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 #include <stdio.h>
  73 #include <stdlib.h>
  74 #include <string.h>
  75
  76 #include "e_os.h"
  77
  78 #include <openssl/bio.h>
  79 #include <openssl/bn.h>
  80 #include <openssl/rand.h>
  81 #include <openssl/x509.h>
  82 #include <openssl/err.h>
  83
  84 #ifdef OPENSSL_SYS_WINDOWS
  85 #include "../bio/bss_file.c"
  86 #endif
  87
  88 const int num0 = 100; /* number of tests */
  89 const int num1 = 50;  /* additional tests for some functions */
  90 const int num2 = 5;   /* number of tests for slow functions */
  91
  92 int test_add(BIO *bp);
  93 int test_sub(BIO *bp);
  94 int test_lshift1(BIO *bp);
  95 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
  96 int test_rshift1(BIO *bp);
  97 int test_rshift(BIO *bp,BN_CTX *ctx);
  98 int test_div(BIO *bp,BN_CTX *ctx);
  99 int test_div_recp(BIO *bp,BN_CTX *ctx);
 100 int test_mul(BIO *bp);
 101 int test_sqr(BIO *bp,BN_CTX *ctx);
 102 int test_mont(BIO *bp,BN_CTX *ctx);
 103 int test_mod(BIO *bp,BN_CTX *ctx);
 104 int test_mod_mul(BIO *bp,BN_CTX *ctx);
 105 int test_mod_exp(BIO *bp,BN_CTX *ctx);
 106 int test_exp(BIO *bp,BN_CTX *ctx);
 107 int test_gf2m_add(BIO *bp);
 108 int test_gf2m_mod(BIO *bp);
 109 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
 110 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
 111 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
 112 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
 113 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
 114 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
 115 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
 116 int test_kron(BIO *bp,BN_CTX *ctx);
 117 int test_sqrt(BIO *bp,BN_CTX *ctx);
 118 int rand_neg(void);
 119 static int results=0;
 120
 121 #ifdef OPENSSL_NO_STDIO
 122 #define APPS_WIN16
 123 #include "bss_file.c"
 124 #endif
 125
 126 static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
 127 "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";
 128
 129 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
 130
 131 static void message(BIO *out, char *m)
 132         {
 133         fprintf(stderr, "test %s\n", m);
 134         BIO_puts(out, "print \"test ");
 135         BIO_puts(out, m);
 136         BIO_puts(out, "\\n\"\n");
 137         }
 138
 139 int main(int argc, char *argv[])
 140         {
 141         BN_CTX *ctx;
 142         BIO *out;
 143         char *outfile=NULL;
 144
 145         results = 0;
 146
 147         RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
 148
 149         argc--;
 150         argv++;
 151         while (argc >= 1)
 152                 {
 153                 if (strcmp(*argv,"-results") == 0)
 154                         results=1;
 155                 else if (strcmp(*argv,"-out") == 0)
 156                         {
 157                         if (--argc < 1) break;
 158                         outfile= *(++argv);
 159                         }
 160                 argc--;
 161                 argv++;
 162                 }
 163
 164
 165         ctx=BN_CTX_new();
 166         if (ctx == NULL) exit(1);
 167
 168         out=BIO_new(BIO_s_file());
 169         if (out == NULL) exit(1);
 170         if (outfile == NULL)
 171                 {
 172                 BIO_set_fp(out,stdout,BIO_NOCLOSE);
 173                 }
 174         else
 175                 {
 176                 if (!BIO_write_filename(out,outfile))
 177                         {
 178                         perror(outfile);
 179                         exit(1);
 180                         }
 181                 }
 182
 183         if (!results)
 184                 BIO_puts(out,"obase=16\nibase=16\n");
 185
 186         message(out,"BN_add");
 187         if (!test_add(out)) goto err;
 188         BIO_flush(out);
 189
 190         message(out,"BN_sub");
 191         if (!test_sub(out)) goto err;
 192         BIO_flush(out);
 193
 194         message(out,"BN_lshift1");
 195         if (!test_lshift1(out)) goto err;
 196         BIO_flush(out);
 197
 198         message(out,"BN_lshift (fixed)");
 199         if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
 200             goto err;
 201         BIO_flush(out);
 202
 203         message(out,"BN_lshift");
 204         if (!test_lshift(out,ctx,NULL)) goto err;
 205         BIO_flush(out);
 206
 207         message(out,"BN_rshift1");
 208         if (!test_rshift1(out)) goto err;
 209         BIO_flush(out);
 210
 211         message(out,"BN_rshift");
 212         if (!test_rshift(out,ctx)) goto err;
 213         BIO_flush(out);
 214
 215         message(out,"BN_sqr");
 216         if (!test_sqr(out,ctx)) goto err;
 217         BIO_flush(out);
 218
 219         message(out,"BN_mul");
 220         if (!test_mul(out)) goto err;
 221         BIO_flush(out);
 222
 223         message(out,"BN_div");
 224         if (!test_div(out,ctx)) goto err;
 225         BIO_flush(out);
 226
 227         message(out,"BN_div_recp");
 228         if (!test_div_recp(out,ctx)) goto err;
 229         BIO_flush(out);
 230
 231         message(out,"BN_mod");
 232         if (!test_mod(out,ctx)) goto err;
 233         BIO_flush(out);
 234
 235         message(out,"BN_mod_mul");
 236         if (!test_mod_mul(out,ctx)) goto err;
 237         BIO_flush(out);
 238
 239         message(out,"BN_mont");
 240         if (!test_mont(out,ctx)) goto err;
 241         BIO_flush(out);
 242
 243         message(out,"BN_mod_exp");
 244         if (!test_mod_exp(out,ctx)) goto err;
 245         BIO_flush(out);
 246
 247         message(out,"BN_exp");
 248         if (!test_exp(out,ctx)) goto err;
 249         BIO_flush(out);
 250
 251         message(out,"BN_kronecker");
 252         if (!test_kron(out,ctx)) goto err;
 253         BIO_flush(out);
 254
 255         message(out,"BN_mod_sqrt");
 256         if (!test_sqrt(out,ctx)) goto err;
 257         BIO_flush(out);
 258
 259         message(out,"BN_GF2m_add");
 260         if (!test_gf2m_add(out)) goto err;
 261         BIO_flush(out);
 262
 263         message(out,"BN_GF2m_mod");
 264         if (!test_gf2m_mod(out)) goto err;
 265         BIO_flush(out);
 266
 267         message(out,"BN_GF2m_mod_mul");
 268         if (!test_gf2m_mod_mul(out,ctx)) goto err;
 269         BIO_flush(out);
 270
 271         message(out,"BN_GF2m_mod_sqr");
 272         if (!test_gf2m_mod_sqr(out,ctx)) goto err;
 273         BIO_flush(out);
 274
 275         message(out,"BN_GF2m_mod_inv");
 276         if (!test_gf2m_mod_inv(out,ctx)) goto err;
 277         BIO_flush(out);
 278
 279         message(out,"BN_GF2m_mod_div");
 280         if (!test_gf2m_mod_div(out,ctx)) goto err;
 281         BIO_flush(out);
 282
 283         message(out,"BN_GF2m_mod_exp");
 284         if (!test_gf2m_mod_exp(out,ctx)) goto err;
 285         BIO_flush(out);
 286
 287         message(out,"BN_GF2m_mod_sqrt");
 288         if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
 289         BIO_flush(out);
 290
 291         message(out,"BN_GF2m_mod_solve_quad");
 292         if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
 293         BIO_flush(out);
 294
 295         BN_CTX_free(ctx);
 296         BIO_free(out);
 297
 298 /**/
 299         exit(0);
 300 err:
 301         BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
 302                               * the failure, see test_bn in test/Makefile.ssl*/
 303         BIO_flush(out);
 304         ERR_load_crypto_strings();
 305         ERR_print_errors_fp(stderr);
 306         exit(1);
 307         return(1);
 308         }
 309
 310 int test_add(BIO *bp)
 311         {
 312         BIGNUM a,b,c;
 313         int i;
 314
 315         BN_init(&a);
 316         BN_init(&b);
 317         BN_init(&c);
 318
 319         BN_bntest_rand(&a,512,0,0);
 320         for (i=0; i<num0; i++)
 321                 {
 322                 BN_bntest_rand(&b,450+i,0,0);
 323                 a.neg=rand_neg();
 324                 b.neg=rand_neg();
 325                 BN_add(&c,&a,&b);
 326                 if (bp != NULL)
 327                         {
 328                         if (!results)
