Bilinear pairings on elliptic curves
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ENGE, Andreas | |
| dc.date.accessioned | 2024-04-04T02:19:35Z | |
| dc.date.available | 2024-04-04T02:19:35Z | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0013-8584 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189416 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | Zürich International Mathematical Society Publishing House | |
| dc.title.en | Bilinear pairings on elliptic curves | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1301.5520 | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.journal | L'Enseignement Mathématique | |
| bordeaux.page | 211–243 | |
| bordeaux.volume | 61 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00767404 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00767404v1 | |
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