FCL/sf/os/ossrv: comparison ssl/libcrypto/src/crypto/bn/bn

equal deleted inserted replaced

--1:000000000000
+:e4d67989cc36
+/* 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);
+	}