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bntest.c

/* crypto/bn/bntest.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 * 
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 * 
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from 
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 * 
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 * 
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */
/* ====================================================================
 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
 *
 * Portions of the attached software ("Contribution") are developed by 
 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
 *
 * The Contribution is licensed pursuant to the Eric Young open source
 * license provided above.
 *
 * The binary polynomial arithmetic software is originally written by 
 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
 *
 */

/* Until the key-gen callbacks are modified to use newer prototypes, we allow
 * deprecated functions for openssl-internal code */
#ifdef OPENSSL_NO_DEPRECATED
#undef OPENSSL_NO_DEPRECATED
#endif

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include "e_os.h"

#include <openssl/bio.h>
#include <openssl/bn.h>
#include <openssl/rand.h>
#include <openssl/x509.h>
#include <openssl/err.h>

const int num0 = 100; /* number of tests */
const int num1 = 50;  /* additional tests for some functions */
const int num2 = 5;   /* number of tests for slow functions */

int test_add(BIO *bp);
int test_sub(BIO *bp);
int test_lshift1(BIO *bp);
int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_);
int test_rshift1(BIO *bp);
int test_rshift(BIO *bp,BN_CTX *ctx);
int test_div(BIO *bp,BN_CTX *ctx);
int test_div_word(BIO *bp);
int test_div_recp(BIO *bp,BN_CTX *ctx);
int test_mul(BIO *bp);
int test_sqr(BIO *bp,BN_CTX *ctx);
int test_mont(BIO *bp,BN_CTX *ctx);
int test_mod(BIO *bp,BN_CTX *ctx);
int test_mod_mul(BIO *bp,BN_CTX *ctx);
int test_mod_exp(BIO *bp,BN_CTX *ctx);
int test_mod_exp_mont_consttime(BIO *bp,BN_CTX *ctx);
int test_exp(BIO *bp,BN_CTX *ctx);
int test_gf2m_add(BIO *bp);
int test_gf2m_mod(BIO *bp);
int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
int test_kron(BIO *bp,BN_CTX *ctx);
int test_sqrt(BIO *bp,BN_CTX *ctx);
int rand_neg(void);
static int results=0;

static unsigned char lst[]="\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9"
"\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0";

static const char rnd_seed[] = "string to make the random number generator think it has entropy";

static void message(BIO *out, char *m)
      {
      fprintf(stderr, "test %s\n", m);
      BIO_puts(out, "print \"test ");
      BIO_puts(out, m);
      BIO_puts(out, "\\n\"\n");
      }

int main(int argc, char *argv[])
      {
      BN_CTX *ctx;
      BIO *out;
      char *outfile=NULL;

      results = 0;

      RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */

      argc--;
      argv++;
      while (argc >= 1)
            {
            if (strcmp(*argv,"-results") == 0)
                  results=1;
            else if (strcmp(*argv,"-out") == 0)
                  {
                  if (--argc < 1) break;
                  outfile= *(++argv);
                  }
            argc--;
            argv++;
            }


      ctx=BN_CTX_new();
      if (ctx == NULL) EXIT(1);

      out=BIO_new(BIO_s_file());
      if (out == NULL) EXIT(1);
      if (outfile == NULL)
            {
            BIO_set_fp(out,stdout,BIO_NOCLOSE);
            }
      else
            {
            if (!BIO_write_filename(out,outfile))
                  {
                  perror(outfile);
                  EXIT(1);
                  }
            }

      if (!results)
            BIO_puts(out,"obase=16\nibase=16\n");

      message(out,"BN_add");
      if (!test_add(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_sub");
      if (!test_sub(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_lshift1");
      if (!test_lshift1(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_lshift (fixed)");
      if (!test_lshift(out,ctx,BN_bin2bn(lst,sizeof(lst)-1,NULL)))
          goto err;
      (void)BIO_flush(out);

      message(out,"BN_lshift");
      if (!test_lshift(out,ctx,NULL)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_rshift1");
      if (!test_rshift1(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_rshift");
      if (!test_rshift(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_sqr");
      if (!test_sqr(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_mul");
      if (!test_mul(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_div");
      if (!test_div(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_div_word");
      if (!test_div_word(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_div_recp");
      if (!test_div_recp(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_mod");
      if (!test_mod(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_mod_mul");
      if (!test_mod_mul(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_mont");
      if (!test_mont(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_mod_exp");
      if (!test_mod_exp(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_mod_exp_mont_consttime");
      if (!test_mod_exp_mont_consttime(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_exp");
      if (!test_exp(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_kronecker");
      if (!test_kron(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_mod_sqrt");
      if (!test_sqrt(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_add");
      if (!test_gf2m_add(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod");
      if (!test_gf2m_mod(out)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod_mul");
      if (!test_gf2m_mod_mul(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod_sqr");
      if (!test_gf2m_mod_sqr(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod_inv");
      if (!test_gf2m_mod_inv(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod_div");
      if (!test_gf2m_mod_div(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod_exp");
      if (!test_gf2m_mod_exp(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod_sqrt");
      if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
      (void)BIO_flush(out);

      message(out,"BN_GF2m_mod_solve_quad");
      if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
      (void)BIO_flush(out);

