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diff --git a/src/lib/libcrypto/bn/bn_prime.c b/src/lib/libcrypto/bn/bn_prime.c
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1/* $OpenBSD: bn_prime.c,v 1.13 2015/02/09 15:49:22 jsing Exp $ */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58/* ====================================================================
59 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
111
112#include <stdio.h>
113#include <time.h>
114
115#include "bn_lcl.h"
116
117/* NB: these functions have been "upgraded", the deprecated versions (which are
118 * compatibility wrappers using these functions) are in bn_depr.c.
119 * - Geoff
120 */
121
122/* The quick sieve algorithm approach to weeding out primes is
123 * Philip Zimmermann's, as implemented in PGP. I have had a read of
124 * his comments and implemented my own version.
125 */
126#include "bn_prime.h"
127
128static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
129 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
130static int probable_prime(BIGNUM *rnd, int bits);
131static int probable_prime_dh(BIGNUM *rnd, int bits,
132 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
133static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
134 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
135
136int
137BN_GENCB_call(BN_GENCB *cb, int a, int b)
138{
139 /* No callback means continue */
140 if (!cb)
141 return 1;
142 switch (cb->ver) {
143 case 1:
144 /* Deprecated-style callbacks */
145 if (!cb->cb.cb_1)
146 return 1;
147 cb->cb.cb_1(a, b, cb->arg);
148 return 1;
149 case 2:
150 /* New-style callbacks */
151 return cb->cb.cb_2(a, b, cb);
152 default:
153 break;
154 }
155 /* Unrecognised callback type */
156 return 0;
157}
158
159int
160BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
161 const BIGNUM *rem, BN_GENCB *cb)
162{
163 BIGNUM *t;
164 int found = 0;
165 int i, j, c1 = 0;
166 BN_CTX *ctx;
167 int checks = BN_prime_checks_for_size(bits);
168
169 ctx = BN_CTX_new();
170 if (ctx == NULL)
171 goto err;
172 BN_CTX_start(ctx);
173 if ((t = BN_CTX_get(ctx)) == NULL)
174 goto err;
175loop:
176 /* make a random number and set the top and bottom bits */
177 if (add == NULL) {
178 if (!probable_prime(ret, bits))
179 goto err;
180 } else {
181 if (safe) {
182 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
183 goto err;
184 } else {
185 if (!probable_prime_dh(ret, bits, add, rem, ctx))
186 goto err;
187 }
188 }
189 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
190 if (!BN_GENCB_call(cb, 0, c1++))
191 /* aborted */
192 goto err;
193
194 if (!safe) {
195 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
196 if (i == -1)
197 goto err;
198 if (i == 0)
199 goto loop;
200 } else {
201 /* for "safe prime" generation,
202 * check that (p-1)/2 is prime.
203 * Since a prime is odd, We just
204 * need to divide by 2 */
205 if (!BN_rshift1(t, ret))
206 goto err;
207
208 for (i = 0; i < checks; i++) {
209 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
210 if (j == -1)
211 goto err;
212 if (j == 0)
213 goto loop;
214
215 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
216 if (j == -1)
217 goto err;
218 if (j == 0)
219 goto loop;
220
221 if (!BN_GENCB_call(cb, 2, c1 - 1))
222 goto err;
223 /* We have a safe prime test pass */
224 }
