1*0Sstevel@tonic-gate /* crypto/bn/bn_prime.c */ 2*0Sstevel@tonic-gate /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 3*0Sstevel@tonic-gate * All rights reserved. 4*0Sstevel@tonic-gate * 5*0Sstevel@tonic-gate * This package is an SSL implementation written 6*0Sstevel@tonic-gate * by Eric Young (eay@cryptsoft.com). 7*0Sstevel@tonic-gate * The implementation was written so as to conform with Netscapes SSL. 8*0Sstevel@tonic-gate * 9*0Sstevel@tonic-gate * This library is free for commercial and non-commercial use as long as 10*0Sstevel@tonic-gate * the following conditions are aheared to. The following conditions 11*0Sstevel@tonic-gate * apply to all code found in this distribution, be it the RC4, RSA, 12*0Sstevel@tonic-gate * lhash, DES, etc., code; not just the SSL code. The SSL documentation 13*0Sstevel@tonic-gate * included with this distribution is covered by the same copyright terms 14*0Sstevel@tonic-gate * except that the holder is Tim Hudson (tjh@cryptsoft.com). 15*0Sstevel@tonic-gate * 16*0Sstevel@tonic-gate * Copyright remains Eric Young's, and as such any Copyright notices in 17*0Sstevel@tonic-gate * the code are not to be removed. 18*0Sstevel@tonic-gate * If this package is used in a product, Eric Young should be given attribution 19*0Sstevel@tonic-gate * as the author of the parts of the library used. 20*0Sstevel@tonic-gate * This can be in the form of a textual message at program startup or 21*0Sstevel@tonic-gate * in documentation (online or textual) provided with the package. 22*0Sstevel@tonic-gate * 23*0Sstevel@tonic-gate * Redistribution and use in source and binary forms, with or without 24*0Sstevel@tonic-gate * modification, are permitted provided that the following conditions 25*0Sstevel@tonic-gate * are met: 26*0Sstevel@tonic-gate * 1. Redistributions of source code must retain the copyright 27*0Sstevel@tonic-gate * notice, this list of conditions and the following disclaimer. 28*0Sstevel@tonic-gate * 2. Redistributions in binary form must reproduce the above copyright 29*0Sstevel@tonic-gate * notice, this list of conditions and the following disclaimer in the 30*0Sstevel@tonic-gate * documentation and/or other materials provided with the distribution. 31*0Sstevel@tonic-gate * 3. All advertising materials mentioning features or use of this software 32*0Sstevel@tonic-gate * must display the following acknowledgement: 33*0Sstevel@tonic-gate * "This product includes cryptographic software written by 34*0Sstevel@tonic-gate * Eric Young (eay@cryptsoft.com)" 35*0Sstevel@tonic-gate * The word 'cryptographic' can be left out if the rouines from the library 36*0Sstevel@tonic-gate * being used are not cryptographic related :-). 37*0Sstevel@tonic-gate * 4. If you include any Windows specific code (or a derivative thereof) from 38*0Sstevel@tonic-gate * the apps directory (application code) you must include an acknowledgement: 39*0Sstevel@tonic-gate * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" 40*0Sstevel@tonic-gate * 41*0Sstevel@tonic-gate * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 42*0Sstevel@tonic-gate * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 43*0Sstevel@tonic-gate * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 44*0Sstevel@tonic-gate * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 45*0Sstevel@tonic-gate * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 46*0Sstevel@tonic-gate * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 47*0Sstevel@tonic-gate * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 48*0Sstevel@tonic-gate * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 49*0Sstevel@tonic-gate * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 50*0Sstevel@tonic-gate * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 51*0Sstevel@tonic-gate * SUCH DAMAGE. 