ssss-0.5/0002755000175100001440000000000010362426623013173 5ustar bertramusers00000000000000ssss-0.5/Makefile0000644000175100001440000000060310362426611014625 0ustar bertramusers00000000000000all: ssss-split ssss-combine ssss.1 ssss.1.html ssss-split: ssss.c $(CC) -W -Wall -O2 -lgmp -o ssss-split ssss.c strip ssss-split ssss-combine: ssss-split ln -f ssss-split ssss-combine ssss.1: ssss.manpage.xml xmltoman ssss.manpage.xml > ssss.1 ssss.1.html: ssss.manpage.xml xmlmantohtml ssss.manpage.xml > ssss.1.html clean: rm -rf ssss-split ssss-combine ssss.1 ssss.1.html ssss-0.5/ssss.c0000644000175100001440000004064510362426611014336 0ustar bertramusers00000000000000/* * ssss version 0.5 - Copyright 2005,2006 B. Poettering * * This program is free software; you can redistribute it and/or * modify it under the terms of the GNU General Public License as * published by the Free Software Foundation; either version 2 of the * License, or (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA * 02111-1307 USA */ /* * http://point-at-infinity.org/ssss/ * * This is an implementation of Shamir's Secret Sharing Scheme. See * the project's homepage http://point-at-infinity.org/ssss/ for more * information on this topic. * * This code links against the GNU multiprecision library "libgmp". * I compiled the code successfully with gmp 4.1.4. * You will need a system that has a /dev/random entropy source. * * Compile with * "gcc -O2 -lgmp -o ssss-split ssss.c && ln ssss-split ssss-combine" * * Compile with -DNOMLOCK to obtain a version without memory locking. * * Report bugs to: ssss AT point-at-infinity.org * */ #include #include #include #include #include #include #include #include #include #include #include #define VERSION "0.5" #define RANDOM_SOURCE "/dev/random" #define MAXDEGREE 1024 #define MAXTOKENLEN 128 #define MAXLINELEN (MAXTOKENLEN + 1 + 10 + 1 + MAXDEGREE / 4 + 10) /* coefficients of some irreducible polynomials over GF(2) */ static const unsigned char irred_coeff[] = { 4,3,1,5,3,1,4,3,1,7,3,2,5,4,3,5,3,2,7,4,2,4,3,1,10,9,3,9,4,2,7,6,2,10,9, 6,4,3,1,5,4,3,4,3,1,7,2,1,5,3,2,7,4,2,6,3,2,5,3,2,15,3,2,11,3,2,9,8,7,7, 2,1,5,3,2,9,3,1,7,3,1,9,8,3,9,4,2,8,5,3,15,14,10,10,5,2,9,6,2,9,3,2,9,5, 2,11,10,1,7,3,2,11,2,1,9,7,4,4,3,1,8,3,1,7,4,1,7,2,1,13,11,6,5,3,2,7,3,2, 8,7,5,12,3,2,13,10,6,5,3,2,5,3,2,9,5,2,9,7,2,13,4,3,4,3,1,11,6,4,18,9,6, 19,18,13,11,3,2,15,9,6,4,3,1,16,5,2,15,14,6,8,5,2,15,11,2,11,6,2,7,5,3,8, 3,1,19,16,9,11,9,6,15,7,6,13,4,3,14,13,3,13,6,3,9,5,2,19,13,6,19,10,3,11, 6,5,9,2,1,14,3,2,13,3,1,7,5,4,11,9,8,11,6,5,23,16,9,19,14,6,23,10,2,8,3, 2,5,4,3,9,6,4,4,3,2,13,8,6,13,11,1,13,10,3,11,6,5,19,17,4,15,14,7,13,9,6, 9,7,3,9,7,1,14,3,2,11,8,2,11,6,4,13,5,2,11,5,1,11,4,1,19,10,3,21,10,6,13, 3,1,15,7,5,19,18,10,7,5,3,12,7,2,7,5,1,14,9,6,10,3,2,15,13,12,12,11,9,16, 9,7,12,9,3,9,5,2,17,10,6,24,9,3,17,15,13,5,4,3,19,17,8,15,6,3,19,6,1 }; int opt_showversion = 0; int opt_help = 0; int opt_quiet = 0; int opt_QUIET = 0; int opt_hex = 0; int opt_diffusion = 1; int opt_security = 0; int opt_threshold = -1; int opt_number = -1; char *opt_token = NULL; unsigned int degree; mpz_t poly; int cprng; struct termios echo_orig, echo_off; #define mpz_lshift(A, B, l) mpz_mul_2exp(A, B, l) #define mpz_sizeinbits(A) (mpz_cmp_ui(A, 0) ? mpz_sizeinbase(A, 2) : 0) /* emergency abort and warning functions */ void fatal(char *msg) { tcsetattr(0, TCSANOW, &echo_orig); fprintf(stderr, "%sFATAL: %s.