1879 строки
56 KiB
C
1879 строки
56 KiB
C
/* primegen.c - prime number generator
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* Copyright (C) 1998, 2000, 2001, 2002, 2003
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* 2004, 2008 Free Software Foundation, Inc.
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*
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* This file is part of Libgcrypt.
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*
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* Libgcrypt is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser general Public License as
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* published by the Free Software Foundation; either version 2.1 of
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* the License, or (at your option) any later version.
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*
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* Libgcrypt is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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*/
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#include <config.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <errno.h>
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#include "g10lib.h"
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#include "mpi.h"
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#include "cipher.h"
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static gcry_mpi_t gen_prime (unsigned int nbits, int secret, int randomlevel,
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int (*extra_check)(void *, gcry_mpi_t),
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void *extra_check_arg);
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static int check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, int rm_rounds,
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gcry_prime_check_func_t cb_func, void *cb_arg );
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static int is_prime (gcry_mpi_t n, int steps, unsigned int *count);
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static void m_out_of_n( char *array, int m, int n );
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static void (*progress_cb) (void *,const char*,int,int, int );
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static void *progress_cb_data;
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/* Note: 2 is not included because it can be tested more easily by
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looking at bit 0. The last entry in this list is marked by a zero */
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static ushort small_prime_numbers[] = {
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3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
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47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
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103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
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157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
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211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
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269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
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331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
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389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
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449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
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509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
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587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
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643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
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709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
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773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
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853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
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919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
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991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
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1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
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1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
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1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
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1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
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1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
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1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
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1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
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1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
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1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
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1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
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1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
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1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
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1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
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1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
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1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
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1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
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1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
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2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
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2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
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2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
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2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
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2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
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2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
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2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
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2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
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2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
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2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
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2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
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2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
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2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
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2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
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2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
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3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
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3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
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3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
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3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
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3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
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3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
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3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
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3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
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3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
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3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
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3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
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3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
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3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
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3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
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3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
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4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
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4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
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4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
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4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
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4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
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4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
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4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
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4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
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4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
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4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
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4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
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4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
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4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
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4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
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4957, 4967, 4969, 4973, 4987, 4993, 4999,
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0
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};
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static int no_of_small_prime_numbers = DIM (small_prime_numbers) - 1;
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/* An object and a list to build up a global pool of primes. See
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save_pool_prime and get_pool_prime. */
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struct primepool_s
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{
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struct primepool_s *next;
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gcry_mpi_t prime; /* If this is NULL the entry is not used. */
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unsigned int nbits;
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gcry_random_level_t randomlevel;
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};
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struct primepool_s *primepool;
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/* Mutex used to protect access to the primepool. */
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GPGRT_LOCK_DEFINE (primepool_lock);
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gcry_err_code_t
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_gcry_primegen_init (void)
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{
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/* This function was formerly used to initialize the primepool
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Mutex. This has been replace by a static initialization. */
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return 0;
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}
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/* Save PRIME which has been generated at RANDOMLEVEL for later
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use. Needs to be called while primepool_lock is being hold. Note
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that PRIME should be considered released after calling this
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function. */
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static void
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save_pool_prime (gcry_mpi_t prime, gcry_random_level_t randomlevel)
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{
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struct primepool_s *item, *item2;
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size_t n;
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for (n=0, item = primepool; item; item = item->next, n++)
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if (!item->prime)
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break;
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if (!item && n > 100)
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{
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/* Remove some of the entries. Our strategy is removing
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the last third from the list. */
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int i;
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for (i=0, item2 = primepool; item2; item2 = item2->next)
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{
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if (i >= n/3*2)
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{
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_gcry_mpi_release (item2->prime);
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item2->prime = NULL;
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if (!item)
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item = item2;
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}
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}
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}
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if (!item)
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{
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item = xtrycalloc (1, sizeof *item);
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if (!item)
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{
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/* Out of memory. Silently giving up. */
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_gcry_mpi_release (prime);
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return;
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}
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item->next = primepool;
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primepool = item;
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}
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item->prime = prime;
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item->nbits = mpi_get_nbits (prime);
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item->randomlevel = randomlevel;
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}
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/* Return a prime for the prime pool or NULL if none has been found.
