Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. These maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography. This book provides a detailed survey of their main results. It presents a systematic overview of their generalizations and applications, and considers open problems in classification and systematization of bent functions. Appropriate for novices as well as advanced researchers, this book discusses proofs of several results, such as automorphism group of bent functions, lower bound for the number of bent functions, and more. Systematic and detailed survey of hundreds of results in the area of highly nonlinear Boolean functions in cryptographyAppropriate coverage for students new to the topic through advanced specialists in cryptography and mathematics and creators of ciphers INDICE: IntroductionChapter 1 Bent functionsChapter 2 Applications of bent functionsChapter 3 Properties of bent functionsChapter 4 Equivalent representations of bent functionsChapter 5 Bent functions with a small number of variablesChapter 6 Bounds on the number of bent functionsChapter 7 Constructions of bent functions Chapter 8 Algebraic generalizations of bent functionsChapter 9 Combinatorial generalizations of bent functions Chapter 10 Cryptographic generalizations of bent functionsChapter 11 Quantum generalizations of bent functions Chapter 12 k-Bent functionsChapter 13 Bent functions and quadratic cryptanalysis Chapter 14 Properties of quadratic Boolean functions in connection to bent functions Chapter 15 Quaternary and Boolean bent functionsChapter 16 Automorphism group of the set of bent functionsChapter 17 On the number of bent functions from iterative constructionsChapter 18 Bent functions and strongly regular graphsConclusion Bibliography
- ISBN: 978-0-12-802318-1
- Editorial: Academic Press
- Encuadernacion: Rústica
- Páginas: 230
- Fecha Publicación: 13/07/2015
- Nº Volúmenes: 1
- Idioma: Inglés