diff options
Diffstat (limited to 'libgcrypt-1.4.6/cipher/primegen.c')
| -rw-r--r-- | libgcrypt-1.4.6/cipher/primegen.c | 3724 |
1 files changed, 1862 insertions, 1862 deletions
diff --git a/libgcrypt-1.4.6/cipher/primegen.c b/libgcrypt-1.4.6/cipher/primegen.c index b869bee..50dc560 100644 --- a/libgcrypt-1.4.6/cipher/primegen.c +++ b/libgcrypt-1.4.6/cipher/primegen.c @@ -1,1862 +1,1862 @@ -/* primegen.c - prime number generator - * Copyright (C) 1998, 2000, 2001, 2002, 2003 - * 2004, 2008 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 - */ - -#include <config.h> - -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <errno.h> - -#include "g10lib.h" -#include "mpi.h" -#include "cipher.h" -#include "ath.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, int rm_rounds, - gcry_prime_check_func_t cb_func, void *cb_arg ); -static int is_prime (gcry_mpi_t n, int steps, unsigned 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; - - - -/* An object and a list to build up a global pool of primes. See - save_pool_prime and get_pool_prime. */ -struct primepool_s -{ - struct primepool_s *next; - gcry_mpi_t prime; /* If this is NULL the entry is not used. */ - unsigned int nbits; - gcry_random_level_t randomlevel; -}; -struct primepool_s *primepool; -/* Mutex used to protect access to the primepool. */ -static ath_mutex_t primepool_lock = ATH_MUTEX_INITIALIZER; - - - -/* Save PRIME which has been generated at RANDOMLEVEL for later - use. Needs to be called while primepool_lock is being hold. Note - that PRIME should be considered released after calling this - function. */ -static void -save_pool_prime (gcry_mpi_t prime, gcry_random_level_t randomlevel) -{ - struct primepool_s *item, *item2; - size_t n; - - for (n=0, item = primepool; item; item = item->next, n++) - if (!item->prime) - break; - if (!item && n > 100) - { - /* Remove some of the entries. Our strategy is removing - the last third from the list. */ - int i; - - for (i=0, item2 = primepool; item2; item2 = item2->next) - { - if (i >= n/3*2) - { - gcry_mpi_release (item2->prime); - item2->prime = NULL; - if (!item) - item = item2; - } - } - } - if (!item) - { - item = gcry_calloc (1, sizeof *item); - if (!item) - { - /* Out of memory. Silently giving up. */ - gcry_mpi_release (prime); - return; - } - item->next = primepool; - primepool = item; - } - item->prime = prime; - item->nbits = mpi_get_nbits (prime); - item->randomlevel = randomlevel; -} - - -/* Return a prime for the prime pool or NULL if none has been found. - The prime needs to match NBITS and randomlevel. This function needs - to be called why the primepool_look is being hold. */ -static gcry_mpi_t -get_pool_prime (unsigned int nbits, gcry_random_level_t randomlevel) -{ - struct primepool_s *item; - - for (item = primepool; item; item = item->next) - if (item->prime - && item->nbits == nbits && item->randomlevel == randomlevel) - { - gcry_mpi_t prime = item->prime; - item->prime = NULL; - gcry_assert (nbits == mpi_get_nbits (prime)); - return prime; - } - return NULL; -} - - - - - - -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, - gcry_random_level_t random_level, - int (*extra_check)(void*, gcry_mpi_t), - void *extra_check_arg) -{ - gcry_mpi_t prime; - - prime = gen_prime (nbits, 1, random_level, extra_check, extra_check_arg); - progress('\n'); - return prime; -} - - -/* Generate a prime number which may be public, i.e. not allocated in - secure memory. */ -gcry_mpi_t -_gcry_generate_public_prime (unsigned int nbits, - gcry_random_level_t random_level, - int (*extra_check)(void*, gcry_mpi_t), - void *extra_check_arg) -{ - gcry_mpi_t prime; - - prime = gen_prime (nbits, 0, random_level, extra_check, extra_check_arg); - progress('\n'); - return prime; -} - - -/* Core prime generation function. The algorithm used to generate - practically save primes is due to Lim and Lee as described in the - CRYPTO '97 proceedings (ISBN3540633847) page 260. - - NEED_Q_FACTOR: If true make sure that at least one factor is of - size qbits. This is for example required for DSA. - PRIME_GENERATED: Adresss of a variable where the resulting prime - number will be stored. - PBITS: Requested size of the prime number. At least 48. - QBITS: One factor of the prime needs to be of this size. Maybe 0 - if this is not required. See also MODE. - G: If not NULL an MPI which will receive a generator for the prime - for use with Elgamal. - RET_FACTORS: if not NULL, an array with all factors are stored at - that address. - ALL_FACTORS: If set to true all factors of prime-1 are returned. - RANDOMLEVEL: How strong should the random numers be. - FLAGS: Prime generation bit flags. Currently supported: - GCRY_PRIME_FLAG_SECRET - The prime needs to be kept secret. - CB_FUNC, CB_ARG: Callback to be used for extra checks. - - */ -static gcry_err_code_t -prime_generate_internal (int need_q_factor, - 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_random_level_t poolrandomlevel; /* Random level used for pool primes. */ - gcry_mpi_t *pool = NULL; /* Pool of primes. */ - int *pool_in_use = NULL; /* Array with currently used POOL elements. */ - 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(). */ - int is_locked = 0; /* Flag to help unlocking the primepool. */ - 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; - - /* We won't use a too strong random elvel for the pooled subprimes. */ - poolrandomlevel = (randomlevel > GCRY_STRONG_RANDOM? - GCRY_STRONG_RANDOM : randomlevel); - - - /* If QBITS is not given, assume a reasonable value. */ - if (!qbits) - qbits = pbits / 3; - - req_qbits = qbits; - - /* Find number of needed prime factors N. */ - for (n = 1; (pbits - qbits - 1) / n >= qbits; n++) - ; - n--; - - val_2 = mpi_alloc_set_ui (2); - - if ((! n) || ((need_q_factor) && (n < 2))) - { - err = GPG_ERR_INV_ARG; - goto leave; - } - - if (need_q_factor) - { - n--; /* Need one factor less because we want a specific Q-FACTOR. */ - 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); - - /* Allocate an integer to old the new prime. */ - prime = gcry_mpi_new (pbits); - - /* Generate first prime factor. */ - q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL); - - /* Generate a specific Q-Factor if requested. */ - if (need_q_factor) - q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL); - - /* Allocate an array to hold all factors + 2 for later usage. */ - factors = gcry_calloc (n + 2, sizeof (*factors)); - if (!factors) - { - err = gpg_err_code_from_errno (errno); - goto leave; - } - - /* Allocate an array to track pool usage. */ - pool_in_use = gcry_malloc (n * sizeof *pool_in_use); - if (!pool_in_use) - { - err = gpg_err_code_from_errno (errno); - goto leave; - } - for (i=0; i < n; i++) - pool_in_use[i] = -1; - - /* Make a pool of 3n+5 primes (this is an arbitrary value). We - require at least 30 primes for are useful selection process. - - Fixme: We need to research the best formula for sizing the pool. - */ - m = n * 3 + 5; - if (need_q_factor) /* Need some more in this case. */ - m += 5; - if (m < 30) - m = 30; - pool = gcry_calloc (m , sizeof (*pool)); - if (! pool) - { - err = gpg_err_code_from_errno (errno); - goto leave; - } - - /* Permutate over the pool of primes until we find a prime of the - requested length. */ - do - { - next_try: - for (i=0; i < n; i++) - pool_in_use[i] = -1; - - if (!perms) - { - /* Allocate new primes. This is done right at the beginning - of the loop and if we have later run out of 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; - } - - if (ath_mutex_lock (&primepool_lock)) - { - err = GPG_ERR_INTERNAL; - goto leave; - } - is_locked = 1; - for (i = 0; i < n; i++) - { - perms[i] = 1; - /* At a maximum we use strong random for the factors. - This saves us a lot of entropy. Given that Q and - possible Q-factor are also used in the final prime - this should be acceptable. We also don't allocate in - secure memory to save on that scare resource too. If - Q has been allocated in secure memory, the final - prime will be saved there anyway. This is because - our MPI routines take care of that. GnuPG has worked - this way ever since. */ - pool[i] = NULL; - if (is_locked) - { - pool[i] = get_pool_prime (fbits, poolrandomlevel); - if (!pool[i]) - { - if (ath_mutex_unlock (&primepool_lock)) - { - err = GPG_ERR_INTERNAL; - goto leave; - } - is_locked = 0; - } - } - if (!pool[i]) - pool[i] = gen_prime (fbits, 0, poolrandomlevel, NULL, NULL); - pool_in_use[i] = i; - factors[i] = pool[i]; - } - if (is_locked && ath_mutex_unlock (&primepool_lock)) - { - err = GPG_ERR_INTERNAL; - goto leave; - } - is_locked = 0; - } - else - { - /* Get next permutation. */ - m_out_of_n ( (char*)perms, n, m); - if (ath_mutex_lock (&primepool_lock)) - { - err = GPG_ERR_INTERNAL; - goto leave; - } - is_locked = 1; - for (i = j = 0; (i < m) && (j < n); i++) - if (perms[i]) - { - /* If the subprime has not yet beed generated do it now. */ - if (!pool[i] && is_locked) - { - pool[i] = get_pool_prime (fbits, poolrandomlevel); - if (!pool[i]) - { - if (ath_mutex_unlock (&primepool_lock)) - { - err = GPG_ERR_INTERNAL; - goto leave; - } - is_locked = 0; - } - } - if (!pool[i]) - pool[i] = gen_prime (fbits, 0, poolrandomlevel, NULL, NULL); - pool_in_use[j] = i; - factors[j++] = pool[i]; - } - if (is_locked && ath_mutex_unlock (&primepool_lock)) - { - err = GPG_ERR_INTERNAL; - goto leave; - } - is_locked = 0; - if (i == n) - { - /* Ran out of permutations: Allocate new primes. */ - gcry_free (perms); - perms = NULL; - progress ('!'); - goto next_try; - } - } - - /* 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 (need_q_factor) - 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, is_secret, randomlevel, 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, is_secret, randomlevel, NULL, NULL); - goto next_try; - } - } - else - count2 = 0; - } - while (! ((nprime == pbits) && check_prime (prime, val_2, 5, - cb_func, cb_arg))); - - if (DBG_CIPHER) - { - progress ('\n'); - log_mpidump ("prime : ", prime); - log_mpidump ("factor q: ", q); - if (need_q_factor) - 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 (need_q_factor) - 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 (need_q_factor) - factors_new[i++] = mpi_copy (q_factor); - for(j=0; j < n; j++) - factors_new[i++] = mpi_copy (factors[j]); - } - else - { - i = 0; - if (need_q_factor) - { - 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 (need_q_factor) - 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) - { - is_locked = !ath_mutex_lock (&primepool_lock); - for(i = 0; i < m; i++) - { - if (pool[i]) - { - for (j=0; j < n; j++) - if (pool_in_use[j] == i) - break; - if (j == n && is_locked) - { - /* This pooled subprime has not been used. */ - save_pool_prime (pool[i], poolrandomlevel); - } - else - mpi_free (pool[i]); - } - } - if (is_locked && ath_mutex_unlock (&primepool_lock)) - err = GPG_ERR_INTERNAL; - is_locked = 0; - gcry_free (pool); - } - gcry_free (pool_in_use); - 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; -} - - -/* Generate a prime used for discrete logarithm algorithms; i.e. this - prime will be public and no strong random is required. */ -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 == 1), &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 int x, step; - unsigned int 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 - * RM_ROUNDS gives the number of Rabin-Miller tests to run. - */ -static int -check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, int rm_rounds, - gcry_prime_check_func_t cb_func, void *cb_arg) -{ - int i; - unsigned int x; - unsigned 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, rm_rounds, &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, unsigned 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 ); - - if (steps < 5) /* Make sure that we do at least 5 rounds. */ - steps = 5; - - 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 ); - } - gcry_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; -} - - -/* Given ARRAY of size N with M elements set to true produce a - modified array with the next permutation of M elements. Note, that - ARRAY is used in a one-bit-per-byte approach. To detected the last - permutation it is useful to intialize the array with the first M - element set to true and use this test: - m_out_of_n (array, m, n); - for (i = j = 0; i < n && j < m; i++) - if (array[i]) - j++; - if (j == m) - goto ready; - - This code is based on the algorithm 452 from the "Collected - Algorithms From ACM, Volume II" by C. N. Liu and D. T. Tang. -*/ -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; - - /* Need to handle this simple case separately. */ - if( m == 1 ) - { - 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: - /* Now complement the two selected bits. */ - 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==1), &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. */ - - (void)flags; - - /* We use 64 rounds because the prime we are going to test is not - guaranteed to be a random one. */ - if (! check_prime (x, val_2, 64, 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); - } -} - - - -/* Helper for _gcry_derive_x931_prime. */ -static gcry_mpi_t -find_x931_prime (const gcry_mpi_t pfirst) -{ - gcry_mpi_t val_2 = mpi_alloc_set_ui (2); - gcry_mpi_t prime; - - prime = gcry_mpi_copy (pfirst); - /* If P is even add 1. */ - mpi_set_bit (prime, 0); - - /* We use 64 Rabin-Miller rounds which is better and thus - sufficient. We do not have a Lucas test implementaion thus we - can't do it in the X9.31 preferred way of running a few - Rabin-Miller followed by one Lucas test. */ - while ( !check_prime (prime, val_2, 64, NULL, NULL) ) - mpi_add_ui (prime, prime, 2); - - mpi_free (val_2); - - return prime; -} - - -/* Generate a prime using the algorithm from X9.31 appendix B.4. - - This function requires that the provided public exponent E is odd. - XP, XP1 and XP2 are the seed values. All values are mandatory. - - On success the prime is returned. If R_P1 or R_P2 are given the - internal values P1 and P2 are saved at these addresses. On error - NULL is returned. */ -gcry_mpi_t -_gcry_derive_x931_prime (const gcry_mpi_t xp, - const gcry_mpi_t xp1, const gcry_mpi_t xp2, - const gcry_mpi_t e, - gcry_mpi_t *r_p1, gcry_mpi_t *r_p2) -{ - gcry_mpi_t p1, p2, p1p2, yp0; - - if (!xp || !xp1 || !xp2) - return NULL; - if (!e || !mpi_test_bit (e, 0)) - return NULL; /* We support only odd values for E. */ - - p1 = find_x931_prime (xp1); - p2 = find_x931_prime (xp2); - p1p2 = mpi_alloc_like (xp); - mpi_mul (p1p2, p1, p2); - - { - gcry_mpi_t r1, tmp; - - /* r1 = (p2^{-1} mod p1)p2 - (p1^{-1} mod p2) */ - tmp = mpi_alloc_like (p1); - mpi_invm (tmp, p2, p1); - mpi_mul (tmp, tmp, p2); - r1 = tmp; - - tmp = mpi_alloc_like (p2); - mpi_invm (tmp, p1, p2); - mpi_mul (tmp, tmp, p1); - mpi_sub (r1, r1, tmp); - - /* Fixup a negative value. */ - if (mpi_is_neg (r1)) - mpi_add (r1, r1, p1p2); - - /* yp0 = xp + (r1 - xp mod p1*p2) */ - yp0 = tmp; tmp = NULL; - mpi_subm (yp0, r1, xp, p1p2); - mpi_add (yp0, yp0, xp); - mpi_free (r1); - - /* Fixup a negative value. */ - if (mpi_cmp (yp0, xp) < 0 ) - mpi_add (yp0, yp0, p1p2); - } - - /* yp0 is now the first integer greater than xp with p1 being a - large prime factor of yp0-1 and p2 a large prime factor of yp0+1. */ - - /* Note that the first example from X9.31 (D.1.1) which uses - (Xq1 #1A5CF72EE770DE50CB09ACCEA9#) - (Xq2 #134E4CAA16D2350A21D775C404#) - (Xq #CC1092495D867E64065DEE3E7955F2EBC7D47A2D - 7C9953388F97DDDC3E1CA19C35CA659EDC2FC325 - 6D29C2627479C086A699A49C4C9CEE7EF7BD1B34 - 321DE34A#)))) - returns an yp0 of - #CC1092495D867E64065DEE3E7955F2EBC7D47A2D - 7C9953388F97DDDC3E1CA19C35CA659EDC2FC4E3 - BF20CB896EE37E098A906313271422162CB6C642 - 75C1201F# - and not - #CC1092495D867E64065DEE3E7955F2EBC7D47A2D - 7C9953388F97DDDC3E1CA19C35CA659EDC2FC2E6 - C88FE299D52D78BE405A97E01FD71DD7819ECB91 - FA85A076# - as stated in the standard. This seems to be a bug in X9.31. - */ - - { - gcry_mpi_t