- Jean-Luc Beuchat19,
- Jorge E. González-Díaz20,
- Shigeo Mitsunari21,
- Eiji Okamoto19,
- Francisco Rodríguez-Henríquez20 &
- …
- Tadanori Teruya19
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 primep given as,p = 36t4 + 36t3 + 24t2 + 6t + 1, witht = 262 − 254 + 244. This selection oft 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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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
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
Akasaka Twin Tower East 15F, Cybozu Labs, Inc., 2-17-22 Akasaka, Minato-ku, Tokyo, 107-0052
Shigeo Mitsunari
- Jean-Luc Beuchat
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Marc Joye
Japan Advanced Institute of Science and Technology (JAIST), 923-1292, Nomi, Ishikawa, Japan
Atsuko Miyaji
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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