1 /* $OpenBSD: bn_prime.c,v 1.14 2015/10/21 19:02:22 miod Exp $ */
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).
115 #include <openssl/err.h>
119 /* NB: these functions have been "upgraded", the deprecated versions (which are
120 * compatibility wrappers using these functions) are in bn_depr.c.
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.
128 #include "bn_prime.h"
130 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
131 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
132 static int probable_prime(BIGNUM *rnd, int bits);
133 static int probable_prime_dh(BIGNUM *rnd, int bits,
134 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
135 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
136 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
139 BN_GENCB_call(BN_GENCB *cb, int a, int b)
141 /* No callback means continue */
146 /* Deprecated-style callbacks */
149 cb->cb.cb_1(a, b, cb->arg);
152 /* New-style callbacks */
153 return cb->cb.cb_2(a, b, cb);
157 /* Unrecognised callback type */
162 BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
163 const BIGNUM *rem, BN_GENCB *cb)
171 if (bits < 2 || (bits == 2 && safe)) {
173 * There are no prime numbers smaller than 2, and the smallest
174 * safe prime (7) spans three bits.
176 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
184 if ((t = BN_CTX_get(ctx)) == NULL)
187 checks = BN_prime_checks_for_size(bits);
190 /* make a random number and set the top and bottom bits */
192 if (!probable_prime(ret, bits))
196 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
199 if (!probable_prime_dh(ret, bits, add, rem, ctx))
203 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
204 if (!BN_GENCB_call(cb, 0, c1++))
209 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
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))
222 for (i = 0; i < checks; i++) {
223 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
229 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
235 if (!BN_GENCB_call(cb, 2, c1 - 1))
237 /* We have a safe prime test pass */
240 /* we have a prime :-) */
253 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
255 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
259 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
260 int do_trial_division, BN_GENCB *cb)
265 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
266 BN_MONT_CTX *mont = NULL;
267 const BIGNUM *A = NULL;
269 if (BN_cmp(a, BN_value_one()) <= 0)
272 if (checks == BN_prime_checks)
273 checks = BN_prime_checks_for_size(BN_num_bits(a));
275 /* first look for small factors */
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)
287 if (!BN_GENCB_call(cb, 1, -1))
291 if (ctx_passed != NULL)
293 else if ((ctx = BN_CTX_new()) == NULL)
300 if ((t = BN_CTX_get(ctx)) == NULL)
307 if ((A1 = BN_CTX_get(ctx)) == NULL)
309 if ((A1_odd = BN_CTX_get(ctx)) == NULL)
311 if ((check = BN_CTX_get(ctx)) == NULL)
314 /* compute A1 := A - 1 */
317 if (!BN_sub_word(A1, 1))
319 if (BN_is_zero(A1)) {
324 /* write A1 as A1_odd * 2^k */
326 while (!BN_is_bit_set(A1, k))
328 if (!BN_rshift(A1_odd, A1, k))
331 /* Montgomery setup for computations mod A */
332 mont = BN_MONT_CTX_new();
335 if (!BN_MONT_CTX_set(mont, A, ctx))
338 for (i = 0; i < checks; i++) {
339 if (!BN_pseudo_rand_range(check, A1))
341 if (!BN_add_word(check, 1))
343 /* now 1 <= check < A */
345 j = witness(check, A, A1, A1_odd, k, ctx, mont);
352 if (!BN_GENCB_call(cb, 1, i))
360 if (ctx_passed == NULL)
363 BN_MONT_CTX_free(mont);
369 witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd,
370 int k, BN_CTX *ctx, BN_MONT_CTX *mont)
372 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont))
373 /* w := w^a1_odd mod a */
376 return 0; /* probably prime */
377 if (BN_cmp(w, a1) == 0)
378 return 0; /* w == -1 (mod a), 'a' is probably prime */
380 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
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 */
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 */
395 probable_prime(BIGNUM *rnd, int bits)
398 prime_t mods[NUMPRIMES];
399 BN_ULONG delta, maxdelta;
402 if (!BN_rand(rnd, bits, 1, 1))
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)
409 mods[i] = (prime_t)mod;
411 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
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) {
419 if (delta > maxdelta)
424 if (!BN_add_word(rnd, delta))
431 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem,
438 if ((t1 = BN_CTX_get(ctx)) == NULL)
441 if (!BN_rand(rnd, bits, 0, 1))
444 /* we need ((rnd-rem) % add) == 0 */
446 if (!BN_mod(t1, rnd, add, ctx))
448 if (!BN_sub(rnd, rnd, t1))
451 if (!BN_add_word(rnd, 1))
454 if (!BN_add(rnd, rnd, rem))
458 /* we now have a random number 'rand' to test. */
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)
467 if (!BN_add(rnd, rnd, add))
481 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
482 const BIGNUM *rem, BN_CTX *ctx)
485 BIGNUM *t1, *qadd, *q;
489 if ((t1 = BN_CTX_get(ctx)) == NULL)
491 if ((q = BN_CTX_get(ctx)) == NULL)
493 if ((qadd = BN_CTX_get(ctx)) == NULL)
496 if (!BN_rshift1(qadd, padd))
499 if (!BN_rand(q, bits, 0, 1))
502 /* we need ((rnd-rem) % add) == 0 */
503 if (!BN_mod(t1, q,qadd, ctx))
505 if (!BN_sub(q, q, t1))
508 if (!BN_add_word(q, 1))
511 if (!BN_rshift1(t1, rem))
513 if (!BN_add(q, q, t1))
517 /* we now have a random number 'rand' to test. */
518 if (!BN_lshift1(p, q))
520 if (!BN_add_word(p, 1))
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)
532 if (pmod == 0 || qmod == 0) {
533 if (!BN_add(p, p, padd))
535 if (!BN_add(q, q, qadd))