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d02b48c6 | 1 | /* crypto/bn/bn_prime.c */ |
58964a49 | 2 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
d02b48c6 RE |
3 | * All rights reserved. |
4 | * | |
5 | * This package is an SSL implementation written | |
6 | * by Eric Young (eay@cryptsoft.com). | |
7 | * The implementation was written so as to conform with Netscapes SSL. | |
0f113f3e | 8 | * |
d02b48c6 RE |
9 | * This library is free for commercial and non-commercial use as long as |
10 | * the following conditions are aheared to. The following conditions | |
11 | * apply to all code found in this distribution, be it the RC4, RSA, | |
12 | * lhash, DES, etc., code; not just the SSL code. The SSL documentation | |
13 | * included with this distribution is covered by the same copyright terms | |
14 | * except that the holder is Tim Hudson (tjh@cryptsoft.com). | |
0f113f3e | 15 | * |
d02b48c6 RE |
16 | * Copyright remains Eric Young's, and as such any Copyright notices in |
17 | * the code are not to be removed. | |
18 | * If this package is used in a product, Eric Young should be given attribution | |
19 | * as the author of the parts of the library used. | |
20 | * This can be in the form of a textual message at program startup or | |
21 | * in documentation (online or textual) provided with the package. | |
0f113f3e | 22 | * |
d02b48c6 RE |
23 | * Redistribution and use in source and binary forms, with or without |
24 | * modification, are permitted provided that the following conditions | |
25 | * are met: | |
26 | * 1. Redistributions of source code must retain the copyright | |
27 | * notice, this list of conditions and the following disclaimer. | |
28 | * 2. Redistributions in binary form must reproduce the above copyright | |
29 | * notice, this list of conditions and the following disclaimer in the | |
30 | * documentation and/or other materials provided with the distribution. | |
31 | * 3. All advertising materials mentioning features or use of this software | |
32 | * must display the following acknowledgement: | |
33 | * "This product includes cryptographic software written by | |
34 | * Eric Young (eay@cryptsoft.com)" | |
35 | * The word 'cryptographic' can be left out if the rouines from the library | |
36 | * being used are not cryptographic related :-). | |
0f113f3e | 37 | * 4. If you include any Windows specific code (or a derivative thereof) from |
d02b48c6 RE |
38 | * the apps directory (application code) you must include an acknowledgement: |
39 | * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" | |
0f113f3e | 40 | * |
d02b48c6 RE |
41 | * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
42 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
43 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
44 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | |
45 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |
46 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |
47 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
48 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
49 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |
50 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |
51 | * SUCH DAMAGE. | |
0f113f3e | 52 | * |
d02b48c6 RE |
53 | * The licence and distribution terms for any publically available version or |
54 | * derivative of this code cannot be changed. i.e. this code cannot simply be | |
55 | * copied and put under another distribution licence | |
56 | * [including the GNU Public Licence.] | |
57 | */ | |
bfe30e4d | 58 | /* ==================================================================== |
435037d4 | 59 | * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. |
bfe30e4d BM |
60 | * |
61 | * Redistribution and use in source and binary forms, with or without | |
62 | * modification, are permitted provided that the following conditions | |
63 | * are met: | |
64 | * | |
65 | * 1. Redistributions of source code must retain the above copyright | |
0f113f3e | 66 | * notice, this list of conditions and the following disclaimer. |
bfe30e4d BM |
67 | * |
68 | * 2. Redistributions in binary form must reproduce the above copyright | |
