crypto/openssl/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 #ifndef OPENSSL_NO_EC2M
 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 #endif
 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, ret = 0;
 681
 682         a = BN_new();
 683         c = BN_new();
 684         d = BN_new();
 685         e = BN_new();
 686         if (a == NULL || c == NULL || d == NULL || e == NULL)
 687                 {
 688                 goto err;
 689                 }
 690
 691         for (i=0; i<num0; i++)
 692                 {
 693                 BN_bntest_rand(a,40+i*10,0,0);
 694                 a->neg=rand_neg();
 695                 BN_sqr(c,a,ctx);
 696                 if (bp != NULL)
 697                         {
 698                         if (!results)
 699                                 {
 700                                 BN_print(bp,a);
 701                                 BIO_puts(bp," * ");
 702                                 BN_print(bp,a);
 703                                 BIO_puts(bp," - ");
 704                                 }
 705                         BN_print(bp,c);
 706                         BIO_puts(bp,"\n");
 707                         }
 708                 BN_div(d,e,c,a,ctx);
 709                 BN_sub(d,d,a);
 710                 if(!BN_is_zero(d) || !BN_is_zero(e))
 711                         {
 712                         fprintf(stderr,"Square test failed!\n");
 713                         goto err;
 714                         }
 715                 }
 716
 717         /* Regression test for a BN_sqr overflow bug. */
 718         BN_hex2bn(&a,
 719                 "80000000000000008000000000000001FFFFFFFFFFFFFFFE0000000000000000");
 720         BN_sqr(c, a, ctx);
 721         if (bp != NULL)
 722                 {
 723                 if (!results)
 724                         {
 725                         BN_print(bp,a);
 726                         BIO_puts(bp," * ");
 727                         BN_print(bp,a);
 728                         BIO_puts(bp," - ");
 729                         }
 730                 BN_print(bp,c);
 731                 BIO_puts(bp,"\n");
 732                 }
 733         BN_mul(d, a, a, ctx);
 734         if (BN_cmp(c, d))
 735                 {
 736                 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
 737                         "different results!\n");
 738                 goto err;
 739                 }
 740
 741         /* Regression test for a BN_sqr overflow bug. */
 742         BN_hex2bn(&a,
 743                 "80000000000000000000000080000001FFFFFFFE000000000000000000000000");
 744         BN_sqr(c, a, ctx);
 745         if (bp != NULL)
 746                 {
 747                 if (!results)
 748                         {
 749                         BN_print(bp,a);
 750                         BIO_puts(bp," * ");
 751                         BN_print(bp,a);
 752                         BIO_puts(bp," - ");
 753                         }
 754                 BN_print(bp,c);
 755                 BIO_puts(bp,"\n");
 756                 }
 757         BN_mul(d, a, a, ctx);
 758         if (BN_cmp(c, d))
 759                 {
 760                 fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
 761                         "different results!\n");
 762                 goto err;
 763                 }
 764         ret = 1;
 765 err:
 766         if (a != NULL) BN_free(a);
 767         if (c != NULL) BN_free(c);
 768         if (d != NULL) BN_free(d);
 769         if (e != NULL) BN_free(e);
 770         return ret;
 771         }
 772
 773 int test_mont(BIO *bp, BN_CTX *ctx)
 774         {
 775         BIGNUM a,b,c,d,A,B;
 776         BIGNUM n;
 777         int i;
 778         BN_MONT_CTX *mont;
 779
 780         BN_init(&a);
 781         BN_init(&b);
 782         BN_init(&c);
 783         BN_init(&d);
 784         BN_init(&A);
 785         BN_init(&B);
 786         BN_init(&n);
 787
 788         mont=BN_MONT_CTX_new();
 789         if (mont == NULL)
 790                 return 0;
 791
 792         BN_bntest_rand(&a,100,0,0); /**/
 793         BN_bntest_rand(&b,100,0,0); /**/
 794         for (i=0; i<num2; i++)
 795                 {
 796                 int bits = (200*(i+1))/num2;
 797
 798                 if (bits == 0)
 799                         continue;
 800                 BN_bntest_rand(&n,bits,0,1);
 801                 BN_MONT_CTX_set(mont,&n,ctx);
 802
 803                 BN_nnmod(&a,&a,&n,ctx);
 804                 BN_nnmod(&b,&b,&n,ctx);
 805
 806                 BN_to_montgomery(&A,&a,mont,ctx);
 807                 BN_to_montgomery(&B,&b,mont,ctx);
 808
 809                 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
 810                 BN_from_montgomery(&A,&c,mont,ctx);/**/
 811                 if (bp != NULL)
 812                         {
 813                         if (!results)
 814                                 {
 815 #ifdef undef
 816 fprintf(stderr,"%d * %d %% %d\n",
 817 BN_num_bits(&a),
 818 BN_num_bits(&b),
 819 BN_num_bits(mont->N));
 820 #endif
 821                                 BN_print(bp,&a);
 822                                 BIO_puts(bp," * ");
 823                                 BN_print(bp,&b);
 824                                 BIO_puts(bp," % ");
 825                                 BN_print(bp,&(mont->N));
 826                                 BIO_puts(bp," - ");
 827                                 }
 828                         BN_print(bp,&A);
 829                         BIO_puts(bp,"\n");
 830                         }
 831                 BN_mod_mul(&d,&a,&b,&n,ctx);
 832                 BN_sub(&d,&d,&A);
 833                 if(!BN_is_zero(&d))
 834                     {
 835                     fprintf(stderr,"Montgomery multiplication test failed!\n");
 836                     return 0;
 837                     }
 838                 }
 839         BN_MONT_CTX_free(mont);
 840         BN_free(&a);
 841         BN_free(&b);
 842         BN_free(&c);
 843         BN_free(&d);
 844         BN_free(&A);
 845         BN_free(&B);
 846         BN_free(&n);
 847         return(1);
 848         }
 849
 850 int test_mod(BIO *bp, BN_CTX *ctx)
 851         {
 852         BIGNUM *a,*b,*c,*d,*e;
 853         int i;
 854
 855         a=BN_new();
 856         b=BN_new();
 857         c=BN_new();
 858         d=BN_new();
 859         e=BN_new();
 860
 861         BN_bntest_rand(a,1024,0,0); /**/
 862         for (i=0; i<num0; i++)