\n", isatty(2) ? "\a" : "", msg); exit(1); } void warning(char *msg) { if (! opt_QUIET) fprintf(stderr, "%sWARNING: %s.\n", isatty(2) ? "\a" : "", msg); } /* field arithmetic routines */ int field_size_valid(int deg) { return (deg >= 8) && (deg <= MAXDEGREE) && (deg % 8 == 0); } /* initialize 'poly' to a bitfield representing the coefficients of an irreducible polynomial of degree 'deg' */ void field_init(int deg) { assert(field_size_valid(deg)); mpz_init_set_ui(poly, 0); mpz_setbit(poly, deg); mpz_setbit(poly, irred_coeff[3 * (deg / 8 - 1) + 0]); mpz_setbit(poly, irred_coeff[3 * (deg / 8 - 1) + 1]); mpz_setbit(poly, irred_coeff[3 * (deg / 8 - 1) + 2]); mpz_setbit(poly, 0); degree = deg; } void field_deinit(void) { mpz_clear(poly); } /* I/O routines for GF(2^deg) field elements */ void field_import(mpz_t x, const char *s, int hexmode) { if (hexmode) { if (strlen(s) > degree / 4) fatal("input string too long"); if (strlen(s) < degree / 4) warning("input string too short, adding null padding on the left"); if (mpz_set_str(x, s, 16) || (mpz_cmp_ui(x, 0) < 0)) fatal("invalid syntax"); } else { int i; int warn = 0; if (strlen(s) > degree / 8) fatal("input string too long"); for(i = strlen(s) - 1; i >= 0; i--) warn = warn || (s[i] < 32) || (s[i] >= 127); if (warn) warning("binary data detected, use -x mode instead"); mpz_import(x, strlen(s), 1, 1, 0, 0, s); } } void field_print(FILE* stream, const mpz_t x, int hexmode) { int i; if (hexmode) { for(i = degree / 4 - mpz_sizeinbase(x, 16); i; i--) fprintf(stream, "0"); mpz_out_str(stream, 16, x); fprintf(stream, "\n"); } else { char buf[MAXDEGREE / 8 + 1]; size_t t; unsigned int i; int printable, warn = 0; memset(buf, degree / 8 + 1, 0); mpz_export(buf, &t, 1, 1, 0, 0, x); for(i = 0; i < t; i++) { printable = (buf[i] >= 32) && (buf[i] < 127); warn = warn || ! printable; fprintf(stream, "%c", printable ? buf[i] : '.'); } fprintf(stream, "\n"); if (warn) warning("binary data detected, use -x mode instead"); } } /* basic field arithmetic in GF(2^deg) */ void field_add(mpz_t z, const mpz_t x, const mpz_t y) { mpz_xor(z, x, y); } void field_mult(mpz_t z, const mpz_t x, const mpz_t y) { mpz_t b; unsigned int i; assert(z != y); mpz_init_set(b, x); if (mpz_tstbit(y, 0)) mpz_set(z, b); else mpz_set_ui(z, 0); for(i = 1; i < degree; i++) { mpz_lshift(b, b, 1); if (mpz_tstbit(b, degree)) mpz_xor(b, b, poly); if (mpz_tstbit(y, i)) mpz_xor(z, z, b); } mpz_clear(b); } void field_invert(mpz_t z, const mpz_t x) { mpz_t u, v, g, h; int i; assert(mpz_cmp_ui(x, 0)); mpz_init_set(u, x); mpz_init_set(v, poly); mpz_init_set_ui(g, 0); mpz_set_ui(z, 1); mpz_init(h); while (mpz_cmp_ui(u, 1)) { i = mpz_sizeinbits(u) - mpz_sizeinbits(v); if (i < 0) { mpz_swap(u, v); mpz_swap(z, g); i = -i; } mpz_lshift(h, v, i); mpz_xor(u, u, h); mpz_lshift(h, g, i); mpz_xor(z, z, h); } mpz_clear(u); mpz_clear(v); mpz_clear(g); mpz_clear(h); } /* routines for the random number generator */ void cprng_init(void) { if ((cprng = open(RANDOM_SOURCE, O_RDONLY)) < 0) fatal("couldn't open " RANDOM_SOURCE); } void cprng_deinit(void) { if (close(cprng) < 0) fatal("couldn't close " RANDOM_SOURCE); } void