Pairing.Jacobian

Jacobian representation of points on an elliptic curve.

In Jacobian coordinates the triple (x, y, z) represents the affine point (X Z^2, Y Z^3). Curve operations are more optimal in Jacobian coordinates when the time complexity for underlying field inversions is significantly higher than field multiplications.

Documentation

type JPoint k = (k, k, k)

Jacobian coordinates for points on an elliptic curve over a field k.

toJacobian :: GaloisField k => Point k -> JPoint k

Convert affine coordinates to Jacobian coordinates

fromJacobian :: GaloisField k => JPoint k -> Point k

Convert Jacobian coordinates to affine coordinates