mirror of https://github.com/cheat/cheat.git
81 lines
2.2 KiB
Go
81 lines
2.2 KiB
Go
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// Package goldilocks provides elliptic curve operations over the goldilocks curve.
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package goldilocks
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import fp "github.com/cloudflare/circl/math/fp448"
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// Curve is the Goldilocks curve x^2+y^2=z^2-39081x^2y^2.
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type Curve struct{}
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// Identity returns the identity point.
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func (Curve) Identity() *Point {
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return &Point{
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y: fp.One(),
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z: fp.One(),
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}
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}
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// IsOnCurve returns true if the point lies on the curve.
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func (Curve) IsOnCurve(P *Point) bool {
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x2, y2, t, t2, z2 := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}
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rhs, lhs := &fp.Elt{}, &fp.Elt{}
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fp.Mul(t, &P.ta, &P.tb) // t = ta*tb
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fp.Sqr(x2, &P.x) // x^2
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fp.Sqr(y2, &P.y) // y^2
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fp.Sqr(z2, &P.z) // z^2
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fp.Sqr(t2, t) // t^2
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fp.Add(lhs, x2, y2) // x^2 + y^2
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fp.Mul(rhs, t2, ¶mD) // dt^2
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fp.Add(rhs, rhs, z2) // z^2 + dt^2
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fp.Sub(lhs, lhs, rhs) // x^2 + y^2 - (z^2 + dt^2)
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eq0 := fp.IsZero(lhs)
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fp.Mul(lhs, &P.x, &P.y) // xy
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fp.Mul(rhs, t, &P.z) // tz
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fp.Sub(lhs, lhs, rhs) // xy - tz
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eq1 := fp.IsZero(lhs)
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return eq0 && eq1
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}
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// Generator returns the generator point.
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func (Curve) Generator() *Point {
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return &Point{
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x: genX,
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y: genY,
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z: fp.One(),
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ta: genX,
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tb: genY,
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}
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}
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// Order returns the number of points in the prime subgroup.
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func (Curve) Order() Scalar { return order }
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// Double returns 2P.
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func (Curve) Double(P *Point) *Point { R := *P; R.Double(); return &R }
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// Add returns P+Q.
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func (Curve) Add(P, Q *Point) *Point { R := *P; R.Add(Q); return &R }
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// ScalarMult returns kP. This function runs in constant time.
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func (e Curve) ScalarMult(k *Scalar, P *Point) *Point {
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k4 := &Scalar{}
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k4.divBy4(k)
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return e.pull(twistCurve{}.ScalarMult(k4, e.push(P)))
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}
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// ScalarBaseMult returns kG where G is the generator point. This function runs in constant time.
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func (e Curve) ScalarBaseMult(k *Scalar) *Point {
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k4 := &Scalar{}
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k4.divBy4(k)
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return e.pull(twistCurve{}.ScalarBaseMult(k4))
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}
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// CombinedMult returns mG+nP, where G is the generator point. This function is non-constant time.
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func (e Curve) CombinedMult(m, n *Scalar, P *Point) *Point {
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m4 := &Scalar{}
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n4 := &Scalar{}
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m4.divBy4(m)
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n4.divBy4(n)
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return e.pull(twistCurve{}.CombinedMult(m4, n4, twistCurve{}.pull(P)))
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}
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