Line data Source code
1 : /* primegen.c - prime number generator
2 : * Copyright (C) 1998, 2000, 2001, 2002, 2003
3 : * 2004, 2008 Free Software Foundation, Inc.
4 : *
5 : * This file is part of Libgcrypt.
6 : *
7 : * Libgcrypt is free software; you can redistribute it and/or modify
8 : * it under the terms of the GNU Lesser general Public License as
9 : * published by the Free Software Foundation; either version 2.1 of
10 : * the License, or (at your option) any later version.
11 : *
12 : * Libgcrypt is distributed in the hope that it will be useful,
13 : * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 : * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 : * GNU Lesser General Public License for more details.
16 : *
17 : * You should have received a copy of the GNU Lesser General Public
18 : * License along with this program; if not, write to the Free Software
19 : * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
20 : */
21 :
22 : #include <config.h>
23 :
24 : #include <stdio.h>
25 : #include <stdlib.h>
26 : #include <string.h>
27 : #include <errno.h>
28 :
29 : #include "g10lib.h"
30 : #include "mpi.h"
31 : #include "cipher.h"
32 :
33 : static gcry_mpi_t gen_prime (unsigned int nbits, int secret, int randomlevel,
34 : int (*extra_check)(void *, gcry_mpi_t),
35 : void *extra_check_arg);
36 : static int check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, int rm_rounds,
37 : gcry_prime_check_func_t cb_func, void *cb_arg );
38 : static int is_prime (gcry_mpi_t n, int steps, unsigned int *count);
39 : static void m_out_of_n( char *array, int m, int n );
40 :
41 : static void (*progress_cb) (void *,const char*,int,int, int );
42 : static void *progress_cb_data;
43 :
44 : /* Note: 2 is not included because it can be tested more easily by
45 : looking at bit 0. The last entry in this list is marked by a zero */
46 : static ushort small_prime_numbers[] = {
47 : 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
48 : 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
49 : 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
50 : 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
51 : 211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
52 : 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
53 : 331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
54 : 389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
55 : 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
56 : 509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
57 : 587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
58 : 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
59 : 709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
60 : 773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
61 : 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
62 : 919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
63 : 991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
64 : 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
65 : 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
66 : 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
67 : 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
68 : 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
69 : 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
70 : 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
71 : 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
72 : 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
73 : 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
74 : 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
75 : 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
76 : 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
77 : 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
78 : 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
79 : 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
80 : 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
81 : 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
82 : 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
83 : 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
84 : 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
85 : 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
86 : 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
87 : 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
88 : 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
89 : 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
90 : 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
91 : 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
92 : 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
93 : 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
94 : 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
95 : 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
96 : 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
97 : 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
98 : 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
99 : 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
100 : 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
101 : 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
102 : 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
103 : 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
104 : 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
105 : 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
106 : 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
107 : 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
108 : 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
109 : 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
110 : 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
111 : 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
112 : 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
113 : 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
114 : 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
115 : 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
116 : 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
117 : 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
118 : 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
119 : 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
120 : 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
121 : 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
122 : 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
123 : 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
124 : 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
125 : 4957, 4967, 4969, 4973, 4987, 4993, 4999,
126 : 0
127 : };
128 : static int no_of_small_prime_numbers = DIM (small_prime_numbers) - 1;
129 :
130 :
131 :
132 : /* An object and a list to build up a global pool of primes. See
133 : save_pool_prime and get_pool_prime. */
134 : struct primepool_s
135 : {
136 : struct primepool_s *next;
137 : gcry_mpi_t prime; /* If this is NULL the entry is not used. */
138 : unsigned int nbits;
139 : gcry_random_level_t randomlevel;
140 : };
141 : struct primepool_s *primepool;
142 : /* Mutex used to protect access to the primepool. */
143 : GPGRT_LOCK_DEFINE (primepool_lock);
144 :
145 :
146 : gcry_err_code_t
147 0 : _gcry_primegen_init (void)
148 : {
149 : /* This function was formerly used to initialize the primepool
150 : Mutex. This has been replace by a static initialization. */
151 0 : return 0;
152 : }
153 :
154 :
155 : /* Save PRIME which has been generated at RANDOMLEVEL for later
156 : use. Needs to be called while primepool_lock is being hold. Note
157 : that PRIME should be considered released after calling this
158 : function. */
159 : static void
160 0 : save_pool_prime (gcry_mpi_t prime, gcry_random_level_t randomlevel)
161 : {
162 : struct primepool_s *item, *item2;
163 : size_t n;
164 :
165 0 : for (n=0, item = primepool; item; item = item->next, n++)
166 0 : if (!item->prime)
167 0 : break;
168 0 : if (!item && n > 100)
169 : {
170 : /* Remove some of the entries. Our strategy is removing
171 : the last third from the list. */
172 : int i;
173 :
174 0 : for (i=0, item2 = primepool; item2; item2 = item2->next)
175 : {
176 0 : if (i >= n/3*2)
177 : {
178 0 : _gcry_mpi_release (item2->prime);
179 0 : item2->prime = NULL;
180 0 : if (!item)
181 0 : item = item2;
182 : }
183 : }
184 : }
185 0 : if (!item)
186 : {
187 0 : item = xtrycalloc (1, sizeof *item);
188 0 : if (!item)
189 : {
190 : /* Out of memory. Silently giving up. */
191 0 : _gcry_mpi_release (prime);
192 0 : return;
193 : }
194 0 : item->next = primepool;
195 0 : primepool = item;
196 : }
197 0 : item->prime = prime;
198 0 : item->nbits = mpi_get_nbits (prime);
199 0 : item->randomlevel = randomlevel;
200 : }
201 :
202 :
203 : /* Return a prime for the prime pool or NULL if none has been found.
204 : The prime needs to match NBITS and randomlevel. This function needs
205 : to be called with the primepool_look is being hold. */
206 : static gcry_mpi_t
207 0 : get_pool_prime (unsigned int nbits, gcry_random_level_t randomlevel)
208 : {
209 : struct primepool_s *item;
210 :
211 0 : for (item = primepool; item; item = item->next)
212 0 : if (item->prime
213 0 : && item->nbits == nbits && item->randomlevel == randomlevel)
214 : {
215 0 : gcry_mpi_t prime = item->prime;
216 0 : item->prime = NULL;
217 0 : gcry_assert (nbits == mpi_get_nbits (prime));
218 0 : return prime;
219 : }
220 0 : return NULL;
221 : }
222 :
223 :
224 :
225 :
226 :
227 :
228 : void
229 0 : _gcry_register_primegen_progress ( void (*cb)(void *,const char*,int,int,int),
230 : void *cb_data )
231 : {
232 0 : progress_cb = cb;
233 0 : progress_cb_data = cb_data;
234 0 : }
235 :
236 :
237 : static void
238 0 : progress( int c )
239 : {
240 0 : if ( progress_cb )
241 0 : progress_cb ( progress_cb_data, "primegen", c, 0, 0 );
242 0 : }
243 :
244 :
245 : /****************
246 : * Generate a prime number (stored in secure memory)
247 : */
248 : gcry_mpi_t
249 0 : _gcry_generate_secret_prime (unsigned int nbits,
250 : gcry_random_level_t random_level,
251 : int (*extra_check)(void*, gcry_mpi_t),
252 : void *extra_check_arg)
253 : {
254 : gcry_mpi_t prime;
255 :
256 0 : prime = gen_prime (nbits, 1, random_level, extra_check, extra_check_arg);
257 0 : progress('\n');
258 0 : return prime;
259 : }
260 :
261 :
262 : /* Generate a prime number which may be public, i.e. not allocated in
263 : secure memory. */
264 : gcry_mpi_t
265 0 : _gcry_generate_public_prime (unsigned int nbits,
266 : gcry_random_level_t random_level,
267 : int (*extra_check)(void*, gcry_mpi_t),
268 : void *extra_check_arg)
269 : {
270 : gcry_mpi_t prime;
271 :
272 0 : prime = gen_prime (nbits, 0, random_level, extra_check, extra_check_arg);
273 0 : progress('\n');
274 0 : return prime;
275 : }
276 :
277 :
278 : /* Core prime generation function. The algorithm used to generate
279 : practically save primes is due to Lim and Lee as described in the
280 : CRYPTO '97 proceedings (ISBN3540633847) page 260.
281 :
282 : NEED_Q_FACTOR: If true make sure that at least one factor is of
283 : size qbits. This is for example required for DSA.
284 : PRIME_GENERATED: Adresss of a variable where the resulting prime
285 : number will be stored.
286 : PBITS: Requested size of the prime number. At least 48.
287 : QBITS: One factor of the prime needs to be of this size. Maybe 0
288 : if this is not required. See also MODE.
289 : G: If not NULL an MPI which will receive a generator for the prime
290 : for use with Elgamal.
291 : RET_FACTORS: if not NULL, an array with all factors are stored at
292 : that address.
293 : ALL_FACTORS: If set to true all factors of prime-1 are returned.
294 : RANDOMLEVEL: How strong should the random numers be.
295 : FLAGS: Prime generation bit flags. Currently supported:
296 : GCRY_PRIME_FLAG_SECRET - The prime needs to be kept secret.
297 : CB_FUNC, CB_ARG: Callback to be used for extra checks.
