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Cyclic Isogenies for Abelian Varieties with Real Multiplication

hal.structure.identifierEcole Polytechnique Fédérale de Lausanne [EPFL]
dc.contributor.authorDUDEANU, Alina
hal.structure.identifierEcole Polytechnique Fédérale de Lausanne [EPFL]
dc.contributor.authorJETCHEV, Dimitar
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierLaboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
hal.structure.identifierUniversité de Bordeaux [UB]
dc.contributor.authorROBERT, Damien
hal.structure.identifierEcole Polytechnique Fédérale de Lausanne [EPFL]
dc.contributor.authorVUILLE, Marius
dc.date.accessioned2024-04-04T03:08:12Z
dc.date.available2024-04-04T03:08:12Z
dc.date.issued2022
dc.identifier.issn1609-3321
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193509
dc.description.abstractEnWe study quotients of principally polarized abelian varieties with real multiplication by Galois-stable finite subgroups and describe when these quotients are principally polarizable. We use this characterization to provide an algorithm to compute explicit cyclic isogenies from kernel for abelian varieties with real multiplication over finite fields. Our algorithm is polynomial in the size of the finite field as well as in the degree of the isogeny and is based on Mumford's theory of theta functions and theta embeddings. Recently, the algorithm has been successfully applied to obtain new results on the discrete logarithm problem in genus 2 as well as to study the discrete logarithm problem in genus 3.
dc.language.isoen
dc.publisherIndependent University of Moscow
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.title.enCyclic Isogenies for Abelian Varieties with Real Multiplication
dc.typeArticle de revue
dc.subject.halInformatique [cs]/Calcul formel [cs.SC]
bordeaux.journalMoscow Mathematical Journal
bordeaux.page613-655
bordeaux.volume22
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01629829
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01629829v1
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