National Repository of Grey Literature 150 records found  beginprevious85 - 94nextend  jump to record: Search took 0.00 seconds. 
Decidability of the theory of commutative groups
Čech, František ; Šaroch, Jan (advisor) ; Žemlička, Jan (referee)
In this thesis will be demonstrated proof of decidability of theory of commu- tative groups. This result was already shown in year 1955 by author W.Szmielew. However proof shown here takes different path. Result will by shown with use of results from theory of modules and theory of modeles prooved in article by M. Ziegler Model theory of modules. Final part of proof follows proof shown in article The elementary theory of Abelian groups by P. C. Eklofa and E. R. Fishera. 1
Semilinear sets
Bouška, David ; Holub, Štěpán (advisor) ; Žemlička, Jan (referee)
In this thesis we examine a part of the mathematical side of the theory of context free languages, namely semilinear sets. We prove that the semilinear sets are closed under set intersection and difference in a mathematically better digestible and possibly easier way than how it is presented as a non-central result in the referenced literature. Then we introduce the notion of a context-free language and present a result that relates semilinear sets and context-free languages without a proof. 1
Binary codes based on (2,3)-representation
Sternwaldová, Anetta ; Žemlička, Jan (advisor) ; Příhoda, Pavel (referee)
A new class of prefix codes is introduced in this thesis. These codes are based on an integer representation in mixed base with the radices 2 and 3. The goal is to describe (2,3)-representation and its properties with regard to utilization for encoding. The thesis also deals with construction of (2,3)-codes and proves that (2,3)-codes prevent error propagation over many codewords during data transmission. Upper bound of codeword length is obtained and estimate of average expected codeword length is also presented. Powered by TCPDF (www.tcpdf.org)
Algortihms for proving primality
Pavlů, Jiří ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee)
The goal of the thesis is introducing the reader to some of the algori- thms for proving primality along with practical usage of some of these algorithms. The main objective of the thesis is a presentation of Goldwasser-Killian primality test, which can be used to produce primality certificates, which can be verified very quickly. For better understanding of the test the thesis also includes an in- troduction to elliptic curves, which are the basis of the test. The thesis also shows how is a group of points on elliptic curves constructed and how to use this infor- mation for construction of algebraic formula for a sum of two points on a curve. Powered by TCPDF (www.tcpdf.org)
MQ problem
Středa, Adolf ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
The aim of this thesis is to describe a general MQ Problem with a focus on its variant called HFE, outline several attacks on a basic scheme based on HFE and describe a new attack on HFEz, a cryptosystem based on special polynomials over finite fields with a modification, which discards a portion of the output from the initial transformation. This ensures a dependency on more variables while keeping the same size of the field. The attack starts with a translation of HFE into HFE with branches, followed by a branch separating algorithm described in [Fel06]. The separation algorithm uses the public key to derive an operation, which induces (with addition) a non-associative algebra. Utilising some properties of non-associative algebras, a matrix, which can separate variables into distinct sets according to branches, is calculated. This leads to stripping off the HFEz modification and thus allowing us to attack directly the HFE polynomial. Powered by TCPDF (www.tcpdf.org)
Analysis of the SQUFOF algoritm
Langer, Lukáš ; Žemlička, Jan (advisor) ; Příhoda, Pavel (referee)
This thesis deals with collecting facts and making the complete analysis of SQUFOF algorithm. In the beginning you can find a short hystorical re- view and then it continues with desribing how the binary quadratic forms, which represents the number N, continued fractions of √ N, ideals in the ring Z( √ N) and lattices in Q( √ N) are related. This thesis offers the tools usable to switch between these structures and finally it uses these tools to show, how the algorithm SQUFOF works. 1
An attack upon Wieschebrink's version of Niederreiter system
Homer, Miloslav ; Drápal, Aleš (advisor) ; Žemlička, Jan (referee)
In this work an attack upon Wieschebrink's version of Niederreiter cryptosystem using GRS codes by Couvreur et. al. from 2014 is described. Relevant notions of error-correcting code theory are presented, definitions of McEliece scheme, Niederreiter scheme and their respective Wieschebrink's modifications are shown. A description of the attack using distinguisher as described by Couvreur et. al. Based on componentwise code products and shortened codes properties follows, as does Sidelnikov-Shestakov attack on Niederreiter scheme with relevant group theory notions. Implementation details are also outlined. The attack is then summarized and its complexity is mentioned. The attack duration measured by the C++ implementation is presented in the last chapter. The program implementing the cryptosystem as well as the attack is located in the appendix with the program documentation. Powered by TCPDF (www.tcpdf.org)
Minder's structural attack upon Sidelnikov's cryptosystem
Steinhauser, František ; Drápal, Aleš (advisor) ; Žemlička, Jan (referee)
After Sidelnikov proved in 1992 that the cryptosystem of Niederreiter is vulnera- ble, he designed his own cryptosystem in 1993. This new cryptosystem was based on McEliece schema, it was to be resistant to quantum computers and faster than McEliece cryptosystem. However, in 2007, Minder and Shokrollah proposed an attack proving that the cryptosystem of Sidelnikov was vulnerable as well. This thesis uses several well-known and several new theorems to describe algebraic characteristics of the Reed-Muller code, especially from the affinity point of view. It proves that the attack proposed by Minder and Shokrollah really breaks the cryptosystem of Sidelnikov. Implementation of this attack in C/C++ language is presented in the conclusion of the thesis along with a table of duration of this attack on a personal computer.
Tests for generators of pseudorandom numbers
Jurečková, Olha ; Příhoda, Pavel (advisor) ; Žemlička, Jan (referee)
In this work we focus on tests for generators of pseudorandom bits. Generators of pseudorandom bits are one of the most important cryptographic tools. In the first part of this work we introduce statistical theory related for randomness testing. Then we present some basic definitions and facts from cryptography. In the second part of the work we describe ten different statistical tests and their modifications. We also present results of tests performed on Decim stream cipher, Geffe generator and Blum Blum Shub generator. 1
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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See also: similar author names
2 Žemlička, J.
2 Žemlička, Jakub
10 Žemlička, Josef
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