Section: New Results
Explicit Isogenies in Genus 2 and 3
Participant : Enea Milio.
In [22], we present a quasi-linear algorithm to compute isogenies between Jacobians of curves of genus 2 and 3 starting from the equation of the curve and a maximal isotropic subgroup of the -torsion, for an odd prime number, generalizing Vélu’s formula of genus 1. This work is based on the paper “Computing functions on Jacobians and their quotients” of Jean-Marc Couveignes and Tony Ezome. We improve their genus 2 case algorithm, generalize it for genus 3 hyperelliptic curves and introduce a way to deal with the genus 3 non-hyperelliptic case, using algebraic Theta functions.