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Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography], 2013, Volume 4, Issue 1, Pages 59–76
DOI: https://doi.org/10.4213/mvk73 (Mi mvk73) 		 
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (333 kB) Citations (5)
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DOI: https://doi.org/10.4213/mvk73
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.
Received 20.IV.2012
Document Type: Article
UDC: 519.212.2
Language: Russian
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические вопросы криптографии
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