crypto/bn/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 /* Until the key-gen callbacks are modified to use newer prototypes, we allow
  73  * deprecated functions for openssl-internal code */
  74 #ifdef OPENSSL_NO_DEPRECATED
  75 #undef OPENSSL_NO_DEPRECATED
  76 #endif
  77
  78 #include <stdio.h>
  79 #include <stdlib.h>
  80 #include <string.h>
  81
  82 #include "e_os.h"
  83
  84 #include <openssl/bio.h>
  85 #include <openssl/bn.h>
  86 #include <openssl/rand.h>
  87 #include <openssl/x509.h>
  88 #include <openssl/err.h>
  89
  90 const int num0 = 100; /* number of tests */
  91 const int num1 = 50;  /* additional tests for some functions */
  92 const int num2 = 5;   /* number of tests for slow functions */
  93
  94 int test_add(BIO *bp);
  95 int test_sub(BIO *bp);
  96 int test_lshift1(BIO *bp);
  97 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
  98 int test_rshift1(BIO *bp);
  99 int test_rshift(BIO *bp,BN_CTX *ctx);
 100 int test_div(BIO *bp,BN_CTX *ctx);
 101 int test_div_word(BIO *bp);
 102 int test_div_recp(BIO *bp,BN_CTX *ctx);
 103 int test_mul(BIO *bp);
 104 int test_sqr(BIO *bp,BN_CTX *ctx);
 105 int test_mont(BIO *bp,BN_CTX *ctx);
 106 int test_mod(BIO *bp,BN_CTX *ctx);
 107 int test_mod_mul(BIO *bp,BN_CTX *ctx);
 108 int test_mod_exp(BIO *bp,BN_CTX *ctx);
 109 int test_mod_exp_mont_consttime(BIO *bp,BN_CTX *ctx);
 110 int test_exp(BIO *bp,BN_CTX *ctx);
 111 int test_gf2m_add(BIO *bp);
 112 int test_gf2m_mod(BIO *bp);
 113 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
 114 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
 115 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
 116 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
 117 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
 118 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
 119 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
 120 int test_kron(BIO *bp,BN_CTX *ctx);
 121 int test_sqrt(BIO *bp,BN_CTX *ctx);
 122 int rand_neg(void);
 123 static int results=0;
 124
 125 static unsigned char lst[]="\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[] = "string to make the random number generator think it has entropy";
 129
 130 static void message(BIO *out, char *m)
 131         {
 132         fprintf(stderr, "test %s\n", m);
 133         BIO_puts(out, "print \"test ");
 134         BIO_puts(out, m);
 135         BIO_puts(out, "\\n\"\n");
 136         }
 137
 138 int main(int argc, char *argv[])
 139         {
 140         BN_CTX *ctx;
 141         BIO *out;
 142         char *outfile=NULL;
 143
 144         results = 0;
 145
 146         RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
 147
 148         argc--;
 149         argv++;
 150         while (argc >= 1)
 151                 {
 152                 if (strcmp(*argv,"-results") == 0)
 153                         results=1;
 154                 else if (strcmp(*argv,"-out") == 0)
 155                         {
 156                         if (--argc < 1) break;
 157                         outfile= *(++argv);
 158                         }
 159                 argc--;
 160                 argv++;
 161                 }
 162
 163
 164         ctx=BN_CTX_new();
 165         if (ctx == NULL) EXIT(1);
 166
 167         out=BIO_new(BIO_s_file());
 168         if (out == NULL) EXIT(1);
 169         if (outfile == NULL)
 170                 {
 171                 BIO_set_fp(out,stdout,BIO_NOCLOSE);
 172                 }
 173         else
 174                 {
 175                 if (!BIO_write_filename(out,outfile))
 176                         {
 177                         perror(outfile);
 178                         EXIT(1);
 179                         }
 180                 }
 181
 182         if (!results)
 183                 BIO_puts(out,"obase=16\nibase=16\n");
 184
 185         message(out,"BN_add");
 186         if (!test_add(out)) goto err;
 187         (void)BIO_flush(out);
 188
 189         message(out,"BN_sub");
 190         if (!test_sub(out)) goto err;
 191         (void)BIO_flush(out);
 192
 193         message(out,"BN_lshift1");
 194         if (!test_lshift1(out)) 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)) goto err;
 204         (void)BIO_flush(out);
 205
 206         message(out,"BN_rshift1");
 207         if (!test_rshift1(out)) goto err;
 208         (void)BIO_flush(out);
 209
 210         message(out,"BN_rshift");
 211         if (!test_rshift(out,ctx)) goto err;
 212         (void)BIO_flush(out);
 213
 214         message(out,"BN_sqr");
 215         if (!test_sqr(out,ctx)) goto err;
 216         (void)BIO_flush(out);
 217
 218         message(out,"BN_mul");
 219         if (!test_mul(out)) goto err;
 220         (void)BIO_flush(out);
 221
 222         message(out,"BN_div");
 223         if (!test_div(out,ctx)) goto err;
 224         (void)BIO_flush(out);
 225
 226         message(out,"BN_div_word");
 227         if (!test_div_word(out)) goto err;
 228         (void)BIO_flush(out);
 229
 230         message(out,"BN_div_recp");
 231         if (!test_div_recp(out,ctx)) goto err;
 232         (void)BIO_flush(out);
 233
 234         message(out,"BN_mod");
 235         if (!test_mod(out,ctx)) goto err;
 236         (void)BIO_flush(out);
 237
 238         message(out,"BN_mod_mul");
 239         if (!test_mod_mul(out,ctx)) goto err;
 240         (void)BIO_flush(out);
 241
 242         message(out,"BN_mont");
 243         if (!test_mont(out,ctx)) goto err;
 244         (void)BIO_flush(out);
 245
 246         message(out,"BN_mod_exp");
 247         if (!test_mod_exp(out,ctx)) goto err;
 248         (void)BIO_flush(out);
 249
 250         message(out,"BN_mod_exp_mont_consttime");
 251         if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
 252         (void)BIO_flush(out);
 253
 254         message(out,"BN_exp");
 255         if (!test_exp(out,ctx)) goto err;
 256         (void)BIO_flush(out);
 257
 258         message(out,"BN_kronecker");
 259         if (!test_kron(out,ctx)) goto err;
 260         (void)BIO_flush(out);
 261
 262         message(out,"BN_mod_sqrt");
 263         if (!test_sqrt(out,ctx)) goto err;
 264         (void)BIO_flush(out);
 265
 266         message(out,"BN_GF2m_add");
 267         if (!test_gf2m_add(out)) goto err;
 268         (void)BIO_flush(out);
 269
 270         message(out,"BN_GF2m_mod");
 271         if (!test_gf2m_mod(out)) goto err;
 272         (void)BIO_flush(out);
 273
 274         message(out,"BN_GF2m_mod_mul");
 275         if (!test_gf2m_mod_mul(out,ctx)) goto err;
 276         (void)BIO_flush(out);
 277
 278         message(out,"BN_GF2m_mod_sqr");
 279         if (!test_gf2m_mod_sqr(out,ctx)) goto err;
 280         (void)BIO_flush(out);
 281
 282         message(out,"BN_GF2m_mod_inv");
 283         if (!test_gf2m_mod_inv(out,ctx)) goto err;
 284         (void)BIO_flush(out);
 285
 286         message(out,"BN_GF2m_mod_div");
 287         if (!test_gf2m_mod_div(out,ctx)) goto err;
 288         (void)BIO_flush(out);
 289
 290         message(out,"BN_GF2m_mod_exp");
 291         if (!test_gf2m_mod_exp(out,ctx)) goto err;
 292         (void)BIO_flush(out);
 293
 294         message(out,"BN_GF2m_mod_sqrt");
 295         if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
 296         (void)BIO_flush(out);
 297
 298         message(out,"BN_GF2m_mod_solve_quad");
 299         if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
 300         (void)BIO_flush(out);
 301
 302         BN_CTX_free(ctx);
 303         BIO_free(out);
 304
 305 /**/
 306         EXIT(0);
 307 err:
 308         BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
 309                               * the failure, see test_bn in test/Makefile.ssl*/
 310         (void)BIO_flush(out);
 311         ERR_load_crypto_strings();
 312         ERR_print_errors_fp(stderr);
 313         EXIT(1);
 314         return(1);
 315         }
 316
 317 int test_add(BIO *bp)
 318         {
 319         BIGNUM a,b,c;
 320         int i;
 321
 322         BN_init(&a);
 323         BN_init(&b);
 324         BN_init(&c);
 325
 326         BN_bntest_rand(&a,512,0,0);
 327         for (i=0; i<num0; i++)
 328                 {
 329                 BN_bntest_rand(&b,450+i,0,0);
 330                 a.neg=rand_neg();
 331                 b.neg=rand_neg();
 332                 BN_add(&c,&a,&b);
 333                 if (bp != NULL)
 334                         {
 335                         if (!results)
 336                                 {
 337                                 BN_print(bp,&a);
 338                                 BIO_puts(bp," + ");
 339                                 BN_print(bp,&b);
 340                                 BIO_puts(bp," - ");
 341                                 }
 342                         BN_print(bp,&c);