225 }
226 /* we have a prime :-) */
227 found = 1;
228
229err:
230 if (ctx != NULL) {
231 BN_CTX_end(ctx);
232 BN_CTX_free(ctx);
233 }
234 bn_check_top(ret);
235 return found;
236}
237
238int
239BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
240{
241 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
242}
243
244int
245BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
246 int do_trial_division, BN_GENCB *cb)
247{
248 int i, j, ret = -1;
249 int k;
250 BN_CTX *ctx = NULL;
251 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
252 BN_MONT_CTX *mont = NULL;
253 const BIGNUM *A = NULL;
254
255 if (BN_cmp(a, BN_value_one()) <= 0)
256 return 0;
257
258 if (checks == BN_prime_checks)
259 checks = BN_prime_checks_for_size(BN_num_bits(a));
260
261 /* first look for small factors */
262 if (!BN_is_odd(a))
263 /* a is even => a is prime if and only if a == 2 */
264 return BN_is_word(a, 2);
265 if (do_trial_division) {
266 for (i = 1; i < NUMPRIMES; i++)
267 if (BN_mod_word(a, primes[i]) == 0)
268 return 0;
269 if (!BN_GENCB_call(cb, 1, -1))
270 goto err;
271 }
272
273 if (ctx_passed != NULL)
274 ctx = ctx_passed;
275 else if ((ctx = BN_CTX_new()) == NULL)
276 goto err;
277 BN_CTX_start(ctx);
278
279 /* A := abs(a) */
280 if (a->neg) {
281 BIGNUM *t;
282 if ((t = BN_CTX_get(ctx)) == NULL)
283 goto err;
284 BN_copy(t, a);
285 t->neg = 0;
286 A = t;
287 } else
288 A = a;
289 if ((A1 = BN_CTX_get(ctx)) == NULL)
290 goto err;
291 if ((A1_odd = BN_CTX_get(ctx)) == NULL)
292 goto err;
293 if ((check = BN_CTX_get(ctx)) == NULL)
294 goto err;
295
296 /* compute A1 := A - 1 */
297 if (!BN_copy(A1, A))
298 goto err;
299 if (!BN_sub_word(A1, 1))
300 goto err;
301 if (BN_is_zero(A1)) {
302 ret = 0;
303 goto err;
304 }
305
306 /* write A1 as A1_odd * 2^k */
307 k = 1;
308 while (!BN_is_bit_set(A1, k))
309 k++;
310 if (!BN_rshift(A1_odd, A1, k))
311 goto err;
312
313 /* Montgomery setup for computations mod A */
314 mont = BN_MONT_CTX_new();
315 if (mont == NULL)
316 goto err;
317 if (!BN_MONT_CTX_set(mont, A, ctx))
318 goto err;
319
320 for (i = 0; i < checks; i++) {
321 if (!BN_pseudo_rand_range(check, A1))
322 goto err;
323 if (!BN_add_word(check, 1))
324 goto err;
325 /* now 1 <= check < A */
326
327 j = witness(check, A, A1, A1_odd, k, ctx, mont);
328 if (j == -1)
329 goto err;
330 if (j) {
331 ret = 0;
332 goto err;
333 }
334 if (!BN_GENCB_call(cb, 1, i))
335 goto err;
336 }
337 ret = 1;
338
339err:
340 if (ctx != NULL) {
341 BN_CTX_end(ctx);
342 if (ctx_passed == NULL)
343 BN_CTX_free(ctx);
344 }
345 BN_MONT_CTX_free(mont);
346
347 return (ret);
348}
349
350static int
351witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd,
352 int k, BN_CTX *ctx, BN_MONT_CTX *mont)
353{
354 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont))
355 /* w := w^a1_odd mod a */
356 return -1;
357 if (BN_is_one(w))
358 return 0; /* probably prime */
359 if (BN_cmp(w, a1) == 0)
360 return 0; /* w == -1 (mod a), 'a' is probably prime */
361 while (--k) {
362 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
363 return -1;
364 if (BN_is_one(w))
365 return 1; /* 'a' is composite, otherwise a previous 'w' would
366 * have been == -1 (mod 'a') */
367 if (BN_cmp(w, a1) == 0)
368 return 0; /* w == -1 (mod a), 'a' is probably prime */
369 }
370 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
