From: Andy Polyakov <appro@openssl.org>
Date: Mon, 11 Jun 2007 16:15:10 +0000 (+0000)
Subject: Eliminate conditional final subtraction in Montgomery multiplication
X-Git-Tag: OpenSSL_0_9_8f~102
X-Git-Url: https://git.librecmc.org/?a=commitdiff_plain;h=1a56614af2b015fdb79fa1b6df56820d08110523;p=oweals%2Fopenssl.git

Eliminate conditional final subtraction in Montgomery multiplication
[from HEAD].
---

diff --git a/crypto/bn/bn_mont.c b/crypto/bn/bn_mont.c
index 961ca67ea1..bf45fe916d 100644
--- a/crypto/bn/bn_mont.c
+++ b/crypto/bn/bn_mont.c
@@ -176,7 +176,6 @@ int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 
 	max=(nl+al+1); /* allow for overflow (no?) XXX */
 	if (bn_wexpand(r,max) == NULL) goto err;
-	if (bn_wexpand(ret,max) == NULL) goto err;
 
 	r->neg=a->neg^n->neg;
 	np=n->d;
@@ -228,19 +227,76 @@ int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 		}
 	bn_correct_top(r);
 	
-	/* mont->ri will be a multiple of the word size */
-#if 0
-	BN_rshift(ret,r,mont->ri);
-#else
-	ret->neg = r->neg;
-	x=ri;
+	/* 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[x]);
-	if (r->top < x)
-		al=0;
-	else
-		al=r->top-x;
+	ap=&(r->d[ri]);
+	nrp=ap;
+
+	/* This 'if' denotes violation of 2*M<r^(n-1) boundary condition
+	 * formulated by C.D.Walter in "Montgomery exponentiation needs
+	 * no final subtractions." Incurred branch can disclose only
+	 * information about modulus length, which is not really secret. */
+	if ((mont->N.d[ri-1]>>(BN_BITS2-2))!=0)
+		{
+		size_t m1,m2;
+
+		v=bn_sub_words(rp,ap,mont->N.d,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;
+# 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)
 		{
@@ -258,7 +314,7 @@ int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 	al+=4;
 	for (; i<al; i++)
 		rp[i]=ap[i];
-#endif
+# endif
 #else /* !MONT_WORD */ 
 	BIGNUM *t1,*t2;
 
@@ -278,10 +334,12 @@ int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 	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: