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Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves

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Topics in Cryptology – CT-RSA 2012 (CT-RSA 2012)

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Abstract

This article presents a novel pairing algorithm over supersingular genus-2 binary hyperelliptic curves. Starting from Vercauteren’s work on optimal pairings, we describe how to exploit the action of the 23m-th power Verschiebung in order to reduce the loop length of Miller’s algorithm even further than the genus-2 η T approach.

As a proof of concept, we detail an optimized software implementation and an FPGA accelerator for computing the proposed optimal Eta pairing on a genus-2 hyperelliptic curve over \(\mathbb{F}_{2^{367}}\), which satisfies the recommended security level of 128 bits. These designs achieve favourable performance in comparison with the best known implementations of 128-bit-security Type-1 pairings from the literature.

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Author information

Authors and Affiliations

  1. Institute of Computing, University of Campinas, Av. Albert Einstein, 1251, CEP 13084-971, Campinas, Brazil

    Diego F. Aranha

  2. Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Jean-Luc Beuchat

  3. CARAMEL project-team, LORIA, INRIA / CNRS / Nancy Université, Campus Scientifique, BP 239, 54506, Vandoeuvre-lès-Nancy Cedex, France

    Jérémie Detrey & Nicolas Estibals

Authors
  1. Diego F. Aranha
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  2. Jean-Luc Beuchat
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  3. Jérémie Detrey
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  4. Nicolas Estibals
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Editors and Affiliations

  1. Computer Science Department, University of Haifa, 31905, Haifa, Israel

    Orr Dunkelman

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Aranha, D.F., Beuchat, JL., Detrey, J., Estibals, N. (2012). Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves. In: Dunkelman, O. (eds) Topics in Cryptology – CT-RSA 2012. CT-RSA 2012. Lecture Notes in Computer Science, vol 7178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27954-6_7

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  • DOI: https://doi.org/10.1007/978-3-642-27954-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27953-9

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