mirror of
https://github.com/emmansun/gmsm.git
synced 2025-04-26 20:26:19 +08:00
sm9: improve gfP invert & sqrt performance
This commit is contained in:
emmansun
parent
4a5dcf64c1
commit
f58cb10ad9
101
sm9/bn256/generate.go
Normal file
101
sm9/bn256/generate.go
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@ -0,0 +1,101 @@
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//go:build ignore
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// +build ignore
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package main
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import (
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"bytes"
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"go/format"
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"io"
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"log"
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"os"
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"os/exec"
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)
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// Running this generator requires addchain v0.4.0, which can be installed with
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//
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// go install github.com/mmcloughlin/addchain/cmd/addchain@v0.4.0
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//
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func main() {
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tmplAddchainFile, err := os.CreateTemp("", "addchain-template")
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if err != nil {
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log.Fatal(err)
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}
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defer os.Remove(tmplAddchainFile.Name())
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if _, err := io.WriteString(tmplAddchainFile, tmplAddchain); err != nil {
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log.Fatal(err)
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}
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if err := tmplAddchainFile.Close(); err != nil {
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log.Fatal(err)
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}
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log.Printf("Generating gfp_invert.go...")
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f, err := os.CreateTemp("", "addchain-gfp")
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if err != nil {
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log.Fatal(err)
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}
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defer os.Remove(f.Name())
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cmd := exec.Command("addchain", "search", "0xb640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457b")
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cmd.Stderr = os.Stderr
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cmd.Stdout = f
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if err := cmd.Run(); err != nil {
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log.Fatal(err)
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}
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if err := f.Close(); err != nil {
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log.Fatal(err)
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}
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cmd = exec.Command("addchain", "gen", "-tmpl", tmplAddchainFile.Name(), f.Name())
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cmd.Stderr = os.Stderr
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out, err := cmd.Output()
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if err != nil {
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log.Fatal(err)
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}
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out = bytes.Replace(out, []byte("Element"), []byte("gfP"), -1)
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out, err = format.Source(out)
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if err != nil {
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log.Fatal(err)
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}
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if err := os.WriteFile("gfp_invert.go", out, 0644); err != nil {
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log.Fatal(err)
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}
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}
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const tmplAddchain = `// Code generated by {{ .Meta.Name }}. DO NOT EDIT.
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package bn256
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// Invert sets e = 1/x, and returns e.
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//
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// If x == 0, Invert returns e = 0.
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func (e *Element) Invert(x *Element) *Element {
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// Inversion is implemented as exponentiation with exponent p − 2.
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// The sequence of {{ .Ops.Adds }} multiplications and {{ .Ops.Doubles }} squarings is derived from the
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// following addition chain generated with {{ .Meta.Module }} {{ .Meta.ReleaseTag }}.
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//
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{{- range lines (format .Script) }}
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// {{ . }}
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{{- end }}
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//
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var z = new(Element).Set(e)
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{{- range .Program.Temporaries }}
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var {{ . }} = new(Element)
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{{- end }}
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{{ range $i := .Program.Instructions -}}
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{{- with add $i.Op }}
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{{ $i.Output }}.Mul({{ .X }}, {{ .Y }})
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{{- end -}}
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{{- with double $i.Op }}
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{{ $i.Output }}.Square({{ .X }})
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{{- end -}}
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{{- with shift $i.Op -}}
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{{- $first := 0 -}}
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{{- if ne $i.Output.Identifier .X.Identifier }}
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{{ $i.Output }}.Square({{ .X }})
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{{- $first = 1 -}}
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{{- end }}
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for s := {{ $first }}; s < {{ .S }}; s++ {
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{{ $i.Output }}.Square({{ $i.Output }})
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}
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{{- end -}}
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{{- end }}
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return e.Set(z)
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}
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`
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@ -59,11 +59,13 @@ func (e *gfP) String() string {
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return fmt.Sprintf("%16.16x%16.16x%16.16x%16.16x", e[3], e[2], e[1], e[0])
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}
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func (e *gfP) Set(f *gfP) {
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func (e *gfP) Set(f *gfP) *gfP {
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e[0] = f[0]
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e[1] = f[1]
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e[2] = f[2]
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e[3] = f[3]
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return e
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}
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func (e *gfP) exp(f *gfP, bits [4]uint64) {
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@ -84,8 +86,22 @@ func (e *gfP) exp(f *gfP, bits [4]uint64) {
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e.Set(sum)
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}
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func (e *gfP) Invert(f *gfP) {
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e.exp(f, pMinus2)
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func (e *gfP) Mul(a, b *gfP) *gfP {
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gfpMul(e, a, b)
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return e
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}
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func (e *gfP) Square(a *gfP) *gfP {
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gfpMul(e, a, a)
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return e
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}
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// Equal returns 1 if e == t, and zero otherwise.
