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Prikladnaya Diskretnaya Matematika. Supplement, 2017, Issue 10, Pages 33–34
DOI: https://doi.org/10.17223/2226308X/10/12
(Mi pdma313)
 

Discrete Functions

On connection between affine splitting of a Boolean function and its algebraic, combinatorial and cryptographic properties

A. A. Babueva

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Moscow
References:
Abstract: In this paper, the following results are obtained: 1) for an affine splitting of a Boolean function – an upper bound of algebraic degree; 2) for a dual bent function – some sufficient conditions to be affine splitting, and 3) for any Boolean function with a non-trivial subspace of the linear structures – an upper bound of nonlinearity. Besides, the following assertions are proved: 1) affine splitting is an invariant of complete affine group; 2) if a bent function is normal or weakly normal, then its dual function is normal or weakly normal respectively; 3) the coefficients of the incomplete Walsh–Hadamard transformation of a bent function and of its dual function are the same for zero values of variables; 4) a relation connecting the squares of the Walsh–Hadamard coefficients of a function over cosets of a subspace with the squares of the coefficients of the incomplete Walsh–Hadamard transformation of this function.
Keywords: Boolean functions, bent functions, affine splitting.
Document Type: Article
UDC: 519.7
Language: Russian
Citation: A. A. Babueva, “On connection between affine splitting of a Boolean function and its algebraic, combinatorial and cryptographic properties”, Prikl. Diskr. Mat. Suppl., 2017, no. 10, 33–34
Citation in format AMSBIB
\Bibitem{Bab17}
\by A.~A.~Babueva
\paper On connection between affine splitting of a~Boolean function and its algebraic, combinatorial and cryptographic properties
\jour Prikl. Diskr. Mat. Suppl.
\yr 2017
\issue 10
\pages 33--34
\mathnet{http://mi.mathnet.ru/pdma313}
\crossref{https://doi.org/10.17223/2226308X/10/12}
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