 343                         BIO_puts(bp,"\n");
 344                         }
 345                 a.neg=!a.neg;
 346                 b.neg=!b.neg;
 347                 BN_add(&c,&c,&b);
 348                 BN_add(&c,&c,&a);
 349                 if(!BN_is_zero(&c))
 350                     {
 351                     fprintf(stderr,"Add test failed!\n");
 352                     return 0;
 353                     }
 354                 }
 355         BN_free(&a);
 356         BN_free(&b);
 357         BN_free(&c);
 358         return(1);
 359         }
 360
 361 int test_sub(BIO *bp)
 362         {
 363         BIGNUM a,b,c;
 364         int i;
 365
 366         BN_init(&a);
 367         BN_init(&b);
 368         BN_init(&c);
 369
 370         for (i=0; i<num0+num1; i++)
 371                 {
 372                 if (i < num1)
 373                         {
 374                         BN_bntest_rand(&a,512,0,0);
 375                         BN_copy(&b,&a);
 376                         if (BN_set_bit(&a,i)==0) return(0);
 377                         BN_add_word(&b,i);
 378                         }
 379                 else
 380                         {
 381                         BN_bntest_rand(&b,400+i-num1,0,0);
 382                         a.neg=rand_neg();
 383                         b.neg=rand_neg();
 384                         }
 385                 BN_sub(&c,&a,&b);
 386                 if (bp != NULL)
 387                         {
 388                         if (!results)
 389                                 {
 390                                 BN_print(bp,&a);
 391                                 BIO_puts(bp," - ");
 392                                 BN_print(bp,&b);
 393                                 BIO_puts(bp," - ");
 394                                 }
 395                         BN_print(bp,&c);
 396                         BIO_puts(bp,"\n");
 397                         }
 398                 BN_add(&c,&c,&b);
 399                 BN_sub(&c,&c,&a);
 400                 if(!BN_is_zero(&c))
 401                     {
 402                     fprintf(stderr,"Subtract test failed!\n");
 403                     return 0;
 404                     }
 405                 }
 406         BN_free(&a);
 407         BN_free(&b);
 408         BN_free(&c);
 409         return(1);
 410         }
 411
 412 int test_div(BIO *bp, BN_CTX *ctx)
 413         {
 414         BIGNUM a,b,c,d,e;
 415         int i;
 416
 417         BN_init(&a);
 418         BN_init(&b);
 419         BN_init(&c);
 420         BN_init(&d);
 421         BN_init(&e);
 422
 423         for (i=0; i<num0+num1; i++)
 424                 {
 425                 if (i < num1)
 426                         {
 427                         BN_bntest_rand(&a,400,0,0);
 428                         BN_copy(&b,&a);
 429                         BN_lshift(&a,&a,i);
 430                         BN_add_word(&a,i);
 431                         }
 432                 else
 433                         BN_bntest_rand(&b,50+3*(i-num1),0,0);
 434                 a.neg=rand_neg();
 435                 b.neg=rand_neg();
 436                 BN_div(&d,&c,&a,&b,ctx);
 437                 if (bp != NULL)
 438                         {
 439                         if (!results)
 440                                 {
 441                                 BN_print(bp,&a);
 442                                 BIO_puts(bp," / ");
 443                                 BN_print(bp,&b);
 444                                 BIO_puts(bp," - ");
 445                                 }
 446                         BN_print(bp,&d);
 447                         BIO_puts(bp,"\n");
 448
 449                         if (!results)
 450                                 {
 451                                 BN_print(bp,&a);
 452                                 BIO_puts(bp," % ");
 453                                 BN_print(bp,&b);
 454                                 BIO_puts(bp," - ");
 455                                 }
 456                         BN_print(bp,&c);
 457                         BIO_puts(bp,"\n");
 458                         }
 459                 BN_mul(&e,&d,&b,ctx);
 460                 BN_add(&d,&e,&c);
 461                 BN_sub(&d,&d,&a);
 462                 if(!BN_is_zero(&d))
 463                     {
 464                     fprintf(stderr,"Division test failed!\n");
 465                     return 0;
 466                     }
 467                 }
 468         BN_free(&a);
 469         BN_free(&b);
 470         BN_free(&c);
 471         BN_free(&d);
 472         BN_free(&e);
 473         return(1);
 474         }
 475
 476 static void print_word(BIO *bp,BN_ULONG w)
 477         {
 478 #ifdef SIXTY_FOUR_BIT
 479         if (sizeof(w) > sizeof(unsigned long))
 480                 {
 481                 unsigned long   h=(unsigned long)(w>>32),
 482                                 l=(unsigned long)(w);
 483
 484                 if (h)  BIO_printf(bp,"%lX%08lX",h,l);
 485                 else    BIO_printf(bp,"%lX",l);
 486                 return;
 487                 }
 488 #endif
 489         BIO_printf(bp,BN_HEX_FMT1,w);
 490         }
 491
 492 int test_div_word(BIO *bp)
 493         {
 494         BIGNUM   a,b;
 495         BN_ULONG r,s;
 496         int i;
 497
 498         BN_init(&a);
 499         BN_init(&b);
 500
 501         for (i=0; i<num0; i++)
 502                 {
 503                 do {
 504                         BN_bntest_rand(&a,512,-1,0);
 505                         BN_bntest_rand(&b,BN_BITS2,-1,0);
 506                         s = b.d[0];
 507                 } while (!s);
 508
 509                 BN_copy(&b, &a);
 510                 r = BN_div_word(&b, s);
 511
 512                 if (bp != NULL)
 513                         {
 514                         if (!results)
 515                                 {
 516                                 BN_print(bp,&a);
 517                                 BIO_puts(bp," / ");
 518                                 print_word(bp,s);
 519                                 BIO_puts(bp," - ");
 520                                 }
 521                         BN_print(bp,&b);
 522                         BIO_puts(bp,"\n");
 523
 524                         if (!results)
 525                                 {
 526                                 BN_print(bp,&a);
 527                                 BIO_puts(bp," % ");
 528                                 print_word(bp,s);
 529                                 BIO_puts(bp," - ");
 530                                 }
 531                         print_word(bp,r);
 532                         BIO_puts(bp,"\n");
 533                         }
 534                 BN_mul_word(&b,s);
 535                 BN_add_word(&b,r);
 536                 BN_sub(&b,&a,&b);
 537                 if(!BN_is_zero(&b))
 538                     {
 539                     fprintf(stderr,"Division (word) test failed!\n");
 540                     return 0;
 541                     }
 542                 }
 543         BN_free(&a);
 544         BN_free(&b);
 545         return(1);
 546         }
 547
 548 int test_div_recp(BIO *bp, BN_CTX *ctx)
 549         {
 550         BIGNUM a,b,c,d,e;
 551         BN_RECP_CTX recp;
 552         int i;
 553
 554         BN_RECP_CTX_init(&recp);
 555         BN_init(&a);
 556         BN_init(&b);
 557         BN_init(&c);
 558         BN_init(&d);
 559         BN_init(&e);
 560
 561         for (i=0; i<num0+num1; i++)
 562                 {
 563                 if (i < num1)
 564                         {
 565                         BN_bntest_rand(&a,400,0,0);
 566                         BN_copy(&b,&a);
 567                         BN_lshift(&a,&a,i);
 568                         BN_add_word(&a,i);
 569                         }
 570                 else
 571                         BN_bntest_rand(&b,50+3*(i-num1),0,0);
 572                 a.neg=rand_neg();
 573                 b.neg=rand_neg();
 574                 BN_RECP_CTX_set(&recp,&b,ctx);
 575                 BN_div_recp(&d,&c,&a,&recp,ctx);
 576                 if (bp != NULL)
 577                         {
 578                         if (!results)
 579                                 {
 580                                 BN_print(bp,&a);
 581                                 BIO_puts(bp," / ");
 582                                 BN_print(bp,&b);
 583                                 BIO_puts(bp," - ");
 584                                 }
 585                         BN_print(bp,&d);
 586                         BIO_puts(bp,"\n");
 587
 588                         if (!results)
 589                                 {
 590                                 BN_print(bp,&a);
