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Prikl. Diskr. Mat. Suppl., 2019, Issue 12, Pages 75–77 (Mi pdma438)  

Discrete Functions

Class of Boolean functions constructed using significant bits of linear recurrences over the ring $\mathbb{Z}_{2^n}$

D. H. Hernández Piloto

LLC "Certification Research Center", Moscow

Abstract: In this paper, we study a class of functions built with the help of significant bits sequences on the ring $ \mathbb{Z}_{2 ^ n} $. This class is built with the use of a function $ \psi: \mathbb{Z}_{2 ^ n} \rightarrow \mathbb{Z}_2$. In public literature, there are results for a linear function $ \psi $. Here, we use a non-linear $ \psi $ function for this set. The period of a polynomial $F$ in the ring $ \mathbb{Z}_{2^n} $ is equal to $ T(F \bmod 2)2^{\alpha} $, where $ \alpha \in \{0,\ldots, n-1\} $. The polynomials for which $ T(F) = T(F \bmod 2) $, i.e. $ \alpha = 0 $, are called marked polynomials. For our class, we use a marked polynomial of the maximum period. We show the bounds of the given class: non-linearity, the weight of the functions, the Hamming distance between functions. The Hamming distance between these functions and functions of other known classes is also given.

Keywords: Boolean functions, linear recurrent sequences, significant bits sequences.

DOI: https://doi.org/10.17223/2226308X/12/23

Full text: PDF file (580 kB)
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UDC: 621.391:519.7

Citation: D. H. Hernández Piloto, “Class of Boolean functions constructed using significant bits of linear recurrences over the ring $\mathbb{Z}_{2^n}$”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 75–77

Citation in format AMSBIB
\Bibitem{Her19}
\by D.~H.~Hern\'andez Piloto
\paper Class of Boolean functions constructed using significant bits of linear recurrences over the ring $\mathbb{Z}_{2^n}$
\jour Prikl. Diskr. Mat. Suppl.
\yr 2019
\issue 12
\pages 75--77
\mathnet{http://mi.mathnet.ru/pdma438}
\crossref{https://doi.org/10.17223/2226308X/12/23}


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