ssss.c

/*
 *  ssss version 0.3  -  Copyright 2005 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
 */

/*
 * This is an implementation of Shamir's Secret Sharing Scheme. See 
 * http://en.wikipedia.org/wiki/Secret_sharing 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"
 *
 * Report bugs to: ssss AT point-at-infinity.org
 */

#include <stdlib.h>
#include <string.h>
#include <fcntl.h>
#include <unistd.h>
#include <stdio.h>
#include <stdint.h>
#include <assert.h>

#include <gmp.h>

#include <randomkit.h>

#define RANDOM_SOURCE "/dev/random"
#define MAXDEGREE 1024
#define MAXTOKENLEN 128
#define MAXLINELEN (MAXTOKENLEN + 1 + 10 + 1 + MAXDEGREE / 4 + 10)

int opt_help = 0;
int opt_quiet = 0;
int opt_QUIET = 0;
int opt_hex = 0;
int opt_diffusion = 1;
int opt_security = 128;
int opt_threshold = -1;
int opt_number = -1;
char *opt_token = NULL;

int ttyoutput;

unsigned int degree;
mpz_t poly;
int cprng;

/*randomkit stuff*/
unsigned long l;
int i;
rk_state state;
rk_error err;

char *revision = "$Id$";

#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)

void fatal(char *msg)
{
  fprintf(stderr, "%sFATAL: %s.\n", ttyoutput ? "\a" : "", msg);
  exit(1);
}

void warning(char *msg)
{
  if (! opt_QUIET)
    fprintf(stderr, "%sWARNING: %s.\n", ttyoutput ? "\a" : "", msg);
}

int field_size_valid(int deg)
{
  return (deg == 80) || (deg == 112) || (deg == 128) || (deg == 192) 
    || (deg == 256) || (deg == 512) || (deg == 1024);
  assert(deg <= MAXDEGREE);
}

/* initialize 'poly' to a bitfield representing the coefficients of an
   irreducible polynomial of degree 'deg' */

void field_init(int deg)
{
  mpz_init_set_ui(poly, 0);
  switch (deg) {
  case 80: 
    mpz_setbit(poly, 9);
    mpz_setbit(poly, 4);
    mpz_setbit(poly, 2);
    break;
  case 112:
    mpz_setbit(poly, 5);
    mpz_setbit(poly, 4);
    mpz_setbit(poly, 3);
    break;
  case 128:
  case 192:
    mpz_setbit(poly, 7);
    mpz_setbit(poly, 2);
    mpz_setbit(poly, 1);
    break;
  case 256:
    mpz_setbit(poly, 10);
    mpz_setbit(poly, 5);
    mpz_setbit(poly, 2);
    break;
  case 512:
    mpz_setbit(poly, 8);
    mpz_setbit(poly, 5);
    mpz_setbit(poly, 2);
    break;
  case 1024:
    mpz_setbit(poly, 19);
    mpz_setbit(poly, 6);
    mpz_setbit(poly, 1);
    break;
  default:
    assert(0);
  }
  mpz_setbit(poly, deg);
  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)
{
 fprintf(stderr, "Checking random device: ");
	err = rk_randomseed(&state);
	if (err == 0)
		fprintf(stderr, "found.\n");
	else
		fprintf(stderr, "not found.\n"); 
}

void cprng_deinit(void)
{
	// Randomkit doesn't require deinit or close ;-)
}

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);
//    }
	rk_fill(buf, degree / 8, &state);
  	//printf("RNG: %s\n",buf);
	  
  mpz_import(x, degree / 8, 1, 1, 0, 0, buf);
}

/* a 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 encipher_array(uint16_t *data, int len)
{
  int i;
  uint32_t v[2];
  for(i = 0; i < 40 * len; i++) { /* 40 seems more than enough! */
    v[0] = data[(i + 0) % len] << 16 | data[(i + 1) % len];
    v[1] = data[(i + 2) % len] << 16 | data[(i + 3) % len];
    encipher_block(v);
    data[(i + 0) % len] = v[0] >> 16;
    data[(i + 1) % len] = v[0] & 0xffff;
    data[(i + 2) % len] = v[1] >> 16;
    data[(i + 3) % len] = v[1] & 0xffff;
  }
}

