bn_exp.c: further optimizations using more ideas from

http://eprint.iacr.org/2011/239.

crypto/bn/asm/x86_64-mont5.pl

@@ -607,7 +607,6 @@ $code.=<<___;
 	add	$A[1],$N[1]		# np[j]*m1+ap[j]*bp[i]+tp[j]
 	lea	4($j),$j		# j+=2
 	adc	\$0,%rdx
-	mov	$N[1],(%rsp)		# tp[j-1]
 	mov	%rdx,$N[0]
 	jmp	.Linner4x
 .align	16
@@ -626,7 +625,7 @@ $code.=<<___;
 	adc	\$0,%rdx
 	add	$A[0],$N[0]
 	adc	\$0,%rdx
-	mov	$N[0],-24(%rsp,$j,8)	# tp[j-1]
+	mov	$N[1],-32(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$N[1]
 
 	mulq	$m0			# ap[j]*bp[i]
@@ -643,7 +642,7 @@ $code.=<<___;
 	adc	\$0,%rdx
 	add	$A[1],$N[1]
 	adc	\$0,%rdx
-	mov	$N[1],-16(%rsp,$j,8)	# tp[j-1]
+	mov	$N[0],-24(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$N[0]
 
 	mulq	$m0			# ap[j]*bp[i]
@@ -660,7 +659,7 @@ $code.=<<___;
 	adc	\$0,%rdx
 	add	$A[0],$N[0]
 	adc	\$0,%rdx
-	mov	$N[0],-8(%rsp,$j,8)	# tp[j-1]
+	mov	$N[1],-16(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$N[1]
 
 	mulq	$m0			# ap[j]*bp[i]
@@ -678,7 +677,7 @@ $code.=<<___;
 	adc	\$0,%rdx
 	add	$A[1],$N[1]
 	adc	\$0,%rdx
-	mov	$N[1],-32(%rsp,$j,8)	# tp[j-1]
+	mov	$N[0],-40(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$N[0]
 	cmp	$num,$j
 	jl	.Linner4x
@@ -697,7 +696,7 @@ $code.=<<___;
 	adc	\$0,%rdx
 	add	$A[0],$N[0]
 	adc	\$0,%rdx
-	mov	$N[0],-24(%rsp,$j,8)	# tp[j-1]
+	mov	$N[1],-32(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$N[1]
 
 	mulq	$m0			# ap[j]*bp[i]
@@ -715,10 +714,11 @@ $code.=<<___;
 	adc	\$0,%rdx
 	add	$A[1],$N[1]
 	adc	\$0,%rdx
-	mov	$N[1],-16(%rsp,$j,8)	# tp[j-1]
+	mov	$N[0],-24(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$N[0]
 
 	movq	%xmm0,$m0		# bp[i+1]
+	mov	$N[1],-16(%rsp,$j,8)	# tp[j-1]
 
 	xor	$N[1],$N[1]
 	add	$A[0],$N[0]
@@ -831,6 +831,10 @@ ___
 {
 my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%rdx","%r8", "%r9") : # Win64 order
 				("%rdi","%rsi","%rdx","%rcx"); # Unix order
+my $out=$inp;
+my $STRIDE=2**5*8;
+my $N=$STRIDE/4;
+
 $code.=<<___;
 .globl	bn_scatter5
 .type	bn_scatter5,\@abi-omnipotent
@@ -849,6 +853,61 @@ bn_scatter5:
 .Lscatter_epilogue:
 	ret
 .size	bn_scatter5,.-bn_scatter5
+
+.globl	bn_gather5
+.type	bn_gather5,\@abi-omnipotent
+.align	16
+bn_gather5:
+___
+$code.=<<___ if ($win64);
+.LSEH_begin_bn_gather5:
+	# I can't trust assembler to use specific encoding:-(
+	.byte	0x48,0x83,0xec,0x28		#sub	\$0x28,%rsp
+	.byte	0x0f,0x29,0x34,0x24		#movaps	%xmm6,(%rsp)
+	.byte	0x0f,0x29,0x7c,0x24,0x10	#movdqa	%xmm7,0x10(%rsp)
+___
+$code.=<<___;
+	mov	$idx,%r11
+	shr	\$`log($N/8)/log(2)`,$idx
+	and	\$`$N/8-1`,%r11
+	not	$idx
+	lea	.Lmagic_masks(%rip),%rax
+	and	\$`2**5/($N/8)-1`,$idx	# 5 is "window size"
+	lea	96($tbl,%r11,8),$tbl	# pointer within 1st cache line
+	movq	0(%rax,$idx,8),%xmm4	# set of masks denoting which
+	movq	8(%rax,$idx,8),%xmm5	# cache line contains element
+	movq	16(%rax,$idx,8),%xmm6	# denoted by 7th argument
+	movq	24(%rax,$idx,8),%xmm7
+	jmp	.Lgather
+.align	16
+.Lgather:
+	movq	`0*$STRIDE/4-96`($tbl),%xmm0
+	movq	`1*$STRIDE/4-96`($tbl),%xmm1
+	pand	%xmm4,%xmm0
+	movq	`2*$STRIDE/4-96`($tbl),%xmm2
+	pand	%xmm5,%xmm1
+	movq	`3*$STRIDE/4-96`($tbl),%xmm3
+	pand	%xmm6,%xmm2
+	por	%xmm1,%xmm0
+	pand	%xmm7,%xmm3
+	por	%xmm2,%xmm0
+	lea	$STRIDE($tbl),$tbl
+	por	%xmm3,%xmm0
+
+	movq	%xmm0,($out)		# m0=bp[0]
+	lea	8($out),$out
+	sub	\$1,$num
+	jnz	.Lgather
+___
+$code.=<<___ if ($win64);
+	movaps	%xmm6,(%rsp)
+	movaps	%xmm7,0x10(%rsp)
+	lea	0x28(%rsp),%rsp
+___
+$code.=<<___;
+	ret
+.LSEH_end_bn_gather5:
+.size	bn_gather5,.-bn_gather5
 ___
 }
 $code.=<<___;
@@ -980,6 +1039,10 @@ mul_handler:
 	.rva	.LSEH_end_bn_mul4x_mont_gather5
 	.rva	.LSEH_info_bn_mul4x_mont_gather5
 
