COSSET, Romain; ROBERT, Damien

doi:10.1090/S0025-5718-2014-02899-8

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Licencia de uso del documento

COSSET, Romain
Cryptology, Arithmetic: Hardware and Software [CARAMEL]

ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

Idioma

Article de revue

Este ítem está publicado en

Mathematics of Computation. 2015, vol. 84, n° 294, p. 1953-1975

American Mathematical Society

Resumen en inglés

In this paper, we compute l-isogenies between abelian varieties over a field of characteristic different from 2 in polynomial time in l, when l is an odd prime which is coprime to the characteristic. We use level n symmetric theta structure where n = 2 or n = 4. In a second part of this paper we explain how to convert between Mumford coordinates of Jacobians of genus 2 hyperelliptic curves to theta coordinates of level 2 or 4. Combined with the preceding algorithm, this gives a method to compute (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190001

DOI

http://dx.doi.org/10.1090/S0025-5718-2014-02899-8

Proyecto europeo

Algorithmic Number Theory in Computer Science

Proyecto ANR

Courbes Hyperelliptiques : Isogénies et Comptage - ANR-09-BLAN-0020

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251