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Mat. Vopr. Kriptogr., 2013, Volume 4, Issue 1, Pages 59–76 (Mi mvk73)  

This article is cited in 4 scientific papers (total in 4 papers)

Analysis of the spectrum of random symmetric Boolean functions

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: General probabilistic model of a random symmetric Boolean function of $n$ variables is proposed. The characteristic function of the Walsh spectrum of a random symmetric Boolean function is defined; exact and asymptotic distributions of some spectrum characteristics as $n\to\infty$ are obtained in the case of the parametric measure. The basic properties of the Krawtchouk's polynomials (which are used in proofs) are reviewed.

Key words: symmetric Boolean function, Walsh transform, spectrum of function, characteristic function, parametric measure, Krawtchouk's polynomials, Krawtchouk matrix, spectrum characteristics, limit theorems.

DOI: https://doi.org/10.4213/mvk73

Full text: PDF file (333 kB)
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Document Type: Article
UDC: 519.212.2
Received 20.IV.2012

Citation: G. I. Ivchenko, Yu. I. Medvedev, V. A. Mironova, “Analysis of the spectrum of random symmetric Boolean functions”, Mat. Vopr. Kriptogr., 4:1 (2013), 59–76

Citation in format AMSBIB
\Bibitem{IvcMedMir13}
\by G.~I.~Ivchenko, Yu.~I.~Medvedev, V.~A.~Mironova
\paper Analysis of the spectrum of random symmetric Boolean functions
\jour Mat. Vopr. Kriptogr.
\yr 2013
\vol 4
\issue 1
\pages 59--76
\mathnet{http://mi.mathnet.ru/mvk73}
\crossref{https://doi.org/10.4213/mvk73}


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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. G. I. Ivchenko, Yu. I. Medvedev, V. A. Mironova, “Simmetricheskie bulevy funktsii i ikh metricheskie svoistva”, Matem. vopr. kriptogr., 4:4 (2013), 49–63  mathnet  crossref
    2. A. M. Zubkov, “Momenty vesov sluchainykh neravnoveroyatnykh bulevykh funktsii”, Matem. vopr. kriptogr., 5:3 (2014), 5–15  mathnet  crossref
    3. G. I. Ivchenko, Yu. I. Medvedev, V. A. Mironova, “Mnogochleny Kravchuka i ikh primeneniya v zadachakh kriptografii i teorii kodirovaniya”, Matem. vopr. kriptogr., 6:1 (2015), 33–56  mathnet  crossref  mathscinet  elib
    4. O. V. Denisov, “Ob algoritme poiska suschestvennykh argumentov sluchainykh bulevykh funktsii”, Matem. vopr. kriptogr., 6:3 (2015), 19–32  mathnet  crossref  mathscinet  elib
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