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         BIO_flush(out);
 188
 189         message(out,"BN_sub");
 190         if (!test_sub(out)) goto err;
 191         BIO_flush(out);
 192
 193         message(out,"BN_lshift1");
 194         if (!test_lshift1(out)) goto err;
 195         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         BIO_flush(out);
 201
 202         message(out,"BN_lshift");
 203         if (!test_lshift(out,ctx,NULL)) goto err;
 204         BIO_flush(out);
 205
 206         message(out,"BN_rshift1");
 207         if (!test_rshift1(out)) goto err;
 208         BIO_flush(out);
 209
 210         message(out,"BN_rshift");
 211         if (!test_rshift(out,ctx)) goto err;
 212         BIO_flush(out);
 213
 214         message(out,"BN_sqr");
 215         if (!test_sqr(out,ctx)) goto err;
 216         BIO_flush(out);
 217
 218         message(out,"BN_mul");
 219         if (!test_mul(out)) goto err;
 220         BIO_flush(out);
 221
 222         message(out,"BN_div");
 223         if (!test_div(out,ctx)) goto err;
 224         BIO_flush(out);
 225
 226         message(out,"BN_div_word");
 227         if (!test_div_word(out)) goto err;
 228         BIO_flush(out);
 229
 230         message(out,"BN_div_recp");
 231         if (!test_div_recp(out,ctx)) goto err;
 232         BIO_flush(out);
 233
 234         message(out,"BN_mod");
 235         if (!test_mod(out,ctx)) goto err;
 236         BIO_flush(out);
 237
 238         message(out,"BN_mod_mul");
 239         if (!test_mod_mul(out,ctx)) goto err;
 240         BIO_flush(out);
 241
 242         message(out,"BN_mont");
 243         if (!test_mont(out,ctx)) goto err;
 244         BIO_flush(out);
 245
 246         message(out,"BN_mod_exp");
 247         if (!test_mod_exp(out,ctx)) goto err;
 248         BIO_flush(out);
 249
 250         message(out,"BN_mod_exp_mont_consttime");
 251         if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
 252         BIO_flush(out);
 253
 254         message(out,"BN_exp");
 255         if (!test_exp(out,ctx)) goto err;
 256         BIO_flush(out);
 257
 258         message(out,"BN_kronecker");
 259         if (!test_kron(out,ctx)) goto err;
 260         BIO_flush(out);
 261
 262         message(out,"BN_mod_sqrt");
 263         if (!test_sqrt(out,ctx)) goto err;
 264         BIO_flush(out);
 265
 266         message(out,"BN_GF2m_add");
 267         if (!test_gf2m_add(out)) goto err;
 268         BIO_flush(out);
 269
 270         message(out,"BN_GF2m_mod");
 271         if (!test_gf2m_mod(out)) goto err;
 272         BIO_flush(out);
 273
 274         message(out,"BN_GF2m_mod_mul");
 275         if (!test_gf2m_mod_mul(out,ctx)) goto err;
 276         BIO_flush(out);
 277
 278         message(out,"BN_GF2m_mod_sqr");
 279         if (!test_gf2m_mod_sqr(out,ctx)) goto err;
 280         BIO_flush(out);
 281
 282         message(out,"BN_GF2m_mod_inv");
 283         if (!test_gf2m_mod_inv(out,ctx)) goto err;
 284         BIO_flush(out);
 285
 286         message(out,"BN_GF2m_mod_div");
 287         if (!test_gf2m_mod_div(out,ctx)) goto err;
 288         BIO_flush(out);
 289
 290         message(out,"BN_GF2m_mod_exp");
 291         if (!test_gf2m_mod_exp(out,ctx)) goto err;
 292         BIO_flush(out);
 293
 294         message(out,"BN_GF2m_mod_sqrt");
 295         if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
 296         BIO_flush(out);
 297
 298         message(out,"BN_GF2m_mod_solve_quad");
 299         if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
 300         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         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,"%lX",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
 736         BN_bntest_rand(&a,100,0,0); /**/
 737         BN_bntest_rand(&b,100,0,0); /**/
 738         for (i=0; i<num2; i++)
 739                 {
 740                 int bits = (200*(i+1))/num2;
 741
 742                 if (bits == 0)
 743                         continue;
 744                 BN_bntest_rand(&n,bits,0,1);
 745                 BN_MONT_CTX_set(mont,&n,ctx);
 746
 747                 BN_nnmod(&a,&a,&n,ctx);
 748                 BN_nnmod(&b,&b,&n,ctx);
 749
 750                 BN_to_montgomery(&A,&a,mont,ctx);
 751                 BN_to_montgomery(&B,&b,mont,ctx);
 752
 753                 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
 754                 BN_from_montgomery(&A,&c,mont,ctx);/**/
 755                 if (bp != NULL)
 756                         {
 757                         if (!results)
 758                                 {
 759 #ifdef undef
 760 fprintf(stderr,"%d * %d %% %d\n",
 761 BN_num_bits(&a),
 762 BN_num_bits(&b),
 763 BN_num_bits(mont->N));
 764 #endif
 765                                 BN_print(bp,&a);
 766                                 BIO_puts(bp," * ");
 767                                 BN_print(bp,&b);
 768                                 BIO_puts(bp," % ");
 769                                 BN_print(bp,&(mont->N));
 770                                 BIO_puts(bp," - ");
 771                                 }
 772                         BN_print(bp,&A);
 773                         BIO_puts(bp,"\n");
 774                         }
 775                 BN_mod_mul(&d,&a,&b,&n,ctx);
 776                 BN_sub(&d,&d,&A);
 777                 if(!BN_is_zero(&d))
 778                     {
 779                     fprintf(stderr,"Montgomery multiplication test failed!\n");
 780                     return 0;
 781                     }
 782                 }
 783         BN_MONT_CTX_free(mont);
 784         BN_free(&a);
 785         BN_free(&b);
 786         BN_free(&c);
 787         BN_free(&d);
 788         BN_free(&A);
 789         BN_free(&B);
 790         BN_free(&n);
 791         return(1);
 792         }
 793
 794 int test_mod(BIO *bp, BN_CTX *ctx)
 795         {
 796         BIGNUM *a,*b,*c,*d,*e;
 797         int i;
 798
 799         a=BN_new();
 800         b=BN_new();
 801         c=BN_new();
 802         d=BN_new();
 803         e=BN_new();
 804
 805         BN_bntest_rand(a,1024,0,0); /**/
 806         for (i=0; i<num0; i++)
 807                 {
 808                 BN_bntest_rand(b,450+i*10,0,0); /**/
 809                 a->neg=rand_neg();
 810                 b->neg=rand_neg();
 811                 BN_mod(c,a,b,ctx);/**/
 812                 if (bp != NULL)
 813                         {
 814                         if (!results)
 815                                 {
