Cryptology ePrint Archive: Report 2007/045
A Coprocessor for the Final Exponentiation of the $\eta_T$ Pairing in Characteristic Three
Jean-Luc Beuchat and Nicolas Brisebarre and Masaaki Shirase and Tsuyoshi Takagi and 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.
Category / Keywords: implementation / $\eta_T$ pairing, characteristic three, hardware accelerator, FPGA
Date: received 13 Feb 2007
Contact author: beuchat at risk tsukuba ac jp
Available format(s): PDF | BibTeX Citation
Version: 20070214:110206 (All versions of this report)
Short URL: ia.cr/2007/045
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