| /* 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; |
| } |
| |
