sl@0: /* crypto/bn/bn_gcd.c */
sl@0: /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
sl@0:  * All rights reserved.
sl@0:  *
sl@0:  * This package is an SSL implementation written
sl@0:  * by Eric Young (eay@cryptsoft.com).
sl@0:  * The implementation was written so as to conform with Netscapes SSL.
sl@0:  * 
sl@0:  * This library is free for commercial and non-commercial use as long as
sl@0:  * the following conditions are aheared to.  The following conditions
sl@0:  * apply to all code found in this distribution, be it the RC4, RSA,
sl@0:  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
sl@0:  * included with this distribution is covered by the same copyright terms
sl@0:  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
sl@0:  * 
sl@0:  * Copyright remains Eric Young's, and as such any Copyright notices in
sl@0:  * the code are not to be removed.
sl@0:  * If this package is used in a product, Eric Young should be given attribution
sl@0:  * as the author of the parts of the library used.
sl@0:  * This can be in the form of a textual message at program startup or
sl@0:  * in documentation (online or textual) provided with the package.
sl@0:  * 
sl@0:  * Redistribution and use in source and binary forms, with or without
sl@0:  * modification, are permitted provided that the following conditions
sl@0:  * are met:
sl@0:  * 1. Redistributions of source code must retain the copyright
sl@0:  *    notice, this list of conditions and the following disclaimer.
sl@0:  * 2. Redistributions in binary form must reproduce the above copyright
sl@0:  *    notice, this list of conditions and the following disclaimer in the
sl@0:  *    documentation and/or other materials provided with the distribution.
sl@0:  * 3. All advertising materials mentioning features or use of this software
sl@0:  *    must display the following acknowledgement:
sl@0:  *    "This product includes cryptographic software written by
sl@0:  *     Eric Young (eay@cryptsoft.com)"
sl@0:  *    The word 'cryptographic' can be left out if the rouines from the library
sl@0:  *    being used are not cryptographic related :-).
sl@0:  * 4. If you include any Windows specific code (or a derivative thereof) from 
sl@0:  *    the apps directory (application code) you must include an acknowledgement:
sl@0:  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
sl@0:  * 
sl@0:  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
sl@0:  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
sl@0:  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
sl@0:  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
sl@0:  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
sl@0:  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
sl@0:  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
sl@0:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
sl@0:  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
sl@0:  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
sl@0:  * SUCH DAMAGE.
sl@0:  * 
sl@0:  * The licence and distribution terms for any publically available version or
sl@0:  * derivative of this code cannot be changed.  i.e. this code cannot simply be
sl@0:  * copied and put under another distribution licence
sl@0:  * [including the GNU Public Licence.]
sl@0:  */
sl@0: /* ====================================================================
sl@0:  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
sl@0:  *
sl@0:  * Redistribution and use in source and binary forms, with or without
sl@0:  * modification, are permitted provided that the following conditions
sl@0:  * are met:
sl@0:  *
sl@0:  * 1. Redistributions of source code must retain the above copyright
sl@0:  *    notice, this list of conditions and the following disclaimer. 
sl@0:  *
sl@0:  * 2. Redistributions in binary form must reproduce the above copyright
sl@0:  *    notice, this list of conditions and the following disclaimer in
sl@0:  *    the documentation and/or other materials provided with the
sl@0:  *    distribution.
sl@0:  *
sl@0:  * 3. All advertising materials mentioning features or use of this
sl@0:  *    software must display the following acknowledgment:
sl@0:  *    "This product includes software developed by the OpenSSL Project
sl@0:  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
sl@0:  *
sl@0:  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
sl@0:  *    endorse or promote products derived from this software without
sl@0:  *    prior written permission. For written permission, please contact
sl@0:  *    openssl-core@openssl.org.
sl@0:  *
sl@0:  * 5. Products derived from this software may not be called "OpenSSL"
sl@0:  *    nor may "OpenSSL" appear in their names without prior written
sl@0:  *    permission of the OpenSSL Project.
