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Diskr. Mat., 2006, Volume 18, Issue 4, Pages 56–72 (Mi dm80)  

This article is cited in 9 scientific papers (total in 9 papers)

An application of the method of additive chains to inversion in finite fields

S. B. Gashkov, I. S. Sergeev


Abstract: We obtain estimates of complexity and depth of Boolean inverter circuits in normal and polynomial bases of finite fields. In particular, we show that it is possible to construct a Boolean inverter circuit in the normal basis of the field $\mathit{GF}(2^n)$ whose complexity is at most $(\lambda(n-1)+(1+o(1))\lambda(n)/\lambda(\lambda(n)))M(n)$ and the depth is at most $(\lambda(n-1)+2)D(n)$, where $M(n)$, $D(n)$ are the complexity and the depth, respectively, of the circuits for multiplication in this basis and $\lambda(n)=\lfloor\log_2n\rfloor$.

DOI: https://doi.org/10.4213/dm80

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English version:
Discrete Mathematics and Applications, 2006, 16:6, 601–618

Bibliographic databases:

UDC: 519.7
Received: 20.03.2006

Citation: S. B. Gashkov, I. S. Sergeev, “An application of the method of additive chains to inversion in finite fields”, Diskr. Mat., 18:4 (2006), 56–72; Discrete Math. Appl., 16:6 (2006), 601–618

Citation in format AMSBIB
\Bibitem{GasSer06}
\by S.~B.~Gashkov, I.~S.~Sergeev
\paper An application of the method of additive chains to inversion in finite fields
\jour Diskr. Mat.
\yr 2006
\vol 18
\issue 4
\pages 56--72
\mathnet{http://mi.mathnet.ru/dm80}
\crossref{https://doi.org/10.4213/dm80}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2310092}
\zmath{https://zbmath.org/?q=an:1140.11061}
\elib{https://elibrary.ru/item.asp?id=9450348}
\transl
\jour Discrete Math. Appl.
\yr 2006
\vol 16
\issue 6
\pages 601--618
\crossref{https://doi.org/10.1515/156939206779217952}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846856759}


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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, “On design of circuits of logarithmic depth for inversion in finite fields”, Discrete Math. Appl., 18:5 (2008), 483–504  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. Gashkov S.B., Sergeev I.S., “The complexity and depth of Boolean circuits for multiplication and inversion in some fields $\mathrm{GF}(2^n)$”, Moscow Univ. Math. Bull., 64:4 (2009), 139–143  crossref  mathscinet  zmath  elib  scopus
    3. S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685  mathnet  crossref
    4. S. B. Gashkov, I. S. Sergeev, “A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials”, Sb. Math., 203:10 (2012), 1411–1447  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. S. B. Gashkov, I. S. Sergeev, “On complexity and depth of Boolean circuits for multiplication and inversion over finite fields of characteristic 2”, Discrete Math. Appl., 23:1 (2013), 1–37  mathnet  crossref  crossref  mathscinet  elib  elib
    6. V. V. Kochergin, D. V. Kochergin, “Utochnenie nizhnei otsenki slozhnosti vozvedeniya v stepen”, PDM, 2017, no. 38, 119–132  mathnet  crossref
    7. I. S. Sergeev, “Rectifier circuits of bounded depth”, J. Appl. Industr. Math., 12:1 (2018), 153–166  mathnet  crossref  crossref  elib
    8. S. B. Gashkov, I. B. Gashkov, “Fast algorithm of square rooting in some odd characteistic finite field”, Moscow University Mathematics Bulletin, Moscow University Mchanics Bulletin, 73:5 (2018), 176–181  mathnet  crossref  mathscinet  zmath  isi
    9. S. B. Gashkov, “Bystrye algoritmy resheniya uravnenii stepeni ne vyshe chetvertoi v nekotorykh konechnykh polyakh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2021, no. 3, 22–31  mathnet
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