      BN_CTX_free(ctx);
      BIO_free(out);

/**/
      EXIT(0);
err:
      BIO_puts(out,"1\n"); /* make sure the Perl script fed by bc notices
                            * the failure, see test_bn in test/Makefile.ssl*/
      (void)BIO_flush(out);
      ERR_load_crypto_strings();
      ERR_print_errors_fp(stderr);
      EXIT(1);
      return(1);
      }

int test_add(BIO *bp)
      {
      BIGNUM a,b,c;
      int i;

      BN_init(&a);
      BN_init(&b);
      BN_init(&c);

      BN_bntest_rand(&a,512,0,0);
      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(&b,450+i,0,0);
            a.neg=rand_neg();
            b.neg=rand_neg();
            BN_add(&c,&a,&b);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," + ");
                        BN_print(bp,&b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&c);
                  BIO_puts(bp,"\n");
                  }
            a.neg=!a.neg;
            b.neg=!b.neg;
            BN_add(&c,&c,&b);
            BN_add(&c,&c,&a);
            if(!BN_is_zero(&c))
                {
                fprintf(stderr,"Add test failed!\n");
                return 0;
                }
            }
      BN_free(&a);
      BN_free(&b);
      BN_free(&c);
      return(1);
      }

int test_sub(BIO *bp)
      {
      BIGNUM a,b,c;
      int i;

      BN_init(&a);
      BN_init(&b);
      BN_init(&c);

      for (i=0; i<num0+num1; i++)
            {
            if (i < num1)
                  {
                  BN_bntest_rand(&a,512,0,0);
                  BN_copy(&b,&a);
                  if (BN_set_bit(&a,i)==0) return(0);
                  BN_add_word(&b,i);
                  }
            else
                  {
                  BN_bntest_rand(&b,400+i-num1,0,0);
                  a.neg=rand_neg();
                  b.neg=rand_neg();
                  }
            BN_sub(&c,&a,&b);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," - ");
                        BN_print(bp,&b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&c);
                  BIO_puts(bp,"\n");
                  }
            BN_add(&c,&c,&b);
            BN_sub(&c,&c,&a);
            if(!BN_is_zero(&c))
                {
                fprintf(stderr,"Subtract test failed!\n");
                return 0;
                }
            }
      BN_free(&a);
      BN_free(&b);
      BN_free(&c);
      return(1);
      }

int test_div(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM a,b,c,d,e;
      int i;

      BN_init(&a);
      BN_init(&b);
      BN_init(&c);
      BN_init(&d);
      BN_init(&e);

      for (i=0; i<num0+num1; i++)
            {
            if (i < num1)
                  {
                  BN_bntest_rand(&a,400,0,0);
                  BN_copy(&b,&a);
                  BN_lshift(&a,&a,i);
                  BN_add_word(&a,i);
                  }
            else
                  BN_bntest_rand(&b,50+3*(i-num1),0,0);
            a.neg=rand_neg();
            b.neg=rand_neg();
            BN_div(&d,&c,&a,&b,ctx);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," / ");
                        BN_print(bp,&b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&d);
                  BIO_puts(bp,"\n");

                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," % ");
                        BN_print(bp,&b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&c);
                  BIO_puts(bp,"\n");
                  }
            BN_mul(&e,&d,&b,ctx);
            BN_add(&d,&e,&c);
            BN_sub(&d,&d,&a);
            if(!BN_is_zero(&d))
                {
                fprintf(stderr,"Division test failed!\n");
                return 0;
                }
            }
      BN_free(&a);
      BN_free(&b);
      BN_free(&c);
      BN_free(&d);
      BN_free(&e);
      return(1);
      }

static void print_word(BIO *bp,BN_ULONG w)
      {
#ifdef SIXTY_FOUR_BIT
      if (sizeof(w) > sizeof(unsigned long))
            {
            unsigned long     h=(unsigned long)(w>>32),
                        l=(unsigned long)(w);

            if (h)      BIO_printf(bp,"%lX%08lX",h,l);
            else  BIO_printf(bp,"%lX",l);
            return;
            }
#endif
      BIO_printf(bp,"%lX",w);
      }

int test_div_word(BIO *bp)
      {
      BIGNUM   a,b;
      BN_ULONG r,s;
      int i;

      BN_init(&a);
      BN_init(&b);

      for (i=0; i<num0; i++)
            {
            do {
                  BN_bntest_rand(&a,512,-1,0);
                  BN_bntest_rand(&b,BN_BITS2,-1,0);
                  s = b.d[0];
            } while (!s);

            BN_copy(&b, &a);
            r = BN_div_word(&b, s);

            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," / ");
                        print_word(bp,s);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&b);
                  BIO_puts(bp,"\n");

                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," % ");
                        print_word(bp,s);
                        BIO_puts(bp," - ");
                        }
                  print_word(bp,r);
                  BIO_puts(bp,"\n");
                  }
            BN_mul_word(&b,s);
            BN_add_word(&b,r);
            BN_sub(&b,&a,&b);
            if(!BN_is_zero(&b))
                {
                fprintf(stderr,"Division (word) test failed!\n");
                return 0;
                }
            }
      BN_free(&a);
      BN_free(&b);
      return(1);
      }

int test_div_recp(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM a,b,c,d,e;
      BN_RECP_CTX recp;
      int i;

