1 /* crypto/bn/bn_prime.c */
2 /* Copyright (C) 1995-1997 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);
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_strong(BIGNUM *rnd, int bits,
77 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
80 static int probable_prime();
81 static int probable_prime_dh();
82 static int probable_prime_dh_strong();
85 BIGNUM *BN_generate_prime(bits,strong,add,rem,callback)
90 void (*callback)(P_I_I);
99 if (ctx == NULL) goto err;
100 if ((rnd=BN_new()) == NULL) goto err;
102 if ((t=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++);
127 i=BN_is_prime(rnd,BN_prime_checks,callback,ctx);
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);
142 if (j == -1) goto err;
143 if (j == 0) goto loop;
145 j=BN_is_prime(t,1,callback,ctx);
146 if (j == -1) goto err;
147 if (j == 0) goto loop;
149 if (callback != NULL) callback(2,c1-1);
150 /* We have a strong prime test pass */
153 /* we have a prime :-) */
156 if ((ret == NULL) && (rnd != NULL)) BN_free(rnd);
157 if (t != NULL) BN_free(t);
158 if (ctx != NULL) BN_CTX_free(ctx);
162 int BN_is_prime(a,checks,callback,ctx_passed)
165 void (*callback)(P_I_I);
168 int i,j,c2=0,ret= -1;
172 if (ctx_passed != NULL)
175 if ((ctx=BN_CTX_new()) == NULL) goto err;
177 check=ctx->bn[ctx->tos++];
178 for (i=0; i<checks; i++)
180 if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
181 j=witness(check,a,ctx);
182 if (j == -1) goto err;
188 if (callback != NULL) callback(1,c2++);
193 if ((ctx_passed == NULL) && (ctx != NULL))
201 static int witness(a, n,ctx)
208 BIGNUM *d1,*d2,*x,*n1,*inv;
210 d1=ctx->bn[ctx->tos];
211 d2=ctx->bn[ctx->tos+1];
212 x=ctx->bn[ctx->tos+2];
213 n1=ctx->bn[ctx->tos+3];
214 inv=ctx->bn[ctx->tos+4];
219 if (!BN_one(d)) goto err;
220 if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
223 /* i=BN_num_bits(n); */
225 nb=BN_reciprocal(inv,n,ctx); /**/
226 if (nb == -1) goto err;
229 for (i=k-1; i>=0; i--)
231 if (BN_copy(x,d) == NULL) goto err;
233 if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
235 if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
237 if ( BN_is_one(dd) &&
244 if (BN_is_bit_set(n1,i))
247 if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
249 if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;
268 static int probable_prime(rnd, bits)
273 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)
288 /* perhaps need to check for overflow of
289 * delta (but delta can be upto 2^32) */
293 if (!BN_add_word(rnd,delta)) return(0);
297 static int probable_prime_dh(rnd, bits, add, rem,ctx)
307 t1=ctx->bn[ctx->tos++];
309 if (!BN_rand(rnd,bits,0,1)) goto err;
311 /* we need ((rnd-rem) % add) == 0 */
313 if (!BN_mod(t1,rnd,add,ctx)) goto err;
314 if (!BN_sub(rnd,rnd,t1)) goto err;
316 { if (!BN_add_word(rnd,1)) goto err; }
318 { if (!BN_add(rnd,rnd,rem)) goto err; }
320 /* we now have a random number 'rand' to test. */
322 loop: for (i=1; i<NUMPRIMES; i++)
324 /* check that rnd is a prime */
325 if (BN_mod_word(rnd,(BN_LONG)primes[i]) <= 1)
327 if (!BN_add(rnd,rnd,add)) goto err;
337 static int probable_prime_dh_strong(p, bits, padd, rem,ctx)
345 BIGNUM *t1,*qadd=NULL,*q=NULL;
348 t1=ctx->bn[ctx->tos++];
349 q=ctx->bn[ctx->tos++];
350 qadd=ctx->bn[ctx->tos++];
352 if (!BN_rshift1(qadd,padd)) goto err;
354 if (!BN_rand(q,bits,0,1)) goto err;
356 /* we need ((rnd-rem) % add) == 0 */
357 if (!BN_mod(t1,q,qadd,ctx)) goto err;
358 if (!BN_sub(q,q,t1)) goto err;
360 { if (!BN_add_word(q,1)) goto err; }
363 if (!BN_rshift1(t1,rem)) goto err;
364 if (!BN_add(q,q,t1)) goto err;
367 /* we now have a random number 'rand' to test. */
368 if (!BN_lshift1(p,q)) goto err;
369 if (!BN_add_word(p,1)) goto err;
371 loop: for (i=1; i<NUMPRIMES; i++)
373 /* check that p and q are prime */
374 /* check that for p and q
375 * gcd(p-1,primes) == 1 (except for 2) */
376 if ( (BN_mod_word(p,(BN_LONG)primes[i]) == 0) ||
377 (BN_mod_word(q,(BN_LONG)primes[i]) == 0))
379 if (!BN_add(p,p,padd)) goto err;
380 if (!BN_add(q,q,qadd)) goto err;