Syllabus
1. Boolean functions and their representations
2. Hadamard matrices and Walsh transform
3. Bent functions
4. Construction of bent functions
5. Construction of bent functions (cont’d)
6. Vectorial Boolean functions, vectorial bent functions
7. Perfect nonlinear and almost perfect nonlinear functions
8. Almost bent functions
9. Construction of APN and AB functions
10. Polynomials: Permutation polynomials, Dickson polynomials
11. APN permutations: Existence and construction
12. Bent, APN, AB functions and their connections to cryptography
13. Bent, APN, AB functions and their connections to coding theory
14. Bent, APN, AB functions and their connections to combinatorics
Annotation
The course is devoted to vectorial nonlinear Boolean functions.