source: EcnlProtoTool/trunk/openssl-1.1.0e/crypto/bn/bn_prime.c@ 331

Last change on this file since 331 was 331, checked in by coas-nagasima, 6 years ago

prototoolに関連するプロジェクトをnewlibからmuslを使うよう変更・更新
ntshellをnewlibの下位の実装から、muslのsyscallの実装に変更・更新
以下のOSSをアップデート
・mruby-1.3.0
・musl-1.1.18
・onigmo-6.1.3
・tcc-0.9.27
以下のOSSを追加
・openssl-1.1.0e
・curl-7.57.0
・zlib-1.2.11
以下のmrbgemsを追加
・iij/mruby-digest
・iij/mruby-env
・iij/mruby-errno
・iij/mruby-iijson
・iij/mruby-ipaddr
・iij/mruby-mock
・iij/mruby-require
・iij/mruby-tls-openssl
  • Property svn:eol-style set to native
  • Property svn:mime-type set to text/x-csrc
File size: 17.6 KB
Line 
1/*
2 * WARNING: do not edit!
3 * Generated by crypto/bn/bn_prime.pl
4 * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
5 *
6 * Licensed under the OpenSSL license (the "License"). You may not use
7 * this file except in compliance with the License. You can obtain a copy
8 * in the file LICENSE in the source distribution or at
9 * https://www.openssl.org/source/license.html
10 */
11
12#include <stdio.h>
13#include <time.h>
14#include "internal/cryptlib.h"
15#include "bn_lcl.h"
16
17/*
18 * The quick sieve algorithm approach to weeding out primes is Philip
19 * Zimmermann's, as implemented in PGP. I have had a read of his comments
20 * and implemented my own version.
21 */
22#include "bn_prime.h"
23
24static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
25 const BIGNUM *a1_odd, int k, BN_CTX *ctx,
26 BN_MONT_CTX *mont);
27static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
28static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
29 const BIGNUM *add, const BIGNUM *rem,
30 BN_CTX *ctx);
31
32static const int prime_offsets[480] = {
33 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
34 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
35 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229,
36 233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293,
37 299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367,
38 373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433,
39 437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499,
40 503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569,
41 571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631,
42 641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701,
43 703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769,
44 773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839,
45 841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901,
46 907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971,
47 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031,
48 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087,
49 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151,
50 1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213,
51 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271,
52 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319,
53 1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373,
54 1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433,
55 1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489,
56 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549,
57 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609,
58 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667,
59 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721,
60 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781,
61 1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843,
62 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901,
63 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951,
64 1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
65 2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071,
66 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131,
67 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197,
68 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249,
69 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297,
70 2309, 2311
71};
72
73static const int prime_offset_count = 480;
74static const int prime_multiplier = 2310;
75static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <=
76 * |prime_multiplier| */
77static const int first_prime_index = 5;
78
79int BN_GENCB_call(BN_GENCB *cb, int a, int b)
80{
81 /* No callback means continue */
82 if (!cb)
83 return 1;
84 switch (cb->ver) {
85 case 1:
86 /* Deprecated-style callbacks */