cprng_read(mpz_t x) { char buf[MAXDEGREE / 8]; unsigned int count; int i; for(count = 0; count < degree / 8; count += i) if ((i = read(cprng, buf + count, degree / 8 - count)) < 0) { close(cprng); fatal("couldn't read from " RANDOM_SOURCE); } mpz_import(x, degree / 8, 1, 1, 0, 0, buf); } /* a 64 bit pseudo random permutation (based on the XTEA cipher) */ void encipher_block(uint32_t *v) { uint32_t sum = 0, delta = 0x9E3779B9; int i; for(i = 0; i < 32; i++) { v[0] += (((v[1] << 4) ^ (v[1] >> 5)) + v[1]) ^ sum; sum += delta; v[1] += (((v[0] << 4) ^ (v[0] >> 5)) + v[0]) ^ sum; } } void decipher_block(uint32_t *v) { uint32_t sum = 0xC6EF3720, delta = 0x9E3779B9; int i; for(i = 0; i < 32; i++) { v[1] -= ((v[0] << 4 ^ v[0] >> 5) + v[0]) ^ sum; sum -= delta; v[0] -= ((v[1] << 4 ^ v[1] >> 5) + v[1]) ^ sum; } } void encode_slice(uint8_t *data, int idx, int len, void (*process_block)(uint32_t*)) { uint32_t v[2]; int i; for(i = 0; i < 2; i++) v[i] = data[(idx + 4 * i) % len] << 24 | data[(idx + 4 * i + 1) % len] << 16 | data[(idx + 4 * i + 2) % len] << 8 | data[(idx + 4 * i + 3) % len]; process_block(v); for(i = 0; i < 2; i++) { data[(idx + 4 * i + 0) % len] = v[i] >> 24; data[(idx + 4 * i + 1) % len] = (v[i] >> 16) & 0xff; data[(idx + 4 * i + 2) % len] = (v[i] >> 8) & 0xff; data[(idx + 4 * i + 3) % len] = v[i] & 0xff; } } enum encdec {ENCODE, DECODE}; void encode_mpz(mpz_t x, enum encdec encdecmode) { uint8_t v[(MAXDEGREE + 8) / 16 * 2]; size_t t; int i; memset(v, 0, (degree + 8) / 16 * 2); mpz_export(v, &t, -1, 2, 1, 0, x); if (degree % 16 == 8) v[degree / 8 - 1] = v[degree / 8]; if (encdecmode == ENCODE) /* 40 rounds are more than enough!*/ for(i = 0; i < 40 * ((int)degree / 8); i += 2) encode_slice(v, i, degree / 8, encipher_block); else for(i = 40 * (degree / 8) - 2; i >= 0; i -= 2) encode_slice(v, i, degree / 8, decipher_block); if (degree % 16 == 8) { v[degree / 8] = v[degree / 8 - 1]; v[degree / 8 - 1] = 0; } mpz_import(x, (degree + 8) / 16, -1, 2, 1, 0, v); assert(mpz_sizeinbits(x) <= degree); } /* evaluate polynomials efficiently */ void horner(int n, mpz_t y, const mpz_t x, const mpz_t coeff[]) { int i; mpz_set(y, x); for(i = n - 1; i; i--) { field_add(y, y, coeff[i]); field_mult(y, y, x); } field_add(y, y, coeff[0]); } /* calculate the secret from a set of shares solving a linear equation system */ #define MPZ_SWAP(A, B) \ do { mpz_set(h, A); mpz_set(A, B); mpz_set(B, h); } while(0) int restore_secret(int n, mpz_t (*A)[n], mpz_t b[]) { mpz_t (*AA)[n] = (mpz_t (*)[n])A; int i, j, k, found; mpz_t h; mpz_init(h); for(i = 0; i < n; i++) { if (! mpz_cmp_ui(AA[i][i], 0)) { for(found = 0, j = i + 1; j < n; j++) if (mpz_cmp_ui(AA[i][j], 0)) { found = 1; break; } if (! found) return -1; for(k = i; k < n; k++) MPZ_SWAP(AA[k][i], AA[k][j]); MPZ_SWAP(b[i], b[j]); } for(j = i + 1; j < n; j++) { if (mpz_cmp_ui(AA[i][j], 0)) { for(k = i + 1; k < n; k++) { field_mult(h, AA[k][i], AA[i][j]); field_mult(AA[k][j], AA[k][j], AA[i][i]); field_add(AA[k][j], AA[k][j], h); } field_mult(h, b[i], AA[i][j]); field_mult(b[j], b[j], AA[i][i]); field_add(b[j], b[j], h); } } } field_invert(h, AA[n - 1][n - 1]); field_mult(b[n - 1], b[n - 1], h); mpz_clear(h); return 0; } /* Prompt for a secret, generate shares for it */ void split(void) { unsigned int fmt_len; mpz_t x, y, coeff[opt_threshold]; char buf[MAXLINELEN]; int deg, i; for(fmt_len = 1, i = opt_number; i >= 10; i /= 10, fmt_len++); if (! opt_quiet) { printf("Generating shares using a (%d,%d) scheme with ", opt_threshold, opt_number); if (opt_security) printf("a %d bit", opt_security); else printf("dynamic"); printf(" security level.