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 seive 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.
72 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
74 static int probable_prime(BIGNUM *rnd, int bits);
75 static int probable_prime_dh(BIGNUM *rnd, int bits,
76 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
77 static int probable_prime_dh_strong(BIGNUM *rnd, int bits,
78 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
81 static int probable_prime();
82 static int probable_prime_dh();
83 static int probable_prime_dh_strong();
86 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int strong, BIGNUM *add,
87 BIGNUM *rem, void (*callback)(P_I_I_P), char *cb_arg)
95 if (ctx == NULL) goto err;
98 if ((rnd=BN_new()) == NULL) goto err;
104 /* make a random number and set the top and bottom bits */
107 if (!probable_prime(rnd,bits)) goto err;
113 if (!probable_prime_dh_strong(rnd,bits,add,rem,ctx))
118 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
122 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
123 if (callback != NULL) callback(0,c1++,cb_arg);
127 i=BN_is_prime(rnd,BN_prime_checks,callback,ctx,cb_arg);
128 if (i == -1) goto err;
129 if (i == 0) goto loop;
133 /* for a strong prime generation,
134 * check that (p-1)/2 is prime.
135 * Since a prime is odd, We just
136 * need to divide by 2 */
137 if (!BN_rshift1(&t,rnd)) goto err;
139 for (i=0; i<BN_prime_checks; i++)
141 j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
142 if (j == -1) goto err;
143 if (j == 0) goto loop;
145 j=BN_is_prime(&t,1,callback,ctx,cb_arg);
146 if (j == -1) goto err;
147 if (j == 0) goto loop;
149 if (callback != NULL) callback(2,c1-1,cb_arg);
150 /* We have a strong prime test pass */
153 /* we have a prime :-) */
156 if ((ret == NULL) && (rnd != NULL)) BN_free(rnd);
158 if (ctx != NULL) BN_CTX_free(ctx);
162 int BN_is_prime(BIGNUM *a, int checks, void (*callback)(P_I_I_P),
163 BN_CTX *ctx_passed, char *cb_arg)
165 int i,j,c2=0,ret= -1;
167 BN_CTX *ctx=NULL,*ctx2=NULL;
168 BN_MONT_CTX *mont=NULL;
172 if (ctx_passed != NULL)
175 if ((ctx=BN_CTX_new()) == NULL) goto err;
177 if ((ctx2=BN_CTX_new()) == NULL) goto err;
178 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
180 check= &(ctx->bn[ctx->tos++]);
182 /* Setup the montgomery structure */
183 if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
185 for (i=0; i<checks; i++)
187 if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
188 j=witness(check,a,ctx,ctx2,mont);
189 if (j == -1) goto err;
195 if (callback != NULL) callback(1,c2++,cb_arg);
200 if ((ctx_passed == NULL) && (ctx != NULL))
204 if (mont != NULL) BN_MONT_CTX_free(mont);
211 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2,
214 int k,i,ret= -1,good;
215 BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
216 BIGNUM *mont_one,*mont_n1,*mont_a;
218 d1= &(ctx->bn[ctx->tos]);
219 d2= &(ctx->bn[ctx->tos+1]);
220 n1= &(ctx->bn[ctx->tos+2]);
223 mont_one= &(ctx2->bn[ctx2->tos]);
224 mont_n1= &(ctx2->bn[ctx2->tos+1]);
225 mont_a= &(ctx2->bn[ctx2->tos+2]);
230 if (!BN_one(d)) goto err;
231 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
234 if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
235 if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
236 if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