52*0Sstevel@tonic-gate * 53*0Sstevel@tonic-gate * The licence and distribution terms for any publically available version or 54*0Sstevel@tonic-gate * derivative of this code cannot be changed. i.e. this code cannot simply be 55*0Sstevel@tonic-gate * copied and put under another distribution licence 56*0Sstevel@tonic-gate * [including the GNU Public Licence.] 57*0Sstevel@tonic-gate */ 58*0Sstevel@tonic-gate /* ==================================================================== 59*0Sstevel@tonic-gate * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. 60*0Sstevel@tonic-gate * 61*0Sstevel@tonic-gate * Redistribution and use in source and binary forms, with or without 62*0Sstevel@tonic-gate * modification, are permitted provided that the following conditions 63*0Sstevel@tonic-gate * are met: 64*0Sstevel@tonic-gate * 65*0Sstevel@tonic-gate * 1. Redistributions of source code must retain the above copyright 66*0Sstevel@tonic-gate * notice, this list of conditions and the following disclaimer. 67*0Sstevel@tonic-gate * 68*0Sstevel@tonic-gate * 2. Redistributions in binary form must reproduce the above copyright 69*0Sstevel@tonic-gate * notice, this list of conditions and the following disclaimer in 70*0Sstevel@tonic-gate * the documentation and/or other materials provided with the 71*0Sstevel@tonic-gate * distribution. 72*0Sstevel@tonic-gate * 73*0Sstevel@tonic-gate * 3. All advertising materials mentioning features or use of this 74*0Sstevel@tonic-gate * software must display the following acknowledgment: 75*0Sstevel@tonic-gate * "This product includes software developed by the OpenSSL Project 76*0Sstevel@tonic-gate * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 77*0Sstevel@tonic-gate * 78*0Sstevel@tonic-gate * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 79*0Sstevel@tonic-gate * endorse or promote products derived from this software without 80*0Sstevel@tonic-gate * prior written permission. For written permission, please contact 81*0Sstevel@tonic-gate * openssl-core@openssl.org. 82*0Sstevel@tonic-gate * 83*0Sstevel@tonic-gate * 5. Products derived from this software may not be called "OpenSSL" 84*0Sstevel@tonic-gate * nor may "OpenSSL" appear in their names without prior written 85*0Sstevel@tonic-gate * permission of the OpenSSL Project. 86*0Sstevel@tonic-gate * 87*0Sstevel@tonic-gate * 6. Redistributions of any form whatsoever must retain the following 88*0Sstevel@tonic-gate * acknowledgment: 89*0Sstevel@tonic-gate * "This product includes software developed by the OpenSSL Project 90*0Sstevel@tonic-gate * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 91*0Sstevel@tonic-gate * 92*0Sstevel@tonic-gate * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 93*0Sstevel@tonic-gate * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 94*0Sstevel@tonic-gate * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 95*0Sstevel@tonic-gate * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 96*0Sstevel@tonic-gate * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 97*0Sstevel@tonic-gate * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 98*0Sstevel@tonic-gate * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 99*0Sstevel@tonic-gate * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 100*0Sstevel@tonic-gate * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 101*0Sstevel@tonic-gate * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 102*0Sstevel@tonic-gate * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 103*0Sstevel@tonic-gate * OF THE POSSIBILITY OF SUCH DAMAGE. 104*0Sstevel@tonic-gate * ==================================================================== 105*0Sstevel@tonic-gate * 106*0Sstevel@tonic-gate * This product includes cryptographic software written by Eric Young 107*0Sstevel@tonic-gate * (eay@cryptsoft.com). This product includes software written by Tim 108*0Sstevel@tonic-gate * Hudson (tjh@cryptsoft.com). 109*0Sstevel@tonic-gate * 110*0Sstevel@tonic-gate */ 111*0Sstevel@tonic-gate 112*0Sstevel@tonic-gate #include <stdio.h> 113*0Sstevel@tonic-gate #include <time.h> 114*0Sstevel@tonic-gate #include "cryptlib.h" 115*0Sstevel@tonic-gate #include "bn_lcl.h" 116*0Sstevel@tonic-gate #include <openssl/rand.h> 117*0Sstevel@tonic-gate 118*0Sstevel@tonic-gate /* The quick sieve algorithm approach to weeding out primes is 119*0Sstevel@tonic-gate * Philip Zimmermann's, as implemented in PGP. I have had a read of 120*0Sstevel@tonic-gate * his comments and implemented my own version. 121*0Sstevel@tonic-gate */ 122*0Sstevel@tonic-gate #include "bn_prime.h" 123*0Sstevel@tonic-gate 124*0Sstevel@tonic-gate static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 125*0Sstevel@tonic-gate const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); 126*0Sstevel@tonic-gate static int probable_prime(BIGNUM *rnd, int bits); 127*0Sstevel@tonic-gate static int probable_prime_dh(BIGNUM *rnd, int bits, 128*0Sstevel@tonic-gate const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 129*0Sstevel@tonic-gate static int probable_prime_dh_safe(BIGNUM *rnd, int bits, 130*0Sstevel@tonic-gate const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 131*0Sstevel@tonic-gate 132*0Sstevel@tonic-gate BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, 133*0Sstevel@tonic-gate const BIGNUM *add, const BIGNUM *rem, 134*0Sstevel@tonic-gate void (*callback)(int,int,void *), void *cb_arg) 135*0Sstevel@tonic-gate { 136*0Sstevel@tonic-gate BIGNUM *rnd=NULL; 137*0Sstevel@tonic-gate BIGNUM t; 138*0Sstevel@tonic-gate int found=0; 139*0Sstevel@tonic-gate int i,j,c1=0; 140*0Sstevel@tonic-gate BN_CTX *ctx; 141*0Sstevel@tonic-gate int checks = BN_prime_checks_for_size(bits); 142*0Sstevel@tonic-gate 143*0Sstevel@tonic-gate BN_init(&t); 144*0Sstevel@tonic-gate ctx=BN_CTX_new(); 145*0Sstevel@tonic-gate if (ctx == NULL) goto err; 146*0Sstevel@tonic-gate if (ret == NULL) 147*0Sstevel@tonic-gate { 148*0Sstevel@tonic-gate if ((rnd=BN_new()) == NULL) goto err; 149*0Sstevel@tonic-gate } 150*0Sstevel@tonic-gate else 151*0Sstevel@tonic-gate rnd=ret; 152*0Sstevel@tonic-gate loop: 153*0Sstevel@tonic-gate /* make a random number and set the top and bottom bits */ 154*0Sstevel@tonic-gate if (add == NULL) 155*0Sstevel@tonic-gate { 156*0Sstevel@tonic-gate if (!probable_prime(rnd,bits)) goto err; 157*0Sstevel@tonic-gate } 158*0Sstevel@tonic-gate else 159*0Sstevel@tonic-gate { 160*0Sstevel@tonic-gate if (safe) 161*0Sstevel@tonic-gate { 162*0Sstevel@tonic-gate if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx)) 163*0Sstevel@tonic-gate goto err; 164*0Sstevel@tonic-gate } 165*0Sstevel@tonic-gate else 166*0Sstevel@tonic-gate { 167*0Sstevel@tonic-gate if (!probable_prime_dh(rnd,bits,add,rem,ctx)) 168*0Sstevel@tonic-gate goto err; 169*0Sstevel@tonic-gate } 170*0Sstevel@tonic-gate } 171*0Sstevel@tonic-gate /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */ 172*0Sstevel@tonic-gate if (callback != NULL) callback(0,c1++,cb_arg); 173*0Sstevel@tonic-gate 174*0Sstevel@tonic-gate if (!safe) 175*0Sstevel@tonic-gate { 176*0Sstevel@tonic-gate i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0); 177*0Sstevel@tonic-gate if (i == -1) goto err; 178*0Sstevel@tonic-gate if (i == 0) goto loop; 179*0Sstevel@tonic-gate } 180*0Sstevel@tonic-gate else 181*0Sstevel@tonic-gate { 182*0Sstevel@tonic-gate /* for "safe prime" generation, 183*0Sstevel@tonic-gate * check that (p-1)/2 is prime. 184*0Sstevel@tonic-gate * Since a prime is odd, We just 185*0Sstevel@tonic-gate * need to divide by 2 */ 186*0Sstevel@tonic-gate if (!BN_rshift1(&t,rnd)) goto err; 187*0Sstevel@tonic-gate 188*0Sstevel@tonic-gate for (i=0; i<checks; i++) 189*0Sstevel@tonic-gate { 190*0Sstevel@tonic-gate j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0); 191*0Sstevel@tonic-gate if (j == -1) goto err; 192*0Sstevel@tonic-gate if (j == 0) goto loop; 193*0Sstevel@tonic-gate 194*0Sstevel@tonic-gate j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0); 195*0Sstevel@tonic-gate if (j == -1) goto err; 196*0Sstevel@tonic-gate if (j == 0) goto loop; 197*0Sstevel@tonic-gate 198*0Sstevel@tonic-gate if (callback != NULL) callback(2,c1-1,cb_arg); 199*0Sstevel@tonic-gate /* We have a safe prime test pass */ 200*0Sstevel@tonic-gate } 201*0Sstevel@tonic-gate } 202*0Sstevel@tonic-gate /* we have a prime :-) */ 203*0Sstevel@tonic-gate found = 1; 204*0Sstevel@tonic-gate err: 205*0Sstevel@tonic-gate if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd); 206*0Sstevel@tonic-gate BN_free(&t); 207*0Sstevel@tonic-gate if (ctx != NULL) BN_CTX_free(ctx); 208*0Sstevel@tonic-gate return(found ? rnd : NULL); 209*0Sstevel@tonic-gate } 210*0Sstevel@tonic-gate 211*0Sstevel@tonic-gate int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *), 212*0Sstevel@tonic-gate BN_CTX *ctx_passed, void *cb_arg) 213*0Sstevel@tonic-gate { 214*0Sstevel@tonic-gate return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0); 215*0Sstevel@tonic-gate } 216*0Sstevel@tonic-gate 217*0Sstevel@tonic-gate int BN_is_prime_fasttest(const BIGNUM *a, int checks, 218*0Sstevel@tonic-gate void (*callback)(int,int,void *), 219*0Sstevel@tonic-gate BN_CTX *ctx_passed, void *cb_arg, 220*0Sstevel@tonic-gate int do_trial_division) 221*0Sstevel@tonic-gate { 222*0Sstevel@tonic-gate int i, j, ret = -1; 223*0Sstevel@tonic-gate int k; 224*0Sstevel@tonic-gate BN_CTX *ctx = NULL; 225*0Sstevel@tonic-gate BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ 226*0Sstevel@tonic-gate BN_MONT_CTX *mont = NULL; 227*0Sstevel@tonic-gate const BIGNUM *A = NULL; 228*0Sstevel@tonic-gate 229*0Sstevel@tonic-gate if (BN_cmp(a, BN_value_one()) <= 0) 230*0Sstevel@tonic-gate return 0; 231*0Sstevel@tonic-gate 232*0Sstevel@tonic-gate if (checks == BN_prime_checks) 233*0Sstevel@tonic-gate checks = BN_prime_checks_for_size(BN_num_bits(a)); 