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1/* $OpenBSD: bn_prime.c,v 1.15 2016/07/05 02:54:35 bcook 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 <openssl/err.h>
116
117#include "bn_lcl.h"
118
119/* NB: these functions have been "upgraded", the deprecated versions (which are
120 * compatibility wrappers using these functions) are in bn_depr.c.
121 * - Geoff
122 */
123
124/* The quick sieve algorithm approach to weeding out primes is
125 * Philip Zimmermann's, as implemented in PGP. I have had a read of
126 * his comments and implemented my own version.
127 */
128#include "bn_prime.h"
129
130static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
131 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
132static int probable_prime(BIGNUM *rnd, int bits);
133static int probable_prime_dh(BIGNUM *rnd, int bits,
134 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
135static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
136 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
137
138int
139BN_GENCB_call(BN_GENCB *cb, int a, int b)
140{
141 /* No callback means continue */
142 if (!cb)
143 return 1;
144 switch (cb->ver) {
145 case 1:
146 /* Deprecated-style callbacks */
147 if (!cb->cb.cb_1)
148 return 1;
149 cb->cb.cb_1(a, b, cb->arg);
150 return 1;
151 case 2:
152 /* New-style callbacks */
153 return cb->cb.cb_2(a, b, cb);
154 default:
155 break;
156 }
157 /* Unrecognised callback type */
158 return 0;
159}
160
161int
162BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
163 const BIGNUM *rem, BN_GENCB *cb)
164{
165 BIGNUM *t;
166 int found = 0;
167 int i, j, c1 = 0;
168 BN_CTX *ctx;
169 int checks;
170
171 if (bits < 2 || (bits == 2 && safe)) {
172 /*
173 * There are no prime numbers smaller than 2, and the smallest
174 * safe prime (7) spans three bits.
175 */
176 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
177 return 0;
178 }
179
180 ctx = BN_CTX_new();
181 if (ctx == NULL)
182 goto err;
183 BN_CTX_start(ctx);
184 if ((t = BN_CTX_get(ctx)) == NULL)
185 goto err;
186
187 checks = BN_prime_checks_for_size(bits);
188
189loop:
190 /* make a random number and set the top and bottom bits */
191 if (add == NULL) {
192 if (!probable_prime(ret, bits))
193 goto err;
194 } else {
195 if (safe) {
196 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
197 goto err;
198 } else {
199 if (!probable_prime_dh(ret, bits, add, rem, ctx))
200 goto err;
201 }
202 }
203 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
204 if (!BN_GENCB_call(cb, 0, c1++))
205 /* aborted */
206 goto err;
207
208 if (!safe) {
209 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
210 if (i == -1)
211 goto err;
212 if (i == 0)
213 goto loop;
214 } else {
215 /* for "safe prime" generation,
216 * check that (p-1)/2 is prime.
217 * Since a prime is odd, We just
218 * need to divide by 2 */
219 if (!BN_rshift1(t, ret))
220 goto err;
221
222 for (i = 0; i < checks; i++) {
223 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
224 if (j == -1)
225 goto err;
226 if (j == 0)
227 goto loop;
228
229 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
230 if (j == -1)
231 goto err;
232 if (j == 0)
233 goto loop;
234
235 if (!BN_GENCB_call(cb, 2, c1 - 1))
236 goto err;
237 /* We have a safe prime test pass */
238 }
239 }
240 /* we have a prime :-) */
241 found = 1;
242
243err:
244 if (ctx != NULL) {
245 BN_CTX_end(ctx);
246 BN_CTX_free(ctx);