 591                                 BIO_puts(bp," % ");
 592                                 BN_print(bp,&b);
 593                                 BIO_puts(bp," - ");
 594                                 }
 595                         BN_print(bp,&c);
 596                         BIO_puts(bp,"\n");
 597                         }
 598                 BN_mul(&e,&d,&b,ctx);
 599                 BN_add(&d,&e,&c);
 600                 BN_sub(&d,&d,&a);
 601                 if(!BN_is_zero(&d))
 602                     {
 603                     fprintf(stderr,"Reciprocal division test failed!\n");
 604                     fprintf(stderr,"a=");
 605                     BN_print_fp(stderr,&a);
 606                     fprintf(stderr,"\nb=");
 607                     BN_print_fp(stderr,&b);
 608                     fprintf(stderr,"\n");
 609                     return 0;
 610                     }
 611                 }
 612         BN_free(&a);
 613         BN_free(&b);
 614         BN_free(&c);
 615         BN_free(&d);
 616         BN_free(&e);
 617         BN_RECP_CTX_free(&recp);
 618         return(1);
 619         }
 620
 621 int test_mul(BIO *bp)
 622         {
 623         BIGNUM a,b,c,d,e;
 624         int i;
 625         BN_CTX *ctx;
 626
 627         ctx = BN_CTX_new();
 628         if (ctx == NULL) EXIT(1);
 629
 630         BN_init(&a);
 631         BN_init(&b);
 632         BN_init(&c);
 633         BN_init(&d);
 634         BN_init(&e);
 635
 636         for (i=0; i<num0+num1; i++)
 637                 {
 638                 if (i <= num1)
 639                         {
 640                         BN_bntest_rand(&a,100,0,0);
 641                         BN_bntest_rand(&b,100,0,0);
 642                         }
 643                 else
 644                         BN_bntest_rand(&b,i-num1,0,0);
 645                 a.neg=rand_neg();
 646                 b.neg=rand_neg();
 647                 BN_mul(&c,&a,&b,ctx);
 648                 if (bp != NULL)
 649                         {
 650                         if (!results)
 651                                 {
 652                                 BN_print(bp,&a);
 653                                 BIO_puts(bp," * ");
 654                                 BN_print(bp,&b);
 655                                 BIO_puts(bp," - ");
 656                                 }
 657                         BN_print(bp,&c);
 658                         BIO_puts(bp,"\n");
 659                         }
 660                 BN_div(&d,&e,&c,&a,ctx);
 661                 BN_sub(&d,&d,&b);
 662                 if(!BN_is_zero(&d) || !BN_is_zero(&e))
 663                     {
 664                     fprintf(stderr,"Multiplication test failed!\n");
 665                     return 0;
 666                     }
 667                 }
 668         BN_free(&a);
 669         BN_free(&b);
 670         BN_free(&c);
 671         BN_free(&d);
 672         BN_free(&e);
 673         BN_CTX_free(ctx);
 674         return(1);
 675         }
 676
 677 int test_sqr(BIO *bp, BN_CTX *ctx)
 678         {
 679         BIGNUM a,c,d,e;
 680         int i;
 681
 682         BN_init(&a);
 683         BN_init(&c);
 684         BN_init(&d);
 685         BN_init(&e);
 686
 687         for (i=0; i<num0; i++)
 688                 {
 689                 BN_bntest_rand(&a,40+i*10,0,0);
 690                 a.neg=rand_neg();
 691                 BN_sqr(&c,&a,ctx);
 692                 if (bp != NULL)
 693                         {
 694                         if (!results)
 695                                 {
 696                                 BN_print(bp,&a);
 697                                 BIO_puts(bp," * ");
 698                                 BN_print(bp,&a);
 699                                 BIO_puts(bp," - ");
 700                                 }
 701                         BN_print(bp,&c);
 702                         BIO_puts(bp,"\n");
 703                         }
 704                 BN_div(&d,&e,&c,&a,ctx);
 705                 BN_sub(&d,&d,&a);
 706                 if(!BN_is_zero(&d) || !BN_is_zero(&e))
 707                     {
 708                     fprintf(stderr,"Square test failed!\n");
 709                     return 0;
 710                     }
 711                 }
 712         BN_free(&a);
 713         BN_free(&c);
 714         BN_free(&d);
 715         BN_free(&e);
 716         return(1);
 717         }
 718
 719 int test_mont(BIO *bp, BN_CTX *ctx)
 720         {
 721         BIGNUM a,b,c,d,A,B;
 722         BIGNUM n;
 723         int i;
 724         BN_MONT_CTX *mont;
 725
 726         BN_init(&a);
 727         BN_init(&b);
 728         BN_init(&c);
 729         BN_init(&d);
 730         BN_init(&A);
 731         BN_init(&B);
 732         BN_init(&n);
 733
 734         mont=BN_MONT_CTX_new();
 735         if (mont == NULL)
 736                 return 0;
 737
 738         BN_bntest_rand(&a,100,0,0); /**/
 739         BN_bntest_rand(&b,100,0,0); /**/
 740         for (i=0; i<num2; i++)
 741                 {
 742                 int bits = (200*(i+1))/num2;
 743
 744                 if (bits == 0)
 745                         continue;
 746                 BN_bntest_rand(&n,bits,0,1);
 747                 BN_MONT_CTX_set(mont,&n,ctx);
 748
 749                 BN_nnmod(&a,&a,&n,ctx);
 750                 BN_nnmod(&b,&b,&n,ctx);
 751
 752                 BN_to_montgomery(&A,&a,mont,ctx);
 753                 BN_to_montgomery(&B,&b,mont,ctx);
 754
 755                 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
 756                 BN_from_montgomery(&A,&c,mont,ctx);/**/
 757                 if (bp != NULL)
 758                         {
 759                         if (!results)
 760                                 {
 761 #ifdef undef
 762 fprintf(stderr,"%d * %d %% %d\n",
 763 BN_num_bits(&a),
 764 BN_num_bits(&b),
 765 BN_num_bits(mont->N));
 766 #endif
 767                                 BN_print(bp,&a);
 768                                 BIO_puts(bp," * ");
 769                                 BN_print(bp,&b);
 770                                 BIO_puts(bp," % ");
 771                                 BN_print(bp,&(mont->N));
 772                                 BIO_puts(bp," - ");
 773                                 }
 774                         BN_print(bp,&A);
 775                         BIO_puts(bp,"\n");
 776                         }
 777                 BN_mod_mul(&d,&a,&b,&n,ctx);
 778                 BN_sub(&d,&d,&A);
 779                 if(!BN_is_zero(&d))
 780                     {
 781                     fprintf(stderr,"Montgomery multiplication test failed!\n");
 782                     return 0;
 783                     }
 784                 }
 785         BN_MONT_CTX_free(mont);
 786         BN_free(&a);
 787         BN_free(&b);
 788         BN_free(&c);
 789         BN_free(&d);
 790         BN_free(&A);
 791         BN_free(&B);
 792         BN_free(&n);
 793         return(1);
 794         }
 795
 796 int test_mod(BIO *bp, BN_CTX *ctx)
 797         {
 798         BIGNUM *a,*b,*c,*d,*e;
 799         int i;
 800
 801         a=BN_new();
 802         b=BN_new();
 803         c=BN_new();
 804         d=BN_new();
 805         e=BN_new();
 806
 807         BN_bntest_rand(a,1024,0,0); /**/
 808         for (i=0; i<num0; i++)
 809                 {
 810                 BN_bntest_rand(b,450+i*10,0,0); /**/
 811                 a->neg=rand_neg();
 812                 b->neg=rand_neg();
 813                 BN_mod(c,a,b,ctx);/**/
 814                 if (bp != NULL)
 815                         {
 816                         if (!results)
 817                                 {
 818                                 BN_print(bp,a);
 819                                 BIO_puts(bp," % ");
 820                                 BN_print(bp,b);
 821                                 BIO_puts(bp," - ");
 822                                 }
 823                         BN_print(bp,c);
 824                         BIO_puts(bp,"\n");
 825                         }
 826                 BN_div(d,e,a,b,ctx);
 827                 BN_sub(e,e,c);
 828                 if(!BN_is_zero(e))
 829                     {
 830                     fprintf(stderr,"Modulo test failed!\n");
 831                     return 0;
 832                     }
 833                 }
 834         BN_free(a);
 835         BN_free(b);
 836         BN_free(c);
 837         BN_free(d);
 838         BN_free(e);
 839         return(1);
 840         }
 841
 842 int test_mod_mul(BIO *bp, BN_CTX *ctx)
 843         {
 844         BIGNUM *a,*b,*c,*d,*e;
 845         int i,j;
 846
 847         a=BN_new();
 848         b=BN_new();
 849         c=BN_new();
 850         d=BN_new();
 851         e=BN_new();
 852
