/* crypto/bn/bn_gcd.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) 1998-2001 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"

static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);

EXPORT_C int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)

	{

	BIGNUM *a,*b,*t;

	int ret=0;

	bn_check_top(in_a);

	bn_check_top(in_b);

	BN_CTX_start(ctx);

	a = BN_CTX_get(ctx);

	b = BN_CTX_get(ctx);

	if (a == NULL || b == NULL) goto err;

	if (BN_copy(a,in_a) == NULL) goto err;

	if (BN_copy(b,in_b) == NULL) goto err;

	a->neg = 0;

	b->neg = 0;

	if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; }

	t=euclid(a,b);

	if (t == NULL) goto err;

	if (BN_copy(r,t) == NULL) goto err;

	ret=1;

err:

	BN_CTX_end(ctx);

	bn_check_top(r);

	return(ret);

	}

static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)

	{

	BIGNUM *t;

	int shifts=0;

	bn_check_top(a);

	bn_check_top(b);

	/* 0 <= b <= a */

	while (!BN_is_zero(b))

		{

		/* 0 < b <= a */

		if (BN_is_odd(a))

			{

			if (BN_is_odd(b))

				{

				if (!BN_sub(a,a,b)) goto err;

				if (!BN_rshift1(a,a)) goto err;

				if (BN_cmp(a,b) < 0)

					{ t=a; a=b; b=t; }

				}

			else		/* a odd - b even */

				{

				if (!BN_rshift1(b,b)) goto err;

				if (BN_cmp(a,b) < 0)

					{ t=a; a=b; b=t; }

				}

			}

		else			/* a is even */

			{

			if (BN_is_odd(b))

				{

				if (!BN_rshift1(a,a)) goto err;

				if (BN_cmp(a,b) < 0)

					{ t=a; a=b; b=t; }

				}

			else		/* a even - b even */

				{

				if (!BN_rshift1(a,a)) goto err;

				if (!BN_rshift1(b,b)) goto err;

				shifts++;

				}

			}

		/* 0 <= b <= a */

		}

	if (shifts)

		{

		if (!BN_lshift(a,a,shifts)) goto err;

		}

	bn_check_top(a);

	return(a);

err:

	return(NULL);

	}

/* solves ax == 1 (mod n) */

static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,

        const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);

EXPORT_C BIGNUM *BN_mod_inverse(BIGNUM *in,

	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)

	{

	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;

	BIGNUM *ret=NULL;

	int sign;

	if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0))

		{

		return BN_mod_inverse_no_branch(in, a, n, ctx);

		}

	bn_check_top(a);

	bn_check_top(n);

	BN_CTX_start(ctx);

	A = BN_CTX_get(ctx);

	B = BN_CTX_get(ctx);

	X = BN_CTX_get(ctx);

	D = BN_CTX_get(ctx);

	M = BN_CTX_get(ctx);

	Y = BN_CTX_get(ctx);

	T = BN_CTX_get(ctx);

	if (T == NULL) goto err;

	if (in == NULL)

		R=BN_new();

	else

		R=in;

	if (R == NULL) goto err;

	BN_one(X);

	BN_zero(Y);

	if (BN_copy(B,a) == NULL) goto err;

	if (BN_copy(A,n) == NULL) goto err;

	A->neg = 0;

	if (B->neg || (BN_ucmp(B, A) >= 0))

		{

		if (!BN_nnmod(B, B, A, ctx)) goto err;

		}

	sign = -1;

	/* From  B = a mod |n|,  A = |n|  it follows that

	 *

	 *      0 <= B < A,

	 *     -sign*X*a  ==  B   (mod |n|),

	 *      sign*Y*a  ==  A   (mod |n|).

	 */

	if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048)))

		{

		/* Binary inversion algorithm; requires odd modulus.

