# Jacobian Coordinate ## Metadata **Status**:: #x **Zettel**:: #zettel/fleeting **Created**:: [[2024-04-02]] **Topic**:: [[♯ Math]] ## Synopsis **Jacobian Coordinates** are used to represent [[Elliptic Curve]] points on prime curves $y^2 = x^3 + ax + b$. In _Jacobian Coordinates_ the triple $(X, Y, Z)$ represents the affine point $\displaystyle(\frac{X}{Z^2},\frac{Y}{Z^3})$. (**similar**:: [[Homogeneous Coordinate]]) ## References - [Cryptography/Prime Curve/Jacobian Coordinates - Wikibooks, open books for an open world](https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates)