Bent functions: results and applications to cryptography Tokareva, Natalia

Table of Contents:

Chapter 1: Boolean Functions

Chapter 2: Bent Functions: An Introduction

Chapter 3: History of Bent Functions

Chapter 4: Applications of Bent Functions

Chapter 5: Properties of Bent Functions

Chapter 6: Equivalent Representations of Bent Functions

Chapter 7: Bent Functions with a Small Number of Variables

Chapter 8: Combinatorial Constructions of Bent Functions

Chapter 9: Algebraic Constructions of Bent Functions

Chapter 10: Bent Functions and Other Cryptographic Properties

Chapter 11: Distances Between Bent Functions

Chapter 12: Automorphisms of the Set of Bent Functions

Chapter 13: Bounds on the Number of Bent Functions

Chapter 14: Bent Decomposition Problem

Chapter 15: Algebraic Generalizations of Bent Functions

Chapter 16: Combinatorial Generalizations of Bent Functions

Chapter 17: Cryptographic Generalizations of Bent Functions

References
Index

Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography, the text provides a detailed survey of their main results, presenting a systematic overview of their generalizations and applications, and considering open problems in classification and systematization of bent functions.

The text is appropriate for novices and advanced researchers, discussing proofs of several results, including the automorphism group of bent functions, the lower bound for the number of bent functions, and more.

(http://store.elsevier.com/Bent-Functions/Natalia-Tokareva/isbn-9780128023181/)