298 :
299 : */
300 : static gcry_err_code_t
301 0 : prime_generate_internal (int need_q_factor,
302 : gcry_mpi_t *prime_generated, unsigned int pbits,
303 : unsigned int qbits, gcry_mpi_t g,
304 : gcry_mpi_t **ret_factors,
305 : gcry_random_level_t randomlevel, unsigned int flags,
306 : int all_factors,
307 : gcry_prime_check_func_t cb_func, void *cb_arg)
308 : {
309 0 : gcry_err_code_t err = 0;
310 0 : gcry_mpi_t *factors_new = NULL; /* Factors to return to the
311 : caller. */
312 0 : gcry_mpi_t *factors = NULL; /* Current factors. */
313 : gcry_random_level_t poolrandomlevel; /* Random level used for pool primes. */
314 0 : gcry_mpi_t *pool = NULL; /* Pool of primes. */
315 0 : int *pool_in_use = NULL; /* Array with currently used POOL elements. */
316 0 : unsigned char *perms = NULL; /* Permutations of POOL. */
317 0 : gcry_mpi_t q_factor = NULL; /* Used if QBITS is non-zero. */
318 0 : unsigned int fbits = 0; /* Length of prime factors. */
319 0 : unsigned int n = 0; /* Number of factors. */
320 0 : unsigned int m = 0; /* Number of primes in pool. */
321 0 : gcry_mpi_t q = NULL; /* First prime factor. */
322 0 : gcry_mpi_t prime = NULL; /* Prime candidate. */
323 0 : unsigned int nprime = 0; /* Bits of PRIME. */
324 : unsigned int req_qbits; /* The original QBITS value. */
325 : gcry_mpi_t val_2; /* For check_prime(). */
326 0 : int is_locked = 0; /* Flag to help unlocking the primepool. */
327 0 : unsigned int is_secret = (flags & GCRY_PRIME_FLAG_SECRET);
328 0 : unsigned int count1 = 0, count2 = 0;
329 0 : unsigned int i = 0, j = 0;
330 :
331 0 : if (pbits < 48)
332 0 : return GPG_ERR_INV_ARG;
333 :
334 : /* We won't use a too strong random elvel for the pooled subprimes. */
335 0 : poolrandomlevel = (randomlevel > GCRY_STRONG_RANDOM?
336 : GCRY_STRONG_RANDOM : randomlevel);
337 :
338 :
339 : /* If QBITS is not given, assume a reasonable value. */
340 0 : if (!qbits)
341 0 : qbits = pbits / 3;
342 :
343 0 : req_qbits = qbits;
344 :
345 : /* Find number of needed prime factors N. */
346 0 : for (n = 1; (pbits - qbits - 1) / n >= qbits; n++)
347 : ;
348 0 : n--;
349 :
350 0 : val_2 = mpi_alloc_set_ui (2);
351 :
352 0 : if ((! n) || ((need_q_factor) && (n < 2)))
353 : {
354 0 : err = GPG_ERR_INV_ARG;
355 0 : goto leave;
356 : }
357 :
358 0 : if (need_q_factor)
359 : {
360 0 : n--; /* Need one factor less because we want a specific Q-FACTOR. */
361 0 : fbits = (pbits - 2 * req_qbits -1) / n;
362 0 : qbits = pbits - req_qbits - n * fbits;
363 : }
364 : else
365 : {
366 0 : fbits = (pbits - req_qbits -1) / n;
367 0 : qbits = pbits - n * fbits;
368 : }
369 :
370 0 : if (DBG_CIPHER)
371 0 : log_debug ("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
372 : pbits, req_qbits, qbits, fbits, n);
373 :
374 : /* Allocate an integer to old the new prime. */
375 0 : prime = mpi_new (pbits);
376 :
377 : /* Generate first prime factor. */
378 0 : q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
379 :
380 : /* Generate a specific Q-Factor if requested. */
381 0 : if (need_q_factor)
382 0 : q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL);
383 :
384 : /* Allocate an array to hold all factors + 2 for later usage. */
385 0 : factors = xtrycalloc (n + 2, sizeof (*factors));
386 0 : if (!factors)
387 : {
388 0 : err = gpg_err_code_from_errno (errno);
389 0 : goto leave;
390 : }
391 :
392 : /* Allocate an array to track pool usage. */
393 0 : pool_in_use = xtrymalloc (n * sizeof *pool_in_use);
394 0 : if (!pool_in_use)
395 : {
396 0 : err = gpg_err_code_from_errno (errno);
397 0 : goto leave;
398 : }
399 0 : for (i=0; i < n; i++)
400 0 : pool_in_use[i] = -1;
401 :
402 : /* Make a pool of 3n+5 primes (this is an arbitrary value). We
403 : require at least 30 primes for are useful selection process.
404 :
405 : Fixme: We need to research the best formula for sizing the pool.
406 : */
407 0 : m = n * 3 + 5;
408 0 : if (need_q_factor) /* Need some more in this case. */
409 0 : m += 5;
410 0 : if (m < 30)
411 0 : m = 30;
412 0 : pool = xtrycalloc (m , sizeof (*pool));
413 0 : if (! pool)
414 : {
415 0 : err = gpg_err_code_from_errno (errno);
416 0 : goto leave;
417 : }
418 :
419 : /* Permutate over the pool of primes until we find a prime of the
420 : requested length. */
421 : do
422 : {
423 : next_try:
424 0 : for (i=0; i < n; i++)
425 0 : pool_in_use[i] = -1;
426 :
427 0 : if (!perms)
428 : {
429 : /* Allocate new primes. This is done right at the beginning
430 : of the loop and if we have later run out of primes. */
431 0 : for (i = 0; i < m; i++)
432 : {
433 0 : mpi_free (pool[i]);
434 0 : pool[i] = NULL;
435 : }
436 :
437 : /* Init m_out_of_n(). */
438 0 : perms = xtrycalloc (1, m);
439 0 : if (!perms)
440 : {
441 0 : err = gpg_err_code_from_errno (errno);
442 0 : goto leave;
443 : }
444 :
445 0 : err = gpgrt_lock_lock (&primepool_lock);
446 0 : if (err)
447 0 : goto leave;
448 0 : is_locked = 1;
449 :
450 0 : for (i = 0; i < n; i++)
451 : {
452 0 : perms[i] = 1;
453 : /* At a maximum we use strong random for the factors.
454 : This saves us a lot of entropy. Given that Q and
455 : possible Q-factor are also used in the final prime
456 : this should be acceptable. We also don't allocate in
457 : secure memory to save on that scare resource too. If
458 : Q has been allocated in secure memory, the final
459 : prime will be saved there anyway. This is because
460 : our MPI routines take care of that. GnuPG has worked
461 : this way ever since. */
462 0 : pool[i] = NULL;
463 0 : if (is_locked)
464 : {
465 0 : pool[i] = get_pool_prime (fbits, poolrandomlevel);
466 0 : if (!pool[i])
467 : {
468 0 : err = gpgrt_lock_unlock (&primepool_lock);
469 0 : if (err)
470 0 : goto leave;
471 0 : is_locked = 0;
472 : }
473 : }
474 0 : if (!pool[i])
475 0 : pool[i] = gen_prime (fbits, 0, poolrandomlevel, NULL, NULL);
476 0 : pool_in_use[i] = i;
477 0 : factors[i] = pool[i];
478 : }
479 :
480 0 : if (is_locked && (err = gpgrt_lock_unlock (&primepool_lock)))
481 0 : goto leave;
482 0 : is_locked = 0;
483 : }
484 : else
485 : {
486 : /* Get next permutation. */
487 0 : m_out_of_n ( (char*)perms, n, m);
488 :
489 0 : if ((err = gpgrt_lock_lock (&primepool_lock)))
490 0 : goto leave;
491 0 : is_locked = 1;
492 :
493 0 : for (i = j = 0; (i < m) && (j < n); i++)
494 0 : if (perms[i])
495 : {
496 : /* If the subprime has not yet beed generated do it now. */
497 0 : if (!pool[i] && is_locked)
498 : {
499 0 : pool[i] = get_pool_prime (fbits, poolrandomlevel);
500 0 : if (!pool[i])
501 : {
502 0 : if ((err = gpgrt_lock_unlock (&primepool_lock)))
503 0 : goto leave;
504 0 : is_locked = 0;
505 : }
506 : }
507 0 : if (!pool[i])
508 0 : pool[i] = gen_prime (fbits, 0, poolrandomlevel, NULL, NULL);
509 0 : pool_in_use[j] = i;
510 0 : factors[j++] = pool[i];
511 : }
512 :
513 0 : if (is_locked && (err = gpgrt_lock_unlock (&primepool_lock)))
514 0 : goto leave;
515 0 : is_locked = 0;
516 :
517 0 : if (i == n)
518 : {
519 : /* Ran out of permutations: Allocate new primes. */
520 0 : xfree (perms);
521 0 : perms = NULL;
522 0 : progress ('!');
523 0 : goto next_try;
524 : }
525 : }
526 :
527 : /* Generate next prime candidate:
528 : p = 2 * q [ * q_factor] * factor_0 * factor_1 * ... * factor_n + 1.
