diff options
Diffstat (limited to 'grub-core/lib/libgcrypt/cipher/primegen.c')
| -rw-r--r-- | grub-core/lib/libgcrypt/cipher/primegen.c | 1861 |
1 files changed, 1861 insertions, 0 deletions
diff --git a/grub-core/lib/libgcrypt/cipher/primegen.c b/grub-core/lib/libgcrypt/cipher/primegen.c new file mode 100644 index 0000000..b12e79b --- /dev/null +++ b/grub-core/lib/libgcrypt/cipher/primegen.c @@ -0,0 +1,1861 @@ +/* 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_calloc (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_mpi_t prime = NULL; + + if (prime_generate_internal ((mode == 1), &prime, pbits, qbits, g, + ret_factors, GCRY_WEAK_RANDOM, 0, 0, + NULL, NULL)) + prime = NULL; /* (Should be NULL in the error case anyway.) */ + + 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_xcalloc( no_of_small_prime_numbers, sizeof *mods); + /* Make nbits fit into gcry_mpi_t implementation. */ + val_2 = mpi_alloc_set_ui( 2 ); + val_3 = mpi_alloc_set_ui( 3); + prime = secret? gcry_mpi_snew ( nbits ): gcry_mpi_new ( nbits ); + result = mpi_alloc_like( prime ); + pminus1= mpi_alloc_like( prime ); + ptest = mpi_alloc_like( prime ); + count1 = count2 = 0; + for (;;) + { /* try forvever */ + int dotcount=0; + + /* generate a random number */ + gcry_mpi_randomize( prime, nbits, randomlevel ); + + /* Set high order bit to 1, set low order bit to 1. If we are + generating a secret prime we are most probably doing that + for RSA, to make sure that the modulus does have the + requested key size we set the 2 high order bits. */ + mpi_set_highbit (prime, nbits-1); + if (secret) + mpi_set_bit (prime, nbits-2); + mpi_set_bit(prime, 0); + + /* Calculate all remainders. */ + for (i=0; (x = small_prime_numbers[i]); i++ ) + mods[i] = mpi_fdiv_r_ui(NULL, prime, x); + + /* Now try some primes starting with prime. */ + for(step=0; step < 20000; step += 2 ) + { + /* Check against all the small primes we have in mods. */ + count1++; + for (i=0; (x = small_prime_numbers[i]); i++ ) + { + while ( mods[i] + step >= x ) + mods[i] -= x; + if ( !(mods[i] + step) ) + break; + } + if ( x ) + continue; /* Found a multiple of an already known prime. */ + + mpi_add_ui( ptest, prime, step ); + + /* Do a fast Fermat test now. */ + count2++; + mpi_sub_ui( pminus1, ptest, 1); + gcry_mpi_powm( result, val_2, pminus1, ptest ); + if ( !mpi_cmp_ui( result, 1 ) ) + { + /* Not composite, perform stronger tests */ + if (is_prime(ptest, 5, &count2 )) + { + if (!mpi_test_bit( ptest, nbits-1-secret )) + { + progress('\n'); + log_debug ("overflow in prime generation\n"); + break; /* Stop loop, continue with a new prime. */ + } + + if (extra_check && extra_check (extra_check_arg, ptest)) + { + /* The extra check told us that this prime is + not of the caller's taste. */ + progress ('/'); + } + else + { + /* Got it. */ + mpi_free(val_2); + mpi_free(val_3); + mpi_free(result); + mpi_free(pminus1); + mpi_free(prime); + gcry_free(mods); + return ptest; + } + } + } + if (++dotcount == 10 ) + { + progress('.'); + dotcount = 0; + } + } + progress(':'); /* restart with a new random value */ + } +} + +/**************** + * Returns: true if this may be a prime + * RM_ROUNDS gives the number of Rabin-Miller tests to run. + */ +static int +check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, int rm_rounds, + gcry_prime_check_func_t cb_func, void *cb_arg) +{ + int i; + unsigned int x; + unsigned int count=0; + + /* Check against small primes. */ + for (i=0; (x = small_prime_numbers[i]); i++ ) + { + if ( mpi_divisible_ui( prime, x ) ) + return 0; + } + + /* A quick