftM` arbitrary instance Arbitrary SecretKey where arbitrary = SecretKey `liftM` arbitrary instance Arbitrary PublicKey where arbitrary = PublicKey `liftM` arbitrary -------------------------------------------------------------------------------- -- Signatures keypairProp :: ((PublicKey, SecretKey) -> Bool) -> Property keypairProp k = morallyDubiousIOProperty $ k `liftM` createKeypair roundtrip :: ByteString -> Property roundtrip xs = keypairProp $ \(pk,sk) -> verify pk (sign sk xs) roundtrip' :: ByteString -> Property roundtrip' xs = keypairProp $ \(pk,sk) -> dverify pk xs (dsign sk xs) -- Generally the signature format is '' -- and is of a fixed length (crypto_sign_BYTES), which in -- ed25519's case is 64. @'dsign'@ drops the message appended at the -- end, so we just make sure we have constant length signatures. signLength :: (ByteString,ByteString) -> Property signLength (xs,xs2) = keypairProp $ \(_,sk) -> let s1 = unSignature $ dsign sk xs s2 = unSignature $ dsign sk xs2 in S.length s1 == S.length s2 -- ed25519 has a sig length of 64 signLength2 :: ByteString -> Property signLength2 xs = keypairProp $ \(_,sk) -> (64 == S.length (unSignature $ dsign sk xs)) -------------------------------------------------------------------------------- -- Driver main :: IO () main = do args <- getArgs let n = if null args then 100 else read (head args) :: Int (results, passed) <- runTests n printf "Passed %d tests!\n" (sum passed) unless (and results) (fail "Not all tests passed!") runTests :: Int -> IO ([Bool], [Int]) runTests ntests = fmap unzip . forM (tests ntests) $ \(s, a) -> printf "%-40s: " s >> a tests :: Int -> [(String, IO (Bool,Int))] tests ntests = [ ("Signature roundtrip", wrap roundtrip) , ("Detached signature roundtrip", wrap roundtrip') , ("Detached signature length", wrap signLength) , ("Detached signature length (#2)", wrap signLength2) ] where wrap :: Testable prop => prop -> IO (Bool, Int) wrap prop = do r <- quickCheckWithResult stdArgs{maxSuccess=ntests} prop case r of Success n _ _ -> return (True, n) GaveUp n _ _ -> return (True, n) #if MIN_VERSION_QuickCheck(2,7,0) Failure n _ _ _ _ _ _ _ _ _ -> return (False, n) #elif MIN_VERSION_QuickCheck(2,6,0) Failure n _ _ _ _ _ _ _ -> return (False, n) #else Failure n _ _ _ _ _ _ -> return (False, n) #endif _ -> return (False, 0)