/* 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.]

  */

 /* ====================================================================

  * Copyright (c) 1998-2006 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).

  *

  */

 /*

  * 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"

 #define MONT_WORD /* use the faster word-based algorithm */

 EXPORT_C int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,

 			  BN_MONT_CTX *mont, BN_CTX *ctx)

 	{

 	BIGNUM *tmp;

 	int ret=0;

 	BN_CTX_start(ctx);

 	tmp = BN_CTX_get(ctx);

 	if (tmp == NULL) goto err;

 	bn_check_top(tmp);

 	if (a == b)

 		{

 		if (!BN_sqr(tmp,a,ctx)) goto err;

 		}

 	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_check_top(r);

 	ret=1;

 err:

 	BN_CTX_end(ctx);

 	return(ret);

 	}

 EXPORT_C int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,

 	     BN_CTX *ctx)

 	{

 	int retn=0;

 #ifdef MONT_WORD

 	BIGNUM *n,*r;

 	BN_ULONG *ap,*np,*rp,n0,v,*nrp;

 	int al,nl,max,i,x,ri;

 	BN_CTX_start(ctx);

 	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;

 	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

 	fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl);

 #endif

 	for (i=0; i<nl; i++)

 		{

 #ifdef __TANDEM

                 {

                    long long t1;

                    long long t2;

                    long long t3;

                    t1 = rp[0] * (n0 & 0177777);

                    t2 = 037777600000l;

                    t2 = n0 & t2;

                    t3 = rp[0] & 0177777;

                    t2 = (t3 * t2) & BN_MASK2;

                    t1 = t1 + t2;

                    v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);

                 }

 #else

 		v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);

 #endif

 		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_correct_top(r);

 	/* mont->ri will be a multiple of the word size and below code

 	 * is kind of BN_rshift(ret,r,mont->ri) equivalent */

 	if (r->top <= ri)

 		{

 		ret->top=0;

 		retn=1;

 		goto err;

 		}

 	al=r->top-ri;

 # define BRANCH_FREE 1

 # if BRANCH_FREE

 	if (bn_wexpand(ret,ri) == NULL) goto err;

 	x=0-(((al-ri)>>(sizeof(al)*8-1))&1);

 	ret->top=x=(ri&~x)|(al&x);	/* min(ri,al) */

 	ret->neg=r->neg;

 	rp=ret->d;

 	ap=&(r->d[ri]);

 	{

 	size_t m1,m2;

 	v=bn_sub_words(rp,ap,np,ri);

 	/* this ----------------^^ works even in al<ri case

 	 * thanks to zealous zeroing of top of the vector in the

 	 * beginning. */

 	/* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */

 	/* in other words if subtraction result is real, then

 	 * trick unconditional memcpy below to perform in-place

 	 * "refresh" instead of actual copy. */

 	m1=0-(size_t)(((al-ri)>>(sizeof(al)*8-1))&1);	/* al<ri */

 	m2=0-(size_t)(((ri-al)>>(sizeof(al)*8-1))&1);	/* al>ri */

 	m1|=m2;			/* (al!=ri) */

 	m1|=(0-(size_t)v);	/* (al!=ri || v) */

 	m1&=~m2;		/* (al!=ri || v) && !al>ri */

 	nrp=(BN_ULONG *)(((size_t)rp&~m1)|((size_t)ap&m1));

 	}

 	/* 'i<ri' is chosen to eliminate dependency on input data, even

 	 * though it results in redundant copy in al<ri case. */

 	for (i=0,ri-=4; i<ri; i+=4)

 		{

 		BN_ULONG t1,t2,t3,t4;

 		t1=nrp[i+0];

 		t2=nrp[i+1];

 		t3=nrp[i+2];	ap[i+0]=0;

 		t4=nrp[i+3];	ap[i+1]=0;

 		rp[i+0]=t1;	ap[i+2]=0;

 		rp[i+1]=t2;	ap[i+3]=0;

 		rp[i+2]=t3;

 		rp[i+3]=t4;

 		}

 	for (ri+=4; i<ri; i++)

 		rp[i]=nrp[i], ap[i]=0;

 	bn_correct_top(r);

 	bn_correct_top(ret);

 # else

 	if (bn_wexpand(ret,al) == NULL) goto err;

 	ret->top=al;

 	ret->neg=r->neg;

 	rp=ret->d;

 	ap=&(r->d[ri]);

 	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

 #else /* !MONT_WORD */ 

 	BIGNUM *t1,*t2;

 	BN_CTX_start(ctx);

