/* primegen.c - prime number generator * Copyright (C) 1998, 2000, 2001, 2002, 2003 * 2004 Free Software Foundation, Inc. * * This file is part of Libgcrypt. * * Libgcrypt is free software; you can redistribute it and/or modify * it under the terms of the GNU Lesser general Public License as * published by the Free Software Foundation; either version 2.1 of * the License, or (at your option) any later version. * * Libgcrypt 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 Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser 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 * * *********************************************************************** * The algorithm used to generate practically save primes is due to * Lim and Lee as described in the CRYPTO '97 proceedings (ISBN3540633847) * page 260. */ #include #include #include #include #include #include #include "g10lib.h" #include "mpi.h" #include "cipher.h" static gcry_mpi_t gen_prime (unsigned int nbits, int secret, int randomlevel, int (*extra_check)(void *, gcry_mpi_t), void *extra_check_arg); static int check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, gcry_prime_check_func_t cb_func, void *cb_arg ); static int is_prime( gcry_mpi_t n, int steps, int *count ); static void m_out_of_n( char *array, int m, int n ); static void (*progress_cb) (void *,const char*,int,int, int ); static void *progress_cb_data; /* Note: 2 is not included because it can be tested more easily by looking at bit 0. The last entry in this list is marked by a zero */ static ushort small_prime_numbers[] = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 0 }; static int no_of_small_prime_numbers = DIM (small_prime_numbers) - 1; void _gcry_register_primegen_progress ( void (*cb)(void *,const char*,int,int,int), void *cb_data ) { progress_cb = cb; progress_cb_data = cb_data; } static void progress( int c ) { if ( progress_cb ) progress_cb ( progress_cb_data, "primegen", c, 0, 0 ); } /**************** * Generate a prime number (stored in secure memory) */ gcry_mpi_t _gcry_generate_secret_prime (unsigned int nbits, int (*extra_check)(void*, gcry_mpi_t), void *extra_check_arg) { gcry_mpi_t prime; prime = gen_prime( nbits, 1, 2, extra_check, extra_check_arg); progress('\n'); return prime; } gcry_mpi_t _gcry_generate_public_prime( unsigned int nbits, int (*extra_check)(void*, gcry_mpi_t), void *extra_check_arg) { gcry_mpi_t prime; prime = gen_prime( nbits, 0, 2, extra_check, extra_check_arg ); progress('\n'); return prime; } /**************** * We do not need to use the strongest RNG because we gain no extra * security from it - The prime number is public and we could also * offer the factors for those who are willing to check that it is * indeed a strong prime. With ALL_FACTORS set to true all afcors of * prime-1 are returned in FACTORS. * * mode 0: Standard * 1: Make sure that at least one factor is of size qbits. */ static gcry_err_code_t prime_generate_internal (int mode, gcry_mpi_t *prime_generated, unsigned int pbits, unsigned int qbits, gcry_mpi_t g, gcry_mpi_t **ret_factors, gcry_random_level_t randomlevel, unsigned int flags, int all_factors, gcry_prime_check_func_t