Computational methods for finding cryptographic functions

• Thesis title in Czech: Výpočetní metody pro hledání kryptografických funkcí
• Thesis title in English: Computational methods for finding cryptographic functions
• Key words: booleovské funkce|APN|ekvivalence|kvadratická|výpočetní metody
• English key words: Boolean function|APN|equivalence|quadratic|computational methods
• Academic year of topic announcement: 2022/2023
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Department of Algebra (32-KA)
• Supervisor: doc. Faruk Göloglu, Dr. rer. nat.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 09.06.2022
• Date of assignment: 09.06.2022
• Confirmed by Study dept. on: 01.07.2022
• Date and time of defence: 10.06.2024 08:30
• Date of electronic submission: 02.05.2024
• Date of submission of printed version: 02.05.2024
• Date of proceeded defence: 10.06.2024
• Opponents: doc. Mgr. Pavel Růžička, Ph.D.

Guidelines

The thesis is a study on algorithms for finding vectorial Boolean functions that are
cryptographically important (block cipher cryptanalysis).
Several methods that have appeared recently [1,2] contain algorithms that produce many
such functions. These algorithms are not just based on exhaustive search.
The thesis should explain the theory
behind the methods as well as the algorithms themselves. The thesis should
also have practical results (for instance implementations of algorithms and/or
listing of found functions etc.) These are necessary requirements for a successful
thesis. A top grade thesis should also contain new contributions such as improvement
on algorithms, new instances of functions or theoretical work that might lead to
novel algorithms.

References

[1] Christof Beierle, Gregor Leander, Léo Perrin: Trims and extensions of quadratic APN functions. Des. Codes Cryptogr. 90(4): 1009-1036 (2022)

[2] Christof Beierle, Gregor Leander: New Instances of Quadratic APN Functions. IEEE Trans. Inf. Theory 68(1): 670-678 (2022)