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crypto/elliptic: refactor package structure

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Not quite golang.org/wiki/TargetSpecific compliant, but almost.

The only substantial code change is in randFieldElement: it used to use
Params().BitSize instead of Params().N.BitLen(), which is semantically
incorrect, even if the two values are the same for all named curves.

For #52182

Change-Id: Ibc47450552afe23ea74fcf55d1d799d5d7e5487c
Reviewed-on: https://go-review.googlesource.com/c/go/+/315273
Run-TryBot: Filippo Valsorda <filippo@golang.org>
Reviewed-by: Than McIntosh <thanm@google.com>
Reviewed-by: Roland Shoemaker <roland@golang.org>
TryBot-Result: Gopher Robot <gobot@golang.org>
Reviewed-by: Russ Cox <rsc@golang.org>
This commit is contained in:
Filippo Valsorda 2021-10-30 00:27:51 -04:00
parent 24b570354c
commit 6796a7924c
9 changed files with 1496 additions and 1502 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

16
src/crypto/ecdsa/ecdsa.go
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@ -128,7 +128,7 @@ func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error)
params := c.Params() params := c.Params()
// Note that for P-521 this will actually be 63 bits more than the order, as // Note that for P-521 this will actually be 63 bits more than the order, as
// division rounds down, but the extra bit is inconsequential. // division rounds down, but the extra bit is inconsequential.
b := make([]byte, params.BitSize/8+8) // TODO: use params.N.BitLen() b := make([]byte, params.N.BitLen()/8+8)
_, err = io.ReadFull(rand, b) _, err = io.ReadFull(rand, b)
if err != nil { if err != nil {
return return
@ -228,13 +228,13 @@ func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err err
// Create a CSPRNG that xors a stream of zeros with // Create a CSPRNG that xors a stream of zeros with
// the output of the AES-CTR instance. // the output of the AES-CTR instance.
csprng := cipher.StreamReader{ csprng := &cipher.StreamReader{
R: zeroReader, R: zeroReader,
S: cipher.NewCTR(block, []byte(aesIV)), S: cipher.NewCTR(block, []byte(aesIV)),
} }
c := priv.PublicKey.Curve c := priv.PublicKey.Curve
return sign(priv, &csprng, c, hash) return sign(priv, csprng, c, hash)
} }
func signGeneric(priv *PrivateKey, csprng *cipher.StreamReader, c elliptic.Curve, hash []byte) (r, s *big.Int, err error) { func signGeneric(priv *PrivateKey, csprng *cipher.StreamReader, c elliptic.Curve, hash []byte) (r, s *big.Int, err error) {
@ -353,16 +353,14 @@ func VerifyASN1(pub *PublicKey, hash, sig []byte) bool {
return Verify(pub, hash, r, s) return Verify(pub, hash, r, s)
} }
type zr struct { type zr struct{}
io.Reader
}
// Read replaces the contents of dst with zeros. // Read replaces the contents of dst with zeros. It is safe for concurrent use.
func (z *zr) Read(dst []byte) (n int, err error) { func (zr) Read(dst []byte) (n int, err error) {
for i := range dst { for i := range dst {
dst[i] = 0 dst[i] = 0
} }
return len(dst), nil return len(dst), nil
} }
var zeroReader = &zr{} var zeroReader = zr{}

