test/bntest.c

   1 /* crypto/bn/bntest.c */
   2 /* Copyright (C) 1995-1998 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  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  60  *
  61  * Portions of the attached software ("Contribution") are developed by
  62  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
  63  *
  64  * The Contribution is licensed pursuant to the Eric Young open source
  65  * license provided above.
  66  *
  67  * The binary polynomial arithmetic software is originally written by
  68  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
  69  *
  70  */
  71
  72 #include <stdio.h>
  73 #include <stdlib.h>
  74 #include <string.h>
  75
  76 #include "e_os.h"
  77
  78 #include <openssl/bio.h>
  79 #include <openssl/bn.h>
  80 #include <openssl/rand.h>
  81 #include <openssl/x509.h>
  82 #include <openssl/err.h>
  83
  84 #include "../crypto/bn/bn_lcl.h"
  85
  86 const int num0 = 100;           /* number of tests */
  87 const int num1 = 50;            /* additional tests for some functions */
  88 const int num2 = 5;             /* number of tests for slow functions */
  89
  90 int test_add(BIO *bp);
  91 int test_sub(BIO *bp);
  92 int test_lshift1(BIO *bp);
  93 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_);
  94 int test_rshift1(BIO *bp);
  95 int test_rshift(BIO *bp, BN_CTX *ctx);
  96 int test_div(BIO *bp, BN_CTX *ctx);
  97 int test_div_word(BIO *bp);
  98 int test_div_recp(BIO *bp, BN_CTX *ctx);
  99 int test_mul(BIO *bp);
 100 int test_sqr(BIO *bp, BN_CTX *ctx);
 101 int test_mont(BIO *bp, BN_CTX *ctx);
 102 int test_mod(BIO *bp, BN_CTX *ctx);
 103 int test_mod_mul(BIO *bp, BN_CTX *ctx);
 104 int test_mod_exp(BIO *bp, BN_CTX *ctx);
 105 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx);
 106 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx);
 107 int test_exp(BIO *bp, BN_CTX *ctx);
 108 int test_gf2m_add(BIO *bp);
 109 int test_gf2m_mod(BIO *bp);
 110 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx);
 111 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx);
 112 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx);
 113 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx);
 114 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx);
 115 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx);
 116 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx);
 117 int test_kron(BIO *bp, BN_CTX *ctx);
 118 int test_sqrt(BIO *bp, BN_CTX *ctx);
 119 int test_small_prime(BIO *bp, BN_CTX *ctx);
 120 int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx);
 121 int rand_neg(void);
 122 static int results = 0;
 123
 124 static unsigned char lst[] =
 125     "\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
 126     "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
 127
 128 static const char rnd_seed[] =
 129     "string to make the random number generator think it has entropy";
 130
 131 static void message(BIO *out, char *m)
 132 {
 133     fprintf(stderr, "test %s\n", m);
 134     BIO_puts(out, "print \"test ");
 135     BIO_puts(out, m);
 136     BIO_puts(out, "\\n\"\n");
 137 }
 138
 139 int main(int argc, char *argv[])
 140 {
 141     BN_CTX *ctx;
 142     BIO *out;
 143     char *outfile = NULL;
 144
 145     results = 0;
 146
 147     RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
 148
 149     argc--;
 150     argv++;
 151     while (argc >= 1) {
 152         if (strcmp(*argv, "-results") == 0)
 153             results = 1;
 154         else if (strcmp(*argv, "-out") == 0) {
 155             if (--argc < 1)
 156                 break;
 157             outfile = *(++argv);
 158         }
 159         argc--;
 160         argv++;
 161     }
 162
 163     ctx = BN_CTX_new();
 164     if (ctx == NULL)
 165         EXIT(1);
 166
 167     out = BIO_new(BIO_s_file());
 168     if (out == NULL)
 169         EXIT(1);
 170     if (outfile == NULL) {
 171         BIO_set_fp(out, stdout, BIO_NOCLOSE);
 172     } else {
 173         if (!BIO_write_filename(out, outfile)) {
 174             perror(outfile);
 175             EXIT(1);
 176         }
 177     }
 178
 179     if (!results)
 180         BIO_puts(out, "obase=16\nibase=16\n");
 181
 182     message(out, "BN_add");
 183     if (!test_add(out))
 184         goto err;
 185     (void)BIO_flush(out);
 186
 187     message(out, "BN_sub");
 188     if (!test_sub(out))
 189         goto err;
 190     (void)BIO_flush(out);
 191
 192     message(out, "BN_lshift1");
 193     if (!test_lshift1(out))
 194         goto err;
 195     (void)BIO_flush(out);
 196
 197     message(out, "BN_lshift (fixed)");
 198     if (!test_lshift(out, ctx, BN_bin2bn(lst, sizeof(lst) - 1, NULL)))
 199         goto err;
 200     (void)BIO_flush(out);
 201
 202     message(out, "BN_lshift");
 203     if (!test_lshift(out, ctx, NULL))
 204         goto err;
 205     (void)BIO_flush(out);
 206
 207     message(out, "BN_rshift1");
 208     if (!test_rshift1(out))
 209         goto err;
 210     (void)BIO_flush(out);
 211
 212     message(out, "BN_rshift");
 213     if (!test_rshift(out, ctx))
 214         goto err;
 215     (void)BIO_flush(out);
 216
 217     message(out, "BN_sqr");
 218     if (!test_sqr(out, ctx))
 219         goto err;
 220     (void)BIO_flush(out);
 221
 222     message(out, "BN_mul");
 223     if (!test_mul(out))
 224         goto err;
 225     (void)BIO_flush(out);
 226
 227     message(out, "BN_div");
 228     if (!test_div(out, ctx))
 229         goto err;
 230     (void)BIO_flush(out);
 231
 232     message(out, "BN_div_word");
 233     if (!test_div_word(out))
 234         goto err;
 235     (void)BIO_flush(out);
 236
 237     message(out, "BN_div_recp");
 238     if (!test_div_recp(out, ctx))
 239         goto err;
 240     (void)BIO_flush(out);
 241
 242     message(out, "BN_mod");
 243     if (!test_mod(out, ctx))
 244         goto err;
 245     (void)BIO_flush(out);
 246
 247     message(out, "BN_mod_mul");
 248     if (!test_mod_mul(out, ctx))
 249         goto err;
 250     (void)BIO_flush(out);
 251
 252     message(out, "BN_mont");
 253     if (!test_mont(out, ctx))
 254         goto err;
 255     (void)BIO_flush(out);
 256
 257     message(out, "BN_mod_exp");
 258     if (!test_mod_exp(out, ctx))
 259         goto err;
 260     (void)BIO_flush(out);
 261
 262     message(out, "BN_mod_exp_mont_consttime");
 263     if (!test_mod_exp_mont_consttime(out, ctx))
 264         goto err;
 265     if (!test_mod_exp_mont5(out, ctx))
 266         goto err;
 267     (void)BIO_flush(out);
 268
 269     message(out, "BN_exp");
 270     if (!test_exp(out, ctx))
 271         goto err;
 272     (void)BIO_flush(out);
 273
 274     message(out, "BN_kronecker");
 275     if (!test_kron(out, ctx))
 276         goto err;
 277     (void)BIO_flush(out);
 278
 279     message(out, "BN_mod_sqrt");
 280     if (!test_sqrt(out, ctx))
 281         goto err;
 282     (void)BIO_flush(out);
 283
 284     message(out, "Small prime generation");
 285     if (!test_small_prime(out, ctx))
 286         goto err;
 287     (void)BIO_flush(out);
 288
 289 #ifdef OPENSSL_SYS_WIN32
 290     message(out, "Probable prime generation with coprimes disabled");
 291 #else
 292     message(out, "Probable prime generation with coprimes");