529 : */
530 0 : mpi_set (prime, q);
531 0 : mpi_mul_ui (prime, prime, 2);
532 0 : if (need_q_factor)
533 0 : mpi_mul (prime, prime, q_factor);
534 0 : for(i = 0; i < n; i++)
535 0 : mpi_mul (prime, prime, factors[i]);
536 0 : mpi_add_ui (prime, prime, 1);
537 0 : nprime = mpi_get_nbits (prime);
538 :
539 0 : if (nprime < pbits)
540 : {
541 0 : if (++count1 > 20)
542 : {
543 0 : count1 = 0;
544 0 : qbits++;
545 0 : progress('>');
546 0 : mpi_free (q);
547 0 : q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
548 0 : goto next_try;
549 : }
550 : }
551 : else
552 0 : count1 = 0;
553 :
554 0 : if (nprime > pbits)
555 : {
556 0 : if (++count2 > 20)
557 : {
558 0 : count2 = 0;
559 0 : qbits--;
560 0 : progress('<');
561 0 : mpi_free (q);
562 0 : q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
563 0 : goto next_try;
564 : }
565 : }
566 : else
567 0 : count2 = 0;
568 : }
569 0 : while (! ((nprime == pbits) && check_prime (prime, val_2, 5,
570 0 : cb_func, cb_arg)));
571 :
572 0 : if (DBG_CIPHER)
573 : {
574 0 : progress ('\n');
575 0 : log_mpidump ("prime ", prime);
576 0 : log_mpidump ("factor q", q);
577 0 : if (need_q_factor)
578 0 : log_mpidump ("factor q0", q_factor);
579 0 : for (i = 0; i < n; i++)
580 0 : log_mpidump ("factor pi", factors[i]);
581 0 : log_debug ("bit sizes: prime=%u, q=%u",
582 : mpi_get_nbits (prime), mpi_get_nbits (q));
583 0 : if (need_q_factor)
584 0 : log_printf (", q0=%u", mpi_get_nbits (q_factor));
585 0 : for (i = 0; i < n; i++)
586 0 : log_printf (", p%d=%u", i, mpi_get_nbits (factors[i]));
587 0 : log_printf ("\n");
588 : }
589 :
590 0 : if (ret_factors)
591 : {
592 : /* Caller wants the factors. */
593 0 : factors_new = xtrycalloc (n + 4, sizeof (*factors_new));
594 0 : if (! factors_new)
595 : {
596 0 : err = gpg_err_code_from_errno (errno);
597 0 : goto leave;
598 : }
599 :
600 0 : if (all_factors)
601 : {
602 0 : i = 0;
603 0 : factors_new[i++] = mpi_set_ui (NULL, 2);
604 0 : factors_new[i++] = mpi_copy (q);
605 0 : if (need_q_factor)
606 0 : factors_new[i++] = mpi_copy (q_factor);
607 0 : for(j=0; j < n; j++)
608 0 : factors_new[i++] = mpi_copy (factors[j]);
609 : }
610 : else
611 : {
612 0 : i = 0;
613 0 : if (need_q_factor)
614 : {
615 0 : factors_new[i++] = mpi_copy (q_factor);
616 0 : for (; i <= n; i++)
617 0 : factors_new[i] = mpi_copy (factors[i]);
618 : }
619 : else
620 0 : for (; i < n; i++ )
621 0 : factors_new[i] = mpi_copy (factors[i]);
622 : }
623 : }
624 :
625 0 : if (g && need_q_factor)
626 0 : err = GPG_ERR_NOT_IMPLEMENTED;
627 0 : else if (g)
628 : {
629 : /* Create a generator (start with 3). */
630 0 : gcry_mpi_t tmp = mpi_alloc (mpi_get_nlimbs (prime));
631 0 : gcry_mpi_t b = mpi_alloc (mpi_get_nlimbs (prime));
632 0 : gcry_mpi_t pmin1 = mpi_alloc (mpi_get_nlimbs (prime));
633 :
634 0 : factors[n] = q;
635 0 : factors[n + 1] = mpi_alloc_set_ui (2);
636 0 : mpi_sub_ui (pmin1, prime, 1);
637 0 : mpi_set_ui (g, 2);
638 : do
639 : {
640 0 : mpi_add_ui (g, g, 1);
641 0 : if (DBG_CIPHER)
642 0 : log_printmpi ("checking g", g);
643 : else
644 0 : progress('^');
645 0 : for (i = 0; i < n + 2; i++)
646 : {
647 0 : mpi_fdiv_q (tmp, pmin1, factors[i]);
648 : /* No mpi_pow(), but it is okay to use this with mod
649 : prime. */
650 0 : mpi_powm (b, g, tmp, prime);
651 0 : if (! mpi_cmp_ui (b, 1))
652 0 : break;
653 : }
654 0 : if (DBG_CIPHER)
655 0 : progress('\n');
656 : }
657 0 : while (i < n + 2);
658 :
659 0 : mpi_free (factors[n+1]);
660 0 : mpi_free (tmp);
661 0 : mpi_free (b);
662 0 : mpi_free (pmin1);
663 : }
664 :
665 0 : if (! DBG_CIPHER)
666 0 : progress ('\n');
667 :
668 :
669 : leave:
670 0 : if (pool)
671 : {
672 0 : is_locked = !gpgrt_lock_lock (&primepool_lock);
673 0 : for(i = 0; i < m; i++)
674 : {
675 0 : if (pool[i])
676 : {
677 0 : for (j=0; j < n; j++)
678 0 : if (pool_in_use[j] == i)
679 0 : break;
680 0 : if (j == n && is_locked)
681 : {
682 : /* This pooled subprime has not been used. */
683 0 : save_pool_prime (pool[i], poolrandomlevel);
684 : }
685 : else
686 0 : mpi_free (pool[i]);
687 : }
688 : }
689 0 : if (is_locked)
690 0 : err = gpgrt_lock_unlock (&primepool_lock);
691 0 : is_locked = 0;
692 0 : xfree (pool);
693 : }
694 0 : xfree (pool_in_use);
695 0 : if (factors)
696 0 : xfree (factors); /* Factors are shallow copies. */
697 0 : if (perms)
698 0 : xfree (perms);
699 :
700 0 : mpi_free (val_2);
701 0 : mpi_free (q);
702 0 : mpi_free (q_factor);
703 :
704 0 : if (! err)
705 : {
706 0 : *prime_generated = prime;
707 0 : if (ret_factors)
708 0 : *ret_factors = factors_new;
709 : }
710 : else
711 : {
712 0 : if (factors_new)
713 : {
714 0 : for (i = 0; factors_new[i]; i++)
715 0 : mpi_free (factors_new[i]);
716 0 : xfree (factors_new);
717 : }
718 0 : mpi_free (prime);
719 : }
720 :
721 0 : return err;
722 : }
723 :
724 :
725 : /* Generate a prime used for discrete logarithm algorithms; i.e. this
726 : prime will be public and no strong random is required. On success
727 : R_PRIME receives a new MPI with the prime. On error R_PRIME is set
728 : to NULL and an error code is returned. If RET_FACTORS is not NULL
729 : it is set to an allocated array of factors on success or to NULL on
730 : error. */
731 : gcry_err_code_t
732 0 : _gcry_generate_elg_prime (int mode, unsigned pbits, unsigned qbits,
733 : gcry_mpi_t g,
734 : gcry_mpi_t *r_prime, gcry_mpi_t **ret_factors)
735 : {
736 0 : *r_prime = NULL;
737 0 : if (ret_factors)
738 0 : *ret_factors = NULL;
739 0 : return prime_generate_internal ((mode == 1), r_prime, pbits, qbits, g,
740 : ret_factors, GCRY_WEAK_RANDOM, 0, 0,
741 : NULL, NULL);
742 : }
743 :
744 :
745 : static gcry_mpi_t
746 0 : gen_prime (unsigned int nbits, int secret, int randomlevel,
747 : int (*extra_check)(void *, gcry_mpi_t), void *extra_check_arg)
748 : {
749 : gcry_mpi_t prime, ptest, pminus1, val_2, val_3, result;
750 : int i;
751 : unsigned int x, step;
752 : unsigned int count1, count2;
753 : int *mods;
754 :
755 : /* if ( DBG_CIPHER ) */
756 : /* log_debug ("generate a prime of %u bits ", nbits ); */
757 :
758 0 : if (nbits < 16)
759 0 : log_fatal ("can't generate a prime with less than %d bits\n", 16);
760 :
761 0 : mods = xmalloc (no_of_small_prime_numbers * sizeof *mods);
762 : /* Make nbits fit into gcry_mpi_t implementation. */
763 0 : val_2 = mpi_alloc_set_ui( 2 );
764 0 : val_3 = mpi_alloc_set_ui( 3);
765 0 : prime = secret? mpi_snew (nbits): mpi_new (nbits);
766 0 : result = mpi_alloc_like( prime );
767 0 : pminus1= mpi_alloc_like( prime );
768 0 : ptest = mpi_alloc_like( prime );
769 0 : count1 = count2 = 0;
770 : for (;;)
771 0 : { /* try forvever */
772 0 : int dotcount=0;
773 :
774 : /* generate a random number */
775 0 : _gcry_mpi_randomize( prime, nbits, randomlevel );
776 :
777 : /* Set high order bit to 1, set low order bit to 1. If we are
778 : generating a secret prime we are most probably doing that
779 : for RSA, to make sure that the modulus does have the
780 : requested key size we set the 2 high order bits. */
781 0 : mpi_set_highbit (prime, nbits-1);
782 0 : if (secret)
783 0 : mpi_set_bit (prime, nbits-2);
784 0 : mpi_set_bit(prime, 0);
785 :
786 : /* Calculate all remainders. */
787 0 : for (i=0; (x = small_prime_numbers[i]); i++ )
788 0 : mods[i] = mpi_fdiv_r_ui(NULL, prime, x);
789 :
790 : /* Now try some primes starting with prime. */
791 0 : for(step=0; step < 20000; step += 2 )
792 : {
793 : /* Check against all the small primes we have in mods. */
794 0 : count1++;
795 0 : for (i=0; (x = small_prime_numbers[i]); i++ )
796 : {
797 0 : while ( mods[i] + step >= x )
798 0 : mods[i] -= x;
799 0 : if ( !(mods[i] + step) )
800 0 : break;
801 : }
802 0 : if ( x )
803 0 : continue; /* Found a multiple of an already known prime. */
804 :
805 0 : mpi_add_ui( ptest, prime, step );
806 :
807 : /* Do a fast Fermat test now. */
808 0 : count2++;
809 0 : mpi_sub_ui( pminus1, ptest, 1);
810 0 : mpi_powm( result, val_2, pminus1, ptest );
811 0 : if ( !mpi_cmp_ui( result, 1 ) )
812 : {
813 : /* Not composite, perform stronger tests */
814 0 : if (is_prime(ptest, 5, &count2 ))
815 : {
816 0 : if (!mpi_test_bit( ptest, nbits-1-secret ))
817 : {
818 0 : progress('\n');
819 0 : log_debug ("overflow in prime generation\n");
820 0 : break; /* Stop loop, continue with a new prime. */
821 : }
822 :
823 0 : if (extra_check && extra_check (extra_check_arg, ptest))
824 : {
825 : /* The extra check told us that this prime is
826 : not of the caller's taste. */
827 0 : progress ('/');
828 : }
829 : else
830 : {
831 : /* Got it. */
832 0 : mpi_free(val_2);
833 0 : mpi_free(val_3);
834 0 : mpi_free(result);
835 0 : mpi_free(pminus1);
836 0 : mpi_free(prime);
837 0 : xfree(mods);
838 0 : return ptest;
839 : }
840 : }
841 : }
842 0 : if (++dotcount == 10 )
843 : {
844 0 : progress('.');
845 0 : dotcount = 0;
846 : }
847 : }
848 0 : progress(':'); /* restart with a new random value */
849 : }
850 : }
851 :
852 : /****************
853 : * Returns: true if this may be a prime
854 : * RM_ROUNDS gives the number of Rabin-Miller tests to run.
