KIEFFER, Jean; PAGE, Aurel; ROBERT, Damien

Métadonnées

Licence d’utilisation du document

KIEFFER, Jean
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

PAGE, Aurel
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]

ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]

Langue

Document de travail - Pré-publication

Résumé en anglais

We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2.< Réduire

Mots clés en anglais

Abelian surfaces

Algorithm

Modular equations

Isogenies

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191788

Project ANR

Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251