val_2 = mpi_alloc_set_ui (2); - gcry_mpi_t gcdtmp = mpi_alloc_like (yp0); - int gcdres; - - mpi_sub_ui (p1p2, p1p2, 1); /* Adjust for loop body. */ - mpi_sub_ui (yp0, yp0, 1); /* Ditto. */ - for (;;) - { - gcdres = gcry_mpi_gcd (gcdtmp, e, yp0); - mpi_add_ui (yp0, yp0, 1); - if (!gcdres) - progress ('/'); /* gcd (e, yp0-1) != 1 */ - else if (check_prime (yp0, val_2, 64, NULL, NULL)) - break; /* Found. */ - /* We add p1p2-1 because yp0 is incremented after the gcd test. */ - mpi_add (yp0, yp0, p1p2); - } - mpi_free (gcdtmp); - mpi_free (val_2); - } - - mpi_free (p1p2); - - progress('\n'); - if (r_p1) - *r_p1 = p1; - else - mpi_free (p1); - if (r_p2) - *r_p2 = p2; - else - mpi_free (p2); - return yp0; -} - - - -/* Generate the two prime used for DSA using the algorithm specified - in FIPS 186-2. PBITS is the desired length of the prime P and a - QBITS the length of the prime Q. If SEED is not supplied and - SEEDLEN is 0 the function generates an appropriate SEED. On - success the generated primes are stored at R_Q and R_P, the counter - value is stored at R_COUNTER and the seed actually used for - generation is stored at R_SEED and R_SEEDVALUE. */ -gpg_err_code_t -_gcry_generate_fips186_2_prime (unsigned int pbits, unsigned int qbits, - const void *seed, size_t seedlen, - gcry_mpi_t *r_q, gcry_mpi_t *r_p, - int *r_counter, - void **r_seed, size_t *r_seedlen) -{ - gpg_err_code_t ec; - unsigned char seed_help_buffer[160/8]; /* Used to hold a generated SEED. */ - unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */ - unsigned char digest[160/8]; /* Helper buffer for SHA-1 digest. */ - gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */ - gcry_mpi_t tmpval = NULL; /* Helper variable. */ - int i; - - unsigned char value_u[160/8]; - int value_n, value_b, value_k; - int counter; - gcry_mpi_t value_w = NULL; - gcry_mpi_t value_x = NULL; - gcry_mpi_t prime_q = NULL; - gcry_mpi_t prime_p = NULL; - - /* FIPS 186-2 allows only for 1024/160 bit. */ - if (pbits != 1024 || qbits != 160) - return GPG_ERR_INV_KEYLEN; - - if (!seed && !seedlen) - ; /* No seed value given: We are asked to generate it. */ - else if (!seed || seedlen < qbits/8) - return GPG_ERR_INV_ARG; - - /* Allocate a buffer to later compute SEED+some_increment. */ - seed_plus = gcry_malloc (seedlen < 20? 20:seedlen); - if (!seed_plus) - { - ec = gpg_err_code_from_syserror (); - goto leave; - } - - val_2 = mpi_alloc_set_ui (2); - value_n = (pbits - 1) / qbits; - value_b = (pbits - 1) - value_n * qbits; - value_w = gcry_mpi_new (pbits); - value_x = gcry_mpi_new (pbits); - - restart: - /* Generate Q. */ - for (;;) - { - /* Step 1: Generate a (new) seed unless one has been supplied. */ - if (!seed) - { - seedlen = sizeof seed_help_buffer; - gcry_create_nonce (seed_help_buffer, seedlen); - seed = seed_help_buffer; - } - - /* Step 2: U = sha1(seed) ^ sha1((seed+1) mod 2^{qbits}) */ - memcpy (seed_plus, seed, seedlen); - for (i=seedlen-1; i >= 0; i--) - { - seed_plus[i]++; - if (seed_plus[i]) - break; - } - gcry_md_hash_buffer (GCRY_MD_SHA1, value_u, seed, seedlen); - gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen); - for (i=0; i < sizeof value_u; i++) - value_u[i] ^= digest[i]; - - /* Step 3: Form q from U */ - gcry_mpi_release (prime_q); prime_q = NULL; - ec = gpg_err_code (gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG, - value_u, sizeof value_u, NULL)); - if (ec) - goto leave; - mpi_set_highbit (prime_q, qbits-1 ); - mpi_set_bit (prime_q, 0); - - /* Step 4: Test whether Q is prime using 64 round of Rabin-Miller. */ - if (check_prime (prime_q, val_2, 64, NULL, NULL)) - break; /* Yes, Q is prime. */ - - /* Step 5. */ - seed = NULL; /* Force a new seed at Step 1. */ - } - - /* Step 6. Note that we do no use an explicit offset but increment - SEED_PLUS accordingly. SEED_PLUS is currently SEED+1. */ - counter = 0; - - /* Generate P. */ - prime_p = gcry_mpi_new (pbits); - for (;;) - { - /* Step 7: For k = 0,...n let - V_k = sha1(seed+offset+k) mod 2^{qbits} - Step 8: W = V_0 + V_1*2^160 + - ... - + V_{n-1}*2^{(n-1)*160} - + (V_{n} mod 2^b)*2^{n*160} - */ - mpi_set_ui (value_w, 0); - for (value_k=0; value_k <= value_n; value_k++) - { - /* There is no need to have an explicit offset variable: In - the first round we shall have an offset of 2, this is - achieved by using SEED_PLUS which is already at SEED+1, - thus we just need to increment it once again. The - requirement for the next round is to update offset by N, - which we implictly did at the end of this loop, and then - to add one; this one is the same as in the first round. */ - for (i=seedlen-1; i >= 0; i--) - { - seed_plus[i]++; - if (seed_plus[i]) - break; - } - gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen); - - gcry_mpi_release (tmpval); tmpval = NULL; - ec = gpg_err_code (gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG, - digest, sizeof digest, NULL)); - if (ec) - goto leave; - if (value_k == value_n) - mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */ - mpi_lshift (tmpval, tmpval, value_k*qbits); - mpi_add (value_w, value_w, tmpval); - } - - /* Step 8 continued: X = W + 2^{L-1} */ - mpi_set_ui (value_x, 0); - mpi_set_highbit (value_x, pbits-1); - mpi_add (value_x, value_x, value_w); - - /* Step 9: c = X mod 2q, p = X - (c - 1) */ - mpi_mul_2exp (tmpval, prime_q, 1); - mpi_mod (tmpval, value_x, tmpval); - mpi_sub_ui (tmpval, tmpval, 1); - mpi_sub (prime_p, value_x, tmpval); - - /* Step 10: If p < 2^{L-1} skip the primality test. */ - /* Step 11 and 12: Primality test. */ - if (mpi_get_nbits (prime_p) >= pbits-1 - && check_prime (prime_p, val_2, 64, NULL, NULL) ) - break; /* Yes, P is prime, continue with Step 15. */ - - /* Step 13: counter = counter + 1, offset = offset + n + 1. */ - counter++; - - /* Step 14: If counter >= 2^12 goto Step 1. */ - if (counter >= 4096) - goto restart; - } - - /* Step 15: Save p, q, counter and seed. */ -/* log_debug ("fips186-2 pbits p=%u q=%u counter=%d\n", */ -/* mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter); */ -/* log_printhex("fips186-2 seed:", seed, seedlen); */ -/* log_mpidump ("fips186-2 prime p", prime_p); */ -/* log_mpidump ("fips186-2 prime q", prime_q); */ - if (r_q) - { - *r_q = prime_q; - prime_q = NULL; - } - if (r_p) - { - *r_p = prime_p; - prime_p = NULL; - } - if (r_counter) - *r_counter = counter; - if (r_seed && r_seedlen) - { - memcpy (seed_plus, seed, seedlen); - *r_seed = seed_plus; - seed_plus = NULL; - *r_seedlen = seedlen; - } - - - leave: - gcry_mpi_release (tmpval); - gcry_mpi_release (value_x); - gcry_mpi_release (value_w); - gcry_mpi_release (prime_p); - gcry_mpi_release (prime_q); - gcry_free (seed_plus); - gcry_mpi_release (val_2); - return ec; -} - - - -/* WARNING: The code below has not yet been tested! However, it is - not yet used. We need to wait for FIPS 186-3 final and for test - vectors. - - Generate the two prime used for DSA using the algorithm specified - in FIPS 186-3, A.1.1.2. PBITS is the desired length of the prime P - and a QBITS the length of the prime Q. If SEED is not supplied and - SEEDLEN is 0 the function generates an appropriate SEED. On - success the generated primes are stored at R_Q and R_P, the counter - value is stored at R_COUNTER and the seed actually used for - generation is stored at R_SEED and R_SEEDVALUE. The hash algorithm - used is stored at R_HASHALGO. - - Note that this function is very similar to the fips186_2 code. Due - to the minor differences, other buffer sizes and for documentarion, - we use a separate function. -*/ -gpg_err_code_t -_gcry_generate_fips186_3_prime (unsigned int pbits, unsigned int qbits, - const void *seed, size_t seedlen, - gcry_mpi_t *r_q, gcry_mpi_t *r_p, - int *r_counter, - void **r_seed, size_t *r_seedlen, - int *r_hashalgo) -{ - gpg_err_code_t ec; - unsigned char seed_help_buffer[256/8]; /* Used to hold a generated SEED. */ - unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */ - unsigned char digest[256/8]; /* Helper buffer for SHA-1 digest. */ - gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */ - gcry_mpi_t tmpval = NULL; /* Helper variable. */ - int hashalgo; /* The id of the Approved Hash Function. */ - int i; - - unsigned char value_u[256/8]; - int value_n, value_b, value_j; - int counter; - gcry_mpi_t value_w = NULL; - gcry_mpi_t value_x = NULL; - gcry_mpi_t prime_q = NULL; - gcry_mpi_t prime_p = NULL; - - gcry_assert (sizeof seed_help_buffer == sizeof digest - && sizeof seed_help_buffer == sizeof value_u); - - /* Step 1: Check the requested prime lengths. */ - /* Note that due to the size of our buffers QBITS is limited to 256. */ - if (pbits == 1024 && qbits == 160) - hashalgo = GCRY_MD_SHA1; - else if (pbits == 2048 && qbits == 224) - hashalgo = GCRY_MD_SHA224; - else if (pbits == 2048 && qbits == 256) - hashalgo = GCRY_MD_SHA256; - else if (pbits == 3072 && qbits == 256) - hashalgo = GCRY_MD_SHA256; - else - return GPG_ERR_INV_KEYLEN; - - /* Also check that the hash algorithm is available. */ - ec = gpg_err_code (gcry_md_test_algo (hashalgo)); - if (ec) - return ec; - gcry_assert (qbits/8 <= sizeof digest); - gcry_assert (gcry_md_get_algo_dlen (hashalgo) == qbits/8); - - - /* Step 2: Check seedlen. */ - if (!seed && !seedlen) - ; /* No seed value given: We are asked to generate it. */ - else if (!seed || seedlen < qbits/8) - return GPG_ERR_INV_ARG; - - /* Allocate a buffer to later compute SEED+some_increment and a few - helper variables. */ - seed_plus = gcry_malloc (seedlen < sizeof seed_help_buffer? - sizeof seed_help_buffer : seedlen); - if (!seed_plus) - { - ec = gpg_err_code_from_syserror (); - goto leave; - } - val_2 = mpi_alloc_set_ui (2); - value_w = gcry_mpi_new (pbits); - value_x = gcry_mpi_new (pbits); - - /* Step 3: n = \lceil L / outlen \rceil - 1 */ - value_n = (pbits + qbits - 1) / qbits - 1; - /* Step 4: b = L - 1 - (n * outlen) */ - value_b = pbits - 1 - (value_n * qbits); - - restart: - /* Generate Q. */ - for (;;) - { - /* Step 5: Generate a (new) seed unless one has been supplied. */ - if (!seed) - { - seedlen = qbits/8; - gcry_assert (seedlen <= sizeof seed_help_buffer); - gcry_create_nonce (seed_help_buffer, seedlen); - seed = seed_help_buffer; - } - - /* Step 6: U = hash(seed) */ - gcry_md_hash_buffer (hashalgo, value_u, seed, seedlen); - - /* Step 7: q = 2^{N-1} + U + 1 - (U mod 2) */ - if ( !(value_u[qbits/8-1] & 0x01) ) - { - for (i=qbits/8-1; i >= 0; i--) - { - value_u[i]++; - if (value_u[i]) - break; - } - } - gcry_mpi_release (prime_q); prime_q = NULL; - ec = gpg_err_code (gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG, - value_u, sizeof value_u, NULL)); - if (ec) - goto leave; - mpi_set_highbit (prime_q, qbits-1 ); - - /* Step 8: Test whether Q is prime using 64 round of Rabin-Miller. - According to table C.1 this is sufficient for all - supported prime sizes (i.e. up 3072/256). */ - if (check_prime (prime_q, val_2, 64, NULL, NULL)) - break; /* Yes, Q is prime. */ - - /* Step 8. */ - seed = NULL; /* Force a new seed at Step 5. */ - } - - /* Step 11. Note that we do no use an explicit offset but increment - SEED_PLUS accordingly. */ - memcpy (seed_plus, seed, seedlen); - counter = 0; - - /* Generate P. */ - prime_p = gcry_mpi_new (pbits); - for (;;) - { - /* Step 11.1: For j = 0,...n let - V_j = hash(seed+offset+j) - Step 11.2: W = V_0 + V_1*2^outlen + - ... - + V_{n-1}*2^{(n-1)*outlen} - + (V_{n} mod 2^b)*2^{n*outlen} - */ - mpi_set_ui (value_w, 0); - for (value_j=0; value_j <= value_n; value_j++) - { - /* There is no need to have an explicit offset variable: In - the first round we shall have an offset of 1 and a j of - 0. This is achieved by incrementing SEED_PLUS here. For - the next round offset is implicitly updated by using - SEED_PLUS again. */ - for (i=seedlen-1; i >= 0; i--) - { - seed_plus[i]++; - if (seed_plus[i]) - break; - } - gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen); - - gcry_mpi_release (tmpval); tmpval = NULL; - ec = gpg_err_code (gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG, - digest, sizeof digest, NULL)); - if (ec) - goto leave; - if (value_j == value_n) - mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */ - mpi_lshift (tmpval, tmpval, value_j*qbits); - mpi_add (value_w, value_w, tmpval); - } - - /* Step 11.3: X = W + 2^{L-1} */ - mpi_set_ui (value_x, 0); - mpi_set_highbit (value_x, pbits-1); - mpi_add (value_x, value_x, value_w); - - /* Step 11.4: c = X mod 2q */ - mpi_mul_2exp (tmpval, prime_q, 1); - mpi_mod (tmpval, value_x, tmpval); - - /* Step 11.5: p = X - (c - 1) */ - mpi_sub_ui (tmpval, tmpval, 1); - mpi_sub (prime_p, value_x, tmpval); - - /* Step 11.6: If p < 2^{L-1} skip the primality test. */ - /* Step 11.7 and 11.8: Primality test. */ - if (mpi_get_nbits (prime_p) >= pbits-1 - && check_prime (prime_p, val_2, 64, NULL, NULL) ) - break; /* Yes, P is prime, continue with Step 15. */ - - /* Step 11.9: counter = counter + 1, offset = offset + n + 1. - If counter >= 4L goto Step 5. */ - counter++; - if (counter >= 4*pbits) - goto restart; - } - - /* Step 12: Save p, q, counter and seed. */ - log_debug ("fips186-3 pbits p=%u q=%u counter=%d\n", - mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter); - log_printhex("fips186-3 seed:", seed, seedlen); - log_mpidump ("fips186-3 prime p", prime_p); - log_mpidump ("fips186-3 prime q", prime_q); - if (r_q) - { - *r_q = prime_q; - prime_q = NULL; - } - if (r_p) - { - *r_p = prime_p; - prime_p = NULL; - } - if (r_counter) - *r_counter = counter; - if (r_seed && r_seedlen) - { - memcpy (seed_plus, seed, seedlen); - *r_seed = seed_plus; - seed_plus = NULL; - *r_seedlen = seedlen; - } - if (r_hashalgo) - *r_hashalgo = hashalgo; - - leave: - gcry_mpi_release (tmpval); - gcry_mpi_release (value_x); - gcry_mpi_release (value_w); - gcry_mpi_release (prime_p); - gcry_mpi_release (prime_q); - gcry_free (seed_plus); - gcry_mpi_release (val_2); - return ec; -} - +/* primegen.c - prime number generator
+ * Copyright (C) 1998, 2000, 2001, 2002, 2003
+ * 2004, 2008 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
+ */
+
+#include <config.h>
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <errno.h>
+
+#include "g10lib.h"
+#include "mpi.h"
+#include "cipher.h"
+#include "ath.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, int rm_rounds,
+ gcry_prime_check_func_t cb_func, void *cb_arg );
+static int is_prime (gcry_mpi_t n, int steps, unsigned 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;
+
+
+
+/* An object and a list to build up a global pool of primes. See
+ save_pool_prime and get_pool_prime. */
+struct primepool_s
+{
+ struct primepool_s *next;
+ gcry_mpi_t prime; /* If this is NULL the entry is not used. */
+ unsigned int nbits;
+ gcry_random_level_t randomlevel;
+};
+struct primepool_s *primepool;
+/* Mutex used to protect access to the primepool. */
+static ath_mutex_t primepool_lock = ATH_MUTEX_INITIALIZER;
+
+
+
+/* Save PRIME which has been generated at RANDOMLEVEL for later
+ use. Needs to be called while primepool_lock is being hold. Note
+ that PRIME should be considered released after calling this
+ function. */
+static void
+save_pool_prime (gcry_mpi_t prime, gcry_random_level_t randomlevel)
+{
+ struct primepool_s *item, *item2;
+ size_t n;
+
+ for (n=0, item = primepool; item; item = item->next, n++)
+ if (!item->prime)
+ break;
+ if (!item && n > 100)
+ {
+ /* Remove some of the entries. Our strategy is removing
+ the last third from the list. */
+ int i;
+
+ for (i=0, item2 = primepool; item2; item2 = item2->next)
+ {
+ if (i >= n/3*2)
+ {
+ gcry_mpi_release (item2->prime);
+ item2->prime = NULL;
+ if (!item)
+ item = item2;
+ }
+ }
+ }
+ if (!item)
+ {
+ item = gcry_calloc (1, sizeof *item);
+ if (!item)
+ {
+ /* Out of memory. Silently giving up. */
+ gcry_mpi_release (prime);
+ return;
+ }
+ item->next = primepool;
+ primepool = item;
+ }
+ item->prime = prime;
+ item->nbits = mpi_get_nbits (prime);
+ item->randomlevel = randomlevel;
+}
+
+
+/* Return a prime for the prime pool or NULL if none has been found.
