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Security of an Electronic Voting System
Fritzová, Petra ; Růžička, Pavel (advisor) ; Hojsík, Michal (referee)
Electronic elections, also known as i-voting might help in removing the crisis in our democracy, which is reflected in non-cooperation in the opportunity of expressing their opinions during direct elections. A reasonable set up of information and communication technologies in technical and financial terms could help that elections would be attended by more voters. The implementation of electronic elections could achieve that the way of governance in the democratic republic will be truly represented by the view of the vast majority of people who are authorized to elect. The introduction of the i-voting system could be efficient from the financial point of view. This electoral process could reduce the risk of human error as well as the risk of manipulation of votes since most of the processes would be automated. Thesis proposes a definition of the basic requirements for an ideal i-voting system which compares the requirements for ensuring the safety of two previously proposed electronic electoral systems. Thanks to a deeper analysis of these two systems the thesis also describes the imperfection in safety and it raises the possibility of basic attacks on components and systems properties due to imperfections in security.
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The arity of NU polymorphisms
Draganov, Ondřej ; Barto, Libor (advisor) ; Růžička, Pavel (referee)
This paper deals with an arity of NU polymorphisms of relational structures. The goal is to simplify and clearly describe an already existing example of a relational structure, which has an NU polymorphism, but no NU polymorphisms of low arity in respect to arity of relations and to a number of elements in the relational structure. We explicitly describe m-ary relational structures with n elements, n ≥ 2, m ≥ 3, which have no NU polymorphisms of arity (m − 1)2n−2 , but have an NU polymorphism of arity (m − 1)2n−2 + 1, which is constructed in the paper, and binary relational structures with n elements, n ≥ 3, which have no NU polymorphisms of arity 22n−3 , but have an NU polymorphism of arity 22n−3 + 1.
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Combinatorial group theory and cryptography
Ferov, Michal ; Příhoda, Pavel (advisor) ; Růžička, Pavel (referee)
In the presented work we focus on applications of decision problems from combinatorial group theory. Namely we analyse the Shpilrain-Zapata pro- tocol. We give formal proof that small cancellation groups are good platform for the protocol because the word problem is solvable in linear time and they are generic. We also analyse the complexity of the brute force attack on the protocol and show that in a theoretical way the protocol is immune to attack by adversary with arbitrary computing power.
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Banschewského funkce na komplementárních modulárních svazech
Mokriš, Samuel ; Růžička, Pavel (advisor) ; Žemlička, Jan (referee)
Title: Banaschewski function on countable complemented modular lattices Author: Samuel Mokriš Department: Department of Algebra Supervisor of the bachelor thesis: Mgr. Pavel Růžička, Ph.D., Department of Algebra Abstract: A Banaschewski function on a bounded lattice L is an antitone self-map on L that picks a complement for each element of L. On any at most countable complemented modular lattice L, there exists a Banaschewski function with a Boolean range M. Moreover, such M is a maximal Boolean sublattice of L and is uniquely determined up to isomorphism. In the thesis we give a negative answer to the related question whether all maximal Boolean sublattices in an arbitrary countable complemented modular lattice are isomorphic and whether every max- imal Boolean sublattice in an arbitrary countable complemented modular lattice L is the range of some Banaschewski function on L. We also generalize the coun- terexample to greater cardinalities; for a given infinite cardinal κ we construct a complemented modular lattice L of cardinality κ and maximal Boolean sublat- tices B and E of L such that B is not the range of any Banaschewski function on L, that there exists a Banaschewski function on L of range E, and that B is not isomorphic to E. Keywords: complemented modular lattice, Banaschewski function, von...
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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.
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Abelian regular rings
Vejnar, Benjamin ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
Na/ev praco: Abelovsky regularni okruhy Autor: Benjamin Vejnar Katedra (listav): Katedra algebry VcdoLici bakalafske prace: Mgr. Jan 2emlicka, Ph.D. E-mail vedouctho: Jan.Zcmlicka&mJJ. cuni.cz Abstrakt: V pfcdloxene praci studujeme aritmeticke a strukturni vlastnosti abelovsky regularnich okruhu, tedy okruhu, jcjichx ka/xly levy i pravy konecne generova.ny ideal jo generovan idempotentnim prvkem, klery Ic/i v centra danoho okruhu. Napfiklad ka/,dy Boohmv okruh je abelovsky regularni. Venujume ye podininkam, ktere uplne diarakterizuji tn'du abelovsky regu- larnieli okruhu, jako napfiklad silna regularita. Vsimame si souvislosti mexi Booleovou algebrou vsch centralnich idempo1,entu daneho okruhu a hlavnimi idealy. Dale popiHUJeme topologit na nmo/ine visecli prvoidealu a avcdoniujeine si, '/e splyva s Lo])ologii ultrafiltrii na Booleove algebre idciiipotontd. Klicova slova: okruhy, idempoteiitni prvky, silne regularni okruhy Title: Abelian regular rings Author: Benjamin Vejnar Department: Department of Algebra Supervisor: Mgr. Jan Zemlieka, Ph.D. Supervisor's e-mail address: Jan.Zc:ttilicka((})'niff.cu'iii.cz Abstract: In the present work we study arithmetic and structural properties of abelian regular' rings. This means rings whose every left and right finitely generated ideal is generated by an idempotent...
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Searching optimal strategies for the number field sieve
Perůtka, Lukáš ; Drápal, Aleš (advisor) ; Růžička, Pavel (referee)
In this work we study the number field sieve algorithm. Our main focus is on its theoretical background. We present all important theorems which are needed for a full understanding of the algorithm. We also describe the most widely used implementation of the parts of the algorithm and we discuss in which situation they should be used. At the end we show results from measurements of sieving phase on the implementation which was written for our Department of Algebra.
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