 816                                 BN_print(bp,a);
 817                                 BIO_puts(bp," % ");
 818                                 BN_print(bp,b);
 819                                 BIO_puts(bp," - ");
 820                                 }
 821                         BN_print(bp,c);
 822                         BIO_puts(bp,"\n");
 823                         }
 824                 BN_div(d,e,a,b,ctx);
 825                 BN_sub(e,e,c);
 826                 if(!BN_is_zero(e))
 827                     {
 828                     fprintf(stderr,"Modulo test failed!\n");
 829                     return 0;
 830                     }
 831                 }
 832         BN_free(a);
 833         BN_free(b);
 834         BN_free(c);
 835         BN_free(d);
 836         BN_free(e);
 837         return(1);
 838         }
 839
 840 int test_mod_mul(BIO *bp, BN_CTX *ctx)
 841         {
 842         BIGNUM *a,*b,*c,*d,*e;
 843         int i,j;
 844
 845         a=BN_new();
 846         b=BN_new();
 847         c=BN_new();
 848         d=BN_new();
 849         e=BN_new();
 850
 851         for (j=0; j<3; j++) {
 852         BN_bntest_rand(c,1024,0,0); /**/
 853         for (i=0; i<num0; i++)
 854                 {
 855                 BN_bntest_rand(a,475+i*10,0,0); /**/
 856                 BN_bntest_rand(b,425+i*11,0,0); /**/
 857                 a->neg=rand_neg();
 858                 b->neg=rand_neg();
 859                 if (!BN_mod_mul(e,a,b,c,ctx))
 860                         {
 861                         unsigned long l;
 862
 863                         while ((l=ERR_get_error()))
 864                                 fprintf(stderr,"ERROR:%s\n",
 865                                         ERR_error_string(l,NULL));
 866                         EXIT(1);
 867                         }
 868                 if (bp != NULL)
 869                         {
 870                         if (!results)
 871                                 {
 872                                 BN_print(bp,a);
 873                                 BIO_puts(bp," * ");
 874                                 BN_print(bp,b);
 875                                 BIO_puts(bp," % ");
 876                                 BN_print(bp,c);
 877                                 if ((a->neg ^ b->neg) && !BN_is_zero(e))
 878                                         {
 879                                         /* If  (a*b) % c  is negative,  c  must be added
 880                                          * in order to obtain the normalized remainder
 881                                          * (new with OpenSSL 0.9.7, previous versions of
 882                                          * BN_mod_mul could generate negative results)
 883                                          */
 884                                         BIO_puts(bp," + ");
 885                                         BN_print(bp,c);
 886                                         }
 887                                 BIO_puts(bp," - ");
 888                                 }
 889                         BN_print(bp,e);
 890                         BIO_puts(bp,"\n");
 891                         }
 892                 BN_mul(d,a,b,ctx);
 893                 BN_sub(d,d,e);
 894                 BN_div(a,b,d,c,ctx);
 895                 if(!BN_is_zero(b))
 896                     {
 897                     fprintf(stderr,"Modulo multiply test failed!\n");
 898                     ERR_print_errors_fp(stderr);
 899                     return 0;
 900                     }
 901                 }
 902         }
 903         BN_free(a);
 904         BN_free(b);
 905         BN_free(c);
 906         BN_free(d);
 907         BN_free(e);
 908         return(1);
 909         }
 910
 911 int test_mod_exp(BIO *bp, BN_CTX *ctx)
 912         {
 913         BIGNUM *a,*b,*c,*d,*e;
 914         int i;
 915
 916         a=BN_new();
 917         b=BN_new();
 918         c=BN_new();
 919         d=BN_new();
 920         e=BN_new();
 921
 922         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
 923         for (i=0; i<num2; i++)
 924                 {
 925                 BN_bntest_rand(a,20+i*5,0,0); /**/
 926                 BN_bntest_rand(b,2+i,0,0); /**/
 927
 928                 if (!BN_mod_exp(d,a,b,c,ctx))
 929                         return(00);
 930
 931                 if (bp != NULL)
 932                         {
 933                         if (!results)
 934                                 {
 935                                 BN_print(bp,a);
 936                                 BIO_puts(bp," ^ ");
 937                                 BN_print(bp,b);
 938                                 BIO_puts(bp," % ");
 939                                 BN_print(bp,c);
 940                                 BIO_puts(bp," - ");
 941                                 }
 942                         BN_print(bp,d);
 943                         BIO_puts(bp,"\n");
 944                         }
 945                 BN_exp(e,a,b,ctx);
 946                 BN_sub(e,e,d);
 947                 BN_div(a,b,e,c,ctx);
 948                 if(!BN_is_zero(b))
 949                     {
 950                     fprintf(stderr,"Modulo exponentiation test failed!\n");
 951                     return 0;
 952                     }
 953                 }
 954         BN_free(a);
 955         BN_free(b);
 956         BN_free(c);
 957         BN_free(d);
 958         BN_free(e);
 959         return(1);
 960         }
 961
 962 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
 963         {
 964         BIGNUM *a,*b,*c,*d,*e;
 965         int i;
 966
 967         a=BN_new();
 968         b=BN_new();
 969         c=BN_new();
 970         d=BN_new();
 971         e=BN_new();
 972
 973         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
 974         for (i=0; i<num2; i++)
 975                 {
 976                 BN_bntest_rand(a,20+i*5,0,0); /**/
 977                 BN_bntest_rand(b,2+i,0,0); /**/
 978
 979                 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
 980                         return(00);
 981
 982                 if (bp != NULL)
 983                         {
 984                         if (!results)
 985                                 {
 986                                 BN_print(bp,a);
 987                                 BIO_puts(bp," ^ ");
 988                                 BN_print(bp,b);
 989                                 BIO_puts(bp," % ");
