3 * Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL project
6 /* ====================================================================
7 * Copyright (c) 2005 The OpenSSL Project. All rights reserved.
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10 * modification, are permitted provided that the following conditions
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37 * "This product includes software developed by the OpenSSL Project
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52 * ====================================================================
54 * This product includes cryptographic software written by Eric Young
55 * (eay@cryptsoft.com). This product includes software written by Tim
56 * Hudson (tjh@cryptsoft.com).
61 #include <openssl/bn.h>
64 /* X9.31 routines for prime derivation */
67 * X9.31 prime derivation. This is used to generate the primes pi (p1, p2,
68 * q1, q2) from a parameter Xpi by checking successive odd integers.
71 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
75 if (!BN_copy(pi, Xpi))
77 if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
81 BN_GENCB_call(cb, 0, i);
82 /* NB 27 MR is specificed in X9.31 */
83 if (BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb))
85 if (!BN_add_word(pi, 2))
88 BN_GENCB_call(cb, 2, i);
93 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
94 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
95 * will be returned too: this is needed for testing.
98 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
99 const BIGNUM *Xp, const BIGNUM *Xp1,
100 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
105 BIGNUM *t, *p1p2, *pm1;
107 /* Only even e supported */
113 p1 = BN_CTX_get(ctx);
116 p2 = BN_CTX_get(ctx);
120 p1p2 = BN_CTX_get(ctx);
122 pm1 = BN_CTX_get(ctx);
124 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
127 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
130 if (!BN_mul(p1p2, p1, p2, ctx))
133 /* First set p to value of Rp */
135 if (!BN_mod_inverse(p, p2, p1, ctx))
138 if (!BN_mul(p, p, p2, ctx))
141 if (!BN_mod_inverse(t, p1, p2, ctx))
144 if (!BN_mul(t, t, p1, ctx))
147 if (!BN_sub(p, p, t))
150 if (p->neg && !BN_add(p, p, p1p2))
153 /* p now equals Rp */
155 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
158 if (!BN_add(p, p, Xp))
161 /* p now equals Yp0 */
165 BN_GENCB_call(cb, 0, i++);
166 if (!BN_copy(pm1, p))
168 if (!BN_sub_word(pm1, 1))
170 if (!BN_gcd(t, pm1, e, ctx))
174 * X9.31 specifies 8 MR and 1 Lucas test or any prime test
175 * offering similar or better guarantees 50 MR is considerably
178 && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
180 if (!BN_add(p, p, p1p2))
184 BN_GENCB_call(cb, 3, 0);
196 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
197 * parameter is sum of number of bits in both.
200 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
205 * Number of bits for each prime is of the form 512+128s for s = 0, 1,
208 if ((nbits < 1024) || (nbits & 0xff))
212 * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
213 * - 1. By setting the top two bits we ensure that the lower bound is
216 if (!BN_rand(Xp, nbits, 1, 0))
222 for (i = 0; i < 1000; i++) {
223 if (!BN_rand(Xq, nbits, 1, 0))
225 /* Check that |Xp - Xq| > 2^(nbits - 100) */
227 if (BN_num_bits(t) > (nbits - 100))
244 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
245 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
246 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
247 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
248 * previous function and supplied as input.
251 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
252 BIGNUM *Xp1, BIGNUM *Xp2,
254 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
260 Xp1 = BN_CTX_get(ctx);
262 Xp2 = BN_CTX_get(ctx);
264 if (!BN_rand(Xp1, 101, 0, 0))
266 if (!BN_rand(Xp2, 101, 0, 0))
268 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))