isogeny.go raw

   1  package goldilocks
   2  
   3  import fp "github.com/cloudflare/circl/math/fp448"
   4  
   5  func (Curve) pull(P *twistPoint) *Point      { return twistCurve{}.push(P) }
   6  func (twistCurve) pull(P *Point) *twistPoint { return Curve{}.push(P) }
   7  
   8  // push sends a point on the Goldilocks curve to a point on the twist curve.
   9  func (Curve) push(P *Point) *twistPoint {
  10  	Q := &twistPoint{}
  11  	Px, Py, Pz := &P.x, &P.y, &P.z
  12  	a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb
  13  	fp.Add(e, Px, Py)  // x+y
  14  	fp.Sqr(a, Px)      // A = x^2
  15  	fp.Sqr(b, Py)      // B = y^2
  16  	fp.Sqr(c, Pz)      // z^2
  17  	fp.Add(c, c, c)    // C = 2*z^2
  18  	*d = *a            // D = A
  19  	fp.Sqr(e, e)       // (x+y)^2
  20  	fp.Sub(e, e, a)    // (x+y)^2-A
  21  	fp.Sub(e, e, b)    // E = (x+y)^2-A-B
  22  	fp.Add(h, b, d)    // H = B+D
  23  	fp.Sub(g, b, d)    // G = B-D
  24  	fp.Sub(f, c, h)    // F = C-H
  25  	fp.Mul(&Q.z, f, g) // Z = F * G
  26  	fp.Mul(&Q.x, e, f) // X = E * F
  27  	fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H
  28  	return Q
  29  }
  30  
  31  // push sends a point on the twist curve to a point on the Goldilocks curve.
  32  func (twistCurve) push(P *twistPoint) *Point {
  33  	Q := &Point{}
  34  	Px, Py, Pz := &P.x, &P.y, &P.z
  35  	a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb
  36  	fp.Add(e, Px, Py)  // x+y
  37  	fp.Sqr(a, Px)      // A = x^2
  38  	fp.Sqr(b, Py)      // B = y^2
  39  	fp.Sqr(c, Pz)      // z^2
  40  	fp.Add(c, c, c)    // C = 2*z^2
  41  	fp.Neg(d, a)       // D = -A
  42  	fp.Sqr(e, e)       // (x+y)^2
  43  	fp.Sub(e, e, a)    // (x+y)^2-A
  44  	fp.Sub(e, e, b)    // E = (x+y)^2-A-B
  45  	fp.Add(h, b, d)    // H = B+D
  46  	fp.Sub(g, b, d)    // G = B-D
  47  	fp.Sub(f, c, h)    // F = C-H
  48  	fp.Mul(&Q.z, f, g) // Z = F * G
  49  	fp.Mul(&Q.x, e, f) // X = E * F
  50  	fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H
  51  	return Q
  52  }
  53