      BN_RECP_CTX_init(&recp);
      BN_init(&a);
      BN_init(&b);
      BN_init(&c);
      BN_init(&d);
      BN_init(&e);

      for (i=0; i<num0+num1; i++)
            {
            if (i < num1)
                  {
                  BN_bntest_rand(&a,400,0,0);
                  BN_copy(&b,&a);
                  BN_lshift(&a,&a,i);
                  BN_add_word(&a,i);
                  }
            else
                  BN_bntest_rand(&b,50+3*(i-num1),0,0);
            a.neg=rand_neg();
            b.neg=rand_neg();
            BN_RECP_CTX_set(&recp,&b,ctx);
            BN_div_recp(&d,&c,&a,&recp,ctx);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," / ");
                        BN_print(bp,&b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&d);
                  BIO_puts(bp,"\n");

                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," % ");
                        BN_print(bp,&b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&c);
                  BIO_puts(bp,"\n");
                  }
            BN_mul(&e,&d,&b,ctx);
            BN_add(&d,&e,&c);
            BN_sub(&d,&d,&a);
            if(!BN_is_zero(&d))
                {
                fprintf(stderr,"Reciprocal division test failed!\n");
                fprintf(stderr,"a=");
                BN_print_fp(stderr,&a);
                fprintf(stderr,"\nb=");
                BN_print_fp(stderr,&b);
                fprintf(stderr,"\n");
                return 0;
                }
            }
      BN_free(&a);
      BN_free(&b);
      BN_free(&c);
      BN_free(&d);
      BN_free(&e);
      BN_RECP_CTX_free(&recp);
      return(1);
      }

int test_mul(BIO *bp)
      {
      BIGNUM a,b,c,d,e;
      int i;
      BN_CTX *ctx;

      ctx = BN_CTX_new();
      if (ctx == NULL) EXIT(1);
      
      BN_init(&a);
      BN_init(&b);
      BN_init(&c);
      BN_init(&d);
      BN_init(&e);

      for (i=0; i<num0+num1; i++)
            {
            if (i <= num1)
                  {
                  BN_bntest_rand(&a,100,0,0);
                  BN_bntest_rand(&b,100,0,0);
                  }
            else
                  BN_bntest_rand(&b,i-num1,0,0);
            a.neg=rand_neg();
            b.neg=rand_neg();
            BN_mul(&c,&a,&b,ctx);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," * ");
                        BN_print(bp,&b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&c);
                  BIO_puts(bp,"\n");
                  }
            BN_div(&d,&e,&c,&a,ctx);
            BN_sub(&d,&d,&b);
            if(!BN_is_zero(&d) || !BN_is_zero(&e))
                {
                fprintf(stderr,"Multiplication test failed!\n");
                return 0;
                }
            }
      BN_free(&a);
      BN_free(&b);
      BN_free(&c);
      BN_free(&d);
      BN_free(&e);
      BN_CTX_free(ctx);
      return(1);
      }

int test_sqr(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM a,c,d,e;
      int i;

      BN_init(&a);
      BN_init(&c);
      BN_init(&d);
      BN_init(&e);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(&a,40+i*10,0,0);
            a.neg=rand_neg();
            BN_sqr(&c,&a,ctx);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," * ");
                        BN_print(bp,&a);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&c);
                  BIO_puts(bp,"\n");
                  }
            BN_div(&d,&e,&c,&a,ctx);
            BN_sub(&d,&d,&a);
            if(!BN_is_zero(&d) || !BN_is_zero(&e))
                {
                fprintf(stderr,"Square test failed!\n");
                return 0;
                }
            }
      BN_free(&a);
      BN_free(&c);
      BN_free(&d);
      BN_free(&e);
      return(1);
      }

int test_mont(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM a,b,c,d,A,B;
      BIGNUM n;
      int i;
      BN_MONT_CTX *mont;

      BN_init(&a);
      BN_init(&b);
      BN_init(&c);
      BN_init(&d);
      BN_init(&A);
      BN_init(&B);
      BN_init(&n);

      mont=BN_MONT_CTX_new();

      BN_bntest_rand(&a,100,0,0); /**/
      BN_bntest_rand(&b,100,0,0); /**/
      for (i=0; i<num2; i++)
            {
            int bits = (200*(i+1))/num2;

            if (bits == 0)
                  continue;
            BN_bntest_rand(&n,bits,0,1);
            BN_MONT_CTX_set(mont,&n,ctx);

            BN_nnmod(&a,&a,&n,ctx);
            BN_nnmod(&b,&b,&n,ctx);

            BN_to_montgomery(&A,&a,mont,ctx);
            BN_to_montgomery(&B,&b,mont,ctx);

            BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/
            BN_from_montgomery(&A,&c,mont,ctx);/**/
            if (bp != NULL)
                  {
                  if (!results)
                        {
#ifdef undef
fprintf(stderr,"%d * %d %% %d\n",
BN_num_bits(&a),
BN_num_bits(&b),
BN_num_bits(mont->N));
#endif
                        BN_print(bp,&a);
                        BIO_puts(bp," * ");
                        BN_print(bp,&b);
                        BIO_puts(bp," % ");
                        BN_print(bp,&(mont->N));
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,&A);
                  BIO_puts(bp,"\n");
                  }
            BN_mod_mul(&d,&a,&b,&n,ctx);
            BN_sub(&d,&d,&A);
            if(!BN_is_zero(&d))
                {
                fprintf(stderr,"Montgomery multiplication test failed!\n");
                return 0;
                }
            }
      BN_MONT_CTX_free(mont);
      BN_free(&a);
      BN_free(&b);
      BN_free(&c);
      BN_free(&d);
      BN_free(&A);
      BN_free(&B);
      BN_free(&n);
      return(1);
      }

int test_mod(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM *a,*b,*c,*d,*e;
      int i;

      a=BN_new();
      b=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();

      BN_bntest_rand(a,1024,0,0); /**/
      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(b,450+i*10,0,0); /**/
            a->neg=rand_neg();
            b->neg=rand_neg();
            BN_mod(c,a,b,ctx);/**/
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," % ");
                        BN_print(bp,b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,c);
                  BIO_puts(bp,"\n");
                  }
            BN_div(d,e,a,b,ctx);
            BN_sub(e,e,c);
            if(!BN_is_zero(e))
                {
                fprintf(stderr,"Modulo test failed!\n");
                return 0;
                }
            }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      return(1);
      }

int test_mod_mul(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM *a,*b,*c,*d,*e;
      int i,j;

      a=BN_new();
      b=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();

      for (j=0; j<3; j++) {
      BN_bntest_rand(c,1024,0,0); /**/
      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a,475+i*10,0,0); /**/
            BN_bntest_rand(b,425+i*11,0,0); /**/
            a->neg=rand_neg();
            b->neg=rand_neg();
            if (!BN_mod_mul(e,a,b,c,ctx))
                  {
                  unsigned long l;

                  while ((l=ERR_get_error()))
                        fprintf(stderr,"ERROR:%s\n",
                              ERR_error_string(l,NULL));
                  EXIT(1);
                  }
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," * ");
                        BN_print(bp,b);
                        BIO_puts(bp," % ");
                        BN_print(bp,c);
                        if ((a->neg ^ b->neg) && !BN_is_zero(e))
                              {
                              /* If  (a*b) % c  is negative,  c  must be added
                               * in order to obtain the normalized remainder
                               * (new with OpenSSL 0.9.7, previous versions of
                               * BN_mod_mul could generate negative results)
                               */
                              BIO_puts(bp," + ");
                              BN_print(bp,c);
                              }
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,e);
                  BIO_puts(bp,"\n");
                  }
            BN_mul(d,a,b,ctx);
            BN_sub(d,d,e);
            BN_div(a,b,d,c,ctx);
            if(!BN_is_zero(b))
                {
                fprintf(stderr,"Modulo multiply test failed!\n");
                ERR_print_errors_fp(stderr);
                return 0;
                }
            }
      }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      return(1);
      }

int test_mod_exp(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM *a,*b,*c,*d,*e;
      int i;

      a=BN_new();
      b=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();

      BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
      for (i=0; i<num2; i++)
            {
            BN_bntest_rand(a,20+i*5,0,0); /**/
            BN_bntest_rand(b,2+i,0,0); /**/

            if (!BN_mod_exp(d,a,b,c,ctx))
                  return(00);

            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," ^ ");
                        BN_print(bp,b);
                        BIO_puts(bp," % ");
                        BN_print(bp,c);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,d);
                  BIO_puts(bp,"\n");
                  }
            BN_exp(e,a,b,ctx);
            BN_sub(e,e,d);
            BN_div(a,b,e,c,ctx);
            if(!BN_is_zero(b))
                {
                fprintf(stderr,"Modulo exponentiation test failed!\n");
                return 0;
                }
            }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      return(1);
      }

int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM *a,*b,*c,*d,*e;
      int i;

      a=BN_new();
      b=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();

      BN_bntest_rand(c,30,0,1); /* must be odd for montgomery */
      for (i=0; i<num2; i++)
            {
            BN_bntest_rand(a,20+i*5,0,0); /**/
            BN_bntest_rand(b,2+i,0,0); /**/

            if (!BN_mod_exp_mont_consttime(d,a,b,c,ctx,NULL))
                  return(00);

            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," ^ ");
                        BN_print(bp,b);
                        BIO_puts(bp," % ");
                        BN_print(bp,c);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,d);
                  BIO_puts(bp,"\n");
                  }
            BN_exp(e,a,b,ctx);
            BN_sub(e,e,d);
            BN_div(a,b,e,c,ctx);
            if(!BN_is_zero(b))
                {
                fprintf(stderr,"Modulo exponentiation test failed!\n");
                return 0;
                }
            }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      return(1);
      }

int test_exp(BIO *bp, BN_CTX *ctx)
      {
      BIGNUM *a,*b,*d,*e,*one;
      int i;

      a=BN_new();
      b=BN_new();
      d=BN_new();
      e=BN_new();
      one=BN_new();
      BN_one(one);

      for (i=0; i<num2; i++)
            {
            BN_bntest_rand(a,20+i*5,0,0); /**/
            BN_bntest_rand(b,2+i,0,0); /**/

            if (!BN_exp(d,a,b,ctx))
                  return(00);

