1 /* bn_x931p.c */
2 /* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL
3 * project 2005.
4 */
5 /* ====================================================================
6 * Copyright (c) 2005 The OpenSSL Project. All rights reserved.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 *
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
14 *
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
18 * distribution.
19 *
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/)"
24 *
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.
29 *
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.
33 *
34 * 6. Redistributions of any form whatsoever must retain the following
35 * acknowledgment:
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
38 *
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 * ====================================================================
52 *
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).
56 *
57 */
58
59 #include <stdio.h>
60 #include <openssl/bn.h>
61
62 /* X9.31 routines for prime derivation */
63
64 /* X9.31 prime derivation. This is used to generate the primes pi
65 * (p1, p2, q1, q2) from a parameter Xpi by checking successive odd
66 * integers.
67 */
68
69 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
70 BN_GENCB *cb)
71 {
72 int i = 0;
73 if (!BN_copy(pi, Xpi))
74 return 0;
75 if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
76 return 0;
77 for(;;)
78 {
79 i++;
80 BN_GENCB_call(cb, 0, i);
81 /* NB 27 MR is specificed in X9.31 */
82 if (BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb))
83 break;
84 if (!BN_add_word(pi, 2))
85 return 0;
86 }
87 BN_GENCB_call(cb, 2, i);
88 return 1;
89 }
90
91 /* This is the main X9.31 prime derivation function. From parameters
92 * Xp1, Xp2 and Xp derive the prime p. If the parameters p1 or p2 are
93 * not NULL they will be returned too: this is needed for testing.
94 */
95
96 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
97 const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
98 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
99 {
100 int ret = 0;
101
102 BIGNUM *t, *p1p2, *pm1;
103
104 /* Only even e supported */
105 if (!BN_is_odd(e))
106 return 0;
107
108 BN_CTX_start(ctx);
109 if (!p1)
110 p1 = BN_CTX_get(ctx);
111
112 if (!p2)
113 p2 = BN_CTX_get(ctx);
114
115 t = BN_CTX_get(ctx);
116
117 p1p2 = BN_CTX_get(ctx);
118
119 pm1 = BN_CTX_get(ctx);
120
121 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
122 goto err;
123
124 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
125 goto err;
126
127 if (!BN_mul(p1p2, p1, p2, ctx))
128 goto err;
129
130 /* First set p to value of Rp */
131
132 if (!BN_mod_inverse(p, p2, p1, ctx))
133 goto err;
134
135 if (!BN_mul(p, p, p2, ctx))
136 goto err;
137
138 if (!BN_mod_inverse(t, p1, p2, ctx))
139 goto err;
140
141 if (!BN_mul(t, t, p1, ctx))
142 goto err;
143
144 if (!BN_sub(p, p, t))
145 goto err;
146
147 if (p->neg && !BN_add(p, p, p1p2))
148 goto err;
149
150 /* p now equals Rp */
151
152 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
153 goto err;
154
155 if (!BN_add(p, p, Xp))
156 goto err;
157
158 /* p now equals Yp0 */
159
160 for (;;)
161 {
162 int i = 1;
163 BN_GENCB_call(cb, 0, i++);
164 if (!BN_copy(pm1, p))
165 goto err;
166 if (!BN_sub_word(pm1, 1))
167 goto err;
168 if (!BN_gcd(t, pm1, e, ctx))
169 goto err;
170 if (BN_is_one(t)
171 /* X9.31 specifies 8 MR and 1 Lucas test or any prime test
172 * offering similar or better guarantees 50 MR is considerably
173 * better.
174 */
175 && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
176 break;
177 if (!BN_add(p, p, p1p2))
178 goto err;
179 }
180
181 BN_GENCB_call(cb, 3, 0);
182
183 ret = 1;
184
185 err:
186
187 BN_CTX_end(ctx);
188
189 return ret;
190 }
191
192 /* Generate pair of paramters Xp, Xq for X9.31 prime generation.
193 * Note: nbits paramter is sum of number of bits in both.
194 */
195
196 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
197 {
198 BIGNUM *t;
199 int i;
200 /* Number of bits for each prime is of the form
201 * 512+128s for s = 0, 1, ...
202 */
203 if ((nbits < 1024) || (nbits & 0xff))
204 return 0;
205 nbits >>= 1;
206 /* The random value Xp must be between sqrt(2) * 2^(nbits-1) and
207 * 2^nbits - 1. By setting the top two bits we ensure that the lower
208 * bound is exceeded.
209 */
210 if (!BN_rand(Xp, nbits, 1, 0))
211 return 0;
212
213 BN_CTX_start(ctx);
214 t = BN_CTX_get(ctx);
215
216 for (i = 0; i < 1000; i++)
217 {
218 if (!BN_rand(Xq, nbits, 1, 0))
219 return 0;
220 /* Check that |Xp - Xq| > 2^(nbits - 100) */
221 BN_sub(t, Xp, Xq);
222 if (BN_num_bits(t) > (nbits - 100))
223 break;
224 }
225
226 BN_CTX_end(ctx);
227
228 if (i < 1000)
229 return 1;
230
231 return 0;
232
233 }
234
235 /* Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1
236 * and Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL
237 * the relevant parameter will be stored in it.
238 *
239 * Due to the fact that |Xp - Xq| > 2^(nbits - 100) must be satisfied Xp and Xq
240 * are generated using the previous function and supplied as input.
241 */
242
243 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
244 BIGNUM *Xp1, BIGNUM *Xp2,
245 const BIGNUM *Xp,
246 const BIGNUM *e, BN_CTX *ctx,
247 BN_GENCB *cb)
248 {
249 int ret = 0;
250
251 BN_CTX_start(ctx);
252 if (!Xp1)
253 Xp1 = BN_CTX_get(ctx);
254 if (!Xp2)
255 Xp2 = BN_CTX_get(ctx);
256
257 if (!BN_rand(Xp1, 101, 0, 0))
258 goto error;
259 if (!BN_rand(Xp2, 101, 0, 0))
260 goto error;
261 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
262 goto error;
263
264 ret = 1;
265
266 error:
267 BN_CTX_end(ctx);
268
269 return ret;
270
271 }