crypto/bn/bn_mont.c - third_party/openssl - Git at Google

 /* crypto/bn/bn_mont.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.]
  */

 /*
  * Details about Montgomery multiplication algorithms can be found at
  * http://security.ece.orst.edu/publications.html, e.g.
  * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
  * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
  */

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

 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
 			  BN_MONT_CTX *mont, BN_CTX *ctx)
 	{
 	BIGNUM *tmp,*tmp2;

 	BN_CTX_start(ctx);
 	tmp = BN_CTX_get(ctx);
 	tmp2 = BN_CTX_get(ctx);
 	if (tmp == NULL || tmp2 == NULL) goto err;

 	bn_check_top(tmp);
 	bn_check_top(tmp2);

 	if (a == b)
 		{
 #if 0
 		bn_wexpand(tmp,a->top*2);
 		bn_wexpand(tmp2,a->top*4);
 		bn_sqr_recursive(tmp->d,a->d,a->top,tmp2->d);
 		tmp->top=a->top*2;
 		if (tmp->d[tmp->top-1] == 0)
 			tmp->top--;
 #else
 		if (!BN_sqr(tmp,a,ctx)) goto err;
 #endif
 		}
 	else
 		{
 		if (!BN_mul(tmp,a,b,ctx)) goto err;
 		}
 	/* reduce from aRR to aR */
 	if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
 	BN_CTX_end(ctx);
 	return(1);
 err:
 	return(0);
 	}

 #define BN_RECURSION_MONT

 int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
 	     BN_CTX *ctx)
 	{
 	int retn=0;
 	BN_CTX_start(ctx);

 #ifdef BN_RECURSION_MONT
 	if (mont->use_word)
 #endif
 		{
 		BIGNUM *n,*r;
 		BN_ULONG *ap,*np,*rp,n0,v,*nrp;
 		int al,nl,max,i,x,ri;

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

 		if (!BN_copy(r,a)) goto err;
 		n= &(mont->N);

 		ap=a->d;
 		/* mont->ri is the size of mont->N in bits (rounded up
                    to the word size) */
 		al=ri=mont->ri/BN_BITS2;

 		nl=n->top;
 		if ((al == 0) || (nl == 0)) { r->top=0; return(1); }

 		max=(nl+al+1); /* allow for overflow (no?) XXX */
 		if (bn_wexpand(r,max) == NULL) goto err;
 		if (bn_wexpand(ret,max) == NULL) goto err;

 		r->neg=a->neg^n->neg;
 		np=n->d;
 		rp=r->d;
 		nrp= &(r->d[nl]);

 		/* clear the top words of T */
 #if 1
 		for (i=r->top; i<max; i++) /* memset? XXX */
 			r->d[i]=0;
 #else
 		memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
 #endif

 		r->top=max;
 		n0=mont->n0;

 #ifdef BN_COUNT
 printf("word BN_from_montgomery %d * %d\n",nl,nl);
 #endif
 		for (i=0; i<nl; i++)
 			{
 			v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
 			nrp++;
 			rp++;
 			if (((nrp[-1]+=v)&BN_MASK2) >= v)
 				continue;
 			else
 				{
 				if (((++nrp[0])&BN_MASK2) != 0) continue;
 				if (((++nrp[1])&BN_MASK2) != 0) continue;
 				for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
 				}
 			}
 		bn_fix_top(r);

 		/* mont->ri will be a multiple of the word size */
 #if 0
 		BN_rshift(ret,r,mont->ri);
 #else
 		x=ri;
 		rp=ret->d;
 		ap= &(r->d[x]);
 		if (r->top < x)
 			al=0;
 		else
 			al=r->top-x;
 		ret->top=al;
 		al-=4;
 		for (i=0; i<al; i+=4)
 			{
 			BN_ULONG t1,t2,t3,t4;

 			t1=ap[i+0];
 			t2=ap[i+1];
 			t3=ap[i+2];
 			t4=ap[i+3];
 			rp[i+0]=t1;
 			rp[i+1]=t2;
 			rp[i+2]=t3;
 			rp[i+3]=t4;
 			}
 		al+=4;
 		for (; i<al; i++)
 			rp[i]=ap[i];
 #endif

 		if (BN_ucmp(ret, &(mont->N)) >= 0)
 			{
 			BN_usub(ret,ret,&(mont->N)); /* XXX */
 			}
 		retn=1;
 		}
 #ifdef BN_RECURSION_MONT
 	else /* bignum version */
 		{
 		BIGNUM *t1,*t2;