 863                 {
 864                 BN_bntest_rand(b,450+i*10,0,0); /**/
 865                 a->neg=rand_neg();
 866                 b->neg=rand_neg();
 867                 BN_mod(c,a,b,ctx);/**/
 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                                 }
 877                         BN_print(bp,c);
 878                         BIO_puts(bp,"\n");
 879                         }
 880                 BN_div(d,e,a,b,ctx);
 881                 BN_sub(e,e,c);
 882                 if(!BN_is_zero(e))
 883                     {
 884                     fprintf(stderr,"Modulo test failed!\n");
 885                     return 0;
 886                     }
 887                 }
 888         BN_free(a);
 889         BN_free(b);
 890         BN_free(c);
 891         BN_free(d);
 892         BN_free(e);
 893         return(1);
 894         }
 895
 896 int test_mod_mul(BIO *bp, BN_CTX *ctx)
 897         {
 898         BIGNUM *a,*b,*c,*d,*e;
 899         int i,j;
 900
 901         a=BN_new();
 902         b=BN_new();
 903         c=BN_new();
 904         d=BN_new();
 905         e=BN_new();
 906
 907         for (j=0; j<3; j++) {
 908         BN_bntest_rand(c,1024,0,0); /**/
 909         for (i=0; i<num0; i++)
 910                 {
 911                 BN_bntest_rand(a,475+i*10,0,0); /**/
 912                 BN_bntest_rand(b,425+i*11,0,0); /**/
 913                 a->neg=rand_neg();
 914                 b->neg=rand_neg();
 915                 if (!BN_mod_mul(e,a,b,c,ctx))
 916                         {
 917                         unsigned long l;
 918
 919                         while ((l=ERR_get_error()))
 920                                 fprintf(stderr,"ERROR:%s\n",
 921                                         ERR_error_string(l,NULL));
 922                         EXIT(1);
 923                         }
 924                 if (bp != NULL)
 925                         {
 926                         if (!results)
 927                                 {
 928                                 BN_print(bp,a);
 929                                 BIO_puts(bp," * ");
 930                                 BN_print(bp,b);
 931                                 BIO_puts(bp," % ");
 932                                 BN_print(bp,c);
 933                                 if ((a->neg ^ b->neg) && !BN_is_zero(e))
 934                                         {
 935                                         /* If  (a*b) % c  is negative,  c  must be added
 936                                          * in order to obtain the normalized remainder
 937                                          * (new with OpenSSL 0.9.7, previous versions of
 938                                          * BN_mod_mul could generate negative results)
 939                                          */
 940                                         BIO_puts(bp," + ");
 941                                         BN_print(bp,c);
 942                                         }
 943                                 BIO_puts(bp," - ");
 944                                 }
 945                         BN_print(bp,e);
 946                         BIO_puts(bp,"\n");
 947                         }
 948                 BN_mul(d,a,b,ctx);
 949                 BN_sub(d,d,e);
 950                 BN_div(a,b,d,c,ctx);
 951                 if(!BN_is_zero(b))
 952                     {
 953                     fprintf(stderr,"Modulo multiply test failed!\n");
 954                     ERR_print_errors_fp(stderr);
 955                     return 0;
 956                     }
 957                 }
 958         }
 959         BN_free(a);
 960         BN_free(b);
 961         BN_free(c);
 962         BN_free(d);
 963         BN_free(e);
 964         return(1);
 965         }
 966
 967 int test_mod_exp(BIO *bp, BN_CTX *ctx)
 968         {
 969         BIGNUM *a,*b,*c,*d,*e;
 970         int i;
 971
 972         a=BN_new();
 973         b=BN_new();
 974         c=BN_new();
 975         d=BN_new();
 976         e=BN_new();
 977
 978         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
 979         for (i=0; i<num2; i++)
 980                 {
 981                 BN_bntest_rand(a,20+i*5,0,0); /**/
 982                 BN_bntest_rand(b,2+i,0,0); /**/
 983
 984                 if (!BN_mod_exp(d,a,b,c,ctx))
 985                         return(0);
 986
 987                 if (bp != NULL)
 988                         {
 989                         if (!results)
 990                                 {
 991                                 BN_print(bp,a);
 992                                 BIO_puts(bp," ^ ");
 993                                 BN_print(bp,b);
 994                                 BIO_puts(bp," % ");
 995                                 BN_print(bp,c);
 996                                 BIO_puts(bp," - ");
 997                                 }
 998                         BN_print(bp,d);
 999                         BIO_puts(bp,"\n");
1000                         }
1001                 BN_exp(e,a,b,ctx);
1002                 BN_sub(e,e,d);
1003                 BN_div(a,b,e,c,ctx);
1004                 if(!BN_is_zero(b))
1005                     {
1006                     fprintf(stderr,"Modulo exponentiation test failed!\n");
1007                     return 0;
1008                     }
1009                 }
1010         BN_free(a);
1011         BN_free(b);
1012         BN_free(c);
1013         BN_free(d);
1014         BN_free(e);
1015         return(1);
1016         }
1017
1018 int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
1019         {
1020         BIGNUM *a,*b,*c,*d,*e;
1021         int i;
1022
1023         a=BN_new();
1024         b=BN_new();
1025         c=BN_new();
1026         d=BN_new();
1027         e=BN_new();
1028
1029         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
1030         for (i=0; i<num2; i++)
1031                 {
1032                 BN_bntest_rand(a,20+i*5,0,0); /**/
1033                 BN_bntest_rand(b,2+i,0,0); /**/
1034
1035                 if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
1036                         return(00);
1037
1038                 if (bp != NULL)
1039                         {
1040                         if (!results)
1041                                 {
1042                                 BN_print(bp,a);
1043                                 BIO_puts(bp," ^ ");
1044                                 BN_print(bp,b);