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The prime needs to match NBITS and randomlevel. This function needs
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to be called with the primepool_look is being hold. */
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static gcry_mpi_t
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get_pool_prime (unsigned int nbits, gcry_random_level_t randomlevel)
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{
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struct primepool_s *item;
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for (item = primepool; item; item = item->next)
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if (item->prime
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&& item->nbits == nbits && item->randomlevel == randomlevel)
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{
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gcry_mpi_t prime = item->prime;
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item->prime = NULL;
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gcry_assert (nbits == mpi_get_nbits (prime));
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return prime;
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}
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return NULL;
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}
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void
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_gcry_register_primegen_progress ( void (*cb)(void *,const char*,int,int,int),
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void *cb_data )
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{
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progress_cb = cb;
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progress_cb_data = cb_data;
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}
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static void
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progress( int c )
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{
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if ( progress_cb )
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progress_cb ( progress_cb_data, "primegen", c, 0, 0 );
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}
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/****************
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* Generate a prime number (stored in secure memory)
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*/
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gcry_mpi_t
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_gcry_generate_secret_prime (unsigned int nbits,
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gcry_random_level_t random_level,
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int (*extra_check)(void*, gcry_mpi_t),
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void *extra_check_arg)
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{
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gcry_mpi_t prime;
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prime = gen_prime (nbits, 1, random_level, extra_check, extra_check_arg);
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progress('\n');
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return prime;
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}
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/* Generate a prime number which may be public, i.e. not allocated in
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secure memory. */
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gcry_mpi_t
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_gcry_generate_public_prime (unsigned int nbits,
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gcry_random_level_t random_level,
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int (*extra_check)(void*, gcry_mpi_t),
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void *extra_check_arg)
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{
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gcry_mpi_t prime;
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prime = gen_prime (nbits, 0, random_level, extra_check, extra_check_arg);
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progress('\n');
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return prime;
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}
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/* Core prime generation function. The algorithm used to generate
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practically save primes is due to Lim and Lee as described in the
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CRYPTO '97 proceedings (ISBN3540633847) page 260.
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NEED_Q_FACTOR: If true make sure that at least one factor is of
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size qbits. This is for example required for DSA.
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PRIME_GENERATED: Adresss of a variable where the resulting prime
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number will be stored.
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PBITS: Requested size of the prime number. At least 48.
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QBITS: One factor of the prime needs to be of this size. Maybe 0
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if this is not required. See also MODE.
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G: If not NULL an MPI which will receive a generator for the prime
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for use with Elgamal.
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RET_FACTORS: if not NULL, an array with all factors are stored at
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that address.
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ALL_FACTORS: If set to true all factors of prime-1 are returned.
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RANDOMLEVEL: How strong should the random numers be.
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FLAGS: Prime generation bit flags. Currently supported:
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GCRY_PRIME_FLAG_SECRET - The prime needs to be kept secret.
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CB_FUNC, CB_ARG: Callback to be used for extra checks.
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*/
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static gcry_err_code_t
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prime_generate_internal (int need_q_factor,
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gcry_mpi_t *prime_generated, unsigned int pbits,
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unsigned int qbits, gcry_mpi_t g,
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gcry_mpi_t **ret_factors,
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gcry_random_level_t randomlevel, unsigned int flags,
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int all_factors,
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gcry_prime_check_func_t cb_func, void *cb_arg)
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{
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gcry_err_code_t err = 0;
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gcry_mpi_t *factors_new = NULL; /* Factors to return to the
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caller. */
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gcry_mpi_t *factors = NULL; /* Current factors. */
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gcry_random_level_t poolrandomlevel; /* Random level used for pool primes. */
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gcry_mpi_t *pool = NULL; /* Pool of primes. */
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int *pool_in_use = NULL; /* Array with currently used POOL elements. */
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unsigned char *perms = NULL; /* Permutations of POOL. */
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gcry_mpi_t q_factor = NULL; /* Used if QBITS is non-zero. */
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unsigned int fbits = 0; /* Length of prime factors. */
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unsigned int n = 0; /* Number of factors. */
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unsigned int m = 0; /* Number of primes in pool. */
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gcry_mpi_t q = NULL; /* First prime factor. */
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gcry_mpi_t prime = NULL; /* Prime candidate. */
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unsigned int nprime = 0; /* Bits of PRIME. */
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unsigned int req_qbits; /* The original QBITS value. */
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gcry_mpi_t val_2; /* For check_prime(). */
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int is_locked = 0; /* Flag to help unlocking the primepool. */
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unsigned int is_secret = (flags & GCRY_PRIME_FLAG_SECRET);
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unsigned int count1 = 0, count2 = 0;
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unsigned int i = 0, j = 0;
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if (pbits < 48)
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return GPG_ERR_INV_ARG;
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/* We won't use a too strong random elvel for the pooled subprimes. */
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poolrandomlevel = (randomlevel > GCRY_STRONG_RANDOM?
