## IACR paper details

Title | Algorithms and Arithmetic Operators for Computing the $\eta_T$ Pairing in Characteristic Three |
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Booktitle | IACR Eprint archive |
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Pages | |
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Year | 2007 |
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URL | http://eprint.iacr.org/2007/417 |
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Author | Jean-Luc Beuchat |
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Author | Nicolas Brisebarre |
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Author | Jérémie Detrey |
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Author | Eiji Okamoto |
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Author | Masaaki Shirase |
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Author | Tsuyoshi Takagi |
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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 discuss several algorithms to compute the $\eta_T$
pairing in characteristic three and suggest further improvements.
These algorithms involve addition, multiplication, cubing, inversion,
and sometimes cube root extraction over $\mathbb{F}_{3^m}$. We propose
a hardware accelerator based on a unified arithmetic operator able to
perform the operations required by a given algorithm. We describe the
implementation of a compact coprocessor for the field
$\mathbb{F}_{3^{97}}$ given by $\mathbb{F}_3[x]/(x^{97}+x^{12}+2)$,
which compares favorably with other solutions described in the open
literature. |
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Search for the paper

@misc{eprint-2007-13697,
title={Algorithms and Arithmetic Operators for Computing the $\eta_T$ Pairing in Characteristic Three},
booktitle={IACR Eprint archive},
keywords={implementation / $\eta_T$ pairing, finite field arithmetic, elliptic curve, hardware accelerator, FPGA},
url={http://eprint.iacr.org/2007/417},
note={ beuchat@risk.tsukuba.ac.jp 13818 received 1 Nov 2007},
author={Jean-Luc Beuchat and Nicolas Brisebarre and Jérémie Detrey and Eiji Okamoto and Masaaki Shirase and Tsuyoshi Takagi},
year=2007
}

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