1045                                 BIO_puts(bp," % ");
1046                                 BN_print(bp,c);
1047                                 BIO_puts(bp," - ");
1048                                 }
1049                         BN_print(bp,d);
1050                         BIO_puts(bp,"\n");
1051                         }
1052                 BN_exp(e,a,b,ctx);
1053                 BN_sub(e,e,d);
1054                 BN_div(a,b,e,c,ctx);
1055                 if(!BN_is_zero(b))
1056                     {
1057                     fprintf(stderr,"Modulo exponentiation test failed!\n");
1058                     return 0;
1059                     }
1060                 }
1061         BN_free(a);
1062         BN_free(b);
1063         BN_free(c);
1064         BN_free(d);
1065         BN_free(e);
1066         return(1);
1067         }
1068
1069 int test_exp(BIO *bp, BN_CTX *ctx)
1070         {
1071         BIGNUM *a,*b,*d,*e,*one;
1072         int i;
1073
1074         a=BN_new();
1075         b=BN_new();
1076         d=BN_new();
1077         e=BN_new();
1078         one=BN_new();
1079         BN_one(one);
1080
1081         for (i=0; i<num2; i++)
1082                 {
1083                 BN_bntest_rand(a,20+i*5,0,0); /**/
1084                 BN_bntest_rand(b,2+i,0,0); /**/
1085
1086                 if (BN_exp(d,a,b,ctx) <= 0)
1087                         return(0);
1088
1089                 if (bp != NULL)
1090                         {
1091                         if (!results)
1092                                 {
1093                                 BN_print(bp,a);
1094                                 BIO_puts(bp," ^ ");
1095                                 BN_print(bp,b);
1096                                 BIO_puts(bp," - ");
1097                                 }
1098                         BN_print(bp,d);
1099                         BIO_puts(bp,"\n");
1100                         }
1101                 BN_one(e);
1102                 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
1103                     BN_mul(e,e,a,ctx);
1104                 BN_sub(e,e,d);
1105                 if(!BN_is_zero(e))
1106                     {
1107                     fprintf(stderr,"Exponentiation test failed!\n");
1108                     return 0;
1109                     }
1110                 }
1111         BN_free(a);
1112         BN_free(b);
1113         BN_free(d);
1114         BN_free(e);
1115         BN_free(one);
1116         return(1);
1117         }
1118 #ifndef OPENSSL_NO_EC2M
1119 int test_gf2m_add(BIO *bp)
1120         {
1121         BIGNUM a,b,c;
1122         int i, ret = 0;
1123
1124         BN_init(&a);
1125         BN_init(&b);
1126         BN_init(&c);
1127
1128         for (i=0; i<num0; i++)
1129                 {
1130                 BN_rand(&a,512,0,0);
1131                 BN_copy(&b, BN_value_one());
1132                 a.neg=rand_neg();
1133                 b.neg=rand_neg();
1134                 BN_GF2m_add(&c,&a,&b);
1135 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1136                 if (bp != NULL)
1137                         {
1138                         if (!results)
1139                                 {
1140                                 BN_print(bp,&a);
1141                                 BIO_puts(bp," ^ ");
1142                                 BN_print(bp,&b);
1143                                 BIO_puts(bp," = ");
1144                                 }
1145                         BN_print(bp,&c);
1146                         BIO_puts(bp,"\n");
1147                         }
1148 #endif
1149                 /* Test that two added values have the correct parity. */
1150                 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
1151                         {
1152                     fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
1153                         goto err;
1154                         }
1155                 BN_GF2m_add(&c,&c,&c);
1156                 /* Test that c + c = 0. */
1157                 if(!BN_is_zero(&c))
1158                     {
1159                     fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
1160                         goto err;
1161                     }
1162                 }
1163         ret = 1;
1164   err:
1165         BN_free(&a);
1166         BN_free(&b);
1167         BN_free(&c);
1168         return ret;
1169         }
1170
1171 int test_gf2m_mod(BIO *bp)
1172         {
1173         BIGNUM *a,*b[2],*c,*d,*e;
1174         int i, j, ret = 0;
1175         int p0[] = {163,7,6,3,0,-1};
1176         int p1[] = {193,15,0,-1};
1177
1178         a=BN_new();
1179         b[0]=BN_new();
1180         b[1]=BN_new();
1181         c=BN_new();
1182         d=BN_new();
1183         e=BN_new();
1184
1185         BN_GF2m_arr2poly(p0, b[0]);
1186         BN_GF2m_arr2poly(p1, b[1]);
1187
1188         for (i=0; i<num0; i++)
1189                 {
1190                 BN_bntest_rand(a, 1024, 0, 0);
1191                 for (j=0; j < 2; j++)
1192                         {
1193                         BN_GF2m_mod(c, a, b[j]);
1194 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1195                         if (bp != NULL)
1196                                 {
1197                                 if (!results)
1198                                         {
1199                                         BN_print(bp,a);
1200                                         BIO_puts(bp," % ");
1201                                         BN_print(bp,b[j]);
1202                                         BIO_puts(bp," - ");
1203                                         BN_print(bp,c);
1204                                         BIO_puts(bp,"\n");
1205                                         }
1206                                 }
1207 #endif
1208                         BN_GF2m_add(d, a, c);
1209                         BN_GF2m_mod(e, d, b[j]);
1210                         /* Test that a + (a mod p) mod p == 0. */
1211                         if(!BN_is_zero(e))
1212                                 {
1213                                 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1214                                 goto err;
1215                                 }
1216                         }
1217                 }
1218         ret = 1;
1219   err:
1220         BN_free(a);
1221         BN_free(b[0]);
1222         BN_free(b[1]);
1223         BN_free(c);
1224         BN_free(d);
1225         BN_free(e);
