Computing isogenies between Jacobian of curves of genus 2 and 3

Enea Milio 1
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

Littérature citée [34 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01589683
Contributeur : Enea Milio <>
Soumis le : lundi 18 septembre 2017 - 19:41:53
Dernière modification le : mercredi 20 septembre 2017 - 01:10:42

Fichier

artJM.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01589683, version 1

Collections

Citation

Enea Milio. Computing isogenies between Jacobian of curves of genus 2 and 3. 2017. 〈hal-01589683〉

Partager

Métriques

Consultations de
la notice

67

Téléchargements du document

10