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 η 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.
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References
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Beuchat, JL., Brisebarre, N., Detrey, J., Okamoto, E. (2007). Arithmetic Operators for Pairing-Based Cryptography. In: Paillier, P., Verbauwhede, I. (eds) Cryptographic Hardware and Embedded Systems - CHES 2007. CHES 2007. Lecture Notes in Computer Science, vol 4727. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74735-2_17
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DOI: https://doi.org/10.1007/978-3-540-74735-2_17
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