 		t1 = BN_CTX_get(ctx);
 		t2 = BN_CTX_get(ctx);
 		if (t1 == NULL || t2 == NULL) goto err;

 		if (!BN_copy(t1,a)) goto err;
 		BN_mask_bits(t1,mont->ri);

 		if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
 		BN_mask_bits(t2,mont->ri);

 		if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
 		if (!BN_add(t2,a,t1)) goto err;
 		BN_rshift(ret,t2,mont->ri);

 		if (BN_ucmp(ret,&mont->N) >= 0)
 			BN_usub(ret,ret,&mont->N);
 		retn=1;
 		}
 #endif
  err:
 	BN_CTX_end(ctx);
 	return(retn);
 	}

 BN_MONT_CTX *BN_MONT_CTX_new(void)
 	{
 	BN_MONT_CTX *ret;

 	if ((ret=(BN_MONT_CTX *)Malloc(sizeof(BN_MONT_CTX))) == NULL)
 		return(NULL);

 	BN_MONT_CTX_init(ret);
 	ret->flags=BN_FLG_MALLOCED;
 	return(ret);
 	}

 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 	{
 	ctx->use_word=0;
 	ctx->ri=0;
 	BN_init(&(ctx->RR));
 	BN_init(&(ctx->N));
 	BN_init(&(ctx->Ni));
 	ctx->flags=0;
 	}

 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 	{
 	if(mont == NULL)
 	    return;

 	BN_free(&(mont->RR));
 	BN_free(&(mont->N));
 	BN_free(&(mont->Ni));
 	if (mont->flags & BN_FLG_MALLOCED)
 		Free(mont);
 	}

 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 	{
 	BIGNUM Ri,*R;

 	BN_init(&Ri);
 	R= &(mont->RR);					/* grab RR as a temp */
 	BN_copy(&(mont->N),mod);			/* Set N */

 #ifdef BN_RECURSION_MONT
 	/* the word-based algorithm is faster */
 	if (mont->N.top > BN_MONT_CTX_SET_SIZE_WORD)
 #endif
 		{
 		BIGNUM tmod;
 		BN_ULONG buf[2];

 		mont->use_word=1;

 		mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
 		BN_zero(R);
 		BN_set_bit(R,BN_BITS2);			/* R */

 		buf[0]=mod->d[0]; /* tmod = N mod word size */
 		buf[1]=0;
 		tmod.d=buf;
 		tmod.top=1;
 		tmod.max=2;
 		tmod.neg=mod->neg;
 							/* Ri = R^-1 mod N*/
 		if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
 			goto err;
 		BN_lshift(&Ri,&Ri,BN_BITS2);		/* R*Ri */
 		if (!BN_is_zero(&Ri))
 			BN_sub_word(&Ri,1);
 		else /* if N mod word size == 1 */
 			BN_set_word(&Ri,BN_MASK2);  /* Ri-- (mod word size) */
 		BN_div(&Ri,NULL,&Ri,&tmod,ctx);	/* Ni = (R*Ri-1)/N,
 		                                 * keep only least significant word: */
 		mont->n0=Ri.d[0];
 		BN_free(&Ri);
 		}
 #ifdef BN_RECURSION_MONT
 	else
 		{ /* bignum version */
 		mont->use_word=0;
 		mont->ri=BN_num_bits(mod);
 		BN_zero(R);
 		BN_set_bit(R,mont->ri);			/* R = 2^ri */
 							/* Ri = R^-1 mod N*/
 		if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
 			goto err;
 		BN_lshift(&Ri,&Ri,mont->ri);		/* R*Ri */
 		BN_sub_word(&Ri,1);
 							/* Ni = (R*Ri-1) / N */
 		BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
 		BN_free(&Ri);
 		}
 #endif

 	/* setup RR for conversions */
 	BN_zero(&(mont->RR));
 	BN_set_bit(&(mont->RR),mont->ri*2);
 	BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);

 	return(1);
 err:
 	return(0);
 	}

 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 	{
 	if (to == from) return(to);

 	BN_copy(&(to->RR),&(from->RR));
 	BN_copy(&(to->N),&(from->N));
 	BN_copy(&(to->Ni),&(from->Ni));
 	to->use_word=from->use_word;
 	to->ri=from->ri;
 	to->n0=from->n0;
 	return(to);
 	}
	/* crypto/bn/bn_mont.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.]
	*/