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func (e *gfP) Equal(t *gfP) int {
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if *e == *t {
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return 1
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}
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return 0
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}
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func (e *gfP) Sqrt(f *gfP) {
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@ -95,7 +111,7 @@ func (e *gfP) Sqrt(f *gfP) {
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// https://eprint.iacr.org/2012/685.pdf
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//
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a1, b, i := &gfP{}, &gfP{}, &gfP{}
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a1.exp(f, pMinus5Over8)
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sqrtCandidate(a1, f)
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gfpMul(b, twoExpPMinus5Over8, a1) // b=ta1
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gfpMul(a1, f, b) // a1=fb
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gfpMul(i, two, a1) // i=2(fb)
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221
sm9/bn256/gfp_invert.go
Normal file
221
sm9/bn256/gfp_invert.go
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@ -0,0 +1,221 @@
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// Code generated by addchain. DO NOT EDIT.
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package bn256
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// Invert sets e = 1/x, and returns e.
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//
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// If x == 0, Invert returns e = 0.
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func (e *gfP) Invert(x *gfP) *gfP {
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// Inversion is implemented as exponentiation with exponent p − 2.
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// The sequence of 56 multiplications and 250 squarings is derived from the
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// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
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//
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// _10 = 2*1
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// _100 = 2*_10
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// _110 = _10 + _100
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// _1010 = _100 + _110
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// _1011 = 1 + _1010
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// _1101 = _10 + _1011
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// _10000 = _110 + _1010
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// _10101 = _1010 + _1011
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// _11011 = _110 + _10101
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// _11101 = _10 + _11011
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// _11111 = _10 + _11101
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// _101001 = _1010 + _11111
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// _101011 = _10 + _101001
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// _111011 = _10000 + _101011
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// _1000101 = _1010 + _111011
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// _1001111 = _1010 + _1000101
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// _1010001 = _10 + _1001111
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// _1011011 = _1010 + _1010001
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// _1011101 = _10 + _1011011
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// _1011111 = _10 + _1011101
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// _1100011 = _100 + _1011111
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// _1101001 = _110 + _1100011
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// _1101101 = _100 + _1101001
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// _1101111 = _10 + _1101101
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// _1110101 = _110 + _1101111
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// _1111011 = _110 + _1110101
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// _10110110 = _111011 + _1111011
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// i72 = ((_10110110 << 2 + 1) << 33 + _10101) << 8
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// i94 = ((_11101 + i72) << 9 + _1101111) << 10 + _1110101
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// i116 = ((2*i94 + 1) << 14 + _1110101) << 5
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// i129 = 2*((_1101 + i116) << 9 + _1111011 + _100)
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// i146 = ((1 + i129) << 5 + _1011) << 9 + _111011
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// i174 = ((i146 << 8 + _11101) << 9 + _101001) << 9
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// i194 = ((_11111 + i174) << 8 + _101001) << 9 + _1101001
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// i220 = ((i194 << 8 + _1100011) << 8 + _1001111) << 8
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// i237 = ((_1011101 + i220) << 7 + _1101101) << 7 + _1011111
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// i260 = ((i237 << 8 + _101011) << 6 + _11111) << 7
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// i279 = ((_11011 + i260) << 9 + _1001111) << 7 + _1100011
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// i305 = ((i279 << 8 + _1010001) << 8 + _1000101) << 8
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// return _1111011 + i305
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//
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var z = new(gfP).Set(e)
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var t0 = new(gfP)
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var t1 = new(gfP)
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var t2 = new(gfP)
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var t3 = new(gfP)
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var t4 = new(gfP)
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var t5 = new(gfP)
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var t6 = new(gfP)
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var t7 = new(gfP)
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var t8 = new(gfP)
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var t9 = new(gfP)
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var t10 = new(gfP)
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var t11 = new(gfP)
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var t12 = new(gfP)
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var t13 = new(gfP)
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var t14 = new(gfP)
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var t15 = new(gfP)
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var t16 = new(gfP)
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var t17 = new(gfP)
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var t18 = new(gfP)
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var t19 = new(gfP)
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var t20 = new(gfP)
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t17.Square(x)
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t15.Square(t17)
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z.Mul(t17, t15)
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t2.Mul(t15, z)
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t14.Mul(x, t2)
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t16.Mul(t17, t14)
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t0.Mul(z, t2)
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t19.Mul(t2, t14)
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t4.Mul(z, t19)
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t12.Mul(t17, t4)
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t5.Mul(t17, t12)
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t11.Mul(t2, t5)
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t6.Mul(t17, t11)
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t13.Mul(t0, t6)
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t0.Mul(t2, t13)
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t3.Mul(t2, t0)
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t1.Mul(t17, t3)
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t2.Mul(t2, t1)
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t9.Mul(t17, t2)
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t7.Mul(t17, t9)
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t2.Mul(t15, t7)
