/* 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)