 853         for (j=0; j<3; j++) {
 854         BN_bntest_rand(c,1024,0,0); /**/
 855         for (i=0; i<num0; i++)
 856                 {
 857                 BN_bntest_rand(a,475+i*10,0,0); /**/
 858                 BN_bntest_rand(b,425+i*11,0,0); /**/
 859                 a->neg=rand_neg();
 860                 b->neg=rand_neg();
 861                 if (!BN_mod_mul(e,a,b,c,ctx))
 862                         {
 863                         unsigned long l;
 864
 865                         while ((l=ERR_get_error()))
 866                                 fprintf(stderr,"ERROR:%s\n",
 867                                         ERR_error_string(l,NULL));
 868                         EXIT(1);
 869                         }
 870                 if (bp != NULL)
 871                         {
 872                         if (!results)
 873                                 {
 874                                 BN_print(bp,a);
 875                                 BIO_puts(bp," * ");
 876                                 BN_print(bp,b);
 877                                 BIO_puts(bp," % ");
 878                                 BN_print(bp,c);
 879                                 if ((a->neg ^ b->neg) && !BN_is_zero(e))
 880                                         {
 881                                         /* If  (a*b) % c  is negative,  c  must be added
 882                                          * in order to obtain the normalized remainder
 883                                          * (new with OpenSSL 0.9.7, previous versions of
 884                                          * BN_mod_mul could generate negative results)
 885                                          */
 886                                         BIO_puts(bp," + ");
 887                                         BN_print(bp,c);
 888                                         }
 889                                 BIO_puts(bp," - ");
 890                                 }
 891                         BN_print(bp,e);
 892                         BIO_puts(bp,"\n");
 893                         }
 894                 BN_mul(d,a,b,ctx);
 895                 BN_sub(d,d,e);
 896                 BN_div(a,b,d,c,ctx);
 897                 if(!BN_is_zero(b))
 898                     {
 899                     fprintf(stderr,"Modulo multiply test failed!\n");
 900                     ERR_print_errors_fp(stderr);
 901                     return 0;
 902                     }
 903                 }
 904         }
 905         BN_free(a);
 906         BN_free(b);
 907         BN_free(c);
 908         BN_free(d);
 909         BN_free(e);
 910         return(1);
 911         }
 912
 913 int test_mod_exp(BIO *bp, BN_CTX *ctx)
 914         {
 915         BIGNUM *a,*b,*c,*d,*e;
 916         int i;
 917
 918         a=BN_new();
 919         b=BN_new();
 920         c=BN_new();
 921         d=BN_new();
 922         e=BN_new();
 923
 924         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
 925         for (i=0; i<num2; i++)
 926                 {
 927                 BN_bntest_rand(a,20+i*5,0,0); /**/
 928                 BN_bntest_rand(b,2+i,0,0); /**/
 929
 930                 if (!BN_mod_exp(d,a,b,c,ctx))
 931                         return(0);
 932
 933                 if (bp != NULL)
 934                         {
 935                         if (!results)
 936                                 {
 937                                 BN_print(bp,a);
 938                                 BIO_puts(bp," ^ ");
 939                                 BN_print(bp,b);
 940                                 BIO_puts(bp," % ");
 941                                 BN_print(bp,c);
 942                                 BIO_puts(bp," - ");
 943                                 }
 944                         BN_print(bp,d);
 945                         BIO_puts(bp,"\n");
 946                         }
 947                 BN_exp(e,a,b,ctx);
 948                 BN_sub(e,e,d);
 949                 BN_div(a,b,e,c,ctx);
 950                 if(!BN_is_zero(b))
 951                     {
 952                     fprintf(stderr,"Modulo exponentiation test failed!\n");
 953                     return 0;
 954                     }
 955                 }
 956         BN_free(a);
 957         BN_free(b);
 958         BN_free(c);
 959         BN_free(d);
 960         BN_free(e);
 961         return(1);
 962         }
 963
 964 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
 965         {
 966         BIGNUM *a,*b,*c,*d,*e;
 967         int i;
 968
 969         a=BN_new();
 970         b=BN_new();
 971         c=BN_new();
 972         d=BN_new();
 973         e=BN_new();
 974
 975         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
 976         for (i=0; i<num2; i++)
 977                 {
 978                 BN_bntest_rand(a,20+i*5,0,0); /**/
 979                 BN_bntest_rand(b,2+i,0,0); /**/
 980
 981                 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
 982                         return(00);
 983
 984                 if (bp != NULL)
 985                         {
 986                         if (!results)
 987                                 {
 988                                 BN_print(bp,a);
 989                                 BIO_puts(bp," ^ ");
 990                                 BN_print(bp,b);
 991                                 BIO_puts(bp," % ");
 992                                 BN_print(bp,c);
 993                                 BIO_puts(bp," - ");
 994                                 }
 995                         BN_print(bp,d);
 996                         BIO_puts(bp,"\n");
 997                         }
 998                 BN_exp(e,a,b,ctx);
 999                 BN_sub(e,e,d);
1000                 BN_div(a,b,e,c,ctx);
1001                 if(!BN_is_zero(b))
1002                     {
1003                     fprintf(stderr,"Modulo exponentiation test failed!\n");
1004                     return 0;
1005                     }
1006                 }
1007         BN_free(a);
1008         BN_free(b);
1009         BN_free(c);
1010         BN_free(d);
1011         BN_free(e);
1012         return(1);
1013         }
1014
1015 int test_exp(BIO *bp, BN_CTX *ctx)
1016         {
1017         BIGNUM *a,*b,*d,*e,*one;
1018         int i;
1019
1020         a=BN_new();
1021         b=BN_new();
1022         d=BN_new();
1023         e=BN_new();
1024         one=BN_new();
1025         BN_one(one);
1026
1027         for (i=0; i<num2; i++)
1028                 {
1029                 BN_bntest_rand(a,20+i*5,0,0); /**/
1030                 BN_bntest_rand(b,2+i,0,0); /**/
1031
1032                 if (!BN_exp(d,a,b,ctx))
1033                         return(0);
1034
1035                 if (bp != NULL)
1036                         {
1037                         if (!results)
1038                                 {
1039                                 BN_print(bp,a);
1040                                 BIO_puts(bp," ^ ");
1041                                 BN_print(bp,b);
1042                                 BIO_puts(bp," - ");
1043                                 }
1044                         BN_print(bp,d);
1045                         BIO_puts(bp,"\n");
1046                         }
1047                 BN_one(e);
1048                 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1049                     BN_mul(e,e,a,ctx);
1050                 BN_sub(e,e,d);
1051                 if(!BN_is_zero(e))
1052                     {
1053                     fprintf(stderr,"Exponentiation test failed!\n");
1054                     return 0;
1055                     }
1056                 }
1057         BN_free(a);
1058         BN_free(b);
1059         BN_free(d);
1060         BN_free(e);
1061         BN_free(one);
1062         return(1);
1063         }
1064
1065 int test_gf2m_add(BIO *bp)
1066         {
1067         BIGNUM a,b,c;
1068         int i, ret = 0;
1069
1070         BN_init(&a);
1071         BN_init(&b);
1072         BN_init(&c);
1073
1074         for (i=0; i<num0; i++)
1075                 {
1076                 BN_rand(&a,512,0,0);
1077                 BN_copy(&b, BN_value_one());
1078                 a.neg=rand_neg();
1079                 b.neg=rand_neg();
1080                 BN_GF2m_add(&c,&a,&b);
1081 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1082                 if (bp != NULL)
1083                         {
1084                         if (!results)
1085                                 {
1086                                 BN_print(bp,&a);
1087                                 BIO_puts(bp," ^ ");
1088                                 BN_print(bp,&b);
1089                                 BIO_puts(bp," = ");
1090                                 }
