blob: 0204bc1233c49a5304c08733682443efc22a0409 [file] [log] [blame]
// Copyright 2022 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
//go:build ignore
package main
// Running this generator requires addchain v0.4.0, which can be installed with
//
// go install github.com/mmcloughlin/addchain/cmd/addchain@v0.4.0
//
import (
"bytes"
"crypto/elliptic"
"fmt"
"go/format"
"io"
"log"
"math/big"
"os"
"os/exec"
"strings"
"text/template"
)
var curves = []struct {
P string
Element string
Params *elliptic.CurveParams
BuildTags string
}{
{
P: "P224",
Element: "fiat.P224Element",
Params: elliptic.P224().Params(),
},
{
P: "P256",
Element: "fiat.P256Element",
Params: elliptic.P256().Params(),
BuildTags: "!amd64 && !arm64 && !ppc64le",
},
{
P: "P384",
Element: "fiat.P384Element",
Params: elliptic.P384().Params(),
},
{
P: "P521",
Element: "fiat.P521Element",
Params: elliptic.P521().Params(),
},
}
func main() {
t := template.Must(template.New("tmplNISTEC").Parse(tmplNISTEC))
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)
}
for _, c := range curves {
p := strings.ToLower(c.P)
elementLen := (c.Params.BitSize + 7) / 8
B := fmt.Sprintf("%#v", c.Params.B.FillBytes(make([]byte, elementLen)))
Gx := fmt.Sprintf("%#v", c.Params.Gx.FillBytes(make([]byte, elementLen)))
Gy := fmt.Sprintf("%#v", c.Params.Gy.FillBytes(make([]byte, elementLen)))
log.Printf("Generating %s.go...", p)
f, err := os.Create(p + ".go")
if err != nil {
log.Fatal(err)
}
defer f.Close()
buf := &bytes.Buffer{}
if err := t.Execute(buf, map[string]interface{}{
"P": c.P, "p": p, "B": B, "Gx": Gx, "Gy": Gy,
"Element": c.Element, "ElementLen": elementLen,
"BuildTags": c.BuildTags,
}); err != nil {
log.Fatal(err)
}
out, err := format.Source(buf.Bytes())
if err != nil {
log.Fatal(err)
}
if _, err := f.Write(out); err != nil {
log.Fatal(err)
}
// If p = 3 mod 4, implement modular square root by exponentiation.
mod4 := new(big.Int).Mod(c.Params.P, big.NewInt(4))
if mod4.Cmp(big.NewInt(3)) != 0 {
continue
}
exp := new(big.Int).Add(c.Params.P, big.NewInt(1))
exp.Div(exp, big.NewInt(4))
tmp, err := os.CreateTemp("", "addchain-"+p)
if err != nil {
log.Fatal(err)
}
defer os.Remove(tmp.Name())
cmd := exec.Command("addchain", "search", fmt.Sprintf("%d", exp))
cmd.Stderr = os.Stderr
cmd.Stdout = tmp
if err := cmd.Run(); err != nil {
log.Fatal(err)
}
if err := tmp.Close(); err != nil {
log.Fatal(err)
}
cmd = exec.Command("addchain", "gen", "-tmpl", tmplAddchainFile.Name(), tmp.Name())
cmd.Stderr = os.Stderr
out, err = cmd.Output()
if err != nil {
log.Fatal(err)
}
out = bytes.Replace(out, []byte("Element"), []byte(c.Element), -1)
out = bytes.Replace(out, []byte("sqrtCandidate"), []byte(p+"SqrtCandidate"), -1)
out, err = format.Source(out)
if err != nil {
log.Fatal(err)
}
if _, err := f.Write(out); err != nil {
log.Fatal(err)
}
}
}
const tmplNISTEC = `// Copyright 2022 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Code generated by generate.go. DO NOT EDIT.
