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Fundam. Prikl. Mat., 2009, Volume 15, Issue 3, Pages 75–111 (Mi fpm1229)  

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

S. B. Gashkova, A. A. Bolotovb, A. A. Burtsevc, S. Yu. Zhebetd, A. B. Frolovd

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.

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English version:
Journal of Mathematical Sciences (New York), 2010, 168:1, 49–75

Bibliographic databases:

UDC: 515.1

Citation: 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., 15:3 (2009), 75–111; J. Math. Sci., 168:1 (2010), 49–75

Citation in format AMSBIB
\Bibitem{GasBolBur09}
\by S.~B.~Gashkov, A.~A.~Bolotov, A.~A.~Burtsev, S.~Yu.~Zhebet, A.~B.~Frolov
\paper On hardware and software implementation of arithmetic in finite fields of characteristic~7 for calculation of pairings
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 3
\pages 75--111
\mathnet{http://mi.mathnet.ru/fpm1229}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2744973}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 168
\issue 1
\pages 49--75
\crossref{https://doi.org/10.1007/s10958-010-9974-1}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954031226}


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  • Фундаментальная и прикладная математика
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