/* crypto/bn/bn_exp.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) 1998-2005 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 "cryptlib.h"

#include "bn_lcl.h"

/* maximum precomputation table size for *variable* sliding windows */

#define TABLE_SIZE	32

/* this one works - simple but works */

EXPORT_C int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)

	{

	int i,bits,ret=0;

	BIGNUM *v,*rr;

	if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)

		{

		/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */

		BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);

		return -1;

		}

	BN_CTX_start(ctx);

	if ((r == a) || (r == p))

		rr = BN_CTX_get(ctx);

	else

		rr = r;

	if ((v = BN_CTX_get(ctx)) == NULL) goto err;

	if (BN_copy(v,a) == NULL) goto err;

	bits=BN_num_bits(p);

	if (BN_is_odd(p))

		{ if (BN_copy(rr,a) == NULL) goto err; }

	else	{ if (!BN_one(rr)) goto err; }

	for (i=1; i<bits; i++)

		{

		if (!BN_sqr(v,v,ctx)) goto err;

		if (BN_is_bit_set(p,i))

			{

			if (!BN_mul(rr,rr,v,ctx)) goto err;

			}

		}

	ret=1;

err:

	if (r != rr) BN_copy(r,rr);

	BN_CTX_end(ctx);

	bn_check_top(r);

	return(ret);

	}

EXPORT_C int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,

	       BN_CTX *ctx)

	{

	int ret;

	bn_check_top(a);

	bn_check_top(p);

	bn_check_top(m);

	/* For even modulus  m = 2^k*m_odd,  it might make sense to compute

	 * a^p mod m_odd  and  a^p mod 2^k  separately (with Montgomery

	 * exponentiation for the odd part), using appropriate exponent

	 * reductions, and combine the results using the CRT.

	 *

	 * For now, we use Montgomery only if the modulus is odd; otherwise,

	 * exponentiation using the reciprocal-based quick remaindering

	 * algorithm is used.

	 *

	 * (Timing obtained with expspeed.c [computations  a^p mod m

	 * where  a, p, m  are of the same length: 256, 512, 1024, 2048,

	 * 4096, 8192 bits], compared to the running time of the

	 * standard algorithm:

	 *

	 *   BN_mod_exp_mont   33 .. 40 %  [AMD K6-2, Linux, debug configuration]

         *                     55 .. 77 %  [UltraSparc processor, but

	 *                                  debug-solaris-sparcv8-gcc conf.]

	 * 

	 *   BN_mod_exp_recp   50 .. 70 %  [AMD K6-2, Linux, debug configuration]

	 *                     62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]

	 *

	 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont

	 * at 2048 and more bits, but at 512 and 1024 bits, it was

	 * slower even than the standard algorithm!

	 *

	 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]

	 * should be obtained when the new Montgomery reduction code

	 * has been integrated into OpenSSL.)

	 */

#define MONT_MUL_MOD

#define MONT_EXP_WORD

#define RECP_MUL_MOD

#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))

		{

#  ifdef MONT_EXP_WORD

		if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))

			{

			BN_ULONG A = a->d[0];

			ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);

			}

		else

#  endif

			ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);

		}

	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

	bn_check_top(r);

	return(ret);

	}

EXPORT_C int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,

		    const BIGNUM *m, BN_CTX *ctx)

	{

	int i,j,bits,ret=0,wstart,wend,window,wvalue;

	int start=1;

	BIGNUM *aa;

	/* Table of variables obtained from 'ctx' */

	BIGNUM *val[TABLE_SIZE];

	BN_RECP_CTX recp;

	if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)

		{

		/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */

		BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);

		return -1;

		}

	bits=BN_num_bits(p);

	if (bits == 0)

		{

		ret = BN_one(r);

		return ret;

		}

	BN_CTX_start(ctx);

	aa = BN_CTX_get(ctx);

	val[0] = BN_CTX_get(ctx);

	if(!aa || !val[0]) goto err;

	BN_RECP_CTX_init(&recp);

	if (m->neg)

		{

		/* ignore sign of 'm' */

		if (!BN_copy(aa, m)) goto err;

		aa->neg = 0;

