bn_exp.c 17.3 KB
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/* crypto/bn/bn_exp.c */
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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 * 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.]
 */
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/* ====================================================================
 * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.
 *
 * 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 above 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 acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED 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 OpenSSL PROJECT OR
 * ITS 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.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

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#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
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#define TABLE_SIZE	32
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/* slow but works */
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int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
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	{
	BIGNUM *t;
	int r=0;

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	bn_check_top(a);
	bn_check_top(b);
	bn_check_top(m);

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	BN_CTX_start(ctx);
	if ((t = BN_CTX_get(ctx)) == NULL) goto err;
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	if (a == b)
		{ if (!BN_sqr(t,a,ctx)) goto err; }
	else
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		{ if (!BN_mul(t,a,b,ctx)) goto err; }
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	if (!BN_mod(ret,t,m,ctx)) goto err;
	r=1;
err:
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	BN_CTX_end(ctx);
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	return(r);
	}


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/* this one works - simple but works */
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int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx)
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	{
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	int i,bits,ret=0;
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	BIGNUM *v,*rr;
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	BN_CTX_start(ctx);
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	if ((r == a) || (r == p))
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		rr = BN_CTX_get(ctx);
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	else
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		rr = r;
	if ((v = BN_CTX_get(ctx)) == NULL) goto err;
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	if (BN_copy(v,a) == NULL) goto err;
	bits=BN_num_bits(p);

	if (BN_is_odd(p))
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		{ if (BN_copy(rr,a) == NULL) goto err; }
	else	{ if (!BN_one(rr)) goto err; }
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	for (i=1; i<bits; i++)
		{
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		if (!BN_sqr(v,v,ctx)) goto err;
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		if (BN_is_bit_set(p,i))
			{
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			if (!BN_mul(rr,rr,v,ctx)) goto err;
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			}
		}
	ret=1;
err:
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	if (r != rr) BN_copy(r,rr);
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	BN_CTX_end(ctx);
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	return(ret);
	}

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int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
	       BN_CTX *ctx)
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	{
	int ret;

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	bn_check_top(a);
	bn_check_top(p);
	bn_check_top(m);

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#ifdef MONT_MUL_MOD
	/* I have finally been able to take out this pre-condition of
	 * the top bit being set.  It was caused by an error in BN_div
	 * with negatives.  There was also another problem when for a^b%m
	 * a >= m.  eay 07-May-97 */
/*	if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */

	if (BN_is_odd(m))
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		{
		if (a->top == 1)
			{
			BN_ULONG A = a->d[0];
			ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
			}
		else
			ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
		}
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	else
#endif
#ifdef RECP_MUL_MOD
		{ ret=BN_mod_exp_recp(r,a,p,m,ctx); }
#else
		{ ret=BN_mod_exp_simple(r,a,p,m,ctx); }
#endif

	return(ret);
	}

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int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
		    const BIGNUM *m, BN_CTX *ctx)
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	{
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	int i,j,bits,ret=0,wstart,wend,window,wvalue;
	int start=1,ts=0;
	BIGNUM *aa;
	BIGNUM val[TABLE_SIZE];
	BN_RECP_CTX recp;
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	bits=BN_num_bits(p);

	if (bits == 0)
		{
		BN_one(r);
		return(1);
		}
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	BN_CTX_start(ctx);
	if ((aa = BN_CTX_get(ctx)) == NULL) goto err;

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	BN_RECP_CTX_init(&recp);
	if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;

	BN_init(&(val[0]));
	ts=1;
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	if (!BN_mod(&(val[0]),a,m,ctx)) goto err;		/* 1 */
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	window = BN_window_bits_for_exponent_size(bits);
	if (window > 1)
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		{
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		if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
			goto err;				/* 2 */
		j=1<<(window-1);
		for (i=1; i<j; i++)
			{
			BN_init(&val[i]);
			if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
				goto err;
			}
		ts=i;
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		}
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	start=1;	/* This is used to avoid multiplication etc
			 * when there is only the value '1' in the
			 * buffer. */
	wvalue=0;	/* The 'value' of the window */
	wstart=bits-1;	/* The top bit of the window */
	wend=0;		/* The bottom bit of the window */

	if (!BN_one(r)) goto err;

	for (;;)
		{
		if (BN_is_bit_set(p,wstart) == 0)
			{
			if (!start)
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				if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
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				goto err;
			if (wstart == 0) break;
			wstart--;
			continue;
			}
		/* We now have wstart on a 'set' bit, we now need to work out
		 * how bit a window to do.  To do this we need to scan
		 * forward until the last set bit before the end of the
		 * window */
		j=wstart;
		wvalue=1;
		wend=0;
		for (i=1; i<window; i++)
			{
			if (wstart-i < 0) break;
			if (BN_is_bit_set(p,wstart-i))
				{
				wvalue<<=(i-wend);
				wvalue|=1;
				wend=i;
				}
			}