1226         return ret;
1227         }
1228
1229 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1230         {
1231         BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1232         int i, j, ret = 0;
1233         int p0[] = {163,7,6,3,0,-1};
1234         int p1[] = {193,15,0,-1};
1235
1236         a=BN_new();
1237         b[0]=BN_new();
1238         b[1]=BN_new();
1239         c=BN_new();
1240         d=BN_new();
1241         e=BN_new();
1242         f=BN_new();
1243         g=BN_new();
1244         h=BN_new();
1245
1246         BN_GF2m_arr2poly(p0, b[0]);
1247         BN_GF2m_arr2poly(p1, b[1]);
1248
1249         for (i=0; i<num0; i++)
1250                 {
1251                 BN_bntest_rand(a, 1024, 0, 0);
1252                 BN_bntest_rand(c, 1024, 0, 0);
1253                 BN_bntest_rand(d, 1024, 0, 0);
1254                 for (j=0; j < 2; j++)
1255                         {
1256                         BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1257 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1258                         if (bp != NULL)
1259                                 {
1260                                 if (!results)
1261                                         {
1262                                         BN_print(bp,a);
1263                                         BIO_puts(bp," * ");
1264                                         BN_print(bp,c);
1265                                         BIO_puts(bp," % ");
1266                                         BN_print(bp,b[j]);
1267                                         BIO_puts(bp," - ");
1268                                         BN_print(bp,e);
1269                                         BIO_puts(bp,"\n");
1270                                         }
1271                                 }
1272 #endif
1273                         BN_GF2m_add(f, a, d);
1274                         BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1275                         BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1276                         BN_GF2m_add(f, e, g);
1277                         BN_GF2m_add(f, f, h);
1278                         /* Test that (a+d)*c = a*c + d*c. */
1279                         if(!BN_is_zero(f))
1280                                 {
1281                                 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1282                                 goto err;
1283                                 }
1284                         }
1285                 }
1286         ret = 1;
1287   err:
1288         BN_free(a);
1289         BN_free(b[0]);
1290         BN_free(b[1]);
1291         BN_free(c);
1292         BN_free(d);
1293         BN_free(e);
1294         BN_free(f);
1295         BN_free(g);
1296         BN_free(h);
1297         return ret;
1298         }
1299
1300 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1301         {
1302         BIGNUM *a,*b[2],*c,*d;
1303         int i, j, ret = 0;
1304         int p0[] = {163,7,6,3,0,-1};
1305         int p1[] = {193,15,0,-1};
1306
1307         a=BN_new();
1308         b[0]=BN_new();
1309         b[1]=BN_new();
1310         c=BN_new();
1311         d=BN_new();
1312
1313         BN_GF2m_arr2poly(p0, b[0]);
1314         BN_GF2m_arr2poly(p1, b[1]);
1315
1316         for (i=0; i<num0; i++)
1317                 {
1318                 BN_bntest_rand(a, 1024, 0, 0);
1319                 for (j=0; j < 2; j++)
1320                         {
1321                         BN_GF2m_mod_sqr(c, a, b[j], ctx);
1322                         BN_copy(d, a);
1323                         BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1324 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1325                         if (bp != NULL)
1326                                 {
1327                                 if (!results)
1328                                         {
1329                                         BN_print(bp,a);
1330                                         BIO_puts(bp," ^ 2 % ");
1331                                         BN_print(bp,b[j]);
1332                                         BIO_puts(bp, " = ");
1333                                         BN_print(bp,c);
1334                                         BIO_puts(bp,"; a * a = ");
1335                                         BN_print(bp,d);
1336                                         BIO_puts(bp,"\n");
1337                                         }
1338                                 }
1339 #endif
1340                         BN_GF2m_add(d, c, d);
1341                         /* Test that a*a = a^2. */
1342                         if(!BN_is_zero(d))
1343                                 {
1344                                 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1345                                 goto err;
1346                                 }
1347                         }
1348                 }
1349         ret = 1;
1350   err:
1351         BN_free(a);
1352         BN_free(b[0]);
1353         BN_free(b[1]);
1354         BN_free(c);
1355         BN_free(d);
1356         return ret;
1357         }
1358
1359 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1360         {
1361         BIGNUM *a,*b[2],*c,*d;
1362         int i, j, ret = 0;
1363         int p0[] = {163,7,6,3,0,-1};
1364         int p1[] = {193,15,0,-1};
1365
1366         a=BN_new();
1367         b[0]=BN_new();
1368         b[1]=BN_new();
1369         c=BN_new();
1370         d=BN_new();
1371
1372         BN_GF2m_arr2poly(p0, b[0]);
1373         BN_GF2m_arr2poly(p1, b[1]);
1374
1375         for (i=0; i<num0; i++)
1376                 {
1377                 BN_bntest_rand(a, 512, 0, 0);
1378                 for (j=0; j < 2; j++)
1379                         {
1380                         BN_GF2m_mod_inv(c, a, b[j], ctx);
1381                         BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1382 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1383                         if (bp != NULL)
1384                                 {
1385                                 if (!results)
1386                                         {
1387                                         BN_print(bp,a);
1388                                         BIO_puts(bp, " * ");
1389                                         BN_print(bp,c);
1390                                         BIO_puts(bp," - 1 % ");
1391                                         BN_print(bp,b[j]);