{{ if .BuildTags }}
//go:build {{ .BuildTags }}
{{ end }}
package nistec
import (
"crypto/internal/nistec/fiat"
"crypto/subtle"
"errors"
"sync"
)
// {{.p}}ElementLength is the length of an element of the base or scalar field,
// which have the same bytes length for all NIST P curves.
const {{.p}}ElementLength = {{ .ElementLen }}
// {{.P}}Point is a {{.P}} point. The zero value is NOT valid.
type {{.P}}Point struct {
// The point is represented in projective coordinates (X:Y:Z),
// where x = X/Z and y = Y/Z.
x, y, z *{{.Element}}
}
// New{{.P}}Point returns a new {{.P}}Point representing the point at infinity point.
func New{{.P}}Point() *{{.P}}Point {
return &{{.P}}Point{
x: new({{.Element}}),
y: new({{.Element}}).One(),
z: new({{.Element}}),
}
}
// SetGenerator sets p to the canonical generator and returns p.
func (p *{{.P}}Point) SetGenerator() *{{.P}}Point {
p.x.SetBytes({{.Gx}})
p.y.SetBytes({{.Gy}})
p.z.One()
return p
}
// Set sets p = q and returns p.
func (p *{{.P}}Point) Set(q *{{.P}}Point) *{{.P}}Point {
p.x.Set(q.x)
p.y.Set(q.y)
p.z.Set(q.z)
return p
}
// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in
// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on
// the curve, it returns nil and an error, and the receiver is unchanged.
// Otherwise, it returns p.
func (p *{{.P}}Point) SetBytes(b []byte) (*{{.P}}Point, error) {
switch {
// Point at infinity.
case len(b) == 1 && b[0] == 0:
return p.Set(New{{.P}}Point()), nil
// Uncompressed form.
case len(b) == 1+2*{{.p}}ElementLength && b[0] == 4:
x, err := new({{.Element}}).SetBytes(b[1 : 1+{{.p}}ElementLength])
if err != nil {
return nil, err
}
y, err := new({{.Element}}).SetBytes(b[1+{{.p}}ElementLength:])
if err != nil {
return nil, err
}
if err := {{.p}}CheckOnCurve(x, y); err != nil {
return nil, err
}
p.x.Set(x)
p.y.Set(y)
p.z.One()
return p, nil
// Compressed form.
case len(b) == 1+{{.p}}ElementLength && (b[0] == 2 || b[0] == 3):
x, err := new({{.Element}}).SetBytes(b[1:])
if err != nil {
return nil, err
}
// y² = x³ - 3x + b
y := {{.p}}Polynomial(new({{.Element}}), x)
if !{{.p}}Sqrt(y, y) {
return nil, errors.New("invalid {{.P}} compressed point encoding")
}
// Select the positive or negative root, as indicated by the least
// significant bit, based on the encoding type byte.
otherRoot := new({{.Element}})
otherRoot.Sub(otherRoot, y)
cond := y.Bytes()[{{.p}}ElementLength-1]&1 ^ b[0]&1
y.Select(otherRoot, y, int(cond))
p.x.Set(x)
p.y.Set(y)
p.z.One()
return p, nil
default:
return nil, errors.New("invalid {{.P}} point encoding")
}
}
var _{{.p}}B *{{.Element}}
var _{{.p}}BOnce sync.Once
func {{.p}}B() *{{.Element}} {
_{{.p}}BOnce.Do(func() {
_{{.p}}B, _ = new({{.Element}}).SetBytes({{.B}})
})
return _{{.p}}B
}
// {{.p}}Polynomial sets y2 to x³ - 3x + b, and returns y2.
func {{.p}}Polynomial(y2, x *{{.Element}}) *{{.Element}} {
y2.Square(x)
y2.Mul(y2, x)
threeX := new({{.Element}}).Add(x, x)
threeX.Add(threeX, x)
y2.Sub(y2, threeX)
return y2.Add(y2, {{.p}}B())
}
func {{.p}}CheckOnCurve(x, y *{{.Element}}) error {
// y² = x³ - 3x + b
rhs := {{.p}}Polynomial(new({{.Element}}), x)
lhs := new({{.Element}}).Square(y)
if rhs.Equal(lhs) != 1 {
return errors.New("{{.P}} point not on curve")
}
return nil
}
// Bytes returns the uncompressed or infinity encoding of p, as specified in
// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at
// infinity is shorter than all other encodings.
func (p *{{.P}}Point) Bytes() []byte {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [1+2*{{.p}}ElementLength]byte
return p.bytes(&out)
}
func (p *{{.P}}Point) bytes(out *[1+2*{{.p}}ElementLength]byte) []byte {
if p.z.IsZero() == 1 {
return append(out[:0], 0)
}
zinv := new({{.Element}}).Invert(p.z)
x := new({{.Element}}).Mul(p.x, zinv)
y := new({{.Element}}).Mul(p.y, zinv)
buf := append(out[:0], 4)
buf = append(buf, x.Bytes()...)