 329                                 {
 330                                 BN_print(bp,&a);
 331                                 BIO_puts(bp," + ");
 332                                 BN_print(bp,&b);
 333                                 BIO_puts(bp," - ");
 334                                 }
 335                         BN_print(bp,&c);
 336                         BIO_puts(bp,"\n");
 337                         }
 338                 a.neg=!a.neg;
 339                 b.neg=!b.neg;
 340                 BN_add(&c,&c,&b);
 341                 BN_add(&c,&c,&a);
 342                 if(!BN_is_zero(&c))
 343                     {
 344                     fprintf(stderr,"Add test failed!\n");
 345                     return 0;
 346                     }
 347                 }
 348         BN_free(&a);
 349         BN_free(&b);
 350         BN_free(&c);
 351         return(1);
 352         }
 353
 354 int test_sub(BIO *bp)
 355         {
 356         BIGNUM a,b,c;
 357         int i;
 358
 359         BN_init(&a);
 360         BN_init(&b);
 361         BN_init(&c);
 362
 363         for (i=0; i<num0+num1; i++)
 364                 {
 365                 if (i < num1)
 366                         {
 367                         BN_bntest_rand(&a,512,0,0);
 368                         BN_copy(&b,&a);
 369                         if (BN_set_bit(&a,i)==0) return(0);
 370                         BN_add_word(&b,i);
 371                         }
 372                 else
 373                         {
 374                         BN_bntest_rand(&b,400+i-num1,0,0);
 375                         a.neg=rand_neg();
 376                         b.neg=rand_neg();
 377                         }
 378                 BN_sub(&c,&a,&b);
 379                 if (bp != NULL)
 380                         {
 381                         if (!results)
 382                                 {
 383                                 BN_print(bp,&a);
 384                                 BIO_puts(bp," - ");
 385                                 BN_print(bp,&b);
 386                                 BIO_puts(bp," - ");
 387                                 }
 388                         BN_print(bp,&c);
 389                         BIO_puts(bp,"\n");
 390                         }
 391                 BN_add(&c,&c,&b);
 392                 BN_sub(&c,&c,&a);
 393                 if(!BN_is_zero(&c))
 394                     {
 395                     fprintf(stderr,"Subtract test failed!\n");
 396                     return 0;
 397                     }
 398                 }
 399         BN_free(&a);
 400         BN_free(&b);
 401         BN_free(&c);
 402         return(1);
 403         }
 404
 405 int test_div(BIO *bp, BN_CTX *ctx)
 406         {
 407         BIGNUM a,b,c,d,e;
 408         int i;
 409
 410         BN_init(&a);
 411         BN_init(&b);
 412         BN_init(&c);
 413         BN_init(&d);
 414         BN_init(&e);
 415
 416         for (i=0; i<num0+num1; i++)
 417                 {
 418                 if (i < num1)
 419                         {
 420                         BN_bntest_rand(&a,400,0,0);
 421                         BN_copy(&b,&a);
 422                         BN_lshift(&a,&a,i);
 423                         BN_add_word(&a,i);
 424                         }
 425                 else
 426                         BN_bntest_rand(&b,50+3*(i-num1),0,0);
 427                 a.neg=rand_neg();
 428                 b.neg=rand_neg();
 429                 BN_div(&d,&c,&a,&b,ctx);
 430                 if (bp != NULL)
 431                         {
 432                         if (!results)
 433                                 {
 434                                 BN_print(bp,&a);
 435                                 BIO_puts(bp," / ");
 436                                 BN_print(bp,&b);
 437                                 BIO_puts(bp," - ");
 438                                 }
 439                         BN_print(bp,&d);
 440                         BIO_puts(bp,"\n");
 441
 442                         if (!results)
 443                                 {
 444                                 BN_print(bp,&a);
 445                                 BIO_puts(bp," % ");
 446                                 BN_print(bp,&b);
 447                                 BIO_puts(bp," - ");
 448                                 }
 449                         BN_print(bp,&c);
 450                         BIO_puts(bp,"\n");
 451                         }
 452                 BN_mul(&e,&d,&b,ctx);
 453                 BN_add(&d,&e,&c);
 454                 BN_sub(&d,&d,&a);
 455                 if(!BN_is_zero(&d))
 456                     {
 457                     fprintf(stderr,"Division test failed!\n");
 458                     return 0;
 459                     }
 460                 }
 461         BN_free(&a);
 462         BN_free(&b);
 463         BN_free(&c);
 464         BN_free(&d);
 465         BN_free(&e);
 466         return(1);
 467         }
 468
 469 int test_div_recp(BIO *bp, BN_CTX *ctx)
 470         {
 471         BIGNUM a,b,c,d,e;
 472         BN_RECP_CTX recp;
 473         int i;
 474
 475         BN_RECP_CTX_init(&recp);
 476         BN_init(&a);
 477         BN_init(&b);
 478         BN_init(&c);
 479         BN_init(&d);
 480         BN_init(&e);
 481
 482         for (i=0; i<num0+num1; i++)
 483                 {
 484                 if (i < num1)
 485                         {
 486                         BN_bntest_rand(&a,400,0,0);
 487                         BN_copy(&b,&a);
 488                         BN_lshift(&a,&a,i);
 489                         BN_add_word(&a,i);
 490                         }
 491                 else
 492                         BN_bntest_rand(&b,50+3*(i-num1),0,0);
 493                 a.neg=rand_neg();
 494                 b.neg=rand_neg();
 495                 BN_RECP_CTX_set(&recp,&b,ctx);
 496                 BN_div_recp(&d,&c,&a,&recp,ctx);
 497                 if (bp != NULL)
 498                         {
 499                         if (!results)
 500                                 {
 501                                 BN_print(bp,&a);
 502                                 BIO_puts(bp," / ");
 503                                 BN_print(bp,&b);
 504                                 BIO_puts(bp," - ");
 505                                 }
 506                         BN_print(bp,&d);
 507                         BIO_puts(bp,"\n");
 508
 509                         if (!results)
 510                                 {
 511                                 BN_print(bp,&a);
 512                                 BIO_puts(bp," % ");
 513                                 BN_print(bp,&b);
 514                                 BIO_puts(bp," - ");
 515                                 }
 516                         BN_print(bp,&c);
 517                         BIO_puts(bp,"\n");
 518                         }
 519                 BN_mul(&e,&d,&b,ctx);
 520                 BN_add(&d,&e,&c);
 521                 BN_sub(&d,&d,&a);
 522                 if(!BN_is_zero(&d))
 523                     {
 524                     fprintf(stderr,"Reciprocal division test failed!\n");
 525                     fprintf(stderr,"a=");
 526                     BN_print_fp(stderr,&a);
 527                     fprintf(stderr,"\nb=");
 528                     BN_print_fp(stderr,&b);
 529                     fprintf(stderr,"\n");
 530                     return 0;
 531                     }
 532                 }
 533         BN_free(&a);
 534         BN_free(&b);
 535         BN_free(&c);
 536         BN_free(&d);
 537         BN_free(&e);
 538         BN_RECP_CTX_free(&recp);
 539         return(1);
 540         }
 541
 542 int test_mul(BIO *bp)
 543         {
 544         BIGNUM a,b,c,d,e;
 545         int i;
 546         BN_CTX *ctx;
 547
 548         ctx = BN_CTX_new();
 549         if (ctx == NULL) exit(1);
 550
 551         BN_init(&a);
 552         BN_init(&b);
 553         BN_init(&c);
 554         BN_init(&d);
 555         BN_init(&e);
 556
 557         for (i=0; i<num0+num1; i++)
