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hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorLUBICZ, David
hal.structure.identifierCryptology, Arithmetic: Hardware and Software [CARAMEL]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorROBERT, Damien
dc.date.accessioned2024-04-04T02:24:33Z
dc.date.available2024-04-04T02:24:33Z
dc.date.created2010-01-11
dc.date.issued2012-09-01
dc.identifier.issn0010-437X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189823
dc.description.abstractEnWe describe an efficient algorithm for the computation of isogenies between abelian varieties represented in the coordinate system provided by algebraic theta functions. We explain how to compute all the isogenies from an abelian variety whose kernel is isomorphic to a given abstract group. We also describe an analog of Vélu's formulas to compute an isogenis with prescribed kernels. All our algorithms rely in an essential manner on a generalization of the Riemann formulas. In order to improve the efficiency of our algorithms, we introduce a point compression algorithm that represents a point of level $4\ell$ of a $g$ dimensional abelian variety using only $g(g+1)/2\cdot 4^g$ coordinates. We also give formulas to compute the Weil and commutator pairing given input points in theta coordinates. All the algorithms presented in this paper work in general for any abelian variety defined over a field of odd characteristic.
dc.description.sponsorshipCourbes Hyperelliptiques : Isogénies et Comptage - ANR-09-BLAN-0020
dc.language.isoen
dc.publisherFoundation Compositio Mathematica
dc.typeArticle de revue
dc.identifier.doi10.1112/S0010437X12000243
dc.subject.halInformatique [cs]/Calcul formel [cs.SC]
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.journalCompositio Mathematica
bordeaux.page1483--1515
bordeaux.volume148
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue05
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00446062
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00446062v1
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