Kryptografické permutace z biprojektivních funkcí
| Thesis title in Czech: | Kryptografické permutace z biprojektivních funkcí |
|---|---|
| Thesis title in English: | Cryptographic permutations from biprojective functions |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | diploma thesis |
| Thesis language: | |
| 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: | 10.11.2023 |
| Date of assignment: | 10.11.2023 |
| Confirmed by Study dept. on: | 13.11.2023 |
| Guidelines |
| Existence of APN (Almost Perfect Nonlinear) permutations
over an even dimensional vector space over GF(2) is an important problem related, for instance, to the optimality of the AES S-box. An example was found in [1] over dimension 6, which is the only known such permutation. Recently, in [2], it was shown that the known example cannot be generalized in a natural way. In this thesis, one object is to extend this result in several directions and prove related theoretical results. The known theoretical results (or the results proved in the thesis) prune the search space efficiently. These observations will be used in an efficient search for such permutations. |
| References |
| [1] K. Browning, J. Dillon, M. McQuistan, and A. Wolfe, “An APN permu-
tation in dimension six,” in Finite Fields: Theory and Applications—FQ9 (Contemporary Mathematics), vol. 518. Providence, RI, USA: AMS, 2010, pp. 33–42. [2] Faruk Göloglu: Classification of (q, q)-Biprojective APN Functions. IEEE Trans. Inf. Theory 69(3): 1988-1999 (2023) |