 558                 {
 559                 if (i <= num1)
 560                         {
 561                         BN_bntest_rand(&a,100,0,0);
 562                         BN_bntest_rand(&b,100,0,0);
 563                         }
 564                 else
 565                         BN_bntest_rand(&b,i-num1,0,0);
 566                 a.neg=rand_neg();
 567                 b.neg=rand_neg();
 568                 BN_mul(&c,&a,&b,ctx);
 569                 if (bp != NULL)
 570                         {
 571                         if (!results)
 572                                 {
 573                                 BN_print(bp,&a);
 574                                 BIO_puts(bp," * ");
 575                                 BN_print(bp,&b);
 576                                 BIO_puts(bp," - ");
 577                                 }
 578                         BN_print(bp,&c);
 579                         BIO_puts(bp,"\n");
 580                         }
 581                 BN_div(&d,&e,&c,&a,ctx);
 582                 BN_sub(&d,&d,&b);
 583                 if(!BN_is_zero(&d) || !BN_is_zero(&e))
 584                     {
 585                     fprintf(stderr,"Multiplication test failed!\n");
 586                     return 0;
 587                     }
 588                 }
 589         BN_free(&a);
 590         BN_free(&b);
 591         BN_free(&c);
 592         BN_free(&d);
 593         BN_free(&e);
 594         BN_CTX_free(ctx);
 595         return(1);
 596         }
 597
 598 int test_sqr(BIO *bp, BN_CTX *ctx)
 599         {
 600         BIGNUM a,c,d,e;
 601         int i;
 602
 603         BN_init(&a);
 604         BN_init(&c);
 605         BN_init(&d);
 606         BN_init(&e);
 607
 608         for (i=0; i<num0; i++)
 609                 {
 610                 BN_bntest_rand(&a,40+i*10,0,0);
 611                 a.neg=rand_neg();
 612                 BN_sqr(&c,&a,ctx);
 613                 if (bp != NULL)
 614                         {
 615                         if (!results)
 616                                 {
 617                                 BN_print(bp,&a);
 618                                 BIO_puts(bp," * ");
 619                                 BN_print(bp,&a);
 620                                 BIO_puts(bp," - ");
 621                                 }
 622                         BN_print(bp,&c);
 623                         BIO_puts(bp,"\n");
 624                         }
 625                 BN_div(&d,&e,&c,&a,ctx);
 626                 BN_sub(&d,&d,&a);
 627                 if(!BN_is_zero(&d) || !BN_is_zero(&e))
 628                     {
 629                     fprintf(stderr,"Square test failed!\n");
 630                     return 0;
 631                     }
 632                 }
 633         BN_free(&a);
 634         BN_free(&c);
 635         BN_free(&d);
 636         BN_free(&e);
 637         return(1);
 638         }
 639
 640 int test_mont(BIO *bp, BN_CTX *ctx)
 641         {
 642         BIGNUM a,b,c,d,A,B;
 643         BIGNUM n;
 644         int i;
 645         BN_MONT_CTX *mont;
 646
 647         BN_init(&a);
 648         BN_init(&b);
 649         BN_init(&c);
 650         BN_init(&d);
 651         BN_init(&A);
 652         BN_init(&B);
 653         BN_init(&n);
 654
 655         mont=BN_MONT_CTX_new();
 656
 657         BN_bntest_rand(&a,100,0,0); /**/
 658         BN_bntest_rand(&b,100,0,0); /**/
 659         for (i=0; i<num2; i++)
 660                 {
 661                 int bits = (200*(i+1))/num2;
 662
 663                 if (bits == 0)
 664                         continue;
 665                 BN_bntest_rand(&n,bits,0,1);
 666                 BN_MONT_CTX_set(mont,&n,ctx);
 667
 668                 BN_nnmod(&a,&a,&n,ctx);
 669                 BN_nnmod(&b,&b,&n,ctx);
 670
 671                 BN_to_montgomery(&A,&a,mont,ctx);
 672                 BN_to_montgomery(&B,&b,mont,ctx);
 673
 674                 BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
 675                 BN_from_montgomery(&A,&c,mont,ctx);/**/
 676                 if (bp != NULL)
 677                         {
 678                         if (!results)
 679                                 {
 680 #ifdef undef
 681 fprintf(stderr,"%d * %d %% %d\n",
 682 BN_num_bits(&a),
 683 BN_num_bits(&b),
 684 BN_num_bits(mont->N));
 685 #endif
 686                                 BN_print(bp,&a);
 687                                 BIO_puts(bp," * ");
 688                                 BN_print(bp,&b);
 689                                 BIO_puts(bp," % ");
 690                                 BN_print(bp,&(mont->N));
 691                                 BIO_puts(bp," - ");
 692                                 }
 693                         BN_print(bp,&A);
 694                         BIO_puts(bp,"\n");
 695                         }
 696                 BN_mod_mul(&d,&a,&b,&n,ctx);
 697                 BN_sub(&d,&d,&A);
 698                 if(!BN_is_zero(&d))
 699                     {
 700                     fprintf(stderr,"Montgomery multiplication test failed!\n");
 701                     return 0;
 702                     }
 703                 }
 704         BN_MONT_CTX_free(mont);
 705         BN_free(&a);
 706         BN_free(&b);
 707         BN_free(&c);
 708         BN_free(&d);
 709         BN_free(&A);
 710         BN_free(&B);
 711         BN_free(&n);
 712         return(1);
 713         }
 714
 715 int test_mod(BIO *bp, BN_CTX *ctx)
 716         {
 717         BIGNUM *a,*b,*c,*d,*e;
 718         int i;
 719
 720         a=BN_new();
 721         b=BN_new();
 722         c=BN_new();
 723         d=BN_new();
 724         e=BN_new();
 725
 726         BN_bntest_rand(a,1024,0,0); /**/
 727         for (i=0; i<num0; i++)
 728                 {
 729                 BN_bntest_rand(b,450+i*10,0,0); /**/
 730                 a->neg=rand_neg();
 731                 b->neg=rand_neg();
 732                 BN_mod(c,a,b,ctx);/**/
 733                 if (bp != NULL)
 734                         {
 735                         if (!results)
 736                                 {
 737                                 BN_print(bp,a);
 738                                 BIO_puts(bp," % ");
 739                                 BN_print(bp,b);
 740                                 BIO_puts(bp," - ");
 741                                 }
 742                         BN_print(bp,c);
 743                         BIO_puts(bp,"\n");
 744                         }
 745                 BN_div(d,e,a,b,ctx);
 746                 BN_sub(e,e,c);
 747                 if(!BN_is_zero(e))
 748                     {
 749                     fprintf(stderr,"Modulo test failed!\n");
 750                     return 0;
 751                     }
 752                 }
 753         BN_free(a);
 754         BN_free(b);
 755         BN_free(c);
 756         BN_free(d);
 757         BN_free(e);
 758         return(1);
 759         }
 760
 761 int test_mod_mul(BIO *bp, BN_CTX *ctx)
 762         {
 763         BIGNUM *a,*b,*c,*d,*e;
 764         int i,j;
 765
 766         a=BN_new();
 767         b=BN_new();
 768         c=BN_new();
 769         d=BN_new();
 770         e=BN_new();
 771
 772         for (j=0; j<3; j++) {
 773         BN_bntest_rand(c,1024,0,0); /**/
 774         for (i=0; i<num0; i++)
 775                 {
 776                 BN_bntest_rand(a,475+i*10,0,0); /**/
 777                 BN_bntest_rand(b,425+i*11,0,0); /**/
 778                 a->neg=rand_neg();
 779                 b->neg=rand_neg();
 780                 if (!BN_mod_mul(e,a,b,c,ctx))
 781                         {
 782                         unsigned long l;
 783
 784                         while ((l=ERR_get_error()))
 785                                 fprintf(stderr,"ERROR:%s\n",
 786                                         ERR_error_string(l,NULL));
 787                         exit(1);
 788                         }
 789                 if (bp != NULL)
 790                         {
 791                         if (!results)
 792                                 {