Fermat test. */ + { + gcry_mpi_t result = mpi_alloc_like( prime ); + gcry_mpi_t pminus1 = mpi_alloc_like( prime ); + mpi_sub_ui( pminus1, prime, 1); + gcry_mpi_powm( result, val_2, pminus1, prime ); + mpi_free( pminus1 ); + if ( mpi_cmp_ui( result, 1 ) ) + { + /* Is composite. */ + mpi_free( result ); + progress('.'); + return 0; + } + mpi_free( result ); + } + + if (!cb_func || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_MAYBE_PRIME, prime)) + { + /* Perform stronger tests. */ + if ( is_prime( prime, rm_rounds, &count ) ) + { + if (!cb_func + || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_GOT_PRIME, prime)) + return 1; /* Probably a prime. */ + } + } + progress('.'); + return 0; +} + + +/* + * Return true if n is probably a prime + */ +static int +is_prime (gcry_mpi_t n, int steps, unsigned int *count) +{ + gcry_mpi_t x = mpi_alloc( mpi_get_nlimbs( n ) ); + gcry_mpi_t y = mpi_alloc( mpi_get_nlimbs( n ) ); + gcry_mpi_t z = mpi_alloc( mpi_get_nlimbs( n ) ); + gcry_mpi_t nminus1 = mpi_alloc( mpi_get_nlimbs( n ) ); + gcry_mpi_t a2 = mpi_alloc_set_ui( 2 ); + gcry_mpi_t q; + unsigned i, j, k; + int rc = 0; + unsigned nbits = mpi_get_nbits( n ); + + if (steps < 5) /* Make sure that we do at least 5 rounds. */ + steps = 5; + + mpi_sub_ui( nminus1, n, 1 ); + + /* Find q and k, so that n = 1 + 2^k * q . */ + q = mpi_copy ( nminus1 ); + k = mpi_trailing_zeros ( q ); + mpi_tdiv_q_2exp (q, q, k); + + for (i=0 ; i < steps; i++ ) + { + ++*count; + if( !i ) + { + mpi_set_ui( x, 2 ); + } + else + { + gcry_mpi_randomize( x, nbits, GCRY_WEAK_RANDOM ); + + /* Make sure that the number is smaller than the prime and + keep the randomness of the high bit. */ + if ( mpi_test_bit ( x, nbits-2) ) + { + mpi_set_highbit ( x, nbits-2); /* Clear all higher bits. */ + } + else + { + mpi_set_highbit( x, nbits-2 ); + mpi_clear_bit( x, nbits-2 ); + } + gcry_assert (mpi_cmp (x, nminus1) < 0 && mpi_cmp_ui (x, 1) > 0); + } + gcry_mpi_powm ( y, x, q, n); + if ( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) ) + { + for ( j=1; j < k && mpi_cmp( y, nminus1 ); j++ ) + { + gcry_mpi_powm(y, y, a2, n); + if( !mpi_cmp_ui( y, 1 ) ) + goto leave; /* Not a prime. */ + } + if (mpi_cmp( y, nminus1 ) ) + goto leave; /* Not a prime. */ + } + progress('+'); + } + rc = 1; /* May be a prime. */ + + leave: + mpi_free( x ); + mpi_free( y ); + mpi_free( z ); + mpi_free( nminus1 ); + mpi_free( q ); + mpi_free( a2 ); + + return rc; +} + + +/* Given ARRAY of size N with M elements set to true produce a + modified array with the next permutation of M elements. Note, that + ARRAY is used in a one-bit-per-byte approach. To detected the last + permutation it is useful to initialize the array with the first M + element set to true and use this test: + m_out_of_n (array, m, n); + for (i = j = 0; i < n && j < m; i++) + if (array[i]) + j++; + if (j == m) + goto ready; + + This code is based on the algorithm 452 from the "Collected + Algorithms From ACM, Volume II" by C. N. Liu and D. T. Tang. +*/ +static void +m_out_of_n ( char *array, int m, int n ) +{ + int i=0, i1=0, j=0, jp=0, j1=0, k1=0, k2=0; + + if( !m || m >= n ) + return; + + /* Need to handle this simple case separately. */ + if( m == 1 ) + { + for (i=0; i < n; i++ ) + { + if ( array[i] ) + { + array[i++] = 0; + if( i >= n ) + i = 0; + array[i] = 1; + return; + } + } + BUG(); + } + + + for (j=1; j < n; j++ ) + { + if ( array[n-1] == array[n-j-1]) + continue; + j1 = j; + break; + } + + if ( (m & 1) ) + { + /* M is odd. */ + if( array[n-1] ) + { + if( j1 & 1 ) + { + k1 = n - j1; + k2 = k1+2; + if( k2 > n ) + k2 = n; + goto leave; + } + goto scan; + } + k2 = n - j1 - 1; + if( k2 == 0 ) + { + k1 = i; + k2 = n - j1; + } + else if( array[k2] && array[k2-1] ) + k1 = n; + else + k1 = k2 + 1; + } + else + { + /* M is even. */ + if( !array[n-1] ) + { + k1 = n - j1; + k2 = k1 + 1; + goto leave; + } + + if( !