		 * This is faster than the general algorithm if the modulus

		 * is sufficiently small (about 400 .. 500 bits on 32-bit

		 * sytems, but much more on 64-bit systems) */

		int shift;

		while (!BN_is_zero(B))

			{

			/*

			 *      0 < B < |n|,

			 *      0 < A <= |n|,

			 * (1) -sign*X*a  ==  B   (mod |n|),

			 * (2)  sign*Y*a  ==  A   (mod |n|)

			 */

			/* Now divide  B  by the maximum possible power of two in the integers,

			 * and divide  X  by the same value mod |n|.

			 * When we're done, (1) still holds. */

			shift = 0;

			while (!BN_is_bit_set(B, shift)) /* note that 0 < B */

				{

				shift++;

				if (BN_is_odd(X))

					{

					if (!BN_uadd(X, X, n)) goto err;

					}

				/* now X is even, so we can easily divide it by two */

				if (!BN_rshift1(X, X)) goto err;

				}

			if (shift > 0)

				{

				if (!BN_rshift(B, B, shift)) goto err;

				}

			/* Same for  A  and  Y.  Afterwards, (2) still holds. */

			shift = 0;

			while (!BN_is_bit_set(A, shift)) /* note that 0 < A */

				{

				shift++;

				if (BN_is_odd(Y))

					{

					if (!BN_uadd(Y, Y, n)) goto err;

					}

				/* now Y is even */

				if (!BN_rshift1(Y, Y)) goto err;

				}

			if (shift > 0)

				{

				if (!BN_rshift(A, A, shift)) goto err;

				}

			/* We still have (1) and (2).

			 * Both  A  and  B  are odd.

			 * The following computations ensure that

			 *

			 *     0 <= B < |n|,

			 *      0 < A < |n|,

			 * (1) -sign*X*a  ==  B   (mod |n|),

			 * (2)  sign*Y*a  ==  A   (mod |n|),

			 *

			 * and that either  A  or  B  is even in the next iteration.

			 */

			if (BN_ucmp(B, A) >= 0)

				{

				/* -sign*(X + Y)*a == B - A  (mod |n|) */

				if (!BN_uadd(X, X, Y)) goto err;

				/* NB: we could use BN_mod_add_quick(X, X, Y, n), but that

				 * actually makes the algorithm slower */

				if (!BN_usub(B, B, A)) goto err;

				}

			else

				{

				/*  sign*(X + Y)*a == A - B  (mod |n|) */

				if (!BN_uadd(Y, Y, X)) goto err;

				/* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */

				if (!BN_usub(A, A, B)) goto err;

				}

			}

		}

	else

		{

		/* general inversion algorithm */

		while (!BN_is_zero(B))

			{

			BIGNUM *tmp;

			/*

			 *      0 < B < A,

			 * (*) -sign*X*a  ==  B   (mod |n|),

			 *      sign*Y*a  ==  A   (mod |n|)

			 */

			/* (D, M) := (A/B, A%B) ... */

			if (BN_num_bits(A) == BN_num_bits(B))

				{

				if (!BN_one(D)) goto err;

				if (!BN_sub(M,A,B)) goto err;

				}

			else if (BN_num_bits(A) == BN_num_bits(B) + 1)

				{

				/* A/B is 1, 2, or 3 */

				if (!BN_lshift1(T,B)) goto err;

				if (BN_ucmp(A,T) < 0)

					{

					/* A < 2*B, so D=1 */

					if (!BN_one(D)) goto err;

					if (!BN_sub(M,A,B)) goto err;

					}

				else

					{

					/* A >= 2*B, so D=2 or D=3 */

					if (!BN_sub(M,A,T)) goto err;

					if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */

					if (BN_ucmp(A,D) < 0)

						{

						/* A < 3*B, so D=2 */

						if (!BN_set_word(D,2)) goto err;

						/* M (= A - 2*B) already has the correct value */

						}

					else

						{

						/* only D=3 remains */

						if (!BN_set_word(D,3)) goto err;

						/* currently  M = A - 2*B,  but we need  M = A - 3*B */

						if (!BN_sub(M,M,B)) goto err;

						}

					}

				}

			else

				{

				if (!BN_div(D,M,A,B,ctx)) goto err;

				}

			/* Now

			 *      A = D*B + M;

			 * thus we have

			 * (**)  sign*Y*a  ==  D*B + M   (mod |n|).

