Algorithms and arithmetic operators for computing the $\eta_T$ pairing in characteristic three - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Transactions on Computers Year : 2008

Algorithms and arithmetic operators for computing the $\eta_T$ pairing in characteristic three

Jérémie Detrey
Masaaki Shirase
  • Function : Author
  • PersonId : 987927
Tsuyoshi Takagi
  • Function : Author
  • PersonId : 987928

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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Dates and versions

inria-00423993 , version 1 (13-10-2009)

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Jean-Luc Beuchat, Nicolas Brisebarre, Jérémie Detrey, Eiji Okamoto, Masaaki Shirase, et al.. Algorithms and arithmetic operators for computing the $\eta_T$ pairing in characteristic three. IEEE Transactions on Computers, 2008, Special Section on Special-Purpose Hardware for Cryptography and Cryptanalysis, 57 (11), pp.1454-1468. ⟨10.1109/TC.2008.103⟩. ⟨inria-00423993⟩
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