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Integral attacks on block ciphers SIMON
Phamová, Kieu Trang ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
This thesis is focused on bit based division property using three subsets. Firstly, we introduce important definitions such as block cipher, integral attack and conventional division property. Then we define bit based division property using three subsets and prove its propagation rules: copy, AND-compression and XOR-compression. We often use these functions in cryptography, therefore in this thesis we will prove how bit based division property with three subsets propagates after the application of these functions.
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Quaternion algebras and units
Mišlanová, Kristína ; Kala, Vítězslav (advisor) ; Růžička, Pavel (referee)
The aim of this work is to study the Hamiltonian quaternions H and quaternion alge- bras. The first two chapters are based on the article Quaternion algebras by K. Conrad and the rest on the book Quaternion algebras by J. Voight. In the beginning, we mainly develop the theory about quaternions, quaternion algebras and study equivalent condi- tions for being a split or non-split quaternion algebra. After that, we also characterize, up to isomorphism, quaternion algebras over several fields such as R, C or Fp. In the third chapter, the thesis deals with orders in quaternion algebras, especially Lipschitz and Hurwitz order. The fourth chapter is dedicated to the relationship between unit quaternions and rotations in R3 , thanks to which we can characterize finite subgroups of H1 , or equivalently H× . This result will be used in the last chapter, where we are mainly focused on the problem of characterization of the group of units in orders in Hamiltonian quaternions. 1
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Permutation group algorithms
Plšková, Petra ; Bulín, Jakub (advisor) ; Růžička, Pavel (referee)
The Schreier Sims algorithm is a fundamental algorithm for permutation groups. Its purpose is to find a base and a strong generating set. Representation of a group using a base and a strong generating set is the core of many other algorithms. The aim of the thesis is to give the reader a detailed description of the algorithm. We present its pseudocode together with the pseudocode of its subroutines. We analyze the complexity with respect to the given pseudocode. Similarly, we describe an efficient, Monte Carlo version of the Schreier Sims algorithm whose time complexity is nearly linear. We give a detailed description of two improved algorithms for subroutines on which this version is based. We introduce the theoretical framework needed to support the correctness of both the deterministic and the probabilistic version of the algorithm. 1
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Sanitation installation and gas installation in the aparthotel
Růžička, Pavel ; Wierzbická, Helena (referee) ; Vrána, Jakub (advisor)
The master thesis focuses on the design of sanitary and gas installations in the particular aparthotel building in Pec pod Sněžkou. It is an aparthotel with two underground and max six above-ground floors incl. a gallery. The upper floors of the towers are used for accommodation. A parking lot and wellness area are situated on the first underground floor. On the second underground floor there is a technical background of the building, shops and a small restaurant for guests. All the roofs and terraces of the aparthotel are made to be green. The calculation part and the project contain the design of the sewerage, water supply, gas pipeline and their connection to the existing engineering networks. The theoretical part deals with increasing the pressure in the indoor plumbing, incl. design of equipment for increasing the pressure in the particular building.
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Production of check valve's part
Růžička, Pavel ; Řiháček, Jan (referee) ; Císařová, Michaela (advisor)
The bachelor's thesis deals with the production innovation of the return valve disc component used in pumping technology. It is a component made of sheet metal with 3 mm thickness, the quality of material is according to ČSN 11 320. Existing production using cutting technology in a process tool will be replaced by a modern, more accurate and especially more economical method by precise cutting with a pressure edge. Based on the literature study of precision cutting, assessment of production technology and processing of design solutions, the cutting tool was designed to be able to significantly speed up and reduce the cost of production of the component. It will be placed in a three-acting press from Feintool, namely XTF Speed with a nominal force of 1500 kN. In the final technical and economic evaluation, it was proved that the newly designed technology is able to bring a component of the same nature to the market, but at a significantly lower price.
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Lattice constructions and Priestley duality
Hartman, Juraj ; Růžička, Pavel (advisor) ; Tůma, Jiří (referee)
In this thesis after recalling some basic definitions and theorems in category theory, lattice theory and topology we first introduce the so called Stone duality of the category of boolean lattices and the category of boolean topological spaces. Then we introduce its generalization, the so called Priestley duality of the category of bounded distributive lattices and the category of total order disconnected topological spaces. Then we introduce the M3[.] lattice construction and prove that for every bounded distributive lattice L there is an isomorphism from the lattice M3[L] to the lattice of all continuous monotone maps from the Priestley space of L to the lattice M3 with discrete topology. Finally we introduce the so called boolean power, which we generalize to the so called priestley power and we prove that for every natural number n ≥ 3 and every bounded distributive lattice L there is an isomorphism from the lattice Mn to the priestley power of the lattice Mn by the lattice L. 1
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Rational linear dependencies of periodic points of the logistic map
Mik, Matěj ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
Period-n points of a polynomial f are roots, and hence elements of the splitting field, of the polynomial fn (x) − x, where fn denotes the nth iterate of f. In the thesis, we will focus on describing rational linear dependencies of period-n points of the polynomial f(x) = 4x(1 − x), which defines the so-called logistic map. We will present a description of the dependencies for n = 1, . . . , 5 and a partial result for n = 6. We will be using computer- calculated factorizations of polynomials over rational numbers and some finite field extensions. The factorizations will give us coordinates of the periodic points relative to some basis of their linear span, which will allow us to use a simple way of describing their dependencies. In the end of the thesis, we will put together an algorithm for describing the dependencies for a general n.
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Sanitation installation and gas installation in a apartment building
Růžička, Pavel ; Vaščáková, Alena (referee) ; Vrána, Jakub (advisor)
The aim of the Bachelor thesis is a design of sanitary installations and gas installations in the apartment building. It is a four-floor apartment building without a cellar. The apartments are located on all overground floors. The theoretical part is focused on infiltration of rainwater. The computation part and project includes a design of sanitary and storm sewers, water supply network, gas main a and their connection to existing utility lines.
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Algorithms for factorization of integers of particular form
Lorenc, Filip ; Příhoda, Pavel (advisor) ; Růžička, Pavel (referee)
This bachelor thesis deals with three factorization algorithms - Pollard p-1 method, Williams p+1 method and elliptic curve method ECM. This work aims to describe these algorithms theoretically and then compare them on real inputs. For each algorithm we describe its basic and extended version and then we derive their time complexity. In the first chapter we define B-powersmooth and B-smooth number and we state their approximation. The second, third and fourth chapter is about description of algorithms and in the last chapter we compare their effectiveness and performance. A part of the work contains basic theory about elliptic curves, which is necessary in ECM. There is also included a program containing all these algorithms.
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Presentations of subgroups
Jakubec, Tomáš ; Růžička, Pavel (advisor) ; Kazda, Alexandr (referee)
This bachelor thesis shows, how to create the presentation of subgroup, if the presentation of group is known by Reidemeister-Schreier method. At first, a term presentation of group is defined and then the text shows, how to obtain the group, which is isomorphic to the original group, from this presentation and how the presentation can be changed, although the group, which is ob- tained from the presentation, stays same. Then the text finds presentation of subgroup from the presentation of group, however this presentation cannot be in general used in practice. The obtained presentation of subgroup can be simplified by Reidemeister theorem, Schreier theorem and appropriate genera- tors of subgroup. This thesis also contains solved examples of application of Reidemeister-Schreier method. The text is intended as an educational material for students of combinatorial group theory. 1
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