Cyklicky-aditivně-diferenční množiny ze Singerových a GMW diferenčních množin.
| Thesis title in Czech: | Cyklicky-aditivně-diferenční množiny ze Singerových a GMW diferenčních množin. |
|---|---|
| Thesis title in English: | Cyclic-additive-difference sets from Singer and GMW difference sets. |
| Key words: | Cyklicky-aditivně-diferenční množiny|Diferenční kryptoanalýza|Singerovy diferenční množiny|APN funkce |
| English key words: | Cyclic-additive-difference set|Differential cryptanalysis|Singer difference sets|APN functions |
| Academic year of topic announcement: | 2021/2022 |
| 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: | 08.07.2021 |
| Date of assignment: | 08.07.2021 |
| Confirmed by Study dept. on: | 05.08.2021 |
| Date and time of defence: | 14.09.2021 09:00 |
| Date of electronic submission: | 22.07.2021 |
| Date of submission of printed version: | 22.07.2021 |
| Date of proceeded defence: | 14.09.2021 |
| Opponents: | prof. RNDr. Aleš Drápal, CSc., DSc. |
| Guidelines |
| Cyclic difference sets are interesting combinatorial objects. Recently, Carlet
introduced [1] the concept of cyclic-additive-difference sets (CADS) and asked several construction problems related to Singer difference sets [2]. These objects are related to differential cryptography. The object of this thesis is to give a detailed study of CADS and exhibit several classes of them arising from Singer and GMW cyclic difference sets. A satisfactory thesis should provide a good detailed study of these objects and a good thesis will provide a few new infinite families of CADS from a Singer difference set. |
| References |
| [1] Carlet, C.: Componentwise APNness, Walsh uniformity of APN functions, and
cyclic-additive difference sets. Finite. Fields Appl. 53, 226–253 (2018). [2] Carlet, C.: On APN exponents, characterizations of differentially uniform functions by the Walsh transform, and related cyclic-difference-set-like structures. Des. Codes. Cryptogr. 87(2-3), 203–224 (2019). |