855 : */
856 : static int
857 0 : check_prime( gcry_mpi_t prime, gcry_mpi_t val_2, int rm_rounds,
858 : gcry_prime_check_func_t cb_func, void *cb_arg)
859 : {
860 : int i;
861 : unsigned int x;
862 0 : unsigned int count=0;
863 :
864 : /* Check against small primes. */
865 0 : for (i=0; (x = small_prime_numbers[i]); i++ )
866 : {
867 0 : if ( mpi_divisible_ui( prime, x ) )
868 0 : return !mpi_cmp_ui (prime, x);
869 : }
870 :
871 : /* A quick Fermat test. */
872 : {
873 0 : gcry_mpi_t result = mpi_alloc_like( prime );
874 0 : gcry_mpi_t pminus1 = mpi_alloc_like( prime );
875 0 : mpi_sub_ui( pminus1, prime, 1);
876 0 : mpi_powm( result, val_2, pminus1, prime );
877 0 : mpi_free( pminus1 );
878 0 : if ( mpi_cmp_ui( result, 1 ) )
879 : {
880 : /* Is composite. */
881 0 : mpi_free( result );
882 0 : progress('.');
883 0 : return 0;
884 : }
885 0 : mpi_free( result );
886 : }
887 :
888 0 : if (!cb_func || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_MAYBE_PRIME, prime))
889 : {
890 : /* Perform stronger tests. */
891 0 : if ( is_prime( prime, rm_rounds, &count ) )
892 : {
893 0 : if (!cb_func
894 0 : || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_GOT_PRIME, prime))
895 0 : return 1; /* Probably a prime. */
896 : }
897 : }
898 0 : progress('.');
899 0 : return 0;
900 : }
901 :
902 :
903 : /*
904 : * Return true if n is probably a prime
905 : */
906 : static int
907 0 : is_prime (gcry_mpi_t n, int steps, unsigned int *count)
908 : {
909 0 : gcry_mpi_t x = mpi_alloc( mpi_get_nlimbs( n ) );
910 0 : gcry_mpi_t y = mpi_alloc( mpi_get_nlimbs( n ) );
911 0 : gcry_mpi_t z = mpi_alloc( mpi_get_nlimbs( n ) );
912 0 : gcry_mpi_t nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
913 0 : gcry_mpi_t a2 = mpi_alloc_set_ui( 2 );
914 : gcry_mpi_t q;
915 : unsigned i, j, k;
916 0 : int rc = 0;
917 0 : unsigned nbits = mpi_get_nbits( n );
918 :
919 0 : if (steps < 5) /* Make sure that we do at least 5 rounds. */
920 0 : steps = 5;
921 :
922 0 : mpi_sub_ui( nminus1, n, 1 );
923 :
924 : /* Find q and k, so that n = 1 + 2^k * q . */
925 0 : q = mpi_copy ( nminus1 );
926 0 : k = mpi_trailing_zeros ( q );
927 0 : mpi_tdiv_q_2exp (q, q, k);
928 :
929 0 : for (i=0 ; i < steps; i++ )
930 : {
931 0 : ++*count;
932 0 : if( !i )
933 : {
934 0 : mpi_set_ui( x, 2 );
935 : }
936 : else
937 : {
938 0 : _gcry_mpi_randomize( x, nbits, GCRY_WEAK_RANDOM );
939 :
940 : /* Make sure that the number is smaller than the prime and
941 : keep the randomness of the high bit. */
942 0 : if ( mpi_test_bit ( x, nbits-2) )
943 : {
944 0 : mpi_set_highbit ( x, nbits-2); /* Clear all higher bits. */
945 : }
946 : else
947 : {
948 0 : mpi_set_highbit( x, nbits-2 );
949 0 : mpi_clear_bit( x, nbits-2 );
950 : }
951 0 : gcry_assert (mpi_cmp (x, nminus1) < 0 && mpi_cmp_ui (x, 1) > 0);
952 : }
953 0 : mpi_powm ( y, x, q, n);
954 0 : if ( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) )
955 : {
956 0 : for ( j=1; j < k && mpi_cmp( y, nminus1 ); j++ )
957 : {
958 0 : mpi_powm(y, y, a2, n);
959 0 : if( !mpi_cmp_ui( y, 1 ) )
960 0 : goto leave; /* Not a prime. */
961 : }
962 0 : if (mpi_cmp( y, nminus1 ) )
963 0 : goto leave; /* Not a prime. */
964 : }
965 0 : progress('+');
966 : }
967 0 : rc = 1; /* May be a prime. */
968 :
969 : leave:
970 0 : mpi_free( x );
971 0 : mpi_free( y );
972 0 : mpi_free( z );
973 0 : mpi_free( nminus1 );
974 0 : mpi_free( q );
975 0 : mpi_free( a2 );
976 :
977 0 : return rc;
978 : }
979 :
980 :
981 : /* Given ARRAY of size N with M elements set to true produce a
982 : modified array with the next permutation of M elements. Note, that
983 : ARRAY is used in a one-bit-per-byte approach. To detected the last
984 : permutation it is useful to initialize the array with the first M
985 : element set to true and use this test:
986 : m_out_of_n (array, m, n);
987 : for (i = j = 0; i < n && j < m; i++)
988 : if (array[i])
989 : j++;
990 : if (j == m)
991 : goto ready;
992 :
993 : This code is based on the algorithm 452 from the "Collected
994 : Algorithms From ACM, Volume II" by C. N. Liu and D. T. Tang.
