Bent Functions

Fundamentals and Results

Sihem Mesnager (Autor)

Buch | Softcover

XXVI, 544 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-81322-6 (ISBN)

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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.

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)

Erscheinungsdatum	05.03.2022
Zusatzinfo	XXVI, 544 p. 11 illus., 6 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	866 g
Themenwelt	Informatik ► Theorie / Studium ► Kryptologie
Schlagworte	bent functions • Boolean functions • coding theory • combinatorics • Difference Sets • Dillon exponents • Exponential sums • Finite Fields • Generalized bent functions • Hyper-bent functions • Kloosterman sums • Near-bent functions • Niho exponents • non-linearity • Plateaued functions • s-boxes • Semi-bent functions • symmetric cryptography • Vectorial functions • Walsh-Hadamard transform
ISBN-10	3-319-81322-6 / 3319813226
ISBN-13	978-3-319-81322-6 / 9783319813226
Zustand	Neuware