Overview
- Provides a detailed survey of leading results in bent functions
- Presents a systematic overview of their generalizations and applications
- Considers open problems in classification and systematization of bent functions
- Discusses proofs of several results and reflects on recent developments and trends in the field
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About this book
This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results. This book uniquely provides a necessary comprehensive coverage of bent functions.
It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.
It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.
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Keywords
- Bent functions
- Boolean functions
- Vectorial functions
- S-boxes
- Non-linearity
- Walsh-Hadamard transform
- Symmetric cryptography
- Coding theory
- Combinatorics
- Plateaued functions
- Hyper-bent functions
- Semi-bent functions
- Near-bent functions
- Generalized bent functions
- Difference Sets
- Finite fields
- Exponential sums
- Kloosterman sums
- Dillon exponents
- Niho exponents
Table of contents (18 chapters)
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Front Matter
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Back Matter
Reviews
“This book is a very significant contribution to the theory of bent functions and will be useful to advanced students and researchers interested in cryptographic Boolean functions.” (Sugata Gangopadhyay, Mathematical Reviews, October, 2017)
“This book is a comprehensive and very detailed collection of results on bent functions obtained in the decades after their introduction. … The book is addressed to researchers in discrete mathematics and their applications in cryptography or coding theory. It can serve as a comprehensive reference book on topics on (Boolean) bent functions. Furthermore it is interesting for theoretical computer scientists or engineers.” (Wilfried Meidl, zbMATH 1364.94008, 2017)
“This book is a comprehensive and very detailed collection of results on bent functions obtained in the decades after their introduction. … The book is addressed to researchers in discrete mathematics and their applications in cryptography or coding theory. It can serve as a comprehensive reference book on topics on (Boolean) bent functions. Furthermore it is interesting for theoretical computer scientists or engineers.” (Wilfried Meidl, zbMATH 1364.94008, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Bent Functions
Book Subtitle: Fundamentals and Results
Authors: Sihem Mesnager
DOI: https://doi.org/10.1007/978-3-319-32595-8
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-32593-4Published: 18 August 2016
Softcover ISBN: 978-3-319-81322-6Published: 11 June 2018
eBook ISBN: 978-3-319-32595-8Published: 09 August 2016
Edition Number: 1
Number of Pages: XXVI, 544
Number of Illustrations: 5 b/w illustrations, 6 illustrations in colour
Topics: Coding and Information Theory, Combinatorics, Difference and Functional Equations