Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves
hal.structure.identifier | Cryptology, Arithmetic: Hardware and Software [CARAMEL] | |
dc.contributor.author | COSSET, Romain | |
hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | ROBERT, Damien | |
dc.date.accessioned | 2024-04-04T02:27:04Z | |
dc.date.available | 2024-04-04T02:27:04Z | |
dc.date.created | 2013-10-01 | |
dc.date.issued | 2015 | |
dc.identifier.issn | 0025-5718 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190001 | |
dc.description.abstractEn | 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. | |
dc.description.sponsorship | Courbes Hyperelliptiques : Isogénies et Comptage - ANR-09-BLAN-0020 | |
dc.language.iso | en | |
dc.publisher | American Mathematical Society | |
dc.title.en | Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves | |
dc.type | Article de revue | |
dc.identifier.doi | 10.1090/S0025-5718-2014-02899-8 | |
dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
bordeaux.journal | Mathematics of Computation | |
bordeaux.page | 1953-1975 | |
bordeaux.volume | 84 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 294 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-00578991 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-00578991v1 | |
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