cb_func, void *cb_arg) { gcry_err_code_t err = 0; gcry_mpi_t *factors_new = NULL; /* Factors to return to the caller. */ gcry_mpi_t *factors = NULL; /* Current factors. */ gcry_mpi_t *pool = NULL; /* Pool of primes. */ unsigned char *perms = NULL; /* Permutations of POOL. */ gcry_mpi_t q_factor = NULL; /* Used if QBITS is non-zero. */ unsigned int fbits = 0; /* Length of prime factors. */ unsigned int n = 0; /* Number of factors. */ unsigned int m = 0; /* Number of primes in pool. */ gcry_mpi_t q = NULL; /* First prime factor. */ gcry_mpi_t prime = NULL; /* Prime candidate. */ unsigned int nprime = 0; /* Bits of PRIME. */ unsigned int req_qbits; /* The original QBITS value. */ gcry_mpi_t val_2; /* For check_prime(). */ unsigned int is_secret = (flags & GCRY_PRIME_FLAG_SECRET); unsigned int count1 = 0, count2 = 0; unsigned int i = 0, j = 0; if (pbits < 48) return GPG_ERR_INV_ARG; /* If QBITS is not given, assume a reasonable value. */ if (!qbits) qbits = pbits / 3; req_qbits = qbits; /* Find number of needed prime factors. */ for (n = 1; (pbits - qbits - 1) / n >= qbits; n++) ; n--; val_2 = mpi_alloc_set_ui (2); if ((! n) || ((mode == 1) && (n < 2))) { err = GPG_ERR_INV_ARG; goto leave; } if (mode == 1) { n--; fbits = (pbits - 2 * req_qbits -1) / n; qbits = pbits - req_qbits - n * fbits; } else { fbits = (pbits - req_qbits -1) / n; qbits = pbits - n * fbits; } if (DBG_CIPHER) log_debug ("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n", pbits, req_qbits, qbits, fbits, n); prime = gcry_mpi_new (pbits); /* Generate first prime factor. */ q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL); if (mode == 1) q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL); /* Allocate an array to hold the factors + 2 for later usage. */ factors = gcry_calloc (n + 2, sizeof (*factors)); if (!factors) { err = gpg_err_code_from_errno (errno); goto leave; } /* Make a pool of 3n+5 primes (this is an arbitrary value). */ m = n * 3 + 5; if (mode == 1) /* Need some more (for e.g. DSA). */ m += 5; if (m < 25) m = 25; pool = gcry_calloc (m , sizeof (*pool)); if (! pool) { err = gpg_err_code_from_errno (errno); goto leave; } /* Permutate over the pool of primes. */ do { next_try: if (! perms) { /* Allocate new primes. */ for(i = 0; i < m; i++) { mpi_free (pool[i]); pool[i] = NULL; } /* Init m_out_of_n(). */ perms = gcry_calloc (1, m); if (! perms) { err = gpg_err_code_from_errno (errno); goto leave; } for(i = 0; i < n; i++) { perms[i] = 1; pool[i] = gen_prime (fbits, is_secret, randomlevel, NULL, NULL); factors[i] = pool[i]; } } else { m_out_of_n (perms, n, m); for (i = j = 0; (i < m) && (j < n); i++) if (perms[i]) { if(! pool[i]) pool[i] = gen_prime (fbits, 0, 1, NULL, NULL); factors[j++] = pool[i]; } if (i == n) { gcry_free (perms); perms = NULL; progress ('!'); goto next_try; /* Allocate new primes. */ } } /* Generate next prime candidate: p = 2 * q [ * q_factor] * factor_0 * factor_1 * ... * factor_n + 1. */ mpi_set (prime, q); mpi_mul_ui (prime, prime, 2); if (mode == 1) mpi_mul (prime, prime, q_factor); for(i = 0; i < n; i++) mpi_mul (prime, prime, factors[i]); mpi_add_ui (prime, prime, 1); nprime = mpi_get_nbits (prime); if (nprime < pbits) { if (++count1 > 20) { count1 = 0; qbits++; progress('>'); mpi_free (q); q = gen_prime (qbits, 0, 0, NULL, NULL); goto next_try; } } else count1 = 0; if (nprime > pbits) { if (++count2 > 20) { count2 = 0; qbits--; progress('<'); mpi_free (q); q = gen_prime (qbits, 0, 0, NULL, NULL); goto next_try; } } else count2 = 0; } while (! ((nprime == pbits) && check_prime (prime, val_2, cb_func, cb_arg))); if (DBG_CIPHER) { progress ('\n'); log_mpidump ("prime : ", prime); log_mpidump ("factor q: ", q); if (mode == 1) log_mpidump ("factor q0: ", q_factor); for (i = 0; i < n; i++) log_mpidump ("factor pi: ", factors[i]); log_debug ("bit sizes: prime=%u, q=%u", mpi_get_nbits (prime), mpi_get_nbits (q)); if (mode == 1) log_debug (", q0=%u", mpi_get_nbits (q_factor)); for (i = 0; i < n; i++) log_debug (", p%d=%u", i, mpi_get_nbits (factors[i])); progress('\n'); } if (ret_factors) { /* Caller wants the factors. */ factors_new = gcry_calloc (n + 4, sizeof (*factors_new)); if (! factors_new) { err = gpg_err_code_from_errno (errno); goto leave; } if (all_factors) { i = 0; factors_new[i++] = gcry_mpi_set_ui (NULL, 2); factors_new[i++] = mpi_copy (q); if (mode == 1) factors_new[i++] = mpi_copy (q_factor); for(j=0; j < n; j++) factors_new[i++] = mpi_copy (factors[j]); } else { i = 0; if (mode == 1) { factors_new[i++] = mpi_copy (q_factor); for (; i <= n; i++) factors_new[i] = mpi_copy (factors[i]); } else for (; i < n; i++ ) factors_new[i] = mpi_copy (factors[i]); } } if (g) { /* Create a generator (start with 3). */ gcry_mpi_t tmp = mpi_alloc (mpi_get_nlimbs (prime)); gcry_mpi_t b = mpi_alloc (mpi_get_nlimbs (prime)); gcry_mpi_t pmin1 = mpi_alloc (mpi_get_nlimbs (prime)); if (mode == 1) err = GPG_ERR_NOT_IMPLEMENTED; else { factors[n] = q; factors[n + 1] = mpi_alloc_set_ui (2); mpi_sub_ui (pmin1, prime, 1); mpi_set_ui (g, 2); do { mpi_add_ui (g, g, 1); if (DBG_CIPHER) { log_debug ("checking g:"); gcry_mpi_dump (g); log_printf ("\n"); } else progress('^'); for (i = 0; i < n + 2; i++) { mpi_fdiv_q (tmp, pmin1, factors[i]); /* No mpi_pow(), but it is okay to use this with mod prime. */ gcry_mpi_powm (b, g, tmp, prime); if (! mpi_cmp_ui (b, 1)) break; } if (DBG_CIPHER) progress('\n'); } while (i < n + 2); mpi_free (factors[n+1]); mpi_free (tmp); mpi_free (b); mpi_free (pmin1); } } if (! DBG_CIPHER) progress ('\n'); leave: if (pool) { for(i = 0; i < m; i++) mpi_free (pool[i]); gcry_free (pool); } if (factors) gcry_free (factors); /* Factors are shallow copies. */ if (perms) gcry_free (perms); mpi_free (val_2); mpi_free (q); mpi_free (q_factor); if (! err) { *prime_generated = prime; if (ret_factors) *ret_factors = factors_new; } else { if (factors_new) { for (i = 0; factors_new[i]; i++) mpi_free (factors_new[i]); gcry_free (factors_new); } mpi_free (prime); } return err; } gcry_mpi_t _gcry_generate_elg_prime (int mode, unsigned pbits, unsigned qbits, gcry_mpi_t g, gcry_mpi_t **ret_factors) { gcry_err_code_t err = GPG_ERR_NO_ERROR; gcry_mpi_t prime = NULL; err = prime_generate_internal (mode, &prime, pbits, qbits, g, ret_factors, GCRY_WEAK_RANDOM, 0, 0, NULL, NULL); return prime; } static gcry_mpi_t gen_prime (unsigned int nbits, int