void decipher_array(uint16_t *data, int len)
{
  int i;
  uint32_t v[2];
  for(i = 40 * len - 1; i >= 0; i--) {
    v[0] = data[(i + 0) % len] << 16 | data[(i + 1) % len];
    v[1] = data[(i + 2) % len] << 16 | data[(i + 3) % len];
    decipher_block(v);
    data[(i + 0) % len] = v[0] >> 16;
    data[(i + 1) % len] = v[0] & 0xffff;
    data[(i + 2) % len] = v[1] >> 16;
    data[(i + 3) % len] = v[1] & 0xffff;
  }
}

void encipher_mpz(mpz_t x)
{
  uint16_t v[MAXDEGREE / 16 + 1];
  size_t t;
  mpz_setbit(x, degree);
  mpz_export(v, &t, -1, 2, 0, 0, x);
  assert(t == degree / 16 + 1);
  encipher_array(v, degree / 16);
  mpz_import(x, degree / 16, -1, 2, 0, 0, v);
  mpz_clrbit(x, degree);
}

void decipher_mpz(mpz_t x)
{
  uint16_t v[MAXDEGREE / 16 + 1];
  size_t t;
  mpz_setbit(x, degree);
  mpz_export(v, &t, -1, 2, 0, 0, x);
  assert(t == degree / 16 + 1);
  decipher_array(v, degree / 16);
  mpz_import(x, degree / 16, -1, 2, 0, 0, v);
  mpz_clrbit(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[][], 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 i;
  for(fmt_len = 1, i = opt_number; i >= 10; i /= 10, fmt_len++);
  field_init(opt_security);

  if (! opt_quiet)
    printf("Generating shares using a (%d,%d) scheme with a %d bit "
	   "security level.\n", opt_threshold, opt_number, opt_security);

  if (! opt_quiet) {
    fprintf(stderr, "Enter the secret, ");
    if (opt_hex)
      fprintf(stderr, "%d hex digits: ", degree / 4);
    else 
      fprintf(stderr, "at most %d ASCII characters: ", degree / 8);
  }
  if (! fgets(buf, sizeof(buf), stdin))
    fatal("I/O error while reading secret");
  buf[strcspn(buf, "\r\n")] = '\0';
  mpz_init(coeff[0]);
  field_import(coeff[0], buf, opt_hex);
  if (opt_diffusion)
    encipher_mpz(coeff[0]);
  
  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)
    decipher_mpz(y[opt_threshold - 1]);

  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[])
{

  printf("Shamir Secret Sharing Scheme - %s\n", revision);
  printf("Copyright 2005 B. Poettering, Win32 port by Alex.Popov@leggettwood.com\n\n");

  
  char *name;
  int i;
  if ((i = fileno(stderr)) < 0)
    fatal("couldn't determine fileno of stderr");
  ttyoutput = isatty(i);

  opt_help = argc == 1;
  while((i = getopt(argc, argv, "DhqQxs:t:n:w:")) != -1)
    switch(i) {
    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) {
      puts("Split secrets using Shamir's Secret Sharing Scheme.\n"
	   "\n"
	   "ssss-split -t threshold -n shares [-s level] [-w token] [-x] [-q] [-Q]");
      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 (! 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) {
      puts("Combine shares using Shamir's Secret Sharing Scheme.\n"
	   "\n"
	   "ssss-combine -t threshold [-x] [-q] [-Q] [-D]");
      exit(0);
    }

    if (opt_threshold < 2)
      fatal("invalid parameters: invalid threshold value");

    combine();
  }

  return 0;
}