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_check_prime(pi, ctx, 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_check_prime(p, ctx, 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 | } |
246 | |