542 lines
18 KiB
Go
542 lines
18 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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package nistec
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import (
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"crypto/subtle"
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"errors"
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"sync"
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"sources.truenas.cloud/code/nistec/internal/fiat"
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)
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// p384ElementLength 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 p384ElementLength = 48
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// P384Point is a P384 point. The zero value is NOT valid.
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type P384Point 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.P384Element
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}
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// NewP384Point returns a new P384Point representing the point at infinity point.
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func NewP384Point() *P384Point {
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return &P384Point{
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x: new(fiat.P384Element),
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y: new(fiat.P384Element).One(),
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z: new(fiat.P384Element),
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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 *P384Point) SetGenerator() *P384Point {
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p.x.SetBytes([]byte{0xaa, 0x87, 0xca, 0x22, 0xbe, 0x8b, 0x5, 0x37, 0x8e, 0xb1, 0xc7, 0x1e, 0xf3, 0x20, 0xad, 0x74, 0x6e, 0x1d, 0x3b, 0x62, 0x8b, 0xa7, 0x9b, 0x98, 0x59, 0xf7, 0x41, 0xe0, 0x82, 0x54, 0x2a, 0x38, 0x55, 0x2, 0xf2, 0x5d, 0xbf, 0x55, 0x29, 0x6c, 0x3a, 0x54, 0x5e, 0x38, 0x72, 0x76, 0xa, 0xb7})
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p.y.SetBytes([]byte{0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f, 0x5d, 0x9e, 0x98, 0xbf, 0x92, 0x92, 0xdc, 0x29, 0xf8, 0xf4, 0x1d, 0xbd, 0x28, 0x9a, 0x14, 0x7c, 0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, 0xb8, 0xc0, 0xa, 0x60, 0xb1, 0xce, 0x1d, 0x7e, 0x81, 0x9d, 0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0xe, 0x5f})
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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 *P384Point) Set(q *P384Point) *P384Point {
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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 *P384Point) SetBytes(b []byte) (*P384Point, 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(NewP384Point()), nil
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// Uncompressed form.
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case len(b) == 1+2*p384ElementLength && b[0] == 4:
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x, err := new(fiat.P384Element).SetBytes(b[1 : 1+p384ElementLength])
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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.P384Element).SetBytes(b[1+p384ElementLength:])
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if err != nil {
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return nil, err
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}
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if err := p384CheckOnCurve(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+p384ElementLength && (b[0] == 2 || b[0] == 3):
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x, err := new(fiat.P384Element).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 := p384Polynomial(new(fiat.P384Element), x)
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if !p384Sqrt(y, y) {
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return nil, errors.New("invalid P384 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.P384Element)
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otherRoot.Sub(otherRoot, y)
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cond := y.Bytes()[p384ElementLength-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 P384 point encoding")
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}
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}
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var _p384B *fiat.P384Element
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var _p384BOnce sync.Once
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func p384B() *fiat.P384Element {
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_p384BOnce.Do(func() {
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_p384B, _ = new(fiat.P384Element).SetBytes([]byte{0xb3, 0x31, 0x2f, 0xa7, 0xe2, 0x3e, 0xe7, 0xe4, 0x98, 0x8e, 0x5, 0x6b, 0xe3, 0xf8, 0x2d, 0x19, 0x18, 0x1d, 0x9c, 0x6e, 0xfe, 0x81, 0x41, 0x12, 0x3, 0x14, 0x8, 0x8f, 0x50, 0x13, 0x87, 0x5a, 0xc6, 0x56, 0x39, 0x8d, 0x8a, 0x2e, 0xd1, 0x9d, 0x2a, 0x85, 0xc8, 0xed, 0xd3, 0xec, 0x2a, 0xef})
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})
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return _p384B
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}
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// p384Polynomial sets y2 to x³ - 3x + b, and returns y2.
