Bent Functions

Bent Functions : Results and Applications to Cryptography

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Description

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.
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Product details

  • Paperback | 220 pages
  • 152 x 229 x 11.94mm | 360g
  • Academic Press Inc
  • San Diego, United States
  • English
  • black & white illustrations
  • 012802318X
  • 9780128023181
  • 1,537,684

Table of contents

Preface
Notation
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
Bibliography
Index
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Review quote

"...will definitely motivate researchers to work on bent functions and in general on cryptographic Boolean functions...it compiles together results published both in Russian and in English. This book will be a cornerstone of research activity on bent functions." --Mathematical Reviews, Bent Functions
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About Natalia Tokareva

Dr. Natalia Tokareva is a senior researcher at the Laboratory of Discrete Analysis in the Sobolev Institute of Mathematics and she teaches courses in cryptology in the Department of Mathematics and Mechanics at Novosibirsk State University. She has studied bent functions and their applications for several years, publishing one monograph (in Russian) and more than 12 articles. She has been a participant of many international conferences and seminars and presentations in the area of bent functions, particularly with applications in cryptography. Her research interests include Boolean functions in cryptography, bent functions, block and stream ciphers, cryptanalysis, coding theory, combinatorics, and algebra. She is chief of the seminar "Cryptography and Cryptanalysis" at the Sobolev Institute of Mathematics and she supervises BS, MS, and PhD students in discrete mathematics and cryptology.
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