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

		}

	else

		{

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

		}

	if (!BN_nnmod(val[0],a,m,ctx)) goto err;		/* 1 */

	if (BN_is_zero(val[0]))

		{

		BN_zero(r);

		ret = 1;

		goto err;

		}

	window = BN_window_bits_for_exponent_size(bits);

	if (window > 1)

		{

		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++)

			{

			if(((val[i] = BN_CTX_get(ctx)) == NULL) ||

					!BN_mod_mul_reciprocal(val[i],val[i-1],

						aa,&recp,ctx))

				goto err;

			}

		}

	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_reciprocal(r,r,r,&recp,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_reciprocal(r,r,r,&recp,ctx))

					goto err;

				}

		/* wvalue will be an odd number < 2^window */

		if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))

			goto err;

		/* move the 'window' down further */

		wstart-=wend+1;

		wvalue=0;

		start=0;

		if (wstart < 0) break;

		}

	ret=1;

err:

	BN_CTX_end(ctx);

	BN_RECP_CTX_free(&recp);

	bn_check_top(r);

	return(ret);

	}

EXPORT_C int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,

		    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)

	{

	int i,j,bits,ret=0,wstart,wend,window,wvalue;

	int start=1;

	BIGNUM *d,*r;

	const BIGNUM *aa;

	/* Table of variables obtained from 'ctx' */

	BIGNUM *val[TABLE_SIZE];

	BN_MONT_CTX *mont=NULL;

	if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)

		{

		return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);

		}

	bn_check_top(a);

	bn_check_top(p);

	bn_check_top(m);

	if (!BN_is_odd(m))

		{

		BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);

		return(0);

		}

	bits=BN_num_bits(p);

	if (bits == 0)

		{

		ret = BN_one(rr);

		return ret;

		}

	BN_CTX_start(ctx);

	d = BN_CTX_get(ctx);

	r = BN_CTX_get(ctx);

	val[0] = BN_CTX_get(ctx);

	if (!d || !r || !val[0]) goto err;

	/* If this is not done, things will break in the montgomery

	 * part */

	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;

		}

	if (a->neg || BN_ucmp(a,m) >= 0)

		{

		if (!BN_nnmod(val[0],a,m,ctx))

			goto err;

		aa= val[0];

		}

	else

		aa=a;

	if (BN_is_zero(aa))

		{

		BN_zero(rr);

		ret = 1;

		goto err;

		}

	if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */

	window = BN_window_bits_for_exponent_size(bits);

	if (window > 1)

		{

		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++)

			{

			if(((val[i] = BN_CTX_get(ctx)) == NULL) ||

					!BN_mod_mul_montgomery(val[i],val[i-1],

						d,mont,ctx))

				goto err;

			}

		}

	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_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;

	for (;;)

		{

		if (BN_is_bit_set(p,wstart) == 0)

			{

			if (!start)

				{

				if (!BN_mod_mul_montgomery(r,r,r,mont,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_montgomery(r,r,r,mont,ctx))

					goto err;

				}

		/* wvalue will be an odd number < 2^window */

		if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))

			goto err;

		/* move the 'window' down further */

		wstart-=wend+1;

		wvalue=0;

		start=0;

		if (wstart < 0) break;

		}

	if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;

	ret=1;

err:

	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);

	BN_CTX_end(ctx);

	bn_check_top(rr);

	return(ret);

	}

/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout

 * so that accessing any of these table values shows the same access pattern as far

 * as cache lines are concerned.  The following functions are used to transfer a BIGNUM

 * from/to that table. */

static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)

	{

	size_t i, j;

	if (bn_wexpand(b, top) == NULL)

		return 0;

	while (b->top < top)

		{

		b->d[b->top++] = 0;

		}

	for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)

		{

		buf[j] = ((unsigned char*)b->d)[i];

		}

	bn_correct_top(b);

	return 1;

	}

static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)

	{

	size_t i, j;

	if (bn_wexpand(b, top) == NULL)

		return 0;

	for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)

		{

		((unsigned char*)b->d)[i] = buf[j];

		}

	b->top = top;

	bn_correct_top(b);

	return 1;

	}	

/* Given a pointer value, compute the next address that is a cache line multiple. */