69 | * notice, this list of conditions and the following disclaimer in | |
70 | * the documentation and/or other materials provided with the | |
71 | * distribution. | |
72 | * | |
73 | * 3. All advertising materials mentioning features or use of this | |
74 | * software must display the following acknowledgment: | |
75 | * "This product includes software developed by the OpenSSL Project | |
76 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
77 | * | |
78 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
79 | * endorse or promote products derived from this software without | |
80 | * prior written permission. For written permission, please contact | |
81 | * openssl-core@openssl.org. | |
82 | * | |
83 | * 5. Products derived from this software may not be called "OpenSSL" | |
84 | * nor may "OpenSSL" appear in their names without prior written | |
85 | * permission of the OpenSSL Project. | |
86 | * | |
87 | * 6. Redistributions of any form whatsoever must retain the following | |
88 | * acknowledgment: | |
89 | * "This product includes software developed by the OpenSSL Project | |
90 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
91 | * | |
92 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
93 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
94 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
95 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
96 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
97 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
98 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
99 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
100 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
101 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
102 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
103 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
104 | * ==================================================================== | |
105 | * | |
106 | * This product includes cryptographic software written by Eric Young | |
107 | * (eay@cryptsoft.com). This product includes software written by Tim | |
108 | * Hudson (tjh@cryptsoft.com). | |
109 | * | |
110 | */ | |
d02b48c6 RE |
111 | |
112 | #include <stdio.h> | |
113 | #include <time.h> | |
114 | #include "cryptlib.h" | |
115 | #include "bn_lcl.h" | |
ec577822 | 116 | #include <openssl/rand.h> |
d02b48c6 | 117 | |
0f113f3e MC |
118 | /* |
119 | * NB: these functions have been "upgraded", the deprecated versions (which | |
120 | * are compatibility wrappers using these functions) are in bn_depr.c. - | |
121 | * Geoff | |
e9224c71 GT |
122 | */ |
123 | ||
0f113f3e MC |
124 | /* |
125 | * The quick sieve algorithm approach to weeding out primes is Philip | |
126 | * Zimmermann's, as implemented in PGP. I have had a read of his comments | |
127 | * and implemented my own version. | |
d02b48c6 RE |
128 | */ |
129 | #include "bn_prime.h" | |
130 | ||
7999c65c | 131 | static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, |
0f113f3e MC |
132 | const BIGNUM *a1_odd, int k, BN_CTX *ctx, |
133 | BN_MONT_CTX *mont); | |
d02b48c6 | 134 | static int probable_prime(BIGNUM *rnd, int bits); |
76aa0ddc | 135 | static int probable_prime_dh_safe(BIGNUM *rnd, int bits, |
0f113f3e MC |
136 | const BIGNUM *add, const BIGNUM *rem, |
137 | BN_CTX *ctx); | |
eb952088 | 138 | |
46838817 | 139 | static const int prime_offsets[480] = { |
0f113f3e MC |
140 | 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, |
141 | 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, | |
142 | 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229, | |
143 | 233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293, | |
144 | 299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367, | |
145 | 373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433, | |
146 | 437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499, | |
147 | 503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569, | |
148 | 571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631, | |
149 | 641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701, | |
150 | 703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769, | |
151 | 773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839, | |