(j1 & 1) ) + { + k1 = n - j1; + k2 = k1+2; + if( k2 > n ) + k2 = n; + goto leave; + } + scan: + jp = n - j1 - 1; + for (i=1; i <= jp; i++ ) + { + i1 = jp + 2 - i; + if( array[i1-1] ) + { + if( array[i1-2] ) + { + k1 = i1 - 1; + k2 = n - j1; + } + else + { + k1 = i1 - 1; + k2 = n + 1 - j1; + } + goto leave; + } + } + k1 = 1; + k2 = n + 1 - m; + } + leave: + /* Now complement the two selected bits. */ + array[k1-1] = !array[k1-1]; + array[k2-1] = !array[k2-1]; +} + + +/* Generate a new prime number of PRIME_BITS bits and store it in + PRIME. If FACTOR_BITS is non-zero, one of the prime factors of + (prime - 1) / 2 must be FACTOR_BITS bits long. If FACTORS is + non-zero, allocate a new, NULL-terminated array holding the prime + factors and store it in FACTORS. FLAGS might be used to influence + the prime number generation process. */ +gcry_error_t +gcry_prime_generate (gcry_mpi_t *prime, unsigned int prime_bits, + unsigned int factor_bits, gcry_mpi_t **factors, + gcry_prime_check_func_t cb_func, void *cb_arg, + gcry_random_level_t random_level, + unsigned int flags) +{ + gcry_err_code_t err = GPG_ERR_NO_ERROR; + gcry_mpi_t *factors_generated = NULL; + gcry_mpi_t prime_generated = NULL; + unsigned int mode = 0; + + if (!prime) + return gpg_error (GPG_ERR_INV_ARG); + *prime = NULL; + + if (flags & GCRY_PRIME_FLAG_SPECIAL_FACTOR) + mode = 1; + + /* Generate. */ + err = prime_generate_internal ((mode==1), &prime_generated, prime_bits, + factor_bits, NULL, + factors? &factors_generated : NULL, + random_level, flags, 1, + cb_func, cb_arg); + + if (! err) + if (cb_func) + { + /* Additional check. */ + if ( !cb_func (cb_arg, GCRY_PRIME_CHECK_AT_FINISH, prime_generated)) + { + /* Failed, deallocate resources. */ + unsigned int i; + + mpi_free (prime_generated); + if (factors) + { + for (i = 0; factors_generated[i]; i++) + mpi_free (factors_generated[i]); + gcry_free (factors_generated); + } + err = GPG_ERR_GENERAL; + } + } + + if (! err) + { + if (factors) + *factors = factors_generated; + *prime = prime_generated; + } + + return gcry_error (err); +} + +/* Check whether the number X is prime. */ +gcry_error_t +gcry_prime_check (gcry_mpi_t x, unsigned int flags) +{ + gcry_err_code_t err = GPG_ERR_NO_ERROR; + gcry_mpi_t val_2 = mpi_alloc_set_ui (2); /* Used by the Fermat test. */ + + (void)flags; + + /* We use 64 rounds because the prime we are going to test is not + guaranteed to be a random one. */ + if (! check_prime (x, val_2, 64, NULL, NULL)) + err = GPG_ERR_NO_PRIME; + + mpi_free (val_2); + + return gcry_error (err); +} + +/* Find a generator for PRIME where the factorization of (prime-1) is + in the NULL terminated array FACTORS. Return the generator as a + newly allocated MPI in R_G. If START_G is not NULL, use this as s + atart for the search. Returns 0 on success.