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t10.Mul(z, t2)
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t8.Mul(t15, t10)
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t18.Mul(t17, t8)
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t17.Mul(z, t18)
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z.Mul(z, t17)
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t20.Mul(t13, z)
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for s := 0; s < 2; s++ {
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t20.Square(t20)
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}
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t20.Mul(x, t20)
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for s := 0; s < 33; s++ {
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t20.Square(t20)
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}
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t19.Mul(t19, t20)
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for s := 0; s < 8; s++ {
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t19.Square(t19)
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}
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t19.Mul(t12, t19)
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for s := 0; s < 9; s++ {
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t19.Square(t19)
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}
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t18.Mul(t18, t19)
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for s := 0; s < 10; s++ {
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t18.Square(t18)
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}
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t18.Mul(t17, t18)
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t18.Square(t18)
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t18.Mul(x, t18)
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for s := 0; s < 14; s++ {
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t18.Square(t18)
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}
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t17.Mul(t17, t18)
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for s := 0; s < 5; s++ {
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t17.Square(t17)
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}
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t16.Mul(t16, t17)
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for s := 0; s < 9; s++ {
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t16.Square(t16)
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}
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t16.Mul(z, t16)
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t15.Mul(t15, t16)
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t15.Square(t15)
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t15.Mul(x, t15)
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for s := 0; s < 5; s++ {
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t15.Square(t15)
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}
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t14.Mul(t14, t15)
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for s := 0; s < 9; s++ {
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t14.Square(t14)
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}
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t13.Mul(t13, t14)
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for s := 0; s < 8; s++ {
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t13.Square(t13)
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}
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t12.Mul(t12, t13)
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for s := 0; s < 9; s++ {
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t12.Square(t12)
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}
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t12.Mul(t11, t12)
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for s := 0; s < 9; s++ {
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t12.Square(t12)
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}
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t12.Mul(t5, t12)
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for s := 0; s < 8; s++ {
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t12.Square(t12)
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}
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t11.Mul(t11, t12)
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for s := 0; s < 9; s++ {
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t11.Square(t11)
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}
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t10.Mul(t10, t11)
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for s := 0; s < 8; s++ {
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t10.Square(t10)
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}
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t10.Mul(t2, t10)
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for s := 0; s < 8; s++ {
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t10.Square(t10)
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}
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t10.Mul(t3, t10)
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for s := 0; s < 8; s++ {
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t10.Square(t10)
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}
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t9.Mul(t9, t10)
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for s := 0; s < 7; s++ {
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t9.Square(t9)
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}
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t8.Mul(t8, t9)
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for s := 0; s < 7; s++ {
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t8.Square(t8)
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}
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t7.Mul(t7, t8)
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for s := 0; s < 8; s++ {
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t7.Square(t7)
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}
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t6.Mul(t6, t7)
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for s := 0; s < 6; s++ {
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t6.Square(t6)
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}
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t5.Mul(t5, t6)
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for s := 0; s < 7; s++ {
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t5.Square(t5)
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}
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t4.Mul(t4, t5)
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for s := 0; s < 9; s++ {
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t4.Square(t4)
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}
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t3.Mul(t3, t4)
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for s := 0; s < 7; s++ {
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t3.Square(t3)
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}
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t2.Mul(t2, t3)
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for s := 0; s < 8; s++ {
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t2.Square(t2)
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}
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t1.Mul(t1, t2)
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for s := 0; s < 8; s++ {
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t1.Square(t1)
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}
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t0.Mul(t0, t1)
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for s := 0; s < 8; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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return e.Set(z)
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}
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232
sm9/bn256/gfp_sqrt.go
Normal file
232
sm9/bn256/gfp_sqrt.go
Normal file
@ -0,0 +1,232 @@
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// Code generated by addchain. DO NOT EDIT.
|
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package bn256
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// Sqrt sets e to a square root of x. If x is not a square, Sqrt returns
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// false and e is unchanged. e and x can overlap.
