Cryptology ePrint Archive: Report 2007/091

Arithmetic Operators for Pairing-Based Cryptography

Jean-Luc Beuchat and Nicolas Brisebarre and J\'er\'emie Detrey and Eiji Okamoto

Abstract: Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we first study an accelerator for the $\eta_T$ pairing over $\mathbb{F}_3[x]/(x^{97}+x^{12}+2)$. Our architecture is based on a unified arithmetic operator which performs addition, multiplication, and cubing over $\mathbb{F}_{3^{97}}$. This design methodology allows us to design a compact coprocessor ($1888$ slices on a Virtex-II Pro~$4$ FPGA) which compares favorably with other solutions described in the open literature. We then describe ways to extend our approach to any characteristic and any extension field.

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

Publication Info: Submitted to CHES 2007

Date: received 11 Mar 2007, last revised 2 Jun 2007

Contact author: beuchat at risk tsukuba ac jp

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Version: 20070603:013734 (All versions of this report)

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