S. B. Gashkov, A. A. Bolotov, A. A. Burtsev, S. Yu. Zhebet, A. B. Frolov, “On hardware and software implementation of arithmetic in finite fields of characteristic 7 for calculation of pairings”, Fundam. Prikl. Mat., 2009, Volume 15, Issue 3,Pages <nobr>75

This article is cited in 1 paper

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

S. B. Gashkov^a, A. A. Bolotov^b, A. A. Burtsev^c, S. Yu. Zhebet^d, A. B. Frolov^d

^a M. V. Lomonosov Moscow State University
^b "L-S-I Logic", Co., USA
^c Moscow Institute of Physics and Technology
^d Moscow Power Engineering Institute (Technical University)

Abstract: 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 $GF(7)$, $GF(7^2)$, $GF(7^n)$, $GF(7^{7n})$, and $GF(7^{14n})$ and estimate the complexity of corresponding schemes and programs.

UDC: 515.1