Bent Functions: Results And Applications To Cryptography

Paperback | August 6, 2015

byNatalia TokarevaEditorNatalia Tokareva

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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. Provides a detailed survey of bent functions and their main results, presenting a systematic overview of their generalizations and applications Presents a systematic and detailed survey of hundreds of results in the area of highly nonlinear Boolean functions in cryptography Appropriate coverage for students from advanced specialists in cryptography, mathematics, and creators of ciphers

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From the Publisher

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 prov...

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 monograp...
Format:PaperbackDimensions:220 pages, 8.75 × 6.35 × 0.68 inPublished:August 6, 2015Publisher:Academic PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:012802318X

ISBN - 13:9780128023181

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Extra Content

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