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func Sqrt(e, x *gfP) (isSquare bool) {
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candidate, b, i := &gfP{}, &gfP{}, &gfP{}
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sqrtCandidate(candidate, x)
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gfpMul(b, twoExpPMinus5Over8, candidate) // b=ta1
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gfpMul(candidate, x, b) // a1=fb
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gfpMul(i, two, candidate) // i=2(fb)
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gfpMul(i, i, b) // i=2(fb)b
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gfpSub(i, i, one) // i=2(fb)b-1
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gfpMul(i, candidate, i) // i=(fb)(2(fb)b-1)
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square := new(gfP).Square(i)
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if square.Equal(x) != 1 {
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return false
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}
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e.Set(i)
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return true
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}
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// sqrtCandidate sets z to a square root candidate for x. z and x must not overlap.
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func sqrtCandidate(z, x *gfP) {
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// Since p = 8k+5, exponentiation by (p - 5) / 8 yields a square root candidate.
|
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//
|
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// The sequence of 54 multiplications and 248 squarings is derived from the
|
||||
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
|
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//
|
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// _10 = 2*1
|
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// _100 = 2*_10
|
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// _110 = _10 + _100
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// _1010 = _100 + _110
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// _1011 = 1 + _1010
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// _1101 = _10 + _1011
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// _1111 = _10 + _1101
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// _10000 = 1 + _1111
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// _10101 = _110 + _1111
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// _11011 = _110 + _10101
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// _11101 = _10 + _11011
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// _11111 = _10 + _11101
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// _101001 = _1010 + _11111
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// _101011 = _10 + _101001
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// _111011 = _10000 + _101011
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// _1000101 = _1010 + _111011
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// _1001111 = _1010 + _1000101
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// _1010001 = _10 + _1001111
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// _1011011 = _1010 + _1010001
