Boolean functions - NMMB331

• Title: Booleovské funkce
• Guaranteed by: Department of Algebra (32-KA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2020
• Semester: winter
• E-Credits: 3
• Hours per week, examination: winter s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: Dr. rer. nat. Faruk Göloglu
• Class: M Mgr. MMIB; M Mgr. MMIB > Povinně volitelné
• Classification: Mathematics > Algebra

Annotation

English

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (09.05.2018)

The course is devoted to vectorial nonlinear Boolean functions.

Czech

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (09.05.2018)

Kurz se zabývá nelineárními vektorovými booleovskými funkcemi.

Course completion requirements

English

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)

Students have to pass final test/oral exam.

Czech

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)

Předmět je zakončen ústní zkouškou.

Literature

English

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (09.05.2018)

Chapters by Carlet, from the book

“Boolean Models and Methods in Mathematics, Computer Science, and Engineering" published by Cambridge University Press, Yves Crama and Peter L. Hammer (eds.), pp. 257-397, 2010.

• Boolean Functions for Cryptography and Error Correcting Codes,

• Vectorial Boolean Functions for Cryptography

Requirements to the exam

English

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (09.05.2018)

Students have to pass final test/oral exam based on the material covered in the lectures.

Czech

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)

Zkouška má ústní formu. Její požadavky odpovídají obsahu přednesené látky.

Syllabus

English

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (09.05.2018)

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