--- /dev/null
+#!/usr/bin/env perl
+
+# ====================================================================
+# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
+# project. The module is, however, dual licensed under OpenSSL and
+# CRYPTOGAMS licenses depending on where you obtain it. For further
+# details see http://www.openssl.org/~appro/cryptogams/.
+# ====================================================================
+
+# August 2011.
+#
+# Companion to x86_64-mont.pl that optimizes cache-timing attack
+# countermeasures. The subroutines are produced by replacing bp[i]
+# references in their x86_64-mont.pl counterparts with cache-neutral
+# references to powers table computed in BN_mod_exp_mont_consttime.
+# In addition subroutine that scatters elements of the powers table
+# is implemented, so that scatter-/gathering can be tuned without
+# bn_exp.c modifications.
+
+$flavour = shift;
+$output = shift;
+if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
+
+$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
+
+$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
+( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
+( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
+die "can't locate x86_64-xlate.pl";
+
+open STDOUT,"| $^X $xlate $flavour $output";
+
+# int bn_mul_mont_gather5(
+$rp="%rdi"; # BN_ULONG *rp,
+$ap="%rsi"; # const BN_ULONG *ap,
+$bp="%rdx"; # const BN_ULONG *bp,
+$np="%rcx"; # const BN_ULONG *np,
+$n0="%r8"; # const BN_ULONG *n0,
+$num="%r9"; # int num,
+ # int idx); # 0 to 2^5-1, "index" in $bp holding
+ # pre-computed powers of a', interlaced
+ # in such manner that b[0] is $bp[idx],
+ # b[1] is [2^5+idx], etc.
+$lo0="%r10";
+$hi0="%r11";
+$hi1="%r13";
+$i="%r14";
+$j="%r15";
+$m0="%rbx";
+$m1="%rbp";
+
+$code=<<___;
+.text
+
+.globl bn_mul_mont_gather5
+.type bn_mul_mont_gather5,\@function,6
+.align 64
+bn_mul_mont_gather5:
+ test \$3,${num}d
+ jnz .Lmul_enter
+ cmp \$8,${num}d
+ jb .Lmul_enter
+ jmp .Lmul4x_enter
+
+.align 16
+.Lmul_enter:
+ mov `($win64?56:8)`(%rsp),%r10d # load 7th argument
+ push %rbx
+ push %rbp
+ push %r12
+ push %r13
+ push %r14
+ push %r15
+
+ mov ${num}d,${num}d
+ lea 2($num),%r11
+ mov %rsp,%rax
+ neg %r11
+ lea (%rsp,%r11,8),%rsp # tp=alloca(8*(num+2))
+ and \$-1024,%rsp # minimize TLB usage
+
+ mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
+.Lmul_body:
+ mov $bp,%r12 # reassign $bp
+___
+ $bp="%r12";
+ $STRIDE=2**5*8; # 5 is "window size"
+ $N=$STRIDE/4; # should match cache line size
+$code.=<<___;
+ mov %r10,%r11
+ shr \$`log($N/8)/log(2)`,%r10
+ and \$`$N/8-1`,%r11
+ not %r10
+ lea .Lmagic_masks(%rip),%rax
+ and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
+ lea 96($bp,%r11,8),$bp # pointer within 1st cache line
+ movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
+ movq 8(%rax,%r10,8),%xmm5 # cache line contains element
+ movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
+ movq 24(%rax,%r10,8),%xmm7
+
+ movq `0*$STRIDE/4-96`($bp),%xmm0
+ movq `1*$STRIDE/4-96`($bp),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bp),%xmm2
+ pand %xmm5,%xmm1
+ movq `3*$STRIDE/4-96`($bp),%xmm3
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ pand %xmm7,%xmm3
+ por %xmm2,%xmm0
