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Implementation of Tate Pairing on Hyperelliptic Curves of Genus 2

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Information Security and Cryptology - ICISC 2003 (ICISC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2971))

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Abstract

Since Tate pairing was suggested to construct a cryptosystem, fast computation of Tate pairing has been researched recently. Barreto et. al [3] and Galbraith [8] provided efficient algorithms for Tate pairing on y 2=x 3-x+b in characteristic 3 and Duursma and Lee [6] gave a closed formula for Tate pairing on y 2=x p-x+d in characteristic p. In this paper, we present completely general and explicit formulae for computing of Tate pairing on hyperelliptic curves of genus 2. We have computed Tate parings on a supersingular hyperelliptic curve over prime fields and the detailed algorithms are explained. This is the first attempt to present the implementation results for Tate pairing on a hyperelliptic curve of genus bigger than 1.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, POSTECH, Pohang, Korea

    YoungJu Choie & Eunjeong Lee

Authors
  1. YoungJu Choie
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  2. Eunjeong Lee
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Editor information

Editors and Affiliations

  1. Center for Information Security Technologies (CIST), Korea University, Seoul, Korea

    Jong-In Lim

  2. CIST (Center for Information Security Technologies), Korea University, Anam Dong, Sungbuk Gu, Seoul, Korea

    Dong-Hoon Lee

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Choie, Y., Lee, E. (2004). Implementation of Tate Pairing on Hyperelliptic Curves of Genus 2. In: Lim, JI., Lee, DH. (eds) Information Security and Cryptology - ICISC 2003. ICISC 2003. Lecture Notes in Computer Science, vol 2971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24691-6_9

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  • DOI: https://doi.org/10.1007/978-3-540-24691-6_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21376-5

  • Online ISBN: 978-3-540-24691-6

  • eBook Packages: Springer Book Archive

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