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func p384Polynomial(y2, x *fiat.P384Element) *fiat.P384Element {
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y2.Square(x)
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y2.Mul(y2, x)
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threeX := new(fiat.P384Element).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, p384B())
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}
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func p384CheckOnCurve(x, y *fiat.P384Element) error {
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// y² = x³ - 3x + b
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rhs := p384Polynomial(new(fiat.P384Element), x)
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lhs := new(fiat.P384Element).Square(y)
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if rhs.Equal(lhs) != 1 {
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return errors.New("P384 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 *P384Point) 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*p384ElementLength]byte
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return p.bytes(&out)
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}
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func (p *P384Point) bytes(out *[1 + 2*p384ElementLength]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.P384Element).Invert(p.z)
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x := new(fiat.P384Element).Mul(p.x, zinv)
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y := new(fiat.P384Element).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 *P384Point) 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 [p384ElementLength]byte
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return p.bytesX(&out)
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}
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func (p *P384Point) bytesX(out *[p384ElementLength]byte) ([]byte, error) {
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if p.z.IsZero() == 1 {
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return nil, errors.New("P384 point is the point at infinity")
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}
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zinv := new(fiat.P384Element).Invert(p.z)
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x := new(fiat.P384Element).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 *P384Point) 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 + p384ElementLength]byte
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return p.bytesCompressed(&out)
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}
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func (p *P384Point) bytesCompressed(out *[1 + p384ElementLength]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.P384Element).Invert(p.z)
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x := new(fiat.P384Element).Mul(p.x, zinv)
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y := new(fiat.P384Element).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()[p384ElementLength-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 *P384Point) Add(p1, p2 *P384Point) *P384Point {
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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.P384Element).Mul(p1.x, p2.x) // t0 := X1 * X2
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t1 := new(fiat.P384Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2
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t2 := new(fiat.P384Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2
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t3 := new(fiat.P384Element).Add(p1.x, p1.y) // t3 := X1 + Y1
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t4 := new(fiat.P384Element).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.P384Element).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.P384Element).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.P384Element).Mul(p384B(), 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(p384B(), 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 *P384Point) Double(p *P384Point) *P384Point {
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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.P384Element).Square(p.x) // t0 := X ^ 2
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t1 := new(fiat.P384Element).Square(p.y) // t1 := Y ^ 2
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t2 := new(fiat.P384Element).Square(p.z) // t2 := Z ^ 2
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t3 := new(fiat.P384Element).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.P384Element).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.P384Element).Mul(p384B(), t2) // Y3 := b * t2
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y3.Sub(y3, z3) // Y3 := Y3 - Z3
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x3 := new(fiat.P384Element).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(p384B(), 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 *P384Point) Select(p1, p2 *P384Point, cond int) *P384Point {
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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 p384Table 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 p384Table [15]*P384Point
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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 *p384Table) Select(p *P384Point, n uint8) {
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if n >= 16 {
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panic("nistec: internal error: p384Table called with out-of-bounds value")
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}
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p.Set(NewP384Point())
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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 *P384Point) ScalarMult(q *P384Point, scalar []byte) (*P384Point, error) {
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// Compute a p384Table for the base point q. The explicit NewP384Point
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// calls get inlined, letting the allocations live on the stack.
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var table = p384Table{NewP384Point(), NewP384Point(), NewP384Point(),
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NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(),
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NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(),
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NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point()}
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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 := NewP384Point()
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p.Set(NewP384Point())
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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)
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p.Double(p)
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p.Double(p)
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windowValue = byte & 0b1111
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table.Select(t, windowValue)
|
||
p.Add(p, t)
|
||
}
|
||
|
||
return p, nil
|
||
}
|
||
|
||
var p384GeneratorTable *[p384ElementLength * 2]p384Table
|
||
var p384GeneratorTableOnce sync.Once
|
||
|
||
// generatorTable returns a sequence of p384Tables. The first table contains
|
||
// multiples of G. Each successive table is the previous table doubled four
|
||
// times.
|
||
func (p *P384Point) generatorTable() *[p384ElementLength * 2]p384Table {
|
||
p384GeneratorTableOnce.Do(func() {
|
||
p384GeneratorTable = new([p384ElementLength * 2]p384Table)
|
||
base := NewP384Point().SetGenerator()
|
||
for i := 0; i < p384ElementLength*2; i++ {
|
||
p384GeneratorTable[i][0] = NewP384Point().Set(base)
|
||
for j := 1; j < 15; j++ {
|
||
p384GeneratorTable[i][j] = NewP384Point().Add(p384GeneratorTable[i][j-1], base)
|
||
}
|
||
base.Double(base)
|
||
base.Double(base)
|
||
base.Double(base)
|
||
base.Double(base)
|
||
}
|
||
})
|
||
return p384GeneratorTable
|
||
}
|
||
|
||
// ScalarBaseMult sets p = scalar * B, where B is the canonical generator, and
|
||
// returns p.
