1 files changed, 296 insertions, 0 deletions
diff --git a/src/crypto/elliptic/params.go b/src/crypto/elliptic/params.go
new file mode 100644
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+++ b/src/crypto/elliptic/params.go
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+// 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
+}