		/* wend is the size of the current window */
		j=wend+1;
		/* add the 'bytes above' */
		if (!start)
			for (i=0; i<j; i++)
				{
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				if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
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					goto err;
				}
		
		/* wvalue will be an odd number < 2^window */
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		if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
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			goto err;

		/* move the 'window' down further */
		wstart-=wend+1;
		wvalue=0;
		start=0;
		if (wstart < 0) break;
		}
	ret=1;
err:
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	BN_CTX_end(ctx);
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	for (i=0; i<ts; i++)
		BN_clear_free(&(val[i]));
	BN_RECP_CTX_free(&recp);
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	return(ret);
	}

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int BN_mod_exp_mont(BIGNUM *rr, BIGNUM *a, const BIGNUM *p,
		    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
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	{
	int i,j,bits,ret=0,wstart,wend,window,wvalue;
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	int start=1,ts=0;
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	BIGNUM *d,*r;
	BIGNUM *aa;
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	BIGNUM val[TABLE_SIZE];
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	BN_MONT_CTX *mont=NULL;

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	bn_check_top(a);
	bn_check_top(p);
	bn_check_top(m);

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	if (!(m->d[0] & 1))
		{
		BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
		return(0);
		}
	bits=BN_num_bits(p);
	if (bits == 0)
		{
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		BN_one(rr);
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		return(1);
		}
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	BN_CTX_start(ctx);
	d = BN_CTX_get(ctx);
	r = BN_CTX_get(ctx);
	if (d == NULL || r == NULL) goto err;
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	/* If this is not done, things will break in the montgomery
	 * part */

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	if (in_mont != NULL)
		mont=in_mont;
	else
		{
		if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
		if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
		}
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	BN_init(&val[0]);
	ts=1;
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	if (BN_ucmp(a,m) >= 0)
		{
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		if (!BN_mod(&(val[0]),a,m,ctx))
			goto err;
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		aa= &(val[0]);
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		}
	else
		aa=a;
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	if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
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	window = BN_window_bits_for_exponent_size(bits);
	if (window > 1)
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		{
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		if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
		j=1<<(window-1);
		for (i=1; i<j; i++)
			{
			BN_init(&(val[i]));
			if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
				goto err;
			}
		ts=i;
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		}

	start=1;	/* This is used to avoid multiplication etc
			 * when there is only the value '1' in the
			 * buffer. */
	wvalue=0;	/* The 'value' of the window */
	wstart=bits-1;	/* The top bit of the window */
	wend=0;		/* The bottom bit of the window */

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	if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
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	for (;;)
		{
		if (BN_is_bit_set(p,wstart) == 0)
			{
			if (!start)
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				{
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				if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
				goto err;
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				}
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			if (wstart == 0) break;
			wstart--;
			continue;
			}
		/* We now have wstart on a 'set' bit, we now need to work out
		 * how bit a window to do.  To do this we need to scan
		 * forward until the last set bit before the end of the
		 * window */
		j=wstart;
		wvalue=1;
		wend=0;
		for (i=1; i<window; i++)
			{
			if (wstart-i < 0) break;
			if (BN_is_bit_set(p,wstart-i))
				{
				wvalue<<=(i-wend);
				wvalue|=1;
				wend=i;
				}
			}

		/* wend is the size of the current window */
		j=wend+1;
		/* add the 'bytes above' */
		if (!start)
			for (i=0; i<j; i++)
				{
				if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
					goto err;
				}
		
		/* wvalue will be an odd number < 2^window */
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		if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx))
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			goto err;

		/* move the 'window' down further */
		wstart-=wend+1;
		wvalue=0;
		start=0;
		if (wstart < 0) break;
		}
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	if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
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	ret=1;
err:
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	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
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	BN_CTX_end(ctx);
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	for (i=0; i<ts; i++)
		BN_clear_free(&(val[i]));
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	return(ret);
	}
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int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
                         const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
	{
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	BN_MONT_CTX *mont = NULL;
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	int b, bits, ret=0;
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	int r_is_one;
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	BN_ULONG w, next_w;
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	BIGNUM *d, *r, *t;
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	BIGNUM *swap_tmp;
#define BN_MOD_MUL_WORD(r, w, m) \
		(BN_mul_word(r, (w)) && \
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		(/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \
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			(BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
		/* BN_MOD_MUL_WORD is only used with 'w' large,
		  * so the BN_ucmp test is probably more overhead
		  * than always using BN_mod (which uses BN_copy if
		  * a similar test returns true). */
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
		(BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
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	bn_check_top(p);
	bn_check_top(m);

	if (!(m->d[0] & 1))
		{
		BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
		return(0);
		}
	bits = BN_num_bits(p);
	if (bits == 0)
		{
		BN_one(rr);
		return(1);
		}
	BN_CTX_start(ctx);
	d = BN_CTX_get(ctx);
	r = BN_CTX_get(ctx);
	t = BN_CTX_get(ctx);
	if (d == NULL || r == NULL || t == NULL) goto err;

	if (in_mont != NULL)
		mont=in_mont;
	else
		{
		if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
		if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
		}

