## Cryptology ePrint Archive: Report 2008/115

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

Jean-Luc Beuchat and Nicolas Brisebarre and Jérémie Detrey and Eiji Okamoto and Francisco Rodríguez-Henríquez

Abstract: In this article we propose a study of the modified Tate pairing in characteristics two and three. Starting from the $\eta_T$ pairing introduced by Barreto {\em et al.} (Des Codes Crypt, 2007), we detail various algorithmic improvements in the case of characteristic two. As far as characteristic three is concerned, we refer to the survey by Beuchat {\em et al.} (ePrint 2007-417). We then show how to get back to the modified Tate pairing at almost no extra cost. Finally, we explore the trade-offs involved in the hardware implementation of this pairing for both characteristics two and three. From our experiments, characteristic three appears to have a slight advantage over characteristic two.

Category / Keywords: implementation / Tate pairing, $\eta_T$ pairing, hardware accelerator, FPGA, finite field arithmetic

Date: received 14 Mar 2008, last revised 17 Mar 2008

Contact author: beuchat at risk tsukuba ac jp

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