 793                                 BN_print(bp,a);
 794                                 BIO_puts(bp," * ");
 795                                 BN_print(bp,b);
 796                                 BIO_puts(bp," % ");
 797                                 BN_print(bp,c);
 798                                 if ((a->neg ^ b->neg) && !BN_is_zero(e))
 799                                         {
 800                                         /* If  (a*b) % c  is negative,  c  must be added
 801                                          * in order to obtain the normalized remainder
 802                                          * (new with OpenSSL 0.9.7, previous versions of
 803                                          * BN_mod_mul could generate negative results)
 804                                          */
 805                                         BIO_puts(bp," + ");
 806                                         BN_print(bp,c);
 807                                         }
 808                                 BIO_puts(bp," - ");
 809                                 }
 810                         BN_print(bp,e);
 811                         BIO_puts(bp,"\n");
 812                         }
 813                 BN_mul(d,a,b,ctx);
 814                 BN_sub(d,d,e);
 815                 BN_div(a,b,d,c,ctx);
 816                 if(!BN_is_zero(b))
 817                     {
 818                     fprintf(stderr,"Modulo multiply test failed!\n");
 819                     ERR_print_errors_fp(stderr);
 820                     return 0;
 821                     }
 822                 }
 823         }
 824         BN_free(a);
 825         BN_free(b);
 826         BN_free(c);
 827         BN_free(d);
 828         BN_free(e);
 829         return(1);
 830         }
 831
 832 int test_mod_exp(BIO *bp, BN_CTX *ctx)
 833         {
 834         BIGNUM *a,*b,*c,*d,*e;
 835         int i;
 836
 837         a=BN_new();
 838         b=BN_new();
 839         c=BN_new();
 840         d=BN_new();
 841         e=BN_new();
 842
 843         BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
 844         for (i=0; i<num2; i++)
 845                 {
 846                 BN_bntest_rand(a,20+i*5,0,0); /**/
 847                 BN_bntest_rand(b,2+i,0,0); /**/
 848
 849                 if (!BN_mod_exp(d,a,b,c,ctx))
 850                         return(00);
 851
 852                 if (bp != NULL)
 853                         {
 854                         if (!results)
 855                                 {
 856                                 BN_print(bp,a);
 857                                 BIO_puts(bp," ^ ");
 858                                 BN_print(bp,b);
 859                                 BIO_puts(bp," % ");
 860                                 BN_print(bp,c);
 861                                 BIO_puts(bp," - ");
 862                                 }
 863                         BN_print(bp,d);
 864                         BIO_puts(bp,"\n");
 865                         }
 866                 BN_exp(e,a,b,ctx);
 867                 BN_sub(e,e,d);
 868                 BN_div(a,b,e,c,ctx);
 869                 if(!BN_is_zero(b))
 870                     {
 871                     fprintf(stderr,"Modulo exponentiation test failed!\n");
 872                     return 0;
 873                     }
 874                 }
 875         BN_free(a);
 876         BN_free(b);
 877         BN_free(c);
 878         BN_free(d);
 879         BN_free(e);
 880         return(1);
 881         }
 882
 883 int test_exp(BIO *bp, BN_CTX *ctx)
 884         {
 885         BIGNUM *a,*b,*d,*e,*one;
 886         int i;
 887
 888         a=BN_new();
 889         b=BN_new();
 890         d=BN_new();
 891         e=BN_new();
 892         one=BN_new();
 893         BN_one(one);
 894
 895         for (i=0; i<num2; i++)
 896                 {
 897                 BN_bntest_rand(a,20+i*5,0,0); /**/
 898                 BN_bntest_rand(b,2+i,0,0); /**/
 899
 900                 if (!BN_exp(d,a,b,ctx))
 901                         return(00);
 902
 903                 if (bp != NULL)
 904                         {
 905                         if (!results)
 906                                 {
 907                                 BN_print(bp,a);
 908                                 BIO_puts(bp," ^ ");
 909                                 BN_print(bp,b);
 910                                 BIO_puts(bp," - ");
 911                                 }
 912                         BN_print(bp,d);
 913                         BIO_puts(bp,"\n");
 914                         }
 915                 BN_one(e);
 916                 for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
 917                     BN_mul(e,e,a,ctx);
 918                 BN_sub(e,e,d);
 919                 if(!BN_is_zero(e))
 920                     {
 921                     fprintf(stderr,"Exponentiation test failed!\n");
 922                     return 0;
 923                     }
 924                 }
 925         BN_free(a);
 926         BN_free(b);
 927         BN_free(d);
 928         BN_free(e);
 929         BN_free(one);
 930         return(1);
 931         }
 932
 933 int test_gf2m_add(BIO *bp)
 934         {
 935         BIGNUM a,b,c;
 936         int i, ret = 0;
 937
 938         BN_init(&a);
 939         BN_init(&b);
 940         BN_init(&c);
 941
 942         for (i=0; i<num0; i++)
 943                 {
 944                 BN_rand(&a,512,0,0);
 945                 BN_copy(&b, BN_value_one());
 946                 a.neg=rand_neg();
 947                 b.neg=rand_neg();
 948                 BN_GF2m_add(&c,&a,&b);
 949 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
 950                 if (bp != NULL)
 951                         {
 952                         if (!results)
 953                                 {
 954                                 BN_print(bp,&a);
 955                                 BIO_puts(bp," ^ ");
 956                                 BN_print(bp,&b);
 957                                 BIO_puts(bp," = ");
 958                                 }
 959                         BN_print(bp,&c);
 960                         BIO_puts(bp,"\n");
 961                         }
 962 #endif
 963                 /* Test that two added values have the correct parity. */
 964                 if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
 965                         {
 966                     fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
 967                         goto err;
 968                         }
 969                 BN_GF2m_add(&c,&c,&c);
 970                 /* Test that c + c = 0. */
 971                 if(!BN_is_zero(&c))
 972                     {
 973                     fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
 974                         goto err;
 975                     }
 976                 }
 977         ret = 1;
 978   err:
 979         BN_free(&a);
 980         BN_free(&b);
 981         BN_free(&c);
 982         return ret;
 983         }
 984
 985 int test_gf2m_mod(BIO *bp)
 986         {
 987         BIGNUM *a,*b[2],*c,*d,*e;
 988         int i, j, ret = 0;
 989         unsigned int p0[] = {163,7,6,3,0};
 990         unsigned int p1[] = {193,15,0};
 991
 992         a=BN_new();
 993         b[0]=BN_new();
 994         b[1]=BN_new();
 995         c=BN_new();
 996         d=BN_new();
 997         e=BN_new();
 998
 999         BN_GF2m_arr2poly(p0, b[0]);
1000         BN_GF2m_arr2poly(p1, b[1]);
1001
1002         for (i=0; i<num0; i++)
1003                 {
1004                 BN_bntest_rand(a, 1024, 0, 0);
1005                 for (j=0; j < 2; j++)
1006                         {
1007                         BN_GF2m_mod(c, a, b[j]);
1008 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1009                         if (bp != NULL)
1010                                 {
1011                                 if (!results)
1012                                         {
1013                                         BN_print(bp,a);
1014                                         BIO_puts(bp," % ");
