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// Copyright 2013 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.
package elliptic
import (
"crypto/internal/nistec"
"errors"
"math/big"
)
var p224 = &nistCurve[*nistec.P224Point]{
newPoint: nistec.NewP224Point,
}
func initP224() {
p224.params = &CurveParams{
Name: "P-224",
BitSize: 224,
// FIPS 186-4, section D.1.2.2
P: bigFromDecimal("26959946667150639794667015087019630673557916260026308143510066298881"),
N: bigFromDecimal("26959946667150639794667015087019625940457807714424391721682722368061"),
B: bigFromHex("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4"),
Gx: bigFromHex("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21"),
Gy: bigFromHex("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"),
}
}
type p256Curve struct {
nistCurve[*nistec.P256Point]
}
var p256 = &p256Curve{nistCurve[*nistec.P256Point]{
newPoint: nistec.NewP256Point,
}}
func initP256() {
p256.params = &CurveParams{
Name: "P-256",
BitSize: 256,
// FIPS 186-4, section D.1.2.3
P: bigFromDecimal("115792089210356248762697446949407573530086143415290314195533631308867097853951"),
N: bigFromDecimal("115792089210356248762697446949407573529996955224135760342422259061068512044369"),
B: bigFromHex("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b"),
Gx: bigFromHex("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296"),
Gy: bigFromHex("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"),
}
}
var p384 = &nistCurve[*nistec.P384Point]{
newPoint: nistec.NewP384Point,
}
func initP384() {
p384.params = &CurveParams{
Name: "P-384",
BitSize: 384,
// FIPS 186-4, section D.1.2.4
P: bigFromDecimal("394020061963944792122790401001436138050797392704654" +
"46667948293404245721771496870329047266088258938001861606973112319"),
N: bigFromDecimal("394020061963944792122790401001436138050797392704654" +
"46667946905279627659399113263569398956308152294913554433653942643"),
B: bigFromHex("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088" +
"f5013875ac656398d8a2ed19d2a85c8edd3ec2aef"),
Gx: bigFromHex("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741" +
"e082542a385502f25dbf55296c3a545e3872760ab7"),
Gy: bigFromHex("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da31" +
"13b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f"),
}
}
var p521 = &nistCurve[*nistec.P521Point]{
newPoint: nistec.NewP521Point,
}
func initP521() {
p521.params = &CurveParams{
Name: "P-521",
BitSize: 521,
// FIPS 186-4, section D.1.2.5
P: bigFromDecimal("68647976601306097149819007990813932172694353001433" +
"0540939446345918554318339765605212255964066145455497729631139148" +
"0858037121987999716643812574028291115057151"),
N: bigFromDecimal("68647976601306097149819007990813932172694353001433" +
"0540939446345918554318339765539424505774633321719753296399637136" +
"3321113864768612440380340372808892707005449"),
B: bigFromHex("0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8" +
"b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef" +
"451fd46b503f00"),
Gx: bigFromHex("00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f8" +
"28af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf9" +
"7e7e31c2e5bd66"),
Gy: bigFromHex("011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817" +
"afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088" +
"be94769fd16650"),
}
}
// nistCurve is a Curve implementation based on a nistec Point.
//
// It's a wrapper that exposes the big.Int-based Curve interface and encodes the
// legacy idiosyncrasies it requires, such as invalid and infinity point
// handling.
//
// To interact with the nistec package, points are encoded into and decoded from
// properly formatted byte slices. All big.Int use is limited to this package.
// Encoding and decoding is 1/1000th of the runtime of a scalar multiplication,
// so the overhead is acceptable.
type nistCurve[Point nistPoint[Point]] struct {
newPoint func() Point
params *CurveParams
}
// nistPoint is a generic constraint for the nistec Point types.
type nistPoint[T any] interface {
Bytes() []byte
SetBytes([]byte) (T, error)
Add(T, T) T
Double(T) T
ScalarMult(T, []byte) (T, error)
ScalarBaseMult([]byte) (T, error)
}
func (curve *nistCurve[Point]) Params() *CurveParams {
return curve.params
}
func (curve *nistCurve[Point]) IsOnCurve(x, y *big.Int) bool {
// IsOnCurve is documented to reject (0, 0), the conventional point at
// infinity, which however is accepted by pointFromAffine.
if x.Sign() == 0 && y.Sign() == 0 {
return false
}
_, err := curve.pointFromAffine(x, y)
return err == nil
}
func (curve *nistCurve[Point]) pointFromAffine(x, y *big.Int) (p Point, err error) {
// (0, 0) is by convention the point at infinity, which can't be represented
// in affine coordinates. See Issue 37294.
if x.Sign() == 0 && y.Sign() == 0 {
return curve.newPoint(), nil
}
// Reject values that would not get correctly encoded.
if x.Sign() < 0 || y.Sign() < 0 {
return p, errors.New("negative coordinate")
}
if x.BitLen() > curve.params.BitSize || y.BitLen() > curve.params.BitSize {
return p, errors.New("overflowing coordinate")
}
// Encode the coordinates and let SetBytes reject invalid points.
