1 /*
2 * Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the OpenSSL license (the "License"). You may not use
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
8 */
9
10 #include <stdio.h>
11 #include <openssl/bn.h>
12 #include "bn_local.h"
13
14 /* X9.31 routines for prime derivation */
15
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.
19 */
20
bn_x931_derive_pi(BIGNUM * pi,const BIGNUM * Xpi,BN_CTX * ctx,BN_GENCB * cb)21 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
22 BN_GENCB *cb)
23 {
24 int i = 0, is_prime;
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);
32 /* NB 27 MR is specified in X9.31 */
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)
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.
49 */
50
BN_X931_derive_prime_ex(BIGNUM * p,BIGNUM * p1,BIGNUM * p2,const BIGNUM * Xp,const BIGNUM * Xp1,const BIGNUM * Xp2,const BIGNUM * e,BN_CTX * ctx,BN_GENCB * cb)51 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
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;
57
58 BIGNUM *t, *p1p2, *pm1;
59
60 /* Only even e supported */
61 if (!BN_is_odd(e))
62 return 0;
63
64 BN_CTX_start(ctx);
65 if (p1 == NULL)
66 p1 = BN_CTX_get(ctx);
67
68 if (p2 == NULL)
69 p2 = BN_CTX_get(ctx);
70
71 t = BN_CTX_get(ctx);
72
73 p1p2 = BN_CTX_get(ctx);
74
75 pm1 = BN_CTX_get(ctx);
76
77 if (pm1 == NULL)
78 goto err;
79
80 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
81 goto err;
82
83 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
84 goto err;
85
86 if (!BN_mul(p1p2, p1, p2, ctx))
87 goto err;
88
89 /* First set p to value of Rp */
90
91 if (!BN_mod_inverse(p, p2, p1, ctx))
92 goto err;
93
94 if (!BN_mul(p, p, p2, ctx))
95 goto err;
96
97 if (!BN_mod_inverse(t, p1, p2, ctx))
98 goto err;
99
100 if (!BN_mul(t, t, p1, ctx))
101 goto err;
102
103 if (!BN_sub(p, p, t))
104 goto err;
105
106 if (p->neg && !BN_add(p, p, p1p2))
107 goto err;
108
109 /* p now equals Rp */
110
111 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
112 goto err;
113
114 if (!BN_add(p, p, Xp))
115 goto err;
116
117 /* p now equals Yp0 */
118
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;
128 if (BN_is_one(t)) {
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 */
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 }
140 if (!BN_add(p, p, p1p2))
141 goto err;
142 }
143
144 BN_GENCB_call(cb, 3, 0);
145
146 ret = 1;
147
148 err:
149
150 BN_CTX_end(ctx);
151
152 return ret;
153 }
154
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.
158 */
159
BN_X931_generate_Xpq(BIGNUM * Xp,BIGNUM * Xq,int nbits,BN_CTX * ctx)160 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
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 */
176 if (!BN_priv_rand(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
177 goto err;
178
179 BN_CTX_start(ctx);
180 t = BN_CTX_get(ctx);
181 if (t == NULL)
182 goto err;
183
184 for (i = 0; i < 1000; i++) {
185 if (!BN_priv_rand(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
186 goto err;
187
188 /* Check that |Xp - Xq| > 2^(nbits - 100) */
189 if (!BN_sub(t, Xp, Xq))
190 goto err;
191 if (BN_num_bits(t) > (nbits - 100))
192 break;
193 }
194
195 BN_CTX_end(ctx);
196
197 if (i < 1000)
198 return 1;
199
200 return 0;
201
202 err:
203 BN_CTX_end(ctx);
204 return 0;
205 }
206
207 /*
208 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
209 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
210 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
211 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
212 * previous function and supplied as input.
213 */
214
BN_X931_generate_prime_ex(BIGNUM * p,BIGNUM * p1,BIGNUM * p2,BIGNUM * Xp1,BIGNUM * Xp2,const BIGNUM * Xp,const BIGNUM * e,BN_CTX * ctx,BN_GENCB * cb)215 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
216 BIGNUM *Xp1, BIGNUM *Xp2,
217 const BIGNUM *Xp,
218 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
219 {
220 int ret = 0;
221
222 BN_CTX_start(ctx);
223 if (Xp1 == NULL)
224 Xp1 = BN_CTX_get(ctx);
225 if (Xp2 == NULL)
226 Xp2 = BN_CTX_get(ctx);
227 if (Xp1 == NULL || Xp2 == NULL)
228 goto error;
229
230 if (!BN_priv_rand(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
231 goto error;
232 if (!BN_priv_rand(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
233 goto error;
234 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
235 goto error;
236
237 ret = 1;
238
239 error:
240 BN_CTX_end(ctx);
241
242 return ret;
243
244 }
245