Discrete Functions

On decomposition of bent functions in $8$ variables into the sum of two bent functions

A. S. Shaporenko<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: A Boolean function in an even number of variables is called bent if it has maximal nonlinearity. We study the well-known hypothesis about the representation of arbitrary Boolean functions in $n$ variables of degree at most $n/2$ as the sum of two bent functions. We prove that bent functions in $8$ variables of degree at most $3$ can be represented as the sum of two bent functions in $8$ variables. It was shown that all quadratic Boolean functions in an even number of variables $n\geqslant 4$ can be represented as the sum of two bent functions of a special form.

Keywords: Boolean functions, bent functions, decomposition into sum of bent functions.

UDC: 519.7

DOI: 10.17223/2226308X/15/10