+ lea $STRIDE($bp),$bp
+ por %xmm3,%xmm0
+
+ movq %xmm0,$m0 # m0=bp[0]
+
+ mov ($n0),$n0 # pull n0[0] value
+ mov ($ap),%rax
+
+ xor $i,$i # i=0
+ xor $j,$j # j=0
+
+ movq `0*$STRIDE/4-96`($bp),%xmm0
+ movq `1*$STRIDE/4-96`($bp),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bp),%xmm2
+ pand %xmm5,%xmm1
+
+ mov $n0,$m1
+ mulq $m0 # ap[0]*bp[0]
+ mov %rax,$lo0
+ mov ($np),%rax
+
+ movq `3*$STRIDE/4-96`($bp),%xmm3
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ pand %xmm7,%xmm3
+
+ imulq $lo0,$m1 # "tp[0]"*n0
+ mov %rdx,$hi0
+
+ por %xmm2,%xmm0
+ lea $STRIDE($bp),$bp
+ por %xmm3,%xmm0
+
+ mulq $m1 # np[0]*m1
+ add %rax,$lo0 # discarded
+ mov 8($ap),%rax
+ adc \$0,%rdx
+ mov %rdx,$hi1
+
+ lea 1($j),$j # j++
+ jmp .L1st_enter
+
+.align 16
+.L1st:
+ add %rax,$hi1
+ mov ($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
+ mov $lo0,$hi0
+ adc \$0,%rdx
+ mov $hi1,-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$hi1
+
+.L1st_enter:
+ mulq $m0 # ap[j]*bp[0]
+ add %rax,$hi0
+ mov ($np,$j,8),%rax
+ adc \$0,%rdx
+ lea 1($j),$j # j++
+ mov %rdx,$lo0
+
+ mulq $m1 # np[j]*m1
+ cmp $num,$j
+ jne .L1st
+
+ movq %xmm0,$m0 # bp[1]
+
+ add %rax,$hi1
+ mov ($ap),%rax # ap[0]
+ adc \$0,%rdx
+ add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
+ adc \$0,%rdx
+ mov $hi1,-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$hi1
+ mov $lo0,$hi0
+
+ xor %rdx,%rdx
+ add $hi0,$hi1
+ adc \$0,%rdx
+ mov $hi1,-8(%rsp,$num,8)
+ mov %rdx,(%rsp,$num,8) # store upmost overflow bit
+
+ lea 1($i),$i # i++
+ jmp .Louter
+.align 16
+.Louter:
+ xor $j,$j # j=0
+ mov $n0,$m1
+ mov (%rsp),$lo0
+
+ movq `0*$STRIDE/4-96`($bp),%xmm0
+ movq `1*$STRIDE/4-96`($bp),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bp),%xmm2
+ pand %xmm5,%xmm1
+
+ mulq $m0 # ap[0]*bp[i]
+ add %rax,$lo0 # ap[0]*bp[i]+tp[0]
+ mov ($np),%rax
+ adc \$0,%rdx
+
+ movq `3*$STRIDE/4-96`($bp),%xmm3
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ pand %xmm7,%xmm3
+
+ imulq $lo0,$m1 # tp[0]*n0
+ mov %rdx,$hi0
+
+ por %xmm2,%xmm0
+ lea $STRIDE($bp),$bp
+ por %xmm3,%xmm0
+
+ mulq $m1 # np[0]*m1
+ add %rax,$lo0 # discarded
+ mov 8($ap),%rax
+ adc \$0,%rdx
+ mov 8(%rsp),$lo0 # tp[1]
+ mov %rdx,$hi1
+
+ lea 1($j),$j # j++
+ jmp .Linner_enter
+
+.align 16
+.Linner:
+ add %rax,$hi1
+ mov ($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
+ mov (%rsp,$j,8),$lo0
+ adc \$0,%rdx
+ mov $hi1,-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$hi1
+
+.Linner_enter:
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$hi0
+ mov ($np,$j,8),%rax
+ adc \$0,%rdx
+ add $hi0,$lo0 # ap[j]*bp[i]+tp[j]
+ mov %rdx,$hi0
+ adc \$0,$hi0
+ lea 1($j),$j # j++
+
+ mulq $m1 # np[j]*m1
+ cmp $num,$j
+ jne .Linner
+
+ movq %xmm0,$m0 # bp[i+1]
+
+ add %rax,$hi1
+ mov ($ap),%rax # ap[0]
+ adc \$0,%rdx
+ add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
+ mov (%rsp,$j,8),$lo0
+ adc \$0,%rdx
+ mov $hi1,-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$hi1
+
+ xor %rdx,%rdx
+ add $hi0,$hi1
+ adc \$0,%rdx
+ add $lo0,$hi1 # pull upmost overflow bit
+ adc \$0,%rdx
+ mov $hi1,-8(%rsp,$num,8)
+ mov %rdx,(%rsp,$num,8) # store upmost overflow bit
+
+ lea 1($i),$i # i++
+ cmp $num,$i
+ jl .Louter
+
+ xor $i,$i # i=0 and clear CF!