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// _1011101 = _10 + _1011011
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// _1011111 = _10 + _1011101
|
||||
// _1100011 = _100 + _1011111
|
||||
// _1101001 = _110 + _1100011
|
||||
// _1101101 = _100 + _1101001
|
||||
// _1101111 = _10 + _1101101
|
||||
// _1110101 = _110 + _1101111
|
||||
// i72 = ((_1011011 << 3 + 1) << 33 + _10101) << 8
|
||||
// i94 = ((_11101 + i72) << 9 + _1101111) << 10 + _1110101
|
||||
// i116 = ((2*i94 + 1) << 14 + _1110101) << 5
|
||||
// i129 = 2*((_1101 + i116) << 9 + _1110101) + _10101
|
||||
// i153 = ((i129 << 5 + _1011) << 9 + _111011) << 8
|
||||
// i174 = ((_11101 + i153) << 9 + _101001) << 9 + _11111
|
||||
// i201 = ((i174 << 8 + _101001) << 9 + _1101001) << 8
|
||||
// i220 = ((_1100011 + i201) << 8 + _1001111) << 8 + _1011101
|
||||
// i244 = ((i220 << 7 + _1101101) << 7 + _1011111) << 8
|
||||
// i260 = ((_101011 + i244) << 6 + _11111) << 7 + _11011
|
||||
// i286 = ((i260 << 9 + _1001111) << 7 + _1100011) << 8
|
||||
// return ((_1010001 + i286) << 8 + _1000101) << 5 + _1111
|
||||
//
|
||||
var t0 = new(gfP)
|
||||
var t1 = new(gfP)
|
||||
var t2 = new(gfP)
|
||||
var t3 = new(gfP)
|
||||
var t4 = new(gfP)
|
||||
var t5 = new(gfP)
|
||||
var t6 = new(gfP)
|
||||
var t7 = new(gfP)
|
||||
var t8 = new(gfP)
|
||||
var t9 = new(gfP)
|
||||
var t10 = new(gfP)
|
||||
var t11 = new(gfP)
|
||||
var t12 = new(gfP)
|
||||
var t13 = new(gfP)
|
||||
var t14 = new(gfP)
|
||||
var t15 = new(gfP)
|
||||
var t16 = new(gfP)
|
||||
var t17 = new(gfP)
|
||||
var t18 = new(gfP)
|
||||
var t19 = new(gfP)
|
||||
|
||||
t18.Square(x)
|
||||
t8.Square(t18)
|
||||
t16.Mul(t18, t8)
|
||||
t2.Mul(t8, t16)
|
||||
t14.Mul(x, t2)
|
||||
t17.Mul(t18, t14)
|
||||
z.Mul(t18, t17)
|
||||
t0.Mul(x, z)
|
||||
t15.Mul(t16, z)
|
||||
t4.Mul(t16, t15)
|
||||
t12.Mul(t18, t4)
|
||||
t5.Mul(t18, t12)
|
||||
t11.Mul(t2, t5)
|
||||
t6.Mul(t18, t11)
|
||||
t13.Mul(t0, t6)
|
||||
t0.Mul(t2, t13)
|
||||
t3.Mul(t2, t0)
|
||||
t1.Mul(t18, t3)
|
||||
t19.Mul(t2, t1)
|
||||
t9.Mul(t18, t19)
|
||||
t7.Mul(t18, t9)
|
||||
t2.Mul(t8, t7)
|
||||
t10.Mul(t16, t2)
|
||||
t8.Mul(t8, t10)
|
||||
t18.Mul(t18, t8)
|
||||
t16.Mul(t16, t18)
|
||||
for s := 0; s < 3; s++ {
|
||||
t19.Square(t19)
|
||||
}
|
||||
t19.Mul(x, t19)
|
||||
for s := 0; s < 33; s++ {
|
||||
t19.Square(t19)
|
||||
}
|
||||
t19.Mul(t15, t19)
|
||||
for s := 0; s < 8; s++ {
|
||||
t19.Square(t19)
|
||||
}
|
||||
t19.Mul(t12, t19)
|
||||
for s := 0; s < 9; s++ {
|
||||
t19.Square(t19)
|
||||
}
|
||||
t18.Mul(t18, t19)
|
||||
for s := 0; s < 10; s++ {
|
||||
t18.Square(t18)
|
||||
}
|
||||
t18.Mul(t16, t18)
|
||||
t18.Square(t18)
|
||||
t18.Mul(x, t18)
|
||||
for s := 0; s < 14; s++ {
|
||||
t18.Square(t18)
|
||||
}
|
||||
t18.Mul(t16, t18)
|
||||
for s := 0; s < 5; s++ {
|
||||
t18.Square(t18)
|
||||
}
|
||||
t17.Mul(t17, t18)
|
||||
for s := 0; s < 9; s++ {
|
||||
t17.Square(t17)
|
||||
}
|
||||
t16.Mul(t16, t17)
|
||||
t16.Square(t16)
|
||||
t15.Mul(t15, t16)
|
||||
for s := 0; s < 5; s++ {
|
||||
t15.Square(t15)
|
||||
}
|
||||
t14.Mul(t14, t15)
|
||||
for s := 0; s < 9; s++ {
|
||||
t14.Square(t14)
|
||||
}
|
||||
t13.Mul(t13, t14)
|
||||
for s := 0; s < 8; s++ {
|
||||
t13.Square(t13)
|
||||
}
|
||||
t12.Mul(t12, t13)
|
||||
for s := 0; s < 9; s++ {
|
||||
t12.Square(t12)
|
||||
}
|
||||
t12.Mul(t11, t12)
|
||||
