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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.
List of contents
Generalities on Boolean functions and p-ary functions.- Mathematical Foundations.- Boolean Functions and Cryptography.- Bent Functions-Generalities.- Bent Functions: Primary Constructions (Part I).- Bent Functions: Secondary Constructions.- Bent Functions: Primary Constructions (Part II).- Class H, Niho Bent Functions and O-Polynomials.- Subclasses of Bent Functions: Hyper-Bent Functions.- Hyper-Bent Functions: Primary Constructions with Multiple Trace Terms.- (Hyper)-Bent Functions, Exponential Sums and (Hyper-)elliptic Curves.- Bent Vectorial Functions.- Bent Functions in Arbitrary Characteristic.- Bent Functions and (Partial-)spreads.- Various Cryptographic and Algebraic Generalizations of Bent Functions.- Plateaued Functions: Generalities and Characterizations.- Plateaued Boolean Functions: Constructions of Semi-Bent Functions.- Linear Codes from Bent, Semi-Bent, and Almost Bent Functions.
Summary
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.
Additional text
“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)
Report
"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)