 990                                 BN_print(bp,c);
 991                                 BIO_puts(bp," - ");
 992                                 }
 993                         BN_print(bp,d);
 994                         BIO_puts(bp,"\n");
 995                         }
 996                 BN_exp(e,a,b,ctx);
 997                 BN_sub(e,e,d);
 998                 BN_div(a,b,e,c,ctx);
 999                 if(!BN_is_zero(b))
1000                     {
1001                     fprintf(stderr,"Modulo exponentiation test failed!\n");
1002                     return 0;
1003                     }
1004                 }
1005         BN_free(a);
1006         BN_free(b);
1007         BN_free(c);
1008         BN_free(d);
1009         BN_free(e);
1010         return(1);
1011         }
1012
1013 int test_exp(BIO *bp, BN_CTX *ctx)
1014         {
1015         BIGNUM *a,*b,*d,*e,*one;
1016         int i;
1017
1018         a=BN_new();
1019         b=BN_new();
1020         d=BN_new();
1021         e=BN_new();
1022         one=BN_new();
1023         BN_one(one);
1024
1025         for (i=0; i<num2; i++)
1026                 {
1027                 BN_bntest_rand(a,20+i*5,0,0); /**/
1028                 BN_bntest_rand(b,2+i,0,0); /**/
1029
1030                 if (!BN_exp(d,a,b,ctx))
1031                         return(00);
1032
1033                 if (bp != NULL)
1034                         {
1035                         if (!results)
1036                                 {
1037                                 BN_print(bp,a);
1038                                 BIO_puts(bp," ^ ");
1039                                 BN_print(bp,b);
1040                                 BIO_puts(bp," - ");
1041                                 }
1042                         BN_print(bp,d);
1043                         BIO_puts(bp,"\n");
1044                         }
1045                 BN_one(e);
1046                 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1047                     BN_mul(e,e,a,ctx);
1048                 BN_sub(e,e,d);
1049                 if(!BN_is_zero(e))
1050                     {
1051                     fprintf(stderr,"Exponentiation test failed!\n");
1052                     return 0;
1053                     }
1054                 }
1055         BN_free(a);
1056         BN_free(b);
1057         BN_free(d);
1058         BN_free(e);
1059         BN_free(one);
1060         return(1);
1061         }
1062
1063 int test_gf2m_add(BIO *bp)
1064         {
1065         BIGNUM a,b,c;
1066         int i, ret = 0;
1067
1068         BN_init(&a);
1069         BN_init(&b);
1070         BN_init(&c);
1071
1072         for (i=0; i<num0; i++)
1073                 {
1074                 BN_rand(&a,512,0,0);
1075                 BN_copy(&b, BN_value_one());
1076                 a.neg=rand_neg();
1077                 b.neg=rand_neg();
1078                 BN_GF2m_add(&c,&a,&b);
1079 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1080                 if (bp != NULL)
1081                         {
1082                         if (!results)
1083                                 {
1084                                 BN_print(bp,&a);
1085                                 BIO_puts(bp," ^ ");
1086                                 BN_print(bp,&b);
1087                                 BIO_puts(bp," = ");
1088                                 }
1089                         BN_print(bp,&c);
1090                         BIO_puts(bp,"\n");
1091                         }
1092 #endif
1093                 /* Test that two added values have the correct parity. */
1094                 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1095                         {
1096                     fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1097                         goto err;
1098                         }
1099                 BN_GF2m_add(&c,&c,&c);
1100                 /* Test that c + c = 0. */
1101                 if(!BN_is_zero(&c))
1102                     {
1103                     fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1104                         goto err;
1105                     }
1106                 }
1107         ret = 1;
1108   err:
1109         BN_free(&a);
1110         BN_free(&b);
1111         BN_free(&c);
1112         return ret;
1113         }
1114
1115 int test_gf2m_mod(BIO *bp)
1116         {
1117         BIGNUM *a,*b[2],*c,*d,*e;
1118         int i, j, ret = 0;
1119         unsigned int p0[] = {163,7,6,3,0};
1120         unsigned int p1[] = {193,15,0};
1121
1122         a=BN_new();
1123         b[0]=BN_new();
1124         b[1]=BN_new();
1125         c=BN_new();
1126         d=BN_new();
1127         e=BN_new();
1128
1129         BN_GF2m_arr2poly(p0, b[0]);
1130         BN_GF2m_arr2poly(p1, b[1]);
1131
1132         for (i=0; i<num0; i++)
1133                 {
1134                 BN_bntest_rand(a, 1024, 0, 0);
1135                 for (j=0; j < 2; j++)
1136                         {
1137                         BN_GF2m_mod(c, a, b[j]);
1138 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1139                         if (bp != NULL)
1140                                 {
1141                                 if (!results)
1142                                         {
1143                                         BN_print(bp,a);
1144                                         BIO_puts(bp," % ");
1145                                         BN_print(bp,b[j]);
1146                                         BIO_puts(bp," - ");
1147                                         BN_print(bp,c);
1148                                         BIO_puts(bp,"\n");
1149                                         }
1150                                 }
1151 #endif
1152                         BN_GF2m_add(d, a, c);
1153                         BN_GF2m_mod(e, d, b[j]);
1154                         /* Test that a + (a mod p) mod p == 0. */
1155                         if(!BN_is_zero(e))
1156                                 {
1157                                 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1158                                 goto err;
1159                                 }
1160                         }
1161                 }
1162         ret = 1;
1163   err:
1164         BN_free(a);
1165         BN_free(b[0]);
1166         BN_free(b[1]);
1167         BN_free(c);
1168         BN_free(d);
1169         BN_free(e);
1170         return ret;
1171         }
1172
