Bent Functions: Results and Applications to Cryptography

ISBN-13: 9780128023181 / Angielski / Miękka / 2015 / 220 str.

Natalia Tokareva

Opis

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

Recenzje

"...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

Spis treści

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

O autorze

Dr. Natalia Tokareva is a senior researcher at the Laboratory of Discrete Analysis in the Sobolev Institute of Mathematics and she teaches courses in cryptology in the Department of Mathematics and Mechanics at Novosibirsk State University. She has studied bent functions and their applications for several years, publishing one monograph (in Russian) and more than 12 articles. She has been a participant of many international conferences and seminars and presentations in the area of bent functions, particularly with applications in cryptography. Her research interests include Boolean functions in cryptography, bent functions, block and stream ciphers, cryptanalysis, coding theory, combinatorics, and algebra. She is chief of the seminar "Cryptography and Cryptanalysis" at the Sobolev Institute of Mathematics and she supervises BS, MS, and PhD students in discrete mathematics and cryptology.