1015                                         BN_print(bp,b[j]);
1016                                         BIO_puts(bp," - ");
1017                                         BN_print(bp,c);
1018                                         BIO_puts(bp,"\n");
1019                                         }
1020                                 }
1021 #endif
1022                         BN_GF2m_add(d, a, c);
1023                         BN_GF2m_mod(e, d, b[j]);
1024                         /* Test that a + (a mod p) mod p == 0. */
1025                         if(!BN_is_zero(e))
1026                                 {
1027                                 fprintf(stderr,"GF(2^m) modulo test failed!\n");
1028                                 goto err;
1029                                 }
1030                         }
1031                 }
1032         ret = 1;
1033   err:
1034         BN_free(a);
1035         BN_free(b[0]);
1036         BN_free(b[1]);
1037         BN_free(c);
1038         BN_free(d);
1039         BN_free(e);
1040         return ret;
1041         }
1042
1043 int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
1044         {
1045         BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
1046         int i, j, ret = 0;
1047         unsigned int p0[] = {163,7,6,3,0};
1048         unsigned int p1[] = {193,15,0};
1049
1050         a=BN_new();
1051         b[0]=BN_new();
1052         b[1]=BN_new();
1053         c=BN_new();
1054         d=BN_new();
1055         e=BN_new();
1056         f=BN_new();
1057         g=BN_new();
1058         h=BN_new();
1059
1060         BN_GF2m_arr2poly(p0, b[0]);
1061         BN_GF2m_arr2poly(p1, b[1]);
1062
1063         for (i=0; i<num0; i++)
1064                 {
1065                 BN_bntest_rand(a, 1024, 0, 0);
1066                 BN_bntest_rand(c, 1024, 0, 0);
1067                 BN_bntest_rand(d, 1024, 0, 0);
1068                 for (j=0; j < 2; j++)
1069                         {
1070                         BN_GF2m_mod_mul(e, a, c, b[j], ctx);
1071 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1072                         if (bp != NULL)
1073                                 {
1074                                 if (!results)
1075                                         {
1076                                         BN_print(bp,a);
1077                                         BIO_puts(bp," * ");
1078                                         BN_print(bp,c);
1079                                         BIO_puts(bp," % ");
1080                                         BN_print(bp,b[j]);
1081                                         BIO_puts(bp," - ");
1082                                         BN_print(bp,e);
1083                                         BIO_puts(bp,"\n");
1084                                         }
1085                                 }
1086 #endif
1087                         BN_GF2m_add(f, a, d);
1088                         BN_GF2m_mod_mul(g, f, c, b[j], ctx);
1089                         BN_GF2m_mod_mul(h, d, c, b[j], ctx);
1090                         BN_GF2m_add(f, e, g);
1091                         BN_GF2m_add(f, f, h);
1092                         /* Test that (a+d)*c = a*c + d*c. */
1093                         if(!BN_is_zero(f))
1094                                 {
1095                                 fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
1096                                 goto err;
1097                                 }
1098                         }
1099                 }
1100         ret = 1;
1101   err:
1102         BN_free(a);
1103         BN_free(b[0]);
1104         BN_free(b[1]);
1105         BN_free(c);
1106         BN_free(d);
1107         BN_free(e);
1108         BN_free(f);
1109         BN_free(g);
1110         BN_free(h);
1111         return ret;
1112         }
1113
1114 int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
1115         {
1116         BIGNUM *a,*b[2],*c,*d;
1117         int i, j, ret = 0;
1118         unsigned int p0[] = {163,7,6,3,0};
1119         unsigned int p1[] = {193,15,0};
1120
1121         a=BN_new();
1122         b[0]=BN_new();
1123         b[1]=BN_new();
1124         c=BN_new();
1125         d=BN_new();
1126
1127         BN_GF2m_arr2poly(p0, b[0]);
1128         BN_GF2m_arr2poly(p1, b[1]);
1129
1130         for (i=0; i<num0; i++)
1131                 {
1132                 BN_bntest_rand(a, 1024, 0, 0);
1133                 for (j=0; j < 2; j++)
1134                         {
1135                         BN_GF2m_mod_sqr(c, a, b[j], ctx);
1136                         BN_copy(d, a);
1137                         BN_GF2m_mod_mul(d, a, d, b[j], ctx);
1138 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1139                         if (bp != NULL)
1140                                 {
1141                                 if (!results)
1142                                         {
1143                                         BN_print(bp,a);
1144                                         BIO_puts(bp," ^ 2 % ");
1145                                         BN_print(bp,b[j]);
1146                                         BIO_puts(bp, " = ");
1147                                         BN_print(bp,c);
1148                                         BIO_puts(bp,"; a * a = ");
1149                                         BN_print(bp,d);
1150                                         BIO_puts(bp,"\n");
1151                                         }
1152                                 }
1153 #endif
1154                         BN_GF2m_add(d, c, d);
1155                         /* Test that a*a = a^2. */
1156                         if(!BN_is_zero(d))
1157                                 {
1158                                 fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
1159                                 goto err;
1160                                 }
1161                         }
1162                 }
1163         ret = 1;
1164   err:
1165         BN_free(a);
1166         BN_free(b[0]);
1167         BN_free(b[1]);
1168         BN_free(c);
1169         BN_free(d);
1170         return ret;
1171         }
1172
1173 int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
1174         {
1175         BIGNUM *a,*b[2],*c,*d;
1176         int i, j, ret = 0;
1177         unsigned int p0[] = {163,7,6,3,0};
1178         unsigned int p1[] = {193,15,0};
1179
1180         a=BN_new();
1181         b[0]=BN_new();
1182         b[1]=BN_new();
1183         c=BN_new();
1184         d=BN_new();
1185
1186         BN_GF2m_arr2poly(p0, b[0]);
1187         BN_GF2m_arr2poly(p1, b[1]);
1188
1189         for (i=0; i<num0; i++)
1190                 {
1191                 BN_bntest_rand(a, 512, 0, 0);
1192                 for (j=0; j < 2; j++)
1193                         {
1194                         BN_GF2m_mod_inv(c, a, b[j], ctx);
1195                         BN_GF2m_mod_mul(d, a, c, b[j], ctx);
1196 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1197                         if (bp != NULL)
1198                                 {
1199                                 if (!results)
1200                                         {
1201                                         BN_print(bp,a);
1202                                         BIO_puts(bp, " * ");
1203                                         BN_print(bp,c);
1204                                         BIO_puts(bp," - 1 % ");
1205                                         BN_print(bp,b[j]);
1206                                         BIO_puts(bp,"\n");
1207                                         }
1208                                 }
1209 #endif
1210                         /* Test that ((1/a)*a) = 1. */
1211                         if(!BN_is_one(d))
1212                                 {
1213                                 fprintf(stderr,"GF(2^m) modular inversion 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         return ret;
1226         }
1227
1228 int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
1229         {
1230         BIGNUM *a,*b[2],*c,*d,*e,*f;
1231         int i, j, ret = 0;