152 | 841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901, | |
153 | 907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971, | |
154 | 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031, | |
155 | 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087, | |
156 | 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151, | |
157 | 1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213, | |
158 | 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271, | |
159 | 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319, | |
160 | 1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373, | |
161 | 1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433, | |
162 | 1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489, | |
163 | 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549, | |
164 | 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609, | |
165 | 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667, | |
166 | 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721, | |
167 | 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781, | |
168 | 1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843, | |
169 | 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901, | |
170 | 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951, | |
171 | 1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, | |
172 | 2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071, | |
173 | 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131, | |
174 | 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197, | |
175 | 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249, | |
176 | 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297, | |
177 | 2309, 2311 | |
178 | }; | |
179 | ||
46838817 BL |
180 | static const int prime_offset_count = 480; |
181 | static const int prime_multiplier = 2310; | |
0f113f3e MC |
182 | static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <= |
183 | * |prime_multiplier| */ | |
46838817 | 184 | static const int first_prime_index = 5; |
b0513819 | 185 | |
e9224c71 | 186 | int BN_GENCB_call(BN_GENCB *cb, int a, int b) |
0f113f3e MC |
187 | { |
188 | /* No callback means continue */ | |
189 | if (!cb) | |
190 | return 1; | |
191 | switch (cb->ver) { | |
192 | case 1: | |
193 | /* Deprecated-style callbacks */ | |
194 | if (!cb->cb.cb_1) | |
195 | return 1; | |
196 | cb->cb.cb_1(a, b, cb->arg); | |
197 | return 1; | |
198 | case 2: | |
199 | /* New-style callbacks */ | |
200 | return cb->cb.cb_2(a, b, cb); | |
201 | default: | |
202 | break; | |
203 | } | |
204 | /* Unrecognised callback type */ | |
205 | return 0; | |
206 | } | |
e9224c71 GT |
207 | |
208 | int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, | |
0f113f3e MC |
209 | const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) |
210 | { | |
211 | BIGNUM *t; | |
212 | int found = 0; | |
213 | int i, j, c1 = 0; | |
214 | BN_CTX *ctx; | |
215 | int checks = BN_prime_checks_for_size(bits); | |
216 | ||
217 | if (bits < 2) { | |
218 | /* There are no prime numbers this small. */ | |
219 | BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL); | |
220 | return 0; | |
221 | } else if (bits == 2 && safe) { | |
222 | /* The smallest safe prime (7) is three bits. */ | |
223 | BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL); | |
224 | return 0; | |
225 | } | |
226 | ||
227 | ctx = BN_CTX_new(); | |
228 | if (ctx == NULL) | |
229 | goto err; | |
230 | BN_CTX_start(ctx); | |
231 | t = BN_CTX_get(ctx); | |
232 | if (!t) | |
233 | goto err; | |
234 | loop: | |
235 | /* make a random number and set the top and bottom bits */ | |
236 | if (add == NULL) { | |
237 | if (!probable_prime(ret, bits)) | |
238 | goto err; | |
239 | } else { | |
240 | if (safe) { | |
241 | if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) | |
242 | goto err; | |
243 | } else { | |
244 | if (!bn_probable_prime_dh(ret, bits, add, rem, ctx)) | |
245 | goto err; | |
246 | } | |
247 | } | |
248 | /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ | |
249 | if (!BN_GENCB_call(cb, 0, c1++)) | |
250 | /* aborted */ | |
251 | goto err; | |
252 | ||
253 | if (!safe) { | |