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GCRY_STRONG_RANDOM : randomlevel);
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/* If QBITS is not given, assume a reasonable value. */
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if (!qbits)
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qbits = pbits / 3;
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req_qbits = qbits;
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/* Find number of needed prime factors N. */
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for (n = 1; (pbits - qbits - 1) / n >= qbits; n++)
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;
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n--;
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val_2 = mpi_alloc_set_ui (2);
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if ((! n) || ((need_q_factor) && (n < 2)))
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{
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err = GPG_ERR_INV_ARG;
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goto leave;
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}
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if (need_q_factor)
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{
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n--; /* Need one factor less because we want a specific Q-FACTOR. */
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fbits = (pbits - 2 * req_qbits -1) / n;
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qbits = pbits - req_qbits - n * fbits;
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}
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else
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{
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fbits = (pbits - req_qbits -1) / n;
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qbits = pbits - n * fbits;
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}
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if (DBG_CIPHER)
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log_debug ("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
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pbits, req_qbits, qbits, fbits, n);
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/* Allocate an integer to old the new prime. */
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prime = mpi_new (pbits);
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/* Generate first prime factor. */
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q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
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/* Generate a specific Q-Factor if requested. */
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if (need_q_factor)
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q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL);
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/* Allocate an array to hold all factors + 2 for later usage. */
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factors = xtrycalloc (n + 2, sizeof (*factors));
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if (!factors)
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{
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err = gpg_err_code_from_errno (errno);
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goto leave;
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}
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/* Allocate an array to track pool usage. */
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pool_in_use = xtrymalloc (n * sizeof *pool_in_use);
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if (!pool_in_use)
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{
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err = gpg_err_code_from_errno (errno);
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goto leave;
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}
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for (i=0; i < n; i++)
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pool_in_use[i] = -1;
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/* Make a pool of 3n+5 primes (this is an arbitrary value). We
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require at least 30 primes for are useful selection process.
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Fixme: We need to research the best formula for sizing the pool.
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*/
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m = n * 3 + 5;
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if (need_q_factor) /* Need some more in this case. */
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m += 5;
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if (m < 30)
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m = 30;
