Diffstat (limited to 'pwmanager/libcrypt/cipher/primegen.c') (more/less context) (ignore whitespace changes)
| -rw-r--r-- | pwmanager/libcrypt/cipher/primegen.c | 1028 |
1 files changed, 1028 insertions, 0 deletions
diff --git a/pwmanager/libcrypt/cipher/primegen.c b/pwmanager/libcrypt/cipher/primegen.c new file mode 100644 index 0000000..afd435e --- a/dev/null +++ b/pwmanager/libcrypt/cipher/primegen.c @@ -0,0 +1,1028 @@ +/* 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 <config.h> + +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <assert.h> +#include <errno.h> + +#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); + } +} |