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Title:
A Coprocessor for the Final Exponentiation of the \eta_T Pairing in Characteristic Three
Authors: Jean-Luc Beuchat, Nicolas Brisebarre, Masaaki Shirase, Tsuyoshi Takagi, Eiji Okamoto
Abstract:Since the introduction of pairings over (hyper)elliptic curves in constructive cryptographic applications, an ever increasing number of protocols based on pairings have appeared in the literature. Software implementations being rather slow, the study of hardware architectures became an active research area. Beuchat et al. proposed for instance a coprocessor which computes the characteristic three \eta_T pairing, from which the Tate pairing can easily be derived, in 33,$\mu$s on a Cyclone II FPGA. However, a final exponentiation is required to ensure a unique output value and the authors proposed to supplement their \eta_T pairing accelerator with a coprocessor for exponentiation. Thus, the challenge consists in designing the smallest possible piece of hardware able to perform this task in less than 33,$\mu$s on a Cyclone~II device. In this paper, we propose a novel arithmetic operator implementing addition, cubing, and multiplication over \mathbb{F}_{3^{97}} and show that a coprocessor based on a single such operator meets this timing constraint.
ePrint: https://eprint.iacr.org/2007/045
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