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 Diskretn. Anal. Issled. Oper., 2021, Volume 28, Issue 2, Pages 74–91 (Mi da1278)

On degree of nonlinearity of the coordinate polynomials for a product of transformations of a binary vector space

V. M. Fomichevabc

a Financial University under the Government of the Russian Federation, 49 Leningradskii Avenue, 125993 Moscow, Russia
b Security Code LLC, 10 Bld. 1 Pervyi Nagatinskii Driveway, 115230 Moscow, Russia
c Institute of Informatics Problems of FRC CSC RAS, 44 Bld. 2 Vavilov Street, 119333 Moscow, Russia

Abstract: We construct a nonnegative integer matrix to evaluate the matrix of nonlinearity characteristics for the coordinate polynomials of a product of transformations of a binary vector space. The matrix of the characteristics of the transformation is defined by the degrees of nonlinearity of the derivatives of all coordinate functions with respect to each input variable. The entries of the evaluation matrix are expressed in terms of the characteristics of the coordinate polynomials of the multiplied transformations. Calculation of the evaluation matrix is easier than calculating the exact values of the characteristics. The estimation method is extended to an arbitrary number of multiplied transformations. Computational examples are given that in particular show the accuracy of the obtained estimates and the domain of their nontriviality. Tab. 1, bibliogr. 18.

Keywords: coordinate polynomial of transformation, maximal monomial of a polynomial, degree of a polynomial.

DOI: https://doi.org/10.33048/daio.2021.28.700

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English version:
Journal of Applied and Industrial Mathematics, 2021, 15:2, 212–222

UDC: 519.17
Revised: 15.02.2021
Accepted:19.02.2021

Citation: V. M. Fomichev, “On degree of nonlinearity of the coordinate polynomials for a product of transformations of a binary vector space”, Diskretn. Anal. Issled. Oper., 28:2 (2021), 74–91; J. Appl. Industr. Math., 15:2 (2021), 212–222

Citation in format AMSBIB
\Bibitem{Fom21} \by V.~M.~Fomichev \paper On~degree of~nonlinearity of~the~coordinate polynomials for~a~product of transformations of~a~binary vector space \jour Diskretn. Anal. Issled. Oper. \yr 2021 \vol 28 \issue 2 \pages 74--91 \mathnet{http://mi.mathnet.ru/da1278} \crossref{https://doi.org/10.33048/daio.2021.28.700} \transl \jour J. Appl. Industr. Math. \yr 2021 \vol 15 \issue 2 \pages 212--222 \crossref{https://doi.org/10.1134/S1990478921020034} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85116200845}