+ The prime needs to match NBITS and randomlevel. This function needs
+ to be called why the primepool_look is being hold. */
+static gcry_mpi_t
+get_pool_prime (unsigned int nbits, gcry_random_level_t randomlevel)
+{
+ struct primepool_s *item;
+
+ for (item = primepool; item; item = item->next)
+ if (item->prime
+ && item->nbits == nbits && item->randomlevel == randomlevel)
+ {
+ gcry_mpi_t prime = item->prime;
+ item->prime = NULL;
+ gcry_assert (nbits == mpi_get_nbits (prime));
+ return prime;
+ }
+ return NULL;
+}
+
+
+
+
+
+
+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,
+ gcry_random_level_t random_level,
+ int (*extra_check)(void*, gcry_mpi_t),
+ void *extra_check_arg)
+{
+ gcry_mpi_t prime;
+
+ prime = gen_prime (nbits, 1, random_level, extra_check, extra_check_arg);
+ progress('\n');
+ return prime;
+}
+
+
+/* Generate a prime number which may be public, i.e. not allocated in
+ secure memory. */
+gcry_mpi_t
+_gcry_generate_public_prime (unsigned int nbits,
+ gcry_random_level_t random_level,
+ int (*extra_check)(void*, gcry_mpi_t),
+ void *extra_check_arg)
+{
+ gcry_mpi_t prime;
+
+ prime = gen_prime (nbits, 0, random_level, extra_check, extra_check_arg);
+ progress('\n');
+ return prime;
+}
+
+
+/* Core prime generation function. The algorithm used to generate
+ practically save primes is due to Lim and Lee as described in the
+ CRYPTO '97 proceedings (ISBN3540633847) page 260.
+
+ NEED_Q_FACTOR: If true make sure that at least one factor is of
+ size qbits. This is for example required for DSA.
+ PRIME_GENERATED: Adresss of a variable where the resulting prime
+ number will be stored.
+ PBITS: Requested size of the prime number. At least 48.
+ QBITS: One factor of the prime needs to be of this size. Maybe 0
+ if this is not required. See also MODE.
+ G: If not NULL an MPI which will receive a generator for the prime
+ for use with Elgamal.
+ RET_FACTORS: if not NULL, an array with all factors are stored at
+ that address.
+ ALL_FACTORS: If set to true all factors of prime-1 are returned.
+ RANDOMLEVEL: How strong should the random numers be.
+ FLAGS: Prime generation bit flags. Currently supported:
+ GCRY_PRIME_FLAG_SECRET - The prime needs to be kept secret.
+ CB_FUNC, CB_ARG: Callback to be used for extra checks.
+
+ */
+static gcry_err_code_t
+prime_generate_internal (int need_q_factor,
+ 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_random_level_t poolrandomlevel; /* Random level used for pool primes. */
+ gcry_mpi_t *pool = NULL; /* Pool of primes. */
+ int *pool_in_use = NULL; /* Array with currently used POOL elements. */
+ 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(). */
+ int is_locked = 0; /* Flag to help unlocking the primepool. */
+ 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;
+
+ /* We won't use a too strong random elvel for the pooled subprimes. */
+ poolrandomlevel = (randomlevel > GCRY_STRONG_RANDOM?
+ GCRY_STRONG_RANDOM : randomlevel);
+
+
+ /* If QBITS is not given, assume a reasonable value. */
+ if (!qbits)
+ qbits = pbits / 3;
+
+ req_qbits = qbits;
+
+ /* Find number of needed prime factors N. */
+ for (n = 1; (pbits - qbits - 1) / n >= qbits; n++)
+ ;
+ n--;
+
+ val_2 = mpi_alloc_set_ui (2);
+
+ if ((! n) || ((need_q_factor) && (n < 2)))
+ {
+ err = GPG_ERR_INV_ARG;
+ goto leave;
+ }
+
+ if (need_q_factor)
+ {
+ n--; /* Need one factor less because we want a specific Q-FACTOR. */
+ 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);
+
+ /* Allocate an integer to old the new prime. */
+ prime = gcry_mpi_new (pbits);
+
+ /* Generate first prime factor. */
+ q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
+
+ /* Generate a specific Q-Factor if requested. */
+ if (need_q_factor)
+ q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL);
+
+ /* Allocate an array to hold all factors + 2 for later usage. */
+ factors = gcry_calloc (n + 2, sizeof (*factors));
+ if (!factors)
+ {
+ err = gpg_err_code_from_errno (errno);
+ goto leave;
+ }
+
+ /* Allocate an array to track pool usage. */
+ pool_in_use = gcry_malloc (n * sizeof *pool_in_use);
+ if (!pool_in_use)
+ {
+ err = gpg_err_code_from_errno (errno);
+ goto leave;
+ }
+ for (i=0; i < n; i++)
+ pool_in_use[i] = -1;
+
+ /* Make a pool of 3n+5 primes (this is an arbitrary value). We
+ require at least 30 primes for are useful selection process.
+
+ Fixme: We need to research the best formula for sizing the pool.
+ */
+ m = n * 3 + 5;
+ if (need_q_factor) /* Need some more in this case. */
+ m += 5;
+ if (m < 30)
+ m = 30;
+ pool = gcry_calloc (m , sizeof (*pool));
+ if (! pool)
+ {
+ err = gpg_err_code_from_errno (errno);
+ goto leave;
+ }
+
+ /* Permutate over the pool of primes until we find a prime of the
+ requested length. */
+ do
+ {
+ next_try:
+ for (i=0; i < n; i++)
+ pool_in_use[i] = -1;
+
+ if (!perms)
+ {
+ /* Allocate new primes. This is done right at the beginning
+ of the loop and if we have later run out of 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;
+ }
+
+ if (ath_mutex_lock (&primepool_lock))
+ {
+ err = GPG_ERR_INTERNAL;
+ goto leave;
+ }
+ is_locked = 1;
+ for (i = 0; i < n; i++)
+ {
+ perms[i] = 1;
+ /* At a maximum we use strong random for the factors.
+ This saves us a lot of entropy. Given that Q and
+ possible Q-factor are also used in the final prime
+ this should be acceptable. We also don't allocate in
+ secure memory to save on that scare resource too. If
+ Q has been allocated in secure memory, the final
+ prime will be saved there anyway. This is because
+ our MPI routines take care of that. GnuPG has worked
+ this way ever since. */
+ pool[i] = NULL;
+ if (is_locked)
+ {
+ pool[i] = get_pool_prime (fbits, poolrandomlevel);
+ if (!pool[i])
+ {
+ if (ath_mutex_unlock (&primepool_lock))
+ {
+ err = GPG_ERR_INTERNAL;
+ goto leave;
+ }
+ is_locked = 0;
+ }
+ }
+ if (!pool[i])
+ pool[i] = gen_prime (fbits, 0, poolrandomlevel, NULL, NULL);
+ pool_in_use[i] = i;
+ factors[i] = pool[i];
+ }
+ if (is_locked && ath_mutex_unlock (&primepool_lock))
+ {
+ err = GPG_ERR_INTERNAL;
+ goto leave;
+ }
+ is_locked = 0;
+ }
+ else
+ {
+ /* Get next permutation. */
+ m_out_of_n ( (char*)perms, n, m);
+ if (ath_mutex_lock (&primepool_lock))
+ {
+ err = GPG_ERR_INTERNAL;
+ goto leave;
+ }
+ is_locked = 1;
+ for (i = j = 0; (i < m) && (j < n); i++)
+ if (perms[i])
+ {
+ /* If the subprime has not yet beed generated do it now. */
+ if (!pool[i] && is_locked)
+ {
+ pool[i] = get_pool_prime (fbits, poolrandomlevel);
+ if (!pool[i])
+ {
+ if (ath_mutex_unlock (&primepool_lock))
+ {
+ err = GPG_ERR_INTERNAL;
+ goto leave;
+ }
+ is_locked = 0;
+ }
+ }
+ if (!pool[i])
+ pool[i] = gen_prime (fbits, 0, poolrandomlevel, NULL, NULL);
+ pool_in_use[j] = i;
+ factors[j++] = pool[i];
+ }
+ if (is_locked && ath_mutex_unlock (&primepool_lock))
+ {
+ err = GPG_ERR_INTERNAL;
+ goto leave;
+ }
+ is_locked = 0;
+ if (i == n)
+ {
+ /* Ran out of permutations: Allocate new primes. */
+ gcry_free (perms);
+ perms = NULL;
+ progress ('!');
+ goto next_try;
+ }
+ }
+
+ /* 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 (need_q_factor)
+ 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, is_secret, randomlevel, 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, is_secret, randomlevel, NULL, NULL);
+ goto next_try;
+ }
+ }
+ else
+ count2 = 0;
+ }
+ while (! ((nprime == pbits) && check_prime (prime, val_2, 5,
+ cb_func, cb_arg)));
+
+ if (DBG_CIPHER)
+ {
+ progress ('\n');
+ log_mpidump ("prime : ", prime);
+ log_mpidump ("factor q: ", q);
+ if (need_q_factor)
+ 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 (need_q_factor)
+ 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 (need_q_factor)
+ factors_new[i++] = mpi_copy (q_factor);
+ for(j=0; j < n; j++)
+ factors_new[i++] = mpi_copy (factors[j]);
+ }
+ else
+ {
+ i = 0;
+ if (need_q_factor)
+ {
+ 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 (need_q_factor)
+ 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)
+ {
+ is_locked = !ath_mutex_lock (&primepool_lock);
+ for(i = 0; i < m; i++)
+ {
+ if (pool[i])
+ {
+ for (j=0; j < n; j++)
+ if (pool_in_use[j] == i)
+ break;
+ if (j == n && is_locked)
+ {
+ /* This pooled subprime has not been used. */
+ save_pool_prime (pool[i], poolrandomlevel);
+ }
+ else
+ mpi_free (pool[i]);
+ }
+ }
+ if (is_locked && ath_mutex_unlock (&primepool_lock))
+ err = GPG_ERR_INTERNAL;
+ is_locked = 0;
+ gcry_free (pool);
+ }
+ gcry_free (pool_in_use);
+ 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;
+}
+
+
+/* Generate a prime used for discrete logarithm algorithms; i.e. this
+ prime will be public and no strong random is required. */
+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 == 1), &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 int x, step;
+ unsigned int 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
+ * RM_ROUNDS gives the number of Rabin-Miller tests to run.
