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 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.
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Pascal Paillier, Ingrid Verbauwhede. 9th Invernational Workshop on Cryptographic Hardware and Embedded Systems – CHES 2007, Sep 2007, Vienne, Austria. Springer, pp.239-255, 2007, LNCS 4727. 〈10.1007/978-3-540-74735-2_17〉
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Jean-Luc Beuchat, Nicolas Brisebarre, Jérémie Detrey, Eiji Okamoto. Arithmetic Operators for Pairing-Based Cryptography. Pascal Paillier, Ingrid Verbauwhede. 9th Invernational Workshop on Cryptographic Hardware and Embedded Systems – CHES 2007, Sep 2007, Vienne, Austria. Springer, pp.239-255, 2007, LNCS 4727. 〈10.1007/978-3-540-74735-2_17〉. 〈ensl-00137918〉

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