byteLen := (curve.params.BitSize + 7) / 8
buf := make([]byte, 1+2*byteLen)
buf[0] = 4 // uncompressed point
x.FillBytes(buf[1 : 1+byteLen])
y.FillBytes(buf[1+byteLen : 1+2*byteLen])
return curve.newPoint().SetBytes(buf)
}
func (curve *nistCurve[Point]) pointToAffine(p Point) (x, y *big.Int) {
out := p.Bytes()
if len(out) == 1 && out[0] == 0 {
// This is the encoding of the point at infinity, which the affine
// coordinates API represents as (0, 0) by convention.
return new(big.Int), new(big.Int)
}
byteLen := (curve.params.BitSize + 7) / 8
x = new(big.Int).SetBytes(out[1 : 1+byteLen])
y = new(big.Int).SetBytes(out[1+byteLen:])
return x, y
}
func (curve *nistCurve[Point]) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
p1, err := curve.pointFromAffine(x1, y1)
if err != nil {
panic("crypto/elliptic: Add was called on an invalid point")
}
p2, err := curve.pointFromAffine(x2, y2)
if err != nil {
panic("crypto/elliptic: Add was called on an invalid point")
}
return curve.pointToAffine(p1.Add(p1, p2))
}
func (curve *nistCurve[Point]) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
p, err := curve.pointFromAffine(x1, y1)
if err != nil {
panic("crypto/elliptic: Double was called on an invalid point")
}
return curve.pointToAffine(p.Double(p))
}
// normalizeScalar brings the scalar within the byte size of the order of the
// curve, as expected by the nistec scalar multiplication functions.
func (curve *nistCurve[Point]) normalizeScalar(scalar []byte) []byte {
byteSize := (curve.params.N.BitLen() + 7) / 8
if len(scalar) == byteSize {
return scalar
}
s := new(big.Int).SetBytes(scalar)
if len(scalar) > byteSize {
s.Mod(s, curve.params.N)
}
out := make([]byte, byteSize)
return s.FillBytes(out)
}
func (curve *nistCurve[Point]) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {
p, err := curve.pointFromAffine(Bx, By)
if err != nil {
panic("crypto/elliptic: ScalarMult was called on an invalid point")
}
scalar = curve.normalizeScalar(scalar)
p, err = p.ScalarMult(p, scalar)
if err != nil {
panic("crypto/elliptic: nistec rejected normalized scalar")
}
return curve.pointToAffine(p)
}
func (curve *nistCurve[Point]) ScalarBaseMult(scalar []byte) (*big.Int, *big.Int) {
scalar = curve.normalizeScalar(scalar)
p, err := curve.newPoint().ScalarBaseMult(scalar)
if err != nil {
panic("crypto/elliptic: nistec rejected normalized scalar")
}
return curve.pointToAffine(p)
}
// CombinedMult returns [s1]G + [s2]P where G is the generator. It's used
// through an interface upgrade in crypto/ecdsa.
func (curve *nistCurve[Point]) CombinedMult(Px, Py *big.Int, s1, s2 []byte) (x, y *big.Int) {
s1 = curve.normalizeScalar(s1)
q, err := curve.newPoint().ScalarBaseMult(s1)
if err != nil {
panic("crypto/elliptic: nistec rejected normalized scalar")
}
p, err := curve.pointFromAffine(Px, Py)
if err != nil {
panic("crypto/elliptic: CombinedMult was called on an invalid point")
}
s2 = curve.normalizeScalar(s2)
p, err = p.ScalarMult(p, s2)
if err != nil {
panic("crypto/elliptic: nistec rejected normalized scalar")
}
return curve.pointToAffine(p.Add(p, q))
}
func (curve *nistCurve[Point]) Unmarshal(data []byte) (x, y *big.Int) {
if len(data) == 0 || data[0] != 4 {
return nil, nil
}
// Use SetBytes to check that data encodes a valid point.
_, err := curve.newPoint().SetBytes(data)
if err != nil {
return nil, nil
}
// We don't use pointToAffine because it involves an expensive field
// inversion to convert from Jacobian to affine coordinates, which we
// already have.
byteLen := (curve.params.BitSize + 7) / 8
x = new(big.Int).SetBytes(data[1 : 1+byteLen])
y = new(big.Int).SetBytes(data[1+byteLen:])
return x, y
}
func (curve *nistCurve[Point]) UnmarshalCompressed(data []byte) (x, y *big.Int) {
if len(data) == 0 || (data[0] != 2 && data[0] != 3) {
return nil, nil
}
p, err := curve.newPoint().SetBytes(data)
if err != nil {
return nil, nil
}
return curve.pointToAffine(p)
}
func bigFromDecimal(s string) *big.Int {
b, ok := new(big.Int).SetString(s, 10)
if !ok {
panic("crypto/elliptic: internal error: invalid encoding")
}
return b
}
func bigFromHex(s string) *big.Int {
b, ok := new(big.Int).SetString(s, 16)
if !ok {
panic("crypto/elliptic: internal error: invalid encoding")
}
return b
}
|
