Kryptografické vlastnosti biprojektivních a podílových projektivních permutací nad konečnými tělesy

• Thesis title in Czech: Kryptografické vlastnosti biprojektivních a podílových projektivních permutací nad konečnými tělesy
• Thesis title in English: Cryptographic properties of fractional projective and biprojective permutations over finite fields
• Academic year of topic announcement: 2021/2022
• Thesis type: diploma thesis
• 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: 16.07.2021
• Date of assignment: 16.07.2021
• Confirmed by Study dept. on: 05.08.2021

Guidelines

A recent direction in the research on cryptographic permutations is the so called fractional projective and
biprojective permutations. Several recent results give [2, 3] biprojective permutations with good boomerang
uniformity which is a cryptographic property for permutations that are used as S-Boxes. Recently in [1],
fractional projective and biprojective permutations over finite fields were classified. The object of this
thesis is the analysis of the cryptographic properties of these permutations and investigate whether they
are related to the S-Boxes of recent cryptographical standards like Streebog and Kuznyechik. A satisfactory
thesis should provide a detailed analysis of these objects including computer experiments. A theoretical
(or a strong computer based) result that explains these ciphers in terms of projective polynomials would
be considered a good thesis.

References

[1] Gologlu, F.; Classification of fractional projective permutations over finite fields, preprint, (2020).
[2] Tu, Z., Li, N., Zeng, X., and Zhou, J. A class of quadrinomial permutations with boomerang uniformity
four. IEEE Trans. Inform. Theory 66, 6 (2020), 3753–3765.
[3] Li, K., Li, C., Helleseth, T., and Qu, L. Cryptographically strong permutations from the butterfly
structure. Designs, Codes and Cryptography (2021).