International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

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

Authors:
Jean-Luc Beuchat
Jorge Enrique González Díaz
Shigeo Mitsunari
Eiji Okamoto
Francisco Rodríguez-Henríquez
Tadanori Teruya
Download:
URL: http://eprint.iacr.org/2010/354
Search ePrint
Search Google
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 $2.63$ million of clock cycles on a single core of an Intel Core i7 $2.8$GHz processor, which implies that the pairing computation takes $0.942$msec. 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 $t = 2^{62} - 2^{54} + 2^{44}$. 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.
BibTeX
@misc{eprint-2010-23255,
  title={High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves},
  booktitle={IACR Eprint archive},
  keywords={implementation /},
  url={http://eprint.iacr.org/2010/354},
  note={ francisco@cs.cinvestav.mx 14845 received 17 Jun 2010, last revised 24 Aug 2010},
  author={Jean-Luc Beuchat and Jorge Enrique González Díaz and Shigeo Mitsunari and Eiji Okamoto and Francisco Rodríguez-Henríquez and Tadanori Teruya},
  year=2010
}