
Taking of evidence in administrative proceedings
Holub, Štěpán ; Kopecký, Martin (advisor) ; Sharp, Vladimír (referee)
Taking of evidence in administrative proceedings Abstract The topic of this thesis is the taking evidence in administrative proceedings, which aims to present compendious knowledge concerning the administrative authority; to eliminate eventual contradictions in established facts; and to decide on the matter. Taking into account the diversity among administrative proceedings, it is essential to discuss the individual types of the incriminate proceedings, eventually their specific phases, and simultaneously to provide connections between individual evidence institutes. Also, possible discrepancies in evidence, or perhaps complete absence of evidence, should not be omitted since the legislator has not established exclusive obligation, even though the evidence poses significant part of the proceedings. The presented thesis is divided into five chapters. The first chapter thoroughly reviews the principles of administrative proceedings, which are tightly connected with the process of taking of evidence. The second chapter discusses the terms in the context of evidence, whereas such terms are not explicitly stated in the law. These terms are defined based on the jurisprudence and specialized literature. The third chapter covers process stamping of individual phases in taking of evidence, which extends to the field...


Graph coloring and formal grammars
Elichová, Sára ; Holub, Štěpán (advisor) ; Barto, Libor (referee)
This thesis deals with two equivalent reformulations of the four color problem. The first of them shows the connection between graph coloring and the vector cross product; the se cond one expands on it and develops a relation to a formal grammar. These reformulations together with the proofs of their equivalence to the four color theorem are the results of two articles motivated by the effort to find a simpler proof of the famous problem, which was proved only by computer. They bring an interesting perspective on the problem of graph coloring and give the possibility to look on it in a new way, which could turn out to be more approachable. This thesis presents the proofs introduced in the source li terature and adds the steps that are not elaborated in detail by the authors. It aims to formalize some of the ideas and to contribute to the comprehensibility of the proofs. 1


Representing Images by Weighted Finite Automata
Hurtišová, Viktória ; Holub, Štěpán (advisor) ; Žemlička, Jan (referee)
The goal of this thesis is to introduce weighted finite automata (WFA) as a means of representing multiresolution raster images. We explain the basic concepts of weighted finite automata. Then we describe an encoding algorithm that converts an image into a WFA and a decoding algorithm that can generate back the original image. We then provide our implementation of the encoding and decoding algorithms. 1

 
 

Analysis of the stream cipher QUAD
Čurilla, Marcel ; Holub, Štěpán (advisor) ; Příhoda, Pavel (referee)
Title: Analysis of the stream cipher QUAD Author: Marcel Čurilla Department: Katedra algebry Supervisor: doc. Mgr. Štěpán Holub, Ph.D. Abstract: Stream cipher QUAD was introduced in 2006 on Eurocrypt by Côme Ber bain, Henri Gilbert a Jacques Patarin cite quad. The authors showed a reduction of this cipher for the problem of solving m quadratic equations of n variables over finite fields known as the MQ problem. For simplicity, they considered only the case of the field GF(2). In this thesis I introduce this stream cipher. I show the proof (reduction) of safety ciphers QUAD for MQ problem over any finite field GF(q). I describe the basic met hods for the solution of system of quadratic equations over finite fields, linearization and relinearization. I focus on XL algorithm  which is currently the fastest algo rithm for solving quadratic systems. This algorithm was designed precisely to deal with overdefined quadratic systems. While analyzing the cipher QUAD I show for what instance is a cipher QUAD breakable and vice versa for what instance is the security guaranteed. Keywords: stream cipher, QUAD, MQ problem, algorithm XL, 1


Covering sets in steganography
Vacek, Jan ; Holub, Štěpán (advisor) ; Hojsík, Michal (referee)
Steganography is a science which is interested in communication hiding. This work is focused on the most recent methods related to this topic. Mainly, it is matrix embedding, which uses coding theory, and sum and difference covering sets (SDCS). Rainbow coloring of grid graphs is used to receive even better results. This technique decrease amplitude of performed changes. It makes stegosystems less likely to be detected. Properties which describe behavior of each stegosystem are included for each technique. 1


Squares in integer sequences
Hudcová, Barbora ; Holub, Štěpán (advisor) ; Bulín, Jakub (referee)
This work is based on an article which provides a construction of the first infinite word over a finite alphabet avoiding additive cubes. We construct other words with the same properties and we choose one of them to show the main idea of the proof that this word avoids additive cubes. 1

 

Compressing Pseudorandom sequences
Vald, Denis ; Holub, Štěpán (advisor) ; Růžička, Pavel (referee)
Generators of pseudorandom sequences are widely used objects, not in the least place because of their application in stream ciphers. One of the ways to improve resistance to different types of attack is to use compression on the generated sequence in order to remove redundant information, that might lead to an attack against the generator. In this work we try to explore from a wider perspective the theoretical foundations for compressing pseudorandom sequences created thus far. Using this general view we will examine some known attacks against the PRN generators and look for a way to resist such attacks.
