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Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves

hal.structure.identifierCryptology, Arithmetic: Hardware and Software [CARAMEL]
dc.contributor.authorCOSSET, Romain
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorROBERT, Damien
dc.date.accessioned2024-04-04T02:27:04Z
dc.date.available2024-04-04T02:27:04Z
dc.date.created2013-10-01
dc.date.issued2015
dc.identifier.issn0025-5718
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190001
dc.description.abstractEnIn 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.sponsorshipCourbes Hyperelliptiques : Isogénies et Comptage - ANR-09-BLAN-0020
dc.language.isoen
dc.publisherAmerican Mathematical Society
dc.title.enComputing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves
dc.typeArticle de revue
dc.identifier.doi10.1090/S0025-5718-2014-02899-8
dc.subject.halInformatique [cs]/Calcul formel [cs.SC]
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.journalMathematics of Computation
bordeaux.page1953-1975
bordeaux.volume84
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue294
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00578991
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00578991v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematics%20of%20Computation&rft.date=2015&rft.volume=84&rft.issue=294&rft.spage=1953-1975&rft.epage=1953-1975&rft.eissn=0025-5718&rft.issn=0025-5718&rft.au=COSSET,%20Romain&ROBERT,%20Damien&rft.genre=article


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