+ mov (%rsp),%rax # tp[0]
+ lea (%rsp),$ap # borrow ap for tp
+ mov $num,$j # j=num
+ jmp .Lsub
+.align 16
+.Lsub: sbb ($np,$i,8),%rax
+ mov %rax,($rp,$i,8) # rp[i]=tp[i]-np[i]
+ mov 8($ap,$i,8),%rax # tp[i+1]
+ lea 1($i),$i # i++
+ dec $j # doesnn't affect CF!
+ jnz .Lsub
+
+ sbb \$0,%rax # handle upmost overflow bit
+ xor $i,$i
+ and %rax,$ap
+ not %rax
+ mov $rp,$np
+ and %rax,$np
+ mov $num,$j # j=num
+ or $np,$ap # ap=borrow?tp:rp
+.align 16
+.Lcopy: # copy or in-place refresh
+ mov ($ap,$i,8),%rax
+ mov $i,(%rsp,$i,8) # zap temporary vector
+ mov %rax,($rp,$i,8) # rp[i]=tp[i]
+ lea 1($i),$i
+ sub \$1,$j
+ jnz .Lcopy
+
+ mov 8(%rsp,$num,8),%rsi # restore %rsp
+ mov \$1,%rax
+ mov (%rsi),%r15
+ mov 8(%rsi),%r14
+ mov 16(%rsi),%r13
+ mov 24(%rsi),%r12
+ mov 32(%rsi),%rbp
+ mov 40(%rsi),%rbx
+ lea 48(%rsi),%rsp
+.Lmul_epilogue:
+ ret
+.size bn_mul_mont_gather5,.-bn_mul_mont_gather5
+___
+{{{
+my @A=("%r10","%r11");
+my @N=("%r13","%rdi");
+$code.=<<___;
+.type bn_mul4x_mont_gather5,\@function,6
+.align 16
+bn_mul4x_mont_gather5:
+.Lmul4x_enter:
+ mov `($win64?56:8)`(%rsp),%r10d # load 7th argument
+ push %rbx
+ push %rbp
+ push %r12
+ push %r13
+ push %r14
+ push %r15
+
+ mov ${num}d,${num}d
+ lea 4($num),%r11
+ mov %rsp,%rax # !!!!