            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," ^ ");
                        BN_print(bp,b);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,d);
                  BIO_puts(bp,"\n");
                  }
            BN_one(e);
            for( ; !BN_is_zero(b) ; BN_sub(b,b,one))
                BN_mul(e,e,a,ctx);
            BN_sub(e,e,d);
            if(!BN_is_zero(e))
                {
                fprintf(stderr,"Exponentiation test failed!\n");
                return 0;
                }
            }
      BN_free(a);
      BN_free(b);
      BN_free(d);
      BN_free(e);
      BN_free(one);
      return(1);
      }

int test_gf2m_add(BIO *bp)
      {
      BIGNUM a,b,c;
      int i, ret = 0;

      BN_init(&a);
      BN_init(&b);
      BN_init(&c);

      for (i=0; i<num0; i++)
            {
            BN_rand(&a,512,0,0);
            BN_copy(&b, BN_value_one());
            a.neg=rand_neg();
            b.neg=rand_neg();
            BN_GF2m_add(&c,&a,&b);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,&a);
                        BIO_puts(bp," ^ ");
                        BN_print(bp,&b);
                        BIO_puts(bp," = ");
                        }
                  BN_print(bp,&c);
                  BIO_puts(bp,"\n");
                  }
#endif
            /* Test that two added values have the correct parity. */
            if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
                  {
                fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
                  goto err;
                  }
            BN_GF2m_add(&c,&c,&c);
            /* Test that c + c = 0. */
            if(!BN_is_zero(&c))
                {
                fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
                  goto err;
                }
            }
      ret = 1;
  err:
      BN_free(&a);
      BN_free(&b);
      BN_free(&c);
      return ret;
      }

int test_gf2m_mod(BIO *bp)
      {
      BIGNUM *a,*b[2],*c,*d,*e;
      int i, j, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 1024, 0, 0);
            for (j=0; j < 2; j++)
                  {
                  BN_GF2m_mod(c, a, b[j]);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                  if (bp != NULL)
                        {
                        if (!results)
                              {
                              BN_print(bp,a);
                              BIO_puts(bp," % ");
                              BN_print(bp,b[j]);
                              BIO_puts(bp," - ");
                              BN_print(bp,c);
                              BIO_puts(bp,"\n");
                              }
                        }
#endif
                  BN_GF2m_add(d, a, c);
                  BN_GF2m_mod(e, d, b[j]);
                  /* Test that a + (a mod p) mod p == 0. */
                  if(!BN_is_zero(e))
                        {
                        fprintf(stderr,"GF(2^m) modulo test failed!\n");
                        goto err;
                        }
                  }
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      return ret;
      }

int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
      int i, j, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();
      f=BN_new();
      g=BN_new();
      h=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 1024, 0, 0);
            BN_bntest_rand(c, 1024, 0, 0);
            BN_bntest_rand(d, 1024, 0, 0);
            for (j=0; j < 2; j++)
                  {
                  BN_GF2m_mod_mul(e, a, c, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                  if (bp != NULL)
                        {
                        if (!results)
                              {
                              BN_print(bp,a);
                              BIO_puts(bp," * ");
                              BN_print(bp,c);
                              BIO_puts(bp," % ");
                              BN_print(bp,b[j]);
                              BIO_puts(bp," - ");
                              BN_print(bp,e);
                              BIO_puts(bp,"\n");
                              }
                        }
#endif
                  BN_GF2m_add(f, a, d);
                  BN_GF2m_mod_mul(g, f, c, b[j], ctx);
                  BN_GF2m_mod_mul(h, d, c, b[j], ctx);
                  BN_GF2m_add(f, e, g);
                  BN_GF2m_add(f, f, h);
                  /* Test that (a+d)*c = a*c + d*c. */
                  if(!BN_is_zero(f))
                        {
                        fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
                        goto err;
                        }
                  }
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      BN_free(f);
      BN_free(g);
      BN_free(h);
      return ret;
      }

int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b[2],*c,*d;
      int i, j, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 1024, 0, 0);
            for (j=0; j < 2; j++)
                  {
                  BN_GF2m_mod_sqr(c, a, b[j], ctx);
                  BN_copy(d, a);
                  BN_GF2m_mod_mul(d, a, d, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                  if (bp != NULL)
                        {
                        if (!results)
                              {
                              BN_print(bp,a);
                              BIO_puts(bp," ^ 2 % ");
                              BN_print(bp,b[j]);
                              BIO_puts(bp, " = ");
                              BN_print(bp,c);
                              BIO_puts(bp,"; a * a = ");
                              BN_print(bp,d);
                              BIO_puts(bp,"\n");
                              }
                        }
#endif
                  BN_GF2m_add(d, c, d);
                  /* Test that a*a = a^2. */
                  if(!BN_is_zero(d))
                        {
                        fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
                        goto err;
                        }
                  }
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      return ret;
      }