995 : */
996 : static void
997 0 : m_out_of_n ( char *array, int m, int n )
998 : {
999 0 : int i=0, i1=0, j=0, jp=0, j1=0, k1=0, k2=0;
1000 :
1001 0 : if( !m || m >= n )
1002 0 : return;
1003 :
1004 : /* Need to handle this simple case separately. */
1005 0 : if( m == 1 )
1006 : {
1007 0 : for (i=0; i < n; i++ )
1008 : {
1009 0 : if ( array[i] )
1010 : {
1011 0 : array[i++] = 0;
1012 0 : if( i >= n )
1013 0 : i = 0;
1014 0 : array[i] = 1;
1015 0 : return;
1016 : }
1017 : }
1018 0 : BUG();
1019 : }
1020 :
1021 :
1022 0 : for (j=1; j < n; j++ )
1023 : {
1024 0 : if ( array[n-1] == array[n-j-1])
1025 0 : continue;
1026 0 : j1 = j;
1027 0 : break;
1028 : }
1029 :
1030 0 : if ( (m & 1) )
1031 : {
1032 : /* M is odd. */
1033 0 : if( array[n-1] )
1034 : {
1035 0 : if( j1 & 1 )
1036 : {
1037 0 : k1 = n - j1;
1038 0 : k2 = k1+2;
1039 0 : if( k2 > n )
1040 0 : k2 = n;
1041 0 : goto leave;
1042 : }
1043 0 : goto scan;
1044 : }
1045 0 : k2 = n - j1 - 1;
1046 0 : if( k2 == 0 )
1047 : {
1048 0 : k1 = i;
1049 0 : k2 = n - j1;
1050 : }
1051 0 : else if( array[k2] && array[k2-1] )
1052 0 : k1 = n;
1053 : else
1054 0 : k1 = k2 + 1;
1055 : }
1056 : else
1057 : {
1058 : /* M is even. */
1059 0 : if( !array[n-1] )
1060 : {
1061 0 : k1 = n - j1;
1062 0 : k2 = k1 + 1;
1063 0 : goto leave;
1064 : }
1065 :
1066 0 : if( !(j1 & 1) )
1067 : {
1068 0 : k1 = n - j1;
1069 0 : k2 = k1+2;
1070 0 : if( k2 > n )
1071 0 : k2 = n;
1072 0 : goto leave;
1073 : }
1074 : scan:
1075 0 : jp = n - j1 - 1;
1076 0 : for (i=1; i <= jp; i++ )
1077 : {
1078 0 : i1 = jp + 2 - i;
1079 0 : if( array[i1-1] )
1080 : {
1081 0 : if( array[i1-2] )
1082 : {
1083 0 : k1 = i1 - 1;
1084 0 : k2 = n - j1;
1085 : }
1086 : else
1087 : {
1088 0 : k1 = i1 - 1;
1089 0 : k2 = n + 1 - j1;
1090 : }
1091 0 : goto leave;
1092 : }
1093 : }
1094 0 : k1 = 1;
1095 0 : k2 = n + 1 - m;
1096 : }
1097 : leave:
1098 : /* Now complement the two selected bits. */
1099 0 : array[k1-1] = !array[k1-1];
1100 0 : array[k2-1] = !array[k2-1];
1101 : }
1102 :
1103 :
1104 : /* Generate a new prime number of PRIME_BITS bits and store it in
1105 : PRIME. If FACTOR_BITS is non-zero, one of the prime factors of
1106 : (prime - 1) / 2 must be FACTOR_BITS bits long. If FACTORS is
1107 : non-zero, allocate a new, NULL-terminated array holding the prime
1108 : factors and store it in FACTORS. FLAGS might be used to influence
1109 : the prime number generation process. */
1110 : gcry_err_code_t
1111 0 : _gcry_prime_generate (gcry_mpi_t *prime, unsigned int prime_bits,
1112 : unsigned int factor_bits, gcry_mpi_t **factors,
1113 : gcry_prime_check_func_t cb_func, void *cb_arg,
1114 : gcry_random_level_t random_level,
1115 : unsigned int flags)
1116 : {
1117 0 : gcry_err_code_t rc = 0;
1118 0 : gcry_mpi_t *factors_generated = NULL;
1119 0 : gcry_mpi_t prime_generated = NULL;
1120 0 : unsigned int mode = 0;
1121 :
1122 0 : if (!prime)
1123 0 : return GPG_ERR_INV_ARG;
1124 0 : *prime = NULL;
1125 :
1126 0 : if (flags & GCRY_PRIME_FLAG_SPECIAL_FACTOR)
1127 0 : mode = 1;
1128 :
1129 : /* Generate. */
1130 0 : rc = prime_generate_internal ((mode==1), &prime_generated, prime_bits,
1131 : factor_bits, NULL,
1132 : factors? &factors_generated : NULL,
1133 : random_level, flags, 1,
1134 : cb_func, cb_arg);
1135 :
1136 0 : if (!rc && cb_func)
1137 : {
1138 : /* Additional check. */
1139 0 : if ( !cb_func (cb_arg, GCRY_PRIME_CHECK_AT_FINISH, prime_generated))
1140 : {
1141 : /* Failed, deallocate resources. */
1142 : unsigned int i;
1143 :
1144 0 : mpi_free (prime_generated);
1145 0 : if (factors)
1146 : {
1147 0 : for (i = 0; factors_generated[i]; i++)
1148 0 : mpi_free (factors_generated[i]);
1149 0 : xfree (factors_generated);
1150 : }
1151 0 : rc = GPG_ERR_GENERAL;
1152 : }
1153 : }
1154 :
1155 0 : if (!rc)
1156 : {
1157 0 : if (factors)
1158 0 : *factors = factors_generated;
1159 0 : *prime = prime_generated;
1160 : }
1161 :
1162 0 : return rc;
1163 : }
1164 :
1165 : /* Check whether the number X is prime. */
1166 : gcry_err_code_t
1167 0 : _gcry_prime_check (gcry_mpi_t x, unsigned int flags)
1168 : {
1169 : (void)flags;
1170 :
1171 0 : switch (mpi_cmp_ui (x, 2))
1172 : {
1173 0 : case 0: return 0; /* 2 is a prime */
1174 0 : case -1: return GPG_ERR_NO_PRIME; /* Only numbers > 1 are primes. */
1175 : }
1176 :
1177 : /* We use 64 rounds because the prime we are going to test is not
1178 : guaranteed to be a random one. */
1179 0 : if (check_prime (x, mpi_const (MPI_C_TWO), 64, NULL, NULL))
1180 0 : return 0;
1181 :
1182 0 : return GPG_ERR_NO_PRIME;
1183 : }
1184 :
1185 :
1186 : /* Check whether the number X is prime according to FIPS 186-4 table C.2. */
1187 : gcry_err_code_t
1188 0 : _gcry_fips186_4_prime_check (gcry_mpi_t x, unsigned int bits)
1189 : {
1190 0 : gcry_err_code_t ec = GPG_ERR_NO_ERROR;
1191 :
1192 0 : switch (mpi_cmp_ui (x, 2))
1193 : {
1194 0 : case 0: return ec; /* 2 is a prime */
1195 0 : case -1: return GPG_ERR_NO_PRIME; /* Only numbers > 1 are primes. */
1196 : }
1197 :
1198 : /* We use 5 or 4 rounds as specified in table C.2 */
1199 0 : if (! check_prime (x, mpi_const (MPI_C_TWO), bits > 1024 ? 4 : 5, NULL, NULL))
1200 0 : ec = GPG_ERR_NO_PRIME;
1201 :
1202 0 : return ec;
1203 : }
1204 :
1205 :
1206 : /* Find a generator for PRIME where the factorization of (prime-1) is
1207 : in the NULL terminated array FACTORS. Return the generator as a
1208 : newly allocated MPI in R_G. If START_G is not NULL, use this as s
1209 : atart for the search. Returns 0 on success.*/
1210 : gcry_err_code_t
1211 0 : _gcry_prime_group_generator (gcry_mpi_t *r_g,
1212 : gcry_mpi_t prime, gcry_mpi_t *factors,
1213 : gcry_mpi_t start_g)
1214 : {
1215 : gcry_mpi_t tmp, b, pmin1, g;
1216 : int first, i, n;
1217 :
1218 0 : if (!r_g)
1219 0 : return GPG_ERR_INV_ARG;
1220 0 : *r_g = NULL;
1221 0 : if (!factors || !prime)
1222 0 : return GPG_ERR_INV_ARG;
1223 :
1224 0 : for (n=0; factors[n]; n++)
1225 : ;
1226 0 : if (n < 2)
1227 0 : return GPG_ERR_INV_ARG;
1228 :
1229 0 : tmp = mpi_new (0);
1230 0 : b = mpi_new (0);
1231 0 : pmin1 = mpi_new (0);
1232 0 : g = start_g? mpi_copy (start_g) : mpi_set_ui (NULL, 3);
1233 :
1234 : /* Extra sanity check - usually disabled. */
1235 : /* mpi_set (tmp, factors[0]); */
1236 : /* for(i = 1; i < n; i++) */
1237 : /* mpi_mul (tmp, tmp, factors[i]); */
1238 : /* mpi_add_ui (tmp, tmp, 1); */
1239 : /* if (mpi_cmp (prime, tmp)) */
1240 : /* return gpg_error (GPG_ERR_INV_ARG); */
1241 :
1242 0 : mpi_sub_ui (pmin1, prime, 1);
1243 0 : first = 1;
1244 : do
1245 : {
1246 0 : if (first)
1247 0 : first = 0;
1248 : else
1249 0 : mpi_add_ui (g, g, 1);
1250 :
1251 0 : if (DBG_CIPHER)
1252 0 : log_printmpi ("checking g", g);
1253 : else
1254 0 : progress('^');
1255 :
1256 0 : for (i = 0; i < n; i++)
1257 : {
1258 0 : mpi_fdiv_q (tmp, pmin1, factors[i]);
1259 0 : mpi_powm (b, g, tmp, prime);
1260 0 : if (! mpi_cmp_ui (b, 1))
1261 0 : break;
1262 : }
1263 0 : if (DBG_CIPHER)
1264 0 : progress('\n');
1265 : }
1266 0 : while (i < n);
1267 :
1268 0 : _gcry_mpi_release (tmp);
1269 0 : _gcry_mpi_release (b);
1270 0 : _gcry_mpi_release (pmin1);
1271 0 : *r_g = g;
1272 :
1273 0 : return 0;
1274 : }
1275 :
1276 : /* Convenience function to release the factors array. */
1277 : void
1278 0 : _gcry_prime_release_factors (gcry_mpi_t *factors)
1279 : {
1280 0 : if (factors)
1281 : {
1282 : int i;
1283 :
1284 0 : for (i=0; factors[i]; i++)
1285 0 : mpi_free (factors[i]);
1286 0 : xfree (factors);
1287 : }
1288 0 : }
1289 :
1290 :
1291 :
1292 : /* Helper for _gcry_derive_x931_prime. */
1293 : static gcry_mpi_t
1294 0 : find_x931_prime (const gcry_mpi_t pfirst)
1295 : {
1296 0 : gcry_mpi_t val_2 = mpi_alloc_set_ui (2);
1297 : gcry_mpi_t prime;
1298 :
1299 0 : prime = mpi_copy (pfirst);
1300 : /* If P is even add 1. */
1301 0 : mpi_set_bit (prime, 0);
1302 :
1303 : /* We use 64 Rabin-Miller rounds which is better and thus
1304 : sufficient. We do not have a Lucas test implementaion thus we
1305 : can't do it in the X9.31 preferred way of running a few
1306 : Rabin-Miller followed by one Lucas test. */
1307 0 : while ( !check_prime (prime, val_2, 64, NULL, NULL) )
1308 0 : mpi_add_ui (prime, prime, 2);
1309 :
1310 0 : mpi_free (val_2);
1311 :
1312 0 : return prime;
1313 : }
1314 :
1315 :
1316 : /* Generate a prime using the algorithm from X9.31 appendix B.4.