+	.rva	.LSEH_begin_bn_gather5
+	.rva	.LSEH_end_bn_gather5
+	.rva	.LSEH_info_bn_gather5
+
 .section	.xdata
 .align	8
 .LSEH_info_bn_mul_mont_gather5:
@@ -992,6 +1055,12 @@ mul_handler:
 	.rva	mul_handler
 	.rva	.Lmul4x_alloca,.Lmul4x_body,.Lmul4x_epilogue	# HandlerData[]
 .align	8
+.LSEH_info_bn_gather5:
+        .byte   0x01,0x0d,0x05,0x00
+        .byte   0x0d,0x78,0x01,0x00	#movaps	0x10(rsp),xmm7
+        .byte   0x08,0x68,0x00,0x00	#movaps	(rsp),xmm6
+        .byte   0x04,0x42,0x00,0x00	#sub	rsp,0x28
+.align	8
 ___
 }
 

crypto/bn/bn_exp.c

@@ -535,23 +535,17 @@ err:
  * as cache lines are concerned.  The following functions are used to transfer a BIGNUM
  * from/to that table. */
 
-static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
+static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
 	{
 	size_t i, j;
 
-	if (bn_wexpand(b, top) == NULL)
-		return 0;
-	while (b->top < top)
-		{
-		b->d[b->top++] = 0;
-		}
-	
+	if (top > b->top)
+		top = b->top; /* this works because 'buf' is explicitly zeroed */
 	for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
 		{
 		buf[j] = ((unsigned char*)b->d)[i];
 		}
 
-	bn_correct_top(b);
 	return 1;
 	}
 
@@ -587,14 +581,13 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 	{
 	int i,bits,ret=0,window,wvalue;
 	int top;
- 	BIGNUM *r;
 	BN_MONT_CTX *mont=NULL;
 
 	int numPowers;
 	unsigned char *powerbufFree=NULL;
 	int powerbufLen = 0;
 	unsigned char *powerbuf=NULL;
-	BIGNUM computeTemp, *am=NULL;
+	BIGNUM tmp, am;
 
 	bn_check_top(a);
 	bn_check_top(p);
@@ -614,10 +607,7 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 		return ret;
 		}
 
- 	/* Initialize BIGNUM context and allocate intermediate result */
 	BN_CTX_start(ctx);
-	r = BN_CTX_get(ctx);
-	if (r == NULL) goto err;
 
 	/* Allocate a montgomery context if it was not supplied by the caller.
 	 * If this is not done, things will break in the montgomery part.
@@ -635,25 +625,13 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 #if defined(OPENSSL_BN_ASM_MONT5)
 	if (window==6 && bits<=1024) window=5;	/* ~5% improvement of 2048-bit RSA sign */
 #endif
- 	/* Adjust the number of bits up to a multiple of the window size.
- 	 * If the exponent length is not a multiple of the window size, then
- 	 * this pads the most significant bits with zeros to normalize the
- 	 * scanning loop to there's no special cases.
- 	 *
- 	 * * NOTE: Making the window size a power of two less than the native
-	 * * word size ensures that the padded bits won't go past the last
- 	 * * word in the internal BIGNUM structure. Going past the end will
- 	 * * still produce the correct result, but causes a different branch
- 	 * * to be taken in the BN_is_bit_set function.
- 	 */
- 	bits = ((bits+window-1)/window)*window;
 