1091                         BN_print(bp,&c);
1092                         BIO_puts(bp,"\n");
1093                         }
1094 #endif
1095                 /* Test that two added values have the correct parity. */
1096                 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1097                         {
1098                     fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1099                         goto err;
1100                         }
1101                 BN_GF2m_add(&c,&c,&c);
1102                 /* Test that c + c = 0. */
1103                 if(!BN_is_zero(&c))
1104                     {
1105                     fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1106                         goto err;
1107                     }
1108                 }
1109         ret = 1;
1110   err:
1111         BN_free(&a);
1112         BN_free(&b);
1113         BN_free(&c);
1114         return ret;
1115         }
1116
1117 int test_gf2m_mod(BIO *bp)
1118         {
1119         BIGNUM *a,*b[2],*c,*d,*e;
1120         int i, j, ret = 0;
1121         int p0[] = {163,7,6,3,0,-1};
1122         int p1[] = {193,15,0,-1};
1123
1124         a=BN_new();
1125         b[0]=BN_new();
1126         b[1]=BN_new();
1127         c=BN_new();
1128         d=BN_new();
1129         e=BN_new();
1130
1131         BN_GF2m_arr2poly(p0, b[0]);
1132         BN_GF2m_arr2poly(p1, b[1]);
1133
1134         for (i=0; i<num0; i++)
1135                 {
1136                 BN_bntest_rand(a, 1024, 0, 0);
1137                 for (j=0; j < 2; j++)
1138                         {
1139                         BN_GF2m_mod(c, a, b[j]);
1140 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1141                         if (bp != NULL)
1142                                 {
1143                                 if (!results)
1144                                         {
1145                                         BN_print(bp,a);
1146                                         BIO_puts(bp," % ");
1147                                         BN_print(bp,b[j]);
1148                                         BIO_puts(bp," - ");
1149                                         BN_print(bp,c);
1150                                         BIO_puts(bp,"\n");
1151                                         }
1152                                 }
1153 #endif
1154                         BN_GF2m_add(d, a, c);
1155                         BN_GF2m_mod(e, d, b[j]);
1156                         /* Test that a + (a mod p) mod p == 0. */
1157                         if(!BN_is_zero(e))
1158                                 {
1159                                 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1160                                 goto err;
1161                                 }
1162                         }
1163                 }
1164         ret = 1;
1165   err:
1166         BN_free(a);
1167         BN_free(b[0]);
1168         BN_free(b[1]);
1169         BN_free(c);
1170         BN_free(d);
1171         BN_free(e);
1172         return ret;
1173         }
1174
1175 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1176         {
1177         BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1178         int i, j, ret = 0;
1179         int p0[] = {163,7,6,3,0,-1};
1180         int p1[] = {193,15,0,-1};
1181
1182         a=BN_new();
1183         b[0]=BN_new();
1184         b[1]=BN_new();
1185         c=BN_new();
1186         d=BN_new();
1187         e=BN_new();
1188         f=BN_new();
1189         g=BN_new();
1190         h=BN_new();
1191
1192         BN_GF2m_arr2poly(p0, b[0]);
1193         BN_GF2m_arr2poly(p1, b[1]);
1194
1195         for (i=0; i<num0; i++)
1196                 {
1197                 BN_bntest_rand(a, 1024, 0, 0);
1198                 BN_bntest_rand(c, 1024, 0, 0);
1199                 BN_bntest_rand(d, 1024, 0, 0);
1200                 for (j=0; j < 2; j++)
1201                         {
1202                         BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1203 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1204                         if (bp != NULL)
1205                                 {
1206                                 if (!results)
1207                                         {
1208                                         BN_print(bp,a);
1209                                         BIO_puts(bp," * ");
1210                                         BN_print(bp,c);
1211                                         BIO_puts(bp," % ");
1212                                         BN_print(bp,b[j]);
1213                                         BIO_puts(bp," - ");
1214                                         BN_print(bp,e);
1215                                         BIO_puts(bp,"\n");
1216                                         }
1217                                 }
1218 #endif
1219                         BN_GF2m_add(f, a, d);
1220                         BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1221                         BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1222                         BN_GF2m_add(f, e, g);
1223                         BN_GF2m_add(f, f, h);
1224                         /* Test that (a+d)*c = a*c + d*c. */
1225                         if(!BN_is_zero(f))
1226                                 {
1227                                 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1228                                 goto err;
1229                                 }
1230                         }
1231                 }
1232         ret = 1;
1233   err:
1234         BN_free(a);
1235         BN_free(b[0]);
1236         BN_free(b[1]);
1237         BN_free(c);
1238         BN_free(d);
1239         BN_free(e);
1240         BN_free(f);
1241         BN_free(g);
1242         BN_free(h);
1243         return ret;
1244         }
1245
1246 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1247         {
1248         BIGNUM *a,*b[2],*c,*d;
1249         int i, j, ret = 0;
1250         int p0[] = {163,7,6,3,0,-1};
1251         int p1[] = {193,15,0,-1};
1252
1253         a=BN_new();
1254         b[0]=BN_new();
1255         b[1]=BN_new();
1256         c=BN_new();
1257         d=BN_new();
1258
1259         BN_GF2m_arr2poly(p0, b[0]);
1260         BN_GF2m_arr2poly(p1, b[1]);
1261
1262         for (i=0; i<num0; i++)
1263                 {
1264                 BN_bntest_rand(a, 1024, 0, 0);
1265                 for (j=0; j < 2; j++)
1266                         {
1267                         BN_GF2m_mod_sqr(c, a, b[j], ctx);
1268                         BN_copy(d, a);
1269                         BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1270 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1271                         if (bp != NULL)
1272                                 {
1273                                 if (!results)
1274                                         {
1275                                         BN_print(bp,a);
1276                                         BIO_puts(bp," ^ 2 % ");
1277                                         BN_print(bp,b[j]);
1278                                         BIO_puts(bp, " = ");
1279                                         BN_print(bp,c);
1280                                         BIO_puts(bp,"; a * a = ");
1281                                         BN_print(bp,d);
1282                                         BIO_puts(bp,"\n");
1283                                         }
1284                                 }
1285 #endif
1286                         BN_GF2m_add(d, c, d);
1287                         /* Test that a*a = a^2. */
1288                         if(!BN_is_zero(d))
1289                                 {
1290                                 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1291                                 goto err;
1292                                 }
1293                         }
1294                 }
1295         ret = 1;
1296   err:
1297         BN_free(a);
1298         BN_free(b[0]);
1299         BN_free(b[1]);
1300         BN_free(c);
1301         BN_free(d);
1302         return ret;
1303         }
1304
1305 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1306         {
1307         BIGNUM *a,*b[2],*c,*d;
1308         int i, j, ret = 0;
1309         int p0[] = {163,7,6,3,0,-1};
1310         int p1[] = {193,15,0,-1};
1311
1312         a=BN_new();
1313         b[0]=BN_new();
1314         b[1]=BN_new();
1315         c=BN_new();
1316         d=BN_new();
1317
1318         BN_GF2m_arr2poly(p0, b[0]);
1319         BN_GF2m_arr2poly(p1, b[1]);
1320
1321         for (i=0; i<num0; i++)
1322                 {
1323                 BN_bntest_rand(a, 512, 0, 0);
1324                 for (j=0; j < 2; j++)