1392                                         BIO_puts(bp,"\n");
1393                                         }
1394                                 }
1395 #endif
1396                         /* Test that ((1/a)*a) = 1. */
1397                         if(!BN_is_one(d))
1398                                 {
1399                                 fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
1400                                 goto err;
1401                                 }
1402                         }
1403                 }
1404         ret = 1;
1405   err:
1406         BN_free(a);
1407         BN_free(b[0]);
1408         BN_free(b[1]);
1409         BN_free(c);
1410         BN_free(d);
1411         return ret;
1412         }
1413
1414 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1415         {
1416         BIGNUM *a,*b[2],*c,*d,*e,*f;
1417         int i, j, ret = 0;
1418         int p0[] = {163,7,6,3,0,-1};
1419         int p1[] = {193,15,0,-1};
1420
1421         a=BN_new();
1422         b[0]=BN_new();
1423         b[1]=BN_new();
1424         c=BN_new();
1425         d=BN_new();
1426         e=BN_new();
1427         f=BN_new();
1428
1429         BN_GF2m_arr2poly(p0, b[0]);
1430         BN_GF2m_arr2poly(p1, b[1]);
1431
1432         for (i=0; i<num0; i++)
1433                 {
1434                 BN_bntest_rand(a, 512, 0, 0);
1435                 BN_bntest_rand(c, 512, 0, 0);
1436                 for (j=0; j < 2; j++)
1437                         {
1438                         BN_GF2m_mod_div(d, a, c, b[j], ctx);
1439                         BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1440                         BN_GF2m_mod_div(f, a, e, b[j], ctx);
1441 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1442                         if (bp != NULL)
1443                                 {
1444                                 if (!results)
1445                                         {
1446                                         BN_print(bp,a);
1447                                         BIO_puts(bp, " = ");
1448                                         BN_print(bp,c);
1449                                         BIO_puts(bp," * ");
1450                                         BN_print(bp,d);
1451                                         BIO_puts(bp, " % ");
1452                                         BN_print(bp,b[j]);
1453                                         BIO_puts(bp,"\n");
1454                                         }
1455                                 }
1456 #endif
1457                         /* Test that ((a/c)*c)/a = 1. */
1458                         if(!BN_is_one(f))
1459                                 {
1460                                 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1461                                 goto err;
1462                                 }
1463                         }
1464                 }
1465         ret = 1;
1466   err:
1467         BN_free(a);
1468         BN_free(b[0]);
1469         BN_free(b[1]);
1470         BN_free(c);
1471         BN_free(d);
1472         BN_free(e);
1473         BN_free(f);
1474         return ret;
1475         }
1476
1477 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1478         {
1479         BIGNUM *a,*b[2],*c,*d,*e,*f;
1480         int i, j, ret = 0;
1481         int p0[] = {163,7,6,3,0,-1};
1482         int p1[] = {193,15,0,-1};
1483
1484         a=BN_new();
1485         b[0]=BN_new();
1486         b[1]=BN_new();
1487         c=BN_new();
1488         d=BN_new();
1489         e=BN_new();
1490         f=BN_new();
1491
1492         BN_GF2m_arr2poly(p0, b[0]);
1493         BN_GF2m_arr2poly(p1, b[1]);
1494
1495         for (i=0; i<num0; i++)
1496                 {
1497                 BN_bntest_rand(a, 512, 0, 0);
1498                 BN_bntest_rand(c, 512, 0, 0);
1499                 BN_bntest_rand(d, 512, 0, 0);
1500                 for (j=0; j < 2; j++)
1501                         {
1502                         BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1503                         BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1504                         BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1505                         BN_add(f, c, d);
1506                         BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1507 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1508                         if (bp != NULL)
1509                                 {
1510                                 if (!results)
1511                                         {
1512                                         BN_print(bp,a);
1513                                         BIO_puts(bp, " ^ (");
1514                                         BN_print(bp,c);
1515                                         BIO_puts(bp," + ");
1516                                         BN_print(bp,d);
1517                                         BIO_puts(bp, ") = ");
1518                                         BN_print(bp,e);
1519                                         BIO_puts(bp, "; - ");
1520                                         BN_print(bp,f);
1521                                         BIO_puts(bp, " % ");
1522                                         BN_print(bp,b[j]);
1523                                         BIO_puts(bp,"\n");
1524                                         }
1525                                 }
1526 #endif
1527                         BN_GF2m_add(f, e, f);
1528                         /* Test that a^(c+d)=a^c*a^d. */
1529                         if(!BN_is_zero(f))
1530                                 {
1531                                 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1532                                 goto err;
1533                                 }
1534                         }
1535                 }
1536         ret = 1;
1537   err:
1538         BN_free(a);
1539         BN_free(b[0]);
1540         BN_free(b[1]);
1541         BN_free(c);
1542         BN_free(d);
1543         BN_free(e);
1544         BN_free(f);
1545         return ret;
1546         }
1547
1548 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1549         {
1550         BIGNUM *a,*b[2],*c,*d,*e,*f;
1551         int i, j, ret = 0;
1552         int p0[] = {163,7,6,3,0,-1};
1553         int p1[] = {193,15,0,-1};
1554
1555         a=BN_new();
1556         b[0]=BN_new();
1557         b[1]=BN_new();
1558         c=BN_new();
1559         d=BN_new();