 293     if (!test_probable_prime_coprime(out, ctx))
 294         goto err;
 295 #endif
 296     (void)BIO_flush(out);
 297
 298 #ifndef OPENSSL_NO_EC2M
 299     message(out, "BN_GF2m_add");
 300     if (!test_gf2m_add(out))
 301         goto err;
 302     (void)BIO_flush(out);
 303
 304     message(out, "BN_GF2m_mod");
 305     if (!test_gf2m_mod(out))
 306         goto err;
 307     (void)BIO_flush(out);
 308
 309     message(out, "BN_GF2m_mod_mul");
 310     if (!test_gf2m_mod_mul(out, ctx))
 311         goto err;
 312     (void)BIO_flush(out);
 313
 314     message(out, "BN_GF2m_mod_sqr");
 315     if (!test_gf2m_mod_sqr(out, ctx))
 316         goto err;
 317     (void)BIO_flush(out);
 318
 319     message(out, "BN_GF2m_mod_inv");
 320     if (!test_gf2m_mod_inv(out, ctx))
 321         goto err;
 322     (void)BIO_flush(out);
 323
 324     message(out, "BN_GF2m_mod_div");
 325     if (!test_gf2m_mod_div(out, ctx))
 326         goto err;
 327     (void)BIO_flush(out);
 328
 329     message(out, "BN_GF2m_mod_exp");
 330     if (!test_gf2m_mod_exp(out, ctx))
 331         goto err;
 332     (void)BIO_flush(out);
 333
 334     message(out, "BN_GF2m_mod_sqrt");
 335     if (!test_gf2m_mod_sqrt(out, ctx))
 336         goto err;
 337     (void)BIO_flush(out);
 338
 339     message(out, "BN_GF2m_mod_solve_quad");
 340     if (!test_gf2m_mod_solve_quad(out, ctx))
 341         goto err;
 342     (void)BIO_flush(out);
 343 #endif
 344     BN_CTX_free(ctx);
 345     BIO_free(out);
 346
 347     EXIT(0);
 348  err:
 349     BIO_puts(out, "1\n");       /* make sure the Perl script fed by bc
 350                                  * notices the failure, see test_bn in
 351                                  * test/Makefile.ssl */
 352     (void)BIO_flush(out);
 353     ERR_load_crypto_strings();
 354     ERR_print_errors_fp(stderr);
 355     EXIT(1);
 356 }
 357
 358 int test_add(BIO *bp)
 359 {
 360     BIGNUM *a, *b, *c;
 361     int i;
 362
 363     a = BN_new();
 364     b = BN_new();
 365     c = BN_new();
 366
 367     BN_bntest_rand(a, 512, 0, 0);
 368     for (i = 0; i < num0; i++) {
 369         BN_bntest_rand(b, 450 + i, 0, 0);
 370         a->neg = rand_neg();
 371         b->neg = rand_neg();
 372         BN_add(c, a, b);
 373         if (bp != NULL) {
 374             if (!results) {
 375                 BN_print(bp, a);
 376                 BIO_puts(bp, " + ");
 377                 BN_print(bp, b);
 378                 BIO_puts(bp, " - ");
 379             }
 380             BN_print(bp, c);
 381             BIO_puts(bp, "\n");
 382         }
 383         a->neg = !a->neg;
 384         b->neg = !b->neg;
 385         BN_add(c, c, b);
 386         BN_add(c, c, a);
 387         if (!BN_is_zero(c)) {
 388             fprintf(stderr, "Add test failed!\n");
 389             return 0;
 390         }
 391     }
 392     BN_free(a);
 393     BN_free(b);
 394     BN_free(c);
 395     return (1);
 396 }
 397
 398 int test_sub(BIO *bp)
 399 {
 400     BIGNUM *a, *b, *c;
 401     int i;
 402
 403     a = BN_new();
 404     b = BN_new();
 405     c = BN_new();
 406
 407     for (i = 0; i < num0 + num1; i++) {
 408         if (i < num1) {
 409             BN_bntest_rand(a, 512, 0, 0);
 410             BN_copy(b, a);
 411             if (BN_set_bit(a, i) == 0)
 412                 return (0);
 413             BN_add_word(b, i);
 414         } else {
 415             BN_bntest_rand(b, 400 + i - num1, 0, 0);
 416             a->neg = rand_neg();
 417             b->neg = rand_neg();
 418         }
 419         BN_sub(c, a, b);
 420         if (bp != NULL) {
 421             if (!results) {
 422                 BN_print(bp, a);
 423                 BIO_puts(bp, " - ");
 424                 BN_print(bp, b);
 425                 BIO_puts(bp, " - ");
 426             }
 427             BN_print(bp, c);
 428             BIO_puts(bp, "\n");
 429         }
 430         BN_add(c, c, b);
 431         BN_sub(c, c, a);
 432         if (!BN_is_zero(c)) {
 433             fprintf(stderr, "Subtract test failed!\n");
 434             return 0;
 435         }
 436     }
 437     BN_free(a);
 438     BN_free(b);
 439     BN_free(c);
 440     return (1);
 441 }
 442
 443 int test_div(BIO *bp, BN_CTX *ctx)
 444 {
 445     BIGNUM *a, *b, *c, *d, *e;
 446     int i;
 447
 448     a = BN_new();
 449     b = BN_new();
 450     c = BN_new();
 451     d = BN_new();
 452     e = BN_new();
 453
 454     for (i = 0; i < num0 + num1; i++) {
 455         if (i < num1) {
 456             BN_bntest_rand(a, 400, 0, 0);
 457             BN_copy(b, a);
 458             BN_lshift(a, a, i);
 459             BN_add_word(a, i);
 460         } else
 461             BN_bntest_rand(b, 50 + 3 * (i - num1), 0, 0);
 462         a->neg = rand_neg();
 463         b->neg = rand_neg();
 464         BN_div(d, c, a, b, ctx);
 465         if (bp != NULL) {
 466             if (!results) {
 467                 BN_print(bp, a);
 468                 BIO_puts(bp, " / ");
 469                 BN_print(bp, b);
 470                 BIO_puts(bp, " - ");
 471             }
 472             BN_print(bp, d);
 473             BIO_puts(bp, "\n");
 474
 475             if (!results) {
 476                 BN_print(bp, a);
 477                 BIO_puts(bp, " % ");
 478                 BN_print(bp, b);
 479                 BIO_puts(bp, " - ");
 480             }
 481             BN_print(bp, c);
 482             BIO_puts(bp, "\n");
 483         }
 484         BN_mul(e, d, b, ctx);
 485         BN_add(d, e, c);
 486         BN_sub(d, d, a);
 487         if (!BN_is_zero(d)) {
 488             fprintf(stderr, "Division test failed!\n");
 489             return 0;
 490         }
 491     }
 492     BN_free(a);
 493     BN_free(b);
 494     BN_free(c);
 495     BN_free(d);
 496     BN_free(e);
 497     return (1);
 498 }
 499
 500 static void print_word(BIO *bp, BN_ULONG w)
 501 {
 502 #ifdef SIXTY_FOUR_BIT
 503     if (sizeof(w) > sizeof(unsigned long)) {
 504         unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w);
 505
 506         if (h)
 507             BIO_printf(bp, "%lX%08lX", h, l);
 508         else
 509             BIO_printf(bp, "%lX", l);
 510         return;
 511     }
 512 #endif
 513     BIO_printf(bp, BN_HEX_FMT1, w);
 514 }
 515
 516 int test_div_word(BIO *bp)
 517 {
 518     BIGNUM *a, *b;
 519     BN_ULONG r, s;
 520     int i;
 521
 522     a = BN_new();
 523     b = BN_new();
 524
 525     for (i = 0; i < num0; i++) {
 526         do {
 527             BN_bntest_rand(a, 512, -1, 0);
 528             BN_bntest_rand(b, BN_BITS2, -1, 0);
 529             s = b->d[0];
 530         } while (!s);
 531
 532         BN_copy(b, a);
 533         r = BN_div_word(b, s);
 534
 535         if (bp != NULL) {
 536             if (!results) {
 537                 BN_print(bp, a);
 538                 BIO_puts(bp, " / ");
 539                 print_word(bp, s);
 540                 BIO_puts(bp, " - ");
 541             }
 542             BN_print(bp, b);
 543             BIO_puts(bp, "\n");
 544
 545             if (!results) {
 546                 BN_print(bp, a);
 547                 BIO_puts(bp, " % ");
 548                 print_word(bp, s);
 549                 BIO_puts(bp, " - ");
 550             }
 551             print_word(bp, r);