			 */

			tmp=A; /* keep the BIGNUM object, the value does not matter */

			/* (A, B) := (B, A mod B) ... */

			A=B;

			B=M;

			/* ... so we have  0 <= B < A  again */

			/* Since the former  M  is now  B  and the former  B  is now  A,

			 * (**) translates into

			 *       sign*Y*a  ==  D*A + B    (mod |n|),

			 * i.e.

			 *       sign*Y*a - D*A  ==  B    (mod |n|).

			 * Similarly, (*) translates into

			 *      -sign*X*a  ==  A          (mod |n|).

			 *

			 * Thus,

			 *   sign*Y*a + D*sign*X*a  ==  B  (mod |n|),

			 * i.e.

			 *        sign*(Y + D*X)*a  ==  B  (mod |n|).

			 *

			 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at

			 *      -sign*X*a  ==  B   (mod |n|),

			 *       sign*Y*a  ==  A   (mod |n|).

			 * Note that  X  and  Y  stay non-negative all the time.

			 */

			/* most of the time D is very small, so we can optimize tmp := D*X+Y */

			if (BN_is_one(D))

				{

				if (!BN_add(tmp,X,Y)) goto err;

				}

			else

				{

				if (BN_is_word(D,2))

					{

					if (!BN_lshift1(tmp,X)) goto err;

					}

				else if (BN_is_word(D,4))

					{

					if (!BN_lshift(tmp,X,2)) goto err;

					}

				else if (D->top == 1)

					{

					if (!BN_copy(tmp,X)) goto err;

					if (!BN_mul_word(tmp,D->d[0])) goto err;

					}

				else

					{

					if (!BN_mul(tmp,D,X,ctx)) goto err;

					}

				if (!BN_add(tmp,tmp,Y)) goto err;

				}

			M=Y; /* keep the BIGNUM object, the value does not matter */

			Y=X;

			X=tmp;

			sign = -sign;

			}

		}

	/*

	 * The while loop (Euclid's algorithm) ends when

	 *      A == gcd(a,n);

	 * we have

	 *       sign*Y*a  ==  A  (mod |n|),

	 * where  Y  is non-negative.

	 */

	if (sign < 0)

		{

		if (!BN_sub(Y,n,Y)) goto err;

		}

	/* Now  Y*a  ==  A  (mod |n|).  */

	if (BN_is_one(A))

		{

		/* Y*a == 1  (mod |n|) */

		if (!Y->neg && BN_ucmp(Y,n) < 0)

			{

			if (!BN_copy(R,Y)) goto err;

			}

		else

			{

			if (!BN_nnmod(R,Y,n,ctx)) goto err;

			}

		}

	else

		{

		BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);

		goto err;

		}

	ret=R;

err:

	if ((ret == NULL) && (in == NULL)) BN_free(R);

	BN_CTX_end(ctx);

	bn_check_top(ret);

	return(ret);

	}

/* BN_mod_inverse_no_branch is a special version of BN_mod_inverse. 

 * It does not contain branches that may leak sensitive information.

 */

static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,

	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)

	{

	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;

	BIGNUM local_A, local_B;

	BIGNUM *pA, *pB;

	BIGNUM *ret=NULL;

	int sign;

	bn_check_top(a);

	bn_check_top(n);

	BN_CTX_start(ctx);

	A = BN_CTX_get(ctx);

	B = BN_CTX_get(ctx);

	X = BN_CTX_get(ctx);

	D = BN_CTX_get(ctx);

	M = BN_CTX_get(ctx);

	Y = BN_CTX_get(ctx);

	T = BN_CTX_get(ctx);

	if (T == NULL) goto err;

	if (in == NULL)

		R=BN_new();

	else

		R=in;

	if (R == NULL) goto err;

	BN_one(X);

	BN_zero(Y);

	if (BN_copy(B,a) == NULL) goto err;

	if (BN_copy(A,n) == NULL) goto err;

	A->neg = 0;

	if (B->neg || (BN_ucmp(B, A) >= 0))

		{

		/* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,

	 	 * BN_div_no_branch will be called eventually.