1317 :
1318 : This function requires that the provided public exponent E is odd.
1319 : XP, XP1 and XP2 are the seed values. All values are mandatory.
1320 :
1321 : On success the prime is returned. If R_P1 or R_P2 are given the
1322 : internal values P1 and P2 are saved at these addresses. On error
1323 : NULL is returned. */
1324 : gcry_mpi_t
1325 0 : _gcry_derive_x931_prime (const gcry_mpi_t xp,
1326 : const gcry_mpi_t xp1, const gcry_mpi_t xp2,
1327 : const gcry_mpi_t e,
1328 : gcry_mpi_t *r_p1, gcry_mpi_t *r_p2)
1329 : {
1330 : gcry_mpi_t p1, p2, p1p2, yp0;
1331 :
1332 0 : if (!xp || !xp1 || !xp2)
1333 0 : return NULL;
1334 0 : if (!e || !mpi_test_bit (e, 0))
1335 0 : return NULL; /* We support only odd values for E. */
1336 :
1337 0 : p1 = find_x931_prime (xp1);
1338 0 : p2 = find_x931_prime (xp2);
1339 0 : p1p2 = mpi_alloc_like (xp);
1340 0 : mpi_mul (p1p2, p1, p2);
1341 :
1342 : {
1343 : gcry_mpi_t r1, tmp;
1344 :
1345 : /* r1 = (p2^{-1} mod p1)p2 - (p1^{-1} mod p2) */
1346 0 : tmp = mpi_alloc_like (p1);
1347 0 : mpi_invm (tmp, p2, p1);
1348 0 : mpi_mul (tmp, tmp, p2);
1349 0 : r1 = tmp;
1350 :
1351 0 : tmp = mpi_alloc_like (p2);
1352 0 : mpi_invm (tmp, p1, p2);
1353 0 : mpi_mul (tmp, tmp, p1);
1354 0 : mpi_sub (r1, r1, tmp);
1355 :
1356 : /* Fixup a negative value. */
1357 0 : if (mpi_has_sign (r1))
1358 0 : mpi_add (r1, r1, p1p2);
1359 :
1360 : /* yp0 = xp + (r1 - xp mod p1*p2) */
1361 0 : yp0 = tmp; tmp = NULL;
1362 0 : mpi_subm (yp0, r1, xp, p1p2);
1363 0 : mpi_add (yp0, yp0, xp);
1364 0 : mpi_free (r1);
1365 :
1366 : /* Fixup a negative value. */
1367 0 : if (mpi_cmp (yp0, xp) < 0 )
1368 0 : mpi_add (yp0, yp0, p1p2);
1369 : }
1370 :
1371 : /* yp0 is now the first integer greater than xp with p1 being a
1372 : large prime factor of yp0-1 and p2 a large prime factor of yp0+1. */
1373 :
1374 : /* Note that the first example from X9.31 (D.1.1) which uses
1375 : (Xq1 #1A5CF72EE770DE50CB09ACCEA9#)
1376 : (Xq2 #134E4CAA16D2350A21D775C404#)
1377 : (Xq #CC1092495D867E64065DEE3E7955F2EBC7D47A2D
1378 : 7C9953388F97DDDC3E1CA19C35CA659EDC2FC325
1379 : 6D29C2627479C086A699A49C4C9CEE7EF7BD1B34
1380 : 321DE34A#))))
1381 : returns an yp0 of
1382 : #CC1092495D867E64065DEE3E7955F2EBC7D47A2D
1383 : 7C9953388F97DDDC3E1CA19C35CA659EDC2FC4E3
1384 : BF20CB896EE37E098A906313271422162CB6C642
1385 : 75C1201F#
1386 : and not
1387 : #CC1092495D867E64065DEE3E7955F2EBC7D47A2D
1388 : 7C9953388F97DDDC3E1CA19C35CA659EDC2FC2E6
1389 : C88FE299D52D78BE405A97E01FD71DD7819ECB91
1390 : FA85A076#
1391 : as stated in the standard. This seems to be a bug in X9.31.
1392 : */
1393 :
1394 : {
1395 0 : gcry_mpi_t val_2 = mpi_alloc_set_ui (2);
1396 0 : gcry_mpi_t gcdtmp = mpi_alloc_like (yp0);
1397 : int gcdres;
1398 :
1399 0 : mpi_sub_ui (p1p2, p1p2, 1); /* Adjust for loop body. */
1400 0 : mpi_sub_ui (yp0, yp0, 1); /* Ditto. */
1401 : for (;;)
1402 : {
1403 0 : gcdres = mpi_gcd (gcdtmp, e, yp0);
1404 0 : mpi_add_ui (yp0, yp0, 1);
1405 0 : if (!gcdres)
1406 0 : progress ('/'); /* gcd (e, yp0-1) != 1 */
1407 0 : else if (check_prime (yp0, val_2, 64, NULL, NULL))
1408 0 : break; /* Found. */
1409 : /* We add p1p2-1 because yp0 is incremented after the gcd test. */
1410 0 : mpi_add (yp0, yp0, p1p2);
1411 : }
1412 0 : mpi_free (gcdtmp);
1413 0 : mpi_free (val_2);
1414 : }
1415 :
1416 0 : mpi_free (p1p2);
1417 :
1418 0 : progress('\n');
1419 0 : if (r_p1)
1420 0 : *r_p1 = p1;
1421 : else
1422 0 : mpi_free (p1);
1423 0 : if (r_p2)
1424 0 : *r_p2 = p2;
1425 : else
1426 0 : mpi_free (p2);
1427 0 : return yp0;
1428 : }
1429 :
1430 :
1431 :
1432 : /* Generate the two prime used for DSA using the algorithm specified
1433 : in FIPS 186-2. PBITS is the desired length of the prime P and a
1434 : QBITS the length of the prime Q. If SEED is not supplied and
1435 : SEEDLEN is 0 the function generates an appropriate SEED. On
1436 : success the generated primes are stored at R_Q and R_P, the counter
1437 : value is stored at R_COUNTER and the seed actually used for
1438 : generation is stored at R_SEED and R_SEEDVALUE. */
1439 : gpg_err_code_t
1440 0 : _gcry_generate_fips186_2_prime (unsigned int pbits, unsigned int qbits,
1441 : const void *seed, size_t seedlen,
1442 : gcry_mpi_t *r_q, gcry_mpi_t *r_p,
1443 : int *r_counter,
1444 : void **r_seed, size_t *r_seedlen)
1445 : {
1446 : gpg_err_code_t ec;
1447 : unsigned char seed_help_buffer[160/8]; /* Used to hold a generated SEED. */
1448 : unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */
1449 : unsigned char digest[160/8]; /* Helper buffer for SHA-1 digest. */
1450 0 : gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */
1451 0 : gcry_mpi_t tmpval = NULL; /* Helper variable. */
1452 : int i;
1453 :
1454 : unsigned char value_u[160/8];
1455 : int value_n, value_b, value_k;
1456 : int counter;
1457 0 : gcry_mpi_t value_w = NULL;
1458 0 : gcry_mpi_t value_x = NULL;
1459 0 : gcry_mpi_t prime_q = NULL;
1460 0 : gcry_mpi_t prime_p = NULL;
1461 :
1462 : /* FIPS 186-2 allows only for 1024/160 bit. */
1463 0 : if (pbits != 1024 || qbits != 160)
1464 0 : return GPG_ERR_INV_KEYLEN;
1465 :
1466 0 : if (!seed && !seedlen)
1467 : ; /* No seed value given: We are asked to generate it. */
1468 0 : else if (!seed || seedlen < qbits/8)
1469 0 : return GPG_ERR_INV_ARG;
1470 :
1471 : /* Allocate a buffer to later compute SEED+some_increment. */
1472 0 : seed_plus = xtrymalloc (seedlen < 20? 20:seedlen);
1473 0 : if (!seed_plus)
1474 : {
1475 0 : ec = gpg_err_code_from_syserror ();
1476 0 : goto leave;
1477 : }
1478 :
1479 0 : val_2 = mpi_alloc_set_ui (2);
1480 0 : value_n = (pbits - 1) / qbits;
1481 0 : value_b = (pbits - 1) - value_n * qbits;
1482 0 : value_w = mpi_new (pbits);
1483 0 : value_x = mpi_new (pbits);
1484 :
1485 : restart:
1486 : /* Generate Q. */
1487 : for (;;)
1488 : {
1489 : /* Step 1: Generate a (new) seed unless one has been supplied. */
1490 0 : if (!seed)
1491 : {
1492 0 : seedlen = sizeof seed_help_buffer;
1493 0 : _gcry_create_nonce (seed_help_buffer, seedlen);
1494 0 : seed = seed_help_buffer;
1495 : }
1496 :
1497 : /* Step 2: U = sha1(seed) ^ sha1((seed+1) mod 2^{qbits}) */
1498 0 : memcpy (seed_plus, seed, seedlen);
1499 0 : for (i=seedlen-1; i >= 0; i--)
1500 : {
1501 0 : seed_plus[i]++;
1502 0 : if (seed_plus[i])
1503 0 : break;
1504 : }
1505 0 : _gcry_md_hash_buffer (GCRY_MD_SHA1, value_u, seed, seedlen);
1506 0 : _gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen);
1507 0 : for (i=0; i < sizeof value_u; i++)
1508 0 : value_u[i] ^= digest[i];
1509 :
1510 : /* Step 3: Form q from U */
1511 0 : _gcry_mpi_release (prime_q); prime_q = NULL;
1512 0 : ec = _gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG,
1513 : value_u, sizeof value_u, NULL);
1514 0 : if (ec)
1515 0 : goto leave;
1516 0 : mpi_set_highbit (prime_q, qbits-1 );
1517 0 : mpi_set_bit (prime_q, 0);
1518 :
1519 : /* Step 4: Test whether Q is prime using 64 round of Rabin-Miller. */
1520 0 : if (check_prime (prime_q, val_2, 64, NULL, NULL))
1521 0 : break; /* Yes, Q is prime. */
1522 :
1523 : /* Step 5. */
1524 0 : seed = NULL; /* Force a new seed at Step 1. */
1525 : }
1526 :
1527 : /* Step 6. Note that we do no use an explicit offset but increment
1528 : SEED_PLUS accordingly. SEED_PLUS is currently SEED+1. */
1529 0 : counter = 0;
1530 :
1531 : /* Generate P. */
1532 0 : prime_p = mpi_new (pbits);
1533 : for (;;)
1534 : {
1535 : /* Step 7: For k = 0,...n let
1536 : V_k = sha1(seed+offset+k) mod 2^{qbits}
1537 : Step 8: W = V_0 + V_1*2^160 +
1538 : ...