 552             BIO_puts(bp, "\n");
 553         }
 554         BN_mul_word(b, s);
 555         BN_add_word(b, r);
 556         BN_sub(b, a, b);
 557         if (!BN_is_zero(b)) {
 558             fprintf(stderr, "Division (word) test failed!\n");
 559             return 0;
 560         }
 561     }
 562     BN_free(a);
 563     BN_free(b);
 564     return (1);
 565 }
 566
 567 int test_div_recp(BIO *bp, BN_CTX *ctx)
 568 {
 569     BIGNUM *a, *b, *c, *d, *e;
 570     BN_RECP_CTX *recp;
 571     int i;
 572
 573     recp = BN_RECP_CTX_new();
 574     a = BN_new();
 575     b = BN_new();
 576     c = BN_new();
 577     d = BN_new();
 578     e = BN_new();
 579
 580     for (i = 0; i < num0 + num1; i++) {
 581         if (i < num1) {
 582             BN_bntest_rand(a, 400, 0, 0);
 583             BN_copy(b, a);
 584             BN_lshift(a, a, i);
 585             BN_add_word(a, i);
 586         } else
 587             BN_bntest_rand(b, 50 + 3 * (i - num1), 0, 0);
 588         a->neg = rand_neg();
 589         b->neg = rand_neg();
 590         BN_RECP_CTX_set(recp, b, ctx);
 591         BN_div_recp(d, c, a, recp, ctx);
 592         if (bp != NULL) {
 593             if (!results) {
 594                 BN_print(bp, a);
 595                 BIO_puts(bp, " / ");
 596                 BN_print(bp, b);
 597                 BIO_puts(bp, " - ");
 598             }
 599             BN_print(bp, d);
 600             BIO_puts(bp, "\n");
 601
 602             if (!results) {
 603                 BN_print(bp, a);
 604                 BIO_puts(bp, " % ");
 605                 BN_print(bp, b);
 606                 BIO_puts(bp, " - ");
 607             }
 608             BN_print(bp, c);
 609             BIO_puts(bp, "\n");
 610         }
 611         BN_mul(e, d, b, ctx);
 612         BN_add(d, e, c);
 613         BN_sub(d, d, a);
 614         if (!BN_is_zero(d)) {
 615             fprintf(stderr, "Reciprocal division test failed!\n");
 616             fprintf(stderr, "a=");
 617             BN_print_fp(stderr, a);
 618             fprintf(stderr, "\nb=");
 619             BN_print_fp(stderr, b);
 620             fprintf(stderr, "\n");
 621             return 0;
 622         }
 623     }
 624     BN_free(a);
 625     BN_free(b);
 626     BN_free(c);
 627     BN_free(d);
 628     BN_free(e);
 629     BN_RECP_CTX_free(recp);
 630     return (1);
 631 }
 632
 633 int test_mul(BIO *bp)
 634 {
 635     BIGNUM *a, *b, *c, *d, *e;
 636     int i;
 637     BN_CTX *ctx;
 638
 639     ctx = BN_CTX_new();
 640     if (ctx == NULL)
 641         EXIT(1);
 642
 643     a = BN_new();
 644     b = BN_new();
 645     c = BN_new();
 646     d = BN_new();
 647     e = BN_new();
 648
 649     for (i = 0; i < num0 + num1; i++) {
 650         if (i <= num1) {
 651             BN_bntest_rand(a, 100, 0, 0);
 652             BN_bntest_rand(b, 100, 0, 0);
 653         } else
 654             BN_bntest_rand(b, i - num1, 0, 0);
 655         a->neg = rand_neg();
 656         b->neg = rand_neg();
 657         BN_mul(c, a, b, ctx);
 658         if (bp != NULL) {
 659             if (!results) {
 660                 BN_print(bp, a);
 661                 BIO_puts(bp, " * ");
 662                 BN_print(bp, b);
 663                 BIO_puts(bp, " - ");
 664             }
 665             BN_print(bp, c);
 666             BIO_puts(bp, "\n");
 667         }
 668         BN_div(d, e, c, a, ctx);
 669         BN_sub(d, d, b);
 670         if (!BN_is_zero(d) || !BN_is_zero(e)) {
 671             fprintf(stderr, "Multiplication test failed!\n");
 672             return 0;
 673         }
 674     }
 675     BN_free(a);
 676     BN_free(b);
 677     BN_free(c);
 678     BN_free(d);
 679     BN_free(e);
 680     BN_CTX_free(ctx);
 681     return (1);
 682 }
 683
 684 int test_sqr(BIO *bp, BN_CTX *ctx)
 685 {
 686     BIGNUM *a, *c, *d, *e;
 687     int i, ret = 0;
 688
 689     a = BN_new();
 690     c = BN_new();
 691     d = BN_new();
 692     e = BN_new();
 693     if (a == NULL || c == NULL || d == NULL || e == NULL) {
 694         goto err;
 695     }
 696
 697     for (i = 0; i < num0; i++) {
 698         BN_bntest_rand(a, 40 + i * 10, 0, 0);
 699         a->neg = rand_neg();
 700         BN_sqr(c, a, ctx);
 701         if (bp != NULL) {
 702             if (!results) {
 703                 BN_print(bp, a);
 704                 BIO_puts(bp, " * ");
 705                 BN_print(bp, a);
 706                 BIO_puts(bp, " - ");
 707             }
 708             BN_print(bp, c);
 709             BIO_puts(bp, "\n");
 710         }
 711         BN_div(d, e, c, a, ctx);
 712         BN_sub(d, d, a);
 713         if (!BN_is_zero(d) || !BN_is_zero(e)) {
 714             fprintf(stderr, "Square test failed!\n");
 715             goto err;
 716         }
 717     }
 718
 719     /* Regression test for a BN_sqr overflow bug. */
 720     BN_hex2bn(&a,
 721               "80000000000000008000000000000001"
 722               "FFFFFFFFFFFFFFFE0000000000000000");
 723     BN_sqr(c, a, ctx);
 724     if (bp != NULL) {
 725         if (!results) {
 726             BN_print(bp, a);
 727             BIO_puts(bp, " * ");
 728             BN_print(bp, a);
 729             BIO_puts(bp, " - ");
 730         }
 731         BN_print(bp, c);
 732         BIO_puts(bp, "\n");
 733     }
 734     BN_mul(d, a, a, ctx);
 735     if (BN_cmp(c, d)) {
 736         fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
 737                 "different results!\n");
 738         goto err;
 739     }
 740
 741     /* Regression test for a BN_sqr overflow bug. */
 742     BN_hex2bn(&a,
 743               "80000000000000000000000080000001"
 744               "FFFFFFFE000000000000000000000000");
 745     BN_sqr(c, a, ctx);
 746     if (bp != NULL) {
 747         if (!results) {
 748             BN_print(bp, a);
 749             BIO_puts(bp, " * ");
 750             BN_print(bp, a);
 751             BIO_puts(bp, " - ");
 752         }
 753         BN_print(bp, c);
 754         BIO_puts(bp, "\n");
 755     }
 756     BN_mul(d, a, a, ctx);
 757     if (BN_cmp(c, d)) {
 758         fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
 759                 "different results!\n");
 760         goto err;
 761     }
 762     ret = 1;
 763  err:
 764     BN_free(a);
 765     BN_free(c);
 766     BN_free(d);
 767     BN_free(e);
 768     return ret;
 769 }
 770
 771 int test_mont(BIO *bp, BN_CTX *ctx)
 772 {
 773     BIGNUM *a, *b, *c, *d, *A, *B;
 774     BIGNUM *n;
 775     int i;
 776     BN_MONT_CTX *mont;
 777
 778     a = BN_new();
 779     b = BN_new();
 780     c = BN_new();
 781     d = BN_new();
 782     A = BN_new();
 783     B = BN_new();
 784     n = BN_new();
 785
 786     mont = BN_MONT_CTX_new();
 787     if (mont == NULL)
 788         return 0;
 789
 790     BN_bntest_rand(a, 100, 0, 0);
 791     BN_bntest_rand(b, 100, 0, 0);
 792     for (i = 0; i < num2; i++) {
 793         int bits = (200 * (i + 1)) / num2;
 794
 795         if (bits == 0)
 796             continue;
 797         BN_bntest_rand(n, bits, 0, 1);
 798         BN_MONT_CTX_set(mont, n, ctx);
 799
 800         BN_nnmod(a, a, n, ctx);
 801         BN_nnmod(b, b, n, ctx);
 802
 803         BN_to_montgomery(A, a, mont, ctx);
 804         BN_to_montgomery(B, b, mont, ctx);
