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528 lines
19 KiB
Go
528 lines
19 KiB
Go
// Copyright 2022 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Code generated by generate.go. DO NOT EDIT.
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//go:build !amd64 && !arm64 || purego
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// +build !amd64,!arm64 purego
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package sm2ec
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import (
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"crypto/subtle"
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"errors"
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"github.com/emmansun/gmsm/internal/sm2ec/fiat"
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"sync"
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)
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// sm2p256ElementLength is the length of an element of the base or scalar field,
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// which have the same bytes length for all NIST P curves.
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const sm2p256ElementLength = 32
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// SM2P256Point is a SM2P256 point. The zero value is NOT valid.
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type SM2P256Point struct {
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// The point is represented in projective coordinates (X:Y:Z),
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// where x = X/Z and y = Y/Z.
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x, y, z *fiat.SM2P256Element
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}
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// NewSM2P256Point returns a new SM2P256Point representing the point at infinity point.
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func NewSM2P256Point() *SM2P256Point {
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return &SM2P256Point{
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x: new(fiat.SM2P256Element),
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y: new(fiat.SM2P256Element).One(),
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z: new(fiat.SM2P256Element),
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}
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}
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// SetGenerator sets p to the canonical generator and returns p.
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func (p *SM2P256Point) SetGenerator() *SM2P256Point {
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p.x.SetBytes([]byte{0x32, 0xc4, 0xae, 0x2c, 0x1f, 0x19, 0x81, 0x19, 0x5f, 0x99, 0x4, 0x46, 0x6a, 0x39, 0xc9, 0x94, 0x8f, 0xe3, 0xb, 0xbf, 0xf2, 0x66, 0xb, 0xe1, 0x71, 0x5a, 0x45, 0x89, 0x33, 0x4c, 0x74, 0xc7})
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p.y.SetBytes([]byte{0xbc, 0x37, 0x36, 0xa2, 0xf4, 0xf6, 0x77, 0x9c, 0x59, 0xbd, 0xce, 0xe3, 0x6b, 0x69, 0x21, 0x53, 0xd0, 0xa9, 0x87, 0x7c, 0xc6, 0x2a, 0x47, 0x40, 0x2, 0xdf, 0x32, 0xe5, 0x21, 0x39, 0xf0, 0xa0})
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p.z.One()
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return p
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}
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// Set sets p = q and returns p.
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func (p *SM2P256Point) Set(q *SM2P256Point) *SM2P256Point {
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p.x.Set(q.x)
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p.y.Set(q.y)
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p.z.Set(q.z)
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return p
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}
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// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in
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// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on
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// the curve, it returns nil and an error, and the receiver is unchanged.
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// Otherwise, it returns p.
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func (p *SM2P256Point) SetBytes(b []byte) (*SM2P256Point, error) {
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switch {
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// Point at infinity.
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case len(b) == 1 && b[0] == 0:
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return p.Set(NewSM2P256Point()), nil
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// Uncompressed form.
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case len(b) == 1+2*sm2p256ElementLength && b[0] == 4:
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x, err := new(fiat.SM2P256Element).SetBytes(b[1 : 1+sm2p256ElementLength])
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if err != nil {
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return nil, err
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}
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y, err := new(fiat.SM2P256Element).SetBytes(b[1+sm2p256ElementLength:])
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if err != nil {
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return nil, err
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}
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if err := sm2p256CheckOnCurve(x, y); err != nil {
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return nil, err
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}
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p.x.Set(x)
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p.y.Set(y)
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p.z.One()
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return p, nil
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// Compressed form.
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case len(b) == 1+sm2p256ElementLength && (b[0] == 2 || b[0] == 3):
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x, err := new(fiat.SM2P256Element).SetBytes(b[1:])
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if err != nil {
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return nil, err
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}
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// y² = x³ - 3x + b
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y := sm2p256Polynomial(new(fiat.SM2P256Element), x)
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if !sm2p256Sqrt(y, y) {
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return nil, errors.New("invalid SM2P256 compressed point encoding")
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}
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// Select the positive or negative root, as indicated by the least
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// significant bit, based on the encoding type byte.
