Prikladnaya Diskretnaya Matematika. Supplement
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Prikladnaya Diskretnaya Matematika. Supplement, 2022, Issue 15, Pages 34–40
DOI: https://doi.org/10.17223/2226308X/15/9
(Mi pdma574)
 

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

Discrete Functions

Correlation-immune functions with optimal algebraic immunity

I. S. Khilchuka, D. A. Zyubinaab, N. N. Tokarevaba

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (870 kB) Citations (1)
References:
Abstract: Boolean functions are the main components of symmetric ciphers, and their properties ensure the cipher's resistance to various types of cryptanalysis. An important problem is to combine several cryptographic properties in one function, since the properties may contradict each other. Also, an interesting way to build Boolean functions is an iterative construction, i.e., constructing functions in a larger number of variables based on functions in a smaller number while preserving cryptographic properties. In this paper, we intersect sets of functions with maximal algebraic immunity and functions with the maximal order of correlation immunity equal to one, of a small number of variables. There are no correlation-immune Boolean functions in 3 variables with maximal algebraic immunity. There are 392 functions in 4 variables with the maximal order of correlation immunity 1 and maximal algebraic immunity, and for the case of 5 variables there are 96 768 such functions. For functions in 4 variables, a classification is obtained based on their Hamming weight and the type of their geometric representation. The construction of functions in 6 variables has been studied on the basis of functions in 4 variables, in which each vertex of the Boolean cube $\mathbb{E}^{4}$ is replaced by a face of dimension 2 containing elements of the support of the 6-variable function only if the original vertex belonged to the support. It has been programmatically verified that this construction preserves the indices of algebraic and correlation immunity.
Keywords: Boolean functions, algebraic immunity, correlation immunity, Boolean cube.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0018
Document Type: Article
UDC: 519.7
Language: Russian
Citation: I. S. Khilchuk, D. A. Zyubina, N. N. Tokareva, “Correlation-immune functions with optimal algebraic immunity”, Prikl. Diskr. Mat. Suppl., 2022, no. 15, 34–40
Citation in format AMSBIB
\Bibitem{KhiZyuTok22}
\by I.~S.~Khilchuk, D.~A.~Zyubina, N.~N.~Tokareva
\paper Correlation-immune functions with optimal algebraic immunity
\jour Prikl. Diskr. Mat. Suppl.
\yr 2022
\issue 15
\pages 34--40
\mathnet{http://mi.mathnet.ru/pdma574}
\crossref{https://doi.org/10.17223/2226308X/15/9}
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  • https://www.mathnet.ru/eng/pdma/y2022/i15/p34
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Prikladnaya Diskretnaya Matematika. Supplement
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    Full-text PDF :59
    References:13
     
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