Chapter 2

Bent Functions

An Introduction

Abstract

In this chapter, three definitions of a bent function are given: via nonlinearity, by using Walsh-Hadamard coefficients, and in terms of derivatives. Nonlinearity of a random Boolean function is discussed. Several open problems in bent functions are included. In the last section, we list surveys on bent functions in separate articles and in chapters in books on discrete mathematics and cryptography.

Keywords

Nonlinearity

A random Boolean function

Bent function

Maximal nonlinear function

Minimal function

Derivative

Introduction

In this chapter, three definitions of a bent function are given: via nonlinearity, by using Walsh-Hadamard coefficients, and in terms of derivatives. Nonlinearity of ...