1173 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1174         {
1175         BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1176         int i, j, ret = 0;
1177         unsigned int p0[] = {163,7,6,3,0};
1178         unsigned int p1[] = {193,15,0};
1179
1180         a=BN_new();
1181         b[0]=BN_new();
1182         b[1]=BN_new();
1183         c=BN_new();
1184         d=BN_new();
1185         e=BN_new();
1186         f=BN_new();
1187         g=BN_new();
1188         h=BN_new();
1189
1190         BN_GF2m_arr2poly(p0, b[0]);
1191         BN_GF2m_arr2poly(p1, b[1]);
1192
1193         for (i=0; i<num0; i++)
1194                 {
1195                 BN_bntest_rand(a, 1024, 0, 0);
1196                 BN_bntest_rand(c, 1024, 0, 0);
1197                 BN_bntest_rand(d, 1024, 0, 0);
1198                 for (j=0; j < 2; j++)
1199                         {
1200                         BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1201 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1202                         if (bp != NULL)
1203                                 {
1204                                 if (!results)
1205                                         {
1206                                         BN_print(bp,a);
1207                                         BIO_puts(bp," * ");
1208                                         BN_print(bp,c);
1209                                         BIO_puts(bp," % ");
1210                                         BN_print(bp,b[j]);
1211                                         BIO_puts(bp," - ");
1212                                         BN_print(bp,e);
1213                                         BIO_puts(bp,"\n");
1214                                         }
1215                                 }
1216 #endif
1217                         BN_GF2m_add(f, a, d);
1218                         BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1219                         BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1220                         BN_GF2m_add(f, e, g);
1221                         BN_GF2m_add(f, f, h);
1222                         /* Test that (a+d)*c = a*c + d*c. */
1223                         if(!BN_is_zero(f))
1224                                 {
1225                                 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1226                                 goto err;
1227                                 }
1228                         }
1229                 }
1230         ret = 1;
1231   err:
1232         BN_free(a);
1233         BN_free(b[0]);
1234         BN_free(b[1]);
1235         BN_free(c);
1236         BN_free(d);
1237         BN_free(e);
1238         BN_free(f);
1239         BN_free(g);
1240         BN_free(h);
1241         return ret;
1242         }
1243
1244 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1245         {
1246         BIGNUM *a,*b[2],*c,*d;
1247         int i, j, ret = 0;
1248         unsigned int p0[] = {163,7,6,3,0};
1249         unsigned int p1[] = {193,15,0};
1250
1251         a=BN_new();
1252         b[0]=BN_new();
1253         b[1]=BN_new();
1254         c=BN_new();
1255         d=BN_new();
1256
1257         BN_GF2m_arr2poly(p0, b[0]);
1258         BN_GF2m_arr2poly(p1, b[1]);
1259
1260         for (i=0; i<num0; i++)
1261                 {
1262                 BN_bntest_rand(a, 1024, 0, 0);
1263                 for (j=0; j < 2; j++)
1264                         {
1265                         BN_GF2m_mod_sqr(c, a, b[j], ctx);
1266                         BN_copy(d, a);
1267                         BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1268 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1269                         if (bp != NULL)
1270                                 {
1271                                 if (!results)
1272                                         {
1273                                         BN_print(bp,a);
1274                                         BIO_puts(bp," ^ 2 % ");
1275                                         BN_print(bp,b[j]);
1276                                         BIO_puts(bp, " = ");
1277                                         BN_print(bp,c);
1278                                         BIO_puts(bp,"; a * a = ");
1279                                         BN_print(bp,d);
1280                                         BIO_puts(bp,"\n");
1281                                         }
1282                                 }
1283 #endif
1284                         BN_GF2m_add(d, c, d);
1285                         /* Test that a*a = a^2. */
1286                         if(!BN_is_zero(d))
1287                                 {
1288                                 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1289                                 goto err;
1290                                 }
1291                         }
1292                 }
1293         ret = 1;
1294   err:
1295         BN_free(a);
1296         BN_free(b[0]);
1297         BN_free(b[1]);
1298         BN_free(c);
1299         BN_free(d);
1300         return ret;
1301         }
1302
1303 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1304         {
1305         BIGNUM *a,*b[2],*c,*d;
1306         int i, j, ret = 0;
1307         unsigned int p0[] = {163,7,6,3,0};
1308         unsigned int p1[] = {193,15,0};
1309
1310         a=BN_new();
1311         b[0]=BN_new();
1312         b[1]=BN_new();
1313         c=BN_new();
1314         d=BN_new();
1315
1316         BN_GF2m_arr2poly(p0, b[0]);
1317         BN_GF2m_arr2poly(p1, b[1]);
1318
1319         for (i=0; i<num0; i++)
1320                 {
1321                 BN_bntest_rand(a, 512, 0, 0);
1322                 for (j=0; j < 2; j++)
1323                         {
1324                         BN_GF2m_mod_inv(c, a, b[j], ctx);
1325                         BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1326 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1327                         if (bp != NULL)
1328                                 {
1329                                 if (!results)
1330                                         {
1331                                         BN_print(bp,a);
1332                                         BIO_puts(bp, " * ");
1333                                         BN_print(bp,c);
1334                                         BIO_puts(bp," - 1 % ");
1335                                         BN_print(bp,b[j]);
1336                                         BIO_puts(bp,"\n");
