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0f113f3e 1/*
1212818e 2 * Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved.
7b1a0451 3 *
367ace68 4 * Licensed under the Apache License 2.0 (the "License"). You may not use
4f22f405
RS
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
7b1a0451
DSH
8 */
9
10#include <stdio.h>
11#include <openssl/bn.h>
706457b7 12#include "bn_local.h"
7b1a0451
DSH
13
14/* X9.31 routines for prime derivation */
15
0f113f3e
MC
16/*
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.
7b1a0451
DSH
19 */
20
21static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
0f113f3e
MC
22 BN_GENCB *cb)
23{
748e8530 24 int i = 0, is_prime;
0f113f3e
MC
25 if (!BN_copy(pi, Xpi))
26 return 0;
27 if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
28 return 0;
29 for (;;) {
30 i++;
31 BN_GENCB_call(cb, 0, i);
0d4fb843 32 /* NB 27 MR is specified in X9.31 */
748e8530
DB
33 is_prime = BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb);
34 if (is_prime < 0)
35 return 0;
36 if (is_prime)
0f113f3e
MC
37 break;
38 if (!BN_add_word(pi, 2))
39 return 0;
40 }
41 BN_GENCB_call(cb, 2, i);
42 return 1;
43}
44
45/*
46 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
47 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
48 * will be returned too: this is needed for testing.
7b1a0451
DSH
49 */
50
51int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
0f113f3e
MC
52 const BIGNUM *Xp, const BIGNUM *Xp1,
53 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
54 BN_GENCB *cb)
55{
56 int ret = 0;
7b1a0451 57
0f113f3e 58 BIGNUM *t, *p1p2, *pm1;
7b1a0451 59
0f113f3e
MC
60 /* Only even e supported */
61 if (!BN_is_odd(e))
62 return 0;
7b1a0451 63
0f113f3e 64 BN_CTX_start(ctx);
edea42c6 65 if (p1 == NULL)
0f113f3e 66 p1 = BN_CTX_get(ctx);
7b1a0451 67
edea42c6 68 if (p2 == NULL)
0f113f3e 69 p2 = BN_CTX_get(ctx);
7b1a0451 70
0f113f3e 71 t = BN_CTX_get(ctx);
7b1a0451 72
0f113f3e 73 p1p2 = BN_CTX_get(ctx);
7b1a0451 74
0f113f3e 75 pm1 = BN_CTX_get(ctx);
7b1a0451 76
4d94bd36
MC
77 if (pm1 == NULL)
78 goto err;
79
0f113f3e
MC
80 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
81 goto err;
7b1a0451 82
0f113f3e
MC
83 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
84 goto err;
7b1a0451 85
0f113f3e
MC
86 if (!BN_mul(p1p2, p1, p2, ctx))
87 goto err;
7b1a0451 88
0f113f3e 89 /* First set p to value of Rp */
7b1a0451 90
0f113f3e
MC
91 if (!BN_mod_inverse(p, p2, p1, ctx))
92 goto err;
7b1a0451 93
0f113f3e
MC
94 if (!BN_mul(p, p, p2, ctx))
95 goto err;
7b1a0451 96
0f113f3e
MC
97 if (!BN_mod_inverse(t, p1, p2, ctx))
98 goto err;
7b1a0451 99
0f113f3e
MC
100 if (!BN_mul(t, t, p1, ctx))
101 goto err;
7b1a0451 102
0f113f3e
MC
103 if (!BN_sub(p, p, t))
104 goto err;
7b1a0451 105
0f113f3e
MC
106 if (p->neg && !BN_add(p, p, p1p2))
107 goto err;
7b1a0451 108
0f113f3e 109 /* p now equals Rp */
7b1a0451 110
0f113f3e
MC
111 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
112 goto err;
7b1a0451 113
0f113f3e
MC
114 if (!BN_add(p, p, Xp))
115 goto err;
7b1a0451 116
0f113f3e 117 /* p now equals Yp0 */
7b1a0451 118
0f113f3e
MC
119 for (;;) {
120 int i = 1;
121 BN_GENCB_call(cb, 0, i++);
122 if (!BN_copy(pm1, p))
123 goto err;
124 if (!BN_sub_word(pm1, 1))
125 goto err;
126 if (!BN_gcd(t, pm1, e, ctx))
127 goto err;
748e8530 128 if (BN_is_one(t)) {
0f113f3e
MC
129 /*
130 * X9.31 specifies 8 MR and 1 Lucas test or any prime test
131 * offering similar or better guarantees 50 MR is considerably
132 * better.