	 	 */

		pB = &local_B;

		BN_with_flags(pB, B, BN_FLG_CONSTTIME);	

		if (!BN_nnmod(B, pB, A, ctx)) goto err;

		}

	sign = -1;

	/* From  B = a mod |n|,  A = |n|  it follows that

	 *

	 *      0 <= B < A,

	 *     -sign*X*a  ==  B   (mod |n|),

	 *      sign*Y*a  ==  A   (mod |n|).

	 */

	while (!BN_is_zero(B))

		{

		BIGNUM *tmp;

		/*

		 *      0 < B < A,

		 * (*) -sign*X*a  ==  B   (mod |n|),

		 *      sign*Y*a  ==  A   (mod |n|)

		 */

		/* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,

	 	 * BN_div_no_branch will be called eventually.

	 	 */

		pA = &local_A;

		BN_with_flags(pA, A, BN_FLG_CONSTTIME);	

		/* (D, M) := (A/B, A%B) ... */		

		if (!BN_div(D,M,pA,B,ctx)) goto err;

		/* Now

		 *      A = D*B + M;

		 * thus we have

		 * (**)  sign*Y*a  ==  D*B + M   (mod |n|).

		 */

		tmp=A; /* keep the BIGNUM object, the value does not matter */

		/* (A, B) := (B, A mod B) ... */

		A=B;

		B=M;

		/* ... so we have  0 <= B < A  again */

		/* Since the former  M  is now  B  and the former  B  is now  A,

		 * (**) translates into

		 *       sign*Y*a  ==  D*A + B    (mod |n|),

		 * i.e.

		 *       sign*Y*a - D*A  ==  B    (mod |n|).

		 * Similarly, (*) translates into

		 *      -sign*X*a  ==  A          (mod |n|).

		 *

		 * Thus,

		 *   sign*Y*a + D*sign*X*a  ==  B  (mod |n|),

		 * i.e.

		 *        sign*(Y + D*X)*a  ==  B  (mod |n|).

		 *

		 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at

		 *      -sign*X*a  ==  B   (mod |n|),

		 *       sign*Y*a  ==  A   (mod |n|).

		 * Note that  X  and  Y  stay non-negative all the time.

		 */

		if (!BN_mul(tmp,D,X,ctx)) goto err;

		if (!BN_add(tmp,tmp,Y)) goto err;

		M=Y; /* keep the BIGNUM object, the value does not matter */

		Y=X;

		X=tmp;

		sign = -sign;

		}

	/*

	 * The while loop (Euclid's algorithm) ends when

	 *      A == gcd(a,n);

	 * we have

	 *       sign*Y*a  ==  A  (mod |n|),

	 * where  Y  is non-negative.

	 */

	if (sign < 0)

		{

		if (!BN_sub(Y,n,Y)) goto err;

		}

	/* Now  Y*a  ==  A  (mod |n|).  */

	if (BN_is_one(A))

		{

		/* Y*a == 1  (mod |n|) */

		if (!Y->neg && BN_ucmp(Y,n) < 0)

			{

			if (!BN_copy(R,Y)) goto err;

			}

		else

			{

			if (!BN_nnmod(R,Y,n,ctx)) goto err;

			}

		}

	else

		{

		BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE);

		goto err;

		}

	ret=R;

err:

	if ((ret == NULL) && (in == NULL)) BN_free(R);

	BN_CTX_end(ctx);

	bn_check_top(ret);

	return(ret);

	}