Formulae for Computation of Tate Pairing on Hyperelliptic Curve Using Hyperelliptic Nets

Christophe Tran

doi:10.1007/978-3-319-06734-6_13

Formulae for Computation of Tate Pairing on Hyperelliptic Curve Using Hyperelliptic Nets

Christophe Tran

https://doi.org/10.1007/978-3-319-06734-6_13

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Publication Date: Jan 1, 2014

Citations: 11

Affiliation: Institut de recherche mathématique de Rennes, Institut Polytechnique de Paris, University of Rennes, French National Centre for Scientific Research

#Hyperelliptic Curve #Hyperelliptic Curve Of Genus + Show 8 more

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Abstract

AbstractStange has showed how to compute the Tate pairing on an elliptic curve using elliptic nets. After that, Uchida and Uchiyama gave a generalization of elliptic nets to hyperelliptic curves. They also gave an algorithm to compute the Tate pairing on a hyperelliptic curve of genus 2. In this paper, we extend their algorithm for curves of all genus. In a computational point of view, we also study the optimality of these algorithms.KeywordsTate pairinghyperelliptic curvehyperelliptic net

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