Arithmetic operators for pairing-based cryptography

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 ηT pairing over double-struck F sign3[x]/(x97 + x12 + 2). Our architecture is based on a unified arithmetic operator which performs addition, multiplication, and cubing over F397. 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. © Springer-Verlag Berlin Heidelberg 2007.