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

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.
Type de document :
Article dans une revue
IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2008, Special Section on Special-Purpose Hardware for Cryptography and Cryptanalysis, 57 (11), pp.1454-1468. 〈10.1109/TC.2008.103〉
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Littérature citée [42 références]

https://hal.inria.fr/inria-00423993
Contributeur : Jérémie Detrey <>
Soumis le : mardi 13 octobre 2009 - 16:18:16
Dernière modification le : mardi 24 avril 2018 - 13:52:39
Document(s) archivé(s) le : mardi 16 octobre 2012 - 12:11:12

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pairing_appendix.pdf
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### Citation

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, Institute of Electrical and Electronics Engineers, 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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