buf = append(buf, y.Bytes()...)
return buf
}
// BytesX returns the encoding of the x-coordinate of p, as specified in SEC 1,
// Version 2.0, Section 2.3.5, or an error if p is the point at infinity.
func (p *{{.P}}Point) BytesX() ([]byte, error) {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [{{.p}}ElementLength]byte
return p.bytesX(&out)
}
func (p *{{.P}}Point) bytesX(out *[{{.p}}ElementLength]byte) ([]byte, error) {
if p.z.IsZero() == 1 {
return nil, errors.New("{{.P}} point is the point at infinity")
}
zinv := new({{.Element}}).Invert(p.z)
x := new({{.Element}}).Mul(p.x, zinv)
return append(out[:0], x.Bytes()...), nil
}
// BytesCompressed returns the compressed or infinity encoding of p, as
// specified in SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the
// point at infinity is shorter than all other encodings.
func (p *{{.P}}Point) BytesCompressed() []byte {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [1 + {{.p}}ElementLength]byte
return p.bytesCompressed(&out)
}
func (p *{{.P}}Point) bytesCompressed(out *[1 + {{.p}}ElementLength]byte) []byte {
if p.z.IsZero() == 1 {
return append(out[:0], 0)
}
zinv := new({{.Element}}).Invert(p.z)
x := new({{.Element}}).Mul(p.x, zinv)
y := new({{.Element}}).Mul(p.y, zinv)
// Encode the sign of the y coordinate (indicated by the least significant
// bit) as the encoding type (2 or 3).
buf := append(out[:0], 2)
buf[0] |= y.Bytes()[{{.p}}ElementLength-1] & 1
buf = append(buf, x.Bytes()...)
return buf
}
// Add sets q = p1 + p2, and returns q. The points may overlap.
func (q *{{.P}}Point) Add(p1, p2 *{{.P}}Point) *{{.P}}Point {
// Complete addition formula for a = -3 from "Complete addition formulas for
// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2.
t0 := new({{.Element}}).Mul(p1.x, p2.x) // t0 := X1 * X2
t1 := new({{.Element}}).Mul(p1.y, p2.y) // t1 := Y1 * Y2
t2 := new({{.Element}}).Mul(p1.z, p2.z) // t2 := Z1 * Z2
t3 := new({{.Element}}).Add(p1.x, p1.y) // t3 := X1 + Y1
t4 := new({{.Element}}).Add(p2.x, p2.y) // t4 := X2 + Y2
t3.Mul(t3, t4) // t3 := t3 * t4
t4.Add(t0, t1) // t4 := t0 + t1
t3.Sub(t3, t4) // t3 := t3 - t4
t4.Add(p1.y, p1.z) // t4 := Y1 + Z1
x3 := new({{.Element}}).Add(p2.y, p2.z) // X3 := Y2 + Z2
t4.Mul(t4, x3) // t4 := t4 * X3
x3.Add(t1, t2) // X3 := t1 + t2
t4.Sub(t4, x3) // t4 := t4 - X3
x3.Add(p1.x, p1.z) // X3 := X1 + Z1
y3 := new({{.Element}}).Add(p2.x, p2.z) // Y3 := X2 + Z2
x3.Mul(x3, y3) // X3 := X3 * Y3
y3.Add(t0, t2) // Y3 := t0 + t2
y3.Sub(x3, y3) // Y3 := X3 - Y3
z3 := new({{.Element}}).Mul({{.p}}B(), t2) // Z3 := b * t2
x3.Sub(y3, z3) // X3 := Y3 - Z3
z3.Add(x3, x3) // Z3 := X3 + X3
x3.Add(x3, z3) // X3 := X3 + Z3
z3.Sub(t1, x3) // Z3 := t1 - X3
x3.Add(t1, x3) // X3 := t1 + X3
y3.Mul({{.p}}B(), y3) // Y3 := b * Y3
t1.Add(t2, t2) // t1 := t2 + t2
t2.Add(t1, t2) // t2 := t1 + t2
y3.Sub(y3, t2) // Y3 := Y3 - t2
y3.Sub(y3, t0) // Y3 := Y3 - t0
t1.Add(y3, y3) // t1 := Y3 + Y3
y3.Add(t1, y3) // Y3 := t1 + Y3
t1.Add(t0, t0) // t1 := t0 + t0
t0.Add(t1, t0) // t0 := t1 + t0
t0.Sub(t0, t2) // t0 := t0 - t2
t1.Mul(t4, y3) // t1 := t4 * Y3
t2.Mul(t0, y3) // t2 := t0 * Y3
y3.Mul(x3, z3) // Y3 := X3 * Z3
y3.Add(y3, t2) // Y3 := Y3 + t2
x3.Mul(t3, x3) // X3 := t3 * X3
x3.Sub(x3, t1) // X3 := X3 - t1
z3.Mul(t4, z3) // Z3 := t4 * Z3
t1.Mul(t3, t0) // t1 := t3 * t0
z3.Add(z3, t1) // Z3 := Z3 + t1
q.x.Set(x3)
q.y.Set(y3)
q.z.Set(z3)
return q
}
// Double sets q = p + p, and returns q. The points may overlap.
