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.
71 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
73 static int probable_prime(BIGNUM *rnd, int bits);
74 static int probable_prime_dh(BIGNUM *rnd, int bits,
75 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
76 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
77 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
79 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
80 BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg)
86 int checks = BN_prime_checks(bits);
89 if (ctx == NULL) goto err;
92 if ((rnd=BN_new()) == NULL) goto err;
98 /* make a random number and set the top and bottom bits */
101 if (!probable_prime(rnd,bits)) goto err;
107 if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
112 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
116 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
117 if (callback != NULL) callback(0,c1++,cb_arg);
121 i=BN_is_prime(rnd,checks,callback,ctx,cb_arg);
122 if (i == -1) goto err;
123 if (i == 0) goto loop;
127 /* for "safe prime" generation,
128 * check that (p-1)/2 is prime.
129 * Since a prime is odd, We just
130 * need to divide by 2 */
131 if (!BN_rshift1(&t,rnd)) goto err;
133 for (i=0; i<checks; i++)
135 j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
136 if (j == -1) goto err;
137 if (j == 0) goto loop;
139 j=BN_is_prime(&t,1,callback,ctx,cb_arg);
140 if (j == -1) goto err;
141 if (j == 0) goto loop;
143 if (callback != NULL) callback(2,c1-1,cb_arg);
144 /* We have a safe prime test pass */
147 /* we have a prime :-) */
150 if ((ret == NULL) && (rnd != NULL)) BN_free(rnd);
152 if (ctx != NULL) BN_CTX_free(ctx);
156 int BN_is_prime(BIGNUM *a, int checks, void (*callback)(int,int,void *),
157 BN_CTX *ctx_passed, void *cb_arg)
159 int i,j,c2=0,ret= -1;
161 BN_CTX *ctx=NULL,*ctx2=NULL;
162 BN_MONT_CTX *mont=NULL;
166 if (ctx_passed != NULL)
169 if ((ctx=BN_CTX_new()) == NULL) goto err;
171 if ((ctx2=BN_CTX_new()) == NULL) goto err;
172 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
174 check= &(ctx->bn[ctx->tos++]);
176 /* Setup the montgomery structure */
177 if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
179 for (i=0; i<checks; i++)
181 if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
182 j=witness(check,a,ctx,ctx2,mont);
183 if (j == -1) goto err;
189 if (callback != NULL) callback(1,c2++,cb_arg);
194 if ((ctx_passed == NULL) && (ctx != NULL))
198 if (mont != NULL) BN_MONT_CTX_free(mont);
205 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2,
208 int k,i,ret= -1,good;
209 BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
210 BIGNUM *mont_one,*mont_n1,*mont_a;
212 d1= &(ctx->bn[ctx->tos]);
213 d2= &(ctx->bn[ctx->tos+1]);
214 n1= &(ctx->bn[ctx->tos+2]);
217 mont_one= &(ctx2->bn[ctx2->tos]);
218 mont_n1= &(ctx2->bn[ctx2->tos+1]);
219 mont_a= &(ctx2->bn[ctx2->tos+2]);
224 if (!BN_one(d)) goto err;
225 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
228 if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
229 if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
230 if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
233 for (i=k-1; i>=0; i--)
235 if ( (BN_cmp(d,mont_one) != 0) &&
236 (BN_cmp(d,mont_n1) != 0))
241 BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
243 if (good && (BN_cmp(dd,mont_one) == 0))
248 if (BN_is_bit_set(n1,i))
250 BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
259 if (BN_cmp(d,mont_one) == 0)
269 static int probable_prime(BIGNUM *rnd, int bits)
272 MS_STATIC BN_ULONG mods[NUMPRIMES];
276 if (!BN_rand(rnd,bits,1,1)) return(0);
277 /* we now have a random number 'rand' to test. */
278 for (i=1; i<NUMPRIMES; i++)
279 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
281 loop: for (i=1; i<NUMPRIMES; i++)
283 /* check that rnd is not a prime and also
284 * that gcd(rnd-1,primes) == 1 (except for 2) */
285 if (((mods[i]+delta)%primes[i]) <= 1)
289 /* perhaps need to check for overflow of
290 * delta (but delta can be upto 2^32)
291 * 21-May-98 eay - added overflow check */
292 if (delta < d) goto again;
296 if (!BN_add_word(rnd,delta)) return(0);
300 static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
306 t1= &(ctx->bn[ctx->tos++]);
308 if (!BN_rand(rnd,bits,0,1)) goto err;
310 /* we need ((rnd-rem) % add) == 0 */
312 if (!BN_mod(t1,rnd,add,ctx)) goto err;
313 if (!BN_sub(rnd,rnd,t1)) goto err;
315 { if (!BN_add_word(rnd,1)) goto err; }
317 { if (!BN_add(rnd,rnd,rem)) goto err; }
319 /* we now have a random number 'rand' to test. */
321 loop: for (i=1; i<NUMPRIMES; i++)
323 /* check that rnd is a prime */
324 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
326 if (!BN_add(rnd,rnd,add)) goto err;
336 static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
337 BIGNUM *rem, BN_CTX *ctx)
340 BIGNUM *t1,*qadd=NULL,*q=NULL;
343 t1= &(ctx->bn[ctx->tos++]);
344 q= &(ctx->bn[ctx->tos++]);
345 qadd= &(ctx->bn[ctx->tos++]);
347 if (!BN_rshift1(qadd,padd)) goto err;
349 if (!BN_rand(q,bits,0,1)) goto err;
351 /* we need ((rnd-rem) % add) == 0 */
352 if (!BN_mod(t1,q,qadd,ctx)) goto err;
353 if (!BN_sub(q,q,t1)) goto err;
355 { if (!BN_add_word(q,1)) goto err; }
358 if (!BN_rshift1(t1,rem)) goto err;
359 if (!BN_add(q,q,t1)) goto err;
362 /* we now have a random number 'rand' to test. */
363 if (!BN_lshift1(p,q)) goto err;
364 if (!BN_add_word(p,1)) goto err;
366 loop: for (i=1; i<NUMPRIMES; i++)
368 /* check that p and q are prime */
369 /* check that for p and q
370 * gcd(p-1,primes) == 1 (except for 2) */
371 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
372 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
374 if (!BN_add(p,p,padd)) goto err;
375 if (!BN_add(q,q,qadd)) goto err;
386 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx)
390 BIGNUM *d1,*d2,*x,*n1,*inv;
392 d1= &(ctx->bn[ctx->tos]);
393 d2= &(ctx->bn[ctx->tos+1]);
394 x= &(ctx->bn[ctx->tos+2]);
395 n1= &(ctx->bn[ctx->tos+3]);
396 inv=&(ctx->bn[ctx->tos+4]);
401 if (!BN_one(d)) goto err;
402 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
405 /* i=BN_num_bits(n); */
407 nb=BN_reciprocal(inv,n,ctx); /**/
408 if (nb == -1) goto err;
411 for (i=k-1; i>=0; i--)
413 if (BN_copy(x,d) == NULL) goto err;
415 if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
417 if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
419 if ( BN_is_one(dd) &&
426 if (BN_is_bit_set(n1,i))
429 if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
431 if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;