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A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties

hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorLUBICZ, David
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierLaboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
dc.contributor.authorROBERT, Damien
dc.date.accessioned2024-04-04T02:22:20Z
dc.date.available2024-04-04T02:22:20Z
dc.date.created2013-03-28
dc.date.issued2015
dc.identifier.issn0747-7171
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189644
dc.description.abstractEnIn this paper, we use the theory of theta functions to generalize to all abelian varieties the usual Miller's algorithm to compute a function associated to a principal divisor. We also explain how to use the Frobenius morphism on abelian varieties defined over a finite field in order to shorten the loop of the Weil and Tate pairings algorithms. This extend preceding results about ate and twisted ate pairings to all abelian varieties. Then building upon the two preceding ingredients, we obtain a variant of optimal pairings on abelian varieties. Finally, by introducing new addition formulas, we explain how to compute optimal pairings on Kummer varieties. We compare in term of performance the resulting algorithms to the algorithms already known in the genus one and two case.
dc.description.sponsorshipEspaces de paramètres pour une arithmétique efficace et une évaluation de la sécurité des courbes - ANR-12-BS01-0010
dc.description.sponsorshipSIM et théorie des couplages pour la sécurité de l'information et des communications - ANR-12-INSE-0014
dc.description.sponsorshipCentre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
dc.language.isoen
dc.publisherElsevier
dc.subject.enPairings
dc.subject.enAbelian varieties
dc.subject.enCryptography
dc.title.enA generalisation of Miller's algorithm and applications to pairing computations on abelian varieties
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jsc.2014.08.001
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.journalJournal of Symbolic Computation
bordeaux.page68-92
bordeaux.volume67
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00806923
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00806923v1
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