2 * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
11 #include <openssl/bn.h>
14 /* X9.31 routines for prime derivation */
17 * X9.31 prime derivation. This is used to generate the primes pi (p1, p2,
18 * q1, q2) from a parameter Xpi by checking successive odd integers.
21 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
25 if (!BN_copy(pi, Xpi))
27 if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
31 BN_GENCB_call(cb, 0, i);
32 /* NB 27 MR is specified in X9.31 */
33 is_prime = BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb);
38 if (!BN_add_word(pi, 2))
41 BN_GENCB_call(cb, 2, i);
46 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
47 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
48 * will be returned too: this is needed for testing.
51 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
52 const BIGNUM *Xp, const BIGNUM *Xp1,
53 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
58 BIGNUM *t, *p1p2, *pm1;
60 /* Only even e supported */
73 p1p2 = BN_CTX_get(ctx);
75 pm1 = BN_CTX_get(ctx);
80 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
83 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
86 if (!BN_mul(p1p2, p1, p2, ctx))
89 /* First set p to value of Rp */
91 if (!BN_mod_inverse(p, p2, p1, ctx))
94 if (!BN_mul(p, p, p2, ctx))
97 if (!BN_mod_inverse(t, p1, p2, ctx))
100 if (!BN_mul(t, t, p1, ctx))
103 if (!BN_sub(p, p, t))
106 if (p->neg && !BN_add(p, p, p1p2))
109 /* p now equals Rp */
111 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
114 if (!BN_add(p, p, Xp))
117 /* p now equals Yp0 */
121 BN_GENCB_call(cb, 0, i++);
122 if (!BN_copy(pm1, p))
124 if (!BN_sub_word(pm1, 1))
126 if (!BN_gcd(t, pm1, e, ctx))
130 * X9.31 specifies 8 MR and 1 Lucas test or any prime test
131 * offering similar or better guarantees 50 MR is considerably
134 int r = BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb);
140 if (!BN_add(p, p, p1p2))
144 BN_GENCB_call(cb, 3, 0);
156 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
157 * parameter is sum of number of bits in both.
160 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
165 * Number of bits for each prime is of the form 512+128s for s = 0, 1,
168 if ((nbits < 1024) || (nbits & 0xff))
172 * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
173 * - 1. By setting the top two bits we ensure that the lower bound is
176 if (!BN_rand(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
182 for (i = 0; i < 1000; i++) {
183 if (!BN_rand(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
185 /* Check that |Xp - Xq| > 2^(nbits - 100) */
187 if (BN_num_bits(t) > (nbits - 100))
204 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
205 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
206 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
207 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
208 * previous function and supplied as input.
211 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
212 BIGNUM *Xp1, BIGNUM *Xp2,
214 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
220 Xp1 = BN_CTX_get(ctx);
222 Xp2 = BN_CTX_get(ctx);
224 if (!BN_rand(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
226 if (!BN_rand(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
228 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))