bn_exp.c: further optimizations using more ideas from
http://eprint.iacr.org/2011/239.
This commit is contained in:
Andy Polyakov
parent
3f66f2040a
commit
8329e2e776
2 changed files with 156 additions and 113 deletions
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@ -607,7 +607,6 @@ $code.=<<___;
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add $A[1],$N[1] # np[j]*m1+ap[j]*bp[i]+tp[j]
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lea 4($j),$j # j+=2
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adc \$0,%rdx
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mov $N[1],(%rsp) # tp[j-1]
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mov %rdx,$N[0]
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jmp .Linner4x
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.align 16
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@ -626,7 +625,7 @@ $code.=<<___;
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adc \$0,%rdx
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add $A[0],$N[0]
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adc \$0,%rdx
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mov $N[0],-24(%rsp,$j,8) # tp[j-1]
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mov $N[1],-32(%rsp,$j,8) # tp[j-1]
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mov %rdx,$N[1]
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mulq $m0 # ap[j]*bp[i]
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@ -643,7 +642,7 @@ $code.=<<___;
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adc \$0,%rdx
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add $A[1],$N[1]
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adc \$0,%rdx
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mov $N[1],-16(%rsp,$j,8) # tp[j-1]
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mov $N[0],-24(%rsp,$j,8) # tp[j-1]
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mov %rdx,$N[0]
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mulq $m0 # ap[j]*bp[i]
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@ -660,7 +659,7 @@ $code.=<<___;
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adc \$0,%rdx
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add $A[0],$N[0]
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adc \$0,%rdx
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mov $N[0],-8(%rsp,$j,8) # tp[j-1]
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mov $N[1],-16(%rsp,$j,8) # tp[j-1]
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mov %rdx,$N[1]
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mulq $m0 # ap[j]*bp[i]
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@ -678,7 +677,7 @@ $code.=<<___;
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adc \$0,%rdx
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add $A[1],$N[1]
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adc \$0,%rdx
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mov $N[1],-32(%rsp,$j,8) # tp[j-1]
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mov $N[0],-40(%rsp,$j,8) # tp[j-1]
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mov %rdx,$N[0]
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cmp $num,$j
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jl .Linner4x
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@ -697,7 +696,7 @@ $code.=<<___;
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adc \$0,%rdx
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add $A[0],$N[0]
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adc \$0,%rdx
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mov $N[0],-24(%rsp,$j,8) # tp[j-1]
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mov $N[1],-32(%rsp,$j,8) # tp[j-1]
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mov %rdx,$N[1]
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mulq $m0 # ap[j]*bp[i]
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@ -715,10 +714,11 @@ $code.=<<___;
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adc \$0,%rdx
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add $A[1],$N[1]
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adc \$0,%rdx
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mov $N[1],-16(%rsp,$j,8) # tp[j-1]
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mov $N[0],-24(%rsp,$j,8) # tp[j-1]
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mov %rdx,$N[0]
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movq %xmm0,$m0 # bp[i+1]
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mov $N[1],-16(%rsp,$j,8) # tp[j-1]
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xor $N[1],$N[1]
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add $A[0],$N[0]
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@ -831,6 +831,10 @@ ___
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{
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my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%rdx","%r8", "%r9") : # Win64 order
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("%rdi","%rsi","%rdx","%rcx"); # Unix order
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my $out=$inp;
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my $STRIDE=2**5*8;
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my $N=$STRIDE/4;
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$code.=<<___;
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.globl bn_scatter5
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.type bn_scatter5,\@abi-omnipotent
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@ -849,6 +853,61 @@ bn_scatter5:
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.Lscatter_epilogue:
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ret
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.size bn_scatter5,.-bn_scatter5
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.globl bn_gather5
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.type bn_gather5,\@abi-omnipotent
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.align 16
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bn_gather5:
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___
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$code.=<<___ if ($win64);
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.LSEH_begin_bn_gather5:
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# I can't trust assembler to use specific encoding:-(
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.byte 0x48,0x83,0xec,0x28 #sub \$0x28,%rsp
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.byte 0x0f,0x29,0x34,0x24 #movaps %xmm6,(%rsp)
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.byte 0x0f,0x29,0x7c,0x24,0x10 #movdqa %xmm7,0x10(%rsp)
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___
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$code.=<<___;
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mov $idx,%r11
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shr \$`log($N/8)/log(2)`,$idx
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and \$`$N/8-1`,%r11
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not $idx
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lea .Lmagic_masks(%rip),%rax
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and \$`2**5/($N/8)-1`,$idx # 5 is "window size"
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lea 96($tbl,%r11,8),$tbl # pointer within 1st cache line
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movq 0(%rax,$idx,8),%xmm4 # set of masks denoting which
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movq 8(%rax,$idx,8),%xmm5 # cache line contains element
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movq 16(%rax,$idx,8),%xmm6 # denoted by 7th argument
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movq 24(%rax,$idx,8),%xmm7
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jmp .Lgather
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.align 16
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.Lgather:
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movq `0*$STRIDE/4-96`($tbl),%xmm0
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movq `1*$STRIDE/4-96`($tbl),%xmm1
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pand %xmm4,%xmm0
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movq `2*$STRIDE/4-96`($tbl),%xmm2
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pand %xmm5,%xmm1
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movq `3*$STRIDE/4-96`($tbl),%xmm3
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pand %xmm6,%xmm2
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por %xmm1,%xmm0