sl@0:  *
sl@0:  * 6. Redistributions of any form whatsoever must retain the following
sl@0:  *    acknowledgment:
sl@0:  *    "This product includes software developed by the OpenSSL Project
sl@0:  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
sl@0:  *
sl@0:  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
sl@0:  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
sl@0:  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
sl@0:  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
sl@0:  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
sl@0:  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
sl@0:  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
sl@0:  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
sl@0:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
sl@0:  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
sl@0:  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
sl@0:  * OF THE POSSIBILITY OF SUCH DAMAGE.
sl@0:  * ====================================================================
sl@0:  *
sl@0:  * This product includes cryptographic software written by Eric Young
sl@0:  * (eay@cryptsoft.com).  This product includes software written by Tim
sl@0:  * Hudson (tjh@cryptsoft.com).
sl@0:  *
sl@0:  */
sl@0: 
sl@0: #include "cryptlib.h"
sl@0: #include "bn_lcl.h"
sl@0: 
sl@0: static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
sl@0: 
sl@0: EXPORT_C int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
sl@0: 	{
sl@0: 	BIGNUM *a,*b,*t;
sl@0: 	int ret=0;
sl@0: 
sl@0: 	bn_check_top(in_a);
sl@0: 	bn_check_top(in_b);
sl@0: 
sl@0: 	BN_CTX_start(ctx);
sl@0: 	a = BN_CTX_get(ctx);
sl@0: 	b = BN_CTX_get(ctx);
sl@0: 	if (a == NULL || b == NULL) goto err;
sl@0: 
sl@0: 	if (BN_copy(a,in_a) == NULL) goto err;
sl@0: 	if (BN_copy(b,in_b) == NULL) goto err;
sl@0: 	a->neg = 0;
sl@0: 	b->neg = 0;
sl@0: 
sl@0: 	if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; }
sl@0: 	t=euclid(a,b);
sl@0: 	if (t == NULL) goto err;
sl@0: 
sl@0: 	if (BN_copy(r,t) == NULL) goto err;
sl@0: 	ret=1;
sl@0: err:
sl@0: 	BN_CTX_end(ctx);
sl@0: 	bn_check_top(r);
sl@0: 	return(ret);
sl@0: 	}
sl@0: 
sl@0: static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
sl@0: 	{
sl@0: 	BIGNUM *t;
sl@0: 	int shifts=0;
sl@0: 
sl@0: 	bn_check_top(a);
sl@0: 	bn_check_top(b);
sl@0: 
sl@0: 	/* 0 <= b <= a */
sl@0: 	while (!BN_is_zero(b))
sl@0: 		{
sl@0: 		/* 0 < b <= a */
sl@0: 
sl@0: 		if (BN_is_odd(a))
sl@0: 			{
sl@0: 			if (BN_is_odd(b))
sl@0: 				{
sl@0: 				if (!BN_sub(a,a,b)) goto err;
sl@0: 				if (!BN_rshift1(a,a)) goto err;
sl@0: 				if (BN_cmp(a,b) < 0)
sl@0: 					{ t=a; a=b; b=t; }
sl@0: 				}
sl@0: 			else		/* a odd - b even */
sl@0: 				{
sl@0: 				if (!BN_rshift1(b,b)) goto err;
sl@0: 				if (BN_cmp(a,b) < 0)
sl@0: 					{ t=a; a=b; b=t; }