 	/* Allocate a buffer large enough to hold all of the pre-computed
-	 * powers of a, plus computeTemp.
+	 * powers of am, am itself and tmp.
 	 */
 	numPowers = 1 << window;
 	powerbufLen = sizeof(m->d[0])*(top*numPowers +
-				(top>numPowers?top:numPowers));
+				((2*top)>numPowers?(2*top):numPowers));
 #ifdef alloca
 	if (powerbufLen < 3072)
 		powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
@@ -670,28 +648,31 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 		powerbufFree = NULL;
 #endif
 
-	computeTemp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
-	computeTemp.top = computeTemp.dmax = top;
-	computeTemp.neg = 0;
-	computeTemp.flags = BN_FLG_STATIC_DATA;
-
- 	/* Initialize the intermediate result. Do this early to save double conversion,
-	 * once each for a^0 and intermediate result.
-	 */
- 	if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
-
-	/* Initialize computeTemp as a^1 with montgomery precalcs */
-	am = BN_CTX_get(ctx);
-	if (am==NULL) goto err;
+	/* lay down tmp and am right after powers table */
+	tmp.d     = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
+	am.d      = tmp.d + top;
+	tmp.top   = am.top  = 0;
+	tmp.dmax  = am.dmax = top;
+	tmp.neg   = am.neg  = 0;
+	tmp.flags = am.flags = BN_FLG_STATIC_DATA;
+
+	/* prepare a^0 in Montgomery domain */
+#if 1
+ 	if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx))	goto err;
+#else
+	tmp.d[0] = (0-m->d[0])&BN_MASK2;	/* 2^(top*BN_BITS2) - m */
+	for (i=1;i<top;i++)
+		tmp.d[i] = (~m->d[i])&BN_MASK2;
+	tmp.top = top;
+#endif
 
+	/* prepare a^1 in Montgomery domain */
 	if (a->neg || BN_ucmp(a,m) >= 0)
 		{
-		if (!BN_mod(am,a,m,ctx))		goto err;
-		if (!BN_to_montgomery(am,am,mont,ctx))	goto err;
+		if (!BN_mod(&am,a,m,ctx))			goto err;
+		if (!BN_to_montgomery(&am,&am,mont,ctx))	goto err;
 		}
-	else	if (!BN_to_montgomery(am,a,mont,ctx))	goto err;
-
-	if (!BN_copy(&computeTemp, am)) goto err;
+	else	if (!BN_to_montgomery(&am,a,mont,ctx))		goto err;
 
 #if defined(OPENSSL_BN_ASM_MONT5)
     /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
@@ -707,95 +688,83 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 			const BN_ULONG *n0,int num,int power);
 	void bn_scatter5(const BN_ULONG *inp,size_t num,
 			void *table,size_t power);
+	void bn_gather5(BN_ULONG *out,size_t num,
+			void *table,size_t power);
 
-	BN_ULONG *acc, *np=mont->N.d, *n0=mont->n0;
+	BN_ULONG *np=mont->N.d, *n0=mont->n0;
 
-	bn_scatter5(r->d,r->top,powerbuf,0);
-	bn_scatter5(am->d,am->top,powerbuf,1);
+	bn_scatter5(tmp.d,top,powerbuf,0);
+	bn_scatter5(am.d,am.top,powerbuf,1);
+	bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
+	bn_scatter5(tmp.d,top,powerbuf,2);
 
