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>
118 /* NB: these functions have been "upgraded", the deprecated versions (which are
119 * compatibility wrappers using these functions) are in bn_depr.c.
123 /* The quick sieve algorithm approach to weeding out primes is
124 * Philip Zimmermann's, as implemented in PGP. I have had a read of
125 * his comments and implemented my own version.
127 #include "bn_prime.h"
129 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
130 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
131 static int probable_prime(BIGNUM *rnd, int bits);
132 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
133 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
135 int BN_GENCB_call(BN_GENCB *cb, int a, int b)
137 /* No callback means continue */
142 /* Deprecated-style callbacks */
145 cb->cb.cb_1(a, b, cb->arg);
148 /* New-style callbacks */
149 return cb->cb.cb_2(a, b, cb);
153 /* Unrecognised callback type */
157 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
158 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
164 int checks = BN_prime_checks_for_size(bits);
168 /* There are no prime numbers this small. */
169 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
172 else if (bits == 2 && safe)
174 /* The smallest safe prime (7) is three bits. */
175 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
180 if (ctx == NULL) goto err;
185 /* make a random number and set the top and bottom bits */
188 if (!probable_prime(ret,bits)) goto err;
194 if (!probable_prime_dh_safe(ret,bits,add,rem,ctx))
199 if (!bn_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++))
210 i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb);
211 if (i == -1) goto err;
212 if (i == 0) goto loop;
216 /* for "safe prime" generation,
217 * check that (p-1)/2 is prime.
218 * Since a prime is odd, We just
219 * need to divide by 2 */
220 if (!BN_rshift1(t,ret)) goto err;
222 for (i=0; i<checks; i++)
224 j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb);
225 if (j == -1) goto err;
226 if (j == 0) goto loop;
228 j=BN_is_prime_fasttest_ex(t,1,ctx,0,cb);
229 if (j == -1) goto err;
230 if (j == 0) goto loop;
232 if(!BN_GENCB_call(cb, 2, c1-1))
234 /* We have a safe prime test pass */
237 /* we have a prime :-) */
249 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
251 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
254 int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
255 int do_trial_division, BN_GENCB *cb)
260 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
261 BN_MONT_CTX *mont = NULL;
262 const BIGNUM *A = NULL;
264 if (BN_cmp(a, BN_value_one()) <= 0)
267 if (checks == BN_prime_checks)
268 checks = BN_prime_checks_for_size(BN_num_bits(a));
270 /* first look for small factors */
272 /* a is even => a is prime if and only if a == 2 */
273 return BN_is_word(a, 2);
274 if (do_trial_division)
276 for (i = 1; i < NUMPRIMES; i++)
277 if (BN_mod_word(a, primes[i]) == 0)
279 if(!BN_GENCB_call(cb, 1, -1))
283 if (ctx_passed != NULL)
286 if ((ctx=BN_CTX_new()) == NULL)
294 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
301 A1 = BN_CTX_get(ctx);
302 A1_odd = BN_CTX_get(ctx);
303 check = BN_CTX_get(ctx);
304 if (check == NULL) goto err;
306 /* compute A1 := A - 1 */
309 if (!BN_sub_word(A1, 1))
317 /* write A1 as A1_odd * 2^k */
319 while (!BN_is_bit_set(A1, k))
321 if (!BN_rshift(A1_odd, A1, k))
324 /* Montgomery setup for computations mod A */
325 mont = BN_MONT_CTX_new();
328 if (!BN_MONT_CTX_set(mont, A, ctx))
331 for (i = 0; i < checks; i++)
333 if (!BN_pseudo_rand_range(check, A1))
335 if (!BN_add_word(check, 1))
337 /* now 1 <= check < A */
339 j = witness(check, A, A1, A1_odd, k, ctx, mont);
340 if (j == -1) goto err;
346 if(!BN_GENCB_call(cb, 1, i))