1337                                         }
1338                                 }
1339 #endif
1340                         /* Test that ((1/a)*a) = 1. */
1341                         if(!BN_is_one(d))
1342                                 {
1343                                 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1344                                 goto err;
1345                                 }
1346                         }
1347                 }
1348         ret = 1;
1349   err:
1350         BN_free(a);
1351         BN_free(b[0]);
1352         BN_free(b[1]);
1353         BN_free(c);
1354         BN_free(d);
1355         return ret;
1356         }
1357
1358 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1359         {
1360         BIGNUM *a,*b[2],*c,*d,*e,*f;
1361         int i, j, ret = 0;
1362         unsigned int p0[] = {163,7,6,3,0};
1363         unsigned int p1[] = {193,15,0};
1364
1365         a=BN_new();
1366         b[0]=BN_new();
1367         b[1]=BN_new();
1368         c=BN_new();
1369         d=BN_new();
1370         e=BN_new();
1371         f=BN_new();
1372
1373         BN_GF2m_arr2poly(p0, b[0]);
1374         BN_GF2m_arr2poly(p1, b[1]);
1375
1376         for (i=0; i<num0; i++)
1377                 {
1378                 BN_bntest_rand(a, 512, 0, 0);
1379                 BN_bntest_rand(c, 512, 0, 0);
1380                 for (j=0; j < 2; j++)
1381                         {
1382                         BN_GF2m_mod_div(d, a, c, b[j], ctx);
1383                         BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1384                         BN_GF2m_mod_div(f, a, e, b[j], ctx);
1385 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1386                         if (bp != NULL)
1387                                 {
1388                                 if (!results)
1389                                         {
1390                                         BN_print(bp,a);
1391                                         BIO_puts(bp, " = ");
1392                                         BN_print(bp,c);
1393                                         BIO_puts(bp," * ");
1394                                         BN_print(bp,d);
1395                                         BIO_puts(bp, " % ");
1396                                         BN_print(bp,b[j]);
1397                                         BIO_puts(bp,"\n");
1398                                         }
1399                                 }
1400 #endif
1401                         /* Test that ((a/c)*c)/a = 1. */
1402                         if(!BN_is_one(f))
1403                                 {
1404                                 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1405                                 goto err;
1406                                 }
1407                         }
1408                 }
1409         ret = 1;
1410   err:
1411         BN_free(a);
1412         BN_free(b[0]);
1413         BN_free(b[1]);
1414         BN_free(c);
1415         BN_free(d);
1416         BN_free(e);
1417         BN_free(f);
1418         return ret;
1419         }
1420
1421 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1422         {
1423         BIGNUM *a,*b[2],*c,*d,*e,*f;
1424         int i, j, ret = 0;
1425         unsigned int p0[] = {163,7,6,3,0};
1426         unsigned int p1[] = {193,15,0};
1427
1428         a=BN_new();
1429         b[0]=BN_new();
1430         b[1]=BN_new();
1431         c=BN_new();
1432         d=BN_new();
1433         e=BN_new();
1434         f=BN_new();
1435
1436         BN_GF2m_arr2poly(p0, b[0]);
1437         BN_GF2m_arr2poly(p1, b[1]);
1438
1439         for (i=0; i<num0; i++)
1440                 {
1441                 BN_bntest_rand(a, 512, 0, 0);
1442                 BN_bntest_rand(c, 512, 0, 0);
1443                 BN_bntest_rand(d, 512, 0, 0);
1444                 for (j=0; j < 2; j++)
1445                         {
1446                         BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1447                         BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1448                         BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1449                         BN_add(f, c, d);
1450                         BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1451 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1452                         if (bp != NULL)
1453                                 {
1454                                 if (!results)
1455                                         {
1456                                         BN_print(bp,a);
1457                                         BIO_puts(bp, " ^ (");
1458                                         BN_print(bp,c);
1459                                         BIO_puts(bp," + ");
1460                                         BN_print(bp,d);
1461                                         BIO_puts(bp, ") = ");
1462                                         BN_print(bp,e);
1463                                         BIO_puts(bp, "; - ");
1464                                         BN_print(bp,f);
1465                                         BIO_puts(bp, " % ");
1466                                         BN_print(bp,b[j]);
1467                                         BIO_puts(bp,"\n");
1468                                         }
1469                                 }
1470 #endif
1471                         BN_GF2m_add(f, e, f);
1472                         /* Test that a^(c+d)=a^c*a^d. */
1473                         if(!BN_is_zero(f))
1474                                 {
1475                                 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1476                                 goto err;
1477                                 }
1478                         }
1479                 }
1480         ret = 1;
1481   err:
1482         BN_free(a);
1483         BN_free(b[0]);
1484         BN_free(b[1]);
1485         BN_free(c);
1486         BN_free(d);
1487         BN_free(e);
1488         BN_free(f);
1489         return ret;
1490         }
1491
1492 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1493         {
1494         BIGNUM *a,*b[2],*c,*d,*e,*f;
1495         int i, j, ret = 0;
1496         unsigned int p0[] = {163,7,6,3,0};
1497         unsigned int p1[] = {193,15,0};
1498
1499         a=BN_new();
1500         b[0]=BN_new();
1501         b[1]=BN_new();
1502         c=BN_new();
1503         d=BN_new();
