Bent Functions

Fundamentals and Results
Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-3-319-81322-6
Verlag: Springer International Publishing

Buch, Englisch, 544 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 855 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Mesnager, Sihem

Fachgebiete

• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Kryptologie, Informationssicherheit
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit Kryptographie, Datenverschlüsselung
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

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.