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
23static 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
53int 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
162int 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
219int 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