func (q *{{.P}}Point) Double(p *{{.P}}Point) *{{.P}}Point {
// Complete addition formula for a = -3 from "Complete addition formulas for
// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2.
t0 := new({{.Element}}).Square(p.x) // t0 := X ^ 2
t1 := new({{.Element}}).Square(p.y) // t1 := Y ^ 2
t2 := new({{.Element}}).Square(p.z) // t2 := Z ^ 2
t3 := new({{.Element}}).Mul(p.x, p.y) // t3 := X * Y
t3.Add(t3, t3) // t3 := t3 + t3
z3 := new({{.Element}}).Mul(p.x, p.z) // Z3 := X * Z
z3.Add(z3, z3) // Z3 := Z3 + Z3
y3 := new({{.Element}}).Mul({{.p}}B(), t2) // Y3 := b * t2
y3.Sub(y3, z3) // Y3 := Y3 - Z3
x3 := new({{.Element}}).Add(y3, y3) // X3 := Y3 + Y3
y3.Add(x3, y3) // Y3 := X3 + Y3
x3.Sub(t1, y3) // X3 := t1 - Y3
y3.Add(t1, y3) // Y3 := t1 + Y3
y3.Mul(x3, y3) // Y3 := X3 * Y3
x3.Mul(x3, t3) // X3 := X3 * t3
t3.Add(t2, t2) // t3 := t2 + t2
t2.Add(t2, t3) // t2 := t2 + t3
z3.Mul({{.p}}B(), z3) // Z3 := b * Z3
z3.Sub(z3, t2) // Z3 := Z3 - t2
z3.Sub(z3, t0) // Z3 := Z3 - t0
t3.Add(z3, z3) // t3 := Z3 + Z3
z3.Add(z3, t3) // Z3 := Z3 + t3
t3.Add(t0, t0) // t3 := t0 + t0
t0.Add(t3, t0) // t0 := t3 + t0
t0.Sub(t0, t2) // t0 := t0 - t2
t0.Mul(t0, z3) // t0 := t0 * Z3
y3.Add(y3, t0) // Y3 := Y3 + t0
t0.Mul(p.y, p.z) // t0 := Y * Z
t0.Add(t0, t0) // t0 := t0 + t0
z3.Mul(t0, z3) // Z3 := t0 * Z3
x3.Sub(x3, z3) // X3 := X3 - Z3
z3.Mul(t0, t1) // Z3 := t0 * t1
z3.Add(z3, z3) // Z3 := Z3 + Z3
z3.Add(z3, z3) // Z3 := Z3 + Z3
q.x.Set(x3)
q.y.Set(y3)
q.z.Set(z3)
return q
}
// Select sets q to p1 if cond == 1, and to p2 if cond == 0.
func (q *{{.P}}Point) Select(p1, p2 *{{.P}}Point, cond int) *{{.P}}Point {
q.x.Select(p1.x, p2.x, cond)
q.y.Select(p1.y, p2.y, cond)
q.z.Select(p1.z, p2.z, cond)
return q
}
// A {{.p}}Table holds the first 15 multiples of a point at offset -1, so [1]P
// is at table[0], [15]P is at table[14], and [0]P is implicitly the identity
// point.
type {{.p}}Table [15]*{{.P}}Point
// Select selects the n-th multiple of the table base point into p. It works in
// constant time by iterating over every entry of the table. n must be in [0, 15].