1504         e=BN_new();
1505         f=BN_new();
1506
1507         BN_GF2m_arr2poly(p0, b[0]);
1508         BN_GF2m_arr2poly(p1, b[1]);
1509
1510         for (i=0; i<num0; i++)
1511                 {
1512                 BN_bntest_rand(a, 512, 0, 0);
1513                 for (j=0; j < 2; j++)
1514                         {
1515                         BN_GF2m_mod(c, a, b[j]);
1516                         BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1517                         BN_GF2m_mod_sqr(e, d, b[j], ctx);
1518 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1519                         if (bp != NULL)
1520                                 {
1521                                 if (!results)
1522                                         {
1523                                         BN_print(bp,d);
1524                                         BIO_puts(bp, " ^ 2 - ");
1525                                         BN_print(bp,a);
1526                                         BIO_puts(bp,"\n");
1527                                         }
1528                                 }
1529 #endif
1530                         BN_GF2m_add(f, c, e);
1531                         /* Test that d^2 = a, where d = sqrt(a). */
1532                         if(!BN_is_zero(f))
1533                                 {
1534                                 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1535                                 goto err;
1536                                 }
1537                         }
1538                 }
1539         ret = 1;
1540   err:
1541         BN_free(a);
1542         BN_free(b[0]);
1543         BN_free(b[1]);
1544         BN_free(c);
1545         BN_free(d);
1546         BN_free(e);
1547         BN_free(f);
1548         return ret;
1549         }
1550
1551 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1552         {
1553         BIGNUM *a,*b[2],*c,*d,*e;
1554         int i, j, s = 0, t, ret = 0;
1555         unsigned int p0[] = {163,7,6,3,0};
1556         unsigned int p1[] = {193,15,0};
1557
1558         a=BN_new();
1559         b[0]=BN_new();
1560         b[1]=BN_new();
1561         c=BN_new();
1562         d=BN_new();
1563         e=BN_new();
1564
1565         BN_GF2m_arr2poly(p0, b[0]);
1566         BN_GF2m_arr2poly(p1, b[1]);
1567
1568         for (i=0; i<num0; i++)
1569                 {
1570                 BN_bntest_rand(a, 512, 0, 0);
1571                 for (j=0; j < 2; j++)
1572                         {
1573                         t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1574                         if (t)
1575                                 {
1576                                 s++;
1577                                 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1578                                 BN_GF2m_add(d, c, d);
1579                                 BN_GF2m_mod(e, a, b[j]);
1580 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1581                                 if (bp != NULL)
1582                                         {
1583                                         if (!results)
1584                                                 {
1585                                                 BN_print(bp,c);
1586                                                 BIO_puts(bp, " is root of z^2 + z = ");
1587                                                 BN_print(bp,a);
1588                                                 BIO_puts(bp, " % ");
1589                                                 BN_print(bp,b[j]);
1590                                                 BIO_puts(bp, "\n");
1591                                                 }
1592                                         }
1593 #endif
1594                                 BN_GF2m_add(e, e, d);
1595                                 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1596                                 if(!BN_is_zero(e))
1597                                         {
1598                                         fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1599                                         goto err;
1600                                         }
1601
1602                                 }
1603                         else
1604                                 {
1605 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1606                                 if (bp != NULL)
1607                                         {
1608                                         if (!results)
1609                                                 {
1610                                                 BIO_puts(bp, "There are no roots of z^2 + z = ");
1611                                                 BN_print(bp,a);
1612                                                 BIO_puts(bp, " % ");
1613                                                 BN_print(bp,b[j]);
1614                                                 BIO_puts(bp, "\n");
1615                                                 }
1616                                         }
1617 #endif
1618                                 }
1619                         }
1620                 }
1621         if (s == 0)
1622                 {
1623                 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1624                 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1625                 goto err;
1626                 }
1627         ret = 1;
1628   err:
1629         BN_free(a);
1630         BN_free(b[0]);
1631         BN_free(b[1]);
1632         BN_free(c);
1633         BN_free(d);
1634         BN_free(e);
1635         return ret;
1636         }
1637
1638 static int genprime_cb(int p, int n, BN_GENCB *arg)
1639         {
1640         char c='*';
1641
1642         if (p == 0) c='.';
1643         if (p == 1) c='+';
1644         if (p == 2) c='*';
1645         if (p == 3) c='\n';
1646         putc(c, stderr);
1647         fflush(stderr);
1648         return 1;
1649         }
1650
1651 int test_kron(BIO *bp, BN_CTX *ctx)
1652         {
1653         BN_GENCB cb;
1654         BIGNUM *a,*b,*r,*t;
1655         int i;
1656         int legendre, kronecker;
1657         int ret = 0;
1658
1659         a = BN_new();
1660         b = BN_new();
1661         r = BN_new();
1662         t = BN_new();
1663         if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1664
1665         BN_GENCB_set(&cb, genprime_cb, NULL);
1666
1667         /* We test BN_kronecker(a, b, ctx) just for  b  odd (Jacobi symbol).