1560         e=BN_new();
1561         f=BN_new();
1562
1563         BN_GF2m_arr2poly(p0, b[0]);
1564         BN_GF2m_arr2poly(p1, b[1]);
1565
1566         for (i=0; i<num0; i++)
1567                 {
1568                 BN_bntest_rand(a, 512, 0, 0);
1569                 for (j=0; j < 2; j++)
1570                         {
1571                         BN_GF2m_mod(c, a, b[j]);
1572                         BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1573                         BN_GF2m_mod_sqr(e, d, b[j], ctx);
1574 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1575                         if (bp != NULL)
1576                                 {
1577                                 if (!results)
1578                                         {
1579                                         BN_print(bp,d);
1580                                         BIO_puts(bp, " ^ 2 - ");
1581                                         BN_print(bp,a);
1582                                         BIO_puts(bp,"\n");
1583                                         }
1584                                 }
1585 #endif
1586                         BN_GF2m_add(f, c, e);
1587                         /* Test that d^2 = a, where d = sqrt(a). */
1588                         if(!BN_is_zero(f))
1589                                 {
1590                                 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1591                                 goto err;
1592                                 }
1593                         }
1594                 }
1595         ret = 1;
1596   err:
1597         BN_free(a);
1598         BN_free(b[0]);
1599         BN_free(b[1]);
1600         BN_free(c);
1601         BN_free(d);
1602         BN_free(e);
1603         BN_free(f);
1604         return ret;
1605         }
1606
1607 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1608         {
1609         BIGNUM *a,*b[2],*c,*d,*e;
1610         int i, j, s = 0, t, ret = 0;
1611         int p0[] = {163,7,6,3,0,-1};
1612         int p1[] = {193,15,0,-1};
1613
1614         a=BN_new();
1615         b[0]=BN_new();
1616         b[1]=BN_new();
1617         c=BN_new();
1618         d=BN_new();
1619         e=BN_new();
1620
1621         BN_GF2m_arr2poly(p0, b[0]);
1622         BN_GF2m_arr2poly(p1, b[1]);
1623
1624         for (i=0; i<num0; i++)
1625                 {
1626                 BN_bntest_rand(a, 512, 0, 0);
1627                 for (j=0; j < 2; j++)
1628                         {
1629                         t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1630                         if (t)
1631                                 {
1632                                 s++;
1633                                 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1634                                 BN_GF2m_add(d, c, d);
1635                                 BN_GF2m_mod(e, a, b[j]);
1636 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1637                                 if (bp != NULL)
1638                                         {
1639                                         if (!results)
1640                                                 {
1641                                                 BN_print(bp,c);
1642                                                 BIO_puts(bp, " is root of z^2 + z = ");
1643                                                 BN_print(bp,a);
1644                                                 BIO_puts(bp, " % ");
1645                                                 BN_print(bp,b[j]);
1646                                                 BIO_puts(bp, "\n");
1647                                                 }
1648                                         }
1649 #endif
1650                                 BN_GF2m_add(e, e, d);
1651                                 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1652                                 if(!BN_is_zero(e))
1653                                         {
1654                                         fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1655                                         goto err;
1656                                         }
1657
1658                                 }
1659                         else
1660                                 {
1661 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1662                                 if (bp != NULL)
1663                                         {
1664                                         if (!results)
1665                                                 {
1666                                                 BIO_puts(bp, "There are no roots of z^2 + z = ");
1667                                                 BN_print(bp,a);
1668                                                 BIO_puts(bp, " % ");
1669                                                 BN_print(bp,b[j]);
1670                                                 BIO_puts(bp, "\n");
1671                                                 }
1672                                         }
1673 #endif
1674                                 }
1675                         }
1676                 }
1677         if (s == 0)
1678                 {
1679                 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1680                 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1681                 goto err;
1682                 }
1683         ret = 1;
1684   err:
1685         BN_free(a);
1686         BN_free(b[0]);
1687         BN_free(b[1]);
1688         BN_free(c);
1689         BN_free(d);
1690         BN_free(e);
1691         return ret;
1692         }
1693 #endif
1694 static int genprime_cb(int p, int n, BN_GENCB *arg)
1695         {
1696         char c='*';
1697
1698         if (p == 0) c='.';
1699         if (p == 1) c='+';
1700         if (p == 2) c='*';
1701         if (p == 3) c='\n';
1702         putc(c, stderr);
1703         fflush(stderr);
1704         return 1;
1705         }
1706
1707 int test_kron(BIO *bp, BN_CTX *ctx)
1708         {
1709         BN_GENCB cb;
1710         BIGNUM *a,*b,*r,*t;
1711         int i;
1712         int legendre, kronecker;
1713         int ret = 0;
1714
1715         a = BN_new();
1716         b = BN_new();
1717         r = BN_new();
1718         t = BN_new();
1719         if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1720
1721         BN_GENCB_set(&cb, genprime_cb, NULL);
1722
1723         /* We test BN_kronecker(a, b, ctx) just for  b  odd (Jacobi symbol).
