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.]
63 #include <openssl/rand.h>
65 /* The quick sieve algorithm approach to weeding out primes is
66 * Philip Zimmermann's, as implemented in PGP. I have had a read of
67 * his comments and implemented my own version.
71 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
72 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
73 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
74 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
75 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
76 #define BN_prime_checks_size(b) ((b) >= 1300 ? 2 : \
89 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
91 static int probable_prime(BIGNUM *rnd, int bits);
92 static int probable_prime_dh(BIGNUM *rnd, int bits,
93 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
94 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
95 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
97 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
98 BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg)
105 int checks = BN_prime_checks_size(bits);
108 if (ctx == NULL) goto err;
111 if ((rnd=BN_new()) == NULL) goto err;
117 /* make a random number and set the top and bottom bits */
120 if (!probable_prime(rnd,bits)) goto err;
126 if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
131 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
135 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
136 if (callback != NULL) callback(0,c1++,cb_arg);
140 i=BN_is_prime(rnd,checks,callback,ctx,cb_arg);
141 if (i == -1) goto err;
142 if (i == 0) goto loop;
146 /* for "safe prime" generation,
147 * check that (p-1)/2 is prime.
148 * Since a prime is odd, We just
149 * need to divide by 2 */
150 if (!BN_rshift1(&t,rnd)) goto err;
152 for (i=0; i<checks; i++)
154 j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
155 if (j == -1) goto err;
156 if (j == 0) goto loop;
158 j=BN_is_prime(&t,1,callback,ctx,cb_arg);
159 if (j == -1) goto err;
160 if (j == 0) goto loop;
162 if (callback != NULL) callback(2,c1-1,cb_arg);
163 /* We have a safe prime test pass */
166 /* we have a prime :-) */
169 if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
171 if (ctx != NULL) BN_CTX_free(ctx);
172 return(found ? rnd : NULL);
175 int BN_is_prime(BIGNUM *a, int checks, void (*callback)(int,int,void *),
176 BN_CTX *ctx_passed, void *cb_arg)
178 int i,j,c2=0,ret= -1;
180 BN_CTX *ctx=NULL,*ctx2=NULL;
181 BN_MONT_CTX *mont=NULL;
183 if (checks == BN_prime_checks)
185 int bits = BN_num_bits(a);
186 checks = BN_prime_checks_size(bits);
191 if (ctx_passed != NULL)
194 if ((ctx=BN_CTX_new()) == NULL) goto err;
196 if ((ctx2=BN_CTX_new()) == NULL) goto err;
197 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
199 check= &(ctx->bn[ctx->tos++]);
201 /* Setup the montgomery structure */
202 if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
204 for (i=0; i<checks; i++)
206 if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
207 j=witness(check,a,ctx,ctx2,mont);
208 if (j == -1) goto err;
214 if (callback != NULL) callback(1,c2++,cb_arg);
219 if ((ctx_passed == NULL) && (ctx != NULL))
223 if (mont != NULL) BN_MONT_CTX_free(mont);
228 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2,
231 int k,i,ret= -1,good;
232 BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
233 BIGNUM *mont_one,*mont_n1,*mont_a;
235 d1= &(ctx->bn[ctx->tos]);
236 d2= &(ctx->bn[ctx->tos+1]);
237 n1= &(ctx->bn[ctx->tos+2]);
240 mont_one= &(ctx2->bn[ctx2->tos]);
241 mont_n1= &(ctx2->bn[ctx2->tos+1]);
242 mont_a= &(ctx2->bn[ctx2->tos+2]);
247 if (!BN_one(d)) goto err;