1325                         {
1326                         BN_GF2m_mod_inv(c, a, b[j], ctx);
1327                         BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1328 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1329                         if (bp != NULL)
1330                                 {
1331                                 if (!results)
1332                                         {
1333                                         BN_print(bp,a);
1334                                         BIO_puts(bp, " * ");
1335                                         BN_print(bp,c);
1336                                         BIO_puts(bp," - 1 % ");
1337                                         BN_print(bp,b[j]);
1338                                         BIO_puts(bp,"\n");
1339                                         }
1340                                 }
1341 #endif
1342                         /* Test that ((1/a)*a) = 1. */
1343                         if(!BN_is_one(d))
1344                                 {
1345                                 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1346                                 goto err;
1347                                 }
1348                         }
1349                 }
1350         ret = 1;
1351   err:
1352         BN_free(a);
1353         BN_free(b[0]);
1354         BN_free(b[1]);
1355         BN_free(c);
1356         BN_free(d);
1357         return ret;
1358         }
1359
1360 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1361         {
1362         BIGNUM *a,*b[2],*c,*d,*e,*f;
1363         int i, j, ret = 0;
1364         int p0[] = {163,7,6,3,0,-1};
1365         int p1[] = {193,15,0,-1};
1366
1367         a=BN_new();
1368         b[0]=BN_new();
1369         b[1]=BN_new();
1370         c=BN_new();
1371         d=BN_new();
1372         e=BN_new();
1373         f=BN_new();
1374
1375         BN_GF2m_arr2poly(p0, b[0]);
1376         BN_GF2m_arr2poly(p1, b[1]);
1377
1378         for (i=0; i<num0; i++)
1379                 {
1380                 BN_bntest_rand(a, 512, 0, 0);
1381                 BN_bntest_rand(c, 512, 0, 0);
1382                 for (j=0; j < 2; j++)
1383                         {
1384                         BN_GF2m_mod_div(d, a, c, b[j], ctx);
1385                         BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1386                         BN_GF2m_mod_div(f, a, e, b[j], ctx);
1387 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1388                         if (bp != NULL)
1389                                 {
1390                                 if (!results)
1391                                         {
1392                                         BN_print(bp,a);
1393                                         BIO_puts(bp, " = ");
1394                                         BN_print(bp,c);
1395                                         BIO_puts(bp," * ");
1396                                         BN_print(bp,d);
1397                                         BIO_puts(bp, " % ");
1398                                         BN_print(bp,b[j]);
1399                                         BIO_puts(bp,"\n");
1400                                         }
1401                                 }
1402 #endif
1403                         /* Test that ((a/c)*c)/a = 1. */
1404                         if(!BN_is_one(f))
1405                                 {
1406                                 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1407                                 goto err;
1408                                 }
1409                         }
1410                 }
1411         ret = 1;
1412   err:
1413         BN_free(a);
1414         BN_free(b[0]);
1415         BN_free(b[1]);
1416         BN_free(c);
1417         BN_free(d);
1418         BN_free(e);
1419         BN_free(f);
1420         return ret;
1421         }
1422
1423 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1424         {
1425         BIGNUM *a,*b[2],*c,*d,*e,*f;
1426         int i, j, ret = 0;
1427         int p0[] = {163,7,6,3,0,-1};
1428         int p1[] = {193,15,0,-1};
1429
1430         a=BN_new();
1431         b[0]=BN_new();
1432         b[1]=BN_new();
1433         c=BN_new();
1434         d=BN_new();
1435         e=BN_new();
1436         f=BN_new();
1437
1438         BN_GF2m_arr2poly(p0, b[0]);
1439         BN_GF2m_arr2poly(p1, b[1]);
1440
1441         for (i=0; i<num0; i++)
1442                 {
1443                 BN_bntest_rand(a, 512, 0, 0);
1444                 BN_bntest_rand(c, 512, 0, 0);
1445                 BN_bntest_rand(d, 512, 0, 0);
1446                 for (j=0; j < 2; j++)
1447                         {
1448                         BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1449                         BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1450                         BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1451                         BN_add(f, c, d);
1452                         BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1453 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1454                         if (bp != NULL)
1455                                 {
1456                                 if (!results)
1457                                         {
1458                                         BN_print(bp,a);
1459                                         BIO_puts(bp, " ^ (");
1460                                         BN_print(bp,c);
1461                                         BIO_puts(bp," + ");
1462                                         BN_print(bp,d);
1463                                         BIO_puts(bp, ") = ");
1464                                         BN_print(bp,e);
1465                                         BIO_puts(bp, "; - ");
1466                                         BN_print(bp,f);
1467                                         BIO_puts(bp, " % ");
1468                                         BN_print(bp,b[j]);
1469                                         BIO_puts(bp,"\n");
1470                                         }
1471                                 }
1472 #endif
1473                         BN_GF2m_add(f, e, f);
1474                         /* Test that a^(c+d)=a^c*a^d. */
1475                         if(!BN_is_zero(f))
1476                                 {
1477                                 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1478                                 goto err;
1479                                 }
1480                         }
1481                 }
1482         ret = 1;
1483   err:
1484         BN_free(a);
1485         BN_free(b[0]);
1486         BN_free(b[1]);
1487         BN_free(c);
1488         BN_free(d);
1489         BN_free(e);
1490         BN_free(f);
1491         return ret;
1492         }
1493
1494 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1495         {
1496         BIGNUM *a,*b[2],*c,*d,*e,*f;
1497         int i, j, ret = 0;
1498         int p0[] = {163,7,6,3,0,-1};
1499         int p1[] = {193,15,0,-1};
1500
1501         a=BN_new();
1502         b[0]=BN_new();
1503         b[1]=BN_new();
1504         c=BN_new();
1505         d=BN_new();
1506         e=BN_new();
1507         f=BN_new();
1508
1509         BN_GF2m_arr2poly(p0, b[0]);
1510         BN_GF2m_arr2poly(p1, b[1]);
1511
1512         for (i=0; i<num0; i++)
1513                 {
1514                 BN_bntest_rand(a, 512, 0, 0);
1515                 for (j=0; j < 2; j++)
1516                         {
1517                         BN_GF2m_mod(c, a, b[j]);
1518                         BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1519                         BN_GF2m_mod_sqr(e, d, b[j], ctx);
1520 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1521                         if (bp != NULL)
1522                                 {
1523                                 if (!results)
1524                                         {
1525                                         BN_print(bp,d);
1526                                         BIO_puts(bp, " ^ 2 - ");
1527                                         BN_print(bp,a);
1528                                         BIO_puts(bp,"\n");
1529                                         }
1530                                 }
1531 #endif
1532                         BN_GF2m_add(f, c, e);
1533                         /* Test that d^2 = a, where d = sqrt(a). */
1534                         if(!BN_is_zero(f))
1535                                 {
1536                                 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1537                                 goto err;
1538                                 }
1539                         }