\n"); deg = opt_security ? opt_security : MAXDEGREE; fprintf(stderr, "Enter the secret, "); if (opt_hex) fprintf(stderr, "as most %d hex digits: ", deg / 4); else fprintf(stderr, "at most %d ASCII characters: ", deg / 8); } tcsetattr(0, TCSANOW, &echo_off); if (! fgets(buf, sizeof(buf), stdin)) fatal("I/O error while reading secret"); tcsetattr(0, TCSANOW, &echo_orig); buf[strcspn(buf, "\r\n")] = '\0'; if (! opt_security) { opt_security = opt_hex ? 4 * ((strlen(buf) + 1) & ~1): 8 * strlen(buf); if (! field_size_valid(opt_security)) fatal("security level invalid (secret too long?)"); if (! opt_quiet) fprintf(stderr, "Using a %d bit security level.\n", opt_security); } field_init(opt_security); mpz_init(coeff[0]); field_import(coeff[0], buf, opt_hex); if (opt_diffusion) { if (degree >= 64) encode_mpz(coeff[0], ENCODE); else warning("security level too small for the diffusion layer"); } cprng_init(); for(i = 1; i < opt_threshold; i++) { mpz_init(coeff[i]); cprng_read(coeff[i]); } cprng_deinit(); mpz_init(x); mpz_init(y); for(i = 0; i < opt_number; i++) { mpz_set_ui(x, i + 1); horner(opt_threshold, y, x, (const mpz_t*)coeff); if (opt_token) printf("%s-", opt_token); printf("%0*d-", fmt_len, i + 1); field_print(stdout, y, 1); } mpz_clear(x); mpz_clear(y); for(i = 0; i < opt_threshold; i++) mpz_clear(coeff[i]); field_deinit(); } /* Prompt for shares, calculate the secret */ void combine(void) { mpz_t A[opt_threshold][opt_threshold], y[opt_threshold], x; char buf[MAXLINELEN]; char *a, *b; int i, j; unsigned s = 0; mpz_init(x); if (! opt_quiet) printf("Enter %d shares separated by newlines:\n", opt_threshold); for (i = 0; i < opt_threshold; i++) { if (! opt_quiet) printf("Share [%d/%d]: ", i + 1, opt_threshold); if (! fgets(buf, sizeof(buf), stdin)) fatal("I/O error while reading shares"); buf[strcspn(buf, "\r\n")] = '\0'; if (! (a = strchr(buf, '-'))) fatal("invalid syntax"); *a++ = 0; if ((b = strchr(a, '-'))) *b++ = 0; else b = a, a = buf; if (! s) { s = 4 * strlen(b); if (! field_size_valid(s)) fatal("share has illegal length"); field_init(s); } else if (s != 4 * strlen(b)) fatal("shares have different security levels"); if (! (j = atoi(a))) fatal("invalid share"); mpz_set_ui(x, j); mpz_init_set_ui(A[opt_threshold - 1][i], 1); for(j = opt_threshold - 2; j >= 0; j--) { mpz_init(A[j][i]); field_mult(A[j][i], A[j + 1][i], x); } mpz_init(y[i]); field_import(y[i], b, 1); field_mult(x, x, A[0][i]); field_add(y[i], y[i], x); } mpz_clear(x); if (restore_secret(opt_threshold, A, y)) fatal("shares inconsistent. Perhaps a single share was used twice"); if (opt_diffusion) { if (degree >= 64) encode_mpz(y[opt_threshold - 1], DECODE); else warning("security level too small for the diffusion layer"); } if (! opt_quiet) fprintf(stderr, "Resulting secret: "); field_print(stderr, y[opt_threshold - 1], opt_hex); for (i = 0; i < opt_threshold; i++) { for (j = 0; j < opt_threshold; j++) mpz_clear(A[i][j]); mpz_clear(y[i]); } field_deinit(); } int