secret, int randomlevel, int (*extra_check)(void *, gcry_mpi_t), void *extra_check_arg) { gcry_mpi_t prime, ptest, pminus1, val_2, val_3, result; int i; unsigned x, step; unsigned count1, count2; int *mods; /* if ( DBG_CIPHER ) */ /* log_debug ("generate a prime of %u bits ", nbits ); */ if (nbits < 16) log_fatal ("can't generate a prime with less than %d bits\n", 16); mods = gcry_xmalloc( no_of_small_prime_numbers * sizeof *mods ); /* Make nbits fit into gcry_mpi_t implementation. */ val_2 = mpi_alloc_set_ui( 2 ); val_3 = mpi_alloc_set_ui( 3); prime = secret? gcry_mpi_snew ( nbits ): gcry_mpi_new ( nbits ); result = mpi_alloc_like( prime ); pminus1= mpi_alloc_like( prime ); ptest = mpi_alloc_like( prime ); count1 = count2 = 0; for (;;) { /* try forvever */ int dotcount=0; /* generate a random number */ gcry_mpi_randomize( prime, nbits, randomlevel ); /* Set high order bit to 1, set low order bit to 1. If we are generating a secret prime we are most probably doing that for RSA, to make sure that the modulus does have the requested key size we set the 2 high order bits. */ mpi_set_highbit (prime, nbits-1); if (secret) mpi_set_bit (prime, nbits-2); mpi_set_bit(prime, 0); /* Calculate all remainders. */ for (i=0; (x = small_prime_numbers[i]); i++ ) mods[i] = mpi_fdiv_r_ui(NULL, prime, x); /* Now try some primes starting with prime. */ for(step=0; step < 20000; step += 2 ) { /* Check against all the small primes we have in mods. */ count1++; for (i=0; (x = small_prime_numbers[i]); i++ ) { while ( mods[i] + step >= x ) mods[i] -= x; if ( !(mods[i] + step) ) break; } if ( x ) continue; /* Found a multiple of an already known prime. */ mpi_add_ui( ptest, prime, step ); /* Do a fast Fermat test now. */ count2++; mpi_sub_ui( pminus1, ptest, 1); gcry_mpi_powm( result, val_2, pminus1, ptest ); if ( !mpi_cmp_ui( result, 1 ) ) { /* Not composite, perform stronger tests */ if (is_prime(ptest, 5, &count2 )) { if (!mpi_test_bit( ptest, nbits-1-secret )) { progress('\n'); log_debug ("overflow in prime generation\n"); break; /* Stop loop, continue with a new prime. */ } if (extra_check && extra_check (extra_check_arg, ptest)) { /* The extra check told us that this prime is not of the caller's taste. */ progress ('/'); } else { /* Got it. */ mpi_free(val_2); mpi_free(val_3); mpi_free(result); mpi_free(pminus1); mpi_free(prime); gcry_free(mods); return ptest; } } } if (++dotcount == 10 ) { progress('.'); dotcount = 0; } } progress(':'); /* restart with a new random value */ } } /**************** * Returns: true if this may be a prime */ static int check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, gcry_prime_check_func_t cb_func, void *cb_arg) { int i; unsigned int x; int count=0; /* Check against small primes. */ for (i=0; (x = small_prime_numbers[i]); i++ ) { if ( mpi_divisible_ui( prime, x ) ) return 0; } /* A quick Fermat test. */ { gcry_mpi_t result = mpi_alloc_like( prime ); gcry_mpi_t pminus1 = mpi_alloc_like( prime ); mpi_sub_ui( pminus1, prime, 1); gcry_mpi_powm( result, val_2, pminus1, prime ); mpi_free( pminus1 ); if ( mpi_cmp_ui( result, 1 ) ) { /* Is composite. */ mpi_free( result ); progress('.'); return 0; } mpi_free( result ); } if (!cb_func || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_MAYBE_PRIME, prime)) { /* Perform stronger tests. */ if ( is_prime( prime, 5, &count ) ) { if (!cb_func || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_GOT_PRIME, prime)) return 1; /* Probably a prime. */ } } progress('.'); return 0; } /* * Return true if n is probably a prime */ static int is_prime (gcry_mpi_t n, int steps, int *count) { gcry_mpi_t x = mpi_alloc( mpi_get_nlimbs( n ) ); gcry_mpi_t y = mpi_alloc( mpi_get_nlimbs( n ) ); gcry_mpi_t z = mpi_alloc( mpi_get_nlimbs( n ) ); gcry_mpi_t nminus1 = mpi_alloc( mpi_get_nlimbs( n ) ); gcry_mpi_t a2 = mpi_alloc_set_ui( 2 ); gcry_mpi_t q; unsigned i, j, k; int rc = 0; unsigned nbits = mpi_get_nbits( n ); mpi_sub_ui( nminus1, n, 1 ); /* Find q and k, so that n = 1 + 2^k * q . */ q = mpi_copy ( nminus1 ); k = mpi_trailing_zeros ( q ); mpi_tdiv_q_2exp (q, q, k); for (i=0 ; i < steps; i++ ) { ++*count; if( !i ) { mpi_set_ui( x, 2 ); } else { gcry_mpi_randomize( x, nbits, GCRY_WEAK_RANDOM ); /* Make sure that the number is smaller than the prime and keep the randomness of the high bit. */ if ( mpi_test_bit ( x, nbits-2) ) { mpi_set_highbit ( x, nbits-2); /* Clear all higher bits. */ } else { mpi_set_highbit( x, nbits-2 ); mpi_clear_bit( x, nbits-2 ); } assert ( mpi_cmp( x, nminus1 ) < 0 && mpi_cmp_ui( x, 1 ) > 0 ); } gcry_mpi_powm ( y, x, q, n); if ( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) ) { for ( j=1; j < k && mpi_cmp( y, nminus1 ); j++ ) { gcry_mpi_powm(y, y, a2, n); if( !mpi_cmp_ui( y, 1 ) ) goto leave; /* Not a prime. */ } if (mpi_cmp( y, nminus1 ) ) goto leave; /* Not a prime. */ } progress('+'); } rc = 1; /* May be a prime. */ leave: mpi_free( x ); mpi_free( y ); mpi_free( z ); mpi_free( nminus1 ); mpi_free( q ); mpi_free( a2 ); return rc; } static void m_out_of_n ( char *array, int m, int n ) { int i=0, i1=0, j=0, jp=0, j1=0, k1=0, k2=0; if( !m || m >= n ) return; if( m == 1 ) { /* Special case. */ for (i=0; i < n; i++ ) { if( array[i] ) { array[i++] = 0; if( i >= n ) i = 0; array[i] = 1; return; } } BUG(); } for (j=1; j < n; j++ ) { if ( array[n-1] == array[n-j-1]) continue; j1 = j; break; } if ( (m & 1) ) { /* M is odd. */ if( array[n-1] ) { if( j1 & 1 ) { k1 = n - j1; k2 = k1+2; if( k2 > n ) k2 = n; goto leave; } goto scan; } k2 = n - j1 - 1; if( k2 == 0 ) { k1 = i; k2 = n - j1; } else if( array[k2] && array[k2-1] ) k1 = n; else k1 = k2 + 1; } else { /* M is even. */ if( !array[n-1] ) { k1 = n - j1; k2 = k1 + 1; goto leave; } if( !(j1 & 1) ) { k1 = n - j1; k2 = k1+2; if( k2 > n ) k2 = n; goto leave; } scan: jp = n - j1 - 1; for (i=1; i <= jp; i++ ) { i1 = jp + 2 - i; if( array[i1-1] ) { if( array[i1-2] ) { k1 = i1 - 1; k2 = n - j1; } else { k1 = i1 - 1; k2 = n + 1 - j1; } goto leave; } } k1 = 1; k2 = n + 1 - m; } leave: array[k1-1] = !array[k1-1]; array[k2-1] = !array[k2-1]; } /* Generate a new prime number of PRIME_BITS bits and store it in PRIME. If FACTOR_BITS is non-zero, one of the prime factors of (prime - 1) / 2 must be FACTOR_BITS bits long. If FACTORS is non-zero, allocate a new, NULL-terminated array holding the prime factors and store it in FACTORS. FLAGS