Cryptology ePrint Archive: Report 2007/091
Arithmetic Operators for Pairing-Based Cryptography
Jean-Luc Beuchat and Nicolas Brisebarre and Jérémie 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
Available format(s): PDF | BibTeX Citation
Version: 20070603:013734 (All versions of this report)
Short URL: ia.cr/2007/091
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