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7b1a0451 1/* bn_x931p.c */
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MC
2/*
3 * Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL project
4 * 2005.
7b1a0451
DSH
5 */
6/* ====================================================================
7 * Copyright (c) 2005 The OpenSSL Project. All rights reserved.
8 *
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions
11 * are met:
12 *
13 * 1. Redistributions of source code must retain the above copyright
0f113f3e 14 * notice, this list of conditions and the following disclaimer.
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DSH
15 *
16 * 2. Redistributions in binary form must reproduce the above copyright
17 * notice, this list of conditions and the following disclaimer in
18 * the documentation and/or other materials provided with the
19 * distribution.
20 *
21 * 3. All advertising materials mentioning features or use of this
22 * software must display the following acknowledgment:
23 * "This product includes software developed by the OpenSSL Project
24 * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
25 *
26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
27 * endorse or promote products derived from this software without
28 * prior written permission. For written permission, please contact
29 * licensing@OpenSSL.org.
30 *
31 * 5. Products derived from this software may not be called "OpenSSL"
32 * nor may "OpenSSL" appear in their names without prior written
33 * permission of the OpenSSL Project.
34 *
35 * 6. Redistributions of any form whatsoever must retain the following
36 * acknowledgment:
37 * "This product includes software developed by the OpenSSL Project
38 * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
51 * OF THE POSSIBILITY OF SUCH DAMAGE.
52 * ====================================================================
53 *
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).
57 *
58 */
59
60#include <stdio.h>
61#include <openssl/bn.h>
85bcf27c 62#include "bn_lcl.h"
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DSH
63
64/* X9.31 routines for prime derivation */
65
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66/*
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.
7b1a0451
DSH
69 */
70
71static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
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MC
72 BN_GENCB *cb)
73{
74 int i = 0;
75 if (!BN_copy(pi, Xpi))
76 return 0;
77 if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
78 return 0;
79 for (;;) {
80 i++;
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))
84 break;
85 if (!BN_add_word(pi, 2))
86 return 0;
87 }
88 BN_GENCB_call(cb, 2, i);
89 return 1;
90}
91
92/*
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.
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DSH
96 */
97
98int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
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MC
99 const BIGNUM *Xp, const BIGNUM *Xp1,
100 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
101 BN_GENCB *cb)
102{
103 int ret = 0;
7b1a0451 104
0f113f3e 105 BIGNUM *t, *p1p2, *pm1;
7b1a0451 106
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MC
107 /* Only even e supported */
108 if (!BN_is_odd(e))
109 return 0;
7b1a0451 110
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MC
111 BN_CTX_start(ctx);
112 if (!p1)
113 p1 = BN_CTX_get(ctx);
7b1a0451 114
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MC
115 if (!p2)
116 p2 = BN_CTX_get(ctx);
7b1a0451 117
0f113f3e 118 t = BN_CTX_get(ctx);
7b1a0451 119
0f113f3e 120 p1p2 = BN_CTX_get(ctx);
7b1a0451 121
0f113f3e 122 pm1 = BN_CTX_get(ctx);
7b1a0451 123
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MC
124 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
125 goto err;
7b1a0451 126
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127 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
128 goto err;
7b1a0451 129
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130 if (!BN_mul(p1p2, p1, p2, ctx))
131 goto err;
7b1a0451 132
0f113f3e 133 /* First set p to value of Rp */
7b1a0451 134
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135 if (!BN_mod_inverse(p, p2, p1, ctx))
136 goto err;
7b1a0451 137
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MC
138 if (!BN_mul(p, p, p2, ctx))
139 goto err;
7b1a0451 140
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MC
141 if (!BN_mod_inverse(t, p1, p2, ctx))
142 goto err;
7b1a0451 143
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MC
144 if (!BN_mul(t, t, p1, ctx))
145 goto err;
7b1a0451 146
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MC
147 if (!BN_sub(p, p, t))
148 goto err;
7b1a0451 149
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MC
150 if (p->neg && !BN_add(p, p, p1p2))
151 goto err;
7b1a0451 152
0f113f3e 153 /* p now equals Rp */
7b1a0451 154
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MC
155 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
156 goto err;
7b1a0451 157
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158 if (!BN_add(p, p, Xp))
159 goto err;
7b1a0451 160
0f113f3e 161 /* p now equals Yp0 */
7b1a0451 162
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MC
163 for (;;) {
164 int i = 1;
165 BN_GENCB_call(cb, 0, i++);
166 if (!BN_copy(pm1, p))
167 goto err;
168 if (!BN_sub_word(pm1, 1))
169 goto err;
170 if (!BN_gcd(t, pm1, e, ctx))
171 goto err;
172 if (BN_is_one(t)
173 /*
174 * X9.31 specifies 8 MR and 1 Lucas test or any prime test
175 * offering similar or better guarantees 50 MR is considerably
176 * better.
177 */
178 && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
179 break;
180 if (!BN_add(p, p, p1p2))
181 goto err;
182 }
7b1a0451 183
0f113f3e 184 BN_GENCB_call(cb, 3, 0);
7b1a0451 185
0f113f3e 186 ret = 1;
7b1a0451 187
0f113f3e 188 err:
7b1a0451 189
0f113f3e 190 BN_CTX_end(ctx);
7b1a0451 191
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MC
192 return ret;
193}
7b1a0451 194
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195/*
196 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
197 * parameter is sum of number of bits in both.
7b1a0451
DSH
198 */
199
200int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
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MC
201{
202 BIGNUM *t;
203 int i;
204 /*
205 * Number of bits for each prime is of the form 512+128s for s = 0, 1,
206 * ...
207 */
208 if ((nbits < 1024) || (nbits & 0xff))
209 return 0;
210 nbits >>= 1;
211 /*
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
214 * exceeded.
215 */
216 if (!BN_rand(Xp, nbits, 1, 0))
3f6c7691 217 goto err;
0f113f3e
MC
218
219 BN_CTX_start(ctx);
220 t = BN_CTX_get(ctx);
221
222 for (i = 0; i < 1000; i++) {
223 if (!BN_rand(Xq, nbits, 1, 0))
3f6c7691 224 goto err;
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MC
225 /* Check that |Xp - Xq| > 2^(nbits - 100) */
226 BN_sub(t, Xp, Xq);
227 if (BN_num_bits(t) > (nbits - 100))
228 break;
229 }
230
231 BN_CTX_end(ctx);
232
233 if (i < 1000)
234 return 1;
235
236 return 0;
237
3f6c7691
AG
238 err:
239 BN_CTX_end(ctx);
240 return 0;
0f113f3e
MC
241}
242
243/*
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.
7b1a0451
DSH
249 */
250
251int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
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MC
252 BIGNUM *Xp1, BIGNUM *Xp2,
253 const BIGNUM *Xp,
254 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
255{
256 int ret = 0;
7b1a0451 257
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MC
258 BN_CTX_start(ctx);
259 if (!Xp1)
260 Xp1 = BN_CTX_get(ctx);
261 if (!Xp2)
262 Xp2 = BN_CTX_get(ctx);
7b1a0451 263
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MC
264 if (!BN_rand(Xp1, 101, 0, 0))
265 goto error;
266 if (!BN_rand(Xp2, 101, 0, 0))
267 goto error;
268 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
269 goto error;
7b1a0451 270
0f113f3e 271 ret = 1;
7b1a0451 272
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MC
273 error:
274 BN_CTX_end(ctx);
7b1a0451 275
0f113f3e 276 return ret;
7b1a0451 277
0f113f3e 278}