371 * and it is neither -1 nor +1 -- so 'a' cannot be prime */
372 bn_check_top(w);
373 return 1;
374}
375
376static int
377probable_prime(BIGNUM *rnd, int bits)
378{
379 int i;
380 prime_t mods[NUMPRIMES];
381 BN_ULONG delta, maxdelta;
382
383again:
384 if (!BN_rand(rnd, bits, 1, 1))
385 return (0);
386 /* we now have a random number 'rand' to test. */
387 for (i = 1; i < NUMPRIMES; i++)
388 mods[i] = (prime_t)BN_mod_word(rnd, (BN_ULONG)primes[i]);
389 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
390 delta = 0;
391loop:
392 for (i = 1; i < NUMPRIMES; i++) {
393 /* check that rnd is not a prime and also
394 * that gcd(rnd-1,primes) == 1 (except for 2) */
395 if (((mods[i] + delta) % primes[i]) <= 1) {
396 delta += 2;
397 if (delta > maxdelta)
398 goto again;
399 goto loop;
400 }
401 }
402 if (!BN_add_word(rnd, delta))
403 return (0);
404 bn_check_top(rnd);
405 return (1);
406}
407
408static int
409probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem,
410 BN_CTX *ctx)
411{
412 int i, ret = 0;
413 BIGNUM *t1;
414
415 BN_CTX_start(ctx);
416 if ((t1 = BN_CTX_get(ctx)) == NULL)
417 goto err;
418
419 if (!BN_rand(rnd, bits, 0, 1))
420 goto err;
421
422 /* we need ((rnd-rem) % add) == 0 */
423
424 if (!BN_mod(t1, rnd, add, ctx))
425 goto err;
426 if (!BN_sub(rnd, rnd, t1))
427 goto err;
428 if (rem == NULL) {
429 if (!BN_add_word(rnd, 1))
430 goto err;
431 } else {
432 if (!BN_add(rnd, rnd, rem))
433 goto err;
434 }
435
436 /* we now have a random number 'rand' to test. */
437
438loop:
439 for (i = 1; i < NUMPRIMES; i++) {
440 /* check that rnd is a prime */
441 if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
442 if (!BN_add(rnd, rnd, add))
443 goto err;
444 goto loop;
445 }
446 }
447 ret = 1;
448
449err:
450 BN_CTX_end(ctx);
451 bn_check_top(rnd);
452 return (ret);
453}
454
455static int
456probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
457 const BIGNUM *rem, BN_CTX *ctx)
458{
459 int i, ret = 0;
460 BIGNUM *t1, *qadd, *q;
461
462 bits--;
463 BN_CTX_start(ctx);
464 if ((t1 = BN_CTX_get(ctx)) == NULL)
465 goto err;
466 if ((q = BN_CTX_get(ctx)) == NULL)
467 goto err;
468 if ((qadd = BN_CTX_get(ctx)) == NULL)
469 goto err;
470
471 if (!BN_rshift1(qadd, padd))
472 goto err;
473
474 if (!BN_rand(q, bits, 0, 1))
475 goto err;
476
477 /* we need ((rnd-rem) % add) == 0 */
478 if (!BN_mod(t1, q,qadd, ctx))
479 goto err;
480 if (!BN_sub(q, q, t1))
481 goto err;
482 if (rem == NULL) {
483 if (!BN_add_word(q, 1))
484 goto err;
485 } else {
486 if (!BN_rshift1(t1, rem))
487 goto err;
488 if (!BN_add(q, q, t1))
489 goto err;
490 }
491
492 /* we now have a random number 'rand' to test. */
493 if (!BN_lshift1(p, q))
494 goto err;
495 if (!BN_add_word(p, 1))
496 goto err;
497
498loop:
499 for (i = 1; i < NUMPRIMES; i++) {
500 /* check that p and q are prime */
501 /* check that for p and q
502 * gcd(p-1,primes) == 1 (except for 2) */
503 if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) ||
504 (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) {
505 if (!BN_add(p, p, padd))
506 goto err;
507 if (!BN_add(q, q, qadd))
508 goto err;
509 goto loop;
510 }
511 }
512 ret = 1;
513
514err:
515 BN_CTX_end(ctx);
516 bn_check_top(p);
517 return (ret);
518}
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-09 13:54:13 +0000