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.

Location: http://mech.math.msu.su/~fpm/eng/k09/k093/k09307h.htm

Last modified: January 13, 2010