Bent Functions

Chapter 9

Algebraic Constructions of Bent Functions

Abstract

In this chapter, another type of construction of bent functions is considered. This type is called algebraic since bent functions are considered as functions from ${\mathbb{F}}_{2^n}$ to ${\mathbb{F}}_2$ and their constructions are given in trace form. First, we discuss several details of the algebraic approach to the construction of bent functions. Bent functions of the form f(c) = tr(ac^d) are called monomial bent functions. The number d is a bent exponent. Five known bent exponents proposed by Gold; Dillon; Kasami; ...