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Quantum search algorithm
Mejdrech, Lukáš ; Barto, Libor (advisor) ; Holub, Štěpán (referee)
In this work we study Grover's algorithm for quantum computers. This algorithm promises to search in an unstructured database in time comparable with a square root of the number of objects. A description of basic quantum computer principles is followed by the original Grover's formulation and a proof of the algorithm, as well as a later geometrical description of the algorithm. We also mention their suitability for educational purposes. We also include a description of the Grover's algorithm in a programming language, which makes it possible to simulate a quantum computing on classical computers.
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Fast algebraic attacks
Hána, Martin ; Hojsík, Michal (referee) ; Holub, Štěpán (advisor)
In the present work we study algebraic attacks and cascading fast algebraic attack on stream ciphers using in their construction linear feedback shift registers. For deeper understanding of attacks we present some facts which are needed to know from theory of linear recurrence sequences in rst chapter. We show their connection to formalized description of construction we attack. In second chapter we show algebraic attacks on both ciphers using memory or memoryless. We introduce denitions of annihilator and algebraic immunity of Boolean function and show their main properties. In third chapter we use knowledge from rst two chapters and show process and principle of fast algebraic attack.
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The relationship between theoretical and practical lives in H. Arendt and Aristotle
Holub, Štěpán ; Kouba, Pavel (advisor) ; Pechar, Jiří (referee) ; Čapek, Jakub (referee)
The Relationship between Theoretical and Practical Lives in H. Arendt and Aristotle The first part of the work deals with the relationship between thinking, philosophy and political action in Hannah Arendt. The research includes the following: an evaluation of the distance Arendt takes from philosophy; a portrayal of what she herself calls "political theory"; analysis of her critical stance towards the philosophical tradition; and, finally, an outline of her conception of an authentic thinking. The second part is devoted to Aristotle and his position within Arendťs work. It assesses the extent to which Arendt justly ranks among neoaristotelians. Some aspects of Aristotle's philosophy are studied as for their usability within Arendtian approach to politics, as well as for their contribution to the formulation of the ideals of theoretical and practical li ves. In particular, the analysis concerns the Nicomachean Ethics (including reflections on its coherence) and some parts of the Politics. The focus i s on the concept of TÉAos and on the connection between concepts of rrpo~ts and ' I EVEPYEICX.
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Binary equality words
Hadravová, Jana ; Stanovský, David (referee) ; Holub, Štěpán (advisor)
Binary equality language is a set consisting of all solutions of equation g(w) = h(w), where g, h are arbitrary binary morphisms. Recently, it has been prooved that equality set for each pair of morphisms g, h is generated by at most two words. Structure of binary equality language has been already known in the case that at least one of morphisms g, h is periodic or if their equality set is generated exactly by two words. The main objective of the paper was to find a structure of solutions for morphisms whose equality set is generated by one word. The problem in general case remains unsolved but special result for solutions consisting of just one block for marked morphisms was discovered. Using methods established in this paper (covering by the same pattern to find n-multiple p-overflows and working with the cyclic pair (e, f, z)) it is believed that some more results can be achieved in the near future.
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Searching collisions in hash functions
Joščák, Daniel ; Holub, Štěpán (referee) ; Tůma, Jiří (advisor)
The main interest of this paper is finding collisions in the hash function MD5. We present our new algorithm based on Wangs et al. methods of finding collisions in MD5. While writing this thesis Stevens and Klima published their fast algorithms for finding collisions. We give a description of these algorithms and the calculation of computianal complexity of all three algorithms.
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