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	r_is_one = 1; /* except for Montgomery factor */
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	/* bits-1 >= 0 */

	/* The result is accumulated in the product r*w. */
	w = a; /* bit 'bits-1' of 'p' is always set */
	for (b = bits-2; b >= 0; b--)
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		{
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		/* First, square r*w. */
		next_w = w*w;
		if ((next_w/w) != w) /* overflow */
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			{
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			if (r_is_one)
				{
				if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
				r_is_one = 0;
				}
			else
				{
				if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
				}
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			next_w = 1;
			}
		w = next_w;
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		if (!r_is_one)
			{
			if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
			}
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		/* Second, multiply r*w by 'a' if exponent bit is set. */
		if (BN_is_bit_set(p, b))
			{
			next_w = w*a;
			if ((next_w/a) != w) /* overflow */
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				{
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				if (r_is_one)
					{
					if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
					r_is_one = 0;
					}
				else
					{
					if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
					}
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				next_w = a;
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				}
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			w = next_w;
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			}
		}
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	/* Finally, set r:=r*w. */
	if (w != 1)
		{
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		if (r_is_one)
			{
			if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
			r_is_one = 0;
			}
		else
			{
			if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
			}
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		}

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	if (r_is_one) /* can happen only if a == 1*/
		{
		if (!BN_one(rr)) goto err;
		}
	else
		{
		if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
		}
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	ret = 1;
err:
	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
	BN_CTX_end(ctx);
	return(ret);
	}

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/* The old fallback, simple version :-) */
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int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m,
	     BN_CTX *ctx)
595
	{
596
	int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
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	int start=1;
	BIGNUM *d;
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	BIGNUM val[TABLE_SIZE];
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	bits=BN_num_bits(p);

	if (bits == 0)
		{
		BN_one(r);
		return(1);
		}

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	BN_CTX_start(ctx);
	if ((d = BN_CTX_get(ctx)) == NULL) goto err;

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	BN_init(&(val[0]));
	ts=1;
	if (!BN_mod(&(val[0]),a,m,ctx)) goto err;		/* 1 */
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	window = BN_window_bits_for_exponent_size(bits);
	if (window > 1)
618
		{
619 620 621 622 623 624 625 626 627 628
		if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
			goto err;				/* 2 */
		j=1<<(window-1);
		for (i=1; i<j; i++)
			{
			BN_init(&(val[i]));
			if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
				goto err;
			}
		ts=i;
629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679
		}

	start=1;	/* This is used to avoid multiplication etc
			 * when there is only the value '1' in the
			 * buffer. */
	wvalue=0;	/* The 'value' of the window */
	wstart=bits-1;	/* The top bit of the window */
	wend=0;		/* The bottom bit of the window */

	if (!BN_one(r)) goto err;

	for (;;)
		{
		if (BN_is_bit_set(p,wstart) == 0)
			{
			if (!start)
				if (!BN_mod_mul(r,r,r,m,ctx))
				goto err;
			if (wstart == 0) break;
			wstart--;
			continue;
			}
		/* We now have wstart on a 'set' bit, we now need to work out
		 * how bit a window to do.  To do this we need to scan
		 * forward until the last set bit before the end of the
		 * window */
		j=wstart;
		wvalue=1;
		wend=0;
		for (i=1; i<window; i++)
			{
			if (wstart-i < 0) break;
			if (BN_is_bit_set(p,wstart-i))
				{
				wvalue<<=(i-wend);
				wvalue|=1;
				wend=i;
				}
			}

		/* wend is the size of the current window */
		j=wend+1;
		/* add the 'bytes above' */
		if (!start)
			for (i=0; i<j; i++)
				{
				if (!BN_mod_mul(r,r,r,m,ctx))
					goto err;
				}
		
		/* wvalue will be an odd number < 2^window */
680
		if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
681 682 683 684 685 686 687 688 689 690
			goto err;

		/* move the 'window' down further */
		wstart-=wend+1;
		wvalue=0;
		start=0;
		if (wstart < 0) break;
		}
	ret=1;
err:
691
	BN_CTX_end(ctx);
692 693
	for (i=0; i<ts; i++)
		BN_clear_free(&(val[i]));
694 695 696
	return(ret);
	}