	/*
	* Details about Montgomery multiplication algorithms can be found at
	* http://security.ece.orst.edu/publications.html, e.g.
	* http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
	* sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
	*/

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

	int BN_mod_mul_montgomery(BIGNUM r, BIGNUM a, BIGNUM *b,
	BN_MONT_CTX mont, BN_CTX ctx)
	{
	BIGNUM tmp,tmp2;

	BN_CTX_start(ctx);
	tmp = BN_CTX_get(ctx);
	tmp2 = BN_CTX_get(ctx);
	if (tmp == NULL \|\| tmp2 == NULL) goto err;

	bn_check_top(tmp);
	bn_check_top(tmp2);

	if (a == b)
	{
	#if 0
	bn_wexpand(tmp,a->top*2);
	bn_wexpand(tmp2,a->top*4);
	bn_sqr_recursive(tmp->d,a->d,a->top,tmp2->d);
	tmp->top=a->top*2;
	if (tmp->d[tmp->top-1] == 0)
	tmp->top--;
	#else
	if (!BN_sqr(tmp,a,ctx)) goto err;
	#endif
	}
	else
	{
	if (!BN_mul(tmp,a,b,ctx)) goto err;
	}
	/* reduce from aRR to aR */
	if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
	BN_CTX_end(ctx);
	return(1);
	err:
	return(0);
	}

	#define BN_RECURSION_MONT

	int BN_from_montgomery(BIGNUM ret, BIGNUM a, BN_MONT_CTX *mont,
	BN_CTX *ctx)
	{
	int retn=0;
	BN_CTX_start(ctx);

	#ifdef BN_RECURSION_MONT
	if (mont->use_word)
	#endif
	{
	BIGNUM n,r;
	BN_ULONG ap,np,rp,n0,v,nrp;
	int al,nl,max,i,x,ri;

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

	if (!BN_copy(r,a)) goto err;
	n= &(mont->N);

	ap=a->d;
	/* mont->ri is the size of mont->N in bits (rounded up
	to the word size) */
	al=ri=mont->ri/BN_BITS2;

	nl=n->top;
	if ((al == 0) \|\| (nl == 0)) { r->top=0; return(1); }

	max=(nl+al+1); /* allow for overflow (no?) XXX */
	if (bn_wexpand(r,max) == NULL) goto err;
	if (bn_wexpand(ret,max) == NULL) goto err;

	r->neg=a->neg^n->neg;
	np=n->d;
	rp=r->d;
	nrp= &(r->d[nl]);

	/* clear the top words of T */
	#if 1
	for (i=r->top; i<max; i++) /* memset? XXX */
	r->d[i]=0;
	#else
	memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
	#endif

	r->top=max;
	n0=mont->n0;

	#ifdef BN_COUNT
	printf("word BN_from_montgomery %d * %d\n",nl,nl);
	#endif
	for (i=0; i<nl; i++)
	{
	v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
	nrp++;
	rp++;
	if (((nrp[-1]+=v)&BN_MASK2) >= v)
	continue;
	else
	{
	if (((++nrp[0])&BN_MASK2) != 0) continue;
	if (((++nrp[1])&BN_MASK2) != 0) continue;
	for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
	}
	}
	bn_fix_top(r);

	/* mont->ri will be a multiple of the word size */
	#if 0
	BN_rshift(ret,r,mont->ri);
	#else
	x=ri;
	rp=ret->d;
	ap= &(r->d[x]);
	if (r->top < x)
	al=0;
	else
	al=r->top-x;
	ret->top=al;
	al-=4;
	for (i=0; i<al; i+=4)
	{
	BN_ULONG t1,t2,t3,t4;

	t1=ap[i+0];
	t2=ap[i+1];
	t3=ap[i+2];
	t4=ap[i+3];
	rp[i+0]=t1;
	rp[i+1]=t2;
	rp[i+2]=t3;
	rp[i+3]=t4;
	}
	al+=4;
	for (; i<al; i++)
	rp[i]=ap[i];
	#endif

	if (BN_ucmp(ret, &(mont->N)) >= 0)
	{
	BN_usub(ret,ret,&(mont->N)); /* XXX */
	}
	retn=1;
	}
	#ifdef BN_RECURSION_MONT
	else /* bignum version */
	{
	BIGNUM t1,t2;