func (table *{{.p}}Table) Select(p *{{.P}}Point, n uint8) {
if n >= 16 {
panic("nistec: internal error: {{.p}}Table called with out-of-bounds value")
}
p.Set(New{{.P}}Point())
for i := uint8(1); i < 16; i++ {
cond := subtle.ConstantTimeByteEq(i, n)
p.Select(table[i-1], p, cond)
}
}
// ScalarMult sets p = scalar * q, and returns p.
func (p *{{.P}}Point) ScalarMult(q *{{.P}}Point, scalar []byte) (*{{.P}}Point, error) {
// Compute a {{.p}}Table for the base point q. The explicit New{{.P}}Point
// calls get inlined, letting the allocations live on the stack.
var table = {{.p}}Table{New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(),
New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(),
New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(),
New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point()}
table[0].Set(q)
for i := 1; i < 15; i += 2 {
table[i].Double(table[i/2])
table[i+1].Add(table[i], q)
}
// Instead of doing the classic double-and-add chain, we do it with a
// four-bit window: we double four times, and then add [0-15]P.
t := New{{.P}}Point()
p.Set(New{{.P}}Point())
for i, byte := range scalar {
// No need to double on the first iteration, as p is the identity at
// this point, and [N]∞ = ∞.
if i != 0 {
p.Double(p)
p.Double(p)
p.Double(p)
p.Double(p)
}
windowValue := byte >> 4
table.Select(t, windowValue)
p.Add(p, t)
p.Double(p)
p.Double(p)
p.Double(p)
p.Double(p)
windowValue = byte & 0b1111
table.Select(t, windowValue)
p.Add(p, t)
}
return p, nil
}
var {{.p}}GeneratorTable *[{{.p}}ElementLength * 2]{{.p}}Table
var {{.p}}GeneratorTableOnce sync.Once
// generatorTable returns a sequence of {{.p}}Tables. The first table contains
// multiples of G. Each successive table is the previous table doubled four
// times.
func (p *{{.P}}Point) generatorTable() *[{{.p}}ElementLength * 2]{{.p}}Table {
{{.p}}GeneratorTableOnce.Do(func() {
{{.p}}GeneratorTable = new([{{.p}}ElementLength * 2]{{.p}}Table)
base := New{{.P}}Point().SetGenerator()
for i := 0; i < {{.p}}ElementLength*2; i++ {
{{.p}}GeneratorTable[i][0] = New{{.P}}Point().Set(base)
for j := 1; j < 15; j++ {
{{.p}}GeneratorTable[i][j] = New{{.P}}Point().Add({{.p}}GeneratorTable[i][j-1], base)
}
base.Double(base)
base.Double(base)
base.Double(base)
base.Double(base)
}
})
return {{.p}}GeneratorTable
}
// ScalarBaseMult sets p = scalar * B, where B is the canonical generator, and
// returns p.
func (p *{{.P}}Point) ScalarBaseMult(scalar []byte) (*{{.P}}Point, error) {
if len(scalar) != {{.p}}ElementLength {
return nil, errors.New("invalid scalar length")
}
tables := p.generatorTable()
// This is also a scalar multiplication with a four-bit window like in
// ScalarMult, but in this case the doublings are precomputed. The value
// [windowValue]G added at iteration k would normally get doubled
// (totIterations-k)×4 times, but with a larger precomputation we can
// instead add [2^((totIterations-k)×4)][windowValue]G and avoid the
// doublings between iterations.
t := New{{.P}}Point()
p.Set(New{{.P}}Point())
tableIndex := len(tables) - 1
for _, byte := range scalar {
windowValue := byte >> 4
tables[tableIndex].Select(t, windowValue)
p.Add(p, t)
tableIndex--
windowValue = byte & 0b1111
tables[tableIndex].Select(t, windowValue)
p.Add(p, t)
tableIndex--
}
return p, nil
}
// {{.p}}Sqrt sets e to a square root of x. If x is not a square, {{.p}}Sqrt returns
// false and e is unchanged. e and x can overlap.
func {{.p}}Sqrt(e, x *{{ .Element }}) (isSquare bool) {
candidate := new({{ .Element }})
{{.p}}SqrtCandidate(candidate, x)
square := new({{ .Element }}).Square(candidate)
if square.Equal(x) != 1 {
return false
}
e.Set(candidate)
return true
}
`
const tmplAddchain = `
// sqrtCandidate sets z to a square root candidate for x. z and x must not overlap.
func sqrtCandidate(z, x *Element) {
// Since p = 3 mod 4, exponentiation by (p + 1) / 4 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 }}
}
`