X-Git-Url: https://git.openssl.org/gitweb/?p=openssl.git;a=blobdiff_plain;f=crypto%2Fbn%2Fbn_gcd.c;h=233e3f53322bd9e114ff0d815b64aa9b7001d8e9;hp=ea6816a43fc32a6deb82a68f3fb552e3bf19fb0c;hb=1d97c8435171a7af575f73c526d79e1ef0ee5960;hpb=dcbd0d74d5d2732f725228adedab8d689801d20e

diff --git a/crypto/bn/bn_gcd.c b/crypto/bn/bn_gcd.c
index ea6816a43f..233e3f5332 100644
--- a/crypto/bn/bn_gcd.c
+++ b/crypto/bn/bn_gcd.c
@@ -56,7 +56,7 @@
  * [including the GNU Public Licence.]
  */
 /* ====================================================================
- * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.
+ * 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
@@ -109,6 +109,8 @@
  *
  */
 
+
+
 #include "cryptlib.h"
 #include "bn_lcl.h"
 
@@ -140,6 +142,7 @@ int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
 	ret=1;
 err:
 	BN_CTX_end(ctx);
+	bn_check_top(r);
 	return(ret);
 	}
 
@@ -194,6 +197,7 @@ static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
 		{
 		if (!BN_lshift(a,a,shifts)) goto err;
 		}
+	bn_check_top(a);
 	return(a);
 err:
 	return(NULL);
@@ -201,13 +205,35 @@ err:
 
 
 /* solves ax == 1 (mod n) */
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
+        const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
+
 BIGNUM *BN_mod_inverse(BIGNUM *in,
 	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
 	{
-	BIGNUM *A,*B,*X,*Y,*M,*D,*R=NULL;
+	BIGNUM *rv;
+	int noinv;
+	rv = int_bn_mod_inverse(in, a, n, ctx, &noinv);
+	if (noinv)
+		BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);
+	return rv;
+	}
+
+BIGNUM *int_bn_mod_inverse(BIGNUM *in,
+	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx, int *pnoinv)
+	{
+	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
 	BIGNUM *ret=NULL;
 	int sign;
 
+	if (pnoinv)
+		*pnoinv = 0;
+
+	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);
 
@@ -218,7 +244,8 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
 	D = BN_CTX_get(ctx);
 	M = BN_CTX_get(ctx);
 	Y = BN_CTX_get(ctx);
-	if (Y == NULL) goto err;
+	T = BN_CTX_get(ctx);
+	if (T == NULL) goto err;
 
 	if (in == NULL)
 		R=BN_new();
@@ -236,69 +263,387 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
 		if (!BN_nnmod(B, B, A, ctx)) goto err;
 		}
 	sign = -1;
-	/* From  B = a mod |n|,  A = |n|  it follows that
+	/*-
+	 * 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
+		{
+		if (pnoinv)
+			*pnoinv = 1;
+		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,
-	 *           X*a  ==  B   (mod |n|),
-	 *     -sign*Y*a  ==  A   (mod |n|).
+	 *     -sign*X*a  ==  B   (mod |n|),
+	 *      sign*Y*a  ==  A   (mod |n|).
 	 */
 
 	while (!BN_is_zero(B))
 		{
 		BIGNUM *tmp;
-
-		/*
+		
+		/*-
 		 *      0 < B < A,
-		 * (*)       X*a  ==  B   (mod |n|),
-		 *     -sign*Y*a  ==  A   (mod |n|)
+		 * (*) -sign*X*a  ==  B   (mod |n|),
+		 *      sign*Y*a  ==  A   (mod |n|)
 		 */
 
-		if (!BN_div(D,M,A,B,ctx)) goto err;
-		/* Now
+		/* 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|).
+		 * (**)  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,
+		
+		/*-
+		 * Since the former  M  is now  B  and the former  B  is now  A,
 		 * (**) translates into
-		 *      -sign*Y*a  ==  D*A + B    (mod |n|),
+		 *       sign*Y*a  ==  D*A + B    (mod |n|),
 		 * i.e.
-		 *      -sign*Y*a - D*A  ==  B    (mod |n|).
+		 *       sign*Y*a - D*A  ==  B    (mod |n|).
 		 * Similarly, (*) translates into
-		 *      X*a  ==  A          (mod |n|).
+		 *      -sign*X*a  ==  A          (mod |n|).
 		 *
 		 * Thus,
-		 *      -sign*Y*a - D*X*a  ==  B  (mod |n|),
+		 *   sign*Y*a + D*sign*X*a  ==  B  (mod |n|),
 		 * i.e.
-		 *      -sign*(Y + D*X)*a  ==  B  (mod |n|).
+		 *        sign*(Y + D*X)*a  ==  B  (mod |n|).
 		 *
 		 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at
-		 *            X*a  ==  B   (mod |n|),
-		 *      -sign*Y*a  ==  A   (mod |n|).
+		 *      -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 ends when
+		
+	/*-
+	 * The while loop (Euclid's algorithm) ends when
 	 *      A == gcd(a,n);
 	 * we have
-	 *      -sign*Y*a  ==  A  (mod |n|),
+	 *       sign*Y*a  ==  A  (mod |n|),
 	 * where  Y  is non-negative.
 	 */
 
@@ -307,22 +652,28 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
 		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 (!BN_mod(R,Y,n,ctx)) goto err;
+		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);
+		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);
 	}
-