*/ +gcry_error_t +gcry_prime_group_generator (gcry_mpi_t *r_g, + gcry_mpi_t prime, gcry_mpi_t *factors, + gcry_mpi_t start_g) +{ + gcry_mpi_t tmp = gcry_mpi_new (0); + gcry_mpi_t b = gcry_mpi_new (0); + gcry_mpi_t pmin1 = gcry_mpi_new (0); + gcry_mpi_t g = start_g? gcry_mpi_copy (start_g) : gcry_mpi_set_ui (NULL, 3); + int first = 1; + int i, n; + + if (!factors || !r_g || !prime) + return gpg_error (GPG_ERR_INV_ARG); + *r_g = NULL; + + for (n=0; factors[n]; n++) + ; + if (n < 2) + return gpg_error (GPG_ERR_INV_ARG); + + /* Extra sanity check - usually disabled. */ +/* mpi_set (tmp, factors[0]); */ +/* for(i = 1; i < n; i++) */ +/* mpi_mul (tmp, tmp, factors[i]); */ +/* mpi_add_ui (tmp, tmp, 1); */ +/* if (mpi_cmp (prime, tmp)) */ +/* return gpg_error (GPG_ERR_INV_ARG); */ + + gcry_mpi_sub_ui (pmin1, prime, 1); + do + { + if (first) + first = 0; + else + gcry_mpi_add_ui (g, g, 1); + + if (DBG_CIPHER) + { + log_debug ("checking g:"); + gcry_mpi_dump (g); + log_debug ("\n"); + } + else + progress('^'); + + for (i = 0; i < n; i++) + { + mpi_fdiv_q (tmp, pmin1, factors[i]); + gcry_mpi_powm (b, g, tmp, prime); + if (! mpi_cmp_ui (b, 1)) + break; + } + if (DBG_CIPHER) + progress('\n'); + } + while (i < n); + + gcry_mpi_release (tmp); + gcry_mpi_release (b); + gcry_mpi_release (pmin1); + *r_g = g; + + return 0; +} + +/* Convenience function to release the factors array. */ +void +gcry_prime_release_factors (gcry_mpi_t *factors) +{ + if (factors) + { + int i; + + for (i=0; factors[i]; i++) + mpi_free (factors[i]); + gcry_free (factors); + } +} + + + +/* Helper for _gcry_derive_x931_prime. */ +static gcry_mpi_t +find_x931_prime (const gcry_mpi_t pfirst) +{ + gcry_mpi_t val_2 = mpi_alloc_set_ui (2); + gcry_mpi_t prime; + + prime = gcry_mpi_copy (pfirst); + /* If P is even add 1. */ + mpi_set_bit (prime, 0); + + /* We use 64 Rabin-Miller rounds which is better and thus + sufficient. We do not have a Lucas test implementaion thus we + can't do it in the X9.31 preferred way of running a few + Rabin-Miller followed by one Lucas test. */ + while ( !check_prime (prime, val_2, 64, NULL, NULL) ) + mpi_add_ui (prime, prime, 2); + + mpi_free (val_2); + + return prime; +} + + +/* Generate a prime using the algorithm from X9.31 appendix B.4. + + This function requires that the provided public exponent E is odd. + XP, XP1 and XP2 are the seed values. All values are mandatory. + + On success the prime is returned. If R_P1 or R_P2 are given the + internal values P1 and P2 are saved at these addresses. On error + NULL is returned. */ +gcry_mpi_t +_gcry_derive_x931_prime (const gcry_mpi_t xp, + const gcry_mpi_t xp1, const gcry_mpi_t xp2, + const gcry_mpi_t e, + gcry_mpi_t *r_p1, gcry_mpi_t *r_p2) +{ + gcry_mpi_t p1, p2, p1p2, yp0; + + if (!xp || !xp1 || !xp2) + return NULL; + if (!e || !mpi_test_bit (e, 0)) + return NULL; /* We support only odd values for E. */ + + p1 = find_x931_prime (xp1); + p2 = find_x931_prime (xp2); + p1p2 = mpi_alloc_like (xp); + mpi_mul (p1p2, p1, p2); + + { + gcry_mpi_t r1, tmp; + + /* r1 = (p2^{-1} mod p1)p2 - (p1^{-1} mod p2) */ + tmp = mpi_alloc_like (p1); + mpi_invm (tmp, p2, p1); + mpi_mul (tmp, tmp, p2); + r1 = tmp; + + tmp = mpi_alloc_like (p2); + mpi_invm (tmp, p1, p2); + mpi_mul (tmp, tmp, p1); + mpi_sub (r1, r1, tmp); + + /* Fixup a negative value. */ + if (mpi_is_neg (r1)) + mpi_add (r1, r1, p1p2); + + /* yp0 = xp + (r1 - xp mod p1*p2) */ + yp0 = tmp; tmp = NULL; + mpi_subm (yp0, r1, xp, p1p2); + mpi_add (yp0, yp0, xp); + mpi_free (r1); + + /* Fixup a negative value. */ + if (mpi_cmp (yp0, xp) < 0 ) + mpi_add (yp0, yp0, p1p2); + } + + /* yp0 is now the first integer greater than xp with p1 being a + large prime factor of yp0-1 and p2 a large prime factor of yp0+1. */ + + /* Note that the first example from X9.31 (D.1.1) which uses + (Xq1 #1A5CF72EE770DE50CB09ACCEA9#) + (Xq2 #134E4CAA16D2350A21D775C404#) + (Xq #CC1092495D867E64065DEE3E7955F2EBC7D47A2D + 7C9953388F97DDDC3E1CA19C35CA659EDC2FC325 + 6D29C2627479C086A699A49C4C9CEE7EF7BD1B34 + 