1 /* crypto/bn/bn_prime.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
58 /* ====================================================================
59 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
114 #include "cryptlib.h"
116 #include <openssl/rand.h>
119 * NB: these functions have been "upgraded", the deprecated versions (which
120 * are compatibility wrappers using these functions) are in bn_depr.c. -
125 * The quick sieve algorithm approach to weeding out primes is Philip
126 * Zimmermann's, as implemented in PGP. I have had a read of his comments
127 * and implemented my own version.
129 #include "bn_prime.h"
131 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
132 const BIGNUM *a1_odd, int k, BN_CTX *ctx,
134 static int probable_prime(BIGNUM *rnd, int bits);
135 static int probable_prime_dh(BIGNUM *rnd, int bits,
136 const BIGNUM *add, const BIGNUM *rem,
138 static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add,
139 const BIGNUM *rem, BN_CTX *ctx);
141 int BN_GENCB_call(BN_GENCB *cb, int a, int b)
143 /* No callback means continue */
148 /* Deprecated-style callbacks */
151 cb->cb.cb_1(a, b, cb->arg);
154 /* New-style callbacks */
155 return cb->cb.cb_2(a, b, cb);
159 /* Unrecognised callback type */
163 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
164 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
170 int checks = BN_prime_checks_for_size(bits);
180 /* make a random number and set the top and bottom bits */
182 if (!probable_prime(ret, bits))
186 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
189 if (!probable_prime_dh(ret, bits, add, rem, ctx))
193 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
194 if (!BN_GENCB_call(cb, 0, c1++))
199 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
206 * for "safe prime" generation, check that (p-1)/2 is prime. Since a
207 * prime is odd, We just need to divide by 2
209 if (!BN_rshift1(t, ret))
212 for (i = 0; i < checks; i++) {
213 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
219 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
225 if (!BN_GENCB_call(cb, 2, c1 - 1))
227 /* We have a safe prime test pass */
230 /* we have a prime :-) */
241 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
244 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
247 int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
248 int do_trial_division, BN_GENCB *cb)
253 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
254 BN_MONT_CTX *mont = NULL;
255 const BIGNUM *A = NULL;
257 if (BN_cmp(a, BN_value_one()) <= 0)
260 if (checks == BN_prime_checks)
261 checks = BN_prime_checks_for_size(BN_num_bits(a));
263 /* first look for small factors */
265 /* a is even => a is prime if and only if a == 2 */
266 return BN_is_word(a, 2);
267 if (do_trial_division) {
268 for (i = 1; i < NUMPRIMES; i++)
269 if (BN_mod_word(a, primes[i]) == 0)
271 if (!BN_GENCB_call(cb, 1, -1))
275 if (ctx_passed != NULL)
277 else if ((ctx = BN_CTX_new()) == NULL)
284 if ((t = BN_CTX_get(ctx)) == NULL)
286 if (BN_copy(t, a) == NULL)
292 A1 = BN_CTX_get(ctx);
293 A1_odd = BN_CTX_get(ctx);
294 check = BN_CTX_get(ctx);
298 /* compute A1 := A - 1 */
301 if (!BN_sub_word(A1, 1))
303 if (BN_is_zero(A1)) {
308 /* write A1 as A1_odd * 2^k */
310 while (!BN_is_bit_set(A1, k))
312 if (!BN_rshift(A1_odd, A1, k))
315 /* Montgomery setup for computations mod A */
316 mont = BN_MONT_CTX_new();
319 if (!BN_MONT_CTX_set(mont, A, ctx))
322 for (i = 0; i < checks; i++) {
323 if (!BN_pseudo_rand_range(check, A1))
325 if (!BN_add_word(check, 1))
327 /* now 1 <= check < A */
329 j = witness(check, A, A1, A1_odd, k, ctx, mont);
336 if (!BN_GENCB_call(cb, 1, i))
343 if (ctx_passed == NULL)
347 BN_MONT_CTX_free(mont);
352 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
353 const BIGNUM *a1_odd, int k, BN_CTX *ctx,
356 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
359 return 0; /* probably prime */
360 if (BN_cmp(w, a1) == 0)
361 return 0; /* w == -1 (mod a), 'a' is probably prime */
363 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
366 return 1; /* 'a' is composite, otherwise a previous 'w'
367 * would have been == -1 (mod 'a') */
368 if (BN_cmp(w, a1) == 0)
369 return 0; /* w == -1 (mod a), 'a' is probably prime */
372 * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
373 * it is neither -1 nor +1 -- so 'a' cannot be prime
379 static int probable_prime(BIGNUM *rnd, int bits)
382 prime_t mods[NUMPRIMES];
383 BN_ULONG delta, maxdelta;
386 if (!BN_rand(rnd, bits, 1, 1))
388 /* we now have a random number 'rand' to test. */
389 for (i = 1; i < NUMPRIMES; i++)
390 mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]);
391 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
393 loop:for (i = 1; i < NUMPRIMES; i++) {
395 * check that rnd is not a prime and also that gcd(rnd-1,primes) == 1
398 if (((mods[i] + delta) % primes[i]) <= 1) {
400 if (delta > maxdelta)
405 if (!BN_add_word(rnd, delta))
411 static int probable_prime_dh(BIGNUM *rnd, int bits,
412 const BIGNUM *add, const BIGNUM *rem,
419 if ((t1 = BN_CTX_get(ctx)) == NULL)
422 if (!BN_rand(rnd, bits, 0, 1))
425 /* we need ((rnd-rem) % add) == 0 */
427 if (!BN_mod(t1, rnd, add, ctx))
429 if (!BN_sub(rnd, rnd, t1))
432 if (!BN_add_word(rnd, 1))
435 if (!BN_add(rnd, rnd, rem))
439 /* we now have a random number 'rand' to test. */
441 loop:for (i = 1; i < NUMPRIMES; i++) {
442 /* check that rnd is a prime */
443 if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
444 if (!BN_add(rnd, rnd, add))
456 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
457 const BIGNUM *rem, BN_CTX *ctx)
460 BIGNUM *t1, *qadd, *q;
464 t1 = BN_CTX_get(ctx);
466 qadd = BN_CTX_get(ctx);
470 if (!BN_rshift1(qadd, padd))
473 if (!BN_rand(q, bits, 0, 1))
476 /* we need ((rnd-rem) % add) == 0 */
477 if (!BN_mod(t1, q, qadd, ctx))
479 if (!BN_sub(q, q, t1))
482 if (!BN_add_word(q, 1))
485 if (!BN_rshift1(t1, rem))
487 if (!BN_add(q, q, t1))
491 /* we now have a random number 'rand' to test. */
492 if (!BN_lshift1(p, q))
494 if (!BN_add_word(p, 1))
497 loop:for (i = 1; i < NUMPRIMES; i++) {
498 /* check that p and q are prime */
500 * check that for p and q gcd(p-1,primes) == 1 (except for 2)
502 if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) ||
503 (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) {
504 if (!BN_add(p, p, padd))
506 if (!BN_add(q, q, qadd))