A Comparison between Hardware Accelerators for the Modified Tate Pairing over $\mathbb{F}_{2^m}$ and $\mathbb{F}_{3^m}$

Authors:
Jean-Luc Beuchat;Nicolas Brisebarre;Jérémie Detrey;Eiji Okamoto;Francisco Rodríguez-Henríquez
Affiliations:
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan 305-8573;LIP/Arénaire (CNRS --- ENS Lyon --- INRIA --- UCBL), ENS Lyon, Lyon Cedex 07, France F-69364;Cosec group, B-IT, Bonn, Germany D-53113;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan 305-8573;Computer Science Section, Electrical Engineering Department, Centro de Investigación y de Estudios Avanzados del IPN, México City, México 07300
Venue:
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Year:
2008

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Abstract

In this article we propose a study of the modified Tate pairingin characteristics two and three. Starting from the ηTpairing introduced by Barreto etal. [1], we detail various algorithmic improvements inthe case of characteristic two. As far as characteristic three isconcerned, we refer to the survey by Beuchat etal. [5]. We then show how to get back to the modifiedTate pairing at almost no extra cost. Finally, we explore thetrade-offs involved in the hardware implementation of this pairingfor both characteristics two and three. From our experiments,characteristic three appears to have a slight advantage overcharacteristic two.