+ neg %r11
+ lea (%rsp,%r11,8),%rsp # tp=alloca(8*(num+4))
+ and \$-1024,%rsp # minimize TLB usage
+
+ mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
+.Lmul4x_body:
+ mov $rp,16(%rsp,$num,8) # tp[num+2]=$rp
+ mov %rdx,%r12 # reassign $bp
+___
+ $bp="%r12";
+ $STRIDE=2**5*8; # 5 is "window size"
+ $N=$STRIDE/4; # should match cache line size
+$code.=<<___;
+ mov %r10,%r11
+ shr \$`log($N/8)/log(2)`,%r10
+ and \$`$N/8-1`,%r11
+ not %r10
+ lea .Lmagic_masks(%rip),%rax
+ and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
+ lea 96($bp,%r11,8),$bp # pointer within 1st cache line
+ movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
+ movq 8(%rax,%r10,8),%xmm5 # cache line contains element
+ movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
+ movq 24(%rax,%r10,8),%xmm7
+
+ movq `0*$STRIDE/4-96`($bp),%xmm0
+ movq `1*$STRIDE/4-96`($bp),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bp),%xmm2
+ pand %xmm5,%xmm1
+ movq `3*$STRIDE/4-96`($bp),%xmm3
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ pand %xmm7,%xmm3
+ por %xmm2,%xmm0
+ lea $STRIDE($bp),$bp
+ por %xmm3,%xmm0
+
+ movq %xmm0,$m0 # m0=bp[0]
+ mov ($n0),$n0 # pull n0[0] value
+ mov ($ap),%rax
+
+ xor $i,$i # i=0
+ xor $j,$j # j=0
+
+ movq `0*$STRIDE/4-96`($bp),%xmm0
+ movq `1*$STRIDE/4-96`($bp),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bp),%xmm2
+ pand %xmm5,%xmm1
+
+ mov $n0,$m1
+ mulq $m0 # ap[0]*bp[0]
+ mov %rax,$A[0]
+ mov ($np),%rax
+
+ movq `3*$STRIDE/4-96`($bp),%xmm3
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ pand %xmm7,%xmm3
+
+ imulq $A[0],$m1 # "tp[0]"*n0
+ mov %rdx,$A[1]
+
+ por %xmm2,%xmm0
+ lea $STRIDE($bp),$bp
+ por %xmm3,%xmm0
+
+ mulq $m1 # np[0]*m1
+ add %rax,$A[0] # discarded
+ mov 8($ap),%rax
+ adc \$0,%rdx
+ mov %rdx,$N[1]
+
+ mulq $m0
+ add %rax,$A[1]
+ mov 8($np),%rax
+ adc \$0,%rdx
+ mov %rdx,$A[0]
+
+ mulq $m1
+ add %rax,$N[1]
+ mov 16($ap),%rax
+ adc \$0,%rdx
+ add $A[1],$N[1]
+ lea 4($j),$j # j++
+ adc \$0,%rdx
+ mov $N[1],(%rsp)
+ mov %rdx,$N[0]
+ jmp .L1st4x
+.align 16
+.L1st4x:
+ mulq $m0 # ap[j]*bp[0]
+ add %rax,$A[0]
+ mov -16($np,$j,8),%rax
+ adc \$0,%rdx
+ mov %rdx,$A[1]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[0]
+ mov -8($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
+ adc \$0,%rdx
+ mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[1]
+
+ mulq $m0 # ap[j]*bp[0]
+ add %rax,$A[1]
+ mov -8($np,$j,8),%rax
+ adc \$0,%rdx
+ mov %rdx,$A[0]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[1]
+ mov ($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
+ adc \$0,%rdx
+ mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[0]
+
+ mulq $m0 # ap[j]*bp[0]
+ add %rax,$A[0]
+ mov ($np,$j,8),%rax
+ adc \$0,%rdx
+ mov %rdx,$A[1]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[0]
+ mov 8($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