+ */
+static int
+check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, int rm_rounds,
+ gcry_prime_check_func_t cb_func, void *cb_arg)
+{
+ int i;
+ unsigned int x;
+ unsigned 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, rm_rounds, &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, unsigned 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 );
+
+ if (steps < 5) /* Make sure that we do at least 5 rounds. */
+ steps = 5;
+
+ 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 );
+ }
+ gcry_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;
+}
+
+
+/* Given ARRAY of size N with M elements set to true produce a
+ modified array with the next permutation of M elements. Note, that
+ ARRAY is used in a one-bit-per-byte approach. To detected the last
+ permutation it is useful to initialize the array with the first M
+ element set to true and use this test:
+ m_out_of_n (array, m, n);
+ for (i = j = 0; i < n && j < m; i++)
+ if (array[i])
+ j++;
+ if (j == m)
+ goto ready;
+
+ This code is based on the algorithm 452 from the "Collected
+ Algorithms From ACM, Volume II" by C. N. Liu and D. T. Tang.
+*/
+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;
+
+ /* Need to handle this simple case separately. */
+ if( m == 1 )
+ {
+ 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:
+ /* Now complement the two selected bits. */
+ 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==1), &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 whether 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. */
+
+ (void)flags;
+
+ /* We use 64 rounds because the prime we are going to test is not
+ guaranteed to be a random one. */
+ if (! check_prime (x, val_2, 64, 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);
+ }
+}
+
+
+
+/* Helper for _gcry_derive_x931_prime. */
+static gcry_mpi_t
+find_x931_prime (const gcry_mpi_t pfirst)
+{
+ gcry_mpi_t val_2 = mpi_alloc_set_ui (2);
+ gcry_mpi_t prime;
+
+ prime = gcry_mpi_copy (pfirst);
+ /* If P is even add 1. */
+ mpi_set_bit (prime, 0);
+
+ /* We use 64 Rabin-Miller rounds which is better and thus
+ sufficient. We do not have a Lucas test implementaion thus we
+ can't do it in the X9.31 preferred way of running a few
+ Rabin-Miller followed by one Lucas test. */
+ while ( !check_prime (prime, val_2, 64, NULL, NULL) )
+ mpi_add_ui (prime, prime, 2);
+
+ mpi_free (val_2);
+
+ return prime;
+}
+
+
+/* Generate a prime using the algorithm from X9.31 appendix B.4.
+
+ This function requires that the provided public exponent E is odd.
+ XP, XP1 and XP2 are the seed values. All values are mandatory.
+
+ On success the prime is returned. If R_P1 or R_P2 are given the
+ internal values P1 and P2 are saved at these addresses. On error
+ NULL is returned. */
+gcry_mpi_t
+_gcry_derive_x931_prime (const gcry_mpi_t xp,
+ const gcry_mpi_t xp1, const gcry_mpi_t xp2,
+ const gcry_mpi_t e,
+ gcry_mpi_t *r_p1, gcry_mpi_t *r_p2)
+{
+ gcry_mpi_t p1, p2, p1p2, yp0;
+
+ if (!xp || !xp1 || !xp2)
+ return NULL;
+ if (!e || !mpi_test_bit (e, 0))
+ return NULL; /* We support only odd values for E. */
+
+ p1 = find_x931_prime (xp1);
+ p2 = find_x931_prime (xp2);
+ p1p2 = mpi_alloc_like (xp);
+ mpi_mul (p1p2, p1, p2);
+
+ {
+ gcry_mpi_t r1, tmp;
+
+ /* r1 = (p2^{-1} mod p1)p2 - (p1^{-1} mod p2) */
+ tmp = mpi_alloc_like (p1);
+ mpi_invm (tmp, p2, p1);
+ mpi_mul (tmp, tmp, p2);
+ r1 = tmp;
+
+ tmp = mpi_alloc_like (p2);
+ mpi_invm (tmp, p1, p2);
+ mpi_mul (tmp, tmp, p1);
+ mpi_sub (r1, r1, tmp);
+
+ /* Fixup a negative value. */
+ if (mpi_is_neg (r1))
+ mpi_add (r1, r1, p1p2);
+
+ /* yp0 = xp + (r1 - xp mod p1*p2) */
+ yp0 = tmp; tmp = NULL;
+ mpi_subm (yp0, r1, xp, p1p2);
+ mpi_add (yp0, yp0, xp);
+ mpi_free (r1);
+
+ /* Fixup a negative value. */
+ if (mpi_cmp (yp0, xp) < 0 )
+ mpi_add (yp0, yp0, p1p2);
+ }
+
+ /* yp0 is now the first integer greater than xp with p1 being a
+ large prime factor of yp0-1 and p2 a large prime factor of yp0+1. */
+
+ /* Note that the first example from X9.31 (D.1.1) which uses
+ (Xq1 #1A5CF72EE770DE50CB09ACCEA9#)
+ (Xq2 #134E4CAA16D2350A21D775C404#)
+ (Xq #CC1092495D867E64065DEE3E7955F2EBC7D47A2D
+ 7C9953388F97DDDC3E1CA19C35CA659EDC2FC325
+ 6D29C2627479C086A699A49C4C9CEE7EF7BD1B34
+ 321DE34A#))))
+ returns an yp0 of
+ #CC1092495D867E64065DEE3E7955F2EBC7D47A2D
+ 7C9953388F97DDDC3E1CA19C35CA659EDC2FC4E3
+ BF20CB896EE37E098A906313271422162CB6C642
+ 75C1201F#
+ and not
+ #CC1092495D867E64065DEE3E7955F2EBC7D47A2D
+ 7C9953388F97DDDC3E1CA19C35CA659EDC2FC2E6
+ C88FE299D52D78BE405A97E01FD71DD7819ECB91
+ FA85A076#
+ as stated in the standard. This seems to be a bug in X9.31.
