Bent Functions

Chapter 14

Bent Decomposition Problem

Abstract

The following problem is considered in this chapter: Is it true that an arbitrary Boolean function in n variables (n is even, $n\ge 2$) of degree not more than n/2 can be represented as the sum of two bent functions in n variables? This question was raised in 2011 in close connection with the problem of the asymptotic value of the number of all bent functions in n variables. There is a hypothesis that the answer is “yes.” For now all known facts confirm the hypothesis. The hypothesis was checked for n = 2,4,6 and for some special classes of Boolean functions. Some weakened variants of it are also proven. ...