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pool = xtrycalloc (m , sizeof (*pool));
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if (! pool)
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{
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err = gpg_err_code_from_errno (errno);
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goto leave;
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}
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/* Permutate over the pool of primes until we find a prime of the
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requested length. */
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do
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{
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next_try:
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for (i=0; i < n; i++)
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pool_in_use[i] = -1;
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if (!perms)
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{
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/* Allocate new primes. This is done right at the beginning
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of the loop and if we have later run out of primes. */
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for (i = 0; i < m; i++)
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{
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||
mpi_free (pool[i]);
|
||
pool[i] = NULL;
|
||
}
|
||
|
||
/* Init m_out_of_n(). */
|
||
perms = xtrycalloc (1, m);
|
||
if (!perms)
|
||
{
|
||
err = gpg_err_code_from_errno (errno);
|
||
goto leave;
|
||
}
|
||
|
||
err = gpgrt_lock_lock (&primepool_lock);
|
||
if (err)
|
||
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])
|
||
{
|
||
err = gpgrt_lock_unlock (&primepool_lock);
|
||
if (err)
|
||
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 && (err = gpgrt_lock_unlock (&primepool_lock)))
|
||
goto leave;
|
||
is_locked = 0;
|
||
}
|
||
else
|
||
{
|
||
/* Get next permutation. */
|
||
m_out_of_n ( (char*)perms, n, m);
|
||
|
||
if ((err = gpgrt_lock_lock (&primepool_lock)))
|
||
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 ((err = gpgrt_lock_unlock (&primepool_lock)))
|
||
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 && (err = gpgrt_lock_unlock (&primepool_lock)))
|
||
goto leave;
|
||
is_locked = 0;
|
||
|
||
if (i == n)
|
||
{
|
||
/* Ran out of permutations: Allocate new primes. */
|
||
xfree (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_printf (", q0=%u", mpi_get_nbits (q_factor));
|
||
for (i = 0; i < n; i++)
|
||
log_printf (", p%d=%u", i, mpi_get_nbits (factors[i]));
|
||
log_printf ("\n");
|
||
}
|
||
|
||
if (ret_factors)
|
||
{
|
||
/* Caller wants the factors. */
|
||
factors_new = xtrycalloc (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++] = 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 && need_q_factor)
|
||
err = GPG_ERR_NOT_IMPLEMENTED;
|
||
else 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));
|
||
|
||
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_printmpi ("checking g", g);
|
||
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. */
|
||
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 = !gpgrt_lock_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)
|
||
err = gpgrt_lock_unlock (&primepool_lock);
|
||
is_locked = 0;
|
||
xfree (pool);
|
||
}
|
||
xfree (pool_in_use);
|
||
if (factors)
|
||
xfree (factors); /* Factors are shallow copies. */
|
||
if (perms)
|
||
xfree (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]);
|
||
xfree (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. On success
|
||
R_PRIME receives a new MPI with the prime. On error R_PRIME is set
|
||
to NULL and an error code is returned. If RET_FACTORS is not NULL
|
||
it is set to an allocated array of factors on success or to NULL on
|
||
error. */
|
||
gcry_err_code_t
|
||
_gcry_generate_elg_prime (int mode, unsigned pbits, unsigned qbits,
|
||
gcry_mpi_t g,
|
||
gcry_mpi_t *r_prime, gcry_mpi_t **ret_factors)
|
||
{
|
||
*r_prime = NULL;
|
||
if (ret_factors)
|
||
*ret_factors = NULL;
|
||
return prime_generate_internal ((mode == 1), r_prime, pbits, qbits, g,
|
||
ret_factors, GCRY_WEAK_RANDOM, 0, 0,
|
||
NULL, NULL);
|
||
}
|
||
|
||
|
||
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 = (secret? xmalloc_secure (no_of_small_prime_numbers * sizeof *mods)
|
||
/* */ : 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? mpi_snew (nbits): 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);
|
||
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);
|
||
xfree(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 !mpi_cmp_ui (prime, x);
|
||
}
|
||
|
||
/* 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);
|
||
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
|
||
{
|
||
/* We need to loop to avoid an X with value 0 or 1. */
|
||
do
|
||
{
|