might be used to influence the prime number generation process. */ gcry_error_t gcry_prime_generate (gcry_mpi_t *prime, unsigned int prime_bits, unsigned int factor_bits, gcry_mpi_t **factors, gcry_prime_check_func_t cb_func, void *cb_arg, gcry_random_level_t random_level, unsigned int flags) { gcry_err_code_t err = GPG_ERR_NO_ERROR; gcry_mpi_t *factors_generated = NULL; gcry_mpi_t prime_generated = NULL; unsigned int mode = 0; if (!prime) return gpg_error (GPG_ERR_INV_ARG); *prime = NULL; if (flags & GCRY_PRIME_FLAG_SPECIAL_FACTOR) mode = 1; /* Generate. */ err = prime_generate_internal (mode, &prime_generated, prime_bits, factor_bits, NULL, factors? &factors_generated : NULL, random_level, flags, 1, cb_func, cb_arg); if (! err) if (cb_func) { /* Additional check. */ if ( !cb_func (cb_arg, GCRY_PRIME_CHECK_AT_FINISH, prime_generated)) { /* Failed, deallocate resources. */ unsigned int i; mpi_free (prime_generated); if (factors) { for (i = 0; factors_generated[i]; i++) mpi_free (factors_generated[i]); gcry_free (factors_generated); } err = GPG_ERR_GENERAL; } } if (! err) { if (factors) *factors = factors_generated; *prime = prime_generated; } return gcry_error (err); } /* Check wether the number X is prime. */ gcry_error_t gcry_prime_check (gcry_mpi_t x, unsigned int flags) { gcry_err_code_t err = GPG_ERR_NO_ERROR; gcry_mpi_t val_2 = mpi_alloc_set_ui (2); /* Used by the Fermat test. */ if (! check_prime (x, val_2, NULL, NULL)) err = GPG_ERR_NO_PRIME; mpi_free (val_2); return gcry_error (err); } /* Find a generator for PRIME where the factorization of (prime-1) is in the NULL terminated array FACTORS. Return the generator as a newly allocated MPI in R_G. If START_G is not NULL, use this as s atart for the search. Returns 0 on success.*/ gcry_error_t gcry_prime_group_generator (gcry_mpi_t *r_g, gcry_mpi_t prime, gcry_mpi_t *factors, gcry_mpi_t start_g) { gcry_mpi_t tmp = gcry_mpi_new (0); gcry_mpi_t b = gcry_mpi_new (0); gcry_mpi_t pmin1 = gcry_mpi_new (0); gcry_mpi_t g = start_g? gcry_mpi_copy (start_g) : gcry_mpi_set_ui (NULL, 3); int first = 1; int i, n; if (!factors || !r_g || !prime) return gpg_error (GPG_ERR_INV_ARG); *r_g = NULL; for (n=0; factors[n]; n++) ; if (n < 2) return gpg_error (GPG_ERR_INV_ARG); /* Extra sanity check - usually disabled. */ /* mpi_set (tmp, factors[0]); */ /* for(i = 1; i < n; i++) */ /* mpi_mul (tmp, tmp, factors[i]); */ /* mpi_add_ui (tmp, tmp, 1); */ /* if (mpi_cmp (prime, tmp)) */ /* return gpg_error (GPG_ERR_INV_ARG); */ gcry_mpi_sub_ui (pmin1, prime, 1); do { if (first) first = 0; else gcry_mpi_add_ui (g, g, 1); if (DBG_CIPHER) { log_debug ("checking g:"); gcry_mpi_dump (g); log_debug ("\n"); } else progress('^'); for (i = 0; i < n; i++) { mpi_fdiv_q (tmp, pmin1, factors[i]); gcry_mpi_powm (b, g, tmp, prime); if (! mpi_cmp_ui (b, 1)) break; } if (DBG_CIPHER) progress('\n'); } while (i < n); gcry_mpi_release (tmp); gcry_mpi_release (b); gcry_mpi_release (pmin1); *r_g = g; return 0; } /* Convenience function to release the factors array. */ void gcry_prime_release_factors (gcry_mpi_t *factors) { if (factors) { int i; for (i=0; factors[i]; i++) mpi_free (factors[i]); gcry_free (factors); } }