1540                 }
1541         ret = 1;
1542   err:
1543         BN_free(a);
1544         BN_free(b[0]);
1545         BN_free(b[1]);
1546         BN_free(c);
1547         BN_free(d);
1548         BN_free(e);
1549         BN_free(f);
1550         return ret;
1551         }
1552
1553 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1554         {
1555         BIGNUM *a,*b[2],*c,*d,*e;
1556         int i, j, s = 0, t, ret = 0;
1557         int p0[] = {163,7,6,3,0,-1};
1558         int p1[] = {193,15,0,-1};
1559
1560         a=BN_new();
1561         b[0]=BN_new();
1562         b[1]=BN_new();
1563         c=BN_new();
1564         d=BN_new();
1565         e=BN_new();
1566
1567         BN_GF2m_arr2poly(p0, b[0]);
1568         BN_GF2m_arr2poly(p1, b[1]);
1569
1570         for (i=0; i<num0; i++)
1571                 {
1572                 BN_bntest_rand(a, 512, 0, 0);
1573                 for (j=0; j < 2; j++)
1574                         {
1575                         t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1576                         if (t)
1577                                 {
1578                                 s++;
1579                                 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1580                                 BN_GF2m_add(d, c, d);
1581                                 BN_GF2m_mod(e, a, b[j]);
1582 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1583                                 if (bp != NULL)
1584                                         {
1585                                         if (!results)
1586                                                 {
1587                                                 BN_print(bp,c);
1588                                                 BIO_puts(bp, " is root of z^2 + z = ");
1589                                                 BN_print(bp,a);
1590                                                 BIO_puts(bp, " % ");
1591                                                 BN_print(bp,b[j]);
1592                                                 BIO_puts(bp, "\n");
1593                                                 }
1594                                         }
1595 #endif
1596                                 BN_GF2m_add(e, e, d);
1597                                 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1598                                 if(!BN_is_zero(e))
1599                                         {
1600                                         fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1601                                         goto err;
1602                                         }
1603
1604                                 }
1605                         else
1606                                 {
1607 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1608                                 if (bp != NULL)
1609                                         {
1610                                         if (!results)
1611                                                 {
1612                                                 BIO_puts(bp, "There are no roots of z^2 + z = ");
1613                                                 BN_print(bp,a);
1614                                                 BIO_puts(bp, " % ");
1615                                                 BN_print(bp,b[j]);
1616                                                 BIO_puts(bp, "\n");
1617                                                 }
1618                                         }
1619 #endif
1620                                 }
1621                         }
1622                 }
1623         if (s == 0)
1624                 {
1625                 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1626                 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1627                 goto err;
1628                 }
1629         ret = 1;
1630   err:
1631         BN_free(a);
1632         BN_free(b[0]);
1633         BN_free(b[1]);
1634         BN_free(c);
1635         BN_free(d);
1636         BN_free(e);
1637         return ret;
1638         }
1639
1640 static int genprime_cb(int p, int n, BN_GENCB *arg)
1641         {
1642         char c='*';
1643
1644         if (p == 0) c='.';
1645         if (p == 1) c='+';
1646         if (p == 2) c='*';
1647         if (p == 3) c='\n';
1648         putc(c, stderr);
1649         fflush(stderr);
1650         return 1;
1651         }
1652
1653 int test_kron(BIO *bp, BN_CTX *ctx)
1654         {
1655         BN_GENCB cb;
1656         BIGNUM *a,*b,*r,*t;
1657         int i;
1658         int legendre, kronecker;
1659         int ret = 0;
1660
1661         a = BN_new();
1662         b = BN_new();
1663         r = BN_new();
1664         t = BN_new();
1665         if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1666
1667         BN_GENCB_set(&cb, genprime_cb, NULL);
1668
1669         /* We test BN_kronecker(a, b, ctx) just for  b  odd (Jacobi symbol).
1670          * In this case we know that if  b  is prime, then BN_kronecker(a, b, ctx)
1671          * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1672          * So we generate a random prime  b  and compare these values
1673          * for a number of random  a's.  (That is, we run the Solovay-Strassen
1674          * primality test to confirm that  b  is prime, except that we
1675          * don't want to test whether  b  is prime but whether BN_kronecker
1676          * works.) */
1677
1678         if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1679         b->neg = rand_neg();
1680         putc('\n', stderr);
1681
1682         for (i = 0; i < num0; i++)
1683                 {
1684                 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1685                 a->neg = rand_neg();
1686
1687                 /* t := (|b|-1)/2  (note that b is odd) */
1688                 if (!BN_copy(t, b)) goto err;
1689                 t->neg = 0;
1690                 if (!BN_sub_word(t, 1)) goto err;
1691                 if (!BN_rshift1(t, t)) goto err;
1692                 /* r := a^t mod b */
1693                 b->neg=0;
1694
1695                 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1696                 b->neg=1;
1697
1698                 if (BN_is_word(r, 1))
1699                         legendre = 1;
1700                 else if (BN_is_zero(r))
1701                         legendre = 0;
1702                 else
1703                         {
1704                         if (!BN_add_word(r, 1)) goto err;
1705                         if (0 != BN_ucmp(r, b))
1706                                 {
1707                                 fprintf(stderr, "Legendre symbol computation failed\n");
1708                                 goto err;
1709                                 }
1710                         legendre = -1;
1711                         }
1712
1713                 kronecker = BN_kronecker(a, b, ctx);
1714                 if (kronecker < -1) goto err;
1715                 /* we actually need BN_kronecker(a, |b|) */
1716                 if (a->neg && b->neg)
1717                         kronecker = -kronecker;
1718
1719                 if (legendre != kronecker)
1720                         {
1721                         fprintf(stderr, "legendre != kronecker; a = ");
1722                         BN_print_fp(stderr, a);
1723                         fprintf(stderr, ", b = ");
1724                         BN_print_fp(stderr, b);
1725                         fprintf(stderr, "\n");
1726                         goto err;
1727                         }
1728
1729                 putc('.', stderr);
1730                 fflush(stderr);
1731                 }
1732
1733         putc('\n', stderr);
1734         fflush(stderr);
1735         ret = 1;
1736  err:
1737         if (a != NULL) BN_free(a);
1738         if (b != NULL) BN_free(b);
1739         if (r != NULL) BN_free(r);
1740         if (t != NULL) BN_free(t);
1741         return ret;
1742         }
1743
1744 int test_sqrt(BIO *bp, BN_CTX *ctx)
1745         {
1746         BN_GENCB cb;
1747         BIGNUM *a,*p,*r;
1748         int i, j;
1749         int ret = 0;
1750
1751         a = BN_new();
1752         p = BN_new();
1753         r = BN_new();
1754         if (a == NULL || p == NULL || r == NULL) goto err;
1755
1756         BN_GENCB_set(&cb, genprime_cb, NULL);
1757
1758         for (i = 0; i < 16; i++)
1759                 {
1760                 if (i < 8)
1761                         {
1762                         unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1763
1764                         if (!BN_set_word(p, primes[i])) goto err;
1765                         }
1766                 else
1767                         {
1768                         if (!BN_set_word(a, 32)) goto err;
