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High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves

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Pairing-Based Cryptography - Pairing 2010 (Pairing 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6487))

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Abstract

This paper describes the design of a fast software library for the computation of the optimal ate pairing on a Barreto–Naehrig elliptic curve. Our library is able to compute the optimal ate pairing over a 254-bit prime field \(\mathbb{F}_{p}\), in just 2.33 million of clock cycles on a single core of an Intel Core i7 2.8GHz processor, which implies that the pairing computation takes 0.832msec. We are able to achieve this performance by a careful implementation of the base field arithmetic through the usage of the customary Montgomery multiplier for prime fields. The prime field is constructed via the Barreto–Naehrig polynomial parametrization of the prime p given as, p = 36t 4 + 36t 3 + 24t 2 + 6t + 1, with t = 262 − 254 + 244. This selection of t allows us to obtain important savings for both the Miller loop as well as the final exponentiation steps of the optimal ate pairing.

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Authors and Affiliations

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

    Jean-Luc Beuchat, Eiji Okamoto & Tadanori Teruya

  2. Computer Science Department, Centro de Investigación y de Estudios Avanzados del IPN, Av. Instituto Politécnico Nacional No. 2508, 07300, México City, México

    Jorge E. González-Díaz & Francisco Rodríguez-Henríquez

  3. Akasaka Twin Tower East 15F, Cybozu Labs, Inc., 2-17-22 Akasaka, Minato-ku, Tokyo, 107-0052

    Shigeo Mitsunari

Authors
  1. Jean-Luc Beuchat
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  2. Jorge E. González-Díaz
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  3. Shigeo Mitsunari
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  4. Eiji Okamoto
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  5. Francisco Rodríguez-Henríquez
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  6. Tadanori Teruya
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Editors and Affiliations

  1. Technicolor, Security and Content Protection Labs, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné Cedex, France

    Marc Joye

  2. Japan Advanced Institute of Science and Technology (JAIST), 923-1292, Nomi, Ishikawa, Japan

    Atsuko Miyaji

  3. National Institute of Advanced Industrial Science and Technoloy (AIST), 101-0021, Tokyo, Japan

    Akira Otsuka

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Beuchat, JL., González-Díaz, J.E., Mitsunari, S., Okamoto, E., Rodríguez-Henríquez, F., Teruya, T. (2010). High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds) Pairing-Based Cryptography - Pairing 2010. Pairing 2010. Lecture Notes in Computer Science, vol 6487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17455-1_2

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  • DOI: https://doi.org/10.1007/978-3-642-17455-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17454-4

  • Online ISBN: 978-3-642-17455-1

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