for s := 0; s < 9; s++ {
|
||||
t12.Square(t12)
|
||||
}
|
||||
t12.Mul(t5, t12)
|
||||
for s := 0; s < 8; s++ {
|
||||
t12.Square(t12)
|
||||
}
|
||||
t11.Mul(t11, t12)
|
||||
for s := 0; s < 9; s++ {
|
||||
t11.Square(t11)
|
||||
}
|
||||
t10.Mul(t10, t11)
|
||||
for s := 0; s < 8; s++ {
|
||||
t10.Square(t10)
|
||||
}
|
||||
t10.Mul(t2, t10)
|
||||
for s := 0; s < 8; s++ {
|
||||
t10.Square(t10)
|
||||
}
|
||||
t10.Mul(t3, t10)
|
||||
for s := 0; s < 8; s++ {
|
||||
t10.Square(t10)
|
||||
}
|
||||
t9.Mul(t9, t10)
|
||||
for s := 0; s < 7; s++ {
|
||||
t9.Square(t9)
|
||||
}
|
||||
t8.Mul(t8, t9)
|
||||
for s := 0; s < 7; s++ {
|
||||
t8.Square(t8)
|
||||
}
|
||||
t7.Mul(t7, t8)
|
||||
for s := 0; s < 8; s++ {
|
||||
t7.Square(t7)
|
||||
}
|
||||
t6.Mul(t6, t7)
|
||||
for s := 0; s < 6; s++ {
|
||||
t6.Square(t6)
|
||||
}
|
||||
t5.Mul(t5, t6)
|
||||
for s := 0; s < 7; s++ {
|
||||
t5.Square(t5)
|
||||
}
|
||||
t4.Mul(t4, t5)
|
||||
for s := 0; s < 9; s++ {
|
||||
t4.Square(t4)
|
||||
}
|
||||
t3.Mul(t3, t4)
|
||||
for s := 0; s < 7; s++ {
|
||||
t3.Square(t3)
|
||||
}
|
||||
t2.Mul(t2, t3)
|
||||
for s := 0; s < 8; s++ {
|
||||
t2.Square(t2)
|
||||
}
|
||||
t1.Mul(t1, t2)
|
||||
for s := 0; s < 8; s++ {
|
||||
t1.Square(t1)
|
||||
}
|
||||
t0.Mul(t0, t1)
|
||||
for s := 0; s < 5; s++ {
|
||||
t0.Square(t0)
|
||||
}
|
||||
z.Mul(z, t0)
|
||||
}
|
||||
@ -103,6 +103,33 @@ func TestSqrt(t *testing.T) {
|
||||
}
|
||||
}
|
||||
|
||||
func TestGeneratedSqrt(t *testing.T) {
|
||||
tests := []string{
|
||||
"9093a2b979e6186f43a9b28d41ba644d533377f2ede8c66b19774bf4a9c7a596",
|
||||
"92fe90b700fbd4d8cc177d300ed16e4e15471a681b2c9e3728c1b82c885e49c2",
|
||||
}
|
||||
for i, test := range tests {
|
||||
y2 := bigFromHex(test)
|
||||
y21 := new(big.Int).ModSqrt(y2, p)
|
||||
|
||||
y3 := new(big.Int).Mul(y21, y21)
|
||||
y3.Mod(y3, p)
|
||||
if y2.Cmp(y3) != 0 {
|
||||
t.Error("Invalid sqrt")
|
||||
}
|
||||
|
||||
tmp := fromBigInt(y2)
|
||||
e := &gfP{}
|
||||
Sqrt(e, tmp)
|
||||
montDecode(e, e)
|
||||
var res [32]byte
|
||||
e.Marshal(res[:])
|
||||
if hex.EncodeToString(res[:]) != hex.EncodeToString(y21.Bytes()) {
|
||||
t.Errorf("case %v, got %v, expected %v\n", i, hex.EncodeToString(res[:]), hex.EncodeToString(y21.Bytes()))
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestInvert(t *testing.T) {
|
||||
x := fromBigInt(bigFromHex("9093a2b979e6186f43a9b28d41ba644d533377f2ede8c66b19774bf4a9c7a596"))
|
||||
xInv := &gfP{}
|
||||
|
||||
118
sm9/generate.go
Normal file
118
sm9/generate.go
Normal file
@ -0,0 +1,118 @@
|
||||
//go:build ignore
|
||||
// +build ignore
|
||||
|
||||
package main
|
||||
|
||||
import (
|
||||
"bytes"
|
||||
"go/format"
|
||||
"io"
|
||||
"log"
|
||||
"os"
|
||||
"os/exec"
|
||||
)
|
||||
|
||||
// Running this generator requires addchain v0.4.0, which can be installed with
|
||||
//
|
||||
// go install github.com/mmcloughlin/addchain/cmd/addchain@v0.4.0
|
||||
//
|
||||
|
||||
func main() {
|
||||
tmplAddchainFile, err := os.CreateTemp("", "addchain-template")
|
||||
if err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
defer os.Remove(tmplAddchainFile.Name())
|
||||
if _, err := io.WriteString(tmplAddchainFile, tmplAddchain); err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
if err := tmplAddchainFile.Close(); err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
log.Printf("Generating gfp_sqrt.go...")
