| /* crypto/bn/bn_prime.c */ |
| /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| * All rights reserved. |
| * |
| * This package is an SSL implementation written |
| * by Eric Young (eay@cryptsoft.com). |
| * The implementation was written so as to conform with Netscapes SSL. |
| * |
| * This library is free for commercial and non-commercial use as long as |
| * the following conditions are aheared to. The following conditions |
| * apply to all code found in this distribution, be it the RC4, RSA, |
| * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| * included with this distribution is covered by the same copyright terms |
| * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| * |
| * Copyright remains Eric Young's, and as such any Copyright notices in |
| * the code are not to be removed. |
| * If this package is used in a product, Eric Young should be given attribution |
| * as the author of the parts of the library used. |
| * This can be in the form of a textual message at program startup or |
| * in documentation (online or textual) provided with the package. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * 3. All advertising materials mentioning features or use of this software |
| * must display the following acknowledgement: |
| * "This product includes cryptographic software written by |
| * Eric Young (eay@cryptsoft.com)" |
| * The word 'cryptographic' can be left out if the rouines from the library |
| * being used are not cryptographic related :-). |
| * 4. If you include any Windows specific code (or a derivative thereof) from |
| * the apps directory (application code) you must include an acknowledgement: |
| * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| * |
| * The licence and distribution terms for any publically available version or |
| * derivative of this code cannot be changed. i.e. this code cannot simply be |
| * copied and put under another distribution licence |
| * [including the GNU Public Licence.] |
| */ |
| /* ==================================================================== |
| * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in |
| * the documentation and/or other materials provided with the |
| * distribution. |
| * |
| * 3. All advertising materials mentioning features or use of this |
| * software must display the following acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| * |
| * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| * endorse or promote products derived from this software without |
| * prior written permission. For written permission, please contact |
| * openssl-core@openssl.org. |
| * |
| * 5. Products derived from this software may not be called "OpenSSL" |
| * nor may "OpenSSL" appear in their names without prior written |
| * permission of the OpenSSL Project. |
| * |
| * 6. Redistributions of any form whatsoever must retain the following |
| * acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| * OF THE POSSIBILITY OF SUCH DAMAGE. |
| * ==================================================================== |
| * |
| * This product includes cryptographic software written by Eric Young |
| * (eay@cryptsoft.com). This product includes software written by Tim |
| * Hudson (tjh@cryptsoft.com). |
| * |
| */ |
| |
| #include <stdio.h> |
| #include <time.h> |
| #include "cryptlib.h" |
| #include "bn_lcl.h" |
| #include <openssl/rand.h> |
| |
| /* |
| * NB: these functions have been "upgraded", the deprecated versions (which |
| * are compatibility wrappers using these functions) are in bn_depr.c. - |
| * Geoff |
| */ |
| |
| /* |
| * The quick sieve algorithm approach to weeding out primes is Philip |
| * Zimmermann's, as implemented in PGP. I have had a read of his comments |
| * and implemented my own version. |
| */ |
| #include "bn_prime.h" |
| |
| static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, |
| const BIGNUM *a1_odd, int k, BN_CTX *ctx, |
| BN_MONT_CTX *mont); |
| static int probable_prime(BIGNUM *rnd, int bits); |
| static int probable_prime_dh_safe(BIGNUM *rnd, int bits, |
| const BIGNUM *add, const BIGNUM *rem, |
| BN_CTX *ctx); |
| |
| static const int prime_offsets[480] = { |
| 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, |
| 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, |
| 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229, |
| 233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293, |
| 299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367, |
| 373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433, |
| 437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499, |
