diff options
Diffstat (limited to 'src/crypto/bn/prime.c')
| -rw-r--r-- | src/crypto/bn/prime.c | 838 |
1 files changed, 838 insertions, 0 deletions
diff --git a/src/crypto/bn/prime.c b/src/crypto/bn/prime.c new file mode 100644 index 0000000..fc9a3d5 --- /dev/null +++ b/src/crypto/bn/prime.c @@ -0,0 +1,838 @@ +/* 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 <openssl/bn.h> + +#include <openssl/err.h> +#include <openssl/mem.h> + +#include "internal.h" + +/* number of Miller-Rabin iterations for an error rate of less than 2^-80 + * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook + * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996]; + * original paper: Damgaard, Landrock, Pomerance: Average case error estimates + * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */ +#define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \ + (b) >= 850 ? 3 : \ + (b) >= 650 ? 4 : \ + (b) >= 550 ? 5 : \ + (b) >= 450 ? 6 : \ + (b) >= 400 ? 7 : \ + (b) >= 350 ? 8 : \ + (b) >= 300 ? 9 : \ + (b) >= 250 ? 12 : \ + (b) >= 200 ? 15 : \ + (b) >= 150 ? 18 : \ + /* b >= 100 */ 27) + +/* 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. */ + +/* NUMPRIMES is the number of primes that fit into a uint16_t. */ +#define NUMPRIMES 2048 + +/* primes contains all the primes that fit into a uint16_t. */ +static const uint16_t primes[NUMPRIMES] = { + 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, + 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, + 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, + 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, + 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, + 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, + 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, + 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, + 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, + 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, + 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, + 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, + 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, + 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, + 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, + 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, + 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, + 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, + 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, + 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, + 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, + 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, + 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, + 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, + 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, + 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, + 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, + 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, + 2039, 2053, 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14419, 14423, 14431, 14437, 14447, + 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, + 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, + 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, + 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, + 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, + 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, + 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, + 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, + 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, + 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, + 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, + 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, + 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, + 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, + 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, + 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, + 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, + 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, + 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, + 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, + 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, + 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, + 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, + 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, + 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, + 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, + 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, + 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, + 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, + 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, + 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, + 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, + 17851, 17863, +}; + +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(BIGNUM *rnd, int bits, const BIGNUM *add, + const BIGNUM *rem, BN_CTX *ctx); +static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, + const BIGNUM *rem, BN_CTX *ctx); + +void BN_GENCB_set(BN_GENCB *callback, + int (*f)(int event, int n, struct bn_gencb_st *), + void *arg) { + callback->callback = f; + callback->arg = arg; +} + +int BN_GENCB_call(BN_GENCB *callback, int event, int n) { + if (!callback) { + return 1; + } + + return callback->callback(event, n, callback); +} + +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. */ + OPENSSL_PUT_ERROR(BN, BN_generate_prime_ex, BN_R_BITS_TOO_SMALL); + return 0; + } else if (bits == 2 && safe) { + /* The smallest safe prime (7) is three bits. */ + OPENSSL_PUT_ERROR(BN, 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 (!probable_prime_dh(ret, bits, add, rem, ctx)) { + goto err; + } + } + } + + if (!BN_GENCB_call(cb, BN_GENCB_GENERATED, c1++)) { + /* aborted */ + goto err; + } + + if (!safe) { + i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); + if (i == -1) { + goto err; + } else 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, NULL); + if (j == -1) { + goto err; + } else if (j == 0) { + goto loop; + } + + j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, NULL); + if (j == -1) { + goto err; + } else if (j == 0) { + goto loop; + } + + if (!BN_GENCB_call(cb, i, 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); + } + + return found; +} + +int BN_primality_test(int *is_probably_prime, const BIGNUM *candidate, + int checks, BN_CTX *ctx, int do_trial_division, + BN_GENCB *cb) { + switch (BN_is_prime_fasttest_ex(candidate, checks, ctx, do_trial_division, cb)) { + case 1: + *is_probably_prime = 1; + return 1; + case 0: + *is_probably_prime = 0; + return 1; + default: + *is_probably_prime = 0; + return 0; + } +} + +int BN_is_prime_ex(const BIGNUM *candidate, int checks, BN_CTX *ctx, BN_GENCB *cb) { + return BN_is_prime_fasttest_ex(candidate, checks, ctx, 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; +} + +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 */ + return 1; +} + +static BN_ULONG get_word(const BIGNUM *bn) { + if (bn->top == 1) { + return bn->d[0]; + } + return 0; +} + +static int probable_prime(BIGNUM *rnd, int bits) { + int i; + uint16_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] = (uint16_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 = (((BN_ULONG)1) << bits) - get_word(rnd) - 1; + if (size_limit < maxdelta) { + maxdelta = size_limit; + } + } + delta = 0; + +loop: + if (is_single_word) { + BN_ULONG rnd_word = 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; + } + + return 1; +} + +static int 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); + 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); + return ret; +} |