+ */
+
+ {
+ gcry_mpi_t val_2 = mpi_alloc_set_ui (2);
+ gcry_mpi_t gcdtmp = mpi_alloc_like (yp0);
+ int gcdres;
+
+ mpi_sub_ui (p1p2, p1p2, 1); /* Adjust for loop body. */
+ mpi_sub_ui (yp0, yp0, 1); /* Ditto. */
+ for (;;)
+ {
+ gcdres = gcry_mpi_gcd (gcdtmp, e, yp0);
+ mpi_add_ui (yp0, yp0, 1);
+ if (!gcdres)
+ progress ('/'); /* gcd (e, yp0-1) != 1 */
+ else if (check_prime (yp0, val_2, 64, NULL, NULL))
+ break; /* Found. */
+ /* We add p1p2-1 because yp0 is incremented after the gcd test. */
+ mpi_add (yp0, yp0, p1p2);
+ }
+ mpi_free (gcdtmp);
+ mpi_free (val_2);
+ }
+
+ mpi_free (p1p2);
+
+ progress('\n');
+ if (r_p1)
+ *r_p1 = p1;
+ else
+ mpi_free (p1);
+ if (r_p2)
+ *r_p2 = p2;
+ else
+ mpi_free (p2);
+ return yp0;
+}
+
+
+
+/* Generate the two prime used for DSA using the algorithm specified
+ in FIPS 186-2. PBITS is the desired length of the prime P and a
+ QBITS the length of the prime Q. If SEED is not supplied and
+ SEEDLEN is 0 the function generates an appropriate SEED. On
+ success the generated primes are stored at R_Q and R_P, the counter
+ value is stored at R_COUNTER and the seed actually used for
+ generation is stored at R_SEED and R_SEEDVALUE. */
+gpg_err_code_t
+_gcry_generate_fips186_2_prime (unsigned int pbits, unsigned int qbits,
+ const void *seed, size_t seedlen,
+ gcry_mpi_t *r_q, gcry_mpi_t *r_p,
+ int *r_counter,
+ void **r_seed, size_t *r_seedlen)
+{
+ gpg_err_code_t ec;
+ unsigned char seed_help_buffer[160/8]; /* Used to hold a generated SEED. */
+ unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */
+ unsigned char digest[160/8]; /* Helper buffer for SHA-1 digest. */
+ gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */
+ gcry_mpi_t tmpval = NULL; /* Helper variable. */
+ int i;
+
+ unsigned char value_u[160/8];
+ int value_n, value_b, value_k;
+ int counter;
+ gcry_mpi_t value_w = NULL;
+ gcry_mpi_t value_x = NULL;
+ gcry_mpi_t prime_q = NULL;
+ gcry_mpi_t prime_p = NULL;
+
+ /* FIPS 186-2 allows only for 1024/160 bit. */
+ if (pbits != 1024 || qbits != 160)
+ return GPG_ERR_INV_KEYLEN;
+
+ if (!seed && !seedlen)
+ ; /* No seed value given: We are asked to generate it. */
+ else if (!seed || seedlen < qbits/8)
+ return GPG_ERR_INV_ARG;
+
+ /* Allocate a buffer to later compute SEED+some_increment. */
+ seed_plus = gcry_malloc (seedlen < 20? 20:seedlen);
+ if (!seed_plus)
+ {
+ ec = gpg_err_code_from_syserror ();
+ goto leave;
+ }
+
+ val_2 = mpi_alloc_set_ui (2);
+ value_n = (pbits - 1) / qbits;
+ value_b = (pbits - 1) - value_n * qbits;
+ value_w = gcry_mpi_new (pbits);
+ value_x = gcry_mpi_new (pbits);
+
+ restart:
+ /* Generate Q. */
+ for (;;)
+ {
+ /* Step 1: Generate a (new) seed unless one has been supplied. */
+ if (!seed)
+ {
+ seedlen = sizeof seed_help_buffer;
+ gcry_create_nonce (seed_help_buffer, seedlen);
+ seed = seed_help_buffer;
+ }
+
+ /* Step 2: U = sha1(seed) ^ sha1((seed+1) mod 2^{qbits}) */
+ memcpy (seed_plus, seed, seedlen);
+ for (i=seedlen-1; i >= 0; i--)
+ {
+ seed_plus[i]++;
+ if (seed_plus[i])
+ break;
+ }
+ gcry_md_hash_buffer (GCRY_MD_SHA1, value_u, seed, seedlen);
+ gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen);
+ for (i=0; i < sizeof value_u; i++)
+ value_u[i] ^= digest[i];
+
+ /* Step 3: Form q from U */
+ gcry_mpi_release (prime_q); prime_q = NULL;
+ ec = gpg_err_code (gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG,
+ value_u, sizeof value_u, NULL));
+ if (ec)
+ goto leave;
+ mpi_set_highbit (prime_q, qbits-1 );
+ mpi_set_bit (prime_q, 0);
+
+ /* Step 4: Test whether Q is prime using 64 round of Rabin-Miller. */
+ if (check_prime (prime_q, val_2, 64, NULL, NULL))
+ break; /* Yes, Q is prime. */
+
+ /* Step 5. */
+ seed = NULL; /* Force a new seed at Step 1. */
+ }
+
+ /* Step 6. Note that we do no use an explicit offset but increment
+ SEED_PLUS accordingly. SEED_PLUS is currently SEED+1. */
+ counter = 0;
+
+ /* Generate P. */
+ prime_p = gcry_mpi_new (pbits);
+ for (;;)
+ {
+ /* Step 7: For k = 0,...n let
+ V_k = sha1(seed+offset+k) mod 2^{qbits}
+ Step 8: W = V_0 + V_1*2^160 +
+ ...
+ + V_{n-1}*2^{(n-1)*160}
+ + (V_{n} mod 2^b)*2^{n*160}
+ */
+ mpi_set_ui (value_w, 0);
+ for (value_k=0; value_k <= value_n; value_k++)
+ {
+ /* There is no need to have an explicit offset variable: In
+ the first round we shall have an offset of 2, this is
+ achieved by using SEED_PLUS which is already at SEED+1,
+ thus we just need to increment it once again. The
+ requirement for the next round is to update offset by N,
+ which we implictly did at the end of this loop, and then
+ to add one; this one is the same as in the first round. */
+ for (i=seedlen-1; i >= 0; i--)
+ {
+ seed_plus[i]++;
+ if (seed_plus[i])
+ break;
+ }
+ gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen);
+
+ gcry_mpi_release (tmpval); tmpval = NULL;
+ ec = gpg_err_code (gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG,
+ digest, sizeof digest, NULL));
+ if (ec)
+ goto leave;
+ if (value_k == value_n)
+ mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */
+ mpi_lshift (tmpval, tmpval, value_k*qbits);
+ mpi_add (value_w, value_w, tmpval);
+ }
+
+ /* Step 8 continued: X = W + 2^{L-1} */
+ mpi_set_ui (value_x, 0);
+ mpi_set_highbit (value_x, pbits-1);
+ mpi_add (value_x, value_x, value_w);
+
+ /* Step 9: c = X mod 2q, p = X - (c - 1) */
+ mpi_mul_2exp (tmpval, prime_q, 1);
+ mpi_mod (tmpval, value_x, tmpval);
+ mpi_sub_ui (tmpval, tmpval, 1);
+ mpi_sub (prime_p, value_x, tmpval);
+
+ /* Step 10: If p < 2^{L-1} skip the primality test. */
+ /* Step 11 and 12: Primality test. */
+ if (mpi_get_nbits (prime_p) >= pbits-1
+ && check_prime (prime_p, val_2, 64, NULL, NULL) )
+ break; /* Yes, P is prime, continue with Step 15. */
+
+ /* Step 13: counter = counter + 1, offset = offset + n + 1. */
+ counter++;
+
+ /* Step 14: If counter >= 2^12 goto Step 1. */
+ if (counter >= 4096)
+ goto restart;
+ }
+
+ /* Step 15: Save p, q, counter and seed. */
+/* log_debug ("fips186-2 pbits p=%u q=%u counter=%d\n", */
+/* mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter); */
+/* log_printhex("fips186-2 seed:", seed, seedlen); */
+/* log_mpidump ("fips186-2 prime p", prime_p); */
+/* log_mpidump ("fips186-2 prime q", prime_q); */
+ if (r_q)
+ {
+ *r_q = prime_q;
+ prime_q = NULL;
+ }
+ if (r_p)
+ {
+ *r_p = prime_p;
+ prime_p = NULL;
+ }
+ if (r_counter)
+ *r_counter = counter;
+ if (r_seed && r_seedlen)
+ {
+ memcpy (seed_plus, seed, seedlen);
+ *r_seed = seed_plus;
+ seed_plus = NULL;
+ *r_seedlen = seedlen;
+ }
+
+
+ leave:
+ gcry_mpi_release (tmpval);
+ gcry_mpi_release (value_x);
+ gcry_mpi_release (value_w);
+ gcry_mpi_release (prime_p);
+ gcry_mpi_release (prime_q);
+ gcry_free (seed_plus);
+ gcry_mpi_release (val_2);
+ return ec;
+}
+
+
+
+/* WARNING: The code below has not yet been tested! However, it is
+ not yet used. We need to wait for FIPS 186-3 final and for test
+ vectors.
+
+ Generate the two prime used for DSA using the algorithm specified
+ in FIPS 186-3, A.1.1.2. PBITS is the desired length of the prime P
+ and a QBITS the length of the prime Q. If SEED is not supplied and
+ SEEDLEN is 0 the function generates an appropriate SEED. On
+ success the generated primes are stored at R_Q and R_P, the counter
+ value is stored at R_COUNTER and the seed actually used for
+ generation is stored at R_SEED and R_SEEDVALUE. The hash algorithm
+ used is stored at R_HASHALGO.
