ENGE, Andreas

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ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

L'Enseignement Mathématique. 2015, vol. 61, n° 2, p. 211–243

Zürich International Mathematical Society Publishing House

Résumé en anglais

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.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189416

Projet Européen

Algorithmic Number Theory in Computer Science

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251