1232         unsigned int p0[] = {163,7,6,3,0};
1233         unsigned int p1[] = {193,15,0};
1234
1235         a=BN_new();
1236         b[0]=BN_new();
1237         b[1]=BN_new();
1238         c=BN_new();
1239         d=BN_new();
1240         e=BN_new();
1241         f=BN_new();
1242
1243         BN_GF2m_arr2poly(p0, b[0]);
1244         BN_GF2m_arr2poly(p1, b[1]);
1245
1246         for (i=0; i<num0; i++)
1247                 {
1248                 BN_bntest_rand(a, 512, 0, 0);
1249                 BN_bntest_rand(c, 512, 0, 0);
1250                 for (j=0; j < 2; j++)
1251                         {
1252                         BN_GF2m_mod_div(d, a, c, b[j], ctx);
1253                         BN_GF2m_mod_mul(e, d, c, b[j], ctx);
1254                         BN_GF2m_mod_div(f, a, e, b[j], ctx);
1255 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1256                         if (bp != NULL)
1257                                 {
1258                                 if (!results)
1259                                         {
1260                                         BN_print(bp,a);
1261                                         BIO_puts(bp, " = ");
1262                                         BN_print(bp,c);
1263                                         BIO_puts(bp," * ");
1264                                         BN_print(bp,d);
1265                                         BIO_puts(bp, " % ");
1266                                         BN_print(bp,b[j]);
1267                                         BIO_puts(bp,"\n");
1268                                         }
1269                                 }
1270 #endif
1271                         /* Test that ((a/c)*c)/a = 1. */
1272                         if(!BN_is_one(f))
1273                                 {
1274                                 fprintf(stderr,"GF(2^m) modular division test failed!\n");
1275                                 goto err;
1276                                 }
1277                         }
1278                 }
1279         ret = 1;
1280   err:
1281         BN_free(a);
1282         BN_free(b[0]);
1283         BN_free(b[1]);
1284         BN_free(c);
1285         BN_free(d);
1286         BN_free(e);
1287         BN_free(f);
1288         return ret;
1289         }
1290
1291 int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
1292         {
1293         BIGNUM *a,*b[2],*c,*d,*e,*f;
1294         int i, j, ret = 0;
1295         unsigned int p0[] = {163,7,6,3,0};
1296         unsigned int p1[] = {193,15,0};
1297
1298         a=BN_new();
1299         b[0]=BN_new();
1300         b[1]=BN_new();
1301         c=BN_new();
1302         d=BN_new();
1303         e=BN_new();
1304         f=BN_new();
1305
1306         BN_GF2m_arr2poly(p0, b[0]);
1307         BN_GF2m_arr2poly(p1, b[1]);
1308
1309         for (i=0; i<num0; i++)
1310                 {
1311                 BN_bntest_rand(a, 512, 0, 0);
1312                 BN_bntest_rand(c, 512, 0, 0);
1313                 BN_bntest_rand(d, 512, 0, 0);
1314                 for (j=0; j < 2; j++)
1315                         {
1316                         BN_GF2m_mod_exp(e, a, c, b[j], ctx);
1317                         BN_GF2m_mod_exp(f, a, d, b[j], ctx);
1318                         BN_GF2m_mod_mul(e, e, f, b[j], ctx);
1319                         BN_add(f, c, d);
1320                         BN_GF2m_mod_exp(f, a, f, b[j], ctx);
1321 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1322                         if (bp != NULL)
1323                                 {
1324                                 if (!results)
1325                                         {
1326                                         BN_print(bp,a);
1327                                         BIO_puts(bp, " ^ (");
1328                                         BN_print(bp,c);
1329                                         BIO_puts(bp," + ");
1330                                         BN_print(bp,d);
1331                                         BIO_puts(bp, ") = ");
1332                                         BN_print(bp,e);
1333                                         BIO_puts(bp, "; - ");
1334                                         BN_print(bp,f);
1335                                         BIO_puts(bp, " % ");
1336                                         BN_print(bp,b[j]);
1337                                         BIO_puts(bp,"\n");
1338                                         }
1339                                 }
1340 #endif
1341                         BN_GF2m_add(f, e, f);
1342                         /* Test that a^(c+d)=a^c*a^d. */
1343                         if(!BN_is_zero(f))
1344                                 {
1345                                 fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
1346                                 goto err;
1347                                 }
1348                         }
1349                 }
1350         ret = 1;
1351   err:
1352         BN_free(a);
1353         BN_free(b[0]);
1354         BN_free(b[1]);
1355         BN_free(c);
1356         BN_free(d);
1357         BN_free(e);
1358         BN_free(f);
1359         return ret;
1360         }
1361
1362 int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
1363         {
1364         BIGNUM *a,*b[2],*c,*d,*e,*f;
1365         int i, j, ret = 0;
1366         unsigned int p0[] = {163,7,6,3,0};
1367         unsigned int p1[] = {193,15,0};
1368
1369         a=BN_new();
1370         b[0]=BN_new();
1371         b[1]=BN_new();
1372         c=BN_new();
1373         d=BN_new();
1374         e=BN_new();
1375         f=BN_new();
1376
1377         BN_GF2m_arr2poly(p0, b[0]);
1378         BN_GF2m_arr2poly(p1, b[1]);
1379
1380         for (i=0; i<num0; i++)
1381                 {
1382                 BN_bntest_rand(a, 512, 0, 0);
1383                 for (j=0; j < 2; j++)
1384                         {
1385                         BN_GF2m_mod(c, a, b[j]);
1386                         BN_GF2m_mod_sqrt(d, a, b[j], ctx);
1387                         BN_GF2m_mod_sqr(e, d, b[j], ctx);
1388 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1389                         if (bp != NULL)
1390                                 {
1391                                 if (!results)
1392                                         {
1393                                         BN_print(bp,d);
1394                                         BIO_puts(bp, " ^ 2 - ");
1395                                         BN_print(bp,a);
1396                                         BIO_puts(bp,"\n");
1397                                         }
1398                                 }
1399 #endif
1400                         BN_GF2m_add(f, c, e);
1401                         /* Test that d^2 = a, where d = sqrt(a). */
1402                         if(!BN_is_zero(f))
1403                                 {
1404                                 fprintf(stderr,"GF(2^m) modular square root test failed!\n");
1405                                 goto err;
1406                                 }
1407                         }
1408                 }
1409         ret = 1;
1410   err:
1411         BN_free(a);
1412         BN_free(b[0]);
1413         BN_free(b[1]);
1414         BN_free(c);
1415         BN_free(d);
1416         BN_free(e);
1417         BN_free(f);
1418         return ret;
1419         }
1420
1421 int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
1422         {
1423         BIGNUM *a,*b[2],*c,*d,*e;
1424         int i, j, s = 0, t, ret = 0;
1425         unsigned int p0[] = {163,7,6,3,0};
1426         unsigned int p1[] = {193,15,0};
1427
1428         a=BN_new();
1429         b[0]=BN_new();
1430         b[1]=BN_new();
1431         c=BN_new();
1432         d=BN_new();
1433         e=BN_new();
1434
1435         BN_GF2m_arr2poly(p0, b[0]);
1436         BN_GF2m_arr2poly(p1, b[1]);
1437
1438         for (i=0; i<num0; i++)
1439                 {
1440                 BN_bntest_rand(a, 512, 0, 0);
1441                 for (j=0; j < 2; j++)
1442                         {
1443                         t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