+ adc \$0,%rdx
+ mov $N[0],-8(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[1]
+
+ mulq $m0 # ap[j]*bp[0]
+ add %rax,$A[1]
+ mov 8($np,$j,8),%rax
+ adc \$0,%rdx
+ lea 4($j),$j # j++
+ mov %rdx,$A[0]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[1]
+ mov -16($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
+ adc \$0,%rdx
+ mov $N[1],-32(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[0]
+ cmp $num,$j
+ jl .L1st4x
+
+ mulq $m0 # ap[j]*bp[0]
+ add %rax,$A[0]
+ mov -16($np,$j,8),%rax
+ adc \$0,%rdx
+ mov %rdx,$A[1]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[0]
+ mov -8($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
+ adc \$0,%rdx
+ mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[1]
+
+ mulq $m0 # ap[j]*bp[0]
+ add %rax,$A[1]
+ mov -8($np,$j,8),%rax
+ adc \$0,%rdx
+ mov %rdx,$A[0]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[1]
+ mov ($ap),%rax # ap[0]
+ adc \$0,%rdx
+ add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
+ adc \$0,%rdx
+ mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[0]
+
+ movq %xmm0,$m0 # bp[1]
+
+ xor $N[1],$N[1]
+ add $A[0],$N[0]
+ adc \$0,$N[1]
+ mov $N[0],-8(%rsp,$j,8)
+ mov $N[1],(%rsp,$j,8) # store upmost overflow bit
+
+ lea 1($i),$i # i++
+.align 4
+.Louter4x:
+ xor $j,$j # j=0
+ movq `0*$STRIDE/4-96`($bp),%xmm0
+ movq `1*$STRIDE/4-96`($bp),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bp),%xmm2
+ pand %xmm5,%xmm1
+
+ mov (%rsp),$A[0]
+ mov $n0,$m1
+ mulq $m0 # ap[0]*bp[i]
+ add %rax,$A[0] # ap[0]*bp[i]+tp[0]
+ mov ($np),%rax
+ adc \$0,%rdx
+
+ movq `3*$STRIDE/4-96`($bp),%xmm3
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ pand %xmm7,%xmm3
+
+ imulq $A[0],$m1 # tp[0]*n0
+ mov %rdx,$A[1]
+
+ por %xmm2,%xmm0
+ lea $STRIDE($bp),$bp
+ por %xmm3,%xmm0
+
+ mulq $m1 # np[0]*m1
+ add %rax,$A[0] # "$N[0]", discarded
+ mov 8($ap),%rax
+ adc \$0,%rdx
+ mov %rdx,$N[1]
+
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$A[1]
+ mov 8($np),%rax
+ adc \$0,%rdx
+ add 8(%rsp),$A[1] # +tp[1]
+ adc \$0,%rdx
+ mov %rdx,$A[0]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[1]
+ mov 16($ap),%rax
+ adc \$0,%rdx
+ 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
+.Linner4x:
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$A[0]
+ mov -16($np,$j,8),%rax
+ adc \$0,%rdx
+ add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
+ adc \$0,%rdx
+ mov %rdx,$A[1]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[0]
+ mov -8($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[0],$N[0]
+ adc \$0,%rdx
+ mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[1]
+
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$A[1]
+ mov -8($np,$j,8),%rax
+ adc \$0,%rdx
+ add -8(%rsp,$j,8),$A[1]
+ adc \$0,%rdx
+ mov %rdx,$A[0]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[1]
+ mov ($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[1],$N[1]