#define MOD_EXP_CTIME_ALIGN(x_) \

	((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))

/* This variant of BN_mod_exp_mont() uses fixed windows and the special

 * precomputation memory layout to limit data-dependency to a minimum

 * to protect secret exponents (cf. the hyper-threading timing attacks

 * pointed out by Colin Percival,

 * http://www.daemonology.net/hyperthreading-considered-harmful/)

 */

EXPORT_C int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,

		    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)

	{

	int i,bits,ret=0,idx,window,wvalue;

	int top;

 	BIGNUM *r;

	const BIGNUM *aa;

	BN_MONT_CTX *mont=NULL;

	int numPowers;

	unsigned char *powerbufFree=NULL;

	int powerbufLen = 0;

	unsigned char *powerbuf=NULL;

	BIGNUM *computeTemp=NULL, *am=NULL;

	bn_check_top(a);

	bn_check_top(p);

	bn_check_top(m);

	top = m->top;

	if (!(m->d[0] & 1))

		{

		BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);

		return(0);

		}

	bits=BN_num_bits(p);

	if (bits == 0)

		{

		ret = BN_one(rr);

		return ret;

		}

 	/* Initialize BIGNUM context and allocate intermediate result */

	BN_CTX_start(ctx);

	r = BN_CTX_get(ctx);

	if (r == NULL) goto err;

	/* Allocate a montgomery context if it was not supplied by the caller.

	 * If this is not done, things will break in the montgomery part.

 	 */

	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;

		}

	/* Get the window size to use with size of p. */

	window = BN_window_bits_for_ctime_exponent_size(bits);

	/* Allocate a buffer large enough to hold all of the pre-computed

	 * powers of a.

	 */

	numPowers = 1 << window;

	powerbufLen = sizeof(m->d[0])*top*numPowers;

	if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)

		goto err;

	powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);

	memset(powerbuf, 0, powerbufLen);

 	/* Initialize the intermediate result. Do this early to save double conversion,

	 * once each for a^0 and intermediate result.

	 */

 	if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;

	if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;

	/* Initialize computeTemp as a^1 with montgomery precalcs */

	computeTemp = BN_CTX_get(ctx);

	am = BN_CTX_get(ctx);

	if (computeTemp==NULL || am==NULL) goto err;

	if (a->neg || BN_ucmp(a,m) >= 0)

		{

		if (!BN_mod(am,a,m,ctx))

			goto err;

		aa= am;

		}

	else

		aa=a;

	if (!BN_to_montgomery(am,aa,mont,ctx)) goto err;

	if (!BN_copy(computeTemp, am)) goto err;

	if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;

	/* If the window size is greater than 1, then calculate

	 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)

	 * (even powers could instead be computed as (a^(i/2))^2

	 * to use the slight performance advantage of sqr over mul).

	 */

	if (window > 1)

		{

		for (i=2; i<numPowers; i++)

			{

			/* Calculate a^i = a^(i-1) * a */

			if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx))

				goto err;

			if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err;

			}

		}

 	/* Adjust the number of bits up to a multiple of the window size.

 	 * If the exponent length is not a multiple of the window size, then

 	 * this pads the most significant bits with zeros to normalize the

 	 * scanning loop to there's no special cases.

 	 *

 	 * * NOTE: Making the window size a power of two less than the native

	 * * word size ensures that the padded bits won't go past the last

 	 * * word in the internal BIGNUM structure. Going past the end will

 	 * * still produce the correct result, but causes a different branch

 	 * * to be taken in the BN_is_bit_set function.

 	 */

 	bits = ((bits+window-1)/window)*window;

 	idx=bits-1;	/* The top bit of the window */

 	/* Scan the exponent one window at a time starting from the most

 	 * significant bits.