1724          * In this case we know that if  b  is prime, then BN_kronecker(a, b, ctx)
1725          * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1726          * So we generate a random prime  b  and compare these values
1727          * for a number of random  a's.  (That is, we run the Solovay-Strassen
1728          * primality test to confirm that  b  is prime, except that we
1729          * don't want to test whether  b  is prime but whether BN_kronecker
1730          * works.) */
1731
1732         if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
1733         b->neg = rand_neg();
1734         putc('\n', stderr);
1735
1736         for (i = 0; i < num0; i++)
1737                 {
1738                 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1739                 a->neg = rand_neg();
1740
1741                 /* t := (|b|-1)/2  (note that b is odd) */
1742                 if (!BN_copy(t, b)) goto err;
1743                 t->neg = 0;
1744                 if (!BN_sub_word(t, 1)) goto err;
1745                 if (!BN_rshift1(t, t)) goto err;
1746                 /* r := a^t mod b */
1747                 b->neg=0;
1748
1749                 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1750                 b->neg=1;
1751
1752                 if (BN_is_word(r, 1))
1753                         legendre = 1;
1754                 else if (BN_is_zero(r))
1755                         legendre = 0;
1756                 else
1757                         {
1758                         if (!BN_add_word(r, 1)) goto err;
1759                         if (0 != BN_ucmp(r, b))
1760                                 {
1761                                 fprintf(stderr, "Legendre symbol computation failed\n");
1762                                 goto err;
1763                                 }
1764                         legendre = -1;
1765                         }
1766
1767                 kronecker = BN_kronecker(a, b, ctx);
1768                 if (kronecker < -1) goto err;
1769                 /* we actually need BN_kronecker(a, |b|) */
1770                 if (a->neg && b->neg)
1771                         kronecker = -kronecker;
1772
1773                 if (legendre != kronecker)
1774                         {
1775                         fprintf(stderr, "legendre != kronecker; a = ");
1776                         BN_print_fp(stderr, a);
1777                         fprintf(stderr, ", b = ");
1778                         BN_print_fp(stderr, b);
1779                         fprintf(stderr, "\n");
1780                         goto err;
1781                         }
1782
1783                 putc('.', stderr);
1784                 fflush(stderr);
1785                 }
1786
1787         putc('\n', stderr);
1788         fflush(stderr);
1789         ret = 1;
1790  err:
1791         if (a != NULL) BN_free(a);
1792         if (b != NULL) BN_free(b);
1793         if (r != NULL) BN_free(r);
1794         if (t != NULL) BN_free(t);
1795         return ret;
1796         }
1797
1798 int test_sqrt(BIO *bp, BN_CTX *ctx)
1799         {
1800         BN_GENCB cb;
1801         BIGNUM *a,*p,*r;
1802         int i, j;
1803         int ret = 0;
1804
1805         a = BN_new();
1806         p = BN_new();
1807         r = BN_new();
1808         if (a == NULL || p == NULL || r == NULL) goto err;
1809
1810         BN_GENCB_set(&cb, genprime_cb, NULL);
1811
1812         for (i = 0; i < 16; i++)
1813                 {
1814                 if (i < 8)
1815                         {
1816                         unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1817
1818                         if (!BN_set_word(p, primes[i])) goto err;
1819                         }
1820                 else
1821                         {
1822                         if (!BN_set_word(a, 32)) goto err;
1823                         if (!BN_set_word(r, 2*i + 1)) goto err;
1824
1825                         if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
1826                         putc('\n', stderr);
1827                         }
1828                 p->neg = rand_neg();
1829
1830                 for (j = 0; j < num2; j++)
1831                         {
1832                         /* construct 'a' such that it is a square modulo p,
1833                          * but in general not a proper square and not reduced modulo p */
1834                         if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1835                         if (!BN_nnmod(r, r, p, ctx)) goto err;
1836                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1837                         if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1838                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1839                         if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1840                         if (!BN_mul(a, a, r, ctx)) goto err;
1841                         if (rand_neg())
1842                                 if (!BN_sub(a, a, p)) goto err;
1843
1844                         if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1845                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1846
1847                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1848
1849                         if (BN_cmp(a, r) != 0)
1850                                 {
1851                                 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1852                                 BN_print_fp(stderr, a);
1853                                 fprintf(stderr, ", r = ");
1854                                 BN_print_fp(stderr, r);
1855                                 fprintf(stderr, ", p = ");
1856                                 BN_print_fp(stderr, p);
1857                                 fprintf(stderr, "\n");
1858                                 goto err;
1859                                 }
1860
1861                         putc('.', stderr);
1862                         fflush(stderr);
1863                         }
1864
1865                 putc('\n', stderr);
1866                 fflush(stderr);
1867                 }
1868         ret = 1;
1869  err:
1870         if (a != NULL) BN_free(a);
1871         if (p != NULL) BN_free(p);
1872         if (r != NULL) BN_free(r);
