Bent Functions

Table of Contents

Cover image

Title page

Copyright

Foreword

Preface

Notation

Notation

Chapter 1: Boolean Functions

Abstract

Introduction

1.1 Definitions

1.2 Algebraic Normal Form

1.3 Boolean Cube and Hamming Distance

1.4 Extended Affinely Equivalent Functions

1.5 Walsh-Hadamard Transform

1.6 Finite Field and Boolean Functions

1.7 Trace Function

1.8 Polynomial Representation of a Boolean Function

1.9 Trace Representation of a Boolean Function

1.10 Monomial Boolean Functions

Chapter 2: Bent Functions: An Introduction

Abstract

Introduction

2.1 Definition of a Nonlinearity

2.2 Nonlinearity of a Random Boolean Function

2.3 Definition of a Bent Function

2.4 If n Is Odd?

2.5 Open Problems

2.6 Surveys

Chapter 3: History of Bent Functions

Abstract