254 | i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); | |
255 | if (i == -1) | |
256 | goto err; | |
257 | if (i == 0) | |
258 | goto loop; | |
259 | } else { | |
260 | /* | |
261 | * for "safe prime" generation, check that (p-1)/2 is prime. Since a | |
262 | * prime is odd, We just need to divide by 2 | |
263 | */ | |
264 | if (!BN_rshift1(t, ret)) | |
265 | goto err; | |
266 | ||
267 | for (i = 0; i < checks; i++) { | |
268 | j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); | |
269 | if (j == -1) | |
270 | goto err; | |
271 | if (j == 0) | |
272 | goto loop; | |
273 | ||
274 | j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); | |
275 | if (j == -1) | |
276 | goto err; | |
277 | if (j == 0) | |
278 | goto loop; | |
279 | ||
280 | if (!BN_GENCB_call(cb, 2, c1 - 1)) | |
281 | goto err; | |
282 | /* We have a safe prime test pass */ | |
283 | } | |
284 | } | |
285 | /* we have a prime :-) */ | |
286 | found = 1; | |
287 | err: | |
288 | if (ctx != NULL) { | |
289 | BN_CTX_end(ctx); | |
290 | BN_CTX_free(ctx); | |
291 | } | |
292 | bn_check_top(ret); | |
293 | return found; | |
294 | } | |
295 | ||
296 | int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, | |
297 | BN_GENCB *cb) | |
298 | { | |
299 | return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); | |
300 | } | |
e74231ed | 301 | |
e9224c71 | 302 | int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, |
0f113f3e MC |
303 | int do_trial_division, BN_GENCB *cb) |
304 | { | |
305 | int i, j, ret = -1; | |
306 | int k; | |
307 | BN_CTX *ctx = NULL; | |
308 | BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ | |
309 | BN_MONT_CTX *mont = NULL; | |
310 | const BIGNUM *A = NULL; | |
311 | ||
312 | if (BN_cmp(a, BN_value_one()) <= 0) | |
313 | return 0; | |
314 | ||
315 | if (checks == BN_prime_checks) | |
316 | checks = BN_prime_checks_for_size(BN_num_bits(a)); | |
317 | ||
318 | /* first look for small factors */ | |
319 | if (!BN_is_odd(a)) | |
320 | /* a is even => a is prime if and only if a == 2 */ | |
321 | return BN_is_word(a, 2); | |
322 | if (do_trial_division) { | |
323 | for (i = 1; i < NUMPRIMES; i++) | |
324 | if (BN_mod_word(a, primes[i]) == 0) | |
325 | return 0; | |
326 | if (!BN_GENCB_call(cb, 1, -1)) | |
327 | goto err; | |
328 | } | |
329 | ||
330 | if (ctx_passed != NULL) | |
331 | ctx = ctx_passed; | |
332 | else if ((ctx = BN_CTX_new()) == NULL) | |
333 | goto err; | |
334 | BN_CTX_start(ctx); | |
335 | ||
336 | /* A := abs(a) */ | |
337 | if (a->neg) { | |
338 | BIGNUM *t; | |
339 | if ((t = BN_CTX_get(ctx)) == NULL) | |
340 | goto err; | |
341 | BN_copy(t, a); | |
342 | t->neg = 0; | |
343 | A = t; | |
344 | } else | |
345 | A = a; | |
346 | A1 = BN_CTX_get(ctx); | |
347 | A1_odd = BN_CTX_get(ctx); | |
348 | check = BN_CTX_get(ctx); | |
349 | if (check == NULL) | |
350 | goto err; | |
351 | ||
352 | /* compute A1 := A - 1 */ | |
353 | if (!BN_copy(A1, A)) | |
354 | goto err; | |
355 | if (!BN_sub_word(A1, 1)) | |
356 | goto err; | |
357 | if (BN_is_zero(A1)) { | |
358 | ret = 0; | |
359 | goto err; | |
360 | } | |
361 | ||
362 | /* write A1 as A1_odd * 2^k */ | |
363 | k = 1; | |
364 | while (!BN_is_bit_set(A1, k)) | |
365 | k++; | |
366 | if (!BN_rshift(A1_odd, A1, k)) | |
367 | goto err; | |
368 | ||
369 | /* Montgomery setup for computations mod A */ | |
370 | mont = BN_MONT_CTX_new(); | |
371 | if (mont == NULL) | |
372 | goto err; | |
373 | if (!BN_MONT_CTX_set(mont, A, ctx)) | |
374 | goto err; | |
375 | ||
376 | for (i = 0; i < checks; i++) { | |
377 | if (!BN_pseudo_rand_range(check, A1)) | |
378 | goto err; | |
379 | if (!BN_add_word(check, 1)) | |
380 | goto err; | |
381 | /* now 1 <= check < A */ | |
382 | ||
383 | j = witness(check, A, A1, A1_odd, k, ctx, mont); | |
384 | if (j == -1) | |
385 | goto err; | |
386 | if (j) { | |
387 | ret = 0; | |
388 | goto err; | |
389 | } | |
390 | if (!BN_GENCB_call(cb, 1, i)) | |
391 | goto err; | |
392 | } | |
393 | ret = 1; | |
394 | err: | |
395 | if (ctx != NULL) { | |
396 | BN_CTX_end(ctx); | |
397 | if (ctx_passed == NULL) | |
398 | BN_CTX_free(ctx); | |
399 | } | |
400 | if (mont != NULL) | |
401 | BN_MONT_CTX_free(mont); | |
402 | ||
403 | return (ret); | |