|
||||
f, err := os.CreateTemp("", "addchain-gfp")
|
||||
if err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
defer os.Remove(f.Name())
|
||||
cmd := exec.Command("addchain", "search", "0x16c80000005474de3ac07569feb1d8e8a43e5269634f5ddb7cadf364fc6a28af")
|
||||
cmd.Stderr = os.Stderr
|
||||
cmd.Stdout = f
|
||||
if err := cmd.Run(); err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
if err := f.Close(); err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
cmd = exec.Command("addchain", "gen", "-tmpl", tmplAddchainFile.Name(), f.Name())
|
||||
cmd.Stderr = os.Stderr
|
||||
out, err := cmd.Output()
|
||||
if err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
out = bytes.Replace(out, []byte("Element"), []byte("gfP"), -1)
|
||||
out, err = format.Source(out)
|
||||
if err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
if err := os.WriteFile("gfp_sqrt.go", out, 0644); err != nil {
|
||||
log.Fatal(err)
|
||||
}
|
||||
}
|
||||
|
||||
const tmplAddchain = `// Code generated by {{ .Meta.Name }}. DO NOT EDIT.
|
||||
package bn256
|
||||
|
||||
// Sqrt sets e to a square root of x. If x is not a square, Sqrt returns
|
||||
// false and e is unchanged. e and x can overlap.
|
||||
func Sqrt(e, x *Element) (isSquare bool) {
|
||||
candidate, b, i := &gfP{}, &gfP{}, &gfP{}
|
||||
sqrtCandidate(candidate, x)
|
||||
gfpMul(b, twoExpPMinus5Over8, candidate) // b=ta1
|
||||
gfpMul(candidate, x, b) // a1=fb
|
||||
gfpMul(i, two, candidate) // i=2(fb)
|
||||
gfpMul(i, i, b) // i=2(fb)b
|
||||
gfpSub(i, i, one) // i=2(fb)b-1
|
||||
gfpMul(i, candidate, i) // i=(fb)(2(fb)b-1)
|
||||
square := new(Element).Square(i)
|
||||
if square.Equal(x) != 1 {
|
||||
return false
|
||||
}
|
||||
e.Set(i)
|
||||
return true
|
||||
}
|
||||
|
||||
// sqrtCandidate sets z to a square root candidate for x. z and x must not overlap.
|
||||
func sqrtCandidate(z, x *Element) {
|
||||
// Since p = 8k+5, exponentiation by (p - 5) / 8 yields a square root candidate.
|
||||
//
|
||||
// The sequence of {{ .Ops.Adds }} multiplications and {{ .Ops.Doubles }} squarings is derived from the
|
||||
// following addition chain generated with {{ .Meta.Module }} {{ .Meta.ReleaseTag }}.
|
||||
//
|
||||
{{- range lines (format .Script) }}
|
||||
// {{ . }}
|
||||
{{- end }}
|
||||
//
|
||||
{{- range .Program.Temporaries }}
|
||||
var {{ . }} = new(Element)
|
||||
{{- end }}
|
||||
{{ range $i := .Program.Instructions -}}
|
||||
{{- with add $i.Op }}
|
||||
{{ $i.Output }}.Mul({{ .X }}, {{ .Y }})
|
||||
{{- end -}}
|
||||
{{- with double $i.Op }}
|
||||
{{ $i.Output }}.Square({{ .X }})
|
||||
{{- end -}}
|
||||
{{- with shift $i.Op -}}
|
||||
{{- $first := 0 -}}
|
||||
{{- if ne $i.Output.Identifier .X.Identifier }}
|
||||
{{ $i.Output }}.Square({{ .X }})
|
||||
{{- $first = 1 -}}
|
||||
{{- end }}
|
||||
for s := {{ $first }}; s < {{ .S }}; s++ {
|
||||
{{ $i.Output }}.Square({{ $i.Output }})
|
||||
}
|
||||
{{- end -}}
|
||||
{{- end }}
|
||||
}
|
||||
`
|
||||
Loading…
x
Reference in New Issue
Block a user