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

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12001))

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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 \(k = 28\).

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Authors and Affiliations

  1. Laboratory Analysis, Geometry and Applications CNRS (UMR 7539), Galilee Institute, Paris 13 University, Villetaneuse, France

    Mohammed Zitouni & Farid Mokrane

Authors
  1. Mohammed Zitouni
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  2. Farid Mokrane
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Correspondence to Mohammed Zitouni .

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Editors and Affiliations

  1. Polytechnic University of Bucharest, Bucharest, Romania

    Emil Simion

  2. École Normale Supérieure, Paris, France

    Rémi Géraud-Stewart

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Zitouni, M., Mokrane, F. (2020). Implementing Cryptography Pairings over Ordinary Pairing-Friendly Curves of Type \( y^2 = x^5 +a \, x\). In: Simion, E., Géraud-Stewart, R. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2019. Lecture Notes in Computer Science(), vol 12001. Springer, Cham. https://doi.org/10.1007/978-3-030-41025-4_7

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  • DOI: https://doi.org/10.1007/978-3-030-41025-4_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41024-7

  • Online ISBN: 978-3-030-41025-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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