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Diskr. Mat., 2008, Volume 20, Issue 4, Pages 8–28 (Mi dm1023)  

This article is cited in 1 scientific paper (total in 1 paper)

On design of circuits of logarithmic depth for inversion in finite fields

S. B. Gashkov, I. S. Sergeev


Abstract: We suggest a method of realisation of inversion over the standard bases of finite fields $GF(p^n)$ by means of circuits over $GF(p)$ of complexity $O(\varepsilon^{-1}n^{w+\varepsilon})$ and depth $O(\varepsilon^{-1}\log n)$, where $\varepsilon>0$, and $w<1.667$ is the exponent of multiplication of $\sqrt n\times\sqrt n$ and $\sqrt n\times n$ matrices. Inversion over Gaussian normal bases is realised by a circuit of complexity $O(\varepsilon^{-b}n^{1+c\varepsilon|\log\varepsilon|})$ and depth $O(\varepsilon^{-1}\log n)$, where $b,c$ are constants.

DOI: https://doi.org/10.4213/dm1023

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English version:
Discrete Mathematics and Applications, 2008, 18:5, 483–504

Bibliographic databases:

UDC: 519.7
Received: 29.01.2007

Citation: S. B. Gashkov, I. S. Sergeev, “On design of circuits of logarithmic depth for inversion in finite fields”, Diskr. Mat., 20:4 (2008), 8–28; Discrete Math. Appl., 18:5 (2008), 483–504

Citation in format AMSBIB
\Bibitem{GasSer08}
\by S.~B.~Gashkov, I.~S.~Sergeev
\paper On design of circuits of logarithmic depth for inversion in finite fields
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 4
\pages 8--28
\mathnet{http://mi.mathnet.ru/dm1023}
\crossref{https://doi.org/10.4213/dm1023}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500601}
\zmath{https://zbmath.org/?q=an:05618996}
\elib{http://elibrary.ru/item.asp?id=20730263}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 5
\pages 483--504
\crossref{https://doi.org/10.1515/DMA.2008.035}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57649143447}


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  • https://doi.org/10.4213/dm1023
  • http://mi.mathnet.ru/eng/dm/v20/i4/p8

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685  mathnet  crossref
  • Дискретная математика
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