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otherRoot := new(fiat.SM2P256Element)
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otherRoot.Sub(otherRoot, y)
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cond := y.Bytes()[sm2p256ElementLength-1]&1 ^ b[0]&1
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y.Select(otherRoot, y, int(cond))
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p.x.Set(x)
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p.y.Set(y)
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p.z.One()
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return p, nil
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default:
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return nil, errors.New("invalid SM2P256 point encoding")
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}
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}
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var _sm2p256B *fiat.SM2P256Element
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var _sm2p256BOnce sync.Once
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func sm2p256B() *fiat.SM2P256Element {
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_sm2p256BOnce.Do(func() {
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_sm2p256B, _ = new(fiat.SM2P256Element).SetBytes([]byte{0x28, 0xe9, 0xfa, 0x9e, 0x9d, 0x9f, 0x5e, 0x34, 0x4d, 0x5a, 0x9e, 0x4b, 0xcf, 0x65, 0x9, 0xa7, 0xf3, 0x97, 0x89, 0xf5, 0x15, 0xab, 0x8f, 0x92, 0xdd, 0xbc, 0xbd, 0x41, 0x4d, 0x94, 0xe, 0x93})
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})
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return _sm2p256B
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}
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// sm2p256Polynomial sets y2 to x³ - 3x + b, and returns y2.
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func sm2p256Polynomial(y2, x *fiat.SM2P256Element) *fiat.SM2P256Element {
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y2.Square(x)
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y2.Mul(y2, x)
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threeX := new(fiat.SM2P256Element).Add(x, x)
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threeX.Add(threeX, x)
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y2.Sub(y2, threeX)
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return y2.Add(y2, sm2p256B())
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}
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func sm2p256CheckOnCurve(x, y *fiat.SM2P256Element) error {
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// y² = x³ - 3x + b
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rhs := sm2p256Polynomial(new(fiat.SM2P256Element), x)
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lhs := new(fiat.SM2P256Element).Square(y)
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if rhs.Equal(lhs) != 1 {
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return errors.New("SM2P256 point not on curve")
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}
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return nil
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}
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// Bytes returns the uncompressed or infinity encoding of p, as specified in
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// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at
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// infinity is shorter than all other encodings.
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func (p *SM2P256Point) Bytes() []byte {
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// This function is outlined to make the allocations inline in the caller
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// rather than happen on the heap.
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var out [1 + 2*sm2p256ElementLength]byte
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return p.bytes(&out)
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}
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func (p *SM2P256Point) bytes(out *[1 + 2*sm2p256ElementLength]byte) []byte {
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if p.z.IsZero() == 1 {
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return append(out[:0], 0)
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}
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zinv := new(fiat.SM2P256Element).Invert(p.z)
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x := new(fiat.SM2P256Element).Mul(p.x, zinv)
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y := new(fiat.SM2P256Element).Mul(p.y, zinv)
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buf := append(out[:0], 4)
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buf = append(buf, x.Bytes()...)
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buf = append(buf, y.Bytes()...)
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return buf
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}
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// BytesX returns the encoding of the x-coordinate of p, as specified in SEC 1,
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// Version 2.0, Section 2.3.5, or an error if p is the point at infinity.
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func (p *SM2P256Point) BytesX() ([]byte, error) {
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// This function is outlined to make the allocations inline in the caller
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// rather than happen on the heap.
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var out [sm2p256ElementLength]byte
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return p.bytesX(&out)
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}
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func (p *SM2P256Point) bytesX(out *[sm2p256ElementLength]byte) ([]byte, error) {
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if p.z.IsZero() == 1 {
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return nil, errors.New("SM2P256 point is the point at infinity")
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}
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zinv := new(fiat.SM2P256Element).Invert(p.z)
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x := new(fiat.SM2P256Element).Mul(p.x, zinv)
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return append(out[:0], x.Bytes()...), nil
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}
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// BytesCompressed returns the compressed or infinity encoding of p, as
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// specified in SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the
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// point at infinity is shorter than all other encodings.