main(int argc, char *argv[]) { char *name; int i; #if ! NOMLOCK if (mlockall(MCL_CURRENT | MCL_FUTURE) < 0) switch(errno) { case ENOMEM: warning("couldn't get memory lock (ENOMEM, try to adjust RLIMIT_MEMLOCK!)"); break; case EPERM: warning("couldn't get memory lock (EPERM, try UID 0!)"); break; case ENOSYS: warning("couldn't get memory lock (ENOSYS, kernel doesn't allow page locking)"); break; default: warning("couldn't get memory lock"); break; } #endif if (getuid() != geteuid()) seteuid(getuid()); tcgetattr(0, &echo_orig); echo_off = echo_orig; echo_off.c_lflag &= ~ECHO; opt_help = argc == 1; while((i = getopt(argc, argv, "vDhqQxs:t:n:w:")) != -1) switch(i) { case 'v': opt_showversion = 1; break; case 'h': opt_help = 1; break; case 'q': opt_quiet = 1; break; case 'Q': opt_QUIET = opt_quiet = 1; break; case 'x': opt_hex = 1; break; case 's': opt_security = atoi(optarg); break; case 't': opt_threshold = atoi(optarg); break; case 'n': opt_number = atoi(optarg); break; case 'w': opt_token = optarg; break; case 'D': opt_diffusion = 0; break; default: exit(1); } if (! opt_help && (argc != optind)) fatal("invalid argument"); if ((name = strrchr(argv[0], '/')) == NULL) name = argv[0]; if (strstr(name, "split")) { if (opt_help || opt_showversion) { puts("Split secrets using Shamir's Secret Sharing Scheme.\n" "\n" "ssss-split -t threshold -n shares [-w token] [-s level]" " [-x] [-q] [-Q] [-D] [-v]" ); if (opt_showversion) puts("\nVersion: " VERSION); exit(0); } if (opt_threshold < 2) fatal("invalid parameters: invalid threshold value"); if (opt_number < opt_threshold) fatal("invalid parameters: number of shares smaller than threshold"); if (opt_security && ! field_size_valid(opt_security)) fatal("invalid parameters: invalid security level"); if (opt_token && (strlen(opt_token) > MAXTOKENLEN)) fatal("invalid parameters: token too long"); split(); } else { if (opt_help || opt_showversion) { puts("Combine shares using Shamir's Secret Sharing Scheme.\n" "\n" "ssss-combine -t threshold [-x] [-q] [-Q] [-D] [-v]"); if (opt_showversion) puts("\nVersion: " VERSION); exit(0); } if (opt_threshold < 2) fatal("invalid parameters: invalid threshold value"); combine(); } return 0; } ssss-0.5/LICENSE0000444000175100001440000004313310362426611014175 0ustar bertramusers00000000000000 GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. 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If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. ssss-0.5/HISTORY0000644000175100001440000000072210362426611014253 0ustar bertramusers00000000000000v0.5: (January 2006) - introduction of memory locking and tty echo suppression - a buffer overflow was fixed. It seems to be exploitable. v0.4: (October 2005) - the security level now can be chosen freely in the range 8..1024 bits in steps of 8. v0.3: (July 2005) - separation of ssss into ssss-split and ssss-combine - introduction of a man page v0.2: (June 2005) - introduction of the diffusion layer v0.1: (May 2005) - initial release ssss-0.5/ssss.manpage.xml0000644000175100001440000001114410362426611016313 0ustar bertramusers00000000000000 ssss-split -t threshold -n shares [-w token] [-s level] [-x] [-q] [-Q] [-D] [-v] ssss-combine -t threshold [-x] [-q] [-Q] [-D] [-v]