289
src/crypto/elliptic/elliptic.go
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@ -36,295 +36,6 @@ type Curve interface {
ScalarBaseMult(k []byte) (x, y *big.Int) ScalarBaseMult(k []byte) (x, y *big.Int)
} }
func matchesSpecificCurve(params *CurveParams, available ...Curve) (Curve, bool) {
for _, c := range available {
if params == c.Params() {
return c, true
}
}
return nil, false
}
// CurveParams contains the parameters of an elliptic curve and also provides
// a generic, non-constant time implementation of Curve.
type CurveParams struct {
P *big.Int // the order of the underlying field
N *big.Int // the order of the base point
B *big.Int // the constant of the curve equation
Gx, Gy *big.Int // (x,y) of the base point
BitSize int // the size of the underlying field
Name string // the canonical name of the curve
}
func (curve *CurveParams) Params() *CurveParams {
return curve
}
// CurveParams operates, internally, on Jacobian coordinates. For a given
// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, z1)
// where x = x1/z1² and y = y1/z1³. The greatest speedups come when the whole
// calculation can be performed within the transform (as in ScalarMult and
// ScalarBaseMult). But even for Add and Double, it's faster to apply and
// reverse the transform than to operate in affine coordinates.
// polynomial returns x³ - 3x + b.
func (curve *CurveParams) polynomial(x *big.Int) *big.Int {
x3 := new(big.Int).Mul(x, x)
x3.Mul(x3, x)
threeX := new(big.Int).Lsh(x, 1)
threeX.Add(threeX, x)
x3.Sub(x3, threeX)
x3.Add(x3, curve.B)
x3.Mod(x3, curve.P)
return x3
}
func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
return specific.IsOnCurve(x, y)
}
if x.Sign() < 0 || x.Cmp(curve.P) >= 0 ||
y.Sign() < 0 || y.Cmp(curve.P) >= 0 {
return false
}
// y² = x³ - 3x + b
y2 := new(big.Int).Mul(y, y)
y2.Mod(y2, curve.P)
return curve.polynomial(x).Cmp(y2) == 0
}
// zForAffine returns a Jacobian Z value for the affine point (x, y). If x and
// y are zero, it assumes that they represent the point at infinity because (0,
// 0) is not on the any of the curves handled here.
func zForAffine(x, y *big.Int) *big.Int {
z := new(big.Int)
if x.Sign() != 0 || y.Sign() != 0 {
z.SetInt64(1)
}
return z
}
// affineFromJacobian reverses the Jacobian transform. See the comment at the
// top of the file. If the point is ∞ it returns 0, 0.
func (curve *CurveParams) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
if z.Sign() == 0 {
return new(big.Int), new(big.Int)
}
zinv := new(big.Int).ModInverse(z, curve.P)
zinvsq := new(big.Int).Mul(zinv, zinv)
xOut = new(big.Int).Mul(x, zinvsq)
xOut.Mod(xOut, curve.P)
zinvsq.Mul(zinvsq, zinv)
yOut = new(big.Int).Mul(y, zinvsq)
yOut.Mod(yOut, curve.P)
return
}
func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
return specific.Add(x1, y1, x2, y2)
}
z1 := zForAffine(x1, y1)
z2 := zForAffine(x2, y2)
return curve.affineFromJacobian(curve.addJacobian(x1, y1, z1, x2, y2, z2))
}
// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
// (x2, y2, z2) and returns their sum, also in Jacobian form.
func (curve *CurveParams) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
// See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
x3, y3, z3 := new(big.Int), new(big.Int), new(big.Int)
if z1.Sign() == 0 {
x3.Set(x2)
y3.Set(y2)
z3.Set(z2)
return x3, y3, z3
}
if z2.Sign() == 0 {