1539 : + V_{n-1}*2^{(n-1)*160}
1540 : + (V_{n} mod 2^b)*2^{n*160}
1541 : */
1542 0 : mpi_set_ui (value_w, 0);
1543 0 : for (value_k=0; value_k <= value_n; value_k++)
1544 : {
1545 : /* There is no need to have an explicit offset variable: In
1546 : the first round we shall have an offset of 2, this is
1547 : achieved by using SEED_PLUS which is already at SEED+1,
1548 : thus we just need to increment it once again. The
1549 : requirement for the next round is to update offset by N,
1550 : which we implictly did at the end of this loop, and then
1551 : to add one; this one is the same as in the first round. */
1552 0 : for (i=seedlen-1; i >= 0; i--)
1553 : {
1554 0 : seed_plus[i]++;
1555 0 : if (seed_plus[i])
1556 0 : break;
1557 : }
1558 0 : _gcry_md_hash_buffer (GCRY_MD_SHA1, digest, seed_plus, seedlen);
1559 :
1560 0 : _gcry_mpi_release (tmpval); tmpval = NULL;
1561 0 : ec = _gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG,
1562 : digest, sizeof digest, NULL);
1563 0 : if (ec)
1564 0 : goto leave;
1565 0 : if (value_k == value_n)
1566 0 : mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */
1567 0 : mpi_lshift (tmpval, tmpval, value_k*qbits);
1568 0 : mpi_add (value_w, value_w, tmpval);
1569 : }
1570 :
1571 : /* Step 8 continued: X = W + 2^{L-1} */
1572 0 : mpi_set_ui (value_x, 0);
1573 0 : mpi_set_highbit (value_x, pbits-1);
1574 0 : mpi_add (value_x, value_x, value_w);
1575 :
1576 : /* Step 9: c = X mod 2q, p = X - (c - 1) */
1577 0 : mpi_mul_2exp (tmpval, prime_q, 1);
1578 0 : mpi_mod (tmpval, value_x, tmpval);
1579 0 : mpi_sub_ui (tmpval, tmpval, 1);
1580 0 : mpi_sub (prime_p, value_x, tmpval);
1581 :
1582 : /* Step 10: If p < 2^{L-1} skip the primality test. */
1583 : /* Step 11 and 12: Primality test. */
1584 0 : if (mpi_get_nbits (prime_p) >= pbits-1
1585 0 : && check_prime (prime_p, val_2, 64, NULL, NULL) )
1586 0 : break; /* Yes, P is prime, continue with Step 15. */
1587 :
1588 : /* Step 13: counter = counter + 1, offset = offset + n + 1. */
1589 0 : counter++;
1590 :
1591 : /* Step 14: If counter >= 2^12 goto Step 1. */
1592 0 : if (counter >= 4096)
1593 0 : goto restart;
1594 : }
1595 :
1596 : /* Step 15: Save p, q, counter and seed. */
1597 : /* log_debug ("fips186-2 pbits p=%u q=%u counter=%d\n", */
1598 : /* mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter); */
1599 : /* log_printhex("fips186-2 seed:", seed, seedlen); */
1600 : /* log_mpidump ("fips186-2 prime p", prime_p); */
1601 : /* log_mpidump ("fips186-2 prime q", prime_q); */
1602 0 : if (r_q)
1603 : {
1604 0 : *r_q = prime_q;
1605 0 : prime_q = NULL;
1606 : }
1607 0 : if (r_p)
1608 : {
1609 0 : *r_p = prime_p;
1610 0 : prime_p = NULL;
1611 : }
1612 0 : if (r_counter)
1613 0 : *r_counter = counter;
1614 0 : if (r_seed && r_seedlen)
1615 : {
1616 0 : memcpy (seed_plus, seed, seedlen);
1617 0 : *r_seed = seed_plus;
1618 0 : seed_plus = NULL;
1619 0 : *r_seedlen = seedlen;
1620 : }
1621 :
1622 :
1623 : leave:
1624 0 : _gcry_mpi_release (tmpval);
1625 0 : _gcry_mpi_release (value_x);
1626 0 : _gcry_mpi_release (value_w);
1627 0 : _gcry_mpi_release (prime_p);
1628 0 : _gcry_mpi_release (prime_q);
1629 0 : xfree (seed_plus);
1630 0 : _gcry_mpi_release (val_2);
1631 0 : return ec;
1632 : }
1633 :
1634 :
1635 :
1636 : /* WARNING: The code below has not yet been tested!
1637 : *
1638 : * Generate the two prime used for DSA using the algorithm specified
1639 : * in FIPS 186-3, A.1.1.2. PBITS is the desired length of the prime P
1640 : * and a QBITS the length of the prime Q. If SEED is not supplied and
1641 : * SEEDLEN is 0 the function generates an appropriate SEED. On
1642 : * success the generated primes are stored at R_Q and R_P, the counter
1643 : * value is stored at R_COUNTER and the seed actually used for
1644 : * generation is stored at R_SEED and R_SEEDVALUE. The hash algorithm
1645 : * used is stored at R_HASHALGO.
1646 : *
1647 : * Note that this function is very similar to the fips186_2 code. Due
1648 : * to the minor differences, other buffer sizes and for documentarion,
1649 : * we use a separate function.
