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Implementing Cryptography Pairings over Ordinary Pairing-Friendly Curves of Type \( y^2 = x^5 +a \, x\)

  • Mohammed ZitouniEmail author
  • Farid Mokrane
Conference paper
  • 31 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12001)

Abstract

In this paper, we describe an efficient implementation in Sage of the Tate pairing over ordinary hyperelliptic curves of type \( y^2 = x^5 +a \, x\). First, we describe a method of construction of these curves according to Kawazoe and Takahashi [8]. Then, we describe an efficient formula for computing pairings on such curves over prime fields, and develop algorithms to compute Tate pairing. We provide a faster optimisation of the final exponentiation in particular for the embedding degree \(k = 28\).

Keywords

Hyperelliptic curve Tate pairing Finite field Embedding degree Final exponentiation 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Laboratory Analysis, Geometry and Applications CNRS (UMR 7539), Galilee InstituteParis 13 UniversityVilletaneuseFrance

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