239 for (i=k-1; i>=0; i--)
241 if ( (BN_cmp(d,mont_one) != 0) &&
242 (BN_cmp(d,mont_n1) != 0))
247 BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
249 if (good && (BN_cmp(dd,mont_one) == 0))
254 if (BN_is_bit_set(n1,i))
256 BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
265 if (BN_cmp(d,mont_one) == 0)
275 static int probable_prime(BIGNUM *rnd, int bits)
278 MS_STATIC BN_ULONG mods[NUMPRIMES];
282 if (!BN_rand(rnd,bits,1,1)) return(0);
283 /* we now have a random number 'rand' to test. */
284 for (i=1; i<NUMPRIMES; i++)
285 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
287 loop: for (i=1; i<NUMPRIMES; i++)
289 /* check that rnd is not a prime and also
290 * that gcd(rnd-1,primes) == 1 (except for 2) */
291 if (((mods[i]+delta)%primes[i]) <= 1)
295 /* perhaps need to check for overflow of
296 * delta (but delta can be upto 2^32)
297 * 21-May-98 eay - added overflow check */
298 if (delta < d) goto again;
302 if (!BN_add_word(rnd,delta)) return(0);
306 static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
312 t1= &(ctx->bn[ctx->tos++]);
314 if (!BN_rand(rnd,bits,0,1)) goto err;
316 /* we need ((rnd-rem) % add) == 0 */
318 if (!BN_mod(t1,rnd,add,ctx)) goto err;
319 if (!BN_sub(rnd,rnd,t1)) goto err;
321 { if (!BN_add_word(rnd,1)) goto err; }
323 { if (!BN_add(rnd,rnd,rem)) goto err; }
325 /* we now have a random number 'rand' to test. */
327 loop: for (i=1; i<NUMPRIMES; i++)
329 /* check that rnd is a prime */
330 if (BN_mod_word(rnd,(BN_LONG)primes[i]) <= 1)
332 if (!BN_add(rnd,rnd,add)) goto err;
342 static int probable_prime_dh_strong(BIGNUM *p, int bits, BIGNUM *padd,
343 BIGNUM *rem, BN_CTX *ctx)
346 BIGNUM *t1,*qadd=NULL,*q=NULL;
349 t1= &(ctx->bn[ctx->tos++]);
350 q= &(ctx->bn[ctx->tos++]);
351 qadd= &(ctx->bn[ctx->tos++]);
353 if (!BN_rshift1(qadd,padd)) goto err;
355 if (!BN_rand(q,bits,0,1)) goto err;
357 /* we need ((rnd-rem) % add) == 0 */
358 if (!BN_mod(t1,q,qadd,ctx)) goto err;
359 if (!BN_sub(q,q,t1)) goto err;
361 { if (!BN_add_word(q,1)) goto err; }
364 if (!BN_rshift1(t1,rem)) goto err;
365 if (!BN_add(q,q,t1)) goto err;
368 /* we now have a random number 'rand' to test. */
369 if (!BN_lshift1(p,q)) goto err;
370 if (!BN_add_word(p,1)) goto err;
372 loop: for (i=1; i<NUMPRIMES; i++)
374 /* check that p and q are prime */
375 /* check that for p and q
376 * gcd(p-1,primes) == 1 (except for 2) */
377 if ( (BN_mod_word(p,(BN_LONG)primes[i]) == 0) ||
378 (BN_mod_word(q,(BN_LONG)primes[i]) == 0))
380 if (!BN_add(p,p,padd)) goto err;
381 if (!BN_add(q,q,qadd)) goto err;
392 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx)
396 BIGNUM *d1,*d2,*x,*n1,*inv;
398 d1= &(ctx->bn[ctx->tos]);
399 d2= &(ctx->bn[ctx->tos+1]);
400 x= &(ctx->bn[ctx->tos+2]);
401 n1= &(ctx->bn[ctx->tos+3]);
402 inv=&(ctx->bn[ctx->tos+4]);
407 if (!BN_one(d)) goto err;
408 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
411 /* i=BN_num_bits(n); */
413 nb=BN_reciprocal(inv,n,ctx); /**/
414 if (nb == -1) goto err;
417 for (i=k-1; i>=0; i--)
419 if (BN_copy(x,d) == NULL) goto err;
421 if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
423 if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
425 if ( BN_is_one(dd) &&
432 if (BN_is_bit_set(n1,i))
435 if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
437 if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;