1650 : */
1651 : gpg_err_code_t
1652 0 : _gcry_generate_fips186_3_prime (unsigned int pbits, unsigned int qbits,
1653 : const void *seed, size_t seedlen,
1654 : gcry_mpi_t *r_q, gcry_mpi_t *r_p,
1655 : int *r_counter,
1656 : void **r_seed, size_t *r_seedlen,
1657 : int *r_hashalgo)
1658 : {
1659 : gpg_err_code_t ec;
1660 : unsigned char seed_help_buffer[256/8]; /* Used to hold a generated SEED. */
1661 : unsigned char *seed_plus; /* Malloced buffer to hold SEED+x. */
1662 : unsigned char digest[256/8]; /* Helper buffer for SHA-2 digest. */
1663 0 : gcry_mpi_t val_2 = NULL; /* Helper for the prime test. */
1664 0 : gcry_mpi_t tmpval = NULL; /* Helper variable. */
1665 : int hashalgo; /* The id of the Approved Hash Function. */
1666 : int i;
1667 :
1668 : unsigned char value_u[256/8];
1669 : int value_n, value_b, value_j;
1670 : int counter;
1671 0 : gcry_mpi_t value_w = NULL;
1672 0 : gcry_mpi_t value_x = NULL;
1673 0 : gcry_mpi_t prime_q = NULL;
1674 0 : gcry_mpi_t prime_p = NULL;
1675 :
1676 : gcry_assert (sizeof seed_help_buffer == sizeof digest
1677 : && sizeof seed_help_buffer == sizeof value_u);
1678 :
1679 : /* Step 1: Check the requested prime lengths. */
1680 : /* Note that due to the size of our buffers QBITS is limited to 256. */
1681 0 : if (pbits == 2048 && qbits == 224)
1682 0 : hashalgo = GCRY_MD_SHA224;
1683 0 : else if (pbits == 2048 && qbits == 256)
1684 0 : hashalgo = GCRY_MD_SHA256;
1685 0 : else if (pbits == 3072 && qbits == 256)
1686 0 : hashalgo = GCRY_MD_SHA256;
1687 : else
1688 0 : return GPG_ERR_INV_KEYLEN;
1689 :
1690 : /* Also check that the hash algorithm is available. */
1691 0 : ec = _gcry_md_test_algo (hashalgo);
1692 0 : if (ec)
1693 0 : return ec;
1694 0 : gcry_assert (qbits/8 <= sizeof digest);
1695 0 : gcry_assert (_gcry_md_get_algo_dlen (hashalgo) == qbits/8);
1696 :
1697 :
1698 : /* Step 2: Check seedlen. */
1699 0 : if (!seed && !seedlen)
1700 : ; /* No seed value given: We are asked to generate it. */
1701 0 : else if (!seed || seedlen < qbits/8)
1702 0 : return GPG_ERR_INV_ARG;
1703 :
1704 : /* Allocate a buffer to later compute SEED+some_increment and a few
1705 : helper variables. */
1706 0 : seed_plus = xtrymalloc (seedlen < sizeof seed_help_buffer?
1707 : sizeof seed_help_buffer : seedlen);
1708 0 : if (!seed_plus)
1709 : {
1710 0 : ec = gpg_err_code_from_syserror ();
1711 0 : goto leave;
1712 : }
1713 0 : val_2 = mpi_alloc_set_ui (2);
1714 0 : value_w = mpi_new (pbits);
1715 0 : value_x = mpi_new (pbits);
1716 :
1717 : /* Step 3: n = \lceil L / outlen \rceil - 1 */
1718 0 : value_n = (pbits + qbits - 1) / qbits - 1;
1719 : /* Step 4: b = L - 1 - (n * outlen) */
1720 0 : value_b = pbits - 1 - (value_n * qbits);
1721 :
1722 : restart:
1723 : /* Generate Q. */
1724 : for (;;)
1725 : {
1726 : /* Step 5: Generate a (new) seed unless one has been supplied. */
1727 0 : if (!seed)
1728 : {
1729 0 : seedlen = qbits/8;
1730 0 : gcry_assert (seedlen <= sizeof seed_help_buffer);
1731 0 : _gcry_create_nonce (seed_help_buffer, seedlen);
1732 0 : seed = seed_help_buffer;
1733 : }
1734 :
1735 : /* Step 6: U = hash(seed) */
1736 0 : _gcry_md_hash_buffer (hashalgo, value_u, seed, seedlen);
1737 :
1738 : /* Step 7: q = 2^{N-1} + U + 1 - (U mod 2) */
1739 0 : if ( !(value_u[qbits/8-1] & 0x01) )
1740 : {
1741 0 : for (i=qbits/8-1; i >= 0; i--)
1742 : {
1743 0 : value_u[i]++;
1744 0 : if (value_u[i])
1745 0 : break;
1746 : }
1747 : }
1748 0 : _gcry_mpi_release (prime_q); prime_q = NULL;
1749 0 : ec = _gcry_mpi_scan (&prime_q, GCRYMPI_FMT_USG,
1750 0 : value_u, qbits/8, NULL);
1751 0 : if (ec)
1752 0 : goto leave;
1753 0 : mpi_set_highbit (prime_q, qbits-1 );
1754 :
1755 : /* Step 8: Test whether Q is prime using 64 round of Rabin-Miller.
1756 : According to table C.1 this is sufficient for all
1757 : supported prime sizes (i.e. up 3072/256). */
1758 0 : if (check_prime (prime_q, val_2, 64, NULL, NULL))
1759 0 : break; /* Yes, Q is prime. */
1760 :
1761 : /* Step 8. */
1762 0 : seed = NULL; /* Force a new seed at Step 5. */
1763 : }
1764 :
1765 : /* Step 11. Note that we do no use an explicit offset but increment
1766 : SEED_PLUS accordingly. */
1767 0 : memcpy (seed_plus, seed, seedlen);
1768 0 : counter = 0;
1769 :
1770 : /* Generate P. */
1771 0 : prime_p = mpi_new (pbits);
1772 : for (;;)
1773 : {
1774 : /* Step 11.1: For j = 0,...n let
1775 : V_j = hash(seed+offset+j)
1776 : Step 11.2: W = V_0 + V_1*2^outlen +
1777 : ...
1778 : + V_{n-1}*2^{(n-1)*outlen}
1779 : + (V_{n} mod 2^b)*2^{n*outlen}
1780 : */
1781 0 : mpi_set_ui (value_w, 0);
1782 0 : for (value_j=0; value_j <= value_n; value_j++)
1783 : {
1784 : /* There is no need to have an explicit offset variable: In
1785 : the first round we shall have an offset of 1 and a j of
1786 : 0. This is achieved by incrementing SEED_PLUS here. For
1787 : the next round offset is implicitly updated by using
1788 : SEED_PLUS again. */
1789 0 : for (i=seedlen-1; i >= 0; i--)
1790 : {
1791 0 : seed_plus[i]++;
1792 0 : if (seed_plus[i])
1793 0 : break;
1794 : }
1795 0 : _gcry_md_hash_buffer (hashalgo, digest, seed_plus, seedlen);
1796 :
1797 0 : _gcry_mpi_release (tmpval); tmpval = NULL;
1798 0 : ec = _gcry_mpi_scan (&tmpval, GCRYMPI_FMT_USG,
1799 0 : digest, qbits/8, NULL);
1800 0 : if (ec)
1801 0 : goto leave;
1802 0 : if (value_j == value_n)
1803 0 : mpi_clear_highbit (tmpval, value_b); /* (V_n mod 2^b) */
1804 0 : mpi_lshift (tmpval, tmpval, value_j*qbits);
1805 0 : mpi_add (value_w, value_w, tmpval);
1806 : }
1807 :
1808 : /* Step 11.3: X = W + 2^{L-1} */
1809 0 : mpi_set_ui (value_x, 0);
1810 0 : mpi_set_highbit (value_x, pbits-1);
1811 0 : mpi_add (value_x, value_x, value_w);
1812 :
1813 : /* Step 11.4: c = X mod 2q */
1814 0 : mpi_mul_2exp (tmpval, prime_q, 1);
1815 0 : mpi_mod (tmpval, value_x, tmpval);
1816 :
1817 : /* Step 11.5: p = X - (c - 1) */
1818 0 : mpi_sub_ui (tmpval, tmpval, 1);
1819 0 : mpi_sub (prime_p, value_x, tmpval);
1820 :
1821 : /* Step 11.6: If p < 2^{L-1} skip the primality test. */
1822 : /* Step 11.7 and 11.8: Primality test. */
1823 0 : if (mpi_get_nbits (prime_p) >= pbits-1
1824 0 : && check_prime (prime_p, val_2, 64, NULL, NULL) )
1825 0 : break; /* Yes, P is prime, continue with Step 15. */
1826 :
1827 : /* Step 11.9: counter = counter + 1, offset = offset + n + 1.
1828 : If counter >= 4L goto Step 5. */
1829 0 : counter++;
1830 0 : if (counter >= 4*pbits)
1831 0 : goto restart;
1832 : }
1833 :
1834 : /* Step 12: Save p, q, counter and seed. */
1835 : /* log_debug ("fips186-3 pbits p=%u q=%u counter=%d\n", */
1836 : /* mpi_get_nbits (prime_p), mpi_get_nbits (prime_q), counter); */
1837 : /* log_printhex ("fips186-3 seed", seed, seedlen); */
1838 : /* log_printmpi ("fips186-3 p", prime_p); */
1839 : /* log_printmpi ("fips186-3 q", prime_q); */
1840 :
1841 0 : if (r_q)
1842 : {
1843 0 : *r_q = prime_q;
1844 0 : prime_q = NULL;
1845 : }
1846 0 : if (r_p)
1847 : {
1848 0 : *r_p = prime_p;
1849 0 : prime_p = NULL;
1850 : }
1851 0 : if (r_counter)
1852 0 : *r_counter = counter;
1853 0 : if (r_seed && r_seedlen)
1854 : {
1855 0 : memcpy (seed_plus, seed, seedlen);
1856 0 : *r_seed = seed_plus;
1857 0 : seed_plus = NULL;
1858 0 : *r_seedlen = seedlen;
1859 : }
1860 0 : if (r_hashalgo)
1861 0 : *r_hashalgo = hashalgo;
1862 :
1863 : leave:
1864 0 : _gcry_mpi_release (tmpval);
1865 0 : _gcry_mpi_release (value_x);
1866 0 : _gcry_mpi_release (value_w);
1867 0 : _gcry_mpi_release (prime_p);
1868 0 : _gcry_mpi_release (prime_q);
1869 0 : xfree (seed_plus);
1870 0 : _gcry_mpi_release (val_2);
1871 0 : return ec;
1872 : }
|
