International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Arithmetic Operators for Pairing-Based Cryptography

Jean-Luc Beuchat
Nicolas Brisebarre
Jérémie Detrey
Eiji Okamoto
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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.
  title={Arithmetic Operators for Pairing-Based Cryptography},
  booktitle={IACR Eprint archive},
  keywords={implementation / $\eta_T$ pairing, finite field arithmetic, elliptic curve, hardware accelerator, FPGA},
  note={Submitted to CHES 2007 13667 received 11 Mar 2007, last revised 2 Jun 2007},
  author={Jean-Luc Beuchat and Nicolas Brisebarre and Jérémie Detrey and Eiji Okamoto},