1 /*
2 * Copyright 2011-2021 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (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 #define OPENSSL_SUPPRESS_DEPRECATED
11
12 #include <stdio.h>
13 #include <openssl/bn.h>
14 #include "bn_local.h"
15
16 /* X9.31 routines for prime derivation */
17
18 /*
19 * X9.31 prime derivation. This is used to generate the primes pi (p1, p2,
20 * q1, q2) from a parameter Xpi by checking successive odd integers.
21 */
22
bn_x931_derive_pi(BIGNUM * pi,const BIGNUM * Xpi,BN_CTX * ctx,BN_GENCB * cb)23 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
24 BN_GENCB *cb)
25 {
26 int i = 0, is_prime;
27 if (!BN_copy(pi, Xpi))
28 return 0;
29 if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
30 return 0;
31 for (;;) {
32 i++;
33 BN_GENCB_call(cb, 0, i);
34 /* NB 27 MR is specified in X9.31 */
35 is_prime = BN_check_prime(pi, ctx, cb);
36 if (is_prime < 0)
37 return 0;
38 if (is_prime)
39 break;
40 if (!BN_add_word(pi, 2))
41 return 0;
42 }
43 BN_GENCB_call(cb, 2, i);
44 return 1;
45 }
46
47 /*
48 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
49 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
50 * will be returned too: this is needed for testing.
51 */
52
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)53 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
54 const BIGNUM *Xp, const BIGNUM *Xp1,
55 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
56 BN_GENCB *cb)
57 {
58 int ret = 0;
59
60 BIGNUM *t, *p1p2, *pm1;
61
62 /* Only even e supported */
63 if (!BN_is_odd(e))
64 return 0;
65
66 BN_CTX_start(ctx);
67 if (p1 == NULL)
68 p1 = BN_CTX_get(ctx);
69
70 if (p2 == NULL)
71 p2 = BN_CTX_get(ctx);
72
73 t = BN_CTX_get(ctx);
74
75 p1p2 = BN_CTX_get(ctx);
76
77 pm1 = BN_CTX_get(ctx);
78
79 if (pm1 == NULL)
80 goto err;
81
82 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
83 goto err;
84
85 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
86 goto err;
87
88 if (!BN_mul(p1p2, p1, p2, ctx))
89 goto err;
90
91 /* First set p to value of Rp */
92
93 if (!BN_mod_inverse(p, p2, p1, ctx))
94 goto err;
95
96 if (!BN_mul(p, p, p2, ctx))
97 goto err;
98
99 if (!BN_mod_inverse(t, p1, p2, ctx))
100 goto err;
101
102 if (!BN_mul(t, t, p1, ctx))
103 goto err;
104
105 if (!BN_sub(p, p, t))
106 goto err;
107
108 if (p->neg && !BN_add(p, p, p1p2))
109 goto err;
110
111 /* p now equals Rp */
112
113 if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
114 goto err;
115
116 if (!BN_add(p, p, Xp))
117 goto err;
118
119 /* p now equals Yp0 */
120
121 for (;;) {
122 int i = 1;
123 BN_GENCB_call(cb, 0, i++);
124 if (!BN_copy(pm1, p))
125 goto err;
126 if (!BN_sub_word(pm1, 1))
127 goto err;
128 if (!BN_gcd(t, pm1, e, ctx))
129 goto err;
130 if (BN_is_one(t)) {
131 /*
132 * X9.31 specifies 8 MR and 1 Lucas test or any prime test
133 * offering similar or better guarantees 50 MR is considerably
134 * better.
135 */
136 int r = BN_check_prime(p, ctx, cb);
137 if (r < 0)
138 goto err;
139 if (r)
140 break;
141 }
142 if (!BN_add(p, p, p1p2))
143 goto err;
144 }
145
146 BN_GENCB_call(cb, 3, 0);
147
148 ret = 1;
149
150 err:
151
152 BN_CTX_end(ctx);
153
154 return ret;
155 }
156
157 /*
158 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
159 * parameter is sum of number of bits in both.
160 */
161
BN_X931_generate_Xpq(BIGNUM * Xp,BIGNUM * Xq,int nbits,BN_CTX * ctx)162 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
163 {
164 BIGNUM *t;
165 int i;
166 /*
167 * Number of bits for each prime is of the form 512+128s for s = 0, 1,
168 * ...
169 */
170 if ((nbits < 1024) || (nbits & 0xff))
171 return 0;
172 nbits >>= 1;
173 /*
174 * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
175 * - 1. By setting the top two bits we ensure that the lower bound is
176 * exceeded.
177 */
178 if (!BN_priv_rand_ex(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, 0,
179 ctx))
180 return 0;
181
182 BN_CTX_start(ctx);
183 t = BN_CTX_get(ctx);
184 if (t == NULL)
185 goto err;
186
187 for (i = 0; i < 1000; i++) {
188 if (!BN_priv_rand_ex(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, 0,
189 ctx))
190 goto err;
191
192 /* Check that |Xp - Xq| > 2^(nbits - 100) */
193 if (!BN_sub(t, Xp, Xq))
194 goto err;
195 if (BN_num_bits(t) > (nbits - 100))
196 break;
197 }
198
199 BN_CTX_end(ctx);
200
201 if (i < 1000)
202 return 1;
203
204 return 0;
205
206 err:
207 BN_CTX_end(ctx);
208 return 0;
209 }
210
211 /*
212 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
213 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
214 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
215 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
216 * previous function and supplied as input.
217 */
218
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)219 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
220 BIGNUM *Xp1, BIGNUM *Xp2,
221 const BIGNUM *Xp,
222 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
223 {
224 int ret = 0;
225
226 BN_CTX_start(ctx);
227 if (Xp1 == NULL)
228 Xp1 = BN_CTX_get(ctx);
229 if (Xp2 == NULL)
230 Xp2 = BN_CTX_get(ctx);
231 if (Xp1 == NULL || Xp2 == NULL)
232 goto error;
233
234 if (!BN_priv_rand_ex(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, 0, ctx))
235 goto error;
236 if (!BN_priv_rand_ex(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, 0, ctx))
237 goto error;
238 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
239 goto error;
240
241 ret = 1;
242
243 error:
244 BN_CTX_end(ctx);
245
246 return ret;
247
248 }
249