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hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorENGE, Andreas
dc.date.accessioned2024-04-04T02:19:35Z
dc.date.available2024-04-04T02:19:35Z
dc.date.issued2015
dc.identifier.issn0013-8584
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189416
dc.description.abstractEnWe give an elementary and self-contained introduction to pairings on elliptic curves over finite fields. For the first time in the literature, the three different definitions of the Weil pairing are stated correctly and proved to be equivalent using Weil reciprocity. Pairings with shorter loops, such as the ate, ate$_i$, R-ate and optimal pairings, together with their twisted variants, are presented with proofs of their bilinearity and non-degeneracy. Finally, we review different types of pairings in a cryptographic context. This article can be seen as an update chapter to A. Enge, Elliptic Curves and Their Applications to Cryptography - An Introduction, Kluwer Academic Publishers 1999.
dc.language.isoen
dc.publisherZürich International Mathematical Society Publishing House
dc.title.enBilinear pairings on elliptic curves
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1301.5520
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.journalL'Enseignement Mathématique
bordeaux.page211–243
bordeaux.volume61
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00767404
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00767404v1
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