404 | } | |
a87030a1 | 405 | |
982c42cb | 406 | int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx) |
0f113f3e MC |
407 | { |
408 | int i; | |
409 | int ret = 0; | |
410 | ||
411 | loop: | |
412 | if (!BN_rand(rnd, bits, 0, 1)) | |
413 | goto err; | |
414 | ||
415 | /* we now have a random number 'rand' to test. */ | |
416 | ||
417 | for (i = 1; i < NUMPRIMES; i++) { | |
418 | /* check that rnd is a prime */ | |
419 | if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { | |
420 | goto loop; | |
421 | } | |
422 | } | |
423 | ret = 1; | |
424 | ||
425 | err: | |
426 | bn_check_top(rnd); | |
427 | return (ret); | |
428 | } | |
982c42cb FLM |
429 | |
430 | int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx) | |
0f113f3e MC |
431 | { |
432 | int i; | |
433 | BIGNUM *offset_index; | |
434 | BIGNUM *offset_count; | |
435 | int ret = 0; | |
436 | ||
437 | OPENSSL_assert(bits > prime_multiplier_bits); | |
438 | ||
439 | BN_CTX_start(ctx); | |
440 | if ((offset_index = BN_CTX_get(ctx)) == NULL) | |
441 | goto err; | |
442 | if ((offset_count = BN_CTX_get(ctx)) == NULL) | |
443 | goto err; | |
444 | ||
445 | BN_add_word(offset_count, prime_offset_count); | |
446 | ||
447 | loop: | |
448 | if (!BN_rand(rnd, bits - prime_multiplier_bits, 0, 1)) | |
449 | goto err; | |
450 | if (BN_is_bit_set(rnd, bits)) | |
451 | goto loop; | |
452 | if (!BN_rand_range(offset_index, offset_count)) | |
453 | goto err; | |
454 | ||
455 | BN_mul_word(rnd, prime_multiplier); | |
456 | BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]); | |
457 | ||
458 | /* we now have a random number 'rand' to test. */ | |
459 | ||
460 | /* skip coprimes */ | |
461 | for (i = first_prime_index; i < NUMPRIMES; i++) { | |
462 | /* check that rnd is a prime */ | |
463 | if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { | |
464 | goto loop; | |
465 | } | |
466 | } | |
467 | ret = 1; | |
468 | ||
469 | err: | |
470 | BN_CTX_end(ctx); | |
471 | bn_check_top(rnd); | |
472 | return ret; | |
473 | } | |
e46a059e | 474 | |
7999c65c | 475 | static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, |
0f113f3e MC |
476 | const BIGNUM *a1_odd, int k, BN_CTX *ctx, |
477 | BN_MONT_CTX *mont) | |
478 | { | |
479 | if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ | |
480 | return -1; | |
481 | if (BN_is_one(w)) | |
482 | return 0; /* probably prime */ | |
483 | if (BN_cmp(w, a1) == 0) | |
484 | return 0; /* w == -1 (mod a), 'a' is probably prime */ | |
485 | while (--k) { | |
486 | if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ | |
487 | return -1; | |
488 | if (BN_is_one(w)) | |
489 | return 1; /* 'a' is composite, otherwise a previous 'w' | |
490 | * would have been == -1 (mod 'a') */ | |
491 | if (BN_cmp(w, a1) == 0) | |
492 | return 0; /* w == -1 (mod a), 'a' is probably prime */ | |
493 | } | |
494 | /* | |
495 | * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and | |
496 | * it is neither -1 nor +1 -- so 'a' cannot be prime | |
497 | */ | |
498 | bn_check_top(w); | |
499 | return 1; | |
500 | } | |
d02b48c6 | 501 | |
6b691a5c | 502 | static int probable_prime(BIGNUM *rnd, int bits) |
0f113f3e MC |
503 | { |
504 | int i; | |
505 | prime_t mods[NUMPRIMES]; | |
506 | BN_ULONG delta; | |
507 | BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; | |
508 | char is_single_word = bits <= BN_BITS2; | |
509 | ||
510 | again: | |
511 | if (!BN_rand(rnd, bits, 1, 1)) | |
512 | return (0); | |
513 | /* we now have a random number 'rnd' to test. */ | |
514 | for (i = 1; i < NUMPRIMES; i++) | |
515 | mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]); | |
516 | /* | |
517 | * If bits is so small that it fits into a single word then we | |
518 | * additionally don't want to exceed that many bits. | |
519 | */ | |
520 | if (is_single_word) { | |
521 | BN_ULONG size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1; | |
522 | if (size_limit < maxdelta) | |
523 | maxdelta = size_limit; | |
524 | } | |
525 | delta = 0; | |
526 | loop: | |
527 | if (is_single_word) { | |
528 | BN_ULONG rnd_word = BN_get_word(rnd); | |
529 | ||
530 | /*- | |
531 | * In the case that the candidate prime is a single word then | |
532 | * we check that: | |
