Bent Functions

Chapter 5

Properties of Bent Functions

Abstract

Some basic properties of bent functions are discussed in this chapter. The first one is a restriction on the degree of a bent function: if f is bent in n variables, then $2\le \mathrm{deg}(f)\le n/2$. The second one is that a Boolean function extended affinely equivalent to a bent function is bent too. Dual bent functions are defined; relations between degrees and algebraic normal form coefficients of bent functions and their dual functions are presented. It is mentioned that a bent function is a nondegenerate function.

Keywords

Degree

Affine equivalence

Affinely equivalent functions

Dual bent function

Self-dual ...