87 if (!cb->cb.cb_1)
88 return 1;
89 cb->cb.cb_1(a, b, cb->arg);
90 return 1;
91 case 2:
92 /* New-style callbacks */
93 return cb->cb.cb_2(a, b, cb);
94 default:
95 break;
96 }
97 /* Unrecognised callback type */
98 return 0;
99}
100
101int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
102 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
103{
104 BIGNUM *t;
105 int found = 0;
106 int i, j, c1 = 0;
107 BN_CTX *ctx = NULL;
108 prime_t *mods = NULL;
109 int checks = BN_prime_checks_for_size(bits);
110
111 if (bits < 2) {
112 /* There are no prime numbers this small. */
113 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
114 return 0;
115 } else if (bits == 2 && safe) {
116 /* The smallest safe prime (7) is three bits. */
117 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
118 return 0;
119 }
120
121 mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
122 if (mods == NULL)
123 goto err;
124
125 ctx = BN_CTX_new();
126 if (ctx == NULL)
127 goto err;
128 BN_CTX_start(ctx);
129 t = BN_CTX_get(ctx);
130 if (!t)
131 goto err;
132 loop:
133 /* make a random number and set the top and bottom bits */
134 if (add == NULL) {
135 if (!probable_prime(ret, bits, mods))
136 goto err;
137 } else {
138 if (safe) {
139 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
140 goto err;
141 } else {
142 if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
143 goto err;
144 }
145 }
146
147 if (!BN_GENCB_call(cb, 0, c1++))
148 /* aborted */
149 goto err;
150
151 if (!safe) {
152 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
153 if (i == -1)
154 goto err;
155 if (i == 0)
156 goto loop;
157 } else {
158 /*
159 * for "safe prime" generation, check that (p-1)/2 is prime. Since a
160 * prime is odd, We just need to divide by 2
161 */
162 if (!BN_rshift1(t, ret))
163 goto err;
164
165 for (i = 0; i < checks; i++) {
166 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
167 if (j == -1)
168 goto err;
169 if (j == 0)
170 goto loop;
171
172 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
173 if (j == -1)
174 goto err;
175 if (j == 0)
176 goto loop;
177
178 if (!BN_GENCB_call(cb, 2, c1 - 1))
179 goto err;
180 /* We have a safe prime test pass */
181 }
182 }
183 /* we have a prime :-) */
184 found = 1;
185 err:
186 OPENSSL_free(mods);
187 if (ctx != NULL)
188 BN_CTX_end(ctx);
189 BN_CTX_free(ctx);
190 bn_check_top(ret);
191 return found;
192}
193
194int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
195 BN_GENCB *cb)
196{
197 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
198}
199
200int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
201 int do_trial_division, BN_GENCB *cb)
202{
203 int i, j, ret = -1;
204 int k;
205 BN_CTX *ctx = NULL;
206 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
207 BN_MONT_CTX *mont = NULL;
208 const BIGNUM *A = NULL;
209
210 if (BN_cmp(a, BN_value_one()) <= 0)
211 return 0;
212
213 if (checks == BN_prime_checks)
214 checks = BN_prime_checks_for_size(BN_num_bits(a));
215
216 /* first look for small factors */
217 if (!BN_is_odd(a))
218 /* a is even => a is prime if and only if a == 2 */
219 return BN_is_word(a, 2);
220 if (do_trial_division) {
221 for (i = 1; i < NUMPRIMES; i++) {
222 BN_ULONG mod = BN_mod_word(a, primes[i]);
223 if (mod == (BN_ULONG)-1)
224 goto err;
225 if (mod == 0)
226 return 0;
227 }
228 if (!BN_GENCB_call(cb, 1, -1))
229 goto err;
230 }
231
232 if (ctx_passed != NULL)
233 ctx = ctx_passed;
234 else if ((ctx = BN_CTX_new()) == NULL)
235 goto err;
236 BN_CTX_start(ctx);
237
238 /* A := abs(a) */
239 if (a->neg) {
240 BIGNUM *t;
241 if ((t = BN_CTX_get(ctx)) == NULL)
242 goto err;
243 if (BN_copy(t, a) == NULL)
244 goto err;
245 t->neg = 0;
246 A = t;
247 } else
248 A = a;
249 A1 = BN_CTX_get(ctx);
250 A1_odd = BN_CTX_get(ctx);
251 check = BN_CTX_get(ctx);
252 if (check == NULL)
253 goto err;
254
255 /* compute A1 := A - 1 */
256 if (!BN_copy(A1, A))
257 goto err;
258 if (!BN_sub_word(A1, 1))
259 goto err;
260 if (BN_is_zero(A1)) {
261 ret = 0;
262 goto err;
263 }
264
265 /* write A1 as A1_odd * 2^k */
266 k = 1;
267 while (!BN_is_bit_set(A1, k))
268 k++;
269 if (!BN_rshift(A1_odd, A1, k))
270 goto err;
271
272 /* Montgomery setup for computations mod A */
273 mont = BN_MONT_CTX_new();
274 if (mont == NULL)
275 goto err;
276 if (!BN_MONT_CTX_set(mont, A, ctx))
277 goto err;
278
279 for (i = 0; i < checks; i++) {
280 if (!BN_pseudo_rand_range(check, A1))
