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1 | /* | |
2 | * Copyright 2011-2018 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 | #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 | ||
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 | ||
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 | ||
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_ex(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, ctx)) | |
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_ex(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, | |
186 | ctx)) | |
187 | goto err; | |
188 | ||
189 | /* Check that |Xp - Xq| > 2^(nbits - 100) */ | |
190 | if (!BN_sub(t, Xp, Xq)) | |
191 | goto err; | |
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 | ||
203 | err: | |
204 | BN_CTX_end(ctx); | |
205 | return 0; | |
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. | |
214 | */ | |
215 | ||
216 | int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, | |
217 | BIGNUM *Xp1, BIGNUM *Xp2, | |
218 | const BIGNUM *Xp, | |
219 | const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb) | |
220 | { | |
221 | int ret = 0; | |
222 | ||
223 | BN_CTX_start(ctx); | |
224 | if (Xp1 == NULL) | |
225 | Xp1 = BN_CTX_get(ctx); | |
226 | if (Xp2 == NULL) | |
227 | Xp2 = BN_CTX_get(ctx); | |
228 | if (Xp1 == NULL || Xp2 == NULL) | |
229 | goto error; | |
230 | ||
231 | if (!BN_priv_rand_ex(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, ctx)) | |
232 | goto error; | |
233 | if (!BN_priv_rand_ex(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, ctx)) | |
234 | goto error; | |
235 | if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb)) | |
236 | goto error; | |
237 | ||
238 | ret = 1; | |
239 | ||
240 | error: | |
241 | BN_CTX_end(ctx); | |
242 | ||
243 | return ret; | |
244 | ||
245 | } |