FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 3, PAGES 75-111

On hardware and software implementation of arithmetic in finite fields of characteristic 7 for calculation of pairings

S. B. Gashkov
A. A. Bolotov
A. A. Burtsev
S. Yu. Zhebet
A. B. Frolov

Abstract

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We study scheme (hardware) and program (software) methods of multiplication of polynomials over fields of characteristic 7 in order to apply them to parings based cryptographic protocols on hyperelliptic curves of genus three. We consider hardware and software implementations of arithmetic in GF(7), GF(72), GF(7n), GF(77n), and GF(714n) and estimate the complexity of corresponding schemes and programs.

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