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Paper: Algorithms and Arithmetic Operators for Computing the $\eta_T$ Pairing in Characteristic Three

Authors:
Jean-Luc Beuchat
Nicolas Brisebarre
Jérémie Detrey
Eiji Okamoto
Masaaki Shirase
Tsuyoshi Takagi
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URL: http://eprint.iacr.org/2007/417
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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.
BibTeX
@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
}