 	 */

 	while (idx >= 0)

  		{

 		wvalue=0; /* The 'value' of the window */

 		/* Scan the window, squaring the result as we go */

 		for (i=0; i<window; i++,idx--)

 			{

			if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))	goto err;

			wvalue = (wvalue<<1)+BN_is_bit_set(p,idx);

  			}

		/* Fetch the appropriate pre-computed value from the pre-buf */

		if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err;

 		/* Multiply the result into the intermediate result */

 		if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err;

  		}

 	/* Convert the final result from montgomery to standard format */

	if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;

	ret=1;

err:

	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);

	if (powerbuf!=NULL)

		{

		OPENSSL_cleanse(powerbuf,powerbufLen);

		OPENSSL_free(powerbufFree);

		}

 	if (am!=NULL) BN_clear(am);

 	if (computeTemp!=NULL) BN_clear(computeTemp);

	BN_CTX_end(ctx);

	return(ret);

	}

EXPORT_C 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)

	{

	BN_MONT_CTX *mont = NULL;

	int b, bits, ret=0;

	int r_is_one;

	BN_ULONG w, next_w;

	BIGNUM *d, *r, *t;

	BIGNUM *swap_tmp;

#define BN_MOD_MUL_WORD(r, w, m) \

		(BN_mul_word(r, (w)) && \

		(/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \

			(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). */

		/* We can use BN_mod and do not need BN_nnmod because our

		 * accumulator is never negative (the result of BN_mod does

		 * not depend on the sign of the modulus).

		 */

#define BN_TO_MONTGOMERY_WORD(r, w, mont) \

		(BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))

	if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)

		{

		/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */

		BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);

		return -1;

		}

	bn_check_top(p);

	bn_check_top(m);

	if (!BN_is_odd(m))

		{

		BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);

		return(0);

		}

	if (m->top == 1)

		a %= m->d[0]; /* make sure that 'a' is reduced */

	bits = BN_num_bits(p);

	if (bits == 0)

		{

		ret = BN_one(rr);

		return ret;

		}

	if (a == 0)

		{

		BN_zero(rr);

		ret = 1;

		return ret;

		}

	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;

		}

	r_is_one = 1; /* except for Montgomery factor */

	/* 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--)

		{

		/* First, square r*w. */

		next_w = w*w;

		if ((next_w/w) != w) /* overflow */

			{

			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;

				}

			next_w = 1;

			}

		w = next_w;

		if (!r_is_one)

			{

			if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;

			}

		/* 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 */

				{

				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;

					}

				next_w = a;

				}

			w = next_w;

			}

		}

	/* Finally, set r:=r*w. */

	if (w != 1)

		{

		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;

			}

		}

	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;

		}

	ret = 1;

err:

	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);

	BN_CTX_end(ctx);

	bn_check_top(rr);

	return(ret);

	}

/* The old fallback, simple version :-) */

EXPORT_C int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,

		const BIGNUM *m, BN_CTX *ctx)

	{

	int i,j,bits,ret=0,wstart,wend,window,wvalue;

	int start=1;

	BIGNUM *d;

	/* Table of variables obtained from 'ctx' */

	BIGNUM *val[TABLE_SIZE];

	if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)

		{

		/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */

		BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);

		return -1;

		}

	bits=BN_num_bits(p);

	if (bits == 0)

		{

		ret = BN_one(r);

		return ret;

		}

	BN_CTX_start(ctx);

	d = BN_CTX_get(ctx);

	val[0] = BN_CTX_get(ctx);

	if(!d || !val[0]) goto err;

	if (!BN_nnmod(val[0],a,m,ctx)) goto err;		/* 1 */

	if (BN_is_zero(val[0]))

		{

		BN_zero(r);

		ret = 1;

		goto err;

		}

	window = BN_window_bits_for_exponent_size(bits);

	if (window > 1)

		{

		if (!BN_mod_mul(d,val[0],val[0],m,ctx))

			goto err;				/* 2 */

		j=1<<(window-1);

		for (i=1; i<j; i++)

			{

			if(((val[i] = BN_CTX_get(ctx)) == NULL) ||

					!BN_mod_mul(val[i],val[i-1],d,m,ctx))

				goto err;

			}

		}

	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 */

		if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))

			goto err;

		/* move the 'window' down further */

		wstart-=wend+1;

		wvalue=0;

		start=0;

		if (wstart < 0) break;

		}

	ret=1;

err:

	BN_CTX_end(ctx);

	bn_check_top(r);

	return(ret);

	}