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func (p *SM2P256Point) BytesCompressed() []byte {
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// This function is outlined to make the allocations inline in the caller
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// rather than happen on the heap.
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var out [1 + sm2p256ElementLength]byte
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return p.bytesCompressed(&out)
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}
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func (p *SM2P256Point) bytesCompressed(out *[1 + sm2p256ElementLength]byte) []byte {
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if p.z.IsZero() == 1 {
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return append(out[:0], 0)
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}
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zinv := new(fiat.SM2P256Element).Invert(p.z)
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x := new(fiat.SM2P256Element).Mul(p.x, zinv)
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y := new(fiat.SM2P256Element).Mul(p.y, zinv)
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// Encode the sign of the y coordinate (indicated by the least significant
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// bit) as the encoding type (2 or 3).
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buf := append(out[:0], 2)
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buf[0] |= y.Bytes()[sm2p256ElementLength-1] & 1
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buf = append(buf, x.Bytes()...)
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return buf
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}
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// Add sets q = p1 + p2, and returns q. The points may overlap.
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func (q *SM2P256Point) Add(p1, p2 *SM2P256Point) *SM2P256Point {
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// Complete addition formula for a = -3 from "Complete addition formulas for
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// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2.
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t0 := new(fiat.SM2P256Element).Mul(p1.x, p2.x) // t0 := X1 * X2
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t1 := new(fiat.SM2P256Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2
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t2 := new(fiat.SM2P256Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2
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t3 := new(fiat.SM2P256Element).Add(p1.x, p1.y) // t3 := X1 + Y1
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t4 := new(fiat.SM2P256Element).Add(p2.x, p2.y) // t4 := X2 + Y2
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t3.Mul(t3, t4) // t3 := t3 * t4
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t4.Add(t0, t1) // t4 := t0 + t1
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t3.Sub(t3, t4) // t3 := t3 - t4
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t4.Add(p1.y, p1.z) // t4 := Y1 + Z1
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x3 := new(fiat.SM2P256Element).Add(p2.y, p2.z) // X3 := Y2 + Z2
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t4.Mul(t4, x3) // t4 := t4 * X3
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x3.Add(t1, t2) // X3 := t1 + t2
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t4.Sub(t4, x3) // t4 := t4 - X3
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x3.Add(p1.x, p1.z) // X3 := X1 + Z1
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y3 := new(fiat.SM2P256Element).Add(p2.x, p2.z) // Y3 := X2 + Z2
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x3.Mul(x3, y3) // X3 := X3 * Y3
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y3.Add(t0, t2) // Y3 := t0 + t2
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y3.Sub(x3, y3) // Y3 := X3 - Y3
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z3 := new(fiat.SM2P256Element).Mul(sm2p256B(), t2) // Z3 := b * t2
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x3.Sub(y3, z3) // X3 := Y3 - Z3
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z3.Add(x3, x3) // Z3 := X3 + X3
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x3.Add(x3, z3) // X3 := X3 + Z3
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z3.Sub(t1, x3) // Z3 := t1 - X3
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x3.Add(t1, x3) // X3 := t1 + X3
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y3.Mul(sm2p256B(), y3) // Y3 := b * Y3
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t1.Add(t2, t2) // t1 := t2 + t2
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t2.Add(t1, t2) // t2 := t1 + t2
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y3.Sub(y3, t2) // Y3 := Y3 - t2
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y3.Sub(y3, t0) // Y3 := Y3 - t0
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t1.Add(y3, y3) // t1 := Y3 + Y3
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y3.Add(t1, y3) // Y3 := t1 + Y3
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t1.Add(t0, t0) // t1 := t0 + t0
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t0.Add(t1, t0) // t0 := t1 + t0
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t0.Sub(t0, t2) // t0 := t0 - t2
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t1.Mul(t4, y3) // t1 := t4 * Y3
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t2.Mul(t0, y3) // t2 := t0 * Y3
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y3.Mul(x3, z3) // Y3 := X3 * Z3
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y3.Add(y3, t2) // Y3 := Y3 + t2
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x3.Mul(t3, x3) // X3 := t3 * X3
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x3.Sub(x3, t1) // X3 := X3 - t1
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z3.Mul(t4, z3) // Z3 := t4 * Z3
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t1.Mul(t3, t0) // t1 := t3 * t0
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z3.Add(z3, t1) // Z3 := Z3 + t1
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q.x.Set(x3)
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q.y.Set(y3)
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q.z.Set(z3)
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return q
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}
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// Double sets q = p + p, and returns q. The points may overlap.
