crypto/bn/bn_prime.c

   1 /* crypto/bn/bn_prime.c */
   2 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
   3  * All rights reserved.
   4  *
   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.
   8  *
   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).
  15  *
  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.
  22  *
  23  * Redistribution and use in source and binary forms, with or without
  24  * modification, are permitted provided that the following conditions
  25  * are met:
  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)"
  40  *
  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
  51  * SUCH DAMAGE.
  52  *
  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.]
  57  */
  58
  59 #include <stdio.h>
  60 #include <time.h>
  61 #include "cryptlib.h"
  62 #include "bn_lcl.h"
  63 #include "rand.h"
  64
  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.
  68  */
  69 #include "bn_prime.h"
  70
  71 #ifndef NOPROTO
  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);
  78 #else
  79 static int witness();
  80 static int probable_prime();
  81 static int probable_prime_dh();
  82 static int probable_prime_dh_strong();
  83 #endif
  84
  85 BIGNUM *BN_generate_prime(bits,strong,add,rem,callback)
  86 int bits;
  87 int strong;
  88 BIGNUM *add;
  89 BIGNUM *rem;
  90 void (*callback)(P_I_I);
  91         {
  92         BIGNUM *rnd=NULL;
  93         BIGNUM *ret=NULL;
  94         BIGNUM *t=NULL;
  95         int i,j,c1=0;
  96         BN_CTX *ctx;
  97
  98         ctx=BN_CTX_new();
  99         if (ctx == NULL) goto err;
 100         if ((rnd=BN_new()) == NULL) goto err;
 101         if (strong)
 102                 if ((t=BN_new()) == NULL) goto err;
 103 loop:
 104         /* make a random number and set the top and bottom bits */
 105         if (add == NULL)
 106                 {
 107                 if (!probable_prime(rnd,bits)) goto err;
 108                 }
 109         else
 110                 {
 111                 if (strong)
 112                         {
 113                         if (!probable_prime_dh_strong(rnd,bits,add,rem,ctx))
 114                                  goto err;
 115                         }
 116                 else
 117                         {
 118                         if (!probable_prime_dh(rnd,bits,add,rem,ctx))
 119                                 goto err;
 120                         }
 121                 }
 122         /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
 123         if (callback != NULL) callback(0,c1++);
 124
 125         if (!strong)
 126                 {
 127                 i=BN_is_prime(rnd,BN_prime_checks,callback,ctx);
 128                 if (i == -1) goto err;
 129                 if (i == 0) goto loop;
 130                 }
 131         else
 132                 {
 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;
 138
 139                 for (i=0; i<BN_prime_checks; i++)
 140                         {
 141                         j=BN_is_prime(rnd,1,callback,ctx);
 142                         if (j == -1) goto err;
 143                         if (j == 0) goto loop;
 144
 145                         j=BN_is_prime(t,1,callback,ctx);
 146                         if (j == -1) goto err;
 147                         if (j == 0) goto loop;
 148
 149                         if (callback != NULL) callback(2,c1-1);
 150                         /* We have a strong prime test pass */
 151                         }
 152                 }
 153         /* we have a prime :-) */
 154         ret=rnd;
 155 err:
 156         if ((ret == NULL) && (rnd != NULL)) BN_free(rnd);
 157         if (t != NULL) BN_free(t);
 158         if (ctx != NULL) BN_CTX_free(ctx);
 159         return(ret);
 160         }
 161
 162 int BN_is_prime(a,checks,callback,ctx_passed)
 163 BIGNUM *a;
 164 int checks;
 165 void (*callback)(P_I_I);
 166 BN_CTX *ctx_passed;
 167         {
 168         int i,j,c2=0,ret= -1;
 169         BIGNUM *check;
 170         BN_CTX *ctx;
 171
 172         if (ctx_passed != NULL)
 173                 ctx=ctx_passed;
 174         else
 175                 if ((ctx=BN_CTX_new()) == NULL) goto err;
 176
 177         check=ctx->bn[ctx->tos++];
 178         for (i=0; i<checks; i++)
 179                 {
 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;
 183                 if (j)
 184                         {
 185                         ret=0;
 186                         goto err;
 187                         }
 188                 if (callback != NULL) callback(1,c2++);
 189                 }
 190         ret=1;
 191 err:
 192         ctx->tos--;
 193         if ((ctx_passed == NULL) && (ctx != NULL))
 194                 BN_CTX_free(ctx);
 195
 196         return(ret);
 197         }
 198
 199 #define RECP_MUL_MOD
 200
 201 static int witness(a, n,ctx)
 202 BIGNUM *a;
 203 BIGNUM *n;
 204 BN_CTX *ctx;
 205         {
 206         int k,i,nb,ret= -1;
 207         BIGNUM *d,*dd,*tmp;
 208         BIGNUM *d1,*d2,*x,*n1,*inv;
 209
