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