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func (q *SM2P256Point) Double(p *SM2P256Point) *SM2P256Point {
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// Complete addition formula for a = -3 from "Complete addition formulas for
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// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2.
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t0 := new(fiat.SM2P256Element).Square(p.x) // t0 := X ^ 2
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t1 := new(fiat.SM2P256Element).Square(p.y) // t1 := Y ^ 2
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t2 := new(fiat.SM2P256Element).Square(p.z) // t2 := Z ^ 2
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t3 := new(fiat.SM2P256Element).Mul(p.x, p.y) // t3 := X * Y
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t3.Add(t3, t3) // t3 := t3 + t3
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z3 := new(fiat.SM2P256Element).Mul(p.x, p.z) // Z3 := X * Z
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z3.Add(z3, z3) // Z3 := Z3 + Z3
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y3 := new(fiat.SM2P256Element).Mul(sm2p256B(), t2) // Y3 := b * t2
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y3.Sub(y3, z3) // Y3 := Y3 - Z3
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x3 := new(fiat.SM2P256Element).Add(y3, y3) // X3 := Y3 + Y3
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y3.Add(x3, y3) // Y3 := X3 + Y3
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x3.Sub(t1, y3) // X3 := t1 - Y3
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y3.Add(t1, y3) // Y3 := t1 + Y3
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y3.Mul(x3, y3) // Y3 := X3 * Y3
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x3.Mul(x3, t3) // X3 := X3 * t3
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t3.Add(t2, t2) // t3 := t2 + t2
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t2.Add(t2, t3) // t2 := t2 + t3
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z3.Mul(sm2p256B(), z3) // Z3 := b * Z3
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z3.Sub(z3, t2) // Z3 := Z3 - t2
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z3.Sub(z3, t0) // Z3 := Z3 - t0
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t3.Add(z3, z3) // t3 := Z3 + Z3
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z3.Add(z3, t3) // Z3 := Z3 + t3
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t3.Add(t0, t0) // t3 := t0 + t0
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t0.Add(t3, t0) // t0 := t3 + t0
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t0.Sub(t0, t2) // t0 := t0 - t2
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t0.Mul(t0, z3) // t0 := t0 * Z3
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y3.Add(y3, t0) // Y3 := Y3 + t0
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t0.Mul(p.y, p.z) // t0 := Y * Z
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t0.Add(t0, t0) // t0 := t0 + t0
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z3.Mul(t0, z3) // Z3 := t0 * Z3
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x3.Sub(x3, z3) // X3 := X3 - Z3
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z3.Mul(t0, t1) // Z3 := t0 * t1
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z3.Add(z3, z3) // Z3 := Z3 + Z3
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z3.Add(z3, z3) // Z3 := Z3 + Z3
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q.x.Set(x3)
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q.y.Set(y3)
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q.z.Set(z3)
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return q
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}
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// Select sets q to p1 if cond == 1, and to p2 if cond == 0.
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func (q *SM2P256Point) Select(p1, p2 *SM2P256Point, cond int) *SM2P256Point {
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q.x.Select(p1.x, p2.x, cond)
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q.y.Select(p1.y, p2.y, cond)
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q.z.Select(p1.z, p2.z, cond)
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return q
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}
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// A sm2p256Table holds the first 15 multiples of a point at offset -1, so [1]P
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// is at table[0], [15]P is at table[14], and [0]P is implicitly the identity
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// point.
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type sm2p256Table [15]*SM2P256Point
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// Select selects the n-th multiple of the table base point into p. It works in
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// constant time by iterating over every entry of the table. n must be in [0, 15].