234*0Sstevel@tonic-gate 235*0Sstevel@tonic-gate /* first look for small factors */ 236*0Sstevel@tonic-gate if (!BN_is_odd(a)) 237*0Sstevel@tonic-gate return 0; 238*0Sstevel@tonic-gate if (do_trial_division) 239*0Sstevel@tonic-gate { 240*0Sstevel@tonic-gate for (i = 1; i < NUMPRIMES; i++) 241*0Sstevel@tonic-gate if (BN_mod_word(a, primes[i]) == 0) 242*0Sstevel@tonic-gate return 0; 243*0Sstevel@tonic-gate if (callback != NULL) callback(1, -1, cb_arg); 244*0Sstevel@tonic-gate } 245*0Sstevel@tonic-gate 246*0Sstevel@tonic-gate if (ctx_passed != NULL) 247*0Sstevel@tonic-gate ctx = ctx_passed; 248*0Sstevel@tonic-gate else 249*0Sstevel@tonic-gate if ((ctx=BN_CTX_new()) == NULL) 250*0Sstevel@tonic-gate goto err; 251*0Sstevel@tonic-gate BN_CTX_start(ctx); 252*0Sstevel@tonic-gate 253*0Sstevel@tonic-gate /* A := abs(a) */ 254*0Sstevel@tonic-gate if (a->neg) 255*0Sstevel@tonic-gate { 256*0Sstevel@tonic-gate BIGNUM *t; 257*0Sstevel@tonic-gate if ((t = BN_CTX_get(ctx)) == NULL) goto err; 258*0Sstevel@tonic-gate BN_copy(t, a); 259*0Sstevel@tonic-gate t->neg = 0; 260*0Sstevel@tonic-gate A = t; 261*0Sstevel@tonic-gate } 262*0Sstevel@tonic-gate else 263*0Sstevel@tonic-gate A = a; 264*0Sstevel@tonic-gate A1 = BN_CTX_get(ctx); 265*0Sstevel@tonic-gate A1_odd = BN_CTX_get(ctx); 266*0Sstevel@tonic-gate check = BN_CTX_get(ctx); 267*0Sstevel@tonic-gate if (check == NULL) goto err; 268*0Sstevel@tonic-gate 269*0Sstevel@tonic-gate /* compute A1 := A - 1 */ 270*0Sstevel@tonic-gate if (!BN_copy(A1, A)) 271*0Sstevel@tonic-gate goto err; 272*0Sstevel@tonic-gate if (!BN_sub_word(A1, 1)) 273*0Sstevel@tonic-gate goto err; 274*0Sstevel@tonic-gate if (BN_is_zero(A1)) 275*0Sstevel@tonic-gate { 276*0Sstevel@tonic-gate ret = 0; 277*0Sstevel@tonic-gate goto err; 278*0Sstevel@tonic-gate } 279*0Sstevel@tonic-gate 280*0Sstevel@tonic-gate /* write A1 as A1_odd * 2^k */ 281*0Sstevel@tonic-gate k = 1; 282*0Sstevel@tonic-gate while (!BN_is_bit_set(A1, k)) 283*0Sstevel@tonic-gate k++; 284*0Sstevel@tonic-gate if (!BN_rshift(A1_odd, A1, k)) 285*0Sstevel@tonic-gate goto err; 286*0Sstevel@tonic-gate 287*0Sstevel@tonic-gate /* Montgomery setup for computations mod A */ 288*0Sstevel@tonic-gate mont = BN_MONT_CTX_new(); 289*0Sstevel@tonic-gate if (mont == NULL) 290*0Sstevel@tonic-gate goto err; 291*0Sstevel@tonic-gate if (!BN_MONT_CTX_set(mont, A, ctx)) 292*0Sstevel@tonic-gate goto err; 293*0Sstevel@tonic-gate 294*0Sstevel@tonic-gate for (i = 0; i < checks; i++) 295*0Sstevel@tonic-gate { 296*0Sstevel@tonic-gate if (!BN_pseudo_rand_range(check, A1)) 297*0Sstevel@tonic-gate goto err; 298*0Sstevel@tonic-gate if (!BN_add_word(check, 1)) 299*0Sstevel@tonic-gate goto err; 300*0Sstevel@tonic-gate /* now 1 <= check < A */ 301*0Sstevel@tonic-gate 302*0Sstevel@tonic-gate j = witness(check, A, A1, A1_odd, k, ctx, mont); 303*0Sstevel@tonic-gate if (j == -1) goto err; 304*0Sstevel@tonic-gate if (j) 305*0Sstevel@tonic-gate { 306*0Sstevel@tonic-gate ret=0; 307*0Sstevel@tonic-gate goto err; 308*0Sstevel@tonic-gate } 309*0Sstevel@tonic-gate if (callback != NULL) callback(1,i,cb_arg); 310*0Sstevel@tonic-gate } 311*0Sstevel@tonic-gate ret=1; 312*0Sstevel@tonic-gate err: 313*0Sstevel@tonic-gate if (ctx != NULL) 314*0Sstevel@tonic-gate { 315*0Sstevel@tonic-gate BN_CTX_end(ctx); 316*0Sstevel@tonic-gate if (ctx_passed == NULL) 317*0Sstevel@tonic-gate BN_CTX_free(ctx); 318*0Sstevel@tonic-gate } 