| 503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569, |
| 571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631, |
| 641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701, |
| 703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769, |
| 773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839, |
| 841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901, |
| 907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971, |
| 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031, |
| 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087, |
| 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151, |
| 1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213, |
| 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271, |
| 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319, |
| 1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373, |
| 1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433, |
| 1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489, |
| 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549, |
| 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609, |
| 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667, |
| 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721, |
| 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781, |
| 1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843, |
| 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901, |
| 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951, |
| 1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, |
| 2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071, |
| 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131, |
| 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197, |
| 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249, |
| 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297, |
| 2309, 2311 |
| }; |
| |
| static const int prime_offset_count = 480; |
| static const int prime_multiplier = 2310; |
| static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <= |
| * |prime_multiplier| */ |
| static const int first_prime_index = 5; |
| |
| int BN_GENCB_call(BN_GENCB *cb, int a, int b) |
| { |
| /* No callback means continue */ |
| if (!cb) |
| return 1; |
| switch (cb->ver) { |
| case 1: |
| /* Deprecated-style callbacks */ |
| if (!cb->cb.cb_1) |
| return 1; |
| cb->cb.cb_1(a, b, cb->arg); |
| return 1; |
| case 2: |
| /* New-style callbacks */ |
| return cb->cb.cb_2(a, b, cb); |
| default: |
| break; |
| } |
| /* Unrecognised callback type */ |
| return 0; |
| } |
| |
| int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, |
| const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) |
| { |
| BIGNUM *t; |
| int found = 0; |
| int i, j, c1 = 0; |
| BN_CTX *ctx; |
| int checks = BN_prime_checks_for_size(bits); |
| |
| if (bits < 2) { |
| /* There are no prime numbers this small. */ |
| BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL); |
| return 0; |
| } else if (bits == 2 && safe) { |
| /* The smallest safe prime (7) is three bits. */ |
| BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL); |
| return 0; |
| } |
| |
| ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| goto err; |
| BN_CTX_start(ctx); |
| t = BN_CTX_get(ctx); |
| if (!t) |
| goto err; |
| loop: |
| /* make a random number and set the top and bottom bits */ |
| if (add == NULL) { |
| if (!probable_prime(ret, bits)) |
| goto err; |
| } else { |
| if (safe) { |
| if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) |
| goto err; |
| } else { |
| if (!bn_probable_prime_dh(ret, bits, add, rem, ctx)) |
| goto err; |
| } |
| } |
| /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ |
| if (!BN_GENCB_call(cb, 0, c1++)) |
| /* aborted */ |
| goto err; |
| |
| if (!safe) { |
| i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); |
| if (i == -1) |
| goto err; |
| if (i == 0) |
| goto loop; |
| } else { |
| /* |
| * for "safe prime" generation, check that (p-1)/2 is prime. Since a |
| * prime is odd, We just need to divide by 2 |
| */ |
| if (!BN_rshift1(t, ret)) |
| goto err; |
| |
| for (i = 0; i < checks; i++) { |
| j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); |
| if (j == -1) |
| goto err; |
| if (j == 0) |
| goto loop; |
| |
| j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); |
| if (j == -1) |
| goto err; |
| if (j == 0) |
| goto loop; |
| |
| if (!BN_GENCB_call(cb, 2, c1 - 1)) |
| goto err; |
| /* We have a safe prime test pass */ |
| } |
| } |
| /* we have a prime :-) */ |
| found = 1; |
| err: |
| if (ctx != NULL) { |
| BN_CTX_end(ctx); |
| BN_CTX_free(ctx); |
| } |
| bn_check_top(ret); |