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func (table *sm2p256Table) Select(p *SM2P256Point, n uint8) {
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if n >= 16 {
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panic("sm2ec: internal error: sm2p256Table called with out-of-bounds value")
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}
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p.Set(NewSM2P256Point())
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for i := uint8(1); i < 16; i++ {
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cond := subtle.ConstantTimeByteEq(i, n)
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p.Select(table[i-1], p, cond)
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}
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}
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// ScalarMult sets p = scalar * q, and returns p.
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func (p *SM2P256Point) ScalarMult(q *SM2P256Point, scalar []byte) (*SM2P256Point, error) {
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// Compute a sm2p256Table for the base point q. The explicit NewSM2P256Point
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// calls get inlined, letting the allocations live on the stack.
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var table = sm2p256Table{NewSM2P256Point(), NewSM2P256Point(), NewSM2P256Point(),
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NewSM2P256Point(), NewSM2P256Point(), NewSM2P256Point(), NewSM2P256Point(),
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NewSM2P256Point(), NewSM2P256Point(), NewSM2P256Point(), NewSM2P256Point(),
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NewSM2P256Point(), NewSM2P256Point(), NewSM2P256Point(), NewSM2P256Point()}
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table[0].Set(q)
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for i := 1; i < 15; i += 2 {
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table[i].Double(table[i/2])
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table[i+1].Add(table[i], q)
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}
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// Instead of doing the classic double-and-add chain, we do it with a
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// four-bit window: we double four times, and then add [0-15]P.
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t := NewSM2P256Point()
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p.Set(NewSM2P256Point())
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for i, byte := range scalar {
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// No need to double on the first iteration, as p is the identity at
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// this point, and [N]∞ = ∞.
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if i != 0 {
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p.Double(p)
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p.Double(p)
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p.Double(p)
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p.Double(p)
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}
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windowValue := byte >> 4
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table.Select(t, windowValue)
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p.Add(p, t)
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p.Double(p)
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p.Double(p)
|
||
p.Double(p)
|
||
p.Double(p)
|
||
|
||
windowValue = byte & 0b1111
|
||
table.Select(t, windowValue)
|
||
p.Add(p, t)
|
||
}
|
||
|
||
return p, nil
|
||
}
|
||
|
||
var sm2p256GeneratorTable *[sm2p256ElementLength * 2]sm2p256Table
|
||
var sm2p256GeneratorTableOnce sync.Once
|
||
|
||
// generatorTable returns a sequence of sm2p256Tables. The first table contains
|
||
// multiples of G. Each successive table is the previous table doubled four
|
||
// times.
|
||
func (p *SM2P256Point) generatorTable() *[sm2p256ElementLength * 2]sm2p256Table {
|
||
sm2p256GeneratorTableOnce.Do(func() {
|
||
sm2p256GeneratorTable = new([sm2p256ElementLength * 2]sm2p256Table)
|
||
base := NewSM2P256Point().SetGenerator()
|
||
for i := 0; i < sm2p256ElementLength*2; i++ {
|
||
sm2p256GeneratorTable[i][0] = NewSM2P256Point().Set(base)
|
||
for j := 1; j < 15; j++ {
|
||
sm2p256GeneratorTable[i][j] = NewSM2P256Point().Add(sm2p256GeneratorTable[i][j-1], base)
|
||
}
|
||
base.Double(base)
|
||
base.Double(base)
|
||
base.Double(base)
|
||
base.Double(base)
|
||
}
|
||
})
|
||
return sm2p256GeneratorTable
|
||
}
|
||
|
||
// ScalarBaseMult sets p = scalar * B, where B is the canonical generator, and
|
||
// returns p.
|
||
func (p *SM2P256Point) ScalarBaseMult(scalar []byte) (*SM2P256Point, error) {
|
||
if len(scalar) != sm2p256ElementLength {
|
||
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 := NewSM2P256Point()
|
||
p.Set(NewSM2P256Point())
|
||
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
|
||
}
|
||
|
||
// sm2p256Sqrt sets e to a square root of x. If x is not a square, sm2p256Sqrt returns
|
||
// false and e is unchanged. e and x can overlap.
