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Issue No. 11 - November (2008 vol. 57)
ISSN: 0018-9340
pp: 1454-1468
Nicolas Brisebarre , ENS Lyon, Lyon
Eiji Okamoto , University of Tsukuba, Tsukuba
Masaaki Shirase , Future University, Hakodate
Jérémie Detrey , B-it, Bonn
Jean-Luc Beuchat , University of Tsukuba, Tsukuba
Tsuyoshi Takagi , Future University, Hakodate
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.
INDEX TERMS
Eta_T pairing, elliptic curve, finite field arithmetic, hardware accelerator, FPGA
CITATION
Nicolas Brisebarre, Eiji Okamoto, Masaaki Shirase, Jérémie Detrey, Jean-Luc Beuchat, Tsuyoshi Takagi, "Algorithms and Arithmetic Operators for Computing the ηT Pairing in Characteristic Three", IEEE Transactions on Computers, vol. 57, no. , pp. 1454-1468, November 2008, doi:10.1109/TC.2008.103
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