1769                         if (!BN_set_word(r, 2*i + 1)) goto err;
1770
1771                         if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1772                         putc('\n', stderr);
1773                         }
1774                 p->neg = rand_neg();
1775
1776                 for (j = 0; j < num2; j++)
1777                         {
1778                         /* construct 'a' such that it is a square modulo p,
1779                          * but in general not a proper square and not reduced modulo p */
1780                         if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1781                         if (!BN_nnmod(r, r, p, ctx)) goto err;
1782                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1783                         if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1784                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1785                         if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1786                         if (!BN_mul(a, a, r, ctx)) goto err;
1787                         if (rand_neg())
1788                                 if (!BN_sub(a, a, p)) goto err;
1789
1790                         if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1791                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1792
1793                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1794
1795                         if (BN_cmp(a, r) != 0)
1796                                 {
1797                                 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1798                                 BN_print_fp(stderr, a);
1799                                 fprintf(stderr, ", r = ");
1800                                 BN_print_fp(stderr, r);
1801                                 fprintf(stderr, ", p = ");
1802                                 BN_print_fp(stderr, p);
1803                                 fprintf(stderr, "\n");
1804                                 goto err;
1805                                 }
1806
1807                         putc('.', stderr);
1808                         fflush(stderr);
1809                         }
1810
1811                 putc('\n', stderr);
1812                 fflush(stderr);
1813                 }
1814         ret = 1;
1815  err:
1816         if (a != NULL) BN_free(a);
1817         if (p != NULL) BN_free(p);
1818         if (r != NULL) BN_free(r);
1819         return ret;
1820         }
1821
1822 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1823         {
1824         BIGNUM *a,*b,*c,*d;
1825         int i;
1826
1827         b=BN_new();
1828         c=BN_new();
1829         d=BN_new();
1830         BN_one(c);
1831
1832         if(a_)
1833             a=a_;
1834         else
1835             {
1836             a=BN_new();
1837             BN_bntest_rand(a,200,0,0); /**/
1838             a->neg=rand_neg();
1839             }
1840         for (i=0; i<num0; i++)
1841                 {
1842                 BN_lshift(b,a,i+1);
1843                 BN_add(c,c,c);
1844                 if (bp != NULL)
1845                         {
1846                         if (!results)
1847                                 {
1848                                 BN_print(bp,a);
1849                                 BIO_puts(bp," * ");
1850                                 BN_print(bp,c);
1851                                 BIO_puts(bp," - ");
1852                                 }
1853                         BN_print(bp,b);
1854                         BIO_puts(bp,"\n");
1855                         }
1856                 BN_mul(d,a,c,ctx);
1857                 BN_sub(d,d,b);
1858                 if(!BN_is_zero(d))
1859                     {
1860                     fprintf(stderr,"Left shift test failed!\n");
1861                     fprintf(stderr,"a=");
1862                     BN_print_fp(stderr,a);
1863                     fprintf(stderr,"\nb=");
1864                     BN_print_fp(stderr,b);
1865                     fprintf(stderr,"\nc=");
1866                     BN_print_fp(stderr,c);
1867                     fprintf(stderr,"\nd=");
1868                     BN_print_fp(stderr,d);
1869                     fprintf(stderr,"\n");
1870                     return 0;
1871                     }
1872                 }
1873         BN_free(a);
1874         BN_free(b);
1875         BN_free(c);
1876         BN_free(d);
1877         return(1);
1878         }
1879
1880 int test_lshift1(BIO *bp)
1881         {
1882         BIGNUM *a,*b,*c;
1883         int i;
1884
1885         a=BN_new();
1886         b=BN_new();
1887         c=BN_new();
1888
1889         BN_bntest_rand(a,200,0,0); /**/
1890         a->neg=rand_neg();
1891         for (i=0; i<num0; i++)
1892                 {
1893                 BN_lshift1(b,a);
1894                 if (bp != NULL)
1895                         {
1896                         if (!results)
1897                                 {
1898                                 BN_print(bp,a);
1899                                 BIO_puts(bp," * 2");
1900                                 BIO_puts(bp," - ");
1901                                 }
1902                         BN_print(bp,b);
1903                         BIO_puts(bp,"\n");
1904                         }
1905                 BN_add(c,a,a);
1906                 BN_sub(a,b,c);
1907                 if(!BN_is_zero(a))
1908                     {
1909                     fprintf(stderr,"Left shift one test failed!\n");
1910                     return 0;
1911                     }
1912
1913                 BN_copy(a,b);
1914                 }
1915         BN_free(a);
1916         BN_free(b);
1917         BN_free(c);
1918         return(1);
1919         }
1920
1921 int test_rshift(BIO *bp,BN_CTX *ctx)
1922         {
1923         BIGNUM *a,*b,*c,*d,*e;
1924         int i;
1925
1926         a=BN_new();
1927         b=BN_new();
1928         c=BN_new();
1929         d=BN_new();
1930         e=BN_new();
1931         BN_one(c);
1932
1933         BN_bntest_rand(a,200,0,0); /**/
1934         a->neg=rand_neg();
1935         for (i=0; i<num0; i++)
1936                 {
1937                 BN_rshift(b,a,i+1);
1938                 BN_add(c,c,c);
1939                 if (bp != NULL)
1940                         {
1941                         if (!results)
1942                                 {
1943                                 BN_print(bp,a);
1944                                 BIO_puts(bp," / ");
1945                                 BN_print(bp,c);
1946                                 BIO_puts(bp," - ");
1947                                 }
1948                         BN_print(bp,b);
1949                         BIO_puts(bp,"\n");
1950                         }
1951                 BN_div(d,e,a,c,ctx);
1952                 BN_sub(d,d,b);
1953                 if(!BN_is_zero(d))
1954                     {
1955                     fprintf(stderr,"Right shift test failed!\n");
1956                     return 0;
1957                     }
1958                 }
1959         BN_free(a);
1960         BN_free(b);
1961         BN_free(c);
1962         BN_free(d);
1963         BN_free(e);
1964         return(1);
1965         }
1966
1967 int test_rshift1(BIO *bp)
1968         {
1969         BIGNUM *a,*b,*c;
1970         int i;
1971
1972         a=BN_new();
1973         b=BN_new();
1974         c=BN_new();
1975
1976         BN_bntest_rand(a,200,0,0); /**/
1977         a->neg=rand_neg();
1978         for (i=0; i<num0; i++)
1979                 {
1980                 BN_rshift1(b,a);
1981                 if (bp != NULL)
1982                         {
1983                         if (!results)
1984                                 {
1985                                 BN_print(bp,a);
1986                                 BIO_puts(bp," / 2");
1987                                 BIO_puts(bp," - ");
1988                                 }
1989                         BN_print(bp,b);
1990                         BIO_puts(bp,"\n");
1991                         }
1992                 BN_sub(c,a,b);
1993                 BN_sub(c,c,b);
1994                 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1995                     {
1996                     fprintf(stderr,"Right shift one test failed!\n");
1997                     return 0;
1998                     }
1999                 BN_copy(a,b);
2000                 }
2001         BN_free(a);
2002         BN_free(b);
2003         BN_free(c);
2004         return(1);
2005         }
2006
2007 int rand_neg(void)
2008         {
2009         static unsigned int neg=0;
2010         static int sign[8]={0,0,0,1,1,0,1,1};
2011
2012         return(sign[(neg++)%8]);
2013         }