1444                         if (t)
1445                                 {
1446                                 s++;
1447                                 BN_GF2m_mod_sqr(d, c, b[j], ctx);
1448                                 BN_GF2m_add(d, c, d);
1449                                 BN_GF2m_mod(e, a, b[j]);
1450 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1451                                 if (bp != NULL)
1452                                         {
1453                                         if (!results)
1454                                                 {
1455                                                 BN_print(bp,c);
1456                                                 BIO_puts(bp, " is root of z^2 + z = ");
1457                                                 BN_print(bp,a);
1458                                                 BIO_puts(bp, " % ");
1459                                                 BN_print(bp,b[j]);
1460                                                 BIO_puts(bp, "\n");
1461                                                 }
1462                                         }
1463 #endif
1464                                 BN_GF2m_add(e, e, d);
1465                                 /* Test that solution of quadratic c satisfies c^2 + c = a. */
1466                                 if(!BN_is_zero(e))
1467                                         {
1468                                         fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
1469                                         goto err;
1470                                         }
1471
1472                                 }
1473                         else
1474                                 {
1475 #if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
1476                                 if (bp != NULL)
1477                                         {
1478                                         if (!results)
1479                                                 {
1480                                                 BIO_puts(bp, "There are no roots of z^2 + z = ");
1481                                                 BN_print(bp,a);
1482                                                 BIO_puts(bp, " % ");
1483                                                 BN_print(bp,b[j]);
1484                                                 BIO_puts(bp, "\n");
1485                                                 }
1486                                         }
1487 #endif
1488                                 }
1489                         }
1490                 }
1491         if (s == 0)
1492                 {
1493                 fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
1494                 fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
1495                 goto err;
1496                 }
1497         ret = 1;
1498   err:
1499         BN_free(a);
1500         BN_free(b[0]);
1501         BN_free(b[1]);
1502         BN_free(c);
1503         BN_free(d);
1504         BN_free(e);
1505         return ret;
1506         }
1507
1508 static void genprime_cb(int p, int n, void *arg)
1509         {
1510         char c='*';
1511
1512         if (p == 0) c='.';
1513         if (p == 1) c='+';
1514         if (p == 2) c='*';
1515         if (p == 3) c='\n';
1516         putc(c, stderr);
1517         fflush(stderr);
1518         (void)n;
1519         (void)arg;
1520         }
1521
1522 int test_kron(BIO *bp, BN_CTX *ctx)
1523         {
1524         BIGNUM *a,*b,*r,*t;
1525         int i;
1526         int legendre, kronecker;
1527         int ret = 0;
1528
1529         a = BN_new();
1530         b = BN_new();
1531         r = BN_new();
1532         t = BN_new();
1533         if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;
1534
1535         /* We test BN_kronecker(a, b, ctx) just for  b  odd (Jacobi symbol).
1536          * In this case we know that if  b  is prime, then BN_kronecker(a, b, ctx)
1537          * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
1538          * So we generate a random prime  b  and compare these values
1539          * for a number of random  a's.  (That is, we run the Solovay-Strassen
1540          * primality test to confirm that  b  is prime, except that we
1541          * don't want to test whether  b  is prime but whether BN_kronecker
1542          * works.) */
1543
1544         if (!BN_generate_prime(b, 512, 0, NULL, NULL, genprime_cb, NULL)) goto err;
1545         b->neg = rand_neg();
1546         putc('\n', stderr);
1547
1548         for (i = 0; i < num0; i++)
1549                 {
1550                 if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
1551                 a->neg = rand_neg();
1552
1553                 /* t := (|b|-1)/2  (note that b is odd) */
1554                 if (!BN_copy(t, b)) goto err;
1555                 t->neg = 0;
1556                 if (!BN_sub_word(t, 1)) goto err;
1557                 if (!BN_rshift1(t, t)) goto err;
1558                 /* r := a^t mod b */
1559                 b->neg=0;
1560
1561                 if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
1562                 b->neg=1;
1563
1564                 if (BN_is_word(r, 1))
1565                         legendre = 1;
1566                 else if (BN_is_zero(r))
1567                         legendre = 0;
1568                 else
1569                         {
1570                         if (!BN_add_word(r, 1)) goto err;
1571                         if (0 != BN_ucmp(r, b))
1572                                 {
1573                                 fprintf(stderr, "Legendre symbol computation failed\n");
1574                                 goto err;
1575                                 }
1576                         legendre = -1;
1577                         }
1578
1579                 kronecker = BN_kronecker(a, b, ctx);
1580                 if (kronecker < -1) goto err;
1581                 /* we actually need BN_kronecker(a, |b|) */
1582                 if (a->neg && b->neg)
1583                         kronecker = -kronecker;
1584
1585                 if (legendre != kronecker)
1586                         {
1587                         fprintf(stderr, "legendre != kronecker; a = ");
1588                         BN_print_fp(stderr, a);
1589                         fprintf(stderr, ", b = ");
1590                         BN_print_fp(stderr, b);
1591                         fprintf(stderr, "\n");
1592                         goto err;
1593                         }
1594
1595                 putc('.', stderr);
1596                 fflush(stderr);
1597                 }
1598
1599         putc('\n', stderr);
1600         fflush(stderr);
1601         ret = 1;
1602  err:
1603         if (a != NULL) BN_free(a);
1604         if (b != NULL) BN_free(b);
1605         if (r != NULL) BN_free(r);
1606         if (t != NULL) BN_free(t);
1607         return ret;
1608         }
1609
1610 int test_sqrt(BIO *bp, BN_CTX *ctx)
1611         {
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         for (i = 0; i < 16; i++)
1622                 {
1623                 if (i < 8)
1624                         {
1625                         unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
1626
1627                         if (!BN_set_word(p, primes[i])) goto err;
1628                         }
1629                 else
1630                         {
1631                         if (!BN_set_word(a, 32)) goto err;
1632                         if (!BN_set_word(r, 2*i + 1)) goto err;
1633
1634                         if (!BN_generate_prime(p, 256, 0, a, r, genprime_cb, NULL)) goto err;
1635                         putc('\n', stderr);
1636                         }
1637                 p->neg = rand_neg();
1638
1639                 for (j = 0; j < num2; j++)
1640                         {
1641                         /* construct 'a' such that it is a square modulo p,
1642                          * but in general not a proper square and not reduced modulo p */
1643                         if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