sl@0: 				}
sl@0: 			}
sl@0: 		else			/* a is even */
sl@0: 			{
sl@0: 			if (BN_is_odd(b))
sl@0: 				{
sl@0: 				if (!BN_rshift1(a,a)) goto err;
sl@0: 				if (BN_cmp(a,b) < 0)
sl@0: 					{ t=a; a=b; b=t; }
sl@0: 				}
sl@0: 			else		/* a even - b even */
sl@0: 				{
sl@0: 				if (!BN_rshift1(a,a)) goto err;
sl@0: 				if (!BN_rshift1(b,b)) goto err;
sl@0: 				shifts++;
sl@0: 				}
sl@0: 			}
sl@0: 		/* 0 <= b <= a */
sl@0: 		}
sl@0: 
sl@0: 	if (shifts)
sl@0: 		{
sl@0: 		if (!BN_lshift(a,a,shifts)) goto err;
sl@0: 		}
sl@0: 	bn_check_top(a);
sl@0: 	return(a);
sl@0: err:
sl@0: 	return(NULL);
sl@0: 	}
sl@0: 
sl@0: 
sl@0: /* solves ax == 1 (mod n) */
sl@0: static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
sl@0:         const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
sl@0: EXPORT_C BIGNUM *BN_mod_inverse(BIGNUM *in,
sl@0: 	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
sl@0: 	{
sl@0: 	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
sl@0: 	BIGNUM *ret=NULL;
sl@0: 	int sign;
sl@0: 	if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0))
sl@0: 		{
sl@0: 		return BN_mod_inverse_no_branch(in, a, n, ctx);
sl@0: 		}
sl@0: 
sl@0: 	bn_check_top(a);
sl@0: 	bn_check_top(n);
sl@0: 
sl@0: 	BN_CTX_start(ctx);
sl@0: 	A = BN_CTX_get(ctx);
sl@0: 	B = BN_CTX_get(ctx);
sl@0: 	X = BN_CTX_get(ctx);
sl@0: 	D = BN_CTX_get(ctx);
sl@0: 	M = BN_CTX_get(ctx);
sl@0: 	Y = BN_CTX_get(ctx);
sl@0: 	T = BN_CTX_get(ctx);
sl@0: 	if (T == NULL) goto err;
sl@0: 
sl@0: 	if (in == NULL)
sl@0: 		R=BN_new();
sl@0: 	else
sl@0: 		R=in;
sl@0: 	if (R == NULL) goto err;
sl@0: 
sl@0: 	BN_one(X);
sl@0: 	BN_zero(Y);
sl@0: 	if (BN_copy(B,a) == NULL) goto err;
sl@0: 	if (BN_copy(A,n) == NULL) goto err;
sl@0: 	A->neg = 0;
sl@0: 	if (B->neg || (BN_ucmp(B, A) >= 0))
sl@0: 		{
sl@0: 		if (!BN_nnmod(B, B, A, ctx)) goto err;
sl@0: 		}
sl@0: 	sign = -1;
sl@0: 	/* From  B = a mod |n|,  A = |n|  it follows that
sl@0: 	 *
sl@0: 	 *      0 <= B < A,
sl@0: 	 *     -sign*X*a  ==  B   (mod |n|),
sl@0: 	 *      sign*Y*a  ==  A   (mod |n|).
sl@0: 	 */
sl@0: 
sl@0: 	if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048)))
sl@0: 		{
sl@0: 		/* Binary inversion algorithm; requires odd modulus.
sl@0: 		 * This is faster than the general algorithm if the modulus
sl@0: 		 * is sufficiently small (about 400 .. 500 bits on 32-bit
sl@0: 		 * sytems, but much more on 64-bit systems) */
sl@0: 		int shift;
sl@0: 		
sl@0: 		while (!BN_is_zero(B))
sl@0: 			{
sl@0: 			/*
sl@0: 			 *      0 < B < |n|,
sl@0: 			 *      0 < A <= |n|,
sl@0: 			 * (1) -sign*X*a  ==  B   (mod |n|),
sl@0: 			 * (2)  sign*Y*a  ==  A   (mod |n|)
sl@0: 			 */
sl@0: 
sl@0: 			/* Now divide  B  by the maximum possible power of two in the integers,
sl@0: 			 * and divide  X  by the same value mod |n|.