x3.Set(x1)
y3.Set(y1)
z3.Set(z1)
return x3, y3, z3
}
z1z1 := new(big.Int).Mul(z1, z1)
z1z1.Mod(z1z1, curve.P)
z2z2 := new(big.Int).Mul(z2, z2)
z2z2.Mod(z2z2, curve.P)
u1 := new(big.Int).Mul(x1, z2z2)
u1.Mod(u1, curve.P)
u2 := new(big.Int).Mul(x2, z1z1)
u2.Mod(u2, curve.P)
h := new(big.Int).Sub(u2, u1)
xEqual := h.Sign() == 0
if h.Sign() == -1 {
h.Add(h, curve.P)
}
i := new(big.Int).Lsh(h, 1)
i.Mul(i, i)
j := new(big.Int).Mul(h, i)
s1 := new(big.Int).Mul(y1, z2)
s1.Mul(s1, z2z2)
s1.Mod(s1, curve.P)
s2 := new(big.Int).Mul(y2, z1)
s2.Mul(s2, z1z1)
s2.Mod(s2, curve.P)
r := new(big.Int).Sub(s2, s1)
if r.Sign() == -1 {
r.Add(r, curve.P)
}
yEqual := r.Sign() == 0
if xEqual && yEqual {
return curve.doubleJacobian(x1, y1, z1)
}
r.Lsh(r, 1)
v := new(big.Int).Mul(u1, i)
x3.Set(r)
x3.Mul(x3, x3)
x3.Sub(x3, j)
x3.Sub(x3, v)
x3.Sub(x3, v)
x3.Mod(x3, curve.P)
y3.Set(r)
v.Sub(v, x3)
y3.Mul(y3, v)
s1.Mul(s1, j)
s1.Lsh(s1, 1)
y3.Sub(y3, s1)
y3.Mod(y3, curve.P)
z3.Add(z1, z2)
z3.Mul(z3, z3)
z3.Sub(z3, z1z1)
z3.Sub(z3, z2z2)
z3.Mul(z3, h)
z3.Mod(z3, curve.P)
return x3, y3, z3
}
func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
return specific.Double(x1, y1)
}
z1 := zForAffine(x1, y1)
return curve.affineFromJacobian(curve.doubleJacobian(x1, y1, z1))
}
// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
// returns its double, also in Jacobian form.
func (curve *CurveParams) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
// See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
delta := new(big.Int).Mul(z, z)
delta.Mod(delta, curve.P)
gamma := new(big.Int).Mul(y, y)
gamma.Mod(gamma, curve.P)
alpha := new(big.Int).Sub(x, delta)
if alpha.Sign() == -1 {
alpha.Add(alpha, curve.P)
}
alpha2 := new(big.Int).Add(x, delta)
alpha.Mul(alpha, alpha2)
alpha2.Set(alpha)
alpha.Lsh(alpha, 1)
alpha.Add(alpha, alpha2)
beta := alpha2.Mul(x, gamma)
x3 := new(big.Int).Mul(alpha, alpha)
beta8 := new(big.Int).Lsh(beta, 3)
beta8.Mod(beta8, curve.P)
x3.Sub(x3, beta8)
if x3.Sign() == -1 {
x3.Add(x3, curve.P)
}
x3.Mod(x3, curve.P)
z3 := new(big.Int).Add(y, z)
z3.Mul(z3, z3)
z3.Sub(z3, gamma)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Sub(z3, delta)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Mod(z3, curve.P)
beta.Lsh(beta, 2)
beta.Sub(beta, x3)
if beta.Sign() == -1 {
beta.Add(beta, curve.P)
}
y3 := alpha.Mul(alpha, beta)
gamma.Mul(gamma, gamma)
gamma.Lsh(gamma, 3)
gamma.Mod(gamma, curve.P)
y3.Sub(y3, gamma)
if y3.Sign() == -1 {
y3.Add(y3, curve.P)
}
y3.Mod(y3, curve.P)
return x3, y3, z3
}
func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok {
return specific.ScalarMult(Bx, By, k)
}
Bz := new(big.Int).SetInt64(1)
x, y, z := new(big.Int), new(big.Int), new(big.Int)
for _, byte := range k {
for bitNum := 0; bitNum < 8; bitNum++ {
x, y, z = curve.doubleJacobian(x, y, z)
if byte&0x80 == 0x80 {
x, y, z = curve.addJacobian(Bx, By, Bz, x, y, z)
}
byte <<= 1
}
}
return curve.affineFromJacobian(x, y, z)
}
func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok {
return specific.ScalarBaseMult(k)
}
return curve.ScalarMult(curve.Gx, curve.Gy, k)
}
var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f} var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
// GenerateKey returns a public/private key pair. The private key is // GenerateKey returns a public/private key pair. The private key is