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pand %xmm7,%xmm3
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por %xmm2,%xmm0
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lea $STRIDE($tbl),$tbl
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por %xmm3,%xmm0
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movq %xmm0,($out) # m0=bp[0]
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lea 8($out),$out
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sub \$1,$num
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jnz .Lgather
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___
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$code.=<<___ if ($win64);
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movaps %xmm6,(%rsp)
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movaps %xmm7,0x10(%rsp)
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lea 0x28(%rsp),%rsp
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___
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$code.=<<___;
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ret
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.LSEH_end_bn_gather5:
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.size bn_gather5,.-bn_gather5
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___
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}
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$code.=<<___;
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@ -980,6 +1039,10 @@ mul_handler:
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.rva .LSEH_end_bn_mul4x_mont_gather5
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.rva .LSEH_info_bn_mul4x_mont_gather5
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.rva .LSEH_begin_bn_gather5
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.rva .LSEH_end_bn_gather5
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.rva .LSEH_info_bn_gather5
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.section .xdata
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.align 8
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.LSEH_info_bn_mul_mont_gather5:
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@ -992,6 +1055,12 @@ mul_handler:
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.rva mul_handler
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.rva .Lmul4x_alloca,.Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
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.align 8
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.LSEH_info_bn_gather5:
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.byte 0x01,0x0d,0x05,0x00
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.byte 0x0d,0x78,0x01,0x00 #movaps 0x10(rsp),xmm7
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.byte 0x08,0x68,0x00,0x00 #movaps (rsp),xmm6
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.byte 0x04,0x42,0x00,0x00 #sub rsp,0x28
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.align 8
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___
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}
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@ -535,23 +535,17 @@ err:
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* as cache lines are concerned. The following functions are used to transfer a BIGNUM
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* from/to that table. */
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static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
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static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
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{
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size_t i, j;
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if (bn_wexpand(b, top) == NULL)
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return 0;
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while (b->top < top)
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{
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b->d[b->top++] = 0;
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}
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if (top > b->top)
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top = b->top; /* this works because 'buf' is explicitly zeroed */
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for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
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{
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buf[j] = ((unsigned char*)b->d)[i];
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}
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bn_correct_top(b);
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return 1;
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}
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@ -587,14 +581,13 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
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{
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int i,bits,ret=0,window,wvalue;
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int top;
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BIGNUM *r;
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BN_MONT_CTX *mont=NULL;
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int numPowers;
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unsigned char *powerbufFree=NULL;
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int powerbufLen = 0;
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unsigned char *powerbuf=NULL;
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BIGNUM computeTemp, *am=NULL;
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BIGNUM tmp, am;
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bn_check_top(a);
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bn_check_top(p);
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@ -614,10 +607,7 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
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return ret;
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}
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/* Initialize BIGNUM context and allocate intermediate result */
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BN_CTX_start(ctx);
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r = BN_CTX_get(ctx);
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if (r == NULL) goto err;
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/* Allocate a montgomery context if it was not supplied by the caller.
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* If this is not done, things will break in the montgomery part.
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@ -635,25 +625,13 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
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#if defined(OPENSSL_BN_ASM_MONT5)
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if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
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#endif
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/* Adjust the number of bits up to a multiple of the window size.
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* If the exponent length is not a multiple of the window size, then
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* this pads the most significant bits with zeros to normalize the
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* scanning loop to there's no special cases.
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*
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* * NOTE: Making the window size a power of two less than the native
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* * word size ensures that the padded bits won't go past the last
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* * word in the internal BIGNUM structure. Going past the end will
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* * still produce the correct result, but causes a different branch
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* * to be taken in the BN_is_bit_set function.
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*/
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bits = ((bits+window-1)/window)*window;
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/* Allocate a buffer large enough to hold all of the pre-computed
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* powers of a, plus computeTemp.
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* powers of am, am itself and tmp.
