Computing isogenies between Jacobian of curves of genus 2 and 3
Résumé
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 l-torsion, for l an odd prime number, generalizing the Vélu's formula of genus 1.
This work is based from 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.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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