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.]
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(bits,strong,add,rem,callback,cb_arg)
91 void (*callback)(P_I_I_P);
101 if (ctx == NULL) goto err;
102 if ((rnd=BN_new()) == NULL) goto err;
104 if ((t=BN_new()) == NULL) goto err;
106 /* make a random number and set the top and bottom bits */
109 if (!probable_prime(rnd,bits)) goto err;
115 if (!probable_prime_dh_strong(rnd,bits,add,rem,ctx))
120 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
124 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
125 if (callback != NULL) callback(0,c1++,cb_arg);
129 i=BN_is_prime(rnd,BN_prime_checks,callback,ctx,cb_arg);
130 if (i == -1) goto err;
131 if (i == 0) goto loop;
135 /* for a strong prime generation,
136 * check that (p-1)/2 is prime.
137 * Since a prime is odd, We just
138 * need to divide by 2 */
139 if (!BN_rshift1(t,rnd)) goto err;
141 for (i=0; i<BN_prime_checks; i++)
143 j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
144 if (j == -1) goto err;
145 if (j == 0) goto loop;
147 j=BN_is_prime(t,1,callback,ctx,cb_arg);
148 if (j == -1) goto err;
149 if (j == 0) goto loop;
151 if (callback != NULL) callback(2,c1-1,cb_arg);
152 /* We have a strong prime test pass */
155 /* we have a prime :-) */
158 if ((ret == NULL) && (rnd != NULL)) BN_free(rnd);
159 if (t != NULL) BN_free(t);
160 if (ctx != NULL) BN_CTX_free(ctx);
164 int BN_is_prime(a,checks,callback,ctx_passed,cb_arg)
167 void (*callback)(P_I_I_P);
171 int i,j,c2=0,ret= -1;
173 BN_CTX *ctx=NULL,*ctx2=NULL;
174 BN_MONT_CTX *mont=NULL;
178 if (ctx_passed != NULL)
181 if ((ctx=BN_CTX_new()) == NULL) goto err;
183 if ((ctx2=BN_CTX_new()) == NULL) goto err;
184 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
186 check=ctx->bn[ctx->tos++];
188 /* Setup the montgomery structure */
189 if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
191 for (i=0; i<checks; i++)
193 if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
194 j=witness(check,a,ctx,ctx2,mont);
195 if (j == -1) goto err;
201 if (callback != NULL) callback(1,c2++,cb_arg);
206 if ((ctx_passed == NULL) && (ctx != NULL))
210 if (mont != NULL) BN_MONT_CTX_free(mont);
217 static int witness(a,n,ctx,ctx2,mont)
223 int k,i,ret= -1,good;
224 BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
225 BIGNUM *mont_one,*mont_n1,*mont_a;
227 d1=ctx->bn[ctx->tos];
228 d2=ctx->bn[ctx->tos+1];
229 n1=ctx->bn[ctx->tos+2];
232 mont_one=ctx2->bn[ctx2->tos];
233 mont_n1=ctx2->bn[ctx2->tos+1];
234 mont_a=ctx2->bn[ctx2->tos+2];
239 if (!BN_one(d)) goto err;
240 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
243 if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
244 if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
245 if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
248 for (i=k-1; i>=0; i--)
250 if ( (BN_cmp(d,mont_one) != 0) &&
251 (BN_cmp(d,mont_n1) != 0))
256 BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
258 if (good && (BN_cmp(dd,mont_one) == 0))
263 if (BN_is_bit_set(n1,i))
265 BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
274 if (BN_cmp(d,mont_one) == 0)
284 static int probable_prime(rnd, bits)
289 MS_STATIC BN_ULONG mods[NUMPRIMES];
292 if (!BN_rand(rnd,bits,1,1)) return(0);
293 /* we now have a random number 'rand' to test. */
294 for (i=1; i<NUMPRIMES; i++)
295 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
297 loop: for (i=1; i<NUMPRIMES; i++)
299 /* check that rnd is not a prime and also
300 * that gcd(rnd-1,primes) == 1 (except for 2) */
301 if (((mods[i]+delta)%primes[i]) <= 1)
304 /* perhaps need to check for overflow of
305 * delta (but delta can be upto 2^32) */
309 if (!BN_add_word(rnd,delta)) return(0);
313 static int probable_prime_dh(rnd, bits, add, rem,ctx)
323 t1=ctx->bn[ctx->tos++];
325 if (!BN_rand(rnd,bits,0,1)) goto err;
327 /* we need ((rnd-rem) % add) == 0 */
329 if (!BN_mod(t1,rnd,add,ctx)) goto err;
330 if (!BN_sub(rnd,rnd,t1)) goto err;
332 { if (!BN_add_word(rnd,1)) goto err; }
334 { if (!BN_add(rnd,rnd,rem)) goto err; }
336 /* we now have a random number 'rand' to test. */
338 loop: for (i=1; i<NUMPRIMES; i++)
340 /* check that rnd is a prime */
341 if (BN_mod_word(rnd,(BN_LONG)primes[i]) <= 1)
343 if (!BN_add(rnd,rnd,add)) goto err;
353 static int probable_prime_dh_strong(p, bits, padd, rem,ctx)
361 BIGNUM *t1,*qadd=NULL,*q=NULL;
364 t1=ctx->bn[ctx->tos++];
365 q=ctx->bn[ctx->tos++];
366 qadd=ctx->bn[ctx->tos++];
368 if (!BN_rshift1(qadd,padd)) goto err;
370 if (!BN_rand(q,bits,0,1)) goto err;
372 /* we need ((rnd-rem) % add) == 0 */
373 if (!BN_mod(t1,q,qadd,ctx)) goto err;
374 if (!BN_sub(q,q,t1)) goto err;
376 { if (!BN_add_word(q,1)) goto err; }
379 if (!BN_rshift1(t1,rem)) goto err;
380 if (!BN_add(q,q,t1)) goto err;
383 /* we now have a random number 'rand' to test. */
384 if (!BN_lshift1(p,q)) goto err;
385 if (!BN_add_word(p,1)) goto err;
387 loop: for (i=1; i<NUMPRIMES; i++)
389 /* check that p and q are prime */
390 /* check that for p and q
391 * gcd(p-1,primes) == 1 (except for 2) */
392 if ( (BN_mod_word(p,(BN_LONG)primes[i]) == 0) ||
393 (BN_mod_word(q,(BN_LONG)primes[i]) == 0))
395 if (!BN_add(p,p,padd)) goto err;
396 if (!BN_add(q,q,qadd)) goto err;
407 static int witness(a, n,ctx)
414 BIGNUM *d1,*d2,*x,*n1,*inv;
416 d1=ctx->bn[ctx->tos];
417 d2=ctx->bn[ctx->tos+1];
418 x=ctx->bn[ctx->tos+2];
419 n1=ctx->bn[ctx->tos+3];
420 inv=ctx->bn[ctx->tos+4];
425 if (!BN_one(d)) goto err;
426 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
429 /* i=BN_num_bits(n); */
431 nb=BN_reciprocal(inv,n,ctx); /**/
432 if (nb == -1) goto err;
435 for (i=k-1; i>=0; i--)
437 if (BN_copy(x,d) == NULL) goto err;
439 if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
441 if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
443 if ( BN_is_one(dd) &&
450 if (BN_is_bit_set(n1,i))
453 if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
455 if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;