-	acc = computeTemp.d;
-	/* bn_mul_mont() and bn_mul_mont_gather5() assume fixed length inputs.
-	 * Pad the inputs with zeroes.
-	 */
-	if (bn_wexpand(am,top)==NULL ||	bn_wexpand(r,top)==NULL ||
-	    bn_wexpand(&computeTemp,top)==NULL)
-		goto err;
-	for (i = am->top; i < top; ++i)
-		{
-		am->d[i] = 0;
-		}
-	for (i = computeTemp.top; i < top; ++i)
-		{
-		computeTemp.d[i] = 0;
-		}
-	for (i = r->top; i < top; ++i)
-		{
-		r->d[i] = 0;
-		}
 #if 0
-	for (i=2; i<32; i++)
+	for (i=3; i<32; i++)
 		{
-		bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
-		bn_scatter5(acc,top,powerbuf,i);
+		/* Calculate a^i = a^(i-1) * a */
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_scatter5(tmp.d,top,powerbuf,i);
 		}
 #else
 	/* same as above, but uses squaring for 1/2 of operations */
-	for (i=2; i<32; i*=2)
+	for (i=4; i<32; i*=2)
 		{
-		bn_mul_mont(acc,acc,acc,np,n0,top);
-		bn_scatter5(acc,top,powerbuf,i);
+		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+		bn_scatter5(tmp.d,top,powerbuf,i);
 		}
 	for (i=3; i<8; i+=2)
 		{
 		int j;
-		bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
-		bn_scatter5(acc,top,powerbuf,i);
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_scatter5(tmp.d,top,powerbuf,i);
 		for (j=2*i; j<32; j*=2)
 			{
-			bn_mul_mont(acc,acc,acc,np,n0,top);
-			bn_scatter5(acc,top,powerbuf,j);
+			bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+			bn_scatter5(tmp.d,top,powerbuf,j);
 			}
 		}
 	for (; i<16; i+=2)
 		{
-		bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
-		bn_scatter5(acc,top,powerbuf,i);
-		bn_mul_mont(acc,acc,acc,np,n0,top);
-		bn_scatter5(acc,top,powerbuf,2*i);
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_scatter5(tmp.d,top,powerbuf,i);
+		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+		bn_scatter5(tmp.d,top,powerbuf,2*i);
 		}
 	for (; i<32; i+=2)
 		{
-		bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
-		bn_scatter5(acc,top,powerbuf,i);
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_scatter5(tmp.d,top,powerbuf,i);
 		}
 #endif
-	acc = r->d;
+	bits--;
+	for (wvalue=0, i=bits%5; i>=0; i--,bits--)
+		wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
+	bn_gather5(tmp.d,top,powerbuf,wvalue);
 
 	/* Scan the exponent one window at a time starting from the most
 	 * significant bits.
 	 */
-	bits--;
 	while (bits >= 0)
 		{
 		for (wvalue=0, i=0; i<5; i++,bits--)
 			wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
 
-		bn_mul_mont(acc,acc,acc,np,n0,top);
-		bn_mul_mont(acc,acc,acc,np,n0,top);
-		bn_mul_mont(acc,acc,acc,np,n0,top);
-		bn_mul_mont(acc,acc,acc,np,n0,top);
-		bn_mul_mont(acc,acc,acc,np,n0,top);
-		bn_mul_mont_gather5(acc,acc,powerbuf,np,n0,top,wvalue);
+		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
+		bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
 		}
 
-	r->top=top;
-	bn_correct_top(r);
+	tmp.top=top;
+	bn_correct_top(&tmp);
 	}
     else
 #endif
 	{
-	if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;
-	if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;
+	if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
+	if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am,  top, powerbuf, 1, numPowers)) goto err;
 
 	/* If the window size is greater than 1, then calculate
 	 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
@@ -804,19 +773,25 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 	 */
 	if (window > 1)
 		{
-		for (i=2; i<numPowers; i++)
+		if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx))	goto err;
+		if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
+		for (i=3; i<numPowers; i++)
 			{
 			/* Calculate a^i = a^(i-1) * a */
-			if (!BN_mod_mul_montgomery(&computeTemp,am,&computeTemp,mont,ctx))
+			if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
 				goto err;
-			if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&computeTemp, top, powerbuf, i, numPowers)) goto err;
+			if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
 			}
 		}
 
-	/* Scan the exponent one window at a time starting from the most
- 	 * significant bits.
- 	 */
 	bits--;
+	for (wvalue=0, i=bits%window; i>=0; i--,bits--)
+		wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
+	if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
+ 
+	/* Scan the exponent one window at a time starting from the most
+	 * significant bits.
+	 */
  	while (bits >= 0)
   		{
  		wvalue=0; /* The 'value' of the window */
@@ -824,20 +799,20 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
  		/* Scan the window, squaring the result as we go */
  		for (i=0; i<window; i++,bits--)
  			{
-			if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))	goto err;
+			if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx))	goto err;
 			wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
   			}
  		
 		/* Fetch the appropriate pre-computed value from the pre-buf */
-		if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&computeTemp, top, powerbuf, wvalue, numPowers)) goto err;
+		if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
 
  		/* Multiply the result into the intermediate result */
- 		if (!BN_mod_mul_montgomery(r,r,&computeTemp,mont,ctx)) goto err;
+ 		if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
   		}
 	}
 
  	/* Convert the final result from montgomery to standard format */
-	if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
+	if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
 	ret=1;
 err:
 	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
@@ -846,7 +821,6 @@ err:
 		OPENSSL_cleanse(powerbuf,powerbufLen);
 		if (powerbufFree) OPENSSL_free(powerbufFree);
 		}
- 	if (am!=NULL) BN_clear(am);
 	BN_CTX_end(ctx);
 	return(ret);
 	}