|
||
func sm2p256Sqrt(e, x *fiat.SM2P256Element) (isSquare bool) {
|
||
candidate := new(fiat.SM2P256Element)
|
||
sm2p256SqrtCandidate(candidate, x)
|
||
square := new(fiat.SM2P256Element).Square(candidate)
|
||
if square.Equal(x) != 1 {
|
||
return false
|
||
}
|
||
e.Set(candidate)
|
||
return true
|
||
}
|
||
|
||
// sm2p256SqrtCandidate sets z to a square root candidate for x. z and x must not overlap.
|
||
func sm2p256SqrtCandidate(z, x *fiat.SM2P256Element) {
|
||
// Since p = 3 mod 4, exponentiation by (p + 1) / 4 yields a square root candidate.
|
||
//
|
||
// The sequence of 13 multiplications and 253 squarings is derived from the
|
||
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
|
||
//
|
||
// _10 = 2*1
|
||
// _11 = 1 + _10
|
||
// _110 = 2*_11
|
||
// _111 = 1 + _110
|
||
// _1110 = 2*_111
|
||
// _1111 = 1 + _1110
|
||
// _11110 = 2*_1111
|
||
// _111100 = 2*_11110
|
||
// _1111000 = 2*_111100
|
||
// i19 = (_1111000 << 3 + _111100) << 5 + _1111000
|
||
// x31 = (i19 << 2 + _11110) << 14 + i19 + _111
|
||
// i42 = x31 << 4
|
||
// i73 = i42 << 31
|
||
// i74 = i42 + i73
|
||
// i171 = (i73 << 32 + i74) << 62 + i74 + _1111
|
||
// return (i171 << 32 + 1) << 62
|
||
//
|
||
var t0 = new(fiat.SM2P256Element)
|
||
var t1 = new(fiat.SM2P256Element)
|
||
var t2 = new(fiat.SM2P256Element)
|
||
var t3 = new(fiat.SM2P256Element)
|
||
var t4 = new(fiat.SM2P256Element)
|
||
|
||
z.Square(x)
|
||
z.Mul(x, z)
|
||
z.Square(z)
|
||
t0.Mul(x, z)
|
||
z.Square(t0)
|
||
z.Mul(x, z)
|
||
t2.Square(z)
|
||
t3.Square(t2)
|
||
t1.Square(t3)
|
||
t4.Square(t1)
|
||
for s := 1; s < 3; s++ {
|
||
t4.Square(t4)
|
||
}
|
||
t3.Mul(t3, t4)
|
||
for s := 0; s < 5; s++ {
|
||
t3.Square(t3)
|
||
}
|
||
t1.Mul(t1, t3)
|
||
t3.Square(t1)
|
||
for s := 1; s < 2; s++ {
|
||
t3.Square(t3)
|
||
}
|
||
t2.Mul(t2, t3)
|
||
for s := 0; s < 14; s++ {
|
||
t2.Square(t2)
|
||
}
|
||
t1.Mul(t1, t2)
|
||
t0.Mul(t0, t1)
|
||
for s := 0; s < 4; s++ {
|
||
t0.Square(t0)
|
||
}
|
||
t1.Square(t0)
|
||
for s := 1; s < 31; s++ {
|
||
t1.Square(t1)
|
||
}
|
||
t0.Mul(t0, t1)
|
||
for s := 0; s < 32; s++ {
|
||
t1.Square(t1)
|
||
}
|
||
t1.Mul(t0, t1)
|
||
for s := 0; s < 62; s++ {
|
||
t1.Square(t1)
|
||
}
|
||
t0.Mul(t0, t1)
|
||
z.Mul(z, t0)
|
||
for s := 0; s < 32; s++ {
|
||
z.Square(z)
|
||
}
|
||
z.Mul(x, z)
|
||
for s := 0; s < 62; s++ {
|
||
z.Square(z)
|
||
}
|
||
}
|