int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b[2],*c,*d;
      int i, j, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 512, 0, 0); 
            for (j=0; j < 2; j++)
                  {
                  BN_GF2m_mod_inv(c, a, b[j], ctx);
                  BN_GF2m_mod_mul(d, a, c, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                  if (bp != NULL)
                        {
                        if (!results)
                              {
                              BN_print(bp,a);
                              BIO_puts(bp, " * ");
                              BN_print(bp,c);
                              BIO_puts(bp," - 1 % ");
                              BN_print(bp,b[j]);
                              BIO_puts(bp,"\n");
                              }
                        }
#endif
                  /* Test that ((1/a)*a) = 1. */
                  if(!BN_is_one(d))
                        {
                        fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
                        goto err;
                        }
                  }
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      return ret;
      }

int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b[2],*c,*d,*e,*f;
      int i, j, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();
      f=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 512, 0, 0); 
            BN_bntest_rand(c, 512, 0, 0);
            for (j=0; j < 2; j++)
                  {
                  BN_GF2m_mod_div(d, a, c, b[j], ctx);
                  BN_GF2m_mod_mul(e, d, c, b[j], ctx);
                  BN_GF2m_mod_div(f, a, e, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                  if (bp != NULL)
                        {
                        if (!results)
                              {
                              BN_print(bp,a);
                              BIO_puts(bp, " = ");
                              BN_print(bp,c);
                              BIO_puts(bp," * ");
                              BN_print(bp,d);
                              BIO_puts(bp, " % ");
                              BN_print(bp,b[j]);
                              BIO_puts(bp,"\n");
                              }
                        }
#endif
                  /* Test that ((a/c)*c)/a = 1. */
                  if(!BN_is_one(f))
                        {
                        fprintf(stderr,"GF(2^m) modular division test failed!\n");
                        goto err;
                        }
                  }
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      BN_free(f);
      return ret;
      }

int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b[2],*c,*d,*e,*f;
      int i, j, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();
      f=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 512, 0, 0);
            BN_bntest_rand(c, 512, 0, 0);
            BN_bntest_rand(d, 512, 0, 0);
            for (j=0; j < 2; j++)
                  {
                  BN_GF2m_mod_exp(e, a, c, b[j], ctx);
                  BN_GF2m_mod_exp(f, a, d, b[j], ctx);
                  BN_GF2m_mod_mul(e, e, f, b[j], ctx);
                  BN_add(f, c, d);
                  BN_GF2m_mod_exp(f, a, f, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                  if (bp != NULL)
                        {
                        if (!results)
                              {
                              BN_print(bp,a);
                              BIO_puts(bp, " ^ (");
                              BN_print(bp,c);
                              BIO_puts(bp," + ");
                              BN_print(bp,d);
                              BIO_puts(bp, ") = ");
                              BN_print(bp,e);
                              BIO_puts(bp, "; - ");
                              BN_print(bp,f);
                              BIO_puts(bp, " % ");
                              BN_print(bp,b[j]);
                              BIO_puts(bp,"\n");
                              }
                        }
#endif
                  BN_GF2m_add(f, e, f);
                  /* Test that a^(c+d)=a^c*a^d. */
                  if(!BN_is_zero(f))
                        {
                        fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
                        goto err;
                        }
                  }
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      BN_free(f);
      return ret;
      }

int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b[2],*c,*d,*e,*f;
      int i, j, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();
      f=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 512, 0, 0);
            for (j=0; j < 2; j++)
                  {
                  BN_GF2m_mod(c, a, b[j]);
                  BN_GF2m_mod_sqrt(d, a, b[j], ctx);
                  BN_GF2m_mod_sqr(e, d, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                  if (bp != NULL)
                        {
                        if (!results)
                              {
                              BN_print(bp,d);
                              BIO_puts(bp, " ^ 2 - ");
                              BN_print(bp,a);
                              BIO_puts(bp,"\n");
                              }
                        }
#endif
                  BN_GF2m_add(f, c, e);
                  /* Test that d^2 = a, where d = sqrt(a). */
                  if(!BN_is_zero(f))
                        {
                        fprintf(stderr,"GF(2^m) modular square root test failed!\n");
                        goto err;
                        }
                  }
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      BN_free(f);
      return ret;
      }

int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b[2],*c,*d,*e;
      int i, j, s = 0, t, ret = 0;
      unsigned int p0[] = {163,7,6,3,0};
      unsigned int p1[] = {193,15,0};

      a=BN_new();
      b[0]=BN_new();
      b[1]=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();

      BN_GF2m_arr2poly(p0, b[0]);
      BN_GF2m_arr2poly(p1, b[1]);

      for (i=0; i<num0; i++)
            {
            BN_bntest_rand(a, 512, 0, 0);
            for (j=0; j < 2; j++)
                  {
                  t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
                  if (t)
                        {
                        s++;
                        BN_GF2m_mod_sqr(d, c, b[j], ctx);
                        BN_GF2m_add(d, c, d);
                        BN_GF2m_mod(e, a, b[j]);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                        if (bp != NULL)
                              {
                              if (!results)
                                    {
                                    BN_print(bp,c);
                                    BIO_puts(bp, " is root of z^2 + z = ");
                                    BN_print(bp,a);
                                    BIO_puts(bp, " % ");
                                    BN_print(bp,b[j]);
                                    BIO_puts(bp, "\n");
                                    }
                              }
#endif
                        BN_GF2m_add(e, e, d);
                        /* Test that solution of quadratic c satisfies c^2 + c = a. */
                        if(!BN_is_zero(e))
                              {
                              fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
                              goto err;
                              }

