Title :
Algorithms and Arithmetic Operators for Computing the ηT Pairing in Characteristic Three
Author :
Beuchat, Jean-Luc ; Brisebarre, Nicolas ; Detrey, Je Remie ; Okamoto, Eiji ; Shirase, Masaaki ; Takagi, Tsuyoshi
Author_Institution :
Grad. Sch. of Syst. & Inf. Eng., Univ. of Tsukuba, Tsukuba
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.
Keywords :
coprocessors; mathematical operators; arithmetic operators; characteristic three; compact coprocessor; constructive cryptographic application; etaT pairing; hardware accelerator; hyperelliptic curves; unified arithmetic operator; Application software; Arithmetic; Computer architecture; Coprocessors; Cryptographic protocols; Elliptic curve cryptography; Elliptic curves; Hardware; Heart; Information security; Public key cryptography; Security; Eta_T pairing; FPGA; elliptic curve; finite field arithmetic; hardware accelerator;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.2008.103