ssss is an implementation of Shamir's Secret Sharing Scheme. The program suite does both: the generation of shares for a known secret, and the reconstruction of a secret using user-provided shares.

ssss-split: prompt the user for a secret and generate a set of corresponding shares.

ssss-combine: read in a set of shares and reconstruct the secret.

In case you want to protect your login password with a set of ten shares in such a way that any three of them can reconstruct the password, you simply run the command

ssss-split -t 3 -n 10 -w passwd

To reconstruct the password pass three of the generated shares (in any order) to

ssss-combine -t 3

To protect a secret larger than 1024 bits a hybrid technique has to be applied: encrypt the secret with a block cipher and apply secret sharing to just the key. Among others openssl and gpg can do the encryption part:

openssl bf -e < file.plain > file.encrypted

gpg -c < file.plain > file.encrypted

ssss tries to lock its virtual address space into RAM for privacy reasons. But this may fail for two reasons: either the current uid doesn't permit page locking, or the RLIMIT_MEMLOCK is set too low. After printing a warning message ssss will run even without obtaining the desired mlock.

This software (v0.5) was written in 2006 by B. Poettering (ssss AT point-at-infinity.org). Find the newest version of ssss on the project's homepage: .
ssss-0.5/doc.html0000644000175100001440000001672710362426611014636 0ustar bertramusers00000000000000 ssss: Shamir's Secret Sharing Scheme The following text is licensed under the GNU General Public License. Copyright 2005, 2006 by B. Poettering.

What is "Secret Sharing"?

Citing from the Wikipedia article about Secret Sharing:

In cryptography, a secret sharing scheme is a method for distributing a secret amongst a group of participants, each of which is allocated a share of the secret. The secret can only be reconstructed when the shares are combined together; individual shares are of no use on their own.

More formally, in a secret sharing scheme there is one dealer and n players. The dealer gives a secret to the players, but only when specific conditions are fulfilled. The dealer accomplishes this by giving each player a share in such a way that any group of t (for threshold) or more players can together reconstruct the secret but no group of less than t players can. Such a system is called a (t,n)-threshold scheme.

A popular technique to implement threshold schemes uses polynomial interpolation ("Lagrange interpolation"). This method was invented by Adi Shamir in 1979. You can play around with a threshold scheme on the demo page.