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*/
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numPowers = 1 << window;
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powerbufLen = sizeof(m->d[0])*(top*numPowers +
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(top>numPowers?top:numPowers));
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((2*top)>numPowers?(2*top):numPowers));
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#ifdef alloca
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if (powerbufLen < 3072)
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powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
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@ -670,28 +648,31 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
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powerbufFree = NULL;
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#endif
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computeTemp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
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computeTemp.top = computeTemp.dmax = top;
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computeTemp.neg = 0;
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computeTemp.flags = BN_FLG_STATIC_DATA;
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/* lay down tmp and am right after powers table */
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tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
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am.d = tmp.d + top;
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tmp.top = am.top = 0;
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tmp.dmax = am.dmax = top;
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tmp.neg = am.neg = 0;
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tmp.flags = am.flags = BN_FLG_STATIC_DATA;
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/* Initialize the intermediate result. Do this early to save double conversion,
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* once each for a^0 and intermediate result.
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*/
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if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
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/* Initialize computeTemp as a^1 with montgomery precalcs */
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am = BN_CTX_get(ctx);
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if (am==NULL) goto err;
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/* prepare a^0 in Montgomery domain */
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#if 1
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if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
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#else
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tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
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for (i=1;i<top;i++)
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tmp.d[i] = (~m->d[i])&BN_MASK2;
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tmp.top = top;
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#endif
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/* prepare a^1 in Montgomery domain */
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if (a->neg || BN_ucmp(a,m) >= 0)
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{
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if (!BN_mod(am,a,m,ctx)) goto err;
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if (!BN_to_montgomery(am,am,mont,ctx)) goto err;
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if (!BN_mod(&am,a,m,ctx)) goto err;
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if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
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}
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else if (!BN_to_montgomery(am,a,mont,ctx)) goto err;
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if (!BN_copy(&computeTemp, am)) goto err;
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else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
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#if defined(OPENSSL_BN_ASM_MONT5)
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/* This optimization uses ideas from http://eprint.iacr.org/2011/239,
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@ -707,95 +688,83 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
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const BN_ULONG *n0,int num,int power);
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void bn_scatter5(const BN_ULONG *inp,size_t num,
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void *table,size_t power);
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void bn_gather5(BN_ULONG *out,size_t num,
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void *table,size_t power);
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BN_ULONG *acc, *np=mont->N.d, *n0=mont->n0;
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BN_ULONG *np=mont->N.d, *n0=mont->n0;
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bn_scatter5(r->d,r->top,powerbuf,0);
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bn_scatter5(am->d,am->top,powerbuf,1);
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bn_scatter5(tmp.d,top,powerbuf,0);
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bn_scatter5(am.d,am.top,powerbuf,1);
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bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
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bn_scatter5(tmp.d,top,powerbuf,2);
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acc = computeTemp.d;
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/* bn_mul_mont() and bn_mul_mont_gather5() assume fixed length inputs.
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* Pad the inputs with zeroes.
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*/
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if (bn_wexpand(am,top)==NULL || bn_wexpand(r,top)==NULL ||
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bn_wexpand(&computeTemp,top)==NULL)
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goto err;
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for (i = am->top; i < top; ++i)
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{
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am->d[i] = 0;
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}
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for (i = computeTemp.top; i < top; ++i)
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{
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computeTemp.d[i] = 0;
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}
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for (i = r->top; i < top; ++i)
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{
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r->d[i] = 0;
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}
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#if 0
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for (i=2; i<32; i++)
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for (i=3; i<32; i++)
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{
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bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
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bn_scatter5(acc,top,powerbuf,i);
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/* Calculate a^i = a^(i-1) * a */
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bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
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bn_scatter5(tmp.d,top,powerbuf,i);
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}
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#else
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/* same as above, but uses squaring for 1/2 of operations */
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for (i=2; i<32; i*=2)
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for (i=4; i<32; i*=2)
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{
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bn_mul_mont(acc,acc,acc,np,n0,top);
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bn_scatter5(acc,top,powerbuf,i);
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bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
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bn_scatter5(tmp.d,top,powerbuf,i);
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}
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for (i=3; i<8; i+=2)
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{
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int j;
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bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
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bn_scatter5(acc,top,powerbuf,i);
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bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
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bn_scatter5(tmp.d,top,powerbuf,i);
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for (j=2*i; j<32; j*=2)
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{
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bn_mul_mont(acc,acc,acc,np,n0,top);
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bn_scatter5(acc,top,powerbuf,j);
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bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
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bn_scatter5(tmp.d,top,powerbuf,j);
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}
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}
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for (; i<16; i+=2)
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{
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bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
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bn_scatter5(acc,top,powerbuf,i);
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bn_mul_mont(acc,acc,acc,np,n0,top);
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bn_scatter5(acc,top,powerbuf,2*i);
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bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
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bn_scatter5(tmp.d,top,powerbuf,i);
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bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
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bn_scatter5(tmp.d,top,powerbuf,2*i);
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}
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for (; i<32; i+=2)
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{
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bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
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bn_scatter5(acc,top,powerbuf,i);
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bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
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bn_scatter5(tmp.d,top,powerbuf,i);
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}
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#endif
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acc = r->d;
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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);
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue