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Mat. Vopr. Kriptogr., 2015, Volume 6, Issue 1, Pages 33–56 (Mi mvk150)  

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

Krawtchouk polynomials and their applications in cryptography and coding theory

G. I. Ivchenkoa, Yu. I. Medvedevb, V. A. Mironovaa

a NRU Higher School of Economics, Moscow
b Academy of Cryptography of the Russian Federation, Moscow

Abstract: Basic properties of the Krawtchouk polynomials are reviewed, some new results which are of interest for the theory and applications are obtained. We study analytic, number-theoretic properties and asymptotic behaviour of the Krawtchouk polynomials under different relations between their parameters along with the probabilistic properties of polynomials with random parameters. Applications of the Krawtchouk polynomials to the cryptographic properties of Boolean functions and coding theory are discussed.

Key words: Krawtchouk polynomials, random Krawtchouk polynomials, Boolean functions, Hamming codes, asymptotic formulas.

DOI: https://doi.org/10.4213/mvk150

Full text: PDF file (562 kB)
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Bibliographic databases:

UDC: 519.212.2+519.114
Received 20.IV.2012

Citation: G. I. Ivchenko, Yu. I. Medvedev, V. A. Mironova, “Krawtchouk polynomials and their applications in cryptography and coding theory”, Mat. Vopr. Kriptogr., 6:1 (2015), 33–56

Citation in format AMSBIB
\Bibitem{IvcMedMir15}
\by G.~I.~Ivchenko, Yu.~I.~Medvedev, V.~A.~Mironova
\paper Krawtchouk polynomials and their applications in cryptography and coding theory
\jour Mat. Vopr. Kriptogr.
\yr 2015
\vol 6
\issue 1
\pages 33--56
\mathnet{http://mi.mathnet.ru/mvk150}
\crossref{https://doi.org/10.4213/mvk150}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3528058}
\elib{http://elibrary.ru/item.asp?id=23211523}


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  • http://mi.mathnet.ru/eng/mvk150
  • https://doi.org/10.4213/mvk150
  • http://mi.mathnet.ru/eng/mvk/v6/i1/p33

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. R. Minabutdinov, “A higher-order asymptotic expansion of the Krawtchouk polynomials”, J. Math. Sci. (N. Y.), 215:6 (2016), 738–747  mathnet  crossref  mathscinet
  • Математические вопросы криптографии
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