248 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
251 if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
252 if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
253 if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
256 for (i=k-1; i>=0; i--)
258 if ( (BN_cmp(d,mont_one) != 0) &&
259 (BN_cmp(d,mont_n1) != 0))
264 BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
266 if (good && (BN_cmp(dd,mont_one) == 0))
271 if (BN_is_bit_set(n1,i))
273 BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
282 if (BN_cmp(d,mont_one) == 0)
292 static int probable_prime(BIGNUM *rnd, int bits)
295 MS_STATIC BN_ULONG mods[NUMPRIMES];
299 if (!BN_rand(rnd,bits,1,1)) return(0);
300 /* we now have a random number 'rand' to test. */
301 for (i=1; i<NUMPRIMES; i++)
302 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
304 loop: for (i=1; i<NUMPRIMES; i++)
306 /* check that rnd is not a prime and also
307 * that gcd(rnd-1,primes) == 1 (except for 2) */
308 if (((mods[i]+delta)%primes[i]) <= 1)
312 /* perhaps need to check for overflow of
313 * delta (but delta can be upto 2^32)
314 * 21-May-98 eay - added overflow check */
315 if (delta < d) goto again;
319 if (!BN_add_word(rnd,delta)) return(0);
323 static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
329 t1= &(ctx->bn[ctx->tos++]);
331 if (!BN_rand(rnd,bits,0,1)) goto err;
333 /* we need ((rnd-rem) % add) == 0 */
335 if (!BN_mod(t1,rnd,add,ctx)) goto err;
336 if (!BN_sub(rnd,rnd,t1)) goto err;
338 { if (!BN_add_word(rnd,1)) goto err; }
340 { if (!BN_add(rnd,rnd,rem)) goto err; }
342 /* we now have a random number 'rand' to test. */
344 loop: for (i=1; i<NUMPRIMES; i++)
346 /* check that rnd is a prime */
347 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
349 if (!BN_add(rnd,rnd,add)) goto err;
359 static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
360 BIGNUM *rem, BN_CTX *ctx)
363 BIGNUM *t1,*qadd=NULL,*q=NULL;
366 t1= &(ctx->bn[ctx->tos++]);
367 q= &(ctx->bn[ctx->tos++]);
368 qadd= &(ctx->bn[ctx->tos++]);
370 if (!BN_rshift1(qadd,padd)) goto err;
372 if (!BN_rand(q,bits,0,1)) goto err;
374 /* we need ((rnd-rem) % add) == 0 */
375 if (!BN_mod(t1,q,qadd,ctx)) goto err;
376 if (!BN_sub(q,q,t1)) goto err;
378 { if (!BN_add_word(q,1)) goto err; }
381 if (!BN_rshift1(t1,rem)) goto err;
382 if (!BN_add(q,q,t1)) goto err;
385 /* we now have a random number 'rand' to test. */
386 if (!BN_lshift1(p,q)) goto err;
387 if (!BN_add_word(p,1)) goto err;
389 loop: for (i=1; i<NUMPRIMES; i++)
391 /* check that p and q are prime */
392 /* check that for p and q
393 * gcd(p-1,primes) == 1 (except for 2) */
394 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
395 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
397 if (!BN_add(p,p,padd)) goto err;
398 if (!BN_add(q,q,qadd)) goto err;
412 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,
413 BN_CTX *unused, BN_MONT_CTX *unused2)
417 BIGNUM *d1,*d2,*x,*n1;
420 d1= &(ctx->bn[ctx->tos]);
421 d2= &(ctx->bn[ctx->tos+1]);
422 x= &(ctx->bn[ctx->tos+2]);
423 n1= &(ctx->bn[ctx->tos+3]);
428 if (!BN_one(d)) goto err;
429 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
432 /* i=BN_num_bits(n); */
434 BN_RECP_CTX_init(&recp);
435 if (BN_RECP_CTX_set(&recp,n,ctx) <= 0) goto err;
438 for (i=k-1; i>=0; i--)
440 if (BN_copy(x,d) == NULL) goto err;
442 if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
444 if (!BN_mod_mul_reciprocal(dd,d,d,&recp,ctx)) goto err;
446 if ( BN_is_one(dd) &&
453 if (BN_is_bit_set(n1,i))
456 if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
458 if (!BN_mod_mul_reciprocal(d,dd,a,&recp,ctx)) goto err;
475 BN_RECP_CTX_free(&recp);