1873         return ret;
1874         }
1875
1876 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1877         {
1878         BIGNUM *a,*b,*c,*d;
1879         int i;
1880
1881         b=BN_new();
1882         c=BN_new();
1883         d=BN_new();
1884         BN_one(c);
1885
1886         if(a_)
1887             a=a_;
1888         else
1889             {
1890             a=BN_new();
1891             BN_bntest_rand(a,200,0,0); /**/
1892             a->neg=rand_neg();
1893             }
1894         for (i=0; i<num0; i++)
1895                 {
1896                 BN_lshift(b,a,i+1);
1897                 BN_add(c,c,c);
1898                 if (bp != NULL)
1899                         {
1900                         if (!results)
1901                                 {
1902                                 BN_print(bp,a);
1903                                 BIO_puts(bp," * ");
1904                                 BN_print(bp,c);
1905                                 BIO_puts(bp," - ");
1906                                 }
1907                         BN_print(bp,b);
1908                         BIO_puts(bp,"\n");
1909                         }
1910                 BN_mul(d,a,c,ctx);
1911                 BN_sub(d,d,b);
1912                 if(!BN_is_zero(d))
1913                     {
1914                     fprintf(stderr,"Left shift test failed!\n");
1915                     fprintf(stderr,"a=");
1916                     BN_print_fp(stderr,a);
1917                     fprintf(stderr,"\nb=");
1918                     BN_print_fp(stderr,b);
1919                     fprintf(stderr,"\nc=");
1920                     BN_print_fp(stderr,c);
1921                     fprintf(stderr,"\nd=");
1922                     BN_print_fp(stderr,d);
1923                     fprintf(stderr,"\n");
1924                     return 0;
1925                     }
1926                 }
1927         BN_free(a);
1928         BN_free(b);
1929         BN_free(c);
1930         BN_free(d);
1931         return(1);
1932         }
1933
1934 int test_lshift1(BIO *bp)
1935         {
1936         BIGNUM *a,*b,*c;
1937         int i;
1938
1939         a=BN_new();
1940         b=BN_new();
1941         c=BN_new();
1942
1943         BN_bntest_rand(a,200,0,0); /**/
1944         a->neg=rand_neg();
1945         for (i=0; i<num0; i++)
1946                 {
1947                 BN_lshift1(b,a);
1948                 if (bp != NULL)
1949                         {
1950                         if (!results)
1951                                 {
1952                                 BN_print(bp,a);
1953                                 BIO_puts(bp," * 2");
1954                                 BIO_puts(bp," - ");
1955                                 }
1956                         BN_print(bp,b);
1957                         BIO_puts(bp,"\n");
1958                         }
1959                 BN_add(c,a,a);
1960                 BN_sub(a,b,c);
1961                 if(!BN_is_zero(a))
1962                     {
1963                     fprintf(stderr,"Left shift one test failed!\n");
1964                     return 0;
1965                     }
1966
1967                 BN_copy(a,b);
1968                 }
1969         BN_free(a);
1970         BN_free(b);
1971         BN_free(c);
1972         return(1);
1973         }
1974
1975 int test_rshift(BIO *bp,BN_CTX *ctx)
1976         {
1977         BIGNUM *a,*b,*c,*d,*e;
1978         int i;
1979
1980         a=BN_new();
1981         b=BN_new();
1982         c=BN_new();
1983         d=BN_new();
1984         e=BN_new();
1985         BN_one(c);
1986
1987         BN_bntest_rand(a,200,0,0); /**/
1988         a->neg=rand_neg();
1989         for (i=0; i<num0; i++)
1990                 {
1991                 BN_rshift(b,a,i+1);
1992                 BN_add(c,c,c);
1993                 if (bp != NULL)
1994                         {
1995                         if (!results)
1996                                 {
1997                                 BN_print(bp,a);
1998                                 BIO_puts(bp," / ");
1999                                 BN_print(bp,c);
2000                                 BIO_puts(bp," - ");
2001                                 }
2002                         BN_print(bp,b);
2003                         BIO_puts(bp,"\n");
2004                         }
2005                 BN_div(d,e,a,c,ctx);
2006                 BN_sub(d,d,b);
2007                 if(!BN_is_zero(d))
2008                     {
2009                     fprintf(stderr,"Right shift test failed!\n");
2010                     return 0;
2011                     }
2012                 }
2013         BN_free(a);
2014         BN_free(b);
2015         BN_free(c);
2016         BN_free(d);
2017         BN_free(e);
2018         return(1);
2019         }
2020
2021 int test_rshift1(BIO *bp)
2022         {
2023         BIGNUM *a,*b,*c;
2024         int i;
2025
2026         a=BN_new();
2027         b=BN_new();
2028         c=BN_new();
2029
2030         BN_bntest_rand(a,200,0,0); /**/
2031         a->neg=rand_neg();
2032         for (i=0; i<num0; i++)
2033                 {
2034                 BN_rshift1(b,a);
2035                 if (bp != NULL)
2036                         {
2037                         if (!results)
2038                                 {
2039                                 BN_print(bp,a);
2040                                 BIO_puts(bp," / 2");
2041                                 BIO_puts(bp," - ");
2042                                 }
2043                         BN_print(bp,b);
2044                         BIO_puts(bp,"\n");
2045                         }
2046                 BN_sub(c,a,b);
2047                 BN_sub(c,c,b);
2048                 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
2049                     {
2050                     fprintf(stderr,"Right shift one test failed!\n");
2051                     return 0;
2052                     }
2053                 BN_copy(a,b);
2054                 }
2055         BN_free(a);
2056         BN_free(b);
2057         BN_free(c);
2058         return(1);
2059         }
2060
2061 int rand_neg(void)
2062         {
2063         static unsigned int neg=0;
2064         static int sign[8]={0,0,0,1,1,0,1,1};
2065
2066         return(sign[(neg++)%8]);
2067         }