crypto/bn/montgomery.c - boringssl - Git at Google

 /* 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). */

 #include <openssl/bn.h>

 #include <string.h>

 #include <openssl/err.h>
 #include <openssl/mem.h>
 #include <openssl/thread.h>

 #include "internal.h"
 #include "../internal.h"


 #if !defined(OPENSSL_NO_ASM) &&                         \
     (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \
      defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64))
 #define OPENSSL_BN_ASM_MONT
 #endif

 BN_MONT_CTX *BN_MONT_CTX_new(void) {
   BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));

   if (ret == NULL) {
     return NULL;
   }

   memset(ret, 0, sizeof(BN_MONT_CTX));
   BN_init(&ret->RR);
   BN_init(&ret->N);

   return ret;
 }

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

   BN_free(&mont->RR);
   BN_free(&mont->N);
   OPENSSL_free(mont);
 }

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

   if (!BN_copy(&to->RR, &from->RR) ||
       !BN_copy(&to->N, &from->N)) {
     return NULL;
   }
   to->n0[0] = from->n0[0];
   to->n0[1] = from->n0[1];
   return to;
 }

 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) {
   int ret = 0;
   BIGNUM *Ri, *R;
   BIGNUM tmod;
   BN_ULONG buf[2];

   if (BN_is_zero(mod)) {
     OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
     return 0;
   }

   BN_CTX_start(ctx);
   Ri = BN_CTX_get(ctx);
   if (Ri == 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;

   BN_init(&tmod);
   tmod.d = buf;
   tmod.dmax = 2;
   tmod.neg = 0;

 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2 <= 32)
   /* Only certain BN_BITS2<=32 platforms actually make use of
    * n0[1], and we could use the #else case (with a shorter R
    * value) for the others.  However, currently only the assembler
    * files do know which is which. */

   BN_zero(R);
   if (!BN_set_bit(R, 2 * BN_BITS2)) {
     goto err;
   }

   tmod.top = 0;
   if ((buf[0] = mod->d[0])) {
     tmod.top = 1;
   }
   if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) {
     tmod.top = 2;
   }

   if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) {
     goto err;
   }
   if (!BN_lshift(Ri, Ri, 2 * 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_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) {
       goto err;
     }
     /* Ri-- (mod double word size) */
     Ri->neg = 0;
     Ri->d[0] = BN_MASK2;
     Ri->d[1] = BN_MASK2;
     Ri->top = 2;
   }

   if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) {
     goto err;
   }
   /* Ni = (R*Ri-1)/N,
    * keep only couple of least significant words: */
   mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
   mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
 #else
   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.top = buf[0] != 0 ? 1 : 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[0] = (Ri->top > 0) ? Ri->d[0] : 0;
   mont->n0[1] = 0;
 #endif

   /* RR = (2^ri)^2 == 2^(ri*2) == 1 << (ri*2), which has its (ri*2)th bit set. */
   int ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
   BN_zero(&(mont->RR));
   if (!BN_set_bit(&(mont->RR), 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;
 }

 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
                                     const BIGNUM *mod, BN_CTX *bn_ctx) {
   CRYPTO_MUTEX_lock_read(lock);
   BN_MONT_CTX *ctx = *pmont;
   CRYPTO_MUTEX_unlock(lock);

   if (ctx) {
     return ctx;
   }

   CRYPTO_MUTEX_lock_write(lock);
   ctx = *pmont;
   if (ctx) {
     goto out;
   }

   ctx = BN_MONT_CTX_new();
   if (ctx == NULL) {
     goto out;
   }
   if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) {
     BN_MONT_CTX_free(ctx);
     ctx = NULL;
     goto out;
   }
   *pmont = ctx;

 out:
   CRYPTO_MUTEX_unlock(lock);
   return ctx;
 }

 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
                      BN_CTX *ctx) {
   return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
 }

 #if 0
 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r,
                                    const BN_MONT_CTX *mont) {
   const BIGNUM *n;
   BN_ULONG *ap, *np, *rp, n0, v, carry;
   int nl, max, i;

   n = &mont->N;
   nl = n->top;
   if (nl == 0) {
     ret->top = 0;
     return 1;
   }

   max = (2 * nl); /* carry is stored separately */
   if (bn_wexpand(r, max) == NULL) {
     return 0;
   }

   r->neg ^= n->neg;
   np = n->d;
   rp = r->d;

