APPAH, P. Group theoretical properties of the group generated by the action of the AES-128 key schedule [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2023.
Patrick Appah in his thesis studied some group theoretical properties of the AES-128 key schedule related to the theory of primitive groups. The results he described can be found in the following article: R. Aragona, R. Civino, and F. Dalla Volta. On the primitivity of the AES-128 key schedule. Journal of Algebra and its Applications, 2350233, 2022. Even if the results in the thesis are not his, I think Patrick did a good job of trying to clearly describe those results in his own way, managing not to copy and paste the article.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | B | ||
| Vlastní přínos a originalita | C | ||
| Schopnost interpretovat dosažené výsledky a vyvozovat z nich závěry | C | ||
| Využitelnost výsledků v praxi nebo teorii | B | ||
| Logické uspořádání práce a formální náležitosti | B | ||
| Grafická, stylistická úprava a pravopis | B | ||
| Práce s literaturou včetně citací | B | ||
| Samostatnost studenta při zpracování tématu | C |
The thesis deals with cryptographic system AES-128 and focuses on a problem related to its security. The encryption works as an endo-map on a vector space over F_2. This function is performed by an iterative process of several rounds, each of which being a composition of up to 4 steps, performed by linear and nonlinear maps on the vector space. AES selected as a cryptographic standard in 2001 has gone through thorough testing but only in the last few years the attack by a search through an invariant subspace has been investigated. The main result of this thesis is closely related to this topic. Namely it claims that the group generated by all translations and certain maps used within the encryption process does not enable existence of a nontrivial subspace invariant under its action. This result may help understanding of the possibilities of invariant subspace attack. The proof itself is tree-structured and each branch is properly discussed in Section 6.2.1. In general, the results seem correct, however, some argumentation and mathematical formulations could be improved. I have several objections: - Lack of examples. Each of the steps of encryption could have been explained nicely on some example. - Application of the result. It is not clear from the thesis itself, what is be the main result good for. Namely when the conclusion provides an example of an invariant subspace for another related transformation group. - Unbalanced depth of mathematical text. While the proof in Section 6.2.1 is not easily readable for its mathematical complexity, at some points (e.g. in 3.5.2, or AddRoundKey on the page 30) there is a plenty of space spent for description of very simple transformations or repetition of the same argumentation (a note after Corollary 6.5). - Some argumentation issues. We can hardly infer a validity of equations from non-generally valid properties such as bijectivity (the proof of L6.7) or linearity (page 45)? The thesis contains some typos and grammar inconsistencies.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | A | ||
| Vlastní přínos a originalita | B | ||
| Schopnost interpretovat dosaž. výsledky a vyvozovat z nich závěry | C | ||
| Využitelnost výsledků v praxi nebo teorii | B | ||
| Logické uspořádání práce a formální náležitosti | C | ||
| Grafická, stylistická úprava a pravopis | C | ||
| Práce s literaturou včetně citací | A |
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