Bent Functions
Results and Applications to Cryptography

Focused primer on Boolean bent functions and their applications in combinatorics, coding theory, and cryptography

Natalia Tokareva (Author)

9780128023181, Elsevier Science

Paperback, published 6 August 2015

220 pages
22.9 x 15.1 x 1.5 cm, 0.36 kg

"...will definitely motivate researchers to work on bent functions and in general on cryptographic Boolean functions...it compiles together results published both in Russian and in English. This book will be a cornerstone of research activity on bent functions." --Mathematical Reviews

Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography, the text provides a detailed survey of their main results, presenting a systematic overview of their generalizations and applications, and considering open problems in classification and systematization of bent functions.

1. Boolean functions2. Bent functions: An introduction3. History of bent functions4. Applications of bent functions5. Properties of bent functions6. Equivalent representations of bent functions7. Bent functions with a small number of variables8. Combinatorial constructions of bent functions9. Algebraic constructions of bent functions 10. Bent functions and other cryptographic properties11. Distances between bent functions 12. Automorphisms of the set of bent functions13. Bounds on the number of bent functions14. Bent decomposition problem15. Algebraic generalizations of bent functions16. Combinatorial generalizations of bent functions17. Cryptographic generalizations of bent functions

Subject Areas: Data encryption [URY], Combinatorics & graph theory [PBV]