Bent Functions de Natalia Tokareva

Bent Functions: Results and Applications to Cryptography

Natalia Tokareva

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 applications
Presents a systematic and detailed survey of hundreds of results in the area of highly nonlinear Boolean functions in cryptography
Appropriate coverage for students from advanced specialists in cryptography, mathematics, and creators of ciphers

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Cuprins

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