|
||
func (p *P384Point) ScalarBaseMult(scalar []byte) (*P384Point, error) {
|
||
if len(scalar) != p384ElementLength {
|
||
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 := NewP384Point()
|
||
p.Set(NewP384Point())
|
||
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
|
||
}
|
||
|
||
// p384Sqrt sets e to a square root of x. If x is not a square, p384Sqrt returns
|
||
// false and e is unchanged. e and x can overlap.
|
||
func p384Sqrt(e, x *fiat.P384Element) (isSquare bool) {
|
||
candidate := new(fiat.P384Element)
|
||
p384SqrtCandidate(candidate, x)
|
||
square := new(fiat.P384Element).Square(candidate)
|
||
if square.Equal(x) != 1 {
|
||
return false
|
||
}
|
||
e.Set(candidate)
|
||
return true
|
||
}
|
||
|
||
// p384SqrtCandidate sets z to a square root candidate for x. z and x must not overlap.
|
||
func p384SqrtCandidate(z, x *fiat.P384Element) {
|
||
// Since p = 3 mod 4, exponentiation by (p + 1) / 4 yields a square root candidate.
|
||
//
|
||
// The sequence of 14 multiplications and 381 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
|
||
// _111000 = _111 << 3
|
||
// _111111 = _111 + _111000
|
||
// _1111110 = 2*_111111
|
||
// _1111111 = 1 + _1111110
|
||
// x12 = _1111110 << 5 + _111111
|
||
// x24 = x12 << 12 + x12
|
||
// x31 = x24 << 7 + _1111111
|
||
// x32 = 2*x31 + 1
|
||
// x63 = x32 << 31 + x31
|
||
// x126 = x63 << 63 + x63
|
||
// x252 = x126 << 126 + x126
|
||
// x255 = x252 << 3 + _111
|
||
// return ((x255 << 33 + x32) << 64 + 1) << 30
|
||
//
|
||
var t0 = new(fiat.P384Element)
|
||
var t1 = new(fiat.P384Element)
|
||
var t2 = new(fiat.P384Element)
|
||
|
||
z.Square(x)
|
||
z.Mul(x, z)
|
||
z.Square(z)
|
||
t0.Mul(x, z)
|
||
z.Square(t0)
|
||
for s := 1; s < 3; s++ {
|
||
z.Square(z)
|
||
}
|
||
t1.Mul(t0, z)
|
||
t2.Square(t1)
|
||
z.Mul(x, t2)
|
||
for s := 0; s < 5; s++ {
|
||
t2.Square(t2)
|
||
}
|
||
t1.Mul(t1, t2)
|
||
t2.Square(t1)
|
||
for s := 1; s < 12; s++ {
|
||
t2.Square(t2)
|
||
}
|
||
t1.Mul(t1, t2)
|
||
for s := 0; s < 7; s++ {
|
||
t1.Square(t1)
|
||
}
|
||
t1.Mul(z, t1)
|
||
z.Square(t1)
|
||
z.Mul(x, z)
|
||
t2.Square(z)
|
||
for s := 1; s < 31; s++ {
|
||
t2.Square(t2)
|
||
}
|
||
t1.Mul(t1, t2)
|
||
t2.Square(t1)
|
||
for s := 1; s < 63; s++ {
|
||
t2.Square(t2)
|
||
}
|
||
t1.Mul(t1, t2)
|
||
t2.Square(t1)
|
||
for s := 1; s < 126; s++ {
|
||
t2.Square(t2)
|
||
}
|
||
t1.Mul(t1, t2)
|
||
for s := 0; s < 3; s++ {
|
||
t1.Square(t1)
|
||
}
|
||
t0.Mul(t0, t1)
|
||
for s := 0; s < 33; s++ {
|
||
t0.Square(t0)
|
||
}
|
||
z.Mul(z, t0)
|
||
for s := 0; s < 64; s++ {
|
||
z.Square(z)
|
||
}
|
||
z.Mul(x, z)
|
||
for s := 0; s < 30; s++ {
|
||
z.Square(z)
|
||
}
|
||
}
|