281 goto err;
282 if (!BN_add_word(check, 1))
283 goto err;
284 /* now 1 <= check < A */
285
286 j = witness(check, A, A1, A1_odd, k, ctx, mont);
287 if (j == -1)
288 goto err;
289 if (j) {
290 ret = 0;
291 goto err;
292 }
293 if (!BN_GENCB_call(cb, 1, i))
294 goto err;
295 }
296 ret = 1;
297 err:
298 if (ctx != NULL) {
299 BN_CTX_end(ctx);
300 if (ctx_passed == NULL)
301 BN_CTX_free(ctx);
302 }
303 BN_MONT_CTX_free(mont);
304
305 return (ret);
306}
307
308int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
309{
310 int i;
311 int ret = 0;
312
313 loop:
314 if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
315 goto err;
316
317 /* we now have a random number 'rand' to test. */
318
319 for (i = 1; i < NUMPRIMES; i++) {
320 /* check that rnd is a prime */
321 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
322 if (mod == (BN_ULONG)-1)
323 goto err;
324 if (mod <= 1) {
325 goto loop;
326 }
327 }
328 ret = 1;
329
330 err:
331 bn_check_top(rnd);
332 return (ret);
333}
334
335int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
336{
337 int i;
338 BIGNUM *offset_index;
339 BIGNUM *offset_count;
340 int ret = 0;
341
342 OPENSSL_assert(bits > prime_multiplier_bits);
343
344 BN_CTX_start(ctx);
345 if ((offset_index = BN_CTX_get(ctx)) == NULL)
346 goto err;
347 if ((offset_count = BN_CTX_get(ctx)) == NULL)
348 goto err;
349
350 if (!BN_add_word(offset_count, prime_offset_count))
351 goto err;
352
353 loop:
354 if (!BN_rand(rnd, bits - prime_multiplier_bits,
355 BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
356 goto err;
357 if (BN_is_bit_set(rnd, bits))
358 goto loop;
359 if (!BN_rand_range(offset_index, offset_count))
360 goto err;
361
362 if (!BN_mul_word(rnd, prime_multiplier)
363 || !BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]))
364 goto err;
365
366 /* we now have a random number 'rand' to test. */
367
368 /* skip coprimes */
369 for (i = first_prime_index; i < NUMPRIMES; i++) {
370 /* check that rnd is a prime */
371 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
372 if (mod == (BN_ULONG)-1)
373 goto err;
374 if (mod <= 1)
375 goto loop;
376 }
377 ret = 1;
378
379 err:
380 BN_CTX_end(ctx);
381 bn_check_top(rnd);
382 return ret;
383}
384
385static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
386 const BIGNUM *a1_odd, int k, BN_CTX *ctx,
387 BN_MONT_CTX *mont)
388{
389 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
390 return -1;
391 if (BN_is_one(w))
392 return 0; /* probably prime */
393 if (BN_cmp(w, a1) == 0)
394 return 0; /* w == -1 (mod a), 'a' is probably prime */
395 while (--k) {
396 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
397 return -1;
398 if (BN_is_one(w))
399 return 1; /* 'a' is composite, otherwise a previous 'w'
400 * would have been == -1 (mod 'a') */
401 if (BN_cmp(w, a1) == 0)
402 return 0; /* w == -1 (mod a), 'a' is probably prime */
403 }
404 /*
405 * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
406 * it is neither -1 nor +1 -- so 'a' cannot be prime
407 */
408 bn_check_top(w);
409 return 1;
410}
411
412static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
413{
414 int i;
415 BN_ULONG delta;
416 BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
417 char is_single_word = bits <= BN_BITS2;
418
419 again:
420 if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
421 return (0);
422 /* we now have a random number 'rnd' to test. */
423 for (i = 1; i < NUMPRIMES; i++) {
424 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
425 if (mod == (BN_ULONG)-1)
426 return 0;
427 mods[i] = (prime_t) mod;
428 }
429 /*
430 * If bits is so small that it fits into a single word then we
431 * additionally don't want to exceed that many bits.
432 */
433 if (is_single_word) {
434 BN_ULONG size_limit;
435
436 if (bits == BN_BITS2) {
437 /*
438 * Shifting by this much has undefined behaviour so we do it a
439 * different way
440 */
441 size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
442 } else {
443 size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
444 }
445 if (size_limit < maxdelta)
446 maxdelta = size_limit;
447 }
448 delta = 0;
449 loop:
450 if (is_single_word) {
451 BN_ULONG rnd_word = BN_get_word(rnd);
452
453 /*-
454 * In the case that the candidate prime is a single word then
455 * we check that:
456 * 1) It's greater than primes[i] because we shouldn't reject
457 * 3 as being a prime number because it's a multiple of
458 * three.