+ adc \$0,%rdx
+ mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[0]
+
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$A[0]
+ mov ($np,$j,8),%rax
+ adc \$0,%rdx
+ add (%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
+ adc \$0,%rdx
+ mov %rdx,$A[1]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[0]
+ mov 8($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[0],$N[0]
+ adc \$0,%rdx
+ mov $N[0],-8(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[1]
+
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$A[1]
+ mov 8($np,$j,8),%rax
+ adc \$0,%rdx
+ add 8(%rsp,$j,8),$A[1]
+ adc \$0,%rdx
+ lea 4($j),$j # j++
+ mov %rdx,$A[0]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[1]
+ mov -16($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[1],$N[1]
+ adc \$0,%rdx
+ mov $N[1],-32(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[0]
+ cmp $num,$j
+ jl .Linner4x
+
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$A[0]
+ mov -16($np,$j,8),%rax
+ adc \$0,%rdx
+ add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
+ adc \$0,%rdx
+ mov %rdx,$A[1]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[0]
+ mov -8($ap,$j,8),%rax
+ adc \$0,%rdx
+ add $A[0],$N[0]
+ adc \$0,%rdx
+ mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[1]
+
+ mulq $m0 # ap[j]*bp[i]
+ add %rax,$A[1]
+ mov -8($np,$j,8),%rax
+ adc \$0,%rdx
+ add -8(%rsp,$j,8),$A[1]
+ adc \$0,%rdx
+ lea 1($i),$i # i++
+ mov %rdx,$A[0]
+
+ mulq $m1 # np[j]*m1
+ add %rax,$N[1]
+ mov ($ap),%rax # ap[0]
+ adc \$0,%rdx
+ add $A[1],$N[1]
+ adc \$0,%rdx
+ mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov %rdx,$N[0]
+
+ movq %xmm0,$m0 # bp[i+1]
+
+ xor $N[1],$N[1]
+ add $A[0],$N[0]
+ adc \$0,$N[1]
+ add (%rsp,$num,8),$N[0] # pull upmost overflow bit
+ adc \$0,$N[1]
+ mov $N[0],-8(%rsp,$j,8)
+ mov $N[1],(%rsp,$j,8) # store upmost overflow bit
+
+ cmp $num,$i
+ jl .Louter4x
+___
+{
+my @ri=("%rax","%rdx",$m0,$m1);
+$code.=<<___;
+ mov 16(%rsp,$num,8),$rp # restore $rp
+ mov 0(%rsp),@ri[0] # tp[0]
+ pxor %xmm0,%xmm0
+ mov 8(%rsp),@ri[1] # tp[1]
+ shr \$2,$num # num/=4
+ lea (%rsp),$ap # borrow ap for tp
+ xor $i,$i # i=0 and clear CF!
+
+ sub 0($np),@ri[0]
+ mov 16($ap),@ri[2] # tp[2]
+ mov 24($ap),@ri[3] # tp[3]
+ sbb 8($np),@ri[1]
+ lea -1($num),$j # j=num/4-1
+ jmp .Lsub4x
+.align 16
+.Lsub4x:
+ mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
+ mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
+ sbb 16($np,$i,8),@ri[2]
+ mov 32($ap,$i,8),@ri[0] # tp[i+1]
+ mov 40($ap,$i,8),@ri[1]
+ sbb 24($np,$i,8),@ri[3]
+ mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
+ mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
+ sbb 32($np,$i,8),@ri[0]
+ mov 48($ap,$i,8),@ri[2]
+ mov 56($ap,$i,8),@ri[3]
+ sbb 40($np,$i,8),@ri[1]
+ lea 4($i),$i # i++
+ dec $j # doesnn't affect CF!
+ jnz .Lsub4x
+
+ mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
+ mov 32($ap,$i,8),@ri[0] # load overflow bit
+ sbb 16($np,$i,8),@ri[2]
+ mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
+ sbb 24($np,$i,8),@ri[3]
+ mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
+
+ sbb \$0,@ri[0] # handle upmost overflow bit
+ mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
+ xor $i,$i # i=0
+ and @ri[0],$ap
+ not @ri[0]
+ mov $rp,$np
+ and @ri[0],$np
+ lea -1($num),$j
+ or $np,$ap # ap=borrow?tp:rp
+
+ movdqu ($ap),%xmm1
+ movdqa %xmm0,(%rsp)
+ movdqu %xmm1,($rp)
+ jmp .Lcopy4x
+.align 16
+.Lcopy4x: # copy or in-place refresh
+ movdqu 16($ap,$i),%xmm2
+ movdqu 32($ap,$i),%xmm1
+ movdqa %xmm0,16(%rsp,$i)
+ movdqu %xmm2,16($rp,$i)
+ movdqa %xmm0,32(%rsp,$i)
+ movdqu %xmm1,32($rp,$i)
+ lea 32($i),$i
+ dec $j
+ jnz .Lcopy4x
+
+ shl \$2,$num
+ movdqu 16($ap,$i),%xmm2
+ movdqa %xmm0,16(%rsp,$i)
+ movdqu %xmm2,16($rp,$i)
+___
+}
+$code.=<<___;
+ mov 8(%rsp,$num,8),%rsi # restore %rsp
+ mov \$1,%rax
+ mov (%rsi),%r15
+ mov 8(%rsi),%r14
+ mov 16(%rsi),%r13
+ mov 24(%rsi),%r12
+ mov 32(%rsi),%rbp
+ mov 40(%rsi),%rbx
+ lea 48(%rsi),%rsp
+.Lmul4x_epilogue:
+ ret
+.size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
+___
+}}}
+
+{
+my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%rdx","%r8", "%r9") : # Win64 order
+ ("%rdi","%rsi","%rdx","%rcx"); # Unix order
+$code.=<<___;
+.globl bn_scatter5
+.type bn_scatter5,\@abi-omnipotent
+.align 16
+bn_scatter5:
+ lea ($tbl,$idx,8),$tbl
+.Lscatter:
+ mov ($inp),%rax
+ lea 8($inp),$inp
+ mov %rax,($tbl)
+ lea 32*8($tbl),$tbl
+ sub \$1,$num
+ jnz .Lscatter
+ ret
+.size bn_scatter5,.-bn_scatter5
+___
+}
+$code.=<<___;
+.align 64
+.Lmagic_masks:
+ .long 0,0, 0,0, 0,0, -1,-1
+ .long 0,0, 0,0, 0,0, 0,0
+.asciz "Montgomery Multiplication with scatter/gather for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
+___
+
+$code =~ s/\`([^\`]*)\`/eval($1)/gem;
+
+print $code;
+close STDOUT;
#include "cryptlib.h"
#include "bn_lcl.h"
+#include <stdlib.h>
+#ifdef _WIN32
+# include <malloc.h>
+# ifndef alloca
+# define alloca _alloca
+# endif
+#elif defined(__GNUC__)
+# ifndef alloca
+# define alloca(s) __builtin_alloca((s))
+# endif
+#endif
+
/* maximum precomputation table size for *variable* sliding windows */
#define TABLE_SIZE 32
/* Given a pointer value, compute the next address that is a cache line multiple. */
#define MOD_EXP_CTIME_ALIGN(x_) \
- ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
+ ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
/* This variant of BN_mod_exp_mont() uses fixed windows and the special
* precomputation memory layout to limit data-dependency to a minimum
int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
- int i,bits,ret=0,idx,window,wvalue;
+ int i,bits,ret=0,window,wvalue;
int top;
BIGNUM *r;
- const BIGNUM *aa;
BN_MONT_CTX *mont=NULL;
int numPowers;
unsigned char *powerbufFree=NULL;
int powerbufLen = 0;
unsigned char *powerbuf=NULL;
- BIGNUM *computeTemp=NULL, *am=NULL;
+ BIGNUM computeTemp, *am=NULL;
bn_check_top(a);
bn_check_top(p);
/* Get the window size to use with size of p. */
window = BN_window_bits_for_ctime_exponent_size(bits);
+#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.
+ * powers of a, plus computeTemp.
