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On Efficient Pairings on Elliptic Curves over Extension Fields

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Book cover 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

In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairing-based cryptography, however, pairing-friendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller’s algorithm to present further advantage of pairing-friendly curves over extension fields, not relying on the much faster field arithmetic. We propose new pairings on elliptic curves over extension fields can make better use of the multi-pairing technique for the efficient implementation. By using some implementation skills, our new pairings could be implemented much more efficiently than the optimal ate pairing and the optimal twisted ate pairing on elliptic curves over extension fields. At last, we use the similar method to give more efficient pairings on Estibals’s supersingular curves over composite extension fields in parallel implementation.

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Author information

Authors and Affiliations

  1. Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Xusheng Zhang

  2. Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Xusheng Zhang

  3. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100195, China

    Kunpeng Wang & Dongdai Lin

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  1. Xusheng Zhang
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  2. Kunpeng Wang
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  3. Dongdai Lin
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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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Zhang, X., Wang, K., Lin, D. (2013). On Efficient Pairings on Elliptic Curves over Extension Fields. 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_1

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  • DOI: https://doi.org/10.1007/978-3-642-36334-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36333-7

  • Online ISBN: 978-3-642-36334-4

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