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Bent Functions


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Table 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.


“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)

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