sl@0: 			 * When we're done, (1) still holds. */
sl@0: 			shift = 0;
sl@0: 			while (!BN_is_bit_set(B, shift)) /* note that 0 < B */
sl@0: 				{
sl@0: 				shift++;
sl@0: 				
sl@0: 				if (BN_is_odd(X))
sl@0: 					{
sl@0: 					if (!BN_uadd(X, X, n)) goto err;
sl@0: 					}
sl@0: 				/* now X is even, so we can easily divide it by two */
sl@0: 				if (!BN_rshift1(X, X)) goto err;
sl@0: 				}
sl@0: 			if (shift > 0)
sl@0: 				{
sl@0: 				if (!BN_rshift(B, B, shift)) goto err;
sl@0: 				}
sl@0: 
sl@0: 
sl@0: 			/* Same for  A  and  Y.  Afterwards, (2) still holds. */
sl@0: 			shift = 0;
sl@0: 			while (!BN_is_bit_set(A, shift)) /* note that 0 < A */
sl@0: 				{
sl@0: 				shift++;
sl@0: 				
sl@0: 				if (BN_is_odd(Y))
sl@0: 					{
sl@0: 					if (!BN_uadd(Y, Y, n)) goto err;
sl@0: 					}
sl@0: 				/* now Y is even */
sl@0: 				if (!BN_rshift1(Y, Y)) goto err;
sl@0: 				}
sl@0: 			if (shift > 0)
sl@0: 				{
sl@0: 				if (!BN_rshift(A, A, shift)) goto err;
sl@0: 				}
sl@0: 
sl@0: 			
sl@0: 			/* We still have (1) and (2).
sl@0: 			 * Both  A  and  B  are odd.
sl@0: 			 * The following computations ensure that
sl@0: 			 *
sl@0: 			 *     0 <= B < |n|,
sl@0: 			 *      0 < A < |n|,
sl@0: 			 * (1) -sign*X*a  ==  B   (mod |n|),
sl@0: 			 * (2)  sign*Y*a  ==  A   (mod |n|),
sl@0: 			 *
sl@0: 			 * and that either  A  or  B  is even in the next iteration.
sl@0: 			 */
sl@0: 			if (BN_ucmp(B, A) >= 0)
sl@0: 				{
sl@0: 				/* -sign*(X + Y)*a == B - A  (mod |n|) */
sl@0: 				if (!BN_uadd(X, X, Y)) goto err;
sl@0: 				/* NB: we could use BN_mod_add_quick(X, X, Y, n), but that
sl@0: 				 * actually makes the algorithm slower */
sl@0: 				if (!BN_usub(B, B, A)) goto err;
sl@0: 				}
sl@0: 			else
sl@0: 				{
sl@0: 				/*  sign*(X + Y)*a == A - B  (mod |n|) */
sl@0: 				if (!BN_uadd(Y, Y, X)) goto err;
sl@0: 				/* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */
sl@0: 				if (!BN_usub(A, A, B)) goto err;
sl@0: 				}
sl@0: 			}
sl@0: 		}
sl@0: 	else
sl@0: 		{
sl@0: 		/* general inversion algorithm */
sl@0: 
sl@0: 		while (!BN_is_zero(B))
sl@0: 			{
sl@0: 			BIGNUM *tmp;
sl@0: 			
sl@0: 			/*
sl@0: 			 *      0 < B < A,
sl@0: 			 * (*) -sign*X*a  ==  B   (mod |n|),
sl@0: 			 *      sign*Y*a  ==  A   (mod |n|)
sl@0: 			 */
sl@0: 			
sl@0: 			/* (D, M) := (A/B, A%B) ... */
sl@0: 			if (BN_num_bits(A) == BN_num_bits(B))
sl@0: 				{
sl@0: 				if (!BN_one(D)) goto err;
sl@0: 				if (!BN_sub(M,A,B)) goto err;
sl@0: 				}
sl@0: 			else if (BN_num_bits(A) == BN_num_bits(B) + 1)
sl@0: 				{
sl@0: 				/* A/B is 1, 2, or 3 */
sl@0: 				if (!BN_lshift1(T,B)) goto err;
sl@0: 				if (BN_ucmp(A,T) < 0)
sl@0: 					{
sl@0: 					/* A < 2*B, so D=1 */
sl@0: 					if (!BN_one(D)) goto err;
sl@0: 					if (!BN_sub(M,A,B)) goto err;
sl@0: 					}
sl@0: 				else
sl@0: 					{
sl@0: 					/* A >= 2*B, so D=2 or D=3 */
sl@0: 					if (!BN_sub(M,A,T)) goto err;
sl@0: 					if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */
sl@0: 					if (BN_ucmp(A,D) < 0)
sl@0: 						{
sl@0: 						/* A < 3*B, so D=2 */
sl@0: 						if (!BN_set_word(D,2)) goto err;
sl@0: 						/* M (= A - 2*B) already has the correct value */
sl@0: 						}
sl@0: 					else
sl@0: 						{
sl@0: 						/* only D=3 remains */
sl@0: 						if (!BN_set_word(D,3)) goto err;
sl@0: 						/* currently  M = A - 2*B,  but we need  M = A - 3*B */
sl@0: 						if (!BN_sub(M,M,B)) goto err;
sl@0: 						}
sl@0: 					}
sl@0: 				}
sl@0: 			else
sl@0: 				{
sl@0: 				if (!BN_div(D,M,A,B,ctx)) goto err;
sl@0: 				}
sl@0: 			
sl@0: 			/* Now
sl@0: 			 *      A = D*B + M;
sl@0: 			 * thus we have
sl@0: 			 * (**)  sign*Y*a  ==  D*B + M   (mod |n|).