319*0Sstevel@tonic-gate if (mont != NULL) 320*0Sstevel@tonic-gate BN_MONT_CTX_free(mont); 321*0Sstevel@tonic-gate 322*0Sstevel@tonic-gate return(ret); 323*0Sstevel@tonic-gate } 324*0Sstevel@tonic-gate 325*0Sstevel@tonic-gate static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 326*0Sstevel@tonic-gate const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont) 327*0Sstevel@tonic-gate { 328*0Sstevel@tonic-gate if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ 329*0Sstevel@tonic-gate return -1; 330*0Sstevel@tonic-gate if (BN_is_one(w)) 331*0Sstevel@tonic-gate return 0; /* probably prime */ 332*0Sstevel@tonic-gate if (BN_cmp(w, a1) == 0) 333*0Sstevel@tonic-gate return 0; /* w == -1 (mod a), 'a' is probably prime */ 334*0Sstevel@tonic-gate while (--k) 335*0Sstevel@tonic-gate { 336*0Sstevel@tonic-gate if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ 337*0Sstevel@tonic-gate return -1; 338*0Sstevel@tonic-gate if (BN_is_one(w)) 339*0Sstevel@tonic-gate return 1; /* 'a' is composite, otherwise a previous 'w' would 340*0Sstevel@tonic-gate * have been == -1 (mod 'a') */ 341*0Sstevel@tonic-gate if (BN_cmp(w, a1) == 0) 342*0Sstevel@tonic-gate return 0; /* w == -1 (mod a), 'a' is probably prime */ 343*0Sstevel@tonic-gate } 344*0Sstevel@tonic-gate /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', 345*0Sstevel@tonic-gate * and it is neither -1 nor +1 -- so 'a' cannot be prime */ 346*0Sstevel@tonic-gate return 1; 347*0Sstevel@tonic-gate } 348*0Sstevel@tonic-gate 349*0Sstevel@tonic-gate static int probable_prime(BIGNUM *rnd, int bits) 350*0Sstevel@tonic-gate { 351*0Sstevel@tonic-gate int i; 352*0Sstevel@tonic-gate BN_ULONG mods[NUMPRIMES]; 353*0Sstevel@tonic-gate BN_ULONG delta,d; 354*0Sstevel@tonic-gate 355*0Sstevel@tonic-gate again: 356*0Sstevel@tonic-gate if (!BN_rand(rnd,bits,1,1)) return(0); 357*0Sstevel@tonic-gate /* we now have a random number 'rand' to test. */ 358*0Sstevel@tonic-gate for (i=1; i<NUMPRIMES; i++) 359*0Sstevel@tonic-gate mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]); 360*0Sstevel@tonic-gate delta=0; 361*0Sstevel@tonic-gate loop: for (i=1; i<NUMPRIMES; i++) 362*0Sstevel@tonic-gate { 363*0Sstevel@tonic-gate /* check that rnd is not a prime and also 364*0Sstevel@tonic-gate * that gcd(rnd-1,primes) == 1 (except for 2) */ 365*0Sstevel@tonic-gate if (((mods[i]+delta)%primes[i]) <= 1) 366*0Sstevel@tonic-gate { 367*0Sstevel@tonic-gate d=delta; 368*0Sstevel@tonic-gate delta+=2; 369*0Sstevel@tonic-gate /* perhaps need to check for overflow of 370*0Sstevel@tonic-gate * delta (but delta can be up to 2^32) 371*0Sstevel@tonic-gate * 21-May-98 eay - added overflow check */ 372*0Sstevel@tonic-gate if (delta < d) goto again; 373*0Sstevel@tonic-gate goto loop; 374*0Sstevel@tonic-gate } 375*0Sstevel@tonic-gate } 376*0Sstevel@tonic-gate if (!BN_add_word(rnd,delta)) return(0); 377*0Sstevel@tonic-gate return(1); 378*0Sstevel@tonic-gate } 379*0Sstevel@tonic-gate 380*0Sstevel@tonic-gate static int probable_prime_dh(BIGNUM *rnd, int bits, 381*0Sstevel@tonic-gate const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) 382*0Sstevel@tonic-gate { 383*0Sstevel@tonic-gate int i,ret=0; 384*0Sstevel@tonic-gate BIGNUM *t1; 385*0Sstevel@tonic-gate 386*0Sstevel@tonic-gate BN_CTX_start(ctx); 387*0Sstevel@tonic-gate if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; 388*0Sstevel@tonic-gate 389*0Sstevel@tonic-gate if (!BN_rand(rnd,bits,0,1)) goto