Discrete Functions

Properties of classes of Boolean functions constructed from several linear recurrences over the ring of integers modulo $2^n$

A. D. Bugrov

Moscow

Abstract: A class of Boolean functions constructed from high-coordinate sequences of linear recurrences over the ring $\mathbb{Z}_{2^n}$ is defined. Various coordinate sets are used to isolate the coordinate sequences. It is shown that this class consists of functions that are significantly removed from the class of all affine functions.

Keywords: linear recurrent sequences, coordinate sequences, Boolean functions, non-linearity of Boolean functions.

UDC: 511.32

DOI: 10.17223/2226308X/16/3