X-Git-Url: https://git.openssl.org/gitweb/?p=openssl.git;a=blobdiff_plain;f=crypto%2Fbn%2Fbn_prime.c;h=2a7822ef1d907014f48b5db38981263b1cb30e8c;hp=6fa0f9be1ee32b4767e8ed154832b88923601119;hb=e4676e900f165f5272991443225813002300b09b;hpb=b4f76582d4b834fb4e525d500c03ad38f0cea328 diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c index 6fa0f9be1e..2a7822ef1d 100644 --- a/crypto/bn/bn_prime.c +++ b/crypto/bn/bn_prime.c @@ -5,21 +5,21 @@ * 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: @@ -34,10 +34,10 @@ * 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 + * 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 @@ -49,12 +49,65 @@ * 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 #include @@ -62,386 +115,575 @@ #include "bn_lcl.h" #include -/* The quick seive 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. +/* + * 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 *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2, - BN_MONT_CTX *mont); +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, - BIGNUM *add, BIGNUM *rem, BN_CTX *ctx); -static int probable_prime_dh_strong(BIGNUM *rnd, int bits, - BIGNUM *add, BIGNUM *rem, BN_CTX *ctx); -BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int strong, BIGNUM *add, - BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg) - { - BIGNUM *rnd=NULL; - BIGNUM t; - int i,j,c1=0; - BN_CTX *ctx; - - ctx=BN_CTX_new(); - if (ctx == NULL) goto err; - if (ret == NULL) - { - if ((rnd=BN_new()) == NULL) goto err; - } - else - rnd=ret; - BN_init(&t); -loop: - /* make a random number and set the top and bottom bits */ - if (add == NULL) - { - if (!probable_prime(rnd,bits)) goto err; - } - else - { - if (strong) - { - if (!probable_prime_dh_strong(rnd,bits,add,rem,ctx)) - goto err; - } - else - { - if (!probable_prime_dh(rnd,bits,add,rem,ctx)) - goto err; - } - } - /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */ - if (callback != NULL) callback(0,c1++,cb_arg); - - if (!strong) - { - i=BN_is_prime(rnd,BN_prime_checks,callback,ctx,cb_arg); - if (i == -1) goto err; - if (i == 0) goto loop; - } - else - { - /* for a strong 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,rnd)) goto err; - - for (i=0; ibn[ctx->tos++]); - - /* Setup the montgomery structure */ - if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err; - - for (i=0; itos--; - if ((ctx_passed == NULL) && (ctx != NULL)) - BN_CTX_free(ctx); - if (ctx2 != NULL) - BN_CTX_free(ctx2); - if (mont != NULL) BN_MONT_CTX_free(mont); - - return(ret); - } - -#define RECP_MUL_MOD - -static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2, - BN_MONT_CTX *mont) - { - int k,i,ret= -1,good; - BIGNUM *d,*dd,*tmp,*d1,*d2,*n1; - BIGNUM *mont_one,*mont_n1,*mont_a; - - d1= &(ctx->bn[ctx->tos]); - d2= &(ctx->bn[ctx->tos+1]); - n1= &(ctx->bn[ctx->tos+2]); - ctx->tos+=3; - - mont_one= &(ctx2->bn[ctx2->tos]); - mont_n1= &(ctx2->bn[ctx2->tos+1]); - mont_a= &(ctx2->bn[ctx2->tos+2]); - ctx2->tos+=3; - - d=d1; - dd=d2; - if (!BN_one(d)) goto err; - if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */ - k=BN_num_bits(n1); - - if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err; - if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err; - if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err; - - BN_copy(d,mont_one); - for (i=k-1; i>=0; i--) - { - if ( (BN_cmp(d,mont_one) != 0) && - (BN_cmp(d,mont_n1) != 0)) - good=1; - else - good=0; - - BN_mod_mul_montgomery(dd,d,d,mont,ctx2); - - if (good && (BN_cmp(dd,mont_one) == 0)) - { - ret=1; - goto err; - } - if (BN_is_bit_set(n1,i)) - { - BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2); - } - else - { - tmp=d; - d=dd; - dd=tmp; - } - } - if (BN_cmp(d,mont_one) == 0) - i=0; - else i=1; - ret=i; -err: - ctx->tos-=3; - ctx2->tos-=3; - return(ret); - } +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; - MS_STATIC BN_ULONG mods[NUMPRIMES]; - BN_ULONG delta,d; - -again: - if (!BN_rand(rnd,bits,1,1)) return(0); - /* we now have a random number 'rand' to test. */ - for (i=1; ibn[ctx->tos++]); - - 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; itos--; - return(ret); - } - -static int probable_prime_dh_strong(BIGNUM *p, int bits, BIGNUM *padd, - BIGNUM *rem, BN_CTX *ctx) - { - int i,ret=0; - BIGNUM *t1,*qadd=NULL,*q=NULL; - - bits--; - t1= &(ctx->bn[ctx->tos++]); - q= &(ctx->bn[ctx->tos++]); - qadd= &(ctx->bn[ctx->tos++]); - - 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; itos-=3; - return(ret); - } - -#if 0 -static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx) - { - int k,i,nb,ret= -1; - BIGNUM *d,*dd,*tmp; - BIGNUM *d1,*d2,*x,*n1,*inv; - - d1= &(ctx->bn[ctx->tos]); - d2= &(ctx->bn[ctx->tos+1]); - x= &(ctx->bn[ctx->tos+2]); - n1= &(ctx->bn[ctx->tos+3]); - inv=&(ctx->bn[ctx->tos+4]); - ctx->tos+=5; - - d=d1; - dd=d2; - if (!BN_one(d)) goto err; - if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */ - k=BN_num_bits(n1); - - /* i=BN_num_bits(n); */ -#ifdef RECP_MUL_MOD - nb=BN_reciprocal(inv,n,ctx); /**/ - if (nb == -1) goto err; -#endif - - for (i=k-1; i>=0; i--) - { - if (BN_copy(x,d) == NULL) goto err; -#ifndef RECP_MUL_MOD - if (!BN_mod_mul(dd,d,d,n,ctx)) goto err; -#else - if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err; -#endif - if ( BN_is_one(dd) && - !BN_is_one(x) && - (BN_cmp(x,n1) != 0)) - { - ret=1; - goto err; - } - if (BN_is_bit_set(n1,i)) - { -#ifndef RECP_MUL_MOD - if (!BN_mod_mul(d,dd,a,n,ctx)) goto err; -#else - if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err; -#endif - } - else - { - tmp=d; - d=dd; - dd=tmp; - } - } - if (BN_is_one(d)) - i=0; - else i=1; - ret=i; -err: - ctx->tos-=5; - return(ret); - } -#endif +{ + 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); +}