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core/curves/native/isogeny.go

@@ -0,0 +1,62 @@
+package native
+
+// IsogenyParams are the parameters needed to map from an isogeny to the main curve
+type IsogenyParams struct {
+	XNum [][FieldLimbs]uint64
+	XDen [][FieldLimbs]uint64
+	YNum [][FieldLimbs]uint64
+	YDen [][FieldLimbs]uint64
+}
+
+// Map from the isogeny curve to the main curve using the parameters
+func (p *IsogenyParams) Map(xIn, yIn *Field) (x, y *Field) {
+	var xNum, xDen, yNum, yDen, tv [FieldLimbs]uint64
+	var wasInverted int
+
+	xnumL := len(p.XNum)
+	xdenL := len(p.XDen)
+	ynumL := len(p.YNum)
+	ydenL := len(p.YDen)
+
+	degree := 0
+	for _, i := range []int{xnumL, xdenL, ynumL, ydenL} {
+		if degree < i {
+			degree = i
+		}
+	}
+
+	xs := make([][FieldLimbs]uint64, degree)
+	xs[0] = xIn.Params.R                      // x[0] = x^0
+	xs[1] = xIn.Value                         // x[1] = x^1
+	xIn.Arithmetic.Square(&xs[2], &xIn.Value) // x[2] = x^2
+	for i := 3; i < degree; i++ {
+		// x[i] = x^i
+		xIn.Arithmetic.Mul(&xs[i], &xs[i-1], &xIn.Value)
+	}
+
+	computeIsoK(&xNum, &xs, &p.XNum, xIn.Arithmetic)
+	computeIsoK(&xDen, &xs, &p.XDen, xIn.Arithmetic)
+	computeIsoK(&yNum, &xs, &p.YNum, xIn.Arithmetic)
+	computeIsoK(&yDen, &xs, &p.YDen, xIn.Arithmetic)
+
+	xIn.Arithmetic.Invert(&wasInverted, &xDen, &xDen)
+	x = new(Field).Set(xIn)
+	xIn.Arithmetic.Mul(&tv, &xNum, &xDen)
+	xIn.Arithmetic.Selectznz(&x.Value, &x.Value, &tv, wasInverted)
+
+	yIn.Arithmetic.Invert(&wasInverted, &yDen, &yDen)
+	y = new(Field).Set(yIn)
+	yIn.Arithmetic.Mul(&tv, &yNum, &yDen)
+	yIn.Arithmetic.Selectznz(&y.Value, &y.Value, &tv, wasInverted)
+	yIn.Arithmetic.Mul(&y.Value, &y.Value, &yIn.Value)
+	return x, y
+}
+
+func computeIsoK(out *[FieldLimbs]uint64, xxs, k *[][FieldLimbs]uint64, f FieldArithmetic) {
+	var tv [FieldLimbs]uint64
+
+	for i := range *k {
+		f.Mul(&tv, &(*xxs)[i], &(*k)[i])
+		f.Add(out, out, &tv)
+	}
+}