sl@0: 			 */
sl@0: 			
sl@0: 			tmp=A; /* keep the BIGNUM object, the value does not matter */
sl@0: 			
sl@0: 			/* (A, B) := (B, A mod B) ... */
sl@0: 			A=B;
sl@0: 			B=M;
sl@0: 			/* ... so we have  0 <= B < A  again */
sl@0: 			
sl@0: 			/* Since the former  M  is now  B  and the former  B  is now  A,
sl@0: 			 * (**) translates into
sl@0: 			 *       sign*Y*a  ==  D*A + B    (mod |n|),
sl@0: 			 * i.e.
sl@0: 			 *       sign*Y*a - D*A  ==  B    (mod |n|).
sl@0: 			 * Similarly, (*) translates into
sl@0: 			 *      -sign*X*a  ==  A          (mod |n|).
sl@0: 			 *
sl@0: 			 * Thus,
sl@0: 			 *   sign*Y*a + D*sign*X*a  ==  B  (mod |n|),
sl@0: 			 * i.e.
sl@0: 			 *        sign*(Y + D*X)*a  ==  B  (mod |n|).
sl@0: 			 *
sl@0: 			 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at
sl@0: 			 *      -sign*X*a  ==  B   (mod |n|),
sl@0: 			 *       sign*Y*a  ==  A   (mod |n|).
sl@0: 			 * Note that  X  and  Y  stay non-negative all the time.
sl@0: 			 */
sl@0: 			
sl@0: 			/* most of the time D is very small, so we can optimize tmp := D*X+Y */
sl@0: 			if (BN_is_one(D))
sl@0: 				{
sl@0: 				if (!BN_add(tmp,X,Y)) goto err;
sl@0: 				}
sl@0: 			else
sl@0: 				{
sl@0: 				if (BN_is_word(D,2))
sl@0: 					{
sl@0: 					if (!BN_lshift1(tmp,X)) goto err;
sl@0: 					}
sl@0: 				else if (BN_is_word(D,4))
sl@0: 					{
sl@0: 					if (!BN_lshift(tmp,X,2)) goto err;
sl@0: 					}
sl@0: 				else if (D->top == 1)
sl@0: 					{
sl@0: 					if (!BN_copy(tmp,X)) goto err;
sl@0: 					if (!BN_mul_word(tmp,D->d[0])) goto err;
sl@0: 					}
sl@0: 				else
sl@0: 					{
sl@0: 					if (!BN_mul(tmp,D,X,ctx)) goto err;
sl@0: 					}
sl@0: 				if (!BN_add(tmp,tmp,Y)) goto err;
sl@0: 				}
sl@0: 			
sl@0: 			M=Y; /* keep the BIGNUM object, the value does not matter */
sl@0: 			Y=X;
sl@0: 			X=tmp;
sl@0: 			sign = -sign;
sl@0: 			}
sl@0: 		}
sl@0: 		
sl@0: 	/*
sl@0: 	 * The while loop (Euclid's algorithm) ends when
sl@0: 	 *      A == gcd(a,n);
sl@0: 	 * we have
sl@0: 	 *       sign*Y*a  ==  A  (mod |n|),
sl@0: 	 * where  Y  is non-negative.