1178
src/crypto/elliptic/p256.go
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File diff suppressed because it is too large Load Diff

25
src/crypto/elliptic/p256_asm.go
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@ -24,27 +24,18 @@ import (
//go:embed p256_asm_table.bin //go:embed p256_asm_table.bin
var p256Precomputed string var p256Precomputed string
type ( type p256Curve struct {
p256Curve struct { *CurveParams
*CurveParams }
}
p256Point struct { type p256Point struct {
xyz [12]uint64 xyz [12]uint64
} }
)
var p256 p256Curve var p256 p256Curve
func initP256() { func initP256Arch() {
// See FIPS 186-3, section D.2.3 p256 = p256Curve{p256Params}
p256.CurveParams = &CurveParams{Name: "P-256"}
p256.P, _ = new(big.Int).SetString("115792089210356248762697446949407573530086143415290314195533631308867097853951", 10)
p256.N, _ = new(big.Int).SetString("115792089210356248762697446949407573529996955224135760342422259061068512044369", 10)
p256.B, _ = new(big.Int).SetString("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16)
p256.Gx, _ = new(big.Int).SetString("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16)
p256.Gy, _ = new(big.Int).SetString("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16)
p256.BitSize = 256
} }
func (curve p256Curve) Params() *CurveParams { func (curve p256Curve) Params() *CurveParams {

1171
src/crypto/elliptic/p256_generic.go
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File diff suppressed because it is too large Load Diff

15
src/crypto/elliptic/p256_noasm.go Normal file
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@ -0,0 +1,15 @@
// Copyright 2016 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 !amd64 && !s390x && !arm64 && !ppc64le
// +build !amd64,!s390x,!arm64,!ppc64le
package elliptic
var p256 p256Curve
func initP256Arch() {
// Use pure Go constant-time implementation.
p256 = p256Curve{p256Params}
}

7
src/crypto/elliptic/p256_ppc64le.go
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@ -35,7 +35,6 @@ var (
func initP256Arch() { func initP256Arch() {
p256 = p256CurveFast{p256Params} p256 = p256CurveFast{p256Params}
initTable() initTable()
return
} }
func (curve p256CurveFast) Params() *CurveParams { func (curve p256CurveFast) Params() *CurveParams {
@ -73,7 +72,6 @@ func p256MovCond(res, a, b *p256Point, cond int)
//go:noescape //go:noescape
func p256Select(point *p256Point, table []p256Point, idx int) func p256Select(point *p256Point, table []p256Point, idx int)
//
//go:noescape //go:noescape
func p256SelectBase(point *p256Point, table []p256Point, idx int) func p256SelectBase(point *p256Point, table []p256Point, idx int)
@ -85,12 +83,9 @@ func p256SelectBase(point *p256Point, table []p256Point, idx int)
//go:noescape //go:noescape
func p256PointAddAffineAsm(res, in1, in2 *p256Point, sign, sel, zero int) func p256PointAddAffineAsm(res, in1, in2 *p256Point, sign, sel, zero int)
// Point add
//
//go:noescape //go:noescape
func p256PointAddAsm(res, in1, in2 *p256Point) int func p256PointAddAsm(res, in1, in2 *p256Point) int
//
//go:noescape //go:noescape
func p256PointDoubleAsm(res, in *p256Point) func p256PointDoubleAsm(res, in *p256Point)
@ -340,7 +335,6 @@ func boothW7(in uint) (int, int) {
} }
func initTable() { func initTable() {
p256PreFast = new([37][64]p256Point) p256PreFast = new([37][64]p256Point)
// TODO: For big endian, these slices should be in reverse byte order, // TODO: For big endian, these slices should be in reverse byte order,
@ -352,7 +346,6 @@ func initTable() {
0x25, 0xf3, 0x21, 0xdd, 0x88, 0x86, 0xe8, 0xd2, 0x85, 0x5d, 0x88, 0x25, 0x18, 0xff, 0x71, 0x85}, //(p256.y*2^256)%p 0x25, 0xf3, 0x21, 0xdd, 0x88, 0x86, 0xe8, 0xd2, 0x85, 0x5d, 0x88, 0x25, 0x18, 0xff, 0x71, 0x85}, //(p256.y*2^256)%p
z: [32]byte{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, z: [32]byte{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00}, //(p256.z*2^256)%p 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00}, //(p256.z*2^256)%p
} }
t1 := new(p256Point) t1 := new(p256Point)

1
src/crypto/elliptic/p256_s390x.go
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@ -60,7 +60,6 @@ func initP256Arch() {
// No vector support, use pure Go implementation. // No vector support, use pure Go implementation.
p256 = p256Curve{p256Params} p256 = p256Curve{p256Params}
return
} }
func (curve p256CurveFast) Params() *CurveParams { func (curve p256CurveFast) Params() *CurveParams {

