1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
|
/* bn_x931p.c */
/* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL
* project 2005.
*/
/* ====================================================================
* Copyright (c) 2005 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* licensing@OpenSSL.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
#include <stdio.h>
#include <openssl/bn.h>
/* X9.31 routines for prime derivation */
/* X9.31 prime derivation. This is used to generate the primes pi
* (p1, p2, q1, q2) from a parameter Xpi by checking successive odd
* integers.
*/
static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
BN_GENCB *cb)
{
int i = 0;
if (!BN_copy(pi, Xpi))
return 0;
if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
return 0;
for(;;)
{
i++;
BN_GENCB_call(cb, 0, i);
/* NB 27 MR is specificed in X9.31 */
if (BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb))
break;
if (!BN_add_word(pi, 2))
return 0;
}
BN_GENCB_call(cb, 2, i);
return 1;
}
/* This is the main X9.31 prime derivation function. From parameters
* Xp1, Xp2 and Xp derive the prime p. If the parameters p1 or p2 are
* not NULL they will be returned too: this is needed for testing.
*/
int 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)
{
int ret = 0;
BIGNUM *t, *p1p2, *pm1;
/* Only even e supported */
if (!BN_is_odd(e))
return 0;
BN_CTX_start(ctx);
if (!p1)
p1 = BN_CTX_get(ctx);
if (!p2)
p2 = BN_CTX_get(ctx);
t = BN_CTX_get(ctx);
p1p2 = BN_CTX_get(ctx);
pm1 = BN_CTX_get(ctx);
if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
goto err;
if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
goto err;
if (!BN_mul(p1p2, p1, p2, ctx))
goto err;
/* First set p to value of Rp */
if (!BN_mod_inverse(p, p2, p1, ctx))
goto err;
if (!BN_mul(p, p, p2, ctx))
goto err;
if (!BN_mod_inverse(t, p1, p2, ctx))
goto err;
if (!BN_mul(t, t, p1, ctx))
goto err;
if (!BN_sub(p, p, t))
goto err;
if (p->neg && !BN_add(p, p, p1p2))
goto err;
/* p now equals Rp */
if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
goto err;
if (!BN_add(p, p, Xp))
goto err;
/* p now equals Yp0 */
for (;;)
{
int i = 1;
BN_GENCB_call(cb, 0, i++);
if (!BN_copy(pm1, p))
goto err;
if (!BN_sub_word(pm1, 1))
goto err;
if (!BN_gcd(t, pm1, e, ctx))
goto err;
if (BN_is_one(t)
/* X9.31 specifies 8 MR and 1 Lucas test or any prime test
* offering similar or better guarantees 50 MR is considerably
* better.
*/
&& BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
break;
if (!BN_add(p, p, p1p2))
goto err;
}
BN_GENCB_call(cb, 3, 0);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/* Generate pair of paramters Xp, Xq for X9.31 prime generation.
* Note: nbits paramter is sum of number of bits in both.
*/
int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
{
BIGNUM *t;
int i;
/* Number of bits for each prime is of the form
* 512+128s for s = 0, 1, ...
*/
if ((nbits < 1024) || (nbits & 0xff))
return 0;
nbits >>= 1;
/* The random value Xp must be between sqrt(2) * 2^(nbits-1) and
* 2^nbits - 1. By setting the top two bits we ensure that the lower
* bound is exceeded.
*/
if (!BN_rand(Xp, nbits, 1, 0))
return 0;
BN_CTX_start(ctx);
t = BN_CTX_get(ctx);
for (i = 0; i < 1000; i++)
{
if (!BN_rand(Xq, nbits, 1, 0))
return 0;
/* Check that |Xp - Xq| > 2^(nbits - 100) */
BN_sub(t, Xp, Xq);
if (BN_num_bits(t) > (nbits - 100))
break;
}
BN_CTX_end(ctx);
if (i < 1000)
return 1;
return 0;
}
/* Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1
* and Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL
* the relevant parameter will be stored in it.
*
* Due to the fact that |Xp - Xq| > 2^(nbits - 100) must be satisfied Xp and Xq
* are generated using the previous function and supplied as input.
*/
int 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)
{
int ret = 0;
BN_CTX_start(ctx);
if (!Xp1)
Xp1 = BN_CTX_get(ctx);
if (!Xp2)
Xp2 = BN_CTX_get(ctx);
if (!BN_rand(Xp1, 101, 0, 0))
goto error;
if (!BN_rand(Xp2, 101, 0, 0))
goto error;
if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
goto error;
ret = 1;
error:
BN_CTX_end(ctx);
return ret;
}
|