   /* clear the top words of T */
   if (max > r->top) {
     memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG));
   }

   r->top = max;
   n0 = mont->n0[0];

   for (carry = 0, i = 0; i < nl; i++, rp++) {
     v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
     v = (v + carry + rp[nl]) & BN_MASK2;
     carry |= (v != rp[nl]);
     carry &= (v <= rp[nl]);
     rp[nl] = v;
   }

   if (bn_wexpand(ret, nl) == NULL) {
     return 0;
   }
   ret->top = nl;
   ret->neg = r->neg;

   rp = ret->d;
   ap = &(r->d[nl]);

   {
     BN_ULONG *nrp;
     size_t m;

     v = bn_sub_words(rp, ap, np, nl) - carry;
     /* if subtraction result is real, then trick unconditional memcpy below to
      * perform in-place "refresh" instead of actual copy. */
     m = (0 - (size_t)v);
     nrp = (BN_ULONG *)(((intptr_t)rp & ~m) | ((intptr_t)ap & m));

     for (i = 0, nl -= 4; i < nl; 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 (nl += 4; i < nl; i++) {
       rp[i] = nrp[i], ap[i] = 0;
     }
   }

   bn_correct_top(r);
   bn_correct_top(ret);

   return 1;
 }
 #endif

 #define PTR_SIZE_INT size_t

 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, const BN_MONT_CTX *mont)
 	{
 	BN_ULONG *ap,*np,*rp,n0,v,carry;
 	int nl,max,i;

 	const BIGNUM *n = &mont->N;
 	nl=n->top;
 	if (nl == 0) { ret->top=0; return(1); }

 	max=(2*nl); /* carry is stored separately */
 	if (bn_wexpand(r,max) == NULL) return(0);

 	r->neg^=n->neg;
 	np=n->d;
 	rp=r->d;

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

 	r->top=max;
 	n0=mont->n0[0];

 	for (carry=0, i=0; i<nl; i++, rp++)
 		{
 		v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
 		v = (v+carry+rp[nl])&BN_MASK2;
 		carry |= (v != rp[nl]);
 		carry &= (v <= rp[nl]);
 		rp[nl]=v;
 		}

 	if (bn_wexpand(ret,nl) == NULL) return(0);
 	ret->top=nl;
 	ret->neg=r->neg;

 	rp=ret->d;
 	ap=&(r->d[nl]);

 	{
 	BN_ULONG *nrp;
 	size_t m;

 	v=bn_sub_words(rp,ap,np,nl)-carry;
 	/* if subtraction result is real, then
 	 * trick unconditional memcpy below to perform in-place
 	 * "refresh" instead of actual copy. */
 	m=(0-(size_t)v);
 	nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m));

 	for (i=0,nl-=4; i<nl; 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 (nl+=4; i<nl; i++)
 		rp[i]=nrp[i], ap[i]=0;
 	}
 	bn_correct_top(r);
 	bn_correct_top(ret);

 	return(1);
 	}

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

   BN_CTX_start(ctx);
   t = BN_CTX_get(ctx);
   if (t == NULL) {
     return 0;
   }

   if (BN_copy(t, a)) {
     retn = BN_from_montgomery_word(ret, t, mont);
   }
   BN_CTX_end(ctx);

   return retn;
 }

 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                           const BN_MONT_CTX *mont, BN_CTX *ctx) {
   BIGNUM *tmp;
   int ret = 0;

 #if defined(OPENSSL_BN_ASM_MONT)
   int num = mont->N.top;

   if (num > 1 && a->top == num && b->top == num) {
     if (bn_wexpand(r, num) == NULL) {
       return 0;
     }
     if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
       r->neg = a->neg ^ b->neg;
       r->top = num;
       bn_correct_top(r);
       return 1;
     }
   }
 #endif

   BN_CTX_start(ctx);
   tmp = BN_CTX_get(ctx);
   if (tmp == NULL) {
     goto err;
   }

   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_word(r, tmp, mont)) {
     goto err;
   }

   ret = 1;

 err:
   BN_CTX_end(ctx);
   return ret;
 }
	/* 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). */

	#include <openssl/bn.h>

	#include <string.h>

	#include <openssl/err.h>
	#include <openssl/mem.h>
	#include <openssl/thread.h>

	#include "internal.h"
	#include "../internal.h"


	#if !defined(OPENSSL_NO_ASM) && \
	(defined(OPENSSL_X86) \|\| defined(OPENSSL_X86_64) \|\| \
	defined(OPENSSL_ARM) \|\| defined(OPENSSL_AARCH64))
	#define OPENSSL_BN_ASM_MONT
	#endif