321DE34A#)))) + returns an yp0 of + #CC1092495D867E64065DEE3E7955F2EBC7D47A2D + 7C9953388F97DDDC3E1CA19C35CA659EDC2FC4E3 + BF20CB896EE37E098A906313271422162CB6C642 + 75C1201F# + and not + #CC1092495D867E64065DEE3E7955F2EBC7D47A2D + 7C9953388F97DDDC3E1CA19C35CA659EDC2FC2E6 + C88FE299D52D78BE405A97E01FD71DD7819ECB91 + FA85A076# + as stated in the standard. This seems to be a bug in X9.31. + */ + + { + gcry_mpi_t val_2 = mpi_alloc_set_ui (2); + gcry_mpi_t gcdtmp = mpi_alloc_like (yp0); + int gcdres; + + mpi_sub_ui (p1p2, p1p2, 1); /* Adjust for loop body. */ + mpi_sub_ui (yp0, yp0, 1); /* Ditto. */ + for (;;) + { + gcdres = gcry_mpi_gcd (gcdtmp, e, yp0); + mpi_add_ui (yp0, yp0, 1); + if (!gcdres) + progress ('/'); /* gcd (e, yp0-1) != 1 */ + else if (check_prime (yp0, val_2, 64, NULL, NULL)) + break; /* Found. */ + /* We add p1p2-1 because yp0 is incremented after the gcd test. */ + mpi_add (yp0, yp0, p1p2); + } + mpi_free (gcdtmp); + mpi_free (val_2); + } + + mpi_free (p1p2); + + progress('\n'); + if (r_p1) + *r_p1 = p1; + else + mpi_free (p1); + if (r_p2) + *r_p2 = p2; + else + mpi_free (p2); + return yp0; +} + + + +/* Generate the two prime used for DSA using the algorithm specified + in FIPS 186-2. PBITS is the desired length of the prime P and a + QBITS the length of the prime Q. If SEED is not supplied and + SEEDLEN is 0 the function generates an appropriate SEED. On + success the generated primes are stored at R_Q and R_P, the counter + value is stored at R_COUNTER and the seed actually used for + generation is stored at R_SEED and R_SEEDVALUE. */ +gpg_err_code_t +_gcry_generate_fips186_2_prime (unsigned int pbits, unsigned int qbits, + const void *seed, size_t seedlen, + gcry_mpi_t *r_q, gcry_mpi_t *r_p, + int *r_counter, + void **r_seed, size_t *r_seedlen) +{ + gpg_err_code_t ec; + unsigned char seed_help_buffer[160/8]; /* Used to hold a generated SEED. */ + unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */ + unsigned char digest[160/8]; /* Helper buffer for SHA-1 digest. */ + gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */ + gcry_mpi_t tmpval = NULL; /* Helper variable. */ + int i; + + unsigned char value_u[160/8]; + int value_n, value_b, value_k; + int counter; + gcry_mpi_t value_w = NULL; + gcry_mpi_t value_x = NULL; + gcry_mpi_t prime_q = NULL; + gcry_mpi_t prime_p = NULL; + + /* FIPS 186-2 allows only for 1024/160 bit. */ + if (pbits != 1024 || qbits != 160) + return GPG_ERR_INV_KEYLEN; + + if (!seed && !seedlen) + ; /* No seed value given: We are asked to generate it. */ + else if (!seed || seedlen < qbits/8) + return GPG_ERR_INV_ARG; + + /* Allocate a buffer to later compute SEED+some_increment. */ + seed_plus = gcry_malloc (seedlen < 20? 20:seedlen); + if (!seed_plus) + { + ec = gpg_err_code_from_syserror (); + goto leave; + } + + val_2 = mpi_alloc_set_ui (2); + value_n = (pbits - 1) / qbits; + value_b = (pbits - 1) - value_n * qbits; + value_w = gcry_mpi_new (pbits); + value_x = gcry_mpi_new (pbits); + + restart: + /* Generate Q. */ + for (;;) + { + /* Step 1: Generate a (new) seed unless one has been supplied. */ + if (!seed) + { + seedlen = sizeof seed_help_buffer; + gcry_create_nonce (seed_help_buffer, seedlen); + seed = seed_help_buffer; + } + + /* Step 2: U = sha1(seed) ^ sha1((seed+1) mod 2^{qbits}) */ + memcpy (seed_plus, seed, seedlen); + for (i=seedlen-1; i >= 0; i--) + { + seed_plus[i]++; + if (seed_plus[i]) + break; + } + gcry_md_hash_buffer (GCRY_MD_SHA1, value_u, seed, seedlen); + gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen); + for (i=0; i < sizeof