 805
 806         BN_mod_mul_montgomery(c, A, B, mont, ctx);
 807         BN_from_montgomery(A, c, mont, ctx);
 808         if (bp != NULL) {
 809             if (!results) {
 810                 BN_print(bp, a);
 811                 BIO_puts(bp, " * ");
 812                 BN_print(bp, b);
 813                 BIO_puts(bp, " % ");
 814                 BN_print(bp, &mont->N);
 815                 BIO_puts(bp, " - ");
 816             }
 817             BN_print(bp, A);
 818             BIO_puts(bp, "\n");
 819         }
 820         BN_mod_mul(d, a, b, n, ctx);
 821         BN_sub(d, d, A);
 822         if (!BN_is_zero(d)) {
 823             fprintf(stderr, "Montgomery multiplication test failed!\n");
 824             return 0;
 825         }
 826     }
 827     BN_MONT_CTX_free(mont);
 828     BN_free(a);
 829     BN_free(b);
 830     BN_free(c);
 831     BN_free(d);
 832     BN_free(A);
 833     BN_free(B);
 834     BN_free(n);
 835     return (1);
 836 }
 837
 838 int test_mod(BIO *bp, BN_CTX *ctx)
 839 {
 840     BIGNUM *a, *b, *c, *d, *e;
 841     int i;
 842
 843     a = BN_new();
 844     b = BN_new();
 845     c = BN_new();
 846     d = BN_new();
 847     e = BN_new();
 848
 849     BN_bntest_rand(a, 1024, 0, 0);
 850     for (i = 0; i < num0; i++) {
 851         BN_bntest_rand(b, 450 + i * 10, 0, 0);
 852         a->neg = rand_neg();
 853         b->neg = rand_neg();
 854         BN_mod(c, a, b, ctx);
 855         if (bp != NULL) {
 856             if (!results) {
 857                 BN_print(bp, a);
 858                 BIO_puts(bp, " % ");
 859                 BN_print(bp, b);
 860                 BIO_puts(bp, " - ");
 861             }
 862             BN_print(bp, c);
 863             BIO_puts(bp, "\n");
 864         }
 865         BN_div(d, e, a, b, ctx);
 866         BN_sub(e, e, c);
 867         if (!BN_is_zero(e)) {
 868             fprintf(stderr, "Modulo test failed!\n");
 869             return 0;
 870         }
 871     }
 872     BN_free(a);
 873     BN_free(b);
 874     BN_free(c);
 875     BN_free(d);
 876     BN_free(e);
 877     return (1);
 878 }
 879
 880 int test_mod_mul(BIO *bp, BN_CTX *ctx)
 881 {
 882     BIGNUM *a, *b, *c, *d, *e;
 883     int i, j;
 884
 885     a = BN_new();
 886     b = BN_new();
 887     c = BN_new();
 888     d = BN_new();
 889     e = BN_new();
 890
 891     for (j = 0; j < 3; j++) {
 892         BN_bntest_rand(c, 1024, 0, 0);
 893         for (i = 0; i < num0; i++) {
 894             BN_bntest_rand(a, 475 + i * 10, 0, 0);
 895             BN_bntest_rand(b, 425 + i * 11, 0, 0);
 896             a->neg = rand_neg();
 897             b->neg = rand_neg();
 898             if (!BN_mod_mul(e, a, b, c, ctx)) {
 899                 unsigned long l;
 900
 901                 while ((l = ERR_get_error()))
 902                     fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL));
 903                 EXIT(1);
 904             }
 905             if (bp != NULL) {
 906                 if (!results) {
 907                     BN_print(bp, a);
 908                     BIO_puts(bp, " * ");
 909                     BN_print(bp, b);
 910                     BIO_puts(bp, " % ");
 911                     BN_print(bp, c);
 912                     if ((a->neg ^ b->neg) && !BN_is_zero(e)) {
 913                         /*
 914                          * If (a*b) % c is negative, c must be added in order
 915                          * to obtain the normalized remainder (new with
 916                          * OpenSSL 0.9.7, previous versions of BN_mod_mul
 917                          * could generate negative results)
 918                          */
 919                         BIO_puts(bp, " + ");
 920                         BN_print(bp, c);
 921                     }
 922                     BIO_puts(bp, " - ");
 923                 }
 924                 BN_print(bp, e);
 925                 BIO_puts(bp, "\n");
 926             }
 927             BN_mul(d, a, b, ctx);
 928             BN_sub(d, d, e);
 929             BN_div(a, b, d, c, ctx);
 930             if (!BN_is_zero(b)) {
 931                 fprintf(stderr, "Modulo multiply test failed!\n");
 932                 ERR_print_errors_fp(stderr);
 933                 return 0;
 934             }
 935         }
 936     }
 937     BN_free(a);
 938     BN_free(b);
 939     BN_free(c);
 940     BN_free(d);
 941     BN_free(e);
 942     return (1);
 943 }
 944
 945 int test_mod_exp(BIO *bp, BN_CTX *ctx)
 946 {
 947     BIGNUM *a, *b, *c, *d, *e;
 948     int i;
 949
 950     a = BN_new();
 951     b = BN_new();
 952     c = BN_new();
 953     d = BN_new();
 954     e = BN_new();
 955
 956     BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
 957     for (i = 0; i < num2; i++) {
 958         BN_bntest_rand(a, 20 + i * 5, 0, 0);
 959         BN_bntest_rand(b, 2 + i, 0, 0);
 960
 961         if (!BN_mod_exp(d, a, b, c, ctx))
 962             return (0);
 963
 964         if (bp != NULL) {
 965             if (!results) {
 966                 BN_print(bp, a);
 967                 BIO_puts(bp, " ^ ");
 968                 BN_print(bp, b);
 969                 BIO_puts(bp, " % ");
 970                 BN_print(bp, c);
 971                 BIO_puts(bp, " - ");
 972             }
 973             BN_print(bp, d);
 974             BIO_puts(bp, "\n");
 975         }
 976         BN_exp(e, a, b, ctx);
 977         BN_sub(e, e, d);
 978         BN_div(a, b, e, c, ctx);
 979         if (!BN_is_zero(b)) {
 980             fprintf(stderr, "Modulo exponentiation test failed!\n");
 981             return 0;
 982         }
 983     }
 984     BN_free(a);
 985     BN_free(b);
 986     BN_free(c);
 987     BN_free(d);
 988     BN_free(e);
 989     return (1);
 990 }
 991
 992 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
 993 {
 994     BIGNUM *a, *b, *c, *d, *e;
 995     int i;
 996
 997     a = BN_new();
 998     b = BN_new();
 999     c = BN_new();
1000     d = BN_new();
1001     e = BN_new();
1002
1003     BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
1004     for (i = 0; i < num2; i++) {
1005         BN_bntest_rand(a, 20 + i * 5, 0, 0);
1006         BN_bntest_rand(b, 2 + i, 0, 0);
1007
1008         if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL))
1009             return (00);
1010
1011         if (bp != NULL) {
1012             if (!results) {
1013                 BN_print(bp, a);
1014                 BIO_puts(bp, " ^ ");
1015                 BN_print(bp, b);
1016                 BIO_puts(bp, " % ");
1017                 BN_print(bp, c);
1018                 BIO_puts(bp, " - ");
1019             }
1020             BN_print(bp, d);
1021             BIO_puts(bp, "\n");
1022         }
1023         BN_exp(e, a, b, ctx);
1024         BN_sub(e, e, d);
1025         BN_div(a, b, e, c, ctx);
1026         if (!BN_is_zero(b)) {
1027             fprintf(stderr, "Modulo exponentiation test failed!\n");
1028             return 0;
1029         }
1030     }
1031     BN_free(a);
1032     BN_free(b);
1033     BN_free(c);
1034     BN_free(d);
1035     BN_free(e);
1036     return (1);
1037 }
1038
1039 /*
1040  * Test constant-time modular exponentiation with 1024-bit inputs, which on
1041  * x86_64 cause a different code branch to be taken.
