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Multivariate cryptography
Jančaříková, Irena ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
This thesis deals with multivariate cryptography. It includes specifically a description of the MQ problem and the proof of it's NP-completness. In the part of the MQ problem there is a description of a general pattern for the creation of the public part of asymetric cryptosystems based on the MQ problem. It this part the thesis describes the QMLE problem, which is important for the figure of the cryptosystem private key based on the MQ problem. Further, the thesis includes a description of the influence of the structure display, which appears in the QMLE problem, on time solution complexity of QMLE problem. The influence of time complexity has been detected by means of experimental measurement with programed algorithm. At the end of the thesis there is specified description of selected multivariety cryptosystems based on the MQ problem. Selected cryptosystems are provided with detailed description of encryption and decryption by means of selected cryptosystems and time estimations of these operations. The thesis includes estimations of memory requirements on saving of private and public key of the selected cryptosystems. Powered by TCPDF (www.tcpdf.org)
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The carriers of the bishops in the 13th century
Rajterová, Petra ; Doležalová, Eva (advisor) ; Žemlička, Josef (referee)
This submitted paper is focused on career rises of Czech bishops in 13th century. It deals with three of them, serving in Diocese of Prague: Nicholas of Ujezd (bishop between1240-1258), John III. of Drazice (bishop between 1258-1278) and Tobias of Bechyne (bishop between 1278-1296). Considering wider social and political context, this paper tries to describe the possibilities of career life in the Roman Catholic Church. Author uses contemporary sources of information and published literature, newer but even older, applying comparative method and prosopography.
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Structure of self-small groups and modules
Dvořák, Josef ; Žemlička, Jan (advisor) ; Šaroch, Jan (referee)
Title: Structure of self-small groups and modules Author: Josef Dvořák Department: Department of Algebra Supervisor: Mgr. Žemlička Jan, Ph.D. Supervisor's e-mail address: zemlicka@karlin.mff.cuni.cz Abstract: The thesis sums up the basic properties of self-small groups. Furthermore it thoroughly builds the theory od quotient categories by Serre classes, with focus on quotient category modulo the class B of boun- ded groups, which, as demonstrated, is equivalent to the quasicategory, i.e. category of abelian groups with Hom-sets being Q⊗Z HomA (A, B). This approach is developed into the theory of generalized quasi-categories. The dualities between quasi-caterogories od torsion-free and quotient-divisible categories of finite rank, resp. between categories of finite-rank self-small groups are studied and they are emloyed to the partial solution of Fuchs' problem no. 34. Keywords: self-small group, quotient divisible group, quasicategory, quo- tient category 1
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Comparison of public key cryptography algorithms
Mareš, Jiří ; Stanovský, David (advisor) ; Žemlička, Jan (referee)
In the present work we study comparison of basic public key encryption algorithms - RSA, Rabin and ElGamel method. We derive theoretic complexity of encrypting / decrypting of one block and we derive an expected model of its behavior with the key of double size. We also take practical measurements of speed of each algorithm using keys sized 64 - 4096 bits and we statistically analyze the results. We also mention special cases of some algorithms and discuss the advantages and disadvantages of their practical usage. At the end of this thesis we make a comparison of the speed of algorithms and we also compare the measured data with theoretical hypothesis.
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Vychylující moduly nad Gorensteinovými okruhy
Pospíšil, David ; Trlifaj, Jan (advisor) ; Žemlička, Jan (referee)
Let R be a commutative 1-Gorenstein ring. Our main result characterizes all tilting and cotilting R-modules: up to equivalence: they are parametrized by subsets of the set of all prime ideals of height one. More precisely, every tilting (cotilting) R-module is equivalent to some Bass tilting (cotilting) module. This characterization was known in the particular case of Dedekind domains: Chapter 4 contains a new and simpler proof of this fact. Our main result is proved in Chapter 5, while Chapter 6 deals with the cotilting case. In Chapter 4, there is also a proof of the less well-known fact that all finitely generated tilting modules over commutative rings are projective.
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Tall rings
Penk, Tomáš ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
Perfect and max rings are known for over fifty years. Their theory is being steadily and intensively studied. The conditions defining them are mainly interesting while studying non-noetherian modules. In this work we summarize at first basic information about rings and modules with previous knowledge requiring just in elementary level. After summing up basic results in the theory of noetherian modules we will be prepaired for the definition of tall modules and tall rings. We show then that they are a generalization of prefect and max rings in a specific way. We bring out some examples of tall and non-tall rings with accenting commutative rings. Information which we obtain we try to generalize and use for searching some necessary and some sufficient conditions with the goal to be able to say about a commutative ring if it is tall or not. At the end we point out that in case of a commutative noetherian ring they are equivalent to each other and they give together to the concept tall ring an equivalent characterization.
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Hunting in the early Middle Ages
Vaníčková Žemličková, Andrea ; Klápště, Jan (advisor) ; Žemlička, Josef (referee)
(in English): The thesis is devoted to hunting in Early Middle Ages in Czech Republic. The work summarizes the current knowledge of written sources and iconography. This knowledge are compared with zooarchaeological dates from sites dating to the Early Middle Ages. The thesis deals with the hunting law, hunting reserves and the hunting organization. The major part of this work is focused on game and its use. A portion of game on several hill forts and rural sites was also studied because hunting was not available for all social classes.
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Problém realizace von Neumannovsky regulárních okruhů
Mokriš, Samuel ; Růžička, Pavel (advisor) ; Žemlička, Jan (referee)
Title: The realization problem for von Neumann regular rings Author: Samuel Mokriš Department: Department of Algebra Supervisor of the master thesis: Mgr. Pavel Růžička, Ph.D., Department of Algebra Abstract: With every unital ring R, one can associate the abelian monoid V (R) of isomor- phism classes of finitely generated projective right R-modules. Said monoid is a conical monoid with order-unit. Moreover, for von Neumann regular rings, it satisfies the Riesz refinement property. In the thesis, we deal with the question, under what conditions an abelian conical re- finement monoid with order-unit can be realized as V (R) for some unital von Neumann regular ring or algebra, with emphasis on countable monoids. Two generalizations of the construction of V (R) to the context of nonunital rings are presented and their interrelation is analyzed. To that end, necessary properties of rings with local units and modules over such rings are devel- oped. Further, the construction of Leavitt path algebras over quivers is presented, as well as the construction of a monoid associated with a quiver that is isomorphic to V (R) of the Leavitt path algebra over the same quiver. These methods are then used to realize directed unions of finitely generated free abelian monoids as V (R) of algebras over any given field. A method...
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