+
+ Note that this function is very similar to the fips186_2 code. Due
+ to the minor differences, other buffer sizes and for documentarion,
+ we use a separate function.
+*/
+gpg_err_code_t
+_gcry_generate_fips186_3_prime (unsigned int pbits, unsigned int qbits,
+ const void *seed, size_t seedlen,
+ gcry_mpi_t *r_q, gcry_mpi_t *r_p,
+ int *r_counter,
+ void **r_seed, size_t *r_seedlen,
+ int *r_hashalgo)
+{
+ gpg_err_code_t ec;
+ unsigned char seed_help_buffer[256/8]; /* Used to hold a generated SEED. */
+ unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */
+ unsigned char digest[256/8]; /* Helper buffer for SHA-1 digest. */
+ gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */
+ gcry_mpi_t tmpval = NULL; /* Helper variable. */
+ int hashalgo; /* The id of the Approved Hash Function. */
+ int i;
+
+ unsigned char value_u[256/8];
+ int value_n, value_b, value_j;
+ int counter;
+ gcry_mpi_t value_w = NULL;
+ gcry_mpi_t value_x = NULL;
+ gcry_mpi_t prime_q = NULL;
+ gcry_mpi_t prime_p = NULL;
+
+ gcry_assert (sizeof seed_help_buffer == sizeof digest
+ && sizeof seed_help_buffer == sizeof value_u);
+
+ /* Step 1: Check the requested prime lengths. */
+ /* Note that due to the size of our buffers QBITS is limited to 256. */
+ if (pbits == 1024 && qbits == 160)
+ hashalgo = GCRY_MD_SHA1;
+ else if (pbits == 2048 && qbits == 224)
+ hashalgo = GCRY_MD_SHA224;
+ else if (pbits == 2048 && qbits == 256)
+ hashalgo = GCRY_MD_SHA256;
+ else if (pbits == 3072 && qbits == 256)
+ hashalgo = GCRY_MD_SHA256;
+ else
+ return GPG_ERR_INV_KEYLEN;
+
+ /* Also check that the hash algorithm is available. */
+ ec = gpg_err_code (gcry_md_test_algo (hashalgo));
+ if (ec)
+ return ec;
+ gcry_assert (qbits/8 <= sizeof digest);
+ gcry_assert (gcry_md_get_algo_dlen (hashalgo) == qbits/8);
+
+
+ /* Step 2: Check seedlen. */
+ if (!seed && !seedlen)
+ ; /* No seed value given: We are asked to generate it. */
+ else if (!seed || seedlen < qbits/8)
+ return GPG_ERR_INV_ARG;
+
+ /* Allocate a buffer to later compute SEED+some_increment and a few
+ helper variables. */
+ seed_plus = gcry_malloc (seedlen < sizeof seed_help_buffer?
+ sizeof seed_help_buffer : seedlen);
+ if (!seed_plus)
+ {
+ ec = gpg_err_code_from_syserror ();
+ goto leave;
+ }
+ val_2 = mpi_alloc_set_ui (2);
+ value_w = gcry_mpi_new (pbits);
+ value_x = gcry_mpi_new (pbits);
+
+ /* Step 3: n = \lceil L / outlen \rceil - 1 */
+ value_n = (pbits + qbits - 1) / qbits - 1;
+ /* Step 4: b = L - 1 - (n * outlen) */
+ value_b = pbits - 1 - (value_n * qbits);
+
+ restart:
+ /* Generate Q. */
+ for (;;)
+ {
+ /* Step 5: Generate a (new) seed unless one has been supplied. */
+ if (!seed)
+ {
+ seedlen = qbits/8;
+ gcry_assert (seedlen <= sizeof seed_help_buffer);
+ gcry_create_nonce (seed_help_buffer, seedlen);
+ seed = seed_help_buffer;
+ }
+
+ /* Step 6: U = hash(seed) */
+ gcry_md_hash_buffer (hashalgo, value_u, seed, seedlen);
+
+ /* Step 7: q = 2^{N-1} + U + 1 - (U mod 2) */
+ if ( !(value_u[qbits/8-1] & 0x01) )
+ {
+ for (i=qbits/8-1; i >= 0; i--)
+ {
+ value_u[i]++;
+ if (value_u[i])
+ break;
+ }
+ }
+ gcry_mpi_release (prime_q); prime_q = NULL;
+ ec = gpg_err_code (gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG,
+ value_u, sizeof value_u, NULL));
+ if (ec)
+ goto leave;
+ mpi_set_highbit (prime_q, qbits-1 );
+
+ /* Step 8: Test whether Q is prime using 64 round of Rabin-Miller.
+ According to table C.1 this is sufficient for all
+ supported prime sizes (i.e. up 3072/256). */
+ if (check_prime (prime_q, val_2, 64, NULL, NULL))
+ break; /* Yes, Q is prime. */
+
+ /* Step 8. */
+ seed = NULL; /* Force a new seed at Step 5. */
+ }
+
+ /* Step 11. Note that we do no use an explicit offset but increment
+ SEED_PLUS accordingly. */
+ memcpy (seed_plus, seed, seedlen);
+ counter = 0;
+
+ /* Generate P. */
+ prime_p = gcry_mpi_new (pbits);
+ for (;;)
+ {
+ /* Step 11.1: For j = 0,...n let
+ V_j = hash(seed+offset+j)
+ Step 11.2: W = V_0 + V_1*2^outlen +
+ ...
+ + V_{n-1}*2^{(n-1)*outlen}
+ + (V_{n} mod 2^b)*2^{n*outlen}
+ */
+ mpi_set_ui (value_w, 0);
+ for (value_j=0; value_j <= value_n; value_j++)
+ {
+ /* There is no need to have an explicit offset variable: In
+ the first round we shall have an offset of 1 and a j of
+ 0. This is achieved by incrementing SEED_PLUS here. For
+ the next round offset is implicitly updated by using
+ SEED_PLUS again. */
+ for (i=seedlen-1; i >= 0; i--)
+ {
+ seed_plus[i]++;
+ if (seed_plus[i])
+ break;
+ }
+ gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen);
+
+ gcry_mpi_release (tmpval); tmpval = NULL;
+ ec = gpg_err_code (gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG,
+ digest, sizeof digest, NULL));
+ if (ec)
+ goto leave;
+ if (value_j == value_n)
+ mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */
+ mpi_lshift (tmpval, tmpval, value_j*qbits);
+ mpi_add (value_w, value_w, tmpval);
+ }
+
+ /* Step 11.3: X = W + 2^{L-1} */
+ mpi_set_ui (value_x, 0);
+ mpi_set_highbit (value_x, pbits-1);
+ mpi_add (value_x, value_x, value_w);
+
+ /* Step 11.4: c = X mod 2q */
+ mpi_mul_2exp (tmpval, prime_q, 1);
+ mpi_mod (tmpval, value_x, tmpval);
+
+ /* Step 11.5: p = X - (c - 1) */
+ mpi_sub_ui (tmpval, tmpval, 1);
+ mpi_sub (prime_p, value_x, tmpval);
+
+ /* Step 11.6: If p < 2^{L-1} skip the primality test. */
+ /* Step 11.7 and 11.8: Primality test. */
+ if (mpi_get_nbits (prime_p) >= pbits-1
+ && check_prime (prime_p, val_2, 64, NULL, NULL) )
+ break; /* Yes, P is prime, continue with Step 15. */
+
+ /* Step 11.9: counter = counter + 1, offset = offset + n + 1.
+ If counter >= 4L goto Step 5. */
+ counter++;
+ if (counter >= 4*pbits)
+ goto restart;
+ }
+
+ /* Step 12: Save p, q, counter and seed. */
+ log_debug ("fips186-3 pbits p=%u q=%u counter=%d\n",
+ mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter);
+ log_printhex("fips186-3 seed:", seed, seedlen);
+ log_mpidump ("fips186-3 prime p", prime_p);
+ log_mpidump ("fips186-3 prime q", prime_q);
+ if (r_q)
+ {
+ *r_q = prime_q;
+ prime_q = NULL;
+ }
+ if (r_p)
+ {
+ *r_p = prime_p;
+ prime_p = NULL;
+ }
+ if (r_counter)
+ *r_counter = counter;
+ if (r_seed && r_seedlen)
+ {
+ memcpy (seed_plus, seed, seedlen);
+ *r_seed = seed_plus;
+ seed_plus = NULL;
+ *r_seedlen = seedlen;
+ }
+ if (r_hashalgo)
+ *r_hashalgo = hashalgo;
+
+ leave:
+ gcry_mpi_release (tmpval);
+ gcry_mpi_release (value_x);
+ gcry_mpi_release (value_w);
+ gcry_mpi_release (prime_p);
+ gcry_mpi_release (prime_q);
+ gcry_free (seed_plus);
+ gcry_mpi_release (val_2);
+ return ec;
+}
+
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