1042  */
1043 int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx)
1044 {
1045     BIGNUM *a, *p, *m, *d, *e;
1046
1047     BN_MONT_CTX *mont;
1048
1049     a = BN_new();
1050     p = BN_new();
1051     m = BN_new();
1052     d = BN_new();
1053     e = BN_new();
1054
1055     mont = BN_MONT_CTX_new();
1056
1057     BN_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
1058     /* Zero exponent */
1059     BN_bntest_rand(a, 1024, 0, 0);
1060     BN_zero(p);
1061     if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1062         return 0;
1063     if (!BN_is_one(d)) {
1064         fprintf(stderr, "Modular exponentiation test failed!\n");
1065         return 0;
1066     }
1067     /* Zero input */
1068     BN_bntest_rand(p, 1024, 0, 0);
1069     BN_zero(a);
1070     if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
1071         return 0;
1072     if (!BN_is_zero(d)) {
1073         fprintf(stderr, "Modular exponentiation test failed!\n");
1074         return 0;
1075     }
1076     /*
1077      * Craft an input whose Montgomery representation is 1, i.e., shorter
1078      * than the modulus m, in order to test the const time precomputation
1079      * scattering/gathering.
1080      */
1081     BN_one(a);
1082     BN_MONT_CTX_set(mont, m, ctx);
1083     if (!BN_from_montgomery(e, a, mont, ctx))
1084         return 0;
1085     if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1086         return 0;
1087     if (!BN_mod_exp_simple(a, e, p, m, ctx))
1088         return 0;
1089     if (BN_cmp(a, d) != 0) {
1090         fprintf(stderr, "Modular exponentiation test failed!\n");
1091         return 0;
1092     }
1093     /* Finally, some regular test vectors. */
1094     BN_bntest_rand(e, 1024, 0, 0);
1095     if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
1096         return 0;
1097     if (!BN_mod_exp_simple(a, e, p, m, ctx))
1098         return 0;
1099     if (BN_cmp(a, d) != 0) {
1100         fprintf(stderr, "Modular exponentiation test failed!\n");
1101         return 0;
1102     }
1103     BN_free(a);
1104     BN_free(p);
1105     BN_free(m);
1106     BN_free(d);
1107     BN_free(e);
1108     return (1);
1109 }
1110
1111 int test_exp(BIO *bp, BN_CTX *ctx)
1112 {
1113     BIGNUM *a, *b, *d, *e, *one;
1114     int i;
1115
1116     a = BN_new();
1117     b = BN_new();
1118     d = BN_new();
1119     e = BN_new();
1120     one = BN_new();
1121     BN_one(one);
1122
1123     for (i = 0; i < num2; i++) {
1124         BN_bntest_rand(a, 20 + i * 5, 0, 0);
1125         BN_bntest_rand(b, 2 + i, 0, 0);
1126
1127         if (BN_exp(d, a, b, ctx) <= 0)
1128             return (0);
1129
1130         if (bp != NULL) {
1131             if (!results) {
1132                 BN_print(bp, a);
1133                 BIO_puts(bp, " ^ ");
1134                 BN_print(bp, b);
1135                 BIO_puts(bp, " - ");
1136             }
1137             BN_print(bp, d);
1138             BIO_puts(bp, "\n");
1139         }
1140         BN_one(e);
1141         for (; !BN_is_zero(b); BN_sub(b, b, one))
1142             BN_mul(e, e, a, ctx);
1143         BN_sub(e, e, d);
1144         if (!BN_is_zero(e)) {
1145             fprintf(stderr, "Exponentiation test failed!\n");
1146             return 0;
1147         }
1148     }
1149     BN_free(a);
1150     BN_free(b);
1151     BN_free(d);
1152     BN_free(e);
1153     BN_free(one);
1154     return (1);
1155 }
1156
1157 #ifndef OPENSSL_NO_EC2M
1158 int test_gf2m_add(BIO *bp)
1159 {
1160     BIGNUM *a, *b, *c;
1161     int i, ret = 0;
1162
1163     a = BN_new();
1164     b = BN_new();
1165     c = BN_new();
1166
1167     for (i = 0; i < num0; i++) {
1168         BN_rand(a, 512, 0, 0);
1169         BN_copy(b, BN_value_one());
1170         a->neg = rand_neg();
1171         b->neg = rand_neg();
1172         BN_GF2m_add(c, a, b);
1173         /* Test that two added values have the correct parity. */
1174         if ((BN_is_odd(a) && BN_is_odd(c))
1175             || (!BN_is_odd(a) && !BN_is_odd(c))) {
1176             fprintf(stderr, "GF(2^m) addition test (a) failed!\n");
1177             goto err;
1178         }
1179         BN_GF2m_add(c, c, c);
1180         /* Test that c + c = 0. */
1181         if (!BN_is_zero(c)) {
1182             fprintf(stderr, "GF(2^m) addition test (b) failed!\n");
1183             goto err;
1184         }
1185     }
1186     ret = 1;
1187  err:
1188     BN_free(a);
1189     BN_free(b);
1190     BN_free(c);
1191     return ret;
1192 }
1193
1194 int test_gf2m_mod(BIO *bp)
1195 {
1196     BIGNUM *a, *b[2], *c, *d, *e;
1197     int i, j, ret = 0;
1198     int p0[] = { 163, 7, 6, 3, 0, -1 };
1199     int p1[] = { 193, 15, 0, -1 };
1200
1201     a = BN_new();
1202     b[0] = BN_new();
1203     b[1] = BN_new();
1204     c = BN_new();
1205     d = BN_new();
1206     e = BN_new();
1207
1208     BN_GF2m_arr2poly(p0, b[0]);
1209     BN_GF2m_arr2poly(p1, b[1]);
1210
1211     for (i = 0; i < num0; i++) {
1212         BN_bntest_rand(a, 1024, 0, 0);
1213         for (j = 0; j < 2; j++) {
1214             BN_GF2m_mod(c, a, b[j]);
1215             BN_GF2m_add(d, a, c);
1216             BN_GF2m_mod(e, d, b[j]);
1217             /* Test that a + (a mod p) mod p == 0. */
1218             if (!BN_is_zero(e)) {
1219                 fprintf(stderr, "GF(2^m) modulo test failed!\n");
1220                 goto err;
1221             }
1222         }
1223     }
1224     ret = 1;
1225  err:
1226     BN_free(a);
1227     BN_free(b[0]);
1228     BN_free(b[1]);
1229     BN_free(c);
1230     BN_free(d);
1231     BN_free(e);
1232     return ret;
1233 }
1234
1235 int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
1236 {
1237     BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
1238     int i, j, ret = 0;
1239     int p0[] = { 163, 7, 6, 3, 0, -1 };
1240     int p1[] = { 193, 15, 0, -1 };
1241
1242     a = BN_new();
1243     b[0] = BN_new();
1244     b[1] = BN_new();
1245     c = BN_new();
1246     d = BN_new();
1247     e = BN_new();
1248     f = BN_new();
1249     g = BN_new();
1250     h = BN_new();
1251
1252     BN_GF2m_arr2poly(p0, b[0]);
1253     BN_GF2m_arr2poly(p1, b[1]);
1254
1255     for (i = 0; i < num0; i++) {
1256         BN_bntest_rand(a, 1024, 0, 0);
1257         BN_bntest_rand(c, 1024, 0, 0);
1258         BN_bntest_rand(d, 1024, 0, 0);
1259         for (j = 0; j < 2; j++) {
1260             BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1261             BN_GF2m_add(f, a, d);
1262             BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1263             BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1264             BN_GF2m_add(f, e, g);
1265             BN_GF2m_add(f, f, h);
1266             /* Test that (a+d)*c = a*c + d*c. */
1267             if (!BN_is_zero(f)) {
1268                 fprintf(stderr,
1269                         "GF(2^m) modular multiplication test failed!\n");
1270                 goto err;
1271             }
1272         }
1273     }
1274     ret = 1;
1275  err:
1276     BN_free(a);
1277     BN_free(b[0]);
1278     BN_free(b[1]);
1279     BN_free(c);
1280     BN_free(d);
1281     BN_free(e);
1282     BN_free(f);
1283     BN_free(g);
1284     BN_free(h);
1285     return ret;
1286 }
1287
1288 int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