247 }
248 bn_check_top(ret);
249 return found;
250}
251
252int
253BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
254{
255 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
256}
257
258int
259BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
260 int do_trial_division, BN_GENCB *cb)
261{
262 int i, j, ret = -1;
263 int k;
264 BN_CTX *ctx = NULL;
265 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
266 BN_MONT_CTX *mont = NULL;
267 const BIGNUM *A = NULL;
268
269 if (BN_cmp(a, BN_value_one()) <= 0)
270 return 0;
271
272 if (checks == BN_prime_checks)
273 checks = BN_prime_checks_for_size(BN_num_bits(a));
274
275 /* first look for small factors */
276 if (!BN_is_odd(a))
277 /* a is even => a is prime if and only if a == 2 */
278 return BN_is_word(a, 2);
279 if (do_trial_division) {
280 for (i = 1; i < NUMPRIMES; i++) {
281 BN_ULONG mod = BN_mod_word(a, primes[i]);
282 if (mod == (BN_ULONG)-1)
283 goto err;
284 if (mod == 0)
285 return 0;
286 }
287 if (!BN_GENCB_call(cb, 1, -1))
288 goto err;
289 }
290
291 if (ctx_passed != NULL)
292 ctx = ctx_passed;
293 else if ((ctx = BN_CTX_new()) == NULL)
294 goto err;
295 BN_CTX_start(ctx);
296
297 /* A := abs(a) */
298 if (a->neg) {
299 BIGNUM *t;
300 if ((t = BN_CTX_get(ctx)) == NULL)
301 goto err;
302 BN_copy(t, a);
303 t->neg = 0;
304 A = t;
305 } else
306 A = a;
307 if ((A1 = BN_CTX_get(ctx)) == NULL)
308 goto err;
309 if ((A1_odd = BN_CTX_get(ctx)) == NULL)
310 goto err;
311 if ((check = BN_CTX_get(ctx)) == NULL)
312 goto err;
313
314 /* compute A1 := A - 1 */
315 if (!BN_copy(A1, A))
316 goto err;
317 if (!BN_sub_word(A1, 1))
318 goto err;
319 if (BN_is_zero(A1)) {
320 ret = 0;
321 goto err;
322 }
323
324 /* write A1 as A1_odd * 2^k */
325 k = 1;
326 while (!BN_is_bit_set(A1, k))
327 k++;
328 if (!BN_rshift(A1_odd, A1, k))
329 goto err;
330
331 /* Montgomery setup for computations mod A */
332 mont = BN_MONT_CTX_new();
333 if (mont == NULL)
334 goto err;
335 if (!BN_MONT_CTX_set(mont, A, ctx))
336 goto err;
337
338 for (i = 0; i < checks; i++) {
339 if (!BN_pseudo_rand_range(check, A1))
340 goto err;
341 if (!BN_add_word(check, 1))
342 goto err;
343 /* now 1 <= check < A */
344
345 j = witness(check, A, A1, A1_odd, k, ctx, mont);
346 if (j == -1)
347 goto err;
348 if (j) {
349 ret = 0;
350 goto err;
351 }
352 if (!BN_GENCB_call(cb, 1, i))
353 goto err;
354 }
355 ret = 1;
356
357err:
358 if (ctx != NULL) {
359 BN_CTX_end(ctx);
360 if (ctx_passed == NULL)
361 BN_CTX_free(ctx);
362 }
363 BN_MONT_CTX_free(mont);
364
365 return (ret);
366}
367
368static int
369witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd,
370 int k, BN_CTX *ctx, BN_MONT_CTX *mont)
371{
372 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont))
373 /* w := w^a1_odd mod a */
374 return -1;
375 if (BN_is_one(w))
376 return 0; /* probably prime */
377 if (BN_cmp(w, a1) == 0)
378 return 0; /* w == -1 (mod a), 'a' is probably prime */
379 while (--k) {
380 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
381 return -1;
382 if (BN_is_one(w))
383 return 1; /* 'a' is composite, otherwise a previous 'w' would
384 * have been == -1 (mod 'a') */
385 if (BN_cmp(w, a1) == 0)
386 return 0; /* w == -1 (mod a), 'a' is probably prime */
387 }
388 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
389 * and it is neither -1 nor +1 -- so 'a' cannot be prime */
390 bn_check_top(w);
391 return 1;
392}
393
394static int