459 * 2) That it's not a multiple of a known prime. We don't
460 * check that rnd-1 is also coprime to all the known
461 * primes because there aren't many small primes where
462 * that's true.
463 */
464 for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
465 if ((mods[i] + delta) % primes[i] == 0) {
466 delta += 2;
467 if (delta > maxdelta)
468 goto again;
469 goto loop;
470 }
471 }
472 } else {
473 for (i = 1; i < NUMPRIMES; i++) {
474 /*
475 * check that rnd is not a prime and also that gcd(rnd-1,primes)
476 * == 1 (except for 2)
477 */
478 if (((mods[i] + delta) % primes[i]) <= 1) {
479 delta += 2;
480 if (delta > maxdelta)
481 goto again;
482 goto loop;
483 }
484 }
485 }
486 if (!BN_add_word(rnd, delta))
487 return (0);
488 if (BN_num_bits(rnd) != bits)
489 goto again;
490 bn_check_top(rnd);
491 return (1);
492}
493
494int bn_probable_prime_dh(BIGNUM *rnd, int bits,
495 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
496{
497 int i, ret = 0;
498 BIGNUM *t1;
499
500 BN_CTX_start(ctx);
501 if ((t1 = BN_CTX_get(ctx)) == NULL)
502 goto err;
503
504 if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
505 goto err;
506
507 /* we need ((rnd-rem) % add) == 0 */
508
509 if (!BN_mod(t1, rnd, add, ctx))
510 goto err;
511 if (!BN_sub(rnd, rnd, t1))
512 goto err;
513 if (rem == NULL) {
514 if (!BN_add_word(rnd, 1))
515 goto err;
516 } else {
517 if (!BN_add(rnd, rnd, rem))
518 goto err;
519 }
520
521 /* we now have a random number 'rand' to test. */
522
523 loop:
524 for (i = 1; i < NUMPRIMES; i++) {
525 /* check that rnd is a prime */
526 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
527 if (mod == (BN_ULONG)-1)
528 goto err;
529 if (mod <= 1) {
530 if (!BN_add(rnd, rnd, add))
531 goto err;
532 goto loop;
533 }
534 }
535 ret = 1;
536
537 err:
538 BN_CTX_end(ctx);
539 bn_check_top(rnd);
540 return (ret);
541}
542
543static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
544 const BIGNUM *rem, BN_CTX *ctx)
545{
546 int i, ret = 0;
547 BIGNUM *t1, *qadd, *q;
548
549 bits--;
550 BN_CTX_start(ctx);
551 t1 = BN_CTX_get(ctx);
552 q = BN_CTX_get(ctx);
553 qadd = BN_CTX_get(ctx);
554 if (qadd == NULL)
555 goto err;
556
557 if (!BN_rshift1(qadd, padd))
558 goto err;
559
560 if (!BN_rand(q, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
561 goto err;
562
563 /* we need ((rnd-rem) % add) == 0 */
564 if (!BN_mod(t1, q, qadd, ctx))
565 goto err;
566 if (!BN_sub(q, q, t1))
567 goto err;
568 if (rem == NULL) {
569 if (!BN_add_word(q, 1))
570 goto err;
571 } else {
572 if (!BN_rshift1(t1, rem))
573 goto err;
574 if (!BN_add(q, q, t1))
575 goto err;
576 }
577
578 /* we now have a random number 'rand' to test. */
579 if (!BN_lshift1(p, q))
580 goto err;
581 if (!BN_add_word(p, 1))
582 goto err;
583
584 loop:
585 for (i = 1; i < NUMPRIMES; i++) {
586 /* check that p and q are prime */
587 /*
588 * check that for p and q gcd(p-1,primes) == 1 (except for 2)
589 */
590 BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
591 BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
592 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
593 goto err;
594 if (pmod == 0 || qmod == 0) {
595 if (!BN_add(p, p, padd))
596 goto err;
597 if (!BN_add(q, q, qadd))
598 goto err;
599 goto loop;
600 }
601 }
602 ret = 1;
603
604 err:
605 BN_CTX_end(ctx);
606 bn_check_top(p);
607 return (ret);
608}
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