	t1 = BN_CTX_get(ctx);
	t2 = BN_CTX_get(ctx);
	if (t1 == NULL \|\| t2 == NULL) goto err;

	if (!BN_copy(t1,a)) goto err;
	BN_mask_bits(t1,mont->ri);

	if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
	BN_mask_bits(t2,mont->ri);

	if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
	if (!BN_add(t2,a,t1)) goto err;
	BN_rshift(ret,t2,mont->ri);

	if (BN_ucmp(ret,&mont->N) >= 0)
	BN_usub(ret,ret,&mont->N);
	retn=1;
	}
	#endif
	err:
	BN_CTX_end(ctx);
	return(retn);
	}

	BN_MONT_CTX *BN_MONT_CTX_new(void)
	{
	BN_MONT_CTX *ret;

	if ((ret=(BN_MONT_CTX *)Malloc(sizeof(BN_MONT_CTX))) == NULL)
	return(NULL);

	BN_MONT_CTX_init(ret);
	ret->flags=BN_FLG_MALLOCED;
	return(ret);
	}

	void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
	{
	ctx->use_word=0;
	ctx->ri=0;
	BN_init(&(ctx->RR));
	BN_init(&(ctx->N));
	BN_init(&(ctx->Ni));
	ctx->flags=0;
	}

	void BN_MONT_CTX_free(BN_MONT_CTX *mont)
	{
	if(mont == NULL)
	return;

	BN_free(&(mont->RR));
	BN_free(&(mont->N));
	BN_free(&(mont->Ni));
	if (mont->flags & BN_FLG_MALLOCED)
	Free(mont);
	}

	int BN_MONT_CTX_set(BN_MONT_CTX mont, const BIGNUM mod, BN_CTX *ctx)
	{
	BIGNUM Ri,*R;

	BN_init(&Ri);
	R= &(mont->RR); /* grab RR as a temp */
	BN_copy(&(mont->N),mod); /* Set N */

	#ifdef BN_RECURSION_MONT
	/* the word-based algorithm is faster */
	if (mont->N.top > BN_MONT_CTX_SET_SIZE_WORD)
	#endif
	{
	BIGNUM tmod;
	BN_ULONG buf[2];

	mont->use_word=1;

	mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
	BN_zero(R);
	BN_set_bit(R,BN_BITS2); /* R */

	buf[0]=mod->d[0]; /* tmod = N mod word size */
	buf[1]=0;
	tmod.d=buf;
	tmod.top=1;
	tmod.max=2;
	tmod.neg=mod->neg;
	/* Ri = R^-1 mod N*/
	if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
	goto err;
	BN_lshift(&Ri,&Ri,BN_BITS2); /* RRi /
	if (!BN_is_zero(&Ri))
	BN_sub_word(&Ri,1);
	else /* if N mod word size == 1 */
	BN_set_word(&Ri,BN_MASK2); /* Ri-- (mod word size) */
	BN_div(&Ri,NULL,&Ri,&tmod,ctx); /* Ni = (R*Ri-1)/N,
	* keep only least significant word: */
	mont->n0=Ri.d[0];
	BN_free(&Ri);
	}
	#ifdef BN_RECURSION_MONT
	else
	{ /* bignum version */
	mont->use_word=0;
	mont->ri=BN_num_bits(mod);
	BN_zero(R);
	BN_set_bit(R,mont->ri); /* R = 2^ri */
	/* Ri = R^-1 mod N*/
	if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
	goto err;
	BN_lshift(&Ri,&Ri,mont->ri); /* RRi /
	BN_sub_word(&Ri,1);
	/* Ni = (RRi-1) / N /
	BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
	BN_free(&Ri);
	}
	#endif

	/* setup RR for conversions */
	BN_zero(&(mont->RR));
	BN_set_bit(&(mont->RR),mont->ri*2);
	BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);

	return(1);
	err:
	return(0);
	}

	BN_MONT_CTX BN_MONT_CTX_copy(BN_MONT_CTX to, BN_MONT_CTX *from)
	{
	if (to == from) return(to);

	BN_copy(&(to->RR),&(from->RR));
	BN_copy(&(to->N),&(from->N));
	BN_copy(&(to->Ni),&(from->Ni));
	to->use_word=from->use_word;
	to->ri=from->ri;
	to->n0=from->n0;
	return(to);
	}