/* 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]);

 	}