533 | * 1) It's greater than primes[i] because we shouldn't reject | |
534 | * 3 as being a prime number because it's a multiple of | |
535 | * three. | |
536 | * 2) That it's not a multiple of a known prime. We don't | |
537 | * check that rnd-1 is also coprime to all the known | |
538 | * primes because there aren't many small primes where | |
539 | * that's true. | |
540 | */ | |
541 | for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) { | |
542 | if ((mods[i] + delta) % primes[i] == 0) { | |
543 | delta += 2; | |
544 | if (delta > maxdelta) | |
545 | goto again; | |
546 | goto loop; | |
547 | } | |
548 | } | |
549 | } else { | |
550 | for (i = 1; i < NUMPRIMES; i++) { | |
551 | /* | |
552 | * check that rnd is not a prime and also that gcd(rnd-1,primes) | |
553 | * == 1 (except for 2) | |
554 | */ | |
555 | if (((mods[i] + delta) % primes[i]) <= 1) { | |
556 | delta += 2; | |
557 | if (delta > maxdelta) | |
558 | goto again; | |
559 | goto loop; | |
560 | } | |
561 | } | |
562 | } | |
563 | if (!BN_add_word(rnd, delta)) | |
564 | return (0); | |
565 | if (BN_num_bits(rnd) != bits) | |
566 | goto again; | |
567 | bn_check_top(rnd); | |
568 | return (1); | |
569 | } | |
d02b48c6 | 570 | |
982c42cb | 571 | int bn_probable_prime_dh(BIGNUM *rnd, int bits, |
0f113f3e MC |
572 | const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) |
573 | { | |
574 | int i, ret = 0; | |
575 | BIGNUM *t1; | |
576 | ||
577 | BN_CTX_start(ctx); | |
578 | if ((t1 = BN_CTX_get(ctx)) == NULL) | |
579 | goto err; | |
580 | ||
581 | if (!BN_rand(rnd, bits, 0, 1)) | |
582 | goto err; | |
583 | ||
584 | /* we need ((rnd-rem) % add) == 0 */ | |
585 | ||
586 | if (!BN_mod(t1, rnd, add, ctx)) | |
587 | goto err; | |
588 | if (!BN_sub(rnd, rnd, t1)) | |
589 | goto err; | |
590 | if (rem == NULL) { | |
591 | if (!BN_add_word(rnd, 1)) | |
592 | goto err; | |
593 | } else { | |
594 | if (!BN_add(rnd, rnd, rem)) | |
595 | goto err; | |
596 | } | |
597 | ||
598 | /* we now have a random number 'rand' to test. */ | |
599 | ||
600 | loop: | |
601 | for (i = 1; i < NUMPRIMES; i++) { | |
602 | /* check that rnd is a prime */ | |
603 | if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { | |
604 | if (!BN_add(rnd, rnd, add)) | |
605 | goto err; | |
606 | goto loop; | |
607 | } | |
608 | } | |
609 | ret = 1; | |
610 | ||
611 | err: | |
612 | BN_CTX_end(ctx); | |
613 | bn_check_top(rnd); | |
614 | return (ret); | |
615 | } | |
b0513819 | 616 | |
020fc820 | 617 | static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, |
0f113f3e MC |
618 | const BIGNUM *rem, BN_CTX *ctx) |
619 | { | |
620 | int i, ret = 0; | |
621 | BIGNUM *t1, *qadd, *q; | |
622 | ||
623 | bits--; | |
624 | BN_CTX_start(ctx); | |
625 | t1 = BN_CTX_get(ctx); | |
626 | q = BN_CTX_get(ctx); | |
627 | qadd = BN_CTX_get(ctx); | |
628 | if (qadd == NULL) | |
629 | goto err; | |
630 | ||
631 | if (!BN_rshift1(qadd, padd)) | |
632 | goto err; | |
633 | ||
634 | if (!BN_rand(q, bits, 0, 1)) | |
635 | goto err; | |
636 | ||
637 | /* we need ((rnd-rem) % add) == 0 */ | |
638 | if (!BN_mod(t1, q, qadd, ctx)) | |
639 | goto err; | |
640 | if (!BN_sub(q, q, t1)) | |
641 | goto err; | |
642 | if (rem == NULL) { | |
643 | if (!BN_add_word(q, 1)) | |
644 | goto err; | |
645 | } else { | |
646 | if (!BN_rshift1(t1, rem)) | |
647 | goto err; | |
648 | if (!BN_add(q, q, t1)) | |
649 | goto err; | |
650 | } | |
651 | ||
652 | /* we now have a random number 'rand' to test. */ | |
653 | if (!BN_lshift1(p, q)) | |
654 | goto err; | |
655 | if (!BN_add_word(p, 1)) | |
656 | goto err; | |
657 | ||
658 | loop: | |
659 | for (i = 1; i < NUMPRIMES; i++) { | |
660 | /* check that p and q are prime */ | |
661 | /* | |
662 | * check that for p and q gcd(p-1,primes) == 1 (except for 2) | |
663 | */ | |
664 | if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) || | |
665 | (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) { | |
666 | if (!BN_add(p, p, padd)) | |
667 | goto err; | |
668 | if (!BN_add(q, q, qadd)) | |
669 | goto err; | |
670 | goto loop; | |
671 | } | |
672 | } | |
673 | ret = 1; | |
674 | ||
675 | err: | |
676 | BN_CTX_end(ctx); | |
677 | bn_check_top(p); | |
678 | return (ret); | |
679 | } |