Kryptografické permutace z biprojektivních funkcí
| Název práce v češtině: | Kryptografické permutace z biprojektivních funkcí |
|---|---|
| Název v anglickém jazyce: | Cryptographic permutations from biprojective functions |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | diplomová práce |
| Jazyk práce: | |
| Ústav: | Katedra algebry (32-KA) |
| Vedoucí / školitel: | doc. Faruk Göloglu, Dr. rer. nat. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 10.11.2023 |
| Datum zadání: | 10.11.2023 |
| Datum potvrzení stud. oddělením: | 13.11.2023 |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| [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) |