Bent Functions: Results and Applications to Cryptography

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.

The text is appropriate for novices and advanced researchers, discussing proofs of several results, including the automorphism group of bent functions, the lower bound for the number of bent functions, and more.

Provides a detailed survey of bent functions and their main results, presenting a systematic overview of their generalizations and applicationsPresents a systematic and detailed survey of hundreds of results in the area of highly nonlinear Boolean functions in cryptographyAppropriate coverage for students from advanced specialists in cryptography, mathematics, and creators of ciphers

1. Boolean functions
2. Bent functions: An introduction
3. History of bent functions
4. Applications of bent functions
5. Properties of bent functions
6. Equivalent representations of bent functions
7. Bent functions with a small number of variables
8. Combinatorial constructions of bent functions
9. Algebraic constructions of bent functions
10. Bent functions and other cryptographic properties
11. Distances between bent functions
12. Automorphisms of the set of bent functions
13. Bounds on the number of bent functions
14. Bent decomposition problem
15. Algebraic generalizations of bent functions
16. Combinatorial generalizations of bent functions
17. Cryptographic generalizations of bent functions