value_u; i++) + value_u[i] ^= digest[i]; + + /* Step 3: Form q from U */ + gcry_mpi_release (prime_q); prime_q = NULL; + ec = gpg_err_code (gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG, + value_u, sizeof value_u, NULL)); + if (ec) + goto leave; + mpi_set_highbit (prime_q, qbits-1 ); + mpi_set_bit (prime_q, 0); + + /* Step 4: Test whether Q is prime using 64 round of Rabin-Miller. */ + if (check_prime (prime_q, val_2, 64, NULL, NULL)) + break; /* Yes, Q is prime. */ + + /* Step 5. */ + seed = NULL; /* Force a new seed at Step 1. */ + } + + /* Step 6. Note that we do no use an explicit offset but increment + SEED_PLUS accordingly. SEED_PLUS is currently SEED+1. */ + counter = 0; + + /* Generate P. */ + prime_p = gcry_mpi_new (pbits); + for (;;) + { + /* Step 7: For k = 0,...n let + V_k = sha1(seed+offset+k) mod 2^{qbits} + Step 8: W = V_0 + V_1*2^160 + + ... + + V_{n-1}*2^{(n-1)*160} + + (V_{n} mod 2^b)*2^{n*160} + */ + mpi_set_ui (value_w, 0); + for (value_k=0; value_k <= value_n; value_k++) + { + /* There is no need to have an explicit offset variable: In + the first round we shall have an offset of 2, this is + achieved by using SEED_PLUS which is already at SEED+1, + thus we just need to increment it once again. The + requirement for the next round is to update offset by N, + which we implictly did at the end of this loop, and then + to add one; this one is the same as in the first round. */ + for (i=seedlen-1; i >= 0; i--) + { + seed_plus[i]++; + if (seed_plus[i]) + break; + } + gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen); + + gcry_mpi_release (tmpval); tmpval = NULL; + ec = gpg_err_code (gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG, + digest, sizeof digest, NULL)); + if (ec) + goto leave; + if (value_k == value_n) + mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */ + mpi_lshift (tmpval, tmpval, value_k*qbits); + mpi_add (value_w, value_w, tmpval); + } + + /* Step 8 continued: X = W + 2^{L-1} */ + mpi_set_ui (value_x, 0); + mpi_set_highbit (value_x, pbits-1); + mpi_add (value_x, value_x, value_w); + + /* Step 9: c = X mod 2q, p = X - (c - 1) */ + mpi_mul_2exp (tmpval, prime_q, 1); + mpi_mod (tmpval, value_x, tmpval); + mpi_sub_ui (tmpval, tmpval, 1); + mpi_sub (prime_p, value_x, tmpval); + + /* Step 10: If p < 2^{L-1} skip the primality test. */ + /* Step 11 and 12: Primality test. */ + if (mpi_get_nbits (prime_p) >= pbits-1 + && check_prime (prime_p, val_2, 64, NULL, NULL) ) + break; /* Yes, P is prime, continue with Step 15. */ + + /* Step 13: counter = counter + 1, offset = offset + n + 1. */ + counter++; + + /* Step 14: If counter >= 2^12 goto Step 1. */ + if (counter >= 4096) + goto restart; + } + + /* Step 15: Save p, q, counter and seed. */ +/* log_debug ("fips186-2 pbits p=%u q=%u counter=%d\n", */ +/* mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter); */ +/* log_printhex("fips186-2 seed:", seed, seedlen); */ +/* log_mpidump ("fips186-2 prime p", prime_p); */ +/* log_mpidump ("fips186-2 prime q", prime_q); */ + if (r_q) + { + *r_q = prime_q; + prime_q = NULL; + } + if (r_p) + { + *r_p = prime_p; + prime_p = NULL; + } + if (r_counter) + *r_counter = counter; + if (r_seed && r_seedlen) + { + memcpy (seed_plus, seed, seedlen); + *r_seed = seed_plus; + seed_plus = NULL; + *r_seedlen = seedlen; + } + + + leave: + gcry_mpi_release (tmpval); + gcry_mpi_release (value_x); + gcry_mpi_release (value_w); + gcry_mpi_release (prime_p); + gcry_mpi_release (prime_q); + gcry_free (seed_plus); + gcry_mpi_release (val_2); + return ec; +} + + + +/* WARNING: The code