1644                         if (!BN_nnmod(r, r, p, ctx)) goto err;
1645                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1646                         if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
1647                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1648                         if (!BN_mod_sqr(a, a, p, ctx)) goto err;
1649                         if (!BN_mul(a, a, r, ctx)) goto err;
1650                         if (rand_neg())
1651                                 if (!BN_sub(a, a, p)) goto err;
1652
1653                         if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
1654                         if (!BN_mod_sqr(r, r, p, ctx)) goto err;
1655
1656                         if (!BN_nnmod(a, a, p, ctx)) goto err;
1657
1658                         if (BN_cmp(a, r) != 0)
1659                                 {
1660                                 fprintf(stderr, "BN_mod_sqrt failed: a = ");
1661                                 BN_print_fp(stderr, a);
1662                                 fprintf(stderr, ", r = ");
1663                                 BN_print_fp(stderr, r);
1664                                 fprintf(stderr, ", p = ");
1665                                 BN_print_fp(stderr, p);
1666                                 fprintf(stderr, "\n");
1667                                 goto err;
1668                                 }
1669
1670                         putc('.', stderr);
1671                         fflush(stderr);
1672                         }
1673
1674                 putc('\n', stderr);
1675                 fflush(stderr);
1676                 }
1677         ret = 1;
1678  err:
1679         if (a != NULL) BN_free(a);
1680         if (p != NULL) BN_free(p);
1681         if (r != NULL) BN_free(r);
1682         return ret;
1683         }
1684
1685 int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
1686         {
1687         BIGNUM *a,*b,*c,*d;
1688         int i;
1689
1690         b=BN_new();
1691         c=BN_new();
1692         d=BN_new();
1693         BN_one(c);
1694
1695         if(a_)
1696             a=a_;
1697         else
1698             {
1699             a=BN_new();
1700             BN_bntest_rand(a,200,0,0); /**/
1701             a->neg=rand_neg();
1702             }
1703         for (i=0; i<num0; i++)
1704                 {
1705                 BN_lshift(b,a,i+1);
1706                 BN_add(c,c,c);
1707                 if (bp != NULL)
1708                         {
1709                         if (!results)
1710                                 {
1711                                 BN_print(bp,a);
1712                                 BIO_puts(bp," * ");
1713                                 BN_print(bp,c);
1714                                 BIO_puts(bp," - ");
1715                                 }
1716                         BN_print(bp,b);
1717                         BIO_puts(bp,"\n");
1718                         }
1719                 BN_mul(d,a,c,ctx);
1720                 BN_sub(d,d,b);
1721                 if(!BN_is_zero(d))
1722                     {
1723                     fprintf(stderr,"Left shift test failed!\n");
1724                     fprintf(stderr,"a=");
1725                     BN_print_fp(stderr,a);
1726                     fprintf(stderr,"\nb=");
1727                     BN_print_fp(stderr,b);
1728                     fprintf(stderr,"\nc=");
1729                     BN_print_fp(stderr,c);
1730                     fprintf(stderr,"\nd=");
1731                     BN_print_fp(stderr,d);
1732                     fprintf(stderr,"\n");
1733                     return 0;
1734                     }
1735                 }
1736         BN_free(a);
1737         BN_free(b);
1738         BN_free(c);
1739         BN_free(d);
1740         return(1);
1741         }
1742
1743 int test_lshift1(BIO *bp)
1744         {
1745         BIGNUM *a,*b,*c;
1746         int i;
1747
1748         a=BN_new();
1749         b=BN_new();
1750         c=BN_new();
1751
1752         BN_bntest_rand(a,200,0,0); /**/
1753         a->neg=rand_neg();
1754         for (i=0; i<num0; i++)
1755                 {
1756                 BN_lshift1(b,a);
1757                 if (bp != NULL)
1758                         {
1759                         if (!results)
1760                                 {
1761                                 BN_print(bp,a);
1762                                 BIO_puts(bp," * 2");
1763                                 BIO_puts(bp," - ");
1764                                 }
1765                         BN_print(bp,b);
1766                         BIO_puts(bp,"\n");
1767                         }
1768                 BN_add(c,a,a);
1769                 BN_sub(a,b,c);
1770                 if(!BN_is_zero(a))
1771                     {
1772                     fprintf(stderr,"Left shift one test failed!\n");
1773                     return 0;
1774                     }
1775
1776                 BN_copy(a,b);
1777                 }
1778         BN_free(a);
1779         BN_free(b);
1780         BN_free(c);
1781         return(1);
1782         }
1783
1784 int test_rshift(BIO *bp,BN_CTX *ctx)
1785         {
1786         BIGNUM *a,*b,*c,*d,*e;
1787         int i;
1788
1789         a=BN_new();
1790         b=BN_new();
1791         c=BN_new();
1792         d=BN_new();
1793         e=BN_new();
1794         BN_one(c);
1795
1796         BN_bntest_rand(a,200,0,0); /**/
1797         a->neg=rand_neg();
1798         for (i=0; i<num0; i++)
1799                 {
1800                 BN_rshift(b,a,i+1);
1801                 BN_add(c,c,c);
1802                 if (bp != NULL)
1803                         {
1804                         if (!results)
1805                                 {
1806                                 BN_print(bp,a);
1807                                 BIO_puts(bp," / ");
1808                                 BN_print(bp,c);
1809                                 BIO_puts(bp," - ");
1810                                 }
1811                         BN_print(bp,b);
1812                         BIO_puts(bp,"\n");
1813                         }
1814                 BN_div(d,e,a,c,ctx);
1815                 BN_sub(d,d,b);
1816                 if(!BN_is_zero(d))
1817                     {
1818                     fprintf(stderr,"Right shift test failed!\n");
1819                     return 0;
1820                     }
1821                 }
1822         BN_free(a);
1823         BN_free(b);
1824         BN_free(c);
1825         BN_free(d);
1826         BN_free(e);
1827         return(1);
1828         }
1829
1830 int test_rshift1(BIO *bp)
1831         {
1832         BIGNUM *a,*b,*c;
1833         int i;
1834
1835         a=BN_new();
1836         b=BN_new();
1837         c=BN_new();
1838
1839         BN_bntest_rand(a,200,0,0); /**/
1840         a->neg=rand_neg();
1841         for (i=0; i<num0; i++)
1842                 {
1843                 BN_rshift1(b,a);
1844                 if (bp != NULL)
1845                         {
1846                         if (!results)
1847                                 {
1848                                 BN_print(bp,a);
1849                                 BIO_puts(bp," / 2");
1850                                 BIO_puts(bp," - ");
1851                                 }
1852                         BN_print(bp,b);
1853                         BIO_puts(bp,"\n");
1854                         }
1855                 BN_sub(c,a,b);
1856                 BN_sub(c,c,b);
1857                 if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
1858                     {
1859                     fprintf(stderr,"Right shift one test failed!\n");
1860                     return 0;
1861                     }
1862                 BN_copy(a,b);
1863                 }
1864         BN_free(a);
1865         BN_free(b);
1866         BN_free(c);
1867         return(1);
1868         }
1869
1870 int rand_neg(void)
1871         {
1872         static unsigned int neg=0;
1873         static int sign[8]={0,0,0,1,1,0,1,1};
1874
1875         return(sign[(neg++)%8]);
1876         }