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# Bilinear pairings on elliptic curves

1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
Document type :
Preprints, Working Papers, ...

https://hal.inria.fr/hal-00767404
Contributor : Andreas Enge Connect in order to contact the contributor
Submitted on : Wednesday, January 23, 2013 - 1:16:00 PM
Last modification on : Friday, December 3, 2021 - 12:20:06 PM
Long-term archiving on: : Wednesday, April 24, 2013 - 2:45:10 AM

### Files

pairings.pdf
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### Identifiers

• HAL Id : hal-00767404, version 1
• ARXIV : 1301.5520

### Citation

Andreas Enge. Bilinear pairings on elliptic curves. 2013. ⟨hal-00767404v1⟩

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