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The Tate-Lichtenbaum Pairing on a Hyperelliptic Curve via Hyperelliptic Nets

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Pairing-Based Cryptography – Pairing 2012 (Pairing 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7708))

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Abstract

Recently, Stange proposed a new algorithm to compute the Tate pairing on an elliptic curve. Her algorithm is based on elliptic nets, which are also defined by Stange as a generalization of elliptic divisibility sequences. In this paper, we define hyperelliptic nets as a generalization of elliptic nets to hyperelliptic curves. We also give an expression for the Tate-Lichtenbaum pairing on a hyperelliptic curve in terms of hyperelliptic nets. Using this expression, we give an algorithm to compute the Tate-Lichtenbaum pairing on a hyperelliptic curve of genus 2.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo, 192-0397, Japan

    Yukihiro Uchida & Shigenori Uchiyama

Authors
  1. Yukihiro Uchida
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  2. Shigenori Uchiyama
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Editor information

Editors and Affiliations

  1. Départment d’Informatique, École Normale Supérieure and CNRS, 45 rue d’Ulm, 75005, Paris, France

    Michel Abdalla

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Tanja Lange

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Uchida, Y., Uchiyama, S. (2013). The Tate-Lichtenbaum Pairing on a Hyperelliptic Curve via Hyperelliptic Nets. In: Abdalla, M., Lange, T. (eds) Pairing-Based Cryptography – Pairing 2012. Pairing 2012. Lecture Notes in Computer Science, vol 7708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36334-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-36334-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36333-7

  • Online ISBN: 978-3-642-36334-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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