	BN_MONT_CTX *BN_MONT_CTX_new(void) {
	BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));

	if (ret == NULL) {
	return NULL;
	}

	memset(ret, 0, sizeof(BN_MONT_CTX));
	BN_init(&ret->RR);
	BN_init(&ret->N);

	return ret;
	}

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

	BN_free(&mont->RR);
	BN_free(&mont->N);
	OPENSSL_free(mont);
	}

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

	if (!BN_copy(&to->RR, &from->RR) \|\|
	!BN_copy(&to->N, &from->N)) {
	return NULL;
	}
	to->n0[0] = from->n0[0];
	to->n0[1] = from->n0[1];
	return to;
	}

	int BN_MONT_CTX_set(BN_MONT_CTX mont, const BIGNUM mod, BN_CTX *ctx) {
	int ret = 0;
	BIGNUM Ri, R;
	BIGNUM tmod;
	BN_ULONG buf[2];

	if (BN_is_zero(mod)) {
	OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
	return 0;
	}

	BN_CTX_start(ctx);
	Ri = BN_CTX_get(ctx);
	if (Ri == 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;

	BN_init(&tmod);
	tmod.d = buf;
	tmod.dmax = 2;
	tmod.neg = 0;

	#if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2 <= 32)
	/* Only certain BN_BITS2<=32 platforms actually make use of
	* n0[1], and we could use the #else case (with a shorter R
	* value) for the others. However, currently only the assembler
	* files do know which is which. */

	BN_zero(R);
	if (!BN_set_bit(R, 2 * BN_BITS2)) {
	goto err;
	}

	tmod.top = 0;
	if ((buf[0] = mod->d[0])) {
	tmod.top = 1;
	}
	if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) {
	tmod.top = 2;
	}

	if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) {
	goto err;
	}
	if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) {
	goto err; /* RRi /
	}
	if (!BN_is_zero(Ri)) {
	if (!BN_sub_word(Ri, 1)) {
	goto err;
	}
	} else {
	/* if N mod word size == 1 */
	if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) {
	goto err;
	}
	/* Ri-- (mod double word size) */
	Ri->neg = 0;
	Ri->d[0] = BN_MASK2;
	Ri->d[1] = BN_MASK2;
	Ri->top = 2;
	}

	if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) {
	goto err;
	}
	/* Ni = (R*Ri-1)/N,
	* keep only couple of least significant words: */
	mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
	mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
	#else
	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.top = buf[0] != 0 ? 1 : 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; /* RRi /
	}
	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[0] = (Ri->top > 0) ? Ri->d[0] : 0;
	mont->n0[1] = 0;
	#endif

	/* RR = (2^ri)^2 == 2^(ri2) == 1 << (ri2), which has its (ri2)th bit set. /
	int ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
	BN_zero(&(mont->RR));
	if (!BN_set_bit(&(mont->RR), 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;
	}

	BN_MONT_CTX BN_MONT_CTX_set_locked(BN_MONT_CTX pmont, CRYPTO_MUTEX lock,
	const BIGNUM mod, BN_CTX bn_ctx) {
	CRYPTO_MUTEX_lock_read(lock);
	BN_MONT_CTX ctx = pmont;
	CRYPTO_MUTEX_unlock(lock);

	if (ctx) {
	return ctx;
	}

	CRYPTO_MUTEX_lock_write(lock);
	ctx = *pmont;
	if (ctx) {
	goto out;
	}

	ctx = BN_MONT_CTX_new();
	if (ctx == NULL) {
	goto out;
	}
	if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) {
	BN_MONT_CTX_free(ctx);
	ctx = NULL;
	goto out;
	}
	*pmont = ctx;

	out:
	CRYPTO_MUTEX_unlock(lock);
	return ctx;
	}

	int BN_to_montgomery(BIGNUM ret, const BIGNUM a, const BN_MONT_CTX *mont,
	BN_CTX *ctx) {
	return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
	}

	#if 0
	static int BN_from_montgomery_word(BIGNUM ret, BIGNUM r,
	const BN_MONT_CTX *mont) {
	const BIGNUM *n;
	BN_ULONG ap, np, *rp, n0, v, carry;
	int nl, max, i;

	n = &mont->N;
	nl = n->top;
	if (nl == 0) {
	ret->top = 0;
	return 1;
	}

	max = (2 * nl); /* carry is stored separately */
	if (bn_wexpand(r, max) == NULL) {
	return 0;
	}

	r->neg ^= n->neg;
	np = n->d;
	rp = r->d;