1289 {
1290     BIGNUM *a, *b[2], *c, *d;
1291     int i, j, ret = 0;
1292     int p0[] = { 163, 7, 6, 3, 0, -1 };
1293     int p1[] = { 193, 15, 0, -1 };
1294
1295     a = BN_new();
1296     b[0] = BN_new();
1297     b[1] = BN_new();
1298     c = BN_new();
1299     d = BN_new();
1300
1301     BN_GF2m_arr2poly(p0, b[0]);
1302     BN_GF2m_arr2poly(p1, b[1]);
1303
1304     for (i = 0; i < num0; i++) {
1305         BN_bntest_rand(a, 1024, 0, 0);
1306         for (j = 0; j < 2; j++) {
1307             BN_GF2m_mod_sqr(c, a, b[j], ctx);
1308             BN_copy(d, a);
1309             BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1310             BN_GF2m_add(d, c, d);
1311             /* Test that a*a = a^2. */
1312             if (!BN_is_zero(d)) {
1313                 fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
1314                 goto err;
1315             }
1316         }
1317     }
1318     ret = 1;
1319  err:
1320     BN_free(a);
1321     BN_free(b[0]);
1322     BN_free(b[1]);
1323     BN_free(c);
1324     BN_free(d);
1325     return ret;
1326 }
1327
1328 int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
1329 {
1330     BIGNUM *a, *b[2], *c, *d;
1331     int i, j, ret = 0;
1332     int p0[] = { 163, 7, 6, 3, 0, -1 };
1333     int p1[] = { 193, 15, 0, -1 };
1334
1335     a = BN_new();
1336     b[0] = BN_new();
1337     b[1] = BN_new();
1338     c = BN_new();
1339     d = BN_new();
1340
1341     BN_GF2m_arr2poly(p0, b[0]);
1342     BN_GF2m_arr2poly(p1, b[1]);
1343
1344     for (i = 0; i < num0; i++) {
1345         BN_bntest_rand(a, 512, 0, 0);
1346         for (j = 0; j < 2; j++) {
1347             BN_GF2m_mod_inv(c, a, b[j], ctx);
1348             BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1349             /* Test that ((1/a)*a) = 1. */
1350             if (!BN_is_one(d)) {
1351                 fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
1352                 goto err;
1353             }
1354         }
1355     }
1356     ret = 1;
1357  err:
1358     BN_free(a);
1359     BN_free(b[0]);
1360     BN_free(b[1]);
1361     BN_free(c);
1362     BN_free(d);
1363     return ret;
1364 }
1365
1366 int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
1367 {
1368     BIGNUM *a, *b[2], *c, *d, *e, *f;
1369     int i, j, ret = 0;
1370     int p0[] = { 163, 7, 6, 3, 0, -1 };
1371     int p1[] = { 193, 15, 0, -1 };
1372
1373     a = BN_new();
1374     b[0] = BN_new();
1375     b[1] = BN_new();
1376     c = BN_new();
1377     d = BN_new();
1378     e = BN_new();
1379     f = BN_new();
1380
1381     BN_GF2m_arr2poly(p0, b[0]);
1382     BN_GF2m_arr2poly(p1, b[1]);
1383
1384     for (i = 0; i < num0; i++) {
1385         BN_bntest_rand(a, 512, 0, 0);
1386         BN_bntest_rand(c, 512, 0, 0);
1387         for (j = 0; j < 2; j++) {
1388             BN_GF2m_mod_div(d, a, c, b[j], ctx);
1389             BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1390             BN_GF2m_mod_div(f, a, e, b[j], ctx);
1391             /* Test that ((a/c)*c)/a = 1. */
1392             if (!BN_is_one(f)) {
1393                 fprintf(stderr, "GF(2^m) modular division test failed!\n");
1394                 goto err;
1395             }
1396         }
1397     }
1398     ret = 1;
1399  err:
1400     BN_free(a);
1401     BN_free(b[0]);
1402     BN_free(b[1]);
1403     BN_free(c);
1404     BN_free(d);
1405     BN_free(e);
1406     BN_free(f);
1407     return ret;
1408 }
1409
1410 int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
1411 {
1412     BIGNUM *a, *b[2], *c, *d, *e, *f;
1413     int i, j, ret = 0;
1414     int p0[] = { 163, 7, 6, 3, 0, -1 };
1415     int p1[] = { 193, 15, 0, -1 };
1416
1417     a = BN_new();
1418     b[0] = BN_new();
1419     b[1] = BN_new();
1420     c = BN_new();
1421     d = BN_new();
1422     e = BN_new();
1423     f = BN_new();
1424
1425     BN_GF2m_arr2poly(p0, b[0]);
1426     BN_GF2m_arr2poly(p1, b[1]);
1427
1428     for (i = 0; i < num0; i++) {
1429         BN_bntest_rand(a, 512, 0, 0);
1430         BN_bntest_rand(c, 512, 0, 0);
1431         BN_bntest_rand(d, 512, 0, 0);
1432         for (j = 0; j < 2; j++) {
1433             BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1434             BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1435             BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1436             BN_add(f, c, d);
1437             BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1438             BN_GF2m_add(f, e, f);
1439             /* Test that a^(c+d)=a^c*a^d. */
1440             if (!BN_is_zero(f)) {
1441                 fprintf(stderr,
1442                         "GF(2^m) modular exponentiation test failed!\n");
1443                 goto err;
1444             }
1445         }
1446     }
1447     ret = 1;
1448  err:
1449     BN_free(a);
1450     BN_free(b[0]);
1451     BN_free(b[1]);
1452     BN_free(c);
1453     BN_free(d);
1454     BN_free(e);
1455     BN_free(f);
1456     return ret;
1457 }
1458
1459 int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
1460 {
1461     BIGNUM *a, *b[2], *c, *d, *e, *f;
1462     int i, j, ret = 0;
1463     int p0[] = { 163, 7, 6, 3, 0, -1 };
1464     int p1[] = { 193, 15, 0, -1 };
1465
1466     a = BN_new();
1467     b[0] = BN_new();
1468     b[1] = BN_new();
1469     c = BN_new();
1470     d = BN_new();
1471     e = BN_new();
1472     f = BN_new();
1473
1474     BN_GF2m_arr2poly(p0, b[0]);
1475     BN_GF2m_arr2poly(p1, b[1]);
1476
1477     for (i = 0; i < num0; i++) {
1478         BN_bntest_rand(a, 512, 0, 0);
1479         for (j = 0; j < 2; j++) {
1480             BN_GF2m_mod(c, a, b[j]);
1481             BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1482             BN_GF2m_mod_sqr(e, d, b[j], ctx);
1483             BN_GF2m_add(f, c, e);
1484             /* Test that d^2 = a, where d = sqrt(a). */
1485             if (!BN_is_zero(f)) {
1486                 fprintf(stderr, "GF(2^m) modular square root test failed!\n");
1487                 goto err;
1488             }
1489         }
1490     }
1491     ret = 1;
1492  err:
1493     BN_free(a);
1494     BN_free(b[0]);
1495     BN_free(b[1]);
1496     BN_free(c);
1497     BN_free(d);
1498     BN_free(e);
1499     BN_free(f);
1500     return ret;
1501 }
1502
1503 int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
1504 {
1505     BIGNUM *a, *b[2], *c, *d, *e;
1506     int i, j, s = 0, t, ret = 0;
1507     int p0[] = { 163, 7, 6, 3, 0, -1 };
1508     int p1[] = { 193, 15, 0, -1 };
1509
1510     a = BN_new();
1511     b[0] = BN_new();
1512     b[1] = BN_new();
1513     c = BN_new();
1514     d = BN_new();
1515     e = BN_new();
1516
1517     BN_GF2m_arr2poly(p0, b[0]);
1518     BN_GF2m_arr2poly(p1, b[1]);
1519
1520     for (i = 0; i < num0; i++) {
1521         BN_bntest_rand(a, 512, 0, 0);
1522         for (j = 0; j < 2; j++) {
1523             t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1524             if (t) {
1525                 s++;
1526                 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1527                 BN_GF2m_add(d, c, d);
1528                 BN_GF2m_mod(e, a, b[j]);
1529                 BN_GF2m_add(e, e, d);
1530                 /*
1531                  * Test that solution of quadratic c satisfies c^2 + c = a.
