Boolean Functions for Cryptography and Coding Theory

Claude Carlet is Professor Emeritus of Mathematics at the University of Paris VIII, France and member of the Bergen University department of computer science. He has contributed to fifteen books, and published more than 130 papers in international journals and more than sixty papers in international proceedings. He has been a member of eighty program committees of international conferences, and served as co-chair for nine of them. He has overseen the research group 'Codage-Cryptographie', which gathers all French researchers in coding and cryptography, and is editor-in-chief of the journal Cryptography and Communications. He has been an invited plenary speaker at twenty international conferences and the invited speaker at thirty other international conferences and workshops.

1. Introduction to cryptography, codes, Boolean and vectorial functions; 2. Generalities on Boolean and vectorial functions; 3. Boolean functions, vectorial functions and cryptography; 4. Boolean functions, vectorial functions and error correcting codes; 5. Functions with weights, Walsh spectra and nonlinearities easier to study; 6. Bent functions and plateaued functions; 7. Correlation immune and resilient functions; 8. Functions satisfying SAC, PC, EPC, or having good GAC; 9. Algebraic immune functions; 10. Particular classes of Boolean functions; 11. Highly nonlinear vectorial functions with low differential uniformity; 12. Recent uses of Boolean and vectorial functions and related problems; 13. Open questions; 14. Appendix.