| return found; |
| } |
| |
| int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, |
| BN_GENCB *cb) |
| { |
| return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); |
| } |
| |
| int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, |
| int do_trial_division, BN_GENCB *cb) |
| { |
| int i, j, ret = -1; |
| int k; |
| BN_CTX *ctx = NULL; |
| BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ |
| BN_MONT_CTX *mont = NULL; |
| const BIGNUM *A = NULL; |
| |
| if (BN_cmp(a, BN_value_one()) <= 0) |
| return 0; |
| |
| if (checks == BN_prime_checks) |
| checks = BN_prime_checks_for_size(BN_num_bits(a)); |
| |
| /* first look for small factors */ |
| if (!BN_is_odd(a)) |
| /* a is even => a is prime if and only if a == 2 */ |
| return BN_is_word(a, 2); |
| if (do_trial_division) { |
| for (i = 1; i < NUMPRIMES; i++) |
| if (BN_mod_word(a, primes[i]) == 0) |
| return 0; |
| if (!BN_GENCB_call(cb, 1, -1)) |
| goto err; |
| } |
| |
| if (ctx_passed != NULL) |
| ctx = ctx_passed; |
| else if ((ctx = BN_CTX_new()) == NULL) |
| goto err; |
| BN_CTX_start(ctx); |
| |
| /* A := abs(a) */ |
| if (a->neg) { |
| BIGNUM *t; |
| if ((t = BN_CTX_get(ctx)) == NULL) |
| goto err; |
| BN_copy(t, a); |
| t->neg = 0; |
| A = t; |
| } else |
| A = a; |
| A1 = BN_CTX_get(ctx); |
| A1_odd = BN_CTX_get(ctx); |
| check = BN_CTX_get(ctx); |
| if (check == NULL) |
| goto err; |
| |
| /* compute A1 := A - 1 */ |
| if (!BN_copy(A1, A)) |
| goto err; |
| if (!BN_sub_word(A1, 1)) |
| goto err; |
| if (BN_is_zero(A1)) { |
| ret = 0; |
| goto err; |
| } |
| |
| /* write A1 as A1_odd * 2^k */ |
| k = 1; |
| while (!BN_is_bit_set(A1, k)) |
| k++; |
| if (!BN_rshift(A1_odd, A1, k)) |
| goto err; |
| |
| /* Montgomery setup for computations mod A */ |
| mont = BN_MONT_CTX_new(); |
| if (mont == NULL) |
| goto err; |
| if (!BN_MONT_CTX_set(mont, A, ctx)) |
| goto err; |
| |
| for (i = 0; i < checks; i++) { |
| if (!BN_pseudo_rand_range(check, A1)) |
| goto err; |
| if (!BN_add_word(check, 1)) |
| goto err; |
| /* now 1 <= check < A */ |
| |
| j = witness(check, A, A1, A1_odd, k, ctx, mont); |
| if (j == -1) |
| goto err; |
| if (j) { |
| ret = 0; |
| goto err; |
| } |
| if (!BN_GENCB_call(cb, 1, i)) |
| goto err; |
| } |
| ret = 1; |
| err: |
| if (ctx != NULL) { |
| BN_CTX_end(ctx); |
| if (ctx_passed == NULL) |
| BN_CTX_free(ctx); |
| } |
| if (mont != NULL) |
| BN_MONT_CTX_free(mont); |
| |
| return (ret); |
| } |
| |
| int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx) |
| { |
| int i; |
| int ret = 0; |
| |
| loop: |
| if (!BN_rand(rnd, bits, 0, 1)) |
| goto err; |
| |
| /* we now have a random number 'rand' to test. */ |
| |
| for (i = 1; i < NUMPRIMES; i++) { |
| /* check that rnd is a prime */ |
| if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { |
| goto loop; |
| } |
| } |
| ret = 1; |
| |
| err: |
| bn_check_top(rnd); |
| return (ret); |
| } |
| |
| int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx) |
| { |
| int i; |
| BIGNUM *offset_index; |
| BIGNUM *offset_count; |
| int ret = 0; |
| |
| OPENSSL_assert(bits > prime_multiplier_bits); |
| |
| BN_CTX_start(ctx); |
| if ((offset_index = BN_CTX_get(ctx)) == NULL) |
| goto err; |
| if ((offset_count = BN_CTX_get(ctx)) == NULL) |
| goto err; |
| |
| BN_add_word(offset_count, prime_offset_count); |
| |
| loop: |
| if (!BN_rand(rnd, bits - prime_multiplier_bits, 0, 1)) |
| goto err; |
| if (BN_is_bit_set(rnd, bits)) |
| goto loop; |
| if (!BN_rand_range(offset_index, offset_count)) |
| goto err; |
| |
| BN_mul_word(rnd, prime_multiplier); |
| BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]); |
| |
| /* we now have a random number 'rand' to test. */ |
| |
| /* skip coprimes */ |
| for (i = first_prime_index; i < NUMPRIMES; i++) { |
| /* check that rnd is a prime */ |
| if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { |
| goto loop; |
| } |
| } |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| bn_check_top(rnd); |
| return ret; |
| } |
| |
| static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, |
| const BIGNUM *a1_odd, int k, BN_CTX *ctx, |
| BN_MONT_CTX *mont) |
| { |
| if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ |
| return -1; |
| if (BN_is_one(w)) |
| return 0; /* probably prime */ |
| if (BN_cmp(w, a1) == 0) |
| return 0; /* w == -1 (mod a), 'a' is probably prime */ |
| while (--k) { |
| if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ |
| return -1; |
| if (BN_is_one(w)) |
| return 1; /* 'a' is composite, otherwise a previous 'w' |
| * would have been == -1 (mod 'a') */ |
| if (BN_cmp(w, a1) == 0) |
| return 0; /* w == -1 (mod a), 'a' is probably prime */ |