1668          * In this case we know that if  b  is prime, then BN_kronecker(a, b, ctx)
1669          * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1670          * So we generate a random prime  b  and compare these values
1671          * for a number of random  a's.  (That is, we run the Solovay-Strassen
1672          * primality test to confirm that  b  is prime, except that we
1673          * don't want to test whether  b  is prime but whether BN_kronecker
1674          * works.) */
1675
1676         if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1677         b->neg = rand_neg();
1678         putc('\n', stderr);
1679
1680         for (i = 0; i < num0; i++)
1681                 {
1682                 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1683                 a->neg = rand_neg();
1684
1685                 /* t := (|b|-1)/2  (note that b is odd) */
1686                 if (!BN_copy(t, b)) goto err;
1687                 t->neg = 0;
1688                 if (!BN_sub_word(t, 1)) goto err;
1689                 if (!BN_rshift1(t, t)) goto err;
1690                 /* r := a^t mod b */
1691                 b->neg=0;
1692
1693                 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1694                 b->neg=1;
1695
1696                 if (BN_is_word(r, 1))
1697                         legendre = 1;
1698                 else if (BN_is_zero(r))
1699                         legendre = 0;
1700                 else
1701                         {
1702                         if (!BN_add_word(r, 1)) goto err;
1703                         if (0 != BN_ucmp(r, b))
1704                                 {
1705                                 fprintf(stderr, "Legendre symbol computation failed\n");
1706                                 goto err;
1707                                 }
1708                         legendre = -1;
1709                         }
1710
1711                 kronecker = BN_kronecker(a, b, ctx);
1712                 if (kronecker < -1) goto err;
1713                 /* we actually need BN_kronecker(a, |b|) */
1714                 if (a->neg && b->neg)
1715                         kronecker = -kronecker;
1716
1717                 if (legendre != kronecker)
1718                         {
1719                         fprintf(stderr, "legendre != kronecker; a = ");
1720                         BN_print_fp(stderr, a);
1721                         fprintf(stderr, ", b = ");
1722                         BN_print_fp(stderr, b);
1723                         fprintf(stderr, "\n");
1724                         goto err;
1725                         }
1726
1727                 putc('.', stderr);
1728                 fflush(stderr);
1729                 }
1730
1731         putc('\n', stderr);
1732         fflush(stderr);
1733         ret = 1;
1734  err:
1735         if (a != NULL) BN_free(a);
1736         if (b != NULL) BN_free(b);
1737         if (r != NULL) BN_free(r);
1738         if (t != NULL) BN_free(t);
1739         return ret;
1740         }
1741
1742 int test_sqrt(BIO *bp, BN_CTX *ctx)
1743         {
1744         BN_GENCB cb;
1745         BIGNUM *a,*p,*r;
1746         int i, j;
1747         int ret = 0;
1748
1749         a = BN_new();
1750         p = BN_new();
1751         r = BN_new();
1752         if (a == NULL || p == NULL || r == NULL) goto err;
1753
1754         BN_GENCB_set(&cb, genprime_cb, NULL);
1755
1756         for (i = 0; i < 16; i++)
1757                 {
1758                 if (i < 8)
1759                         {
1760                         unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1761
1762                         if (!BN_set_word(p, primes[i])) goto err;
1763                         }
1764                 else
1765                         {
1766                         if (!BN_set_word(a, 32)) goto err;
1767                         if (!BN_set_word(r, 2*i + 1)) goto err;
1768
1769                         if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1770                         putc('\n', stderr);
1771                         }
1772                 p->neg = rand_neg();
1773
1774                 for (j = 0; j < num2; j++)
1775                         {
1776                         /* construct 'a' such that it is a square modulo p,
1777                          * but in general not a proper square and not reduced modulo p */
1778                         if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1779                         if (!BN_nnmod(r, r, p, ctx)) goto err;
1780                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1781                         if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1782                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1783                         if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1784                         if (!BN_mul(a, a, r, ctx)) goto err;
1785                         if (rand_neg())
1786                                 if (!BN_sub(a, a, p)) goto err;
1787
1788                         if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1789                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1790
1791                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1792
1793                         if (BN_cmp(a, r) != 0)
1794                                 {
1795                                 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1796                                 BN_print_fp(stderr, a);
1797                                 fprintf(stderr, ", r = ");
1798                                 BN_print_fp(stderr, r);
1799                                 fprintf(stderr, ", p = ");
1800                                 BN_print_fp(stderr, p);
1801                                 fprintf(stderr, "\n");
1802                                 goto err;
1803                                 }
1804
1805                         putc('.', stderr);
1806                         fflush(stderr);
1807                         }
1808
1809                 putc('\n', stderr);
1810                 fflush(stderr);
1811                 }
1812         ret = 1;
1813  err:
1814         if (a != NULL) BN_free(a);
1815         if (p != NULL) BN_free(p);
1816         if (r != NULL) BN_free(r);