 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];
 215         ctx->tos+=5;
 216
 217         d=d1;
 218         dd=d2;
 219         if (!BN_one(d)) goto err;
 220         if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
 221         k=BN_num_bits(n1);
 222
 223         /* i=BN_num_bits(n); */
 224 #ifdef RECP_MUL_MOD
 225         nb=BN_reciprocal(inv,n,ctx); /**/
 226         if (nb == -1) goto err;
 227 #endif
 228
 229         for (i=k-1; i>=0; i--)
 230                 {
 231                 if (BN_copy(x,d) == NULL) goto err;
 232 #ifndef RECP_MUL_MOD
 233                 if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
 234 #else
 235                 if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
 236 #endif
 237                 if (    BN_is_one(dd) &&
 238                         !BN_is_one(x) &&
 239                         (BN_cmp(x,n1) != 0))
 240                         {
 241                         ret=1;
 242                         goto err;
 243                         }
 244                 if (BN_is_bit_set(n1,i))
 245                         {
 246 #ifndef RECP_MUL_MOD
 247                         if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
 248 #else
 249                         if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;
 250 #endif
 251                         }
 252                 else
 253                         {
 254                         tmp=d;
 255                         d=dd;
 256                         dd=tmp;
 257                         }
 258                 }
 259         if (BN_is_one(d))
 260                 i=0;
 261         else    i=1;
 262         ret=i;
 263 err:
 264         ctx->tos-=5;
 265         return(ret);
 266         }
 267
 268 static int probable_prime(rnd, bits)
 269 BIGNUM *rnd;
 270 int bits;
 271         {
 272         int i;
 273         MS_STATIC BN_ULONG mods[NUMPRIMES];
 274         BN_ULONG delta;
 275
 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]);
 280         delta=0;
 281         loop: for (i=1; i<NUMPRIMES; i++)
 282                 {
 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)
 286                         {
 287                         delta+=2;
 288                         /* perhaps need to check for overflow of
 289                          * delta (but delta can be upto 2^32) */
 290                         goto loop;
 291                         }
 292                 }
 293         if (!BN_add_word(rnd,delta)) return(0);
 294         return(1);
 295         }
 296
 297 static int probable_prime_dh(rnd, bits, add, rem,ctx)
 298 BIGNUM *rnd;
 299 int bits;
 300 BIGNUM *add;
 301 BIGNUM *rem;
 302 BN_CTX *ctx;
 303         {
 304         int i,ret=0;
 305         BIGNUM *t1;
 306
 307         t1=ctx->bn[ctx->tos++];
 308
 309         if (!BN_rand(rnd,bits,0,1)) goto err;
 310
 311         /* we need ((rnd-rem) % add) == 0 */
 312
 313         if (!BN_mod(t1,rnd,add,ctx)) goto err;
 314         if (!BN_sub(rnd,rnd,t1)) goto err;
 315         if (rem == NULL)
 316                 { if (!BN_add_word(rnd,1)) goto err; }
 317         else
 318                 { if (!BN_add(rnd,rnd,rem)) goto err; }
 319
 320         /* we now have a random number 'rand' to test. */
 321
 322         loop: for (i=1; i<NUMPRIMES; i++)
 323                 {
 324                 /* check that rnd is a prime */
 325                 if (BN_mod_word(rnd,(BN_LONG)primes[i]) <= 1)
 326                         {
 327                         if (!BN_add(rnd,rnd,add)) goto err;
 328                         goto loop;
 329                         }
 330                 }
 331         ret=1;
 332 err:
 333         ctx->tos--;
 334         return(ret);
 335         }
 336
 337 static int probable_prime_dh_strong(p, bits, padd, rem,ctx)
 338 BIGNUM *p;
 339 int bits;
 340 BIGNUM *padd;
 341 BIGNUM *rem;
 342 BN_CTX *ctx;
 343         {
 344         int i,ret=0;
 345         BIGNUM *t1,*qadd=NULL,*q=NULL;
 346
 347         bits--;
 348         t1=ctx->bn[ctx->tos++];
 349         q=ctx->bn[ctx->tos++];
 350         qadd=ctx->bn[ctx->tos++];
 351
 352         if (!BN_rshift1(qadd,padd)) goto err;
 353
 354         if (!BN_rand(q,bits,0,1)) goto err;
 355
 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;
 359         if (rem == NULL)
 360                 { if (!BN_add_word(q,1)) goto err; }
 361         else
 362                 {
 363                 if (!BN_rshift1(t1,rem)) goto err;
 364                 if (!BN_add(q,q,t1)) goto err;
 365                 }
 366
 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;
 370
 371         loop: for (i=1; i<NUMPRIMES; i++)
 372                 {
 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))
 378                         {
 379                         if (!BN_add(p,p,padd)) goto err;
 380                         if (!BN_add(q,q,qadd)) goto err;
 381                         goto loop;
 382                         }
 383                 }
 384         ret=1;
 385 err:
 386         ctx->tos-=3;
 387         return(ret);
 388         }
 389