| } |
| /* |
| * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and |
| * it is neither -1 nor +1 -- so 'a' cannot be prime |
| */ |
| bn_check_top(w); |
| return 1; |
| } |
| |
| static int probable_prime(BIGNUM *rnd, int bits) |
| { |
| int i; |
| prime_t mods[NUMPRIMES]; |
| BN_ULONG delta; |
| BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; |
| char is_single_word = bits <= BN_BITS2; |
| |
| again: |
| if (!BN_rand(rnd, bits, 1, 1)) |
| return (0); |
| /* we now have a random number 'rnd' to test. */ |
| for (i = 1; i < NUMPRIMES; i++) |
| mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]); |
| /* |
| * If bits is so small that it fits into a single word then we |
| * additionally don't want to exceed that many bits. |
| */ |
| if (is_single_word) { |
| BN_ULONG size_limit; |
| |
| if (bits == BN_BITS2) { |
| /* |
| * Shifting by this much has undefined behaviour so we do it a |
| * different way |
| */ |
| size_limit = ~((BN_ULONG)0) - BN_get_word(rnd); |
| } else { |
| size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1; |
| } |
| if (size_limit < maxdelta) |
| maxdelta = size_limit; |
| } |
| delta = 0; |
| loop: |
| if (is_single_word) { |
| BN_ULONG rnd_word = BN_get_word(rnd); |
| |
| /*- |
| * In the case that the candidate prime is a single word then |
| * we check that: |
| * 1) It's greater than primes[i] because we shouldn't reject |
| * 3 as being a prime number because it's a multiple of |
| * three. |
| * 2) That it's not a multiple of a known prime. We don't |
| * check that rnd-1 is also coprime to all the known |
| * primes because there aren't many small primes where |
| * that's true. |
| */ |
| for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) { |
| if ((mods[i] + delta) % primes[i] == 0) { |
| delta += 2; |
| if (delta > maxdelta) |
| goto again; |
| goto loop; |
| } |
| } |
| } else { |
| for (i = 1; i < NUMPRIMES; i++) { |
| /* |
| * check that rnd is not a prime and also that gcd(rnd-1,primes) |
| * == 1 (except for 2) |
| */ |
| if (((mods[i] + delta) % primes[i]) <= 1) { |
| delta += 2; |
| if (delta > maxdelta) |
| goto again; |
| goto loop; |
| } |
| } |
| } |
| if (!BN_add_word(rnd, delta)) |
| return (0); |
| if (BN_num_bits(rnd) != bits) |
| goto again; |
| bn_check_top(rnd); |
| return (1); |
| } |
| |
| int bn_probable_prime_dh(BIGNUM *rnd, int bits, |
| const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) |
| { |
| int i, ret = 0; |
| BIGNUM *t1; |
| |
| BN_CTX_start(ctx); |
| if ((t1 = BN_CTX_get(ctx)) == NULL) |
| goto err; |
| |
| if (!BN_rand(rnd, bits, 0, 1)) |
| goto err; |
| |
| /* we need ((rnd-rem) % add) == 0 */ |
| |
| if (!BN_mod(t1, rnd, add, ctx)) |
| goto err; |
| if (!BN_sub(rnd, rnd, t1)) |
| goto err; |
| if (rem == NULL) { |
| if (!BN_add_word(rnd, 1)) |
| goto err; |
| } else { |
| if (!BN_add(rnd, rnd, rem)) |
| goto err; |
| } |
| |
| /* we now have a random number 'rand' to test. */ |
| |
| loop: |
| for (i = 1; i < NUMPRIMES; i++) { |
| /* check that rnd is a prime */ |
| if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { |
| if (!BN_add(rnd, rnd, add)) |
| goto err; |
| goto loop; |
| } |
| } |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| bn_check_top(rnd); |
| return (ret); |
| } |
| |
| static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, |
| const BIGNUM *rem, BN_CTX *ctx) |
| { |
| int i, ret = 0; |
| BIGNUM *t1, *qadd, *q; |
| |
| bits--; |
| BN_CTX_start(ctx); |
| t1 = BN_CTX_get(ctx); |
| q = BN_CTX_get(ctx); |
| qadd = BN_CTX_get(ctx); |
| if (qadd == NULL) |
| goto err; |
| |
| if (!BN_rshift1(qadd, padd)) |
| goto err; |
| |
| if (!BN_rand(q, bits, 0, 1)) |
| goto err; |
| |
| /* we need ((rnd-rem) % add) == 0 */ |
| if (!BN_mod(t1, q, qadd, ctx)) |
| goto err; |
| if (!BN_sub(q, q, t1)) |
| goto err; |
| if (rem == NULL) { |
| if (!BN_add_word(q, 1)) |
| goto err; |
| } else { |
| if (!BN_rshift1(t1, rem)) |
| goto err; |
| if (!BN_add(q, q, t1)) |
| goto err; |
| } |
| |
| /* we now have a random number 'rand' to test. */ |
| if (!BN_lshift1(p, q)) |
| goto err; |
| if (!BN_add_word(p, 1)) |
| goto err; |
| |
| loop: |
| for (i = 1; i < NUMPRIMES; i++) { |
| /* check that p and q are prime */ |
| /* |
| * check that for p and q gcd(p-1,primes) == 1 (except for 2) |
| */ |
| if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) || |
| (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) { |
| if (!BN_add(p, p, padd)) |
| goto err; |
| if (!BN_add(q, q, qadd)) |
| goto err; |
| goto loop; |
| } |
| } |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| bn_check_top(p); |
| return (ret); |
| } |