Note that Shamir's scheme is provable secure, that means: in a (t,n) scheme one can prove that it makes no difference whether an attacker has t-1 valid shares at his disposal or none at all; as long as he has less than t shares, there is no better option than guessing to find out the secret.

Where is "Secret Sharing" used?

Some popular examples are:
  • Good passwords are hard to memorize. A clever user could use a secret sharing scheme to generate a set of shares for a given password and store one share in his address book, one in his bank deposit safe, leave one share with a friend, etc. If one day he forgets his password, he can reconstruct it easily. Of course, writing passwords directly into the address book would pose a security risk, as it could be stolen by an "enemy". If a secret sharing scheme is used, the attacker has to steal many shares from different places.
  • "A dealer could send t shares, all of which are necessary to recover the original secret, to a single recipient, using t different channels. An attacker would have to intercept all t shares to recover the secret, a task which may be more difficult than intercepting a single message" (Wikipedia).
  • The director of a bank could generate shares for the bank's vault unlocking code and hand them out to his employees. Even if the director is not available, the vault can be opened, but only, when a certain number of employees do it together. Here secret sharing schemes allow the employment of not fully trusted people.

What is "ssss"? Where can I download "ssss"?

ssss is an implementation of Shamir's secret sharing scheme for UNIX systems, especially developed for linux machines. The code is licensed under the GNU GPL. ssss does both: the generation of shares for a known secret and the reconstruction of a secret using user provided shares. The software was written in 2006 by B. Poettering, it links against the GNU libgmp multiprecision library (version 4.1.4 works well) and requires the /dev/random entropy source. Please send bug reports to ssss AT point-at-infinity.org.

There is a freshmeat page for ssss. A debian package is also available. If you are the lucky owner of a debian system just run apt-get update && apt-get install ssss to install ssss. Someone even ported (an outdated version of) ssss to Windows (but with a lightly too sloppy random number generation, in my opinion).

Download on the ssss homepage.

How is "ssss" used? Is there an online demonstration?

The generation of shares given a known secret is shown first. A (3,5)-threshold scheme is used, that is: 5 shares are generated, the secret can be reconstructed by any subset of size 3. 

      % ssss-split -t 3 -n 5
      Generating shares using a (3,5) scheme with dynamic security level.
      Enter the secret, at most 128 ASCII characters: my secret root password
      Using a 184 bit security level.
      1-1c41ef496eccfbeba439714085df8437236298da8dd824
      2-fbc74a03a50e14ab406c225afb5f45c40ae11976d2b665
      3-fa1c3a9c6df8af0779c36de6c33f6e36e989d0e0b91309
      4-468de7d6eb36674c9cf008c8e8fc8c566537ad6301eb9e
      5-4756974923c0dce0a55f4774d09ca7a4865f64f56a4ee0
These shares can be combined to recreate the secret: 
      % ssss-combine -t 3
      Enter 3 shares separated by newlines:
      Share [1/3]: 3-fa1c3a9c6df8af0779c36de6c33f6e36e989d0e0b91309
      Share [2/3]: 5-4756974923c0dce0a55f4774d09ca7a4865f64f56a4ee0
      Share [3/3]: 2-fbc74a03a50e14ab406c225afb5f45c40ae11976d2b665
      Resulting secret: my secret root password
You can try it out on the demo page.

If larger secrets are to be shared a hybrid technique has to be applied: encrypt the secret with a block cipher (using openssl, gpg, etc) and apply secret sharing to just the key. See the man page for more information about this topic.

Where is the manpage?

Read it as html or *roff!

If you like this software, think about donating some money via .

Last modified: Sun Jan 15 12:08:48 CET 2006 ssss-0.5/THANKS0000644000175100001440000000035310362426611014102 0ustar bertramusers00000000000000I would like to thank the following people for comments and code: Tamás Tevesz (documentation) Stefan Schlesinger, Daniel Bielefeldt (error reporting) Olaf Mersmann (memory locking, echo suppression) Alex Popov (windows port)