Algorithms and Arithmetic Operators for Computing the ηT Pairing in Characteristic Three

Authors:
Jean-Luc Beuchat;Nicolas Brisebarre;Jérémie Detrey;Eiji Okamoto;Masaaki Shirase;Tsuyoshi Takagi
Affiliations:
University of Tsukuba, Tsukuba;ENS Lyon, Lyon;B-it, Bonn;University of Tsukuba, Tsukuba;Future University, Hakodate;Future University, Hakodate
Venue:
IEEE Transactions on Computers
Year:
2008

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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 ηT pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over GF(3m). 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 GF(397) given by GF(3)[x]/(x97+x12+2), which compares favorably with other solutions described in the open literature.