SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Boolean functions - NMMB331
Title in English: Booleovské funkce
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: Dr. rer. nat. Faruk Göloglu
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
Classification: Mathematics > Algebra
Annotation -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (09.05.2018)
The course is devoted to vectorial nonlinear Boolean functions.
Course completion requirements - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Předmět je zakončen ústní zkouškou.

Literature -
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 -
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.

Syllabus -
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

 
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