1532                  */
1533                 if (!BN_is_zero(e)) {
1534                     fprintf(stderr,
1535                             "GF(2^m) modular solve quadratic test failed!\n");
1536                     goto err;
1537                 }
1538
1539             }
1540         }
1541     }
1542     if (s == 0) {
1543         fprintf(stderr,
1544                 "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
1545                 num0);
1546         fprintf(stderr,
1547                 "this is very unlikely and probably indicates an error.\n");
1548         goto err;
1549     }
1550     ret = 1;
1551  err:
1552     BN_free(a);
1553     BN_free(b[0]);
1554     BN_free(b[1]);
1555     BN_free(c);
1556     BN_free(d);
1557     BN_free(e);
1558     return ret;
1559 }
1560 #endif
1561 static int genprime_cb(int p, int n, BN_GENCB *arg)
1562 {
1563     char c = '*';
1564
1565     if (p == 0)
1566         c = '.';
1567     if (p == 1)
1568         c = '+';
1569     if (p == 2)
1570         c = '*';
1571     if (p == 3)
1572         c = '\n';
1573     putc(c, stderr);
1574     fflush(stderr);
1575     return 1;
1576 }
1577
1578 int test_kron(BIO *bp, BN_CTX *ctx)
1579 {
1580     BN_GENCB cb;
1581     BIGNUM *a, *b, *r, *t;
1582     int i;
1583     int legendre, kronecker;
1584     int ret = 0;
1585
1586     a = BN_new();
1587     b = BN_new();
1588     r = BN_new();
1589     t = BN_new();
1590     if (a == NULL || b == NULL || r == NULL || t == NULL)
1591         goto err;
1592
1593     BN_GENCB_set(&cb, genprime_cb, NULL);
1594
1595     /*
1596      * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
1597      * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
1598      * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
1599      * generate a random prime b and compare these values for a number of
1600      * random a's.  (That is, we run the Solovay-Strassen primality test to
1601      * confirm that b is prime, except that we don't want to test whether b
1602      * is prime but whether BN_kronecker works.)
1603      */
1604
1605     if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
1606         goto err;
1607     b->neg = rand_neg();
1608     putc('\n', stderr);
1609
1610     for (i = 0; i < num0; i++) {
1611         if (!BN_bntest_rand(a, 512, 0, 0))
1612             goto err;
1613         a->neg = rand_neg();
1614
1615         /* t := (|b|-1)/2  (note that b is odd) */
1616         if (!BN_copy(t, b))
1617             goto err;
1618         t->neg = 0;
1619         if (!BN_sub_word(t, 1))
1620             goto err;
1621         if (!BN_rshift1(t, t))
1622             goto err;
1623         /* r := a^t mod b */
1624         b->neg = 0;
1625
1626         if (!BN_mod_exp_recp(r, a, t, b, ctx))
1627             goto err;
1628         b->neg = 1;
1629
1630         if (BN_is_word(r, 1))
1631             legendre = 1;
1632         else if (BN_is_zero(r))
1633             legendre = 0;
1634         else {
1635             if (!BN_add_word(r, 1))
1636                 goto err;
1637             if (0 != BN_ucmp(r, b)) {
1638                 fprintf(stderr, "Legendre symbol computation failed\n");
1639                 goto err;
1640             }
1641             legendre = -1;
1642         }
1643
1644         kronecker = BN_kronecker(a, b, ctx);
1645         if (kronecker < -1)
1646             goto err;
1647         /* we actually need BN_kronecker(a, |b|) */
1648         if (a->neg && b->neg)
1649             kronecker = -kronecker;
1650
1651         if (legendre != kronecker) {
1652             fprintf(stderr, "legendre != kronecker; a = ");
1653             BN_print_fp(stderr, a);
1654             fprintf(stderr, ", b = ");
1655             BN_print_fp(stderr, b);
1656             fprintf(stderr, "\n");
1657             goto err;
1658         }
1659
1660         putc('.', stderr);
1661         fflush(stderr);
1662     }
1663
1664     putc('\n', stderr);
1665     fflush(stderr);
1666     ret = 1;
1667  err:
1668     BN_free(a);
1669     BN_free(b);
1670     BN_free(r);
1671     BN_free(t);
1672     return ret;
1673 }
1674
1675 int test_sqrt(BIO *bp, BN_CTX *ctx)
1676 {
1677     BN_GENCB cb;
1678     BIGNUM *a, *p, *r;
1679     int i, j;
1680     int ret = 0;
1681
1682     a = BN_new();
1683     p = BN_new();
1684     r = BN_new();
1685     if (a == NULL || p == NULL || r == NULL)
1686         goto err;
1687
1688     BN_GENCB_set(&cb, genprime_cb, NULL);
1689
1690     for (i = 0; i < 16; i++) {
1691         if (i < 8) {
1692             unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1693
1694             if (!BN_set_word(p, primes[i]))
1695                 goto err;
1696         } else {
1697             if (!BN_set_word(a, 32))
1698                 goto err;
1699             if (!BN_set_word(r, 2 * i + 1))
1700                 goto err;
1701
1702             if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb))
1703                 goto err;
1704             putc('\n', stderr);
1705         }
1706         p->neg = rand_neg();
1707
1708         for (j = 0; j < num2; j++) {
1709             /*
1710              * construct 'a' such that it is a square modulo p, but in
1711              * general not a proper square and not reduced modulo p
1712              */
1713             if (!BN_bntest_rand(r, 256, 0, 3))
1714                 goto err;
1715             if (!BN_nnmod(r, r, p, ctx))
1716                 goto err;
1717             if (!BN_mod_sqr(r, r, p, ctx))
1718                 goto err;
1719             if (!BN_bntest_rand(a, 256, 0, 3))
1720                 goto err;
1721             if (!BN_nnmod(a, a, p, ctx))
1722                 goto err;
1723             if (!BN_mod_sqr(a, a, p, ctx))
1724                 goto err;
1725             if (!BN_mul(a, a, r, ctx))
1726                 goto err;
1727             if (rand_neg())
1728                 if (!BN_sub(a, a, p))
1729                     goto err;
1730
1731             if (!BN_mod_sqrt(r, a, p, ctx))
1732                 goto err;
1733             if (!BN_mod_sqr(r, r, p, ctx))
1734                 goto err;
1735
1736             if (!BN_nnmod(a, a, p, ctx))
1737                 goto err;
1738
1739             if (BN_cmp(a, r) != 0) {
1740                 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1741                 BN_print_fp(stderr, a);
1742                 fprintf(stderr, ", r = ");
1743                 BN_print_fp(stderr, r);
1744                 fprintf(stderr, ", p = ");
1745                 BN_print_fp(stderr, p);