296
src/crypto/elliptic/params.go Normal file
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@ -0,0 +1,296 @@
// Copyright 2021 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 "math/big"
// CurveParams contains the parameters of an elliptic curve and also provides
// a generic, non-constant time implementation of Curve.
type CurveParams struct {
P *big.Int // the order of the underlying field
N *big.Int // the order of the base point
B *big.Int // the constant of the curve equation
Gx, Gy *big.Int // (x,y) of the base point
BitSize int // the size of the underlying field
Name string // the canonical name of the curve
}
func (curve *CurveParams) Params() *CurveParams {
return curve
}
// CurveParams operates, internally, on Jacobian coordinates. For a given
// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, z1)
// where x = x1/z1² and y = y1/z1³. The greatest speedups come when the whole
// calculation can be performed within the transform (as in ScalarMult and
// ScalarBaseMult). But even for Add and Double, it's faster to apply and
// reverse the transform than to operate in affine coordinates.
// polynomial returns x³ - 3x + b.
func (curve *CurveParams) polynomial(x *big.Int) *big.Int {
x3 := new(big.Int).Mul(x, x)
x3.Mul(x3, x)
threeX := new(big.Int).Lsh(x, 1)
threeX.Add(threeX, x)
x3.Sub(x3, threeX)
x3.Add(x3, curve.B)
x3.Mod(x3, curve.P)
return x3
}
func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
return specific.IsOnCurve(x, y)
}
if x.Sign() < 0 || x.Cmp(curve.P) >= 0 ||
y.Sign() < 0 || y.Cmp(curve.P) >= 0 {
return false
}
// y² = x³ - 3x + b
y2 := new(big.Int).Mul(y, y)
y2.Mod(y2, curve.P)
return curve.polynomial(x).Cmp(y2) == 0
}
// zForAffine returns a Jacobian Z value for the affine point (x, y). If x and
// y are zero, it assumes that they represent the point at infinity because (0,
// 0) is not on the any of the curves handled here.
func zForAffine(x, y *big.Int) *big.Int {
z := new(big.Int)
if x.Sign() != 0 || y.Sign() != 0 {
z.SetInt64(1)
}
return z
}
// affineFromJacobian reverses the Jacobian transform. See the comment at the
// top of the file. If the point is ∞ it returns 0, 0.
func (curve *CurveParams) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
if z.Sign() == 0 {
return new(big.Int), new(big.Int)
}
zinv := new(big.Int).ModInverse(z, curve.P)
zinvsq := new(big.Int).Mul(zinv, zinv)
xOut = new(big.Int).Mul(x, zinvsq)
xOut.Mod(xOut, curve.P)
zinvsq.Mul(zinvsq, zinv)
yOut = new(big.Int).Mul(y, zinvsq)
yOut.Mod(yOut, curve.P)
return
}
func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
return specific.Add(x1, y1, x2, y2)
}
z1 := zForAffine(x1, y1)
z2 := zForAffine(x2, y2)
return curve.affineFromJacobian(curve.addJacobian(x1, y1, z1, x2, y2, z2))
}
// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
// (x2, y2, z2) and returns their sum, also in Jacobian form.
func (curve *CurveParams) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
// See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
x3, y3, z3 := new(big.Int), new(big.Int), new(big.Int)
if z1.Sign() == 0 {
x3.Set(x2)
y3.Set(y2)
z3.Set(z2)
return x3, y3, z3
}
if z2.Sign() == 0 {
x3.Set(x1)
y3.Set(y1)
z3.Set(z1)
return x3, y3, z3
}
z1z1 := new(big.Int).Mul(z1, z1)
z1z1.Mod(z1z1, curve.P)
z2z2 := new(big.Int).Mul(z2, z2)
