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) 1998-2000 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 /* The quick sieve algorithm approach to weeding out primes is
119 * Philip Zimmermann's, as implemented in PGP. I have had a read of
120 * his comments and implemented my own version.
122 #include "bn_prime.h"
124 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
125 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
126 static int probable_prime(BIGNUM *rnd, int bits);
127 static int probable_prime_dh(BIGNUM *rnd, int bits,
128 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
129 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
130 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
132 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
133 BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg)
140 int checks = BN_prime_checks_for_size(bits);
143 if (ctx == NULL) goto err;
146 if ((rnd=BN_new()) == NULL) goto err;
152 /* make a random number and set the top and bottom bits */
155 if (!probable_prime(rnd,bits)) goto err;
161 if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
166 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
170 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
171 if (callback != NULL) callback(0,c1++,cb_arg);
175 i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
176 if (i == -1) goto err;
177 if (i == 0) goto loop;
181 /* for "safe prime" generation,
182 * check that (p-1)/2 is prime.
183 * Since a prime is odd, We just
184 * need to divide by 2 */
185 if (!BN_rshift1(&t,rnd)) goto err;
187 for (i=0; i<checks; i++)
189 j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
190 if (j == -1) goto err;
191 if (j == 0) goto loop;
193 j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
194 if (j == -1) goto err;
195 if (j == 0) goto loop;
197 if (callback != NULL) callback(2,c1-1,cb_arg);
198 /* We have a safe prime test pass */
201 /* we have a prime :-) */
204 if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
206 if (ctx != NULL) BN_CTX_free(ctx);
207 return(found ? rnd : NULL);
210 int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *),
211 BN_CTX *ctx_passed, void *cb_arg)
213 return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
216 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
217 void (*callback)(int,int,void *),
218 BN_CTX *ctx_passed, void *cb_arg,
219 int do_trial_division)
224 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
225 BN_MONT_CTX *mont = NULL;
228 if (checks == BN_prime_checks)
229 checks = BN_prime_checks_for_size(BN_num_bits(a));
231 /* first look for small factors */
234 if (do_trial_division)
236 for (i = 1; i < NUMPRIMES; i++)
237 if (BN_mod_word(a, primes[i]) == 0)
239 if (callback != NULL) callback(1, -1, cb_arg);
242 if (ctx_passed != NULL)
245 if ((ctx=BN_CTX_new()) == NULL)
250 BIGNUM *t = &(ctx->bn[ctx->tos++]);
257 A1 = &(ctx->bn[ctx->tos++]);
258 A1_odd = &(ctx->bn[ctx->tos++]);
259 check = &(ctx->bn[ctx->tos++]);;
261 /* compute A1 := A - 1 */
264 if (!BN_sub_word(A1, 1))
272 /* write A1 as A1_odd * 2^k */
274 while (!BN_is_bit_set(A1, k))
276 if (!BN_rshift(A1_odd, A1, k))
279 /* Montgomery setup for computations mod A */
280 mont = BN_MONT_CTX_new();
283 if (!BN_MONT_CTX_set(mont, A, ctx))
286 for (i = 0; i < checks; i++)
288 if (!BN_pseudo_rand(check, BN_num_bits(A1), 0, 0))
290 if (BN_cmp(check, A1) >= 0)
291 if (!BN_sub(check, check, A1))
293 if (!BN_add_word(check, 1))
295 /* now 1 <= check < A */
297 j = witness(check, A, A1, A1_odd, k, ctx, mont);
298 if (j == -1) goto err;
304 if (callback != NULL) callback(1,i,cb_arg);
308 if (ctx_passed != NULL)
310 ctx_passed->tos -= 3; /* A1, A1_odd, check */
312 --ctx_passed->tos; /* A */
314 else if (ctx != NULL)
317 BN_MONT_CTX_free(mont);
322 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
323 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
325 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
328 return 0; /* probably prime */
329 if (BN_cmp(w, a1) == 0)
330 return 0; /* w == -1 (mod a), 'a' is probably prime */
333 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
336 return 1; /* 'a' is composite, otherwise a previous 'w' would
337 * have been == -1 (mod 'a') */
338 if (BN_cmp(w, a1) == 0)
339 return 0; /* w == -1 (mod a), 'a' is probably prime */
341 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
342 * and it is neither -1 nor +1 -- so 'a' cannot be prime */
346 static int probable_prime(BIGNUM *rnd, int bits)
349 BN_ULONG mods[NUMPRIMES];
353 if (!BN_rand(rnd,bits,1,1)) return(0);
354 /* we now have a random number 'rand' to test. */
355 for (i=1; i<NUMPRIMES; i++)
356 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
358 loop: for (i=1; i<NUMPRIMES; i++)
360 /* check that rnd is not a prime and also
361 * that gcd(rnd-1,primes) == 1 (except for 2) */
362 if (((mods[i]+delta)%primes[i]) <= 1)
366 /* perhaps need to check for overflow of
367 * delta (but delta can be upto 2^32)
368 * 21-May-98 eay - added overflow check */
369 if (delta < d) goto again;
373 if (!BN_add_word(rnd,delta)) return(0);
377 static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
383 t1= &(ctx->bn[ctx->tos++]);
385 if (!BN_rand(rnd,bits,0,1)) goto err;
387 /* we need ((rnd-rem) % add) == 0 */
389 if (!BN_mod(t1,rnd,add,ctx)) goto err;
390 if (!BN_sub(rnd,rnd,t1)) goto err;
392 { if (!BN_add_word(rnd,1)) goto err; }
394 { if (!BN_add(rnd,rnd,rem)) goto err; }
396 /* we now have a random number 'rand' to test. */
398 loop: for (i=1; i<NUMPRIMES; i++)
400 /* check that rnd is a prime */
401 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
403 if (!BN_add(rnd,rnd,add)) goto err;
413 static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
414 BIGNUM *rem, BN_CTX *ctx)
417 BIGNUM *t1,*qadd=NULL,*q=NULL;
420 t1= &(ctx->bn[ctx->tos++]);
421 q= &(ctx->bn[ctx->tos++]);
422 qadd= &(ctx->bn[ctx->tos++]);
424 if (!BN_rshift1(qadd,padd)) goto err;
426 if (!BN_rand(q,bits,0,1)) goto err;
428 /* we need ((rnd-rem) % add) == 0 */
429 if (!BN_mod(t1,q,qadd,ctx)) goto err;
430 if (!BN_sub(q,q,t1)) goto err;
432 { if (!BN_add_word(q,1)) goto err; }
435 if (!BN_rshift1(t1,rem)) goto err;
436 if (!BN_add(q,q,t1)) goto err;
439 /* we now have a random number 'rand' to test. */
440 if (!BN_lshift1(p,q)) goto err;
441 if (!BN_add_word(p,1)) goto err;
443 loop: for (i=1; i<NUMPRIMES; i++)
445 /* check that p and q are prime */
446 /* check that for p and q
447 * gcd(p-1,primes) == 1 (except for 2) */
448 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
449 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
451 if (!BN_add(p,p,padd)) goto err;
452 if (!BN_add(q,q,qadd)) goto err;