MPHELL
4.0.0

These formulas are derived from the paper [BJ03] "The Jacobi Model of an Elliptic Curve and SideChannel Analysis" written by Olivier Billet and Marc Joye published in International Symposium on Applied Algebra, Algebraic Algorithms, and ErrorCorrecting Codes. Springer, Berlin, Heidelberg, 2003. p. 3442 viewable at this address https://link.springer.com/ .
Let a Weierstrass elliptic curve.
Let an extended Jacobi Quartic elliptic curve.
For which can be extented to the Jacobi Quartic (with Projective equation)
The coefficients and of the Weiertrass elliptic curve matching the Jacobi Quartic elliptic curve are:
A point of can be converted to a point of with
Let such that is a 2torsion point the Weierstrass elliptic curve .
The coefficients and of the (extended) Jacobi Quartic matching the Weiertrass elliptic curve are:
A point of can be converted to a point of with
Those formulas are corrected formulas of [BJ03,§3]. More details are available in [BJ03,§3].