354 if (ctx_passed == NULL)
358 BN_MONT_CTX_free(mont);
363 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
364 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
370 if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
372 if (!BN_rand(rnd,bits,0,1)) goto err;
374 /* we need ((rnd-rem) % add) == 0 */
376 if (!BN_mod(t1,rnd,add,ctx)) goto err;
377 if (!BN_sub(rnd,rnd,t1)) goto err;
379 { if (!BN_add_word(rnd,1)) goto err; }
381 { if (!BN_add(rnd,rnd,rem)) goto err; }
383 /* we now have a random number 'rand' to test. */
386 for (i=1; i<NUMPRIMES; i++)
388 /* check that rnd is a prime */
389 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
391 if (!BN_add(rnd,rnd,add)) goto err;
402 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
403 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
405 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
408 return 0; /* probably prime */
409 if (BN_cmp(w, a1) == 0)
410 return 0; /* w == -1 (mod a), 'a' is probably prime */
413 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
416 return 1; /* 'a' is composite, otherwise a previous 'w' would
417 * have been == -1 (mod 'a') */
418 if (BN_cmp(w, a1) == 0)
419 return 0; /* w == -1 (mod a), 'a' is probably prime */
421 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
422 * and it is neither -1 nor +1 -- so 'a' cannot be prime */
427 static int probable_prime(BIGNUM *rnd, int bits)
430 prime_t mods[NUMPRIMES];
432 BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES-1];
433 char is_single_word = bits <= BN_BITS2;
436 if (!BN_rand(rnd,bits,1,1)) return(0);
437 /* we now have a random number 'rnd' to test. */
438 for (i=1; i<NUMPRIMES; i++)
439 mods[i]=(prime_t)BN_mod_word(rnd,(BN_ULONG)primes[i]);
440 /* If bits is so small that it fits into a single word then we
441 * additionally don't want to exceed that many bits. */
444 BN_ULONG size_limit = (((BN_ULONG) 1) << bits) - BN_get_word(rnd) - 1;
445 if (size_limit < maxdelta)
446 maxdelta = size_limit;
452 BN_ULONG rnd_word = BN_get_word(rnd);
454 /* In the case that the candidate prime is a single word then
456 * 1) It's greater than primes[i] because we shouldn't reject
457 * 3 as being a prime number because it's a multiple of
459 * 2) That it's not a multiple of a known prime. We don't
460 * check that rnd-1 is also coprime to all the known
461 * primes because there aren't many small primes where
463 for (i=1; i<NUMPRIMES && primes[i]<rnd_word; i++)
465 if ((mods[i]+delta)%primes[i] == 0)
468 if (delta > maxdelta) goto again;
475 for (i=1; i<NUMPRIMES; i++)
477 /* check that rnd is not a prime and also
478 * that gcd(rnd-1,primes) == 1 (except for 2) */
479 if (((mods[i]+delta)%primes[i]) <= 1)
482 if (delta > maxdelta) goto again;
487 if (!BN_add_word(rnd,delta)) return(0);
488 if (BN_num_bits(rnd) != bits)
494 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
495 const BIGNUM *rem, BN_CTX *ctx)
502 t1 = BN_CTX_get(ctx);
504 qadd = BN_CTX_get(ctx);
505 if (qadd == NULL) goto err;
507 if (!BN_rshift1(qadd,padd)) goto err;
509 if (!BN_rand(q,bits,0,1)) goto err;
511 /* we need ((rnd-rem) % add) == 0 */
512 if (!BN_mod(t1,q,qadd,ctx)) goto err;
513 if (!BN_sub(q,q,t1)) goto err;
515 { if (!BN_add_word(q,1)) goto err; }
518 if (!BN_rshift1(t1,rem)) goto err;
519 if (!BN_add(q,q,t1)) goto err;
522 /* we now have a random number 'rand' to test. */
523 if (!BN_lshift1(p,q)) goto err;
524 if (!BN_add_word(p,1)) goto err;
527 for (i=1; i<NUMPRIMES; i++)
529 /* check that p and q are prime */
530 /* check that for p and q
531 * gcd(p-1,primes) == 1 (except for 2) */
532 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
533 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
535 if (!BN_add(p,p,padd)) goto err;
536 if (!BN_add(q,q,qadd)) goto err;