Arithmetic Operators for Pairing-Based Cryptography

Jean-Luc Beuchat (1) , Nicolas Brisebarre (2, 3) , Jérémie Detrey (2) , Eiji Okamoto (1)

1 LCIS - Laboratory of Cryptography and Information Security
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 LAMUSE - Laboratoire de Mathématiques de l'Université de Saint-Etienne

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 F_3[x]/(x^97 + x^12 + 2). Our architecture is based on a unified arithmetic operator which performs addition, multiplication, and cubing over 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.

Keywords: eta_T pairing; finite field arithmetic; elliptic curve; hardware accelerator; FPGA

Domains: Computer Science [cs]; Cryptography and Security [cs.CR]; Computer Science [cs]; Computer Arithmetic

Jean-Luc Beuchat, Nicolas Brisebarre, Jérémie Detrey, Eiji Okamoto. Arithmetic Operators for Pairing-Based Cryptography. 9th Invernational Workshop on Cryptographic Hardware and Embedded Systems – CHES 2007, Sep 2007, Vienne, Austria. pp.239-255, ⟨10.1007/978-3-540-74735-2_17⟩. ⟨ensl-00137918⟩