sl@0: 	 */
sl@0: 
sl@0: 	if (sign < 0)
sl@0: 		{
sl@0: 		if (!BN_sub(Y,n,Y)) goto err;
sl@0: 		}
sl@0: 	/* Now  Y*a  ==  A  (mod |n|).  */
sl@0: 	
sl@0: 
sl@0: 	if (BN_is_one(A))
sl@0: 		{
sl@0: 		/* Y*a == 1  (mod |n|) */
sl@0: 		if (!Y->neg && BN_ucmp(Y,n) < 0)
sl@0: 			{
sl@0: 			if (!BN_copy(R,Y)) goto err;
sl@0: 			}
sl@0: 		else
sl@0: 			{
sl@0: 			if (!BN_nnmod(R,Y,n,ctx)) goto err;
sl@0: 			}
sl@0: 		}
sl@0: 	else
sl@0: 		{
sl@0: 		BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);
sl@0: 		goto err;
sl@0: 		}
sl@0: 	ret=R;
sl@0: err:
sl@0: 	if ((ret == NULL) && (in == NULL)) BN_free(R);
sl@0: 	BN_CTX_end(ctx);
sl@0: 	bn_check_top(ret);
sl@0: 	return(ret);
sl@0: 	}
sl@0: 
sl@0: 
sl@0: /* BN_mod_inverse_no_branch is a special version of BN_mod_inverse. 
sl@0:  * It does not contain branches that may leak sensitive information.
sl@0:  */
sl@0: static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
sl@0: 	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
sl@0: 	{
sl@0: 	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
sl@0: 	BIGNUM local_A, local_B;
sl@0: 	BIGNUM *pA, *pB;
sl@0: 	BIGNUM *ret=NULL;
sl@0: 	int sign;
sl@0: 
sl@0: 	bn_check_top(a);
sl@0: 	bn_check_top(n);
sl@0: 
sl@0: 	BN_CTX_start(ctx);
sl@0: 	A = BN_CTX_get(ctx);
sl@0: 	B = BN_CTX_get(ctx);
sl@0: 	X = BN_CTX_get(ctx);
sl@0: 	D = BN_CTX_get(ctx);
sl@0: 	M = BN_CTX_get(ctx);
sl@0: 	Y = BN_CTX_get(ctx);
sl@0: 	T = BN_CTX_get(ctx);
sl@0: 	if (T == NULL) goto err;
sl@0: 
sl@0: 	if (in == NULL)
sl@0: 		R=BN_new();
sl@0: 	else
sl@0: 		R=in;
sl@0: 	if (R == NULL) goto err;
sl@0: 
sl@0: 	BN_one(X);
sl@0: 	BN_zero(Y);
sl@0: 	if (BN_copy(B,a) == NULL) goto err;
sl@0: 	if (BN_copy(A,n) == NULL) goto err;
sl@0: 	A->neg = 0;
sl@0: 
sl@0: 	if (B->neg || (BN_ucmp(B, A) >= 0))
sl@0: 		{
sl@0: 		/* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
sl@0: 	 	 * BN_div_no_branch will be called eventually.
sl@0: 	 	 */
sl@0: 		pB = &local_B;
sl@0: 		BN_with_flags(pB, B, BN_FLG_CONSTTIME);	
sl@0: 		if (!BN_nnmod(B, pB, A, ctx)) goto err;
sl@0: 		}
sl@0: 	sign = -1;
sl@0: 	/* From  B = a mod |n|,  A = |n|  it follows that
sl@0: 	 *
sl@0: 	 *      0 <= B < A,
sl@0: 	 *     -sign*X*a  ==  B   (mod |n|),
sl@0: 	 *      sign*Y*a  ==  A   (mod |n|).
sl@0: 	 */
sl@0: 
sl@0: 	while (!BN_is_zero(B))
sl@0: 		{
sl@0: 		BIGNUM *tmp;
sl@0: 		
sl@0: 		/*
sl@0: 		 *      0 < B < A,
sl@0: 		 * (*) -sign*X*a  ==  B   (mod |n|),
sl@0: 		 *      sign*Y*a  ==  A   (mod |n|)
sl@0: 		 */
sl@0: 
sl@0: 		/* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
sl@0: 	 	 * BN_div_no_branch will be called eventually.