||
_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);
|
||
}
|
||
}
|
||
while (mpi_cmp_ui (x, 1) <= 0);
|
||
gcry_assert (mpi_cmp (x, nminus1) < 0);
|
||
}
|
||
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++ )
|
||
{
|
||
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_err_code_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 rc = 0;
|
||
gcry_mpi_t *factors_generated = NULL;
|
||
gcry_mpi_t prime_generated = NULL;
|
||
unsigned int mode = 0;
|
||
|
||
if (!prime)
|
||
return GPG_ERR_INV_ARG;
|
||
*prime = NULL;
|
||
|
||
if (flags & GCRY_PRIME_FLAG_SPECIAL_FACTOR)
|
||
mode = 1;
|
||
|
||
/* Generate. */
|
||
rc = 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 (!rc && 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]);
|
||
xfree (factors_generated);
|
||
}
|
||
rc = GPG_ERR_GENERAL;
|
||
}
|
||
}
|
||
|
||
if (!rc)
|
||
{
|
||
if (factors)
|
||
*factors = factors_generated;
|
||
*prime = prime_generated;
|
||
}
|
||
|
||
return rc;
|
||
}
|
||
|
||
/* Check whether the number X is prime. */
|
||
gcry_err_code_t
|
||
_gcry_prime_check (gcry_mpi_t x, unsigned int flags)
|
||
{
|
||
(void)flags;
|
||
|
||
switch (mpi_cmp_ui (x, 2))
|
||
{
|
||
case 0: return 0; /* 2 is a prime */
|
||
case -1: return GPG_ERR_NO_PRIME; /* Only numbers > 1 are primes. */
|
||
}
|
||
|
||
/* We use 64 rounds because the prime we are going to test is not
|
||
guaranteed to be a random one. */
|
||
if (check_prime (x, mpi_const (MPI_C_TWO), 64, NULL, NULL))
|
||
return 0;
|
||
|
||
return GPG_ERR_NO_PRIME;
|
||
}
|
||
|
||
|
||
/* Check whether the number X is prime according to FIPS 186-4 table C.2. */
|
||
gcry_err_code_t
|
||
_gcry_fips186_4_prime_check (gcry_mpi_t x, unsigned int bits)
|
||
{
|
||
gcry_err_code_t ec = GPG_ERR_NO_ERROR;
|
||
|
||
switch (mpi_cmp_ui (x, 2))
|
||
{
|
||
case 0: return ec; /* 2 is a prime */
|
||
case -1: return GPG_ERR_NO_PRIME; /* Only numbers > 1 are primes. */
|
||
}
|
||
|
||
/* We use 5 or 4 rounds as specified in table C.2 */
|
||
if (! check_prime (x, mpi_const (MPI_C_TWO), bits > 1024 ? 4 : 5, NULL, NULL))
|
||
ec = GPG_ERR_NO_PRIME;
|
||
|
||
return ec;
|
||
}
|
||
|
||
|
||
/* 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_err_code_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, b, pmin1, g;
|
||
int first, i, n;
|
||
|
||
if (!r_g)
|
||
return GPG_ERR_INV_ARG;
|
||
*r_g = NULL;
|
||
if (!factors || !prime)
|
||
return GPG_ERR_INV_ARG;
|
||
|
||
for (n=0; factors[n]; n++)
|
||
;
|
||
if (n < 2)
|
||
return GPG_ERR_INV_ARG;
|
||
|
||
tmp = mpi_new (0);
|
||
b = mpi_new (0);
|
||
pmin1 = mpi_new (0);
|
||
g = start_g? mpi_copy (start_g) : mpi_set_ui (NULL, 3);
|
||
|
||
/* 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); */
|
||
|
||
mpi_sub_ui (pmin1, prime, 1);
|
||
first = 1;
|
||
do
|
||
{
|
||
if (first)
|
||
first = 0;
|
||
else
|
||
mpi_add_ui (g, g, 1);
|
||
|
||
if (DBG_CIPHER)
|
||
log_printmpi ("checking g", g);
|
||
else
|
||
progress('^');
|
||
|
||
for (i = 0; i < n; i++)
|
||
{
|
||
mpi_fdiv_q (tmp, pmin1, factors[i]);
|
||
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]);
|
||
xfree (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 = 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 implementation 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_has_sign (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 = 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 = xtrymalloc (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 = mpi_new (pbits);
|
||
value_x = 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 = _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 = 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 = _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);
|
||
xfree (seed_plus);
|
||
_gcry_mpi_release (val_2);
|
||
return ec;
|
||
}
|
||
|
||
|
||
|
||
/* WARNING: The code below has not yet been tested!
|
||
*
|
||
* 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-2 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 == 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 = _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 = xtrymalloc (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 = mpi_new (pbits);
|
||
value_x = 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 = _gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG,
|
||
value_u, qbits/8, 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 = 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 (hashalgo, digest, seed_plus, seedlen);
|
||
|
||
_gcry_mpi_release (tmpval); tmpval = NULL;
|
||
ec = _gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG,
|
||
digest, qbits/8, 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_printmpi ("fips186-3 p", prime_p); */
|
||
/* log_printmpi ("fips186-3 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);
|
||
xfree (seed_plus);
|
||
_gcry_mpi_release (val_2);
|
||
return ec;
|
||
}
|