z2z2.Mod(z2z2, curve.P)
u1 := new(big.Int).Mul(x1, z2z2)
u1.Mod(u1, curve.P)
u2 := new(big.Int).Mul(x2, z1z1)
u2.Mod(u2, curve.P)
h := new(big.Int).Sub(u2, u1)
xEqual := h.Sign() == 0
if h.Sign() == -1 {
h.Add(h, curve.P)
}
i := new(big.Int).Lsh(h, 1)
i.Mul(i, i)
j := new(big.Int).Mul(h, i)
s1 := new(big.Int).Mul(y1, z2)
s1.Mul(s1, z2z2)
s1.Mod(s1, curve.P)
s2 := new(big.Int).Mul(y2, z1)
s2.Mul(s2, z1z1)
s2.Mod(s2, curve.P)
r := new(big.Int).Sub(s2, s1)
if r.Sign() == -1 {
r.Add(r, curve.P)
}
yEqual := r.Sign() == 0
if xEqual && yEqual {
return curve.doubleJacobian(x1, y1, z1)
}
r.Lsh(r, 1)
v := new(big.Int).Mul(u1, i)
x3.Set(r)
x3.Mul(x3, x3)
x3.Sub(x3, j)
x3.Sub(x3, v)
x3.Sub(x3, v)
x3.Mod(x3, curve.P)
y3.Set(r)
v.Sub(v, x3)
y3.Mul(y3, v)
s1.Mul(s1, j)
s1.Lsh(s1, 1)
y3.Sub(y3, s1)
y3.Mod(y3, curve.P)
z3.Add(z1, z2)
z3.Mul(z3, z3)
z3.Sub(z3, z1z1)
z3.Sub(z3, z2z2)
z3.Mul(z3, h)
z3.Mod(z3, curve.P)
return x3, y3, z3
}
func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
return specific.Double(x1, y1)
}
z1 := zForAffine(x1, y1)
return curve.affineFromJacobian(curve.doubleJacobian(x1, y1, z1))
}
// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
// returns its double, also in Jacobian form.
func (curve *CurveParams) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
// See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
delta := new(big.Int).Mul(z, z)
delta.Mod(delta, curve.P)
gamma := new(big.Int).Mul(y, y)
gamma.Mod(gamma, curve.P)
alpha := new(big.Int).Sub(x, delta)
if alpha.Sign() == -1 {
alpha.Add(alpha, curve.P)
}
alpha2 := new(big.Int).Add(x, delta)
alpha.Mul(alpha, alpha2)
alpha2.Set(alpha)
alpha.Lsh(alpha, 1)
alpha.Add(alpha, alpha2)
beta := alpha2.Mul(x, gamma)
x3 := new(big.Int).Mul(alpha, alpha)
beta8 := new(big.Int).Lsh(beta, 3)
beta8.Mod(beta8, curve.P)
x3.Sub(x3, beta8)
if x3.Sign() == -1 {
x3.Add(x3, curve.P)
}
x3.Mod(x3, curve.P)
z3 := new(big.Int).Add(y, z)
z3.Mul(z3, z3)
z3.Sub(z3, gamma)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Sub(z3, delta)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Mod(z3, curve.P)
beta.Lsh(beta, 2)
beta.Sub(beta, x3)
if beta.Sign() == -1 {
beta.Add(beta, curve.P)
}
y3 := alpha.Mul(alpha, beta)
gamma.Mul(gamma, gamma)
gamma.Lsh(gamma, 3)
gamma.Mod(gamma, curve.P)
y3.Sub(y3, gamma)
if y3.Sign() == -1 {
y3.Add(y3, curve.P)
}
y3.Mod(y3, curve.P)
return x3, y3, z3
}
func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok {
return specific.ScalarMult(Bx, By, k)
}
Bz := new(big.Int).SetInt64(1)
x, y, z := new(big.Int), new(big.Int), new(big.Int)
for _, byte := range k {
for bitNum := 0; bitNum < 8; bitNum++ {
x, y, z = curve.doubleJacobian(x, y, z)
if byte&0x80 == 0x80 {
x, y, z = curve.addJacobian(Bx, By, Bz, x, y, z)
}
byte <<= 1
}
}
return curve.affineFromJacobian(x, y, z)
}
func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
// If there is a dedicated constant-time implementation for this curve operation,
// use that instead of the generic one.
if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok {
return specific.ScalarBaseMult(k)
}
return curve.ScalarMult(curve.Gx, curve.Gy, k)
}
func matchesSpecificCurve(params *CurveParams, available ...Curve) (Curve, bool) {
for _, c := range available {
if params == c.Params() {
return c, true
}
}
return nil, false
}