395probable_prime(BIGNUM *rnd, int bits)
396{
397 int i;
398 prime_t mods[NUMPRIMES];
399 BN_ULONG delta, maxdelta;
400
401again:
402 if (!BN_rand(rnd, bits, 1, 1))
403 return (0);
404 /* we now have a random number 'rand' to test. */
405 for (i = 1; i < NUMPRIMES; i++) {
406 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
407 if (mod == (BN_ULONG)-1)
408 return (0);
409 mods[i] = (prime_t)mod;
410 }
411 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
412 delta = 0;
413loop:
414 for (i = 1; i < NUMPRIMES; i++) {
415 /* check that rnd is not a prime and also
416 * that gcd(rnd-1,primes) == 1 (except for 2) */
417 if (((mods[i] + delta) % primes[i]) <= 1) {
418 delta += 2;
419 if (delta > maxdelta)
420 goto again;
421 goto loop;
422 }
423 }
424 if (!BN_add_word(rnd, delta))
425 return (0);
426 bn_check_top(rnd);
427 return (1);
428}
429
430static int
431probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem,
432 BN_CTX *ctx)
433{
434 int i, ret = 0;
435 BIGNUM *t1;
436
437 BN_CTX_start(ctx);
438 if ((t1 = BN_CTX_get(ctx)) == NULL)
439 goto err;
440
441 if (!BN_rand(rnd, bits, 0, 1))
442 goto err;
443
444 /* we need ((rnd-rem) % add) == 0 */
445
446 if (!BN_mod(t1, rnd, add, ctx))
447 goto err;
448 if (!BN_sub(rnd, rnd, t1))
449 goto err;
450 if (rem == NULL) {
451 if (!BN_add_word(rnd, 1))
452 goto err;
453 } else {
454 if (!BN_add(rnd, rnd, rem))
455 goto err;
456 }
457
458 /* we now have a random number 'rand' to test. */
459
460loop:
461 for (i = 1; i < NUMPRIMES; i++) {
462 /* check that rnd is a prime */
463 BN_LONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
464 if (mod == (BN_ULONG)-1)
465 goto err;
466 if (mod <= 1) {
467 if (!BN_add(rnd, rnd, add))
468 goto err;
469 goto loop;
470 }
471 }
472 ret = 1;
473
474err:
475 BN_CTX_end(ctx);
476 bn_check_top(rnd);
477 return (ret);
478}
479
480static int
481probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
482 const BIGNUM *rem, BN_CTX *ctx)
483{
484 int i, ret = 0;
485 BIGNUM *t1, *qadd, *q;
486
487 bits--;
488 BN_CTX_start(ctx);
489 if ((t1 = BN_CTX_get(ctx)) == NULL)
490 goto err;
491 if ((q = BN_CTX_get(ctx)) == NULL)
492 goto err;
493 if ((qadd = BN_CTX_get(ctx)) == NULL)
494 goto err;
495
496 if (!BN_rshift1(qadd, padd))
497 goto err;
498
499 if (!BN_rand(q, bits, 0, 1))
500 goto err;
501
502 /* we need ((rnd-rem) % add) == 0 */
503 if (!BN_mod(t1, q,qadd, ctx))
504 goto err;
505 if (!BN_sub(q, q, t1))
506 goto err;
507 if (rem == NULL) {
508 if (!BN_add_word(q, 1))
509 goto err;
510 } else {
511 if (!BN_rshift1(t1, rem))
512 goto err;
513 if (!BN_add(q, q, t1))
514 goto err;
515 }
516
517 /* we now have a random number 'rand' to test. */
518 if (!BN_lshift1(p, q))
519 goto err;
520 if (!BN_add_word(p, 1))
521 goto err;
522
523loop:
524 for (i = 1; i < NUMPRIMES; i++) {
525 /* check that p and q are prime */
526 /* check that for p and q
527 * gcd(p-1,primes) == 1 (except for 2) */
528 BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
529 BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
530 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
531 goto err;
532 if (pmod == 0 || qmod == 0) {
533 if (!BN_add(p, p, padd))
534 goto err;
535 if (!BN_add(q, q, qadd))
536 goto err;
537 goto loop;
538 }
539 }
540 ret = 1;
541
542err:
543 BN_CTX_end(ctx);
544 bn_check_top(p);
545 return (ret);
546}
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