sl@0: 	 	 */
sl@0: 		pA = &local_A;
sl@0: 		BN_with_flags(pA, A, BN_FLG_CONSTTIME);	
sl@0: 		
sl@0: 		/* (D, M) := (A/B, A%B) ... */		
sl@0: 		if (!BN_div(D,M,pA,B,ctx)) goto err;
sl@0: 		
sl@0: 		/* Now
sl@0: 		 *      A = D*B + M;
sl@0: 		 * thus we have
sl@0: 		 * (**)  sign*Y*a  ==  D*B + M   (mod |n|).
sl@0: 		 */
sl@0: 		
sl@0: 		tmp=A; /* keep the BIGNUM object, the value does not matter */
sl@0: 		
sl@0: 		/* (A, B) := (B, A mod B) ... */
sl@0: 		A=B;
sl@0: 		B=M;
sl@0: 		/* ... so we have  0 <= B < A  again */
sl@0: 		
sl@0: 		/* Since the former  M  is now  B  and the former  B  is now  A,
sl@0: 		 * (**) translates into
sl@0: 		 *       sign*Y*a  ==  D*A + B    (mod |n|),
sl@0: 		 * i.e.
sl@0: 		 *       sign*Y*a - D*A  ==  B    (mod |n|).
sl@0: 		 * Similarly, (*) translates into
sl@0: 		 *      -sign*X*a  ==  A          (mod |n|).
sl@0: 		 *
sl@0: 		 * Thus,
sl@0: 		 *   sign*Y*a + D*sign*X*a  ==  B  (mod |n|),
sl@0: 		 * i.e.
sl@0: 		 *        sign*(Y + D*X)*a  ==  B  (mod |n|).
sl@0: 		 *
sl@0: 		 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at
sl@0: 		 *      -sign*X*a  ==  B   (mod |n|),
sl@0: 		 *       sign*Y*a  ==  A   (mod |n|).
sl@0: 		 * Note that  X  and  Y  stay non-negative all the time.
sl@0: 		 */
sl@0: 			
sl@0: 		if (!BN_mul(tmp,D,X,ctx)) goto err;
sl@0: 		if (!BN_add(tmp,tmp,Y)) goto err;
sl@0: 
sl@0: 		M=Y; /* keep the BIGNUM object, the value does not matter */
sl@0: 		Y=X;
sl@0: 		X=tmp;
sl@0: 		sign = -sign;
sl@0: 		}
sl@0: 		
sl@0: 	/*
sl@0: 	 * The while loop (Euclid's algorithm) ends when
sl@0: 	 *      A == gcd(a,n);
sl@0: 	 * we have
sl@0: 	 *       sign*Y*a  ==  A  (mod |n|),
sl@0: 	 * where  Y  is non-negative.
sl@0: 	 */
sl@0: 
sl@0: 	if (sign < 0)
sl@0: 		{
sl@0: 		if (!BN_sub(Y,n,Y)) goto err;
sl@0: 		}
sl@0: 	/* Now  Y*a  ==  A  (mod |n|).  */
sl@0: 
sl@0: 	if (BN_is_one(A))
sl@0: 		{
sl@0: 		/* Y*a == 1  (mod |n|) */
sl@0: 		if (!Y->neg && BN_ucmp(Y,n) < 0)
sl@0: 			{
sl@0: 			if (!BN_copy(R,Y)) goto err;
sl@0: 			}
sl@0: 		else
sl@0: 			{
sl@0: 			if (!BN_nnmod(R,Y,n,ctx)) goto err;
sl@0: 			}
sl@0: 		}
sl@0: 	else
sl@0: 		{
sl@0: 		BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE);
sl@0: 		goto err;
sl@0: 		}
sl@0: 	ret=R;
sl@0: err:
sl@0: 	if ((ret == NULL) && (in == NULL)) BN_free(R);
sl@0: 	BN_CTX_end(ctx);
sl@0: 	bn_check_top(ret);
sl@0: 	return(ret);
sl@0: 	}