2 /* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL
5 /* ====================================================================
6 * Copyright (c) 2005 The OpenSSL Project. All rights reserved.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * licensing@OpenSSL.org.
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
60 #include <openssl/bn.h>
63 /* X9.31 routines for prime derivation */
65 /* X9.31 prime derivation. This is used to generate the primes pi
66 * (p1, p2, q1, q2) from a parameter Xpi by checking successive odd
70 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
74 if (!BN_copy(pi, Xpi))
76 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);
92 /* This is the main X9.31 prime derivation function. From parameters
93 * Xp1, Xp2 and Xp derive the prime p. If the parameters p1 or p2 are
94 * not NULL they will be returned too: this is needed for testing.
97 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
98 const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
99 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
103 BIGNUM *t, *p1p2, *pm1;
105 /* Only even e supported */
111 p1 = BN_CTX_get(ctx);
114 p2 = BN_CTX_get(ctx);
118 p1p2 = BN_CTX_get(ctx);
120 pm1 = BN_CTX_get(ctx);
122 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
125 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
128 if (!BN_mul(p1p2, p1, p2, ctx))
131 /* First set p to value of Rp */
133 if (!BN_mod_inverse(p, p2, p1, ctx))
136 if (!BN_mul(p, p, p2, ctx))
139 if (!BN_mod_inverse(t, p1, p2, ctx))
142 if (!BN_mul(t, t, p1, ctx))
145 if (!BN_sub(p, p, t))
148 if (p->neg && !BN_add(p, p, p1p2))
151 /* p now equals Rp */
153 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
156 if (!BN_add(p, p, Xp))
159 /* p now equals Yp0 */
164 BN_GENCB_call(cb, 0, i++);
165 if (!BN_copy(pm1, p))
167 if (!BN_sub_word(pm1, 1))
169 if (!BN_gcd(t, pm1, e, ctx))
172 /* X9.31 specifies 8 MR and 1 Lucas test or any prime test
173 * offering similar or better guarantees 50 MR is considerably
176 && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
178 if (!BN_add(p, p, p1p2))
182 BN_GENCB_call(cb, 3, 0);
193 /* Generate pair of parameters Xp, Xq for X9.31 prime generation.
194 * Note: nbits parameter is sum of number of bits in both.
197 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
201 /* Number of bits for each prime is of the form
202 * 512+128s for s = 0, 1, ...
204 if ((nbits < 1024) || (nbits & 0xff))
207 /* The random value Xp must be between sqrt(2) * 2^(nbits-1) and
208 * 2^nbits - 1. By setting the top two bits we ensure that the lower
211 if (!BN_rand(Xp, nbits, 1, 0))
217 for (i = 0; i < 1000; i++)
219 if (!BN_rand(Xq, nbits, 1, 0))
221 /* Check that |Xp - Xq| > 2^(nbits - 100) */
223 if (BN_num_bits(t) > (nbits - 100))
236 /* Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1
237 * and Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL
238 * the relevant parameter will be stored in it.
240 * Due to the fact that |Xp - Xq| > 2^(nbits - 100) must be satisfied Xp and Xq
241 * are generated using the previous function and supplied as input.
244 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
245 BIGNUM *Xp1, BIGNUM *Xp2,
247 const BIGNUM *e, BN_CTX *ctx,
254 Xp1 = BN_CTX_get(ctx);
256 Xp2 = BN_CTX_get(ctx);
258 if (!BN_rand(Xp1, 101, 0, 0))
260 if (!BN_rand(Xp2, 101, 0, 0))
262 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))