below has not yet been tested! However, it is + not yet used. We need to wait for FIPS 186-3 final and for test + vectors. + + Generate the two prime used for DSA using the algorithm specified + in FIPS 186-3, A.1.1.2. PBITS is the desired length of the prime P + and a QBITS the length of the prime Q. If SEED is not supplied and + SEEDLEN is 0 the function generates an appropriate SEED. On + success the generated primes are stored at R_Q and R_P, the counter + value is stored at R_COUNTER and the seed actually used for + generation is stored at R_SEED and R_SEEDVALUE. The hash algorithm + used is stored at R_HASHALGO. + + Note that this function is very similar to the fips186_2 code. Due + to the minor differences, other buffer sizes and for documentarion, + we use a separate function. +*/ +gpg_err_code_t +_gcry_generate_fips186_3_prime (unsigned int pbits, unsigned int qbits, + const void *seed, size_t seedlen, + gcry_mpi_t *r_q, gcry_mpi_t *r_p, + int *r_counter, + void **r_seed, size_t *r_seedlen, + int *r_hashalgo) +{ + gpg_err_code_t ec; + unsigned char seed_help_buffer[256/8]; /* Used to hold a generated SEED. */ + unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */ + unsigned char digest[256/8]; /* Helper buffer for SHA-1 digest. */ + gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */ + gcry_mpi_t tmpval = NULL; /* Helper variable. */ + int hashalgo; /* The id of the Approved Hash Function. */ + int i; + + unsigned char value_u[256/8]; + int value_n, value_b, value_j; + int counter; + gcry_mpi_t value_w = NULL; + gcry_mpi_t value_x = NULL; + gcry_mpi_t prime_q = NULL; + gcry_mpi_t prime_p = NULL; + + gcry_assert (sizeof seed_help_buffer == sizeof digest + && sizeof seed_help_buffer == sizeof value_u); + + /* Step 1: Check the requested prime lengths. */ + /* Note that due to the size of our buffers QBITS is limited to 256. */ + if (pbits == 1024 && qbits == 160) + hashalgo = GCRY_MD_SHA1; + else if (pbits == 2048 && qbits == 224) + hashalgo = GCRY_MD_SHA224; + else if (pbits == 2048 && qbits == 256) + hashalgo = GCRY_MD_SHA256; + else if (pbits == 3072 && qbits == 256) + hashalgo = GCRY_MD_SHA256; + else + return GPG_ERR_INV_KEYLEN; + + /* Also check that the hash algorithm is available. */ + ec = gpg_err_code (gcry_md_test_algo (hashalgo)); + if (ec) + return ec; + gcry_assert (qbits/8 <= sizeof digest); + gcry_assert (gcry_md_get_algo_dlen (hashalgo) == qbits/8); + + + /* Step 2: Check seedlen. */ + if (!seed && !seedlen) + ; /* No seed value given: We are asked to generate it. */ + else if (!seed || seedlen < qbits/8) + return GPG_ERR_INV_ARG; + + /* Allocate a buffer to later compute SEED+some_increment and a few + helper variables. */ + seed_plus = gcry_malloc (seedlen < sizeof seed_help_buffer? + sizeof seed_help_buffer : seedlen); + if (!seed_plus) + { + ec = gpg_err_code_from_syserror (); + goto leave; + } + val_2 = mpi_alloc_set_ui (2); + value_w = gcry_mpi_new (pbits); + value_x = gcry_mpi_new (pbits); + + /* Step 3: n = \lceil L / outlen \rceil - 1 */ + value_n = (pbits + qbits - 1) / qbits - 1; + /* Step 4: b = L - 1 - (n * outlen) */ + value_b = pbits - 1 - (value_n * qbits); + + restart: + /* Generate Q. */ + for (;;) + { + /* Step 5: Generate a (new) seed unless one has been supplied. */ + if (!seed) + { + seedlen = qbits/8; + gcry_assert (seedlen <= sizeof seed_help_buffer); + gcry_create_nonce (seed_help_buffer, seedlen); + seed = seed_help_buffer; + } + + /* Step 6: U = hash(seed) */ + gcry_md_hash_buffer (hashalgo, value_u, seed, seedlen); + + /* Step 7: q = 2^{N-1} + U + 1 - (U mod 2) */ + if ( !