err; 390*0Sstevel@tonic-gate 391*0Sstevel@tonic-gate /* we need ((rnd-rem) % add) == 0 */ 392*0Sstevel@tonic-gate 393*0Sstevel@tonic-gate if (!BN_mod(t1,rnd,add,ctx)) goto err; 394*0Sstevel@tonic-gate if (!BN_sub(rnd,rnd,t1)) goto err; 395*0Sstevel@tonic-gate if (rem == NULL) 396*0Sstevel@tonic-gate { if (!BN_add_word(rnd,1)) goto err; } 397*0Sstevel@tonic-gate else 398*0Sstevel@tonic-gate { if (!BN_add(rnd,rnd,rem)) goto err; } 399*0Sstevel@tonic-gate 400*0Sstevel@tonic-gate /* we now have a random number 'rand' to test. */ 401*0Sstevel@tonic-gate 402*0Sstevel@tonic-gate loop: for (i=1; i<NUMPRIMES; i++) 403*0Sstevel@tonic-gate { 404*0Sstevel@tonic-gate /* check that rnd is a prime */ 405*0Sstevel@tonic-gate if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1) 406*0Sstevel@tonic-gate { 407*0Sstevel@tonic-gate if (!BN_add(rnd,rnd,add)) goto err; 408*0Sstevel@tonic-gate goto loop; 409*0Sstevel@tonic-gate } 410*0Sstevel@tonic-gate } 411*0Sstevel@tonic-gate ret=1; 412*0Sstevel@tonic-gate err: 413*0Sstevel@tonic-gate BN_CTX_end(ctx); 414*0Sstevel@tonic-gate return(ret); 415*0Sstevel@tonic-gate } 416*0Sstevel@tonic-gate 417*0Sstevel@tonic-gate static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 418*0Sstevel@tonic-gate const BIGNUM *rem, BN_CTX *ctx) 419*0Sstevel@tonic-gate { 420*0Sstevel@tonic-gate int i,ret=0; 421*0Sstevel@tonic-gate BIGNUM *t1,*qadd,*q; 422*0Sstevel@tonic-gate 423*0Sstevel@tonic-gate bits--; 424*0Sstevel@tonic-gate BN_CTX_start(ctx); 425*0Sstevel@tonic-gate t1 = BN_CTX_get(ctx); 426*0Sstevel@tonic-gate q = BN_CTX_get(ctx); 427*0Sstevel@tonic-gate qadd = BN_CTX_get(ctx); 428*0Sstevel@tonic-gate if (qadd == NULL) goto err; 429*0Sstevel@tonic-gate 430*0Sstevel@tonic-gate if (!BN_rshift1(qadd,padd)) goto err; 431*0Sstevel@tonic-gate 432*0Sstevel@tonic-gate if (!BN_rand(q,bits,0,1)) goto err; 433*0Sstevel@tonic-gate 434*0Sstevel@tonic-gate /* we need ((rnd-rem) % add) == 0 */ 435*0Sstevel@tonic-gate if (!BN_mod(t1,q,qadd,ctx)) goto err; 436*0Sstevel@tonic-gate if (!BN_sub(q,q,t1)) goto err; 437*0Sstevel@tonic-gate if (rem == NULL) 438*0Sstevel@tonic-gate { if (!BN_add_word(q,1)) goto err; } 439*0Sstevel@tonic-gate else 440*0Sstevel@tonic-gate { 441*0Sstevel@tonic-gate if (!BN_rshift1(t1,rem)) goto err; 442*0Sstevel@tonic-gate if (!BN_add(q,q,t1)) goto err; 443*0Sstevel@tonic-gate } 444*0Sstevel@tonic-gate 445*0Sstevel@tonic-gate /* we now have a random number 'rand' to test. */ 446*0Sstevel@tonic-gate if (!BN_lshift1(p,q)) goto err; 447*0Sstevel@tonic-gate if (!BN_add_word(p,1)) goto err; 448*0Sstevel@tonic-gate 449*0Sstevel@tonic-gate loop: for (i=1; i<NUMPRIMES; i++) 450*0Sstevel@tonic-gate { 451*0Sstevel@tonic-gate /* check that p and q are prime */ 452*0Sstevel@tonic-gate /* check that for p and q 453*0Sstevel@tonic-gate * gcd(p-1,primes) == 1 (except for 2) */ 454*0Sstevel@tonic-gate if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) || 455*0Sstevel@tonic-gate (BN_mod_word(q,(BN_ULONG)primes[i]) == 0)) 456*0Sstevel@tonic-gate { 457*0Sstevel@tonic-gate if (!BN_add(p,p,padd)) goto err; 458*0Sstevel@tonic-gate if (!BN_add(q,q,qadd)) goto err; 459*0Sstevel@tonic-gate goto loop; 460*0Sstevel@tonic-gate } 461*0Sstevel@tonic-gate } 462*0Sstevel@tonic-gate ret=1; 463*0Sstevel@tonic-gate err: 464*0Sstevel@tonic-gate BN_CTX_end(ctx); 465*0Sstevel@tonic-gate return(ret); 466*0Sstevel@tonic-gate } 467