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 if (BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb))
35 if (!BN_add_word(pi, 2))
38 BN_GENCB_call(cb, 2, i);
43 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
44 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
45 * will be returned too: this is needed for testing.
48 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
49 const BIGNUM *Xp, const BIGNUM *Xp1,
50 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
55 BIGNUM *t, *p1p2, *pm1;
57 /* Only even e supported */
70 p1p2 = BN_CTX_get(ctx);
72 pm1 = BN_CTX_get(ctx);
74 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
77 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
80 if (!BN_mul(p1p2, p1, p2, ctx))
83 /* First set p to value of Rp */
85 if (!BN_mod_inverse(p, p2, p1, ctx))
88 if (!BN_mul(p, p, p2, ctx))
91 if (!BN_mod_inverse(t, p1, p2, ctx))
94 if (!BN_mul(t, t, p1, ctx))
100 if (p->neg && !BN_add(p, p, p1p2))
103 /* p now equals Rp */
105 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
108 if (!BN_add(p, p, Xp))
111 /* p now equals Yp0 */
115 BN_GENCB_call(cb, 0, i++);
116 if (!BN_copy(pm1, p))
118 if (!BN_sub_word(pm1, 1))
120 if (!BN_gcd(t, pm1, e, ctx))
124 * X9.31 specifies 8 MR and 1 Lucas test or any prime test
125 * offering similar or better guarantees 50 MR is considerably
128 && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
130 if (!BN_add(p, p, p1p2))
134 BN_GENCB_call(cb, 3, 0);
146 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
147 * parameter is sum of number of bits in both.
150 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
155 * Number of bits for each prime is of the form 512+128s for s = 0, 1,
158 if ((nbits < 1024) || (nbits & 0xff))
162 * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
163 * - 1. By setting the top two bits we ensure that the lower bound is
166 if (!BN_rand(Xp, nbits, 1, 0))
172 for (i = 0; i < 1000; i++) {
173 if (!BN_rand(Xq, nbits, 1, 0))
175 /* Check that |Xp - Xq| > 2^(nbits - 100) */
177 if (BN_num_bits(t) > (nbits - 100))
194 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
195 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
196 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
197 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
198 * previous function and supplied as input.
201 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
202 BIGNUM *Xp1, BIGNUM *Xp2,
204 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
210 Xp1 = BN_CTX_get(ctx);
212 Xp2 = BN_CTX_get(ctx);
214 if (!BN_rand(Xp1, 101, 0, 0))
216 if (!BN_rand(Xp2, 101, 0, 0))
218 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))