(value_u[qbits/8-1] & 0x01) ) + { + for (i=qbits/8-1; i >= 0; i--) + { + value_u[i]++; + if (value_u[i]) + break; + } + } + gcry_mpi_release (prime_q); prime_q = NULL; + ec = gpg_err_code (gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG, + value_u, sizeof value_u, NULL)); + if (ec) + goto leave; + mpi_set_highbit (prime_q, qbits-1 ); + + /* Step 8: Test whether Q is prime using 64 round of Rabin-Miller. + According to table C.1 this is sufficient for all + supported prime sizes (i.e. up 3072/256). */ + if (check_prime (prime_q, val_2, 64, NULL, NULL)) + break; /* Yes, Q is prime. */ + + /* Step 8. */ + seed = NULL; /* Force a new seed at Step 5. */ + } + + /* Step 11. Note that we do no use an explicit offset but increment + SEED_PLUS accordingly. */ + memcpy (seed_plus, seed, seedlen); + counter = 0; + + /* Generate P. */ + prime_p = gcry_mpi_new (pbits); + for (;;) + { + /* Step 11.1: For j = 0,...n let + V_j = hash(seed+offset+j) + Step 11.2: W = V_0 + V_1*2^outlen + + ... + + V_{n-1}*2^{(n-1)*outlen} + + (V_{n} mod 2^b)*2^{n*outlen} + */ + mpi_set_ui (value_w, 0); + for (value_j=0; value_j <= value_n; value_j++) + { + /* There is no need to have an explicit offset variable: In + the first round we shall have an offset of 1 and a j of + 0. This is achieved by incrementing SEED_PLUS here. For + the next round offset is implicitly updated by using + SEED_PLUS again. */ + for (i=seedlen-1; i >= 0; i--) + { + seed_plus[i]++; + if (seed_plus[i]) + break; + } + gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen); + + gcry_mpi_release (tmpval); tmpval = NULL; + ec = gpg_err_code (gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG, + digest, sizeof digest, NULL)); + if (ec) + goto leave; + if (value_j == value_n) + mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */ + mpi_lshift (tmpval, tmpval, value_j*qbits); + mpi_add (value_w, value_w, tmpval); + } + + /* Step 11.3: X = W + 2^{L-1} */ + mpi_set_ui (value_x, 0); + mpi_set_highbit (value_x, pbits-1); + mpi_add (value_x, value_x, value_w); + + /* Step 11.4: c = X mod 2q */ + mpi_mul_2exp (tmpval, prime_q, 1); + mpi_mod (tmpval, value_x, tmpval); + + /* Step 11.5: p = X - (c - 1) */ + mpi_sub_ui (tmpval, tmpval, 1); + mpi_sub (prime_p, value_x, tmpval); + + /* Step 11.6: If p < 2^{L-1} skip the primality test. */ + /* Step 11.7 and 11.8: Primality test. */ + if (mpi_get_nbits (prime_p) >= pbits-1 + && check_prime (prime_p, val_2, 64, NULL, NULL) ) + break; /* Yes, P is prime, continue with Step 15. */ + + /* Step 11.9: counter = counter + 1, offset = offset + n + 1. + If counter >= 4L goto Step 5. */ + counter++; + if (counter >= 4*pbits) + goto restart; + } + + /* Step 12: Save p, q, counter and seed. */ + log_debug ("fips186-3 pbits p=%u q=%u counter=%d\n", + mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter); + log_printhex("fips186-3 seed:", seed, seedlen); + log_mpidump ("fips186-3 prime p", prime_p); + log_mpidump ("fips186-3 prime q", prime_q); + if (r_q) + { + *r_q = prime_q; + prime_q = NULL; + } + if (r_p) + { + *r_p = prime_p; + prime_p = NULL; + } + if (r_counter) + *r_counter = counter; + if (r_seed && r_seedlen) + { + memcpy (seed_plus, seed, seedlen); + *r_seed = seed_plus; + seed_plus = NULL; + *r_seedlen = seedlen; + } + if (r_hashalgo) + *r_hashalgo = hashalgo; + + leave: + gcry_mpi_release (tmpval); + gcry_mpi_release (value_x); + gcry_mpi_release (value_w); + gcry_mpi_release (prime_p); + gcry_mpi_release (prime_q); + gcry_free (seed_plus); + gcry_mpi_release (val_2); + return ec; +} |