	/* clear the top words of T */
	if (max > r->top) {
	memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG));
	}

	r->top = max;
	n0 = mont->n0[0];

	for (carry = 0, i = 0; i < nl; i++, rp++) {
	v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
	v = (v + carry + rp[nl]) & BN_MASK2;
	carry \|= (v != rp[nl]);
	carry &= (v <= rp[nl]);
	rp[nl] = v;
	}

	if (bn_wexpand(ret, nl) == NULL) {
	return 0;
	}
	ret->top = nl;
	ret->neg = r->neg;

	rp = ret->d;
	ap = &(r->d[nl]);

	{
	BN_ULONG *nrp;
	size_t m;

	v = bn_sub_words(rp, ap, np, nl) - carry;
	/* if subtraction result is real, then trick unconditional memcpy below to
	* perform in-place "refresh" instead of actual copy. */
	m = (0 - (size_t)v);
	nrp = (BN_ULONG *)(((intptr_t)rp & ~m) \| ((intptr_t)ap & m));

	for (i = 0, nl -= 4; i < nl; 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 (nl += 4; i < nl; i++) {
	rp[i] = nrp[i], ap[i] = 0;
	}
	}

	bn_correct_top(r);
	bn_correct_top(ret);

	return 1;
	}
	#endif

	#define PTR_SIZE_INT size_t

	static int BN_from_montgomery_word(BIGNUM ret, BIGNUM r, const BN_MONT_CTX *mont)
	{
	BN_ULONG ap,np,*rp,n0,v,carry;
	int nl,max,i;

	const BIGNUM *n = &mont->N;
	nl=n->top;
	if (nl == 0) { ret->top=0; return(1); }

	max=(2nl); / carry is stored separately */
	if (bn_wexpand(r,max) == NULL) return(0);

	r->neg^=n->neg;
	np=n->d;
	rp=r->d;

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

	r->top=max;
	n0=mont->n0[0];

	for (carry=0, i=0; i<nl; i++, rp++)
	{
	v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
	v = (v+carry+rp[nl])&BN_MASK2;
	carry \|= (v != rp[nl]);
	carry &= (v <= rp[nl]);
	rp[nl]=v;
	}

	if (bn_wexpand(ret,nl) == NULL) return(0);
	ret->top=nl;
	ret->neg=r->neg;

	rp=ret->d;
	ap=&(r->d[nl]);

	{
	BN_ULONG *nrp;
	size_t m;

	v=bn_sub_words(rp,ap,np,nl)-carry;
	/* if subtraction result is real, then
	* trick unconditional memcpy below to perform in-place
	* "refresh" instead of actual copy. */
	m=(0-(size_t)v);
	nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)\|((PTR_SIZE_INT)ap&m));

	for (i=0,nl-=4; i<nl; 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 (nl+=4; i<nl; i++)
	rp[i]=nrp[i], ap[i]=0;
	}
	bn_correct_top(r);
	bn_correct_top(ret);

	return(1);
	}

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

	BN_CTX_start(ctx);
	t = BN_CTX_get(ctx);
	if (t == NULL) {
	return 0;
	}

	if (BN_copy(t, a)) {
	retn = BN_from_montgomery_word(ret, t, mont);
	}
	BN_CTX_end(ctx);

	return retn;
	}

	int BN_mod_mul_montgomery(BIGNUM r, const BIGNUM a, const BIGNUM *b,
	const BN_MONT_CTX mont, BN_CTX ctx) {
	BIGNUM *tmp;
	int ret = 0;

	#if defined(OPENSSL_BN_ASM_MONT)
	int num = mont->N.top;

	if (num > 1 && a->top == num && b->top == num) {
	if (bn_wexpand(r, num) == NULL) {
	return 0;
	}
	if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
	r->neg = a->neg ^ b->neg;
	r->top = num;
	bn_correct_top(r);
	return 1;
	}
	}
	#endif

	BN_CTX_start(ctx);
	tmp = BN_CTX_get(ctx);
	if (tmp == NULL) {
	goto err;
	}

	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_word(r, tmp, mont)) {
	goto err;
	}

	ret = 1;

	err:
	BN_CTX_end(ctx);
	return ret;
	}