*/
numPowers = 1 << window;
- powerbufLen = sizeof(m->d[0])*top*numPowers;
- if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
+ powerbufLen = sizeof(m->d[0])*(top*numPowers +
+ (top>numPowers?top:numPowers));
+ if (powerbufLen < 3072)
+ powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
+ else if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
goto err;
powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
memset(powerbuf, 0, powerbufLen);
+ if (powerbufLen < 3072)
+ powerbufFree = NULL;
+
+ 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;
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;
/* Initialize computeTemp as a^1 with montgomery precalcs */
- computeTemp = BN_CTX_get(ctx);
am = BN_CTX_get(ctx);
- if (computeTemp==NULL || am==NULL) goto err;
+ if (am==NULL) goto err;
if (a->neg || BN_ucmp(a,m) >= 0)
{
- if (!BN_mod(am,a,m,ctx))
- goto err;
- aa= am;
+ if (!BN_mod(am,a,m,ctx)) goto err;
+ if (!BN_to_montgomery(am,am,mont,ctx)) goto err;
}
- else
- aa=a;
- if (!BN_to_montgomery(am,aa,mont,ctx)) goto err;
- if (!BN_copy(computeTemp, am)) goto err;
+ else if (!BN_to_montgomery(am,a,mont,ctx)) goto err;
+
+ if (!BN_copy(&computeTemp, am)) goto err;
+
+ if (bn_wexpand(am,top)==NULL || bn_wexpand(r,top)==NULL)
+ goto err;
+
+#if defined(OPENSSL_BN_ASM_MONT5)
+ /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
+ * specifically optimization of cache-timing attack countermeasures
+ * and pre-computation optimization. */
+
+ /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
+ * 512-bit RSA is hardly relevant, we omit it to spare size... */
+ if (window==5)
+ {
+ void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
+ const void *table,const BN_ULONG *np,
+ const BN_ULONG *n0,int num,int power);
+ void bn_scatter5(const BN_ULONG *inp,size_t num,
+ void *table,size_t power);
+
+ BN_ULONG *acc, *np=mont->N.d, *n0=mont->n0;
+
+ bn_scatter5(r->d,r->top,powerbuf,0);
+ bn_scatter5(am->d,am->top,powerbuf,1);
+
+ acc = computeTemp.d;
+#if 0
+ for (i=2; i<32; i++)
+ {
+ bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
+ bn_scatter5(acc,top,powerbuf,i);
+ }
+#else
+ /* same as above, but uses squaring for 1/2 of operations */
+ for (i=2; i<32; i*=2)
+ {
+ bn_mul_mont(acc,acc,acc,np,n0,top);
+ bn_scatter5(acc,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);
+ for (j=2*i; j<32; j*=2)
+ {
+ bn_mul_mont(acc,acc,acc,np,n0,top);
+ bn_scatter5(acc,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);
+ }
+ for (; i<32; i+=2)
+ {
+ bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
+ bn_scatter5(acc,top,powerbuf,i);
+ }
+#endif
+ acc = r->d;
+
+ /* 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);
+ }
+
+ r->top=top;
+ bn_correct_top(r);
+ }
+ 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 the window size is greater than 1, then calculate
for (i=2; 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(&computeTemp,am,&computeTemp,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(&computeTemp, top, powerbuf, i, numPowers)) goto err;
}
}
- /* 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;
- idx=bits-1; /* The top bit of the window */
-
- /* Scan the exponent one window at a time starting from the most
+ /* Scan the exponent one window at a time starting from the most
* significant bits.
*/
- while (idx >= 0)
+ bits--;
+ while (bits >= 0)
{
wvalue=0; /* The 'value' of the window */
/* Scan the window, squaring the result as we go */
- for (i=0; i<window; i++,idx--)
+ for (i=0; i<window; i++,bits--)
{
if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err;
- wvalue = (wvalue<<1)+BN_is_bit_set(p,idx);
+ 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(&computeTemp, 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(r,r,&computeTemp,mont,ctx)) goto err;
}
+ }
/* Convert the final result from montgomery to standard format */
if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
if (powerbuf!=NULL)
{
OPENSSL_cleanse(powerbuf,powerbufLen);
- OPENSSL_free(powerbufFree);
+ if (powerbufFree) OPENSSL_free(powerbufFree);
}
if (am!=NULL) BN_clear(am);
- if (computeTemp!=NULL) BN_clear(computeTemp);
BN_CTX_end(ctx);
return(ret);
}
projects / openssl / commitdiff