bn_exp2.c

/* crypto/bn/bn_exp2.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 (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).
 *
 */

#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"

#define TABLE_SIZE	32

int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
	const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
	BN_CTX *ctx, BN_MONT_CTX *in_mont)
	{
	int i,j,bits,b,bits1,bits2,ret=0,wpos1,wpos2,window1,window2,wvalue1,wvalue2;
	int r_is_one=1,ts1=0,ts2=0;
	BIGNUM *d,*r;
	const BIGNUM *a_mod_m;
	BIGNUM val1[TABLE_SIZE], val2[TABLE_SIZE];
	BN_MONT_CTX *mont=NULL;

	bn_check_top(a1);
	bn_check_top(p1);
	bn_check_top(a2);
	bn_check_top(p2);
	bn_check_top(m);

	if (!(m->d[0] & 1))
		{
		BNerr(BN_F_BN_MOD_EXP2_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
		return(0);
		}
	bits1=BN_num_bits(p1);
	bits2=BN_num_bits(p2);
	if ((bits1 == 0) && (bits2 == 0))
		{
		BN_one(rr);
		return(1);
		}
	bits=(bits1 > bits2)?bits1:bits2;

	BN_CTX_start(ctx);
	d = BN_CTX_get(ctx);
	r = BN_CTX_get(ctx);
	if (d == NULL || r == 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;
		}

	window1 = BN_window_bits_for_exponent_size(bits1);
	window2 = BN_window_bits_for_exponent_size(bits2);

	/*
	 * Build table for a1:   val1[i] := a1^(2*i + 1) mod m  for i = 0 .. 2^(window1-1)
	 */
	BN_init(&val1[0]);
	ts1=1;
	if (BN_ucmp(a1,m) >= 0)
		{
		if (!BN_mod(&(val1[0]),a1,m,ctx))
			goto err;
		a_mod_m = &(val1[0]);
		}
	else
		a_mod_m = a1;
	if (!BN_to_montgomery(&(val1[0]),a_mod_m,mont,ctx)) goto err;
	if (window1 > 1)
		{
		if (!BN_mod_mul_montgomery(d,&(val1[0]),&(val1[0]),mont,ctx)) goto err;

		j=1<<(window1-1);
		for (i=1; i<j; i++)
			{
			BN_init(&(val1[i]));
			if (!BN_mod_mul_montgomery(&(val1[i]),&(val1[i-1]),d,mont,ctx))
				goto err;
			}
		ts1=i;
		}


	/*
	 * Build table for a2:   val2[i] := a2^(2*i + 1) mod m  for i = 0 .. 2^(window2-1)
	 */
	BN_init(&val2[0]);
	ts2=1;
	if (BN_ucmp(a2,m) >= 0)
		{
		if (!BN_mod(&(val2[0]),a2,m,ctx))
			goto err;
		a_mod_m = &(val2[0]);
		}
	else
		a_mod_m = a2;
	if (!BN_to_montgomery(&(val2[0]),a_mod_m,mont,ctx)) goto err;
	if (window2 > 1)
		{
		if (!BN_mod_mul_montgomery(d,&(val2[0]),&(val2[0]),mont,ctx)) goto err;

		j=1<<(window2-1);
		for (i=1; i<j; i++)
			{
			BN_init(&(val2[i]));
			if (!BN_mod_mul_montgomery(&(val2[i]),&(val2[i-1]),d,mont,ctx))
				goto err;
			}
		ts2=i;
		}


	/* Now compute the power product, using independent windows. */
	r_is_one=1;
	wvalue1=0;  /* The 'value' of the first window */
	wvalue2=0;  /* The 'value' of the second window */
	wpos1=0;    /* If wvalue1 > 0, the bottom bit of the first window */
	wpos2=0;    /* If wvalue2 > 0, the bottom bit of the second window */

	if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
	for (b=bits-1; b>=0; b--)
		{
		if (!r_is_one)
			{
			if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
				goto err;
			}
		
		if (!wvalue1)
			if (BN_is_bit_set(p1, b))
				{
				/* consider bits b-window1+1 .. b for this window */
				i = b-window1+1;
				while (!BN_is_bit_set(p1, i)) /* works for i<0 */
					i++;
				wpos1 = i;
				wvalue1 = 1;
				for (i = b-1; i >= wpos1; i--)
					{
					wvalue1 <<= 1;
					if (BN_is_bit_set(p1, i))
						wvalue1++;
					}
				}
		
		if (!wvalue2)
			if (BN_is_bit_set(p2, b))
				{
				/* consider bits b-window2+1 .. b for this window */
				i = b-window2+1;
				while (!BN_is_bit_set(p2, i))
					i++;
				wpos2 = i;
				wvalue2 = 1;
				for (i = b-1; i >= wpos2; i--)
					{
					wvalue2 <<= 1;
					if (BN_is_bit_set(p2, i))
						wvalue2++;
					}
				}

		if (wvalue1 && b == wpos1)
			{
			/* wvalue1 is odd and < 2^window1 */
			if (!BN_mod_mul_montgomery(r,r,&(val1[wvalue1>>1]),mont,ctx))
				goto err;
			wvalue1 = 0;
			r_is_one = 0;
			}
		
		if (wvalue2 && b == wpos2)
			{
			/* wvalue2 is odd and < 2^window2 */
			if (!BN_mod_mul_montgomery(r,r,&(val2[wvalue2>>1]),mont,ctx))
				goto err;
			wvalue2 = 0;
			r_is_one = 0;
			}
		}
	BN_from_montgomery(rr,r,mont,ctx);
	ret=1;
err:
	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
	BN_CTX_end(ctx);
	for (i=0; i<ts1; i++)
		BN_clear_free(&(val1[i]));
	for (i=0; i<ts2; i++)
		BN_clear_free(&(val2[i]));
	return(ret);
	}