 	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;

 	if (!BN_rshift(ret,t2,mont->ri)) goto err;

 #endif /* MONT_WORD */

 #if !defined(BRANCH_FREE) || BRANCH_FREE==0

 	if (BN_ucmp(ret, &(mont->N)) >= 0)

 		{

 		if (!BN_usub(ret,ret,&(mont->N))) goto err;

 		}

 #endif

 	retn=1;

 	bn_check_top(ret);

  err:

 	BN_CTX_end(ctx);

 	return(retn);

 	}

 EXPORT_C BN_MONT_CTX *BN_MONT_CTX_new(void)

 	{

 	BN_MONT_CTX *ret;

 	if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)

 		return(NULL);

 	BN_MONT_CTX_init(ret);

 	ret->flags=BN_FLG_MALLOCED;

 	return(ret);

 	}

 EXPORT_C void BN_MONT_CTX_init(BN_MONT_CTX *ctx)

 	{

 	ctx->ri=0;

 	BN_init(&(ctx->RR));

 	BN_init(&(ctx->N));

 	BN_init(&(ctx->Ni));

 	ctx->flags=0;

 	}

 EXPORT_C 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)

 		OPENSSL_free(mont);

 	}

 EXPORT_C int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)

 	{

 	int ret = 0;

 	BIGNUM *Ri,*R;

 	BN_CTX_start(ctx);

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

 	R= &(mont->RR);					/* grab RR as a temp */

 	if (!BN_copy(&(mont->N),mod)) goto err;		/* Set N */

 	mont->N.neg = 0;

 #ifdef MONT_WORD

 		{

 		BIGNUM tmod;

 		BN_ULONG buf[2];

 		mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;

 		BN_zero(R);

 		if (!(BN_set_bit(R,BN_BITS2))) goto err;	/* R */

 		buf[0]=mod->d[0]; /* tmod = N mod word size */

 		buf[1]=0;

 		tmod.d=buf;

 		tmod.top = buf[0] != 0 ? 1 : 0;

 		tmod.dmax=2;

 		tmod.neg=0;

 							/* Ri = R^-1 mod N*/

 		if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)

 			goto err;

 		if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */

 		if (!BN_is_zero(Ri))

 			{

 			if (!BN_sub_word(Ri,1)) goto err;

 			}

 		else /* if N mod word size == 1 */

 			{

 			if (!BN_set_word(Ri,BN_MASK2)) goto err;  /* Ri-- (mod word size) */

 			}

 		if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;

 		/* Ni = (R*Ri-1)/N,

 		 * keep only least significant word: */

 		mont->n0 = (Ri->top > 0) ? Ri->d[0] : 0;

 		}

 #else /* !MONT_WORD */

 		{ /* bignum version */

 		mont->ri=BN_num_bits(&mont->N);

 		BN_zero(R);

 		if (!BN_set_bit(R,mont->ri)) goto err;  /* R = 2^ri */

 		                                        /* Ri = R^-1 mod N*/

 		if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)

 			goto err;

 		if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */

 		if (!BN_sub_word(Ri,1)) goto err;

 							/* Ni = (R*Ri-1) / N */

 		if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;

 		}

 #endif

 	/* setup RR for conversions */

 	BN_zero(&(mont->RR));

 	if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;

 	if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;

 	ret = 1;

 err:

 	BN_CTX_end(ctx);

 	return ret;

 	}

 EXPORT_C BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)

 	{

 	if (to == from) return(to);

 	if (!BN_copy(&(to->RR),&(from->RR))) return NULL;

 	if (!BN_copy(&(to->N),&(from->N))) return NULL;

 	if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;

 	to->ri=from->ri;

 	to->n0=from->n0;

 	return(to);

 	}

 EXPORT_C BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,

 					const BIGNUM *mod, BN_CTX *ctx)

 	{

 		int got_write_lock = 0;

 	BN_MONT_CTX *ret;

 	CRYPTO_r_lock(lock);

 	if (!*pmont)

 		{

 		CRYPTO_r_unlock(lock);

 		CRYPTO_w_lock(lock);

 		got_write_lock = 1;

 		if (!*pmont)

 			{

 			ret = BN_MONT_CTX_new();

 			if (ret && !BN_MONT_CTX_set(ret, mod, ctx))

 				BN_MONT_CTX_free(ret);

 			else

 				*pmont = ret;

 			}

 		}

 	ret = *pmont;

 	if (got_write_lock)

 		CRYPTO_w_unlock(lock);

 	else

 		CRYPTO_r_unlock(lock);

 	return ret;

 	}