                        }
                  else 
                        {
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
                        if (bp != NULL)
                              {
                              if (!results)
                                    {
                                    BIO_puts(bp, "There are no roots of z^2 + z = ");
                                    BN_print(bp,a);
                                    BIO_puts(bp, " % ");
                                    BN_print(bp,b[j]);
                                    BIO_puts(bp, "\n");
                                    }
                              }
#endif
                        }
                  }
            }
      if (s == 0)
            {     
            fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
            fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
            goto err;
            }
      ret = 1;
  err:
      BN_free(a);
      BN_free(b[0]);
      BN_free(b[1]);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      return ret;
      }

static int genprime_cb(int p, int n, BN_GENCB *arg)
      {
      char c='*';

      if (p == 0) c='.';
      if (p == 1) c='+';
      if (p == 2) c='*';
      if (p == 3) c='\n';
      putc(c, stderr);
      fflush(stderr);
      return 1;
      }

int test_kron(BIO *bp, BN_CTX *ctx)
      {
      BN_GENCB cb;
      BIGNUM *a,*b,*r,*t;
      int i;
      int legendre, kronecker;
      int ret = 0;

      a = BN_new();
      b = BN_new();
      r = BN_new();
      t = BN_new();
      if (a == NULL || b == NULL || r == NULL || t == NULL) goto err;

      BN_GENCB_set(&cb, genprime_cb, NULL);
      
      /* We test BN_kronecker(a, b, ctx) just for  b  odd (Jacobi symbol).
       * In this case we know that if  b  is prime, then BN_kronecker(a, b, ctx)
       * is congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol).
       * So we generate a random prime  b  and compare these values
       * for a number of random  a's.  (That is, we run the Solovay-Strassen
       * primality test to confirm that  b  is prime, except that we
       * don't want to test whether  b  is prime but whether BN_kronecker
       * works.) */

      if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb)) goto err;
      b->neg = rand_neg();
      putc('\n', stderr);

      for (i = 0; i < num0; i++)
            {
            if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
            a->neg = rand_neg();

            /* t := (|b|-1)/2  (note that b is odd) */
            if (!BN_copy(t, b)) goto err;
            t->neg = 0;
            if (!BN_sub_word(t, 1)) goto err;
            if (!BN_rshift1(t, t)) goto err;
            /* r := a^t mod b */
            b->neg=0;
            
            if (!BN_mod_exp_recp(r, a, t, b, ctx)) goto err;
            b->neg=1;

            if (BN_is_word(r, 1))
                  legendre = 1;
            else if (BN_is_zero(r))
                  legendre = 0;
            else
                  {
                  if (!BN_add_word(r, 1)) goto err;
                  if (0 != BN_ucmp(r, b))
                        {
                        fprintf(stderr, "Legendre symbol computation failed\n");
                        goto err;
                        }
                  legendre = -1;
                  }
            
            kronecker = BN_kronecker(a, b, ctx);
            if (kronecker < -1) goto err;
            /* we actually need BN_kronecker(a, |b|) */
            if (a->neg && b->neg)
                  kronecker = -kronecker;
            
            if (legendre != kronecker)
                  {
                  fprintf(stderr, "legendre != kronecker; a = ");
                  BN_print_fp(stderr, a);
                  fprintf(stderr, ", b = ");
                  BN_print_fp(stderr, b);
                  fprintf(stderr, "\n");
                  goto err;
                  }

            putc('.', stderr);
            fflush(stderr);
            }

      putc('\n', stderr);
      fflush(stderr);
      ret = 1;
 err:
      if (a != NULL) BN_free(a);
      if (b != NULL) BN_free(b);
      if (r != NULL) BN_free(r);
      if (t != NULL) BN_free(t);
      return ret;
      }

int test_sqrt(BIO *bp, BN_CTX *ctx)
      {
      BN_GENCB cb;
      BIGNUM *a,*p,*r;
      int i, j;
      int ret = 0;

      a = BN_new();
      p = BN_new();
      r = BN_new();
      if (a == NULL || p == NULL || r == NULL) goto err;

      BN_GENCB_set(&cb, genprime_cb, NULL);

      for (i = 0; i < 16; i++)
            {
            if (i < 8)
                  {
                  unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 };
                  
                  if (!BN_set_word(p, primes[i])) goto err;
                  }
            else
                  {
                  if (!BN_set_word(a, 32)) goto err;
                  if (!BN_set_word(r, 2*i + 1)) goto err;
            
                  if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err;
                  putc('\n', stderr);
                  }
            p->neg = rand_neg();

            for (j = 0; j < num2; j++)
                  {
                  /* construct 'a' such that it is a square modulo p,
                   * but in general not a proper square and not reduced modulo p */
                  if (!BN_bntest_rand(r, 256, 0, 3)) goto err;
                  if (!BN_nnmod(r, r, p, ctx)) goto err;
                  if (!BN_mod_sqr(r, r, p, ctx)) goto err;
                  if (!BN_bntest_rand(a, 256, 0, 3)) goto err;
                  if (!BN_nnmod(a, a, p, ctx)) goto err;
                  if (!BN_mod_sqr(a, a, p, ctx)) goto err;
                  if (!BN_mul(a, a, r, ctx)) goto err;
                  if (rand_neg())
                        if (!BN_sub(a, a, p)) goto err;

                  if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
                  if (!BN_mod_sqr(r, r, p, ctx)) goto err;

                  if (!BN_nnmod(a, a, p, ctx)) goto err;

                  if (BN_cmp(a, r) != 0)
                        {
                        fprintf(stderr, "BN_mod_sqrt failed: a = ");
                        BN_print_fp(stderr, a);
                        fprintf(stderr, ", r = ");
                        BN_print_fp(stderr, r);
                        fprintf(stderr, ", p = ");
                        BN_print_fp(stderr, p);
                        fprintf(stderr, "\n");
                        goto err;
                        }

                  putc('.', stderr);
                  fflush(stderr);
                  }
            
            putc('\n', stderr);
            fflush(stderr);
            }
      ret = 1;
 err:
      if (a != NULL) BN_free(a);
      if (p != NULL) BN_free(p);
      if (r != NULL) BN_free(r);
      return ret;
      }

int test_lshift(BIO *bp,BN_CTX *ctx,BIGNUM *a_)
      {
      BIGNUM *a,*b,*c,*d;
      int i;

      b=BN_new();
      c=BN_new();
      d=BN_new();
      BN_one(c);

      if(a_)
          a=a_;
      else
          {
          a=BN_new();
          BN_bntest_rand(a,200,0,0); /**/
          a->neg=rand_neg();
          }
      for (i=0; i<num0; i++)
            {
            BN_lshift(b,a,i+1);
            BN_add(c,c,c);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," * ");
                        BN_print(bp,c);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,b);
                  BIO_puts(bp,"\n");
                  }
            BN_mul(d,a,c,ctx);
            BN_sub(d,d,b);
            if(!BN_is_zero(d))
                {
                fprintf(stderr,"Left shift test failed!\n");
                fprintf(stderr,"a=");
                BN_print_fp(stderr,a);
                fprintf(stderr,"\nb=");
                BN_print_fp(stderr,b);
                fprintf(stderr,"\nc=");
                BN_print_fp(stderr,c);
                fprintf(stderr,"\nd=");
                BN_print_fp(stderr,d);
                fprintf(stderr,"\n");
                return 0;
                }
            }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      BN_free(d);
      return(1);
      }

int test_lshift1(BIO *bp)
      {
      BIGNUM *a,*b,*c;
      int i;

      a=BN_new();
      b=BN_new();
      c=BN_new();

      BN_bntest_rand(a,200,0,0); /**/
      a->neg=rand_neg();
      for (i=0; i<num0; i++)
            {
            BN_lshift1(b,a);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," * 2");
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,b);
                  BIO_puts(bp,"\n");
                  }
            BN_add(c,a,a);
            BN_sub(a,b,c);
            if(!BN_is_zero(a))
                {
                fprintf(stderr,"Left shift one test failed!\n");
                return 0;
                }
            
            BN_copy(a,b);
            }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      return(1);
      }

int test_rshift(BIO *bp,BN_CTX *ctx)
      {
      BIGNUM *a,*b,*c,*d,*e;
      int i;

      a=BN_new();
      b=BN_new();
      c=BN_new();
      d=BN_new();
      e=BN_new();
      BN_one(c);

      BN_bntest_rand(a,200,0,0); /**/
      a->neg=rand_neg();
      for (i=0; i<num0; i++)
            {
            BN_rshift(b,a,i+1);
            BN_add(c,c,c);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," / ");
                        BN_print(bp,c);
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,b);
                  BIO_puts(bp,"\n");
                  }
            BN_div(d,e,a,c,ctx);
            BN_sub(d,d,b);
            if(!BN_is_zero(d))
                {
                fprintf(stderr,"Right shift test failed!\n");
                return 0;
                }
            }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      BN_free(d);
      BN_free(e);
      return(1);
      }

int test_rshift1(BIO *bp)
      {
      BIGNUM *a,*b,*c;
      int i;

      a=BN_new();
      b=BN_new();
      c=BN_new();

      BN_bntest_rand(a,200,0,0); /**/
      a->neg=rand_neg();
      for (i=0; i<num0; i++)
            {
            BN_rshift1(b,a);
            if (bp != NULL)
                  {
                  if (!results)
                        {
                        BN_print(bp,a);
                        BIO_puts(bp," / 2");
                        BIO_puts(bp," - ");
                        }
                  BN_print(bp,b);
                  BIO_puts(bp,"\n");
                  }
            BN_sub(c,a,b);
            BN_sub(c,c,b);
            if(!BN_is_zero(c) && !BN_abs_is_word(c, 1))
                {
                fprintf(stderr,"Right shift one test failed!\n");
                return 0;
                }
            BN_copy(a,b);
            }
      BN_free(a);
      BN_free(b);
      BN_free(c);
      return(1);
      }

int rand_neg(void)
      {
      static unsigned int neg=0;
      static int sign[8]={0,0,0,1,1,0,1,1};

      return(sign[(neg++)%8]);
      }

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