1 files changed, 491 insertions, 0 deletions
diff --git a/src/crypto/elliptic/elliptic.go b/src/crypto/elliptic/elliptic.go
new file mode 100644
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+++ b/src/crypto/elliptic/elliptic.go
@@ -0,0 +1,491 @@
+// Copyright 2010 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 implements several standard elliptic curves over prime
+// fields.
+package elliptic
+
+// This package 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.
+
+import (
+	"io"
+	"math/big"
+	"sync"
+)
+
+// A Curve represents a short-form Weierstrass curve with a=-3.
+//
+// Note that the point at infinity (0, 0) is not considered on the curve, and
+// although it can be returned by Add, Double, ScalarMult, or ScalarBaseMult, it
+// can't be marshaled or unmarshaled, and IsOnCurve will return false for it.
+type Curve interface {
+	// Params returns the parameters for the curve.
+	Params() *CurveParams
+	// IsOnCurve reports whether the given (x,y) lies on the curve.
+	IsOnCurve(x, y *big.Int) bool
+	// Add returns the sum of (x1,y1) and (x2,y2)
+	Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int)
+	// Double returns 2*(x,y)
+	Double(x1, y1 *big.Int) (x, y *big.Int)
+	// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
+	ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int)
+	// ScalarBaseMult returns k*G, where G is the base point of the group
+	// and k is an integer in big-endian form.
+	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
+}
+
+// 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, 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, 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, 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, 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, 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}
+
+// GenerateKey returns a public/private key pair. The private key is
+// generated using the given reader, which must return random data.
+func GenerateKey(curve Curve, rand io.Reader) (priv []byte, x, y *big.Int, err error) {
+	N := curve.Params().N
+	bitSize := N.BitLen()
+	byteLen := (bitSize + 7) / 8
+	priv = make([]byte, byteLen)
+
+	for x == nil {
+		_, err = io.ReadFull(rand, priv)
+		if err != nil {
+			return
+		}
+		// We have to mask off any excess bits in the case that the size of the
+		// underlying field is not a whole number of bytes.
+		priv[0] &= mask[bitSize%8]
+		// This is because, in tests, rand will return all zeros and we don't
+		// want to get the point at infinity and loop forever.
+		priv[1] ^= 0x42
+
+		// If the scalar is out of range, sample another random number.
+		if new(big.Int).SetBytes(priv).Cmp(N) >= 0 {
+			continue
+		}
+
+		x, y = curve.ScalarBaseMult(priv)
+	}
+	return
+}
+
+// Marshal converts a point on the curve into the uncompressed form specified in
+// section 4.3.6 of ANSI X9.62.
+func Marshal(curve Curve, x, y *big.Int) []byte {
+	byteLen := (curve.Params().BitSize + 7) / 8
+
+	ret := make([]byte, 1+2*byteLen)
+	ret[0] = 4 // uncompressed point
+
+	x.FillBytes(ret[1 : 1+byteLen])
+	y.FillBytes(ret[1+byteLen : 1+2*byteLen])
+
+	return ret
+}
+
+// MarshalCompressed converts a point on the curve into the compressed form
+// specified in section 4.3.6 of ANSI X9.62.
+func MarshalCompressed(curve Curve, x, y *big.Int) []byte {
+	byteLen := (curve.Params().BitSize + 7) / 8
+	compressed := make([]byte, 1+byteLen)
+	compressed[0] = byte(y.Bit(0)) | 2
+	x.FillBytes(compressed[1:])
+	return compressed
+}
+
+// Unmarshal converts a point, serialized by Marshal, into an x, y pair.
+// It is an error if the point is not in uncompressed form or is not on the curve.
+// On error, x = nil.
+func Unmarshal(curve Curve, data []byte) (x, y *big.Int) {
+	byteLen := (curve.Params().BitSize + 7) / 8
+	if len(data) != 1+2*byteLen {
+		return nil, nil
+	}
+	if data[0] != 4 { // uncompressed form
+		return nil, nil
+	}
+	p := curve.Params().P
+	x = new(big.Int).SetBytes(data[1 : 1+byteLen])
+	y = new(big.Int).SetBytes(data[1+byteLen:])
+	if x.Cmp(p) >= 0 || y.Cmp(p) >= 0 {
+		return nil, nil
+	}
+	if !curve.IsOnCurve(x, y) {
+		return nil, nil
+	}
+	return
+}
+
+// UnmarshalCompressed converts a point, serialized by MarshalCompressed, into an x, y pair.
+// It is an error if the point is not in compressed form or is not on the curve.
+// On error, x = nil.
+func UnmarshalCompressed(curve Curve, data []byte) (x, y *big.Int) {
+	byteLen := (curve.Params().BitSize + 7) / 8
+	if len(data) != 1+byteLen {
+		return nil, nil
+	}
+	if data[0] != 2 && data[0] != 3 { // compressed form
+		return nil, nil
+	}
+	p := curve.Params().P
+	x = new(big.Int).SetBytes(data[1:])
+	if x.Cmp(p) >= 0 {
+		return nil, nil
+	}
+	// y² = x³ - 3x + b
+	y = curve.Params().polynomial(x)
+	y = y.ModSqrt(y, p)
+	if y == nil {
+		return nil, nil
+	}
+	if byte(y.Bit(0)) != data[0]&1 {
+		y.Neg(y).Mod(y, p)
+	}
+	if !curve.IsOnCurve(x, y) {
+		return nil, nil
+	}
+	return
+}
+
+var initonce sync.Once
+var p384 *CurveParams
+
+func initAll() {
+	initP224()
+	initP256()
+	initP384()
+	initP521()
+}
+
+func initP384() {
+	// See FIPS 186-3, section D.2.4
+	p384 = &CurveParams{Name: "P-384"}
+	p384.P, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319", 10)
+	p384.N, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643", 10)
+	p384.B, _ = new(big.Int).SetString("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef", 16)
+	p384.Gx, _ = new(big.Int).SetString("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7", 16)
+	p384.Gy, _ = new(big.Int).SetString("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f", 16)
+	p384.BitSize = 384
+}
+
+// P256 returns a Curve which implements NIST P-256 (FIPS 186-3, section D.2.3),
+// also known as secp256r1 or prime256v1. The CurveParams.Name of this Curve is
+// "P-256".
+//
+// Multiple invocations of this function will return the same value, so it can
+// be used for equality checks and switch statements.
+//
+// ScalarMult and ScalarBaseMult are implemented using constant-time algorithms.
+func P256() Curve {
+	initonce.Do(initAll)
+	return p256
+}
+
+// P384 returns a Curve which implements NIST P-384 (FIPS 186-3, section D.2.4),
+// also known as secp384r1. The CurveParams.Name of this Curve is "P-384".
+//
+// Multiple invocations of this function will return the same value, so it can
+// be used for equality checks and switch statements.
+//
+// The cryptographic operations do not use constant-time algorithms.
+func P384() Curve {
+	initonce.Do(initAll)
+	return p384
+}
+
+// P521 returns a Curve which implements NIST P-521 (FIPS 186-3, section D.2.5),
+// also known as secp521r1. The CurveParams.Name of this Curve is "P-521".
+//
+// Multiple invocations of this function will return the same value, so it can
+// be used for equality checks and switch statements.
+//
+// The cryptographic operations are implemented using constant-time algorithms.
+func P521() Curve {
+	initonce.Do(initAll)
+	return p521
+}