133 */
748e8530
DB
134 int r = BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb);
135 if (r < 0)
136 goto err;
137 if (r)
138 break;
139 }
0f113f3e
MC
140 if (!BN_add(p, p, p1p2))
141 goto err;
142 }
7b1a0451 143
0f113f3e 144 BN_GENCB_call(cb, 3, 0);
7b1a0451 145
0f113f3e 146 ret = 1;
7b1a0451 147
0f113f3e 148 err:
7b1a0451 149
0f113f3e 150 BN_CTX_end(ctx);
7b1a0451 151
0f113f3e
MC
152 return ret;
153}
7b1a0451 154
0f113f3e
MC
155/*
156 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
157 * parameter is sum of number of bits in both.
7b1a0451
DSH
158 */
159
160int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
0f113f3e
MC
161{
162 BIGNUM *t;
163 int i;
164 /*
165 * Number of bits for each prime is of the form 512+128s for s = 0, 1,
166 * ...
167 */
168 if ((nbits < 1024) || (nbits & 0xff))
169 return 0;
170 nbits >>= 1;
171 /*
172 * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
173 * - 1. By setting the top two bits we ensure that the lower bound is
174 * exceeded.
175 */
2934be91 176 if (!BN_priv_rand_ex(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, ctx))
3f6c7691 177 goto err;
0f113f3e
MC
178
179 BN_CTX_start(ctx);
180 t = BN_CTX_get(ctx);
5419dadd
BE
181 if (t == NULL)
182 goto err;
0f113f3e
MC
183
184 for (i = 0; i < 1000; i++) {
2934be91
MC
185 if (!BN_priv_rand_ex(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY,
186 ctx))
3f6c7691 187 goto err;
6bcfcf16 188
0f113f3e 189 /* Check that |Xp - Xq| > 2^(nbits - 100) */
6bcfcf16
P
190 if (!BN_sub(t, Xp, Xq))
191 goto err;
0f113f3e
MC
192 if (BN_num_bits(t) > (nbits - 100))
193 break;
194 }
195
196 BN_CTX_end(ctx);
197
198 if (i < 1000)
199 return 1;
200
201 return 0;
202
3f6c7691
AG
203 err:
204 BN_CTX_end(ctx);
205 return 0;
0f113f3e
MC
206}
207
208/*
209 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
210 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
211 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
212 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
213 * previous function and supplied as input.
7b1a0451
DSH
214 */
215
216int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
0f113f3e
MC
217 BIGNUM *Xp1, BIGNUM *Xp2,
218 const BIGNUM *Xp,
219 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
220{
221 int ret = 0;
7b1a0451 222
0f113f3e 223 BN_CTX_start(ctx);
5419dadd 224 if (Xp1 == NULL)
0f113f3e 225 Xp1 = BN_CTX_get(ctx);
5419dadd 226 if (Xp2 == NULL)
0f113f3e 227 Xp2 = BN_CTX_get(ctx);
5419dadd
BE
228 if (Xp1 == NULL || Xp2 == NULL)
229 goto error;
7b1a0451 230
2934be91 231 if (!BN_priv_rand_ex(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, ctx))
0f113f3e 232 goto error;
2934be91 233 if (!BN_priv_rand_ex(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, ctx))
0f113f3e
MC
234 goto error;
235 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
236 goto error;
7b1a0451 237
0f113f3e 238 ret = 1;
7b1a0451 239
0f113f3e
MC
240 error:
241 BN_CTX_end(ctx);
7b1a0451 242
0f113f3e 243 return ret;
7b1a0451 244
0f113f3e 245}