1746                 fprintf(stderr, "\n");
1747                 goto err;
1748             }
1749
1750             putc('.', stderr);
1751             fflush(stderr);
1752         }
1753
1754         putc('\n', stderr);
1755         fflush(stderr);
1756     }
1757     ret = 1;
1758  err:
1759     BN_free(a);
1760     BN_free(p);
1761     BN_free(r);
1762     return ret;
1763 }
1764
1765 int test_small_prime(BIO *bp, BN_CTX *ctx)
1766 {
1767     static const int bits = 10;
1768     int ret = 0;
1769     BIGNUM *r;
1770
1771     r = BN_new();
1772     if (!BN_generate_prime_ex(r, bits, 0, NULL, NULL, NULL))
1773         goto err;
1774     if (BN_num_bits(r) != bits) {
1775         BIO_printf(bp, "Expected %d bit prime, got %d bit number\n", bits,
1776                    BN_num_bits(r));
1777         goto err;
1778     }
1779
1780     ret = 1;
1781
1782  err:
1783     BN_clear_free(r);
1784     return ret;
1785 }
1786
1787 #ifndef OPENSSL_SYS_WIN32
1788 int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx)
1789 {
1790     int i, j, ret = 0;
1791     BIGNUM *r;
1792     BN_ULONG primes[5] = { 2, 3, 5, 7, 11 };
1793
1794     r = BN_new();
1795
1796     for (i = 0; i < 1000; i++) {
1797         if (!bn_probable_prime_dh_coprime(r, 1024, ctx))
1798             goto err;
1799
1800         for (j = 0; j < 5; j++) {
1801             if (BN_mod_word(r, primes[j]) == 0) {
1802                 BIO_printf(bp, "Number generated is not coprime to "
1803                            BN_DEC_FMT1 ":\n", primes[j]);
1804                 BN_print_fp(stdout, r);
1805                 BIO_printf(bp, "\n");
1806                 goto err;
1807             }
1808         }
1809     }
1810
1811     ret = 1;
1812
1813  err:
1814     BN_clear_free(r);
1815     return ret;
1816 }
1817 #endif
1818 int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_)
1819 {
1820     BIGNUM *a, *b, *c, *d;
1821     int i;
1822
1823     b = BN_new();
1824     c = BN_new();
1825     d = BN_new();
1826     BN_one(c);
1827
1828     if (a_)
1829         a = a_;
1830     else {
1831         a = BN_new();
1832         BN_bntest_rand(a, 200, 0, 0);
1833         a->neg = rand_neg();
1834     }
1835     for (i = 0; i < num0; i++) {
1836         BN_lshift(b, a, i + 1);
1837         BN_add(c, c, c);
1838         if (bp != NULL) {
1839             if (!results) {
1840                 BN_print(bp, a);
1841                 BIO_puts(bp, " * ");
1842                 BN_print(bp, c);
1843                 BIO_puts(bp, " - ");
1844             }
1845             BN_print(bp, b);
1846             BIO_puts(bp, "\n");
1847         }
1848         BN_mul(d, a, c, ctx);
1849         BN_sub(d, d, b);
1850         if (!BN_is_zero(d)) {
1851             fprintf(stderr, "Left shift test failed!\n");
1852             fprintf(stderr, "a=");
1853             BN_print_fp(stderr, a);
1854             fprintf(stderr, "\nb=");
1855             BN_print_fp(stderr, b);
1856             fprintf(stderr, "\nc=");
1857             BN_print_fp(stderr, c);
1858             fprintf(stderr, "\nd=");
1859             BN_print_fp(stderr, d);
1860             fprintf(stderr, "\n");
1861             return 0;
1862         }
1863     }
1864     BN_free(a);
1865     BN_free(b);
1866     BN_free(c);
1867     BN_free(d);
1868     return (1);
1869 }
1870
1871 int test_lshift1(BIO *bp)
1872 {
1873     BIGNUM *a, *b, *c;
1874     int i;
1875
1876     a = BN_new();
1877     b = BN_new();
1878     c = BN_new();
1879
1880     BN_bntest_rand(a, 200, 0, 0);
1881     a->neg = rand_neg();
1882     for (i = 0; i < num0; i++) {
1883         BN_lshift1(b, a);
1884         if (bp != NULL) {
1885             if (!results) {
1886                 BN_print(bp, a);
1887                 BIO_puts(bp, " * 2");
1888                 BIO_puts(bp, " - ");
1889             }
1890             BN_print(bp, b);
1891             BIO_puts(bp, "\n");
1892         }
1893         BN_add(c, a, a);
1894         BN_sub(a, b, c);
1895         if (!BN_is_zero(a)) {
1896             fprintf(stderr, "Left shift one test failed!\n");
1897             return 0;
1898         }
1899
1900         BN_copy(a, b);
1901     }
1902     BN_free(a);
1903     BN_free(b);
1904     BN_free(c);
1905     return (1);
1906 }
1907
1908 int test_rshift(BIO *bp, BN_CTX *ctx)
1909 {
1910     BIGNUM *a, *b, *c, *d, *e;
1911     int i;
1912
1913     a = BN_new();
1914     b = BN_new();
1915     c = BN_new();
1916     d = BN_new();
1917     e = BN_new();
1918     BN_one(c);
1919
1920     BN_bntest_rand(a, 200, 0, 0);
1921     a->neg = rand_neg();
1922     for (i = 0; i < num0; i++) {
1923         BN_rshift(b, a, i + 1);
1924         BN_add(c, c, c);
1925         if (bp != NULL) {
1926             if (!results) {
1927                 BN_print(bp, a);
1928                 BIO_puts(bp, " / ");
1929                 BN_print(bp, c);
1930                 BIO_puts(bp, " - ");
1931             }
1932             BN_print(bp, b);
1933             BIO_puts(bp, "\n");
1934         }
1935         BN_div(d, e, a, c, ctx);
1936         BN_sub(d, d, b);
1937         if (!BN_is_zero(d)) {
1938             fprintf(stderr, "Right shift test failed!\n");
1939             return 0;
1940         }
1941     }
1942     BN_free(a);
1943     BN_free(b);
1944     BN_free(c);
1945     BN_free(d);
1946     BN_free(e);
1947     return (1);
1948 }
1949
1950 int test_rshift1(BIO *bp)
1951 {
1952     BIGNUM *a, *b, *c;
1953     int i;
1954
1955     a = BN_new();
1956     b = BN_new();
1957     c = BN_new();
1958
1959     BN_bntest_rand(a, 200, 0, 0);
1960     a->neg = rand_neg();
1961     for (i = 0; i < num0; i++) {
1962         BN_rshift1(b, a);
1963         if (bp != NULL) {
1964             if (!results) {
1965                 BN_print(bp, a);
1966                 BIO_puts(bp, " / 2");
1967                 BIO_puts(bp, " - ");
1968             }
1969             BN_print(bp, b);
1970             BIO_puts(bp, "\n");
1971         }
1972         BN_sub(c, a, b);
1973         BN_sub(c, c, b);
1974         if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) {
1975             fprintf(stderr, "Right shift one test failed!\n");
1976             return 0;
1977         }
1978         BN_copy(a, b);
1979     }
1980     BN_free(a);
1981     BN_free(b);
1982     BN_free(c);
1983     return (1);
1984 }
1985
1986 int rand_neg(void)
1987 {
1988     static unsigned int neg = 0;
1989     static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
1990
1991     return (sign[(neg++) % 8]);
1992 }