Abstract:
The measure of closeness of vectorial functions is defined by the Hamming distance in the space of their values, and the nonlinearity of a vector function is defined as the Hamming distance to the set of affine mappings. Bounds and estimates for the distribution of nonlinearity of balanced mappings and substitutions are obtained. Classes of vector functions with high nonlinearity are constructed. The nonlinearity introduced in this way is compared with the nonlinearity defined as the minimal nonlinearity over all nontrivial linear combinations of coordinate functions.
Citation:
V. G. Ryabov, “On the question on the approximation of vectorial functions over finite fields by affine analogues”, Mat. Vopr. Kriptogr., 13:4 (2022), 125–146
\Bibitem{Rya22}
\by V.~G.~Ryabov
\paper On the question on the approximation of vectorial functions over finite fields by affine analogues
\jour Mat. Vopr. Kriptogr.
\yr 2022
\vol 13
\issue 4
\pages 125--146
\mathnet{http://mi.mathnet.ru/mvk426}
\crossref{https://doi.org/10.4213/mvk426}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4529121}
Linking options:
https://www.mathnet.ru/eng/mvk426
https://doi.org/10.4213/mvk426
https://www.mathnet.ru/eng/mvk/v13/i4/p125
This publication is cited in the following 3 articles:
V. G. Ryabov, “Nelineinost vektornykh funktsii nad konechnymi polyami”, Diskret. matem., 36:2 (2024), 50–70
V. G. Ryabov, “Udalennost vektornykh bulevykh funktsii ot affinnykh analogov (po sledam Vosmoi mezhdunarodnoi olimpiady po kriptografii)”, Matem. vopr. kriptogr., 15:1 (2024), 127–142
V. G. Ryabov, “Novye granitsy nelineinosti PN-funktsii i APN-funktsii nad konechnymi polyami”, Diskret. matem., 35:3 (2023), 45–59
Citation in format AMSBIB
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