1817         return ret;
1818         }
1819
1820 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1821         {
1822         BIGNUM *a,*b,*c,*d;
1823         int i;
1824
1825         b=BN_new();
1826         c=BN_new();
1827         d=BN_new();
1828         BN_one(c);
1829
1830         if(a_)
1831             a=a_;
1832         else
1833             {
1834             a=BN_new();
1835             BN_bntest_rand(a,200,0,0); /**/
1836             a->neg=rand_neg();
1837             }
1838         for (i=0; i<num0; i++)
1839                 {
1840                 BN_lshift(b,a,i+1);
1841                 BN_add(c,c,c);
1842                 if (bp != NULL)
1843                         {
1844                         if (!results)
1845                                 {
1846                                 BN_print(bp,a);
1847                                 BIO_puts(bp," * ");
1848                                 BN_print(bp,c);
1849                                 BIO_puts(bp," - ");
1850                                 }
1851                         BN_print(bp,b);
1852                         BIO_puts(bp,"\n");
1853                         }
1854                 BN_mul(d,a,c,ctx);
1855                 BN_sub(d,d,b);
1856                 if(!BN_is_zero(d))
1857                     {
1858                     fprintf(stderr,"Left shift test failed!\n");
1859                     fprintf(stderr,"a=");
1860                     BN_print_fp(stderr,a);
1861                     fprintf(stderr,"\nb=");
1862                     BN_print_fp(stderr,b);
1863                     fprintf(stderr,"\nc=");
1864                     BN_print_fp(stderr,c);
1865                     fprintf(stderr,"\nd=");
1866                     BN_print_fp(stderr,d);
1867                     fprintf(stderr,"\n");
1868                     return 0;
1869                     }
1870                 }
1871         BN_free(a);
1872         BN_free(b);
1873         BN_free(c);
1874         BN_free(d);
1875         return(1);
1876         }
1877
1878 int test_lshift1(BIO *bp)
1879         {
1880         BIGNUM *a,*b,*c;
1881         int i;
1882
1883         a=BN_new();
1884         b=BN_new();
1885         c=BN_new();
1886
1887         BN_bntest_rand(a,200,0,0); /**/
1888         a->neg=rand_neg();
1889         for (i=0; i<num0; i++)
1890                 {
1891                 BN_lshift1(b,a);
1892                 if (bp != NULL)
1893                         {
1894                         if (!results)
1895                                 {
1896                                 BN_print(bp,a);
1897                                 BIO_puts(bp," * 2");
1898                                 BIO_puts(bp," - ");
1899                                 }
1900                         BN_print(bp,b);
1901                         BIO_puts(bp,"\n");
1902                         }
1903                 BN_add(c,a,a);
1904                 BN_sub(a,b,c);
1905                 if(!BN_is_zero(a))
1906                     {
1907                     fprintf(stderr,"Left shift one test failed!\n");
1908                     return 0;
1909                     }
1910
1911                 BN_copy(a,b);
1912                 }
1913         BN_free(a);
1914         BN_free(b);
1915         BN_free(c);
1916         return(1);
1917         }
1918
1919 int test_rshift(BIO *bp,BN_CTX *ctx)
1920         {
1921         BIGNUM *a,*b,*c,*d,*e;
1922         int i;
1923
1924         a=BN_new();
1925         b=BN_new();
1926         c=BN_new();
1927         d=BN_new();
1928         e=BN_new();
1929         BN_one(c);
1930
1931         BN_bntest_rand(a,200,0,0); /**/
1932         a->neg=rand_neg();
1933         for (i=0; i<num0; i++)
1934                 {
1935                 BN_rshift(b,a,i+1);
1936                 BN_add(c,c,c);
1937                 if (bp != NULL)
1938                         {
1939                         if (!results)
1940                                 {
1941                                 BN_print(bp,a);
1942                                 BIO_puts(bp," / ");
1943                                 BN_print(bp,c);
1944                                 BIO_puts(bp," - ");
1945                                 }
1946                         BN_print(bp,b);
1947                         BIO_puts(bp,"\n");
1948                         }
1949                 BN_div(d,e,a,c,ctx);
1950                 BN_sub(d,d,b);
1951                 if(!BN_is_zero(d))
1952                     {
1953                     fprintf(stderr,"Right shift test failed!\n");
1954                     return 0;
1955                     }
1956                 }
1957         BN_free(a);
1958         BN_free(b);
1959         BN_free(c);
1960         BN_free(d);
1961         BN_free(e);
1962         return(1);
1963         }
1964
1965 int test_rshift1(BIO *bp)
1966         {
1967         BIGNUM *a,*b,*c;
1968         int i;
1969
1970         a=BN_new();
1971         b=BN_new();
1972         c=BN_new();
1973
1974         BN_bntest_rand(a,200,0,0); /**/
1975         a->neg=rand_neg();
1976         for (i=0; i<num0; i++)
1977                 {
1978                 BN_rshift1(b,a);
1979                 if (bp != NULL)
1980                         {
1981                         if (!results)
1982                                 {
1983                                 BN_print(bp,a);
1984                                 BIO_puts(bp," / 2");
1985                                 BIO_puts(bp," - ");
1986                                 }
1987                         BN_print(bp,b);
1988                         BIO_puts(bp,"\n");
1989                         }
1990                 BN_sub(c,a,b);
1991                 BN_sub(c,c,b);
1992                 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1993                     {
1994                     fprintf(stderr,"Right shift one test failed!\n");
1995                     return 0;
1996                     }
1997                 BN_copy(a,b);
1998                 }
1999         BN_free(a);
2000         BN_free(b);
2001         BN_free(c);
2002         return(1);
2003         }
2004
2005 int rand_neg(void)
2006         {
2007         static unsigned int neg=0;
2008         static int sign[8]={0,0,0,1,1,0,1,1};
2009
2010         return(sign[(neg++)%8]);
2011         }