National Repository of Grey Literature 98 records found  beginprevious51 - 60nextend  jump to record: Search took 0.00 seconds. 
A stream cipher based on continued fractions
Krasnayová, Dáša ; Drápal, Aleš (advisor) ; Holub, Štěpán (referee)
This bachelor thesis deals with the theory of continued fractions which is design of a stream cipher in article On the use of continued fractions for stream ciphers based on. Since results about probability for a positive integer number to be a partial quotient of a generalised continued fraction which are necessary for proving the cipher secure, has not been proved yet, there are summarized previous results which could lead to proving them. In particular, basic properties of classical and generalised continued fractions and proof of Kuzmin theorem are presented here. Distribution of probability for a positive integer number to be a partial quotient of a classical continued fraction follows from Kuzmin theorem. The design of the stream cipher from the article is briefly introduced at the end of the thesis. Powered by TCPDF (www.tcpdf.org)
Continued fractions in coding theory
Fišer, Jan ; Šťovíček, Jan (advisor) ; Holub, Štěpán (referee)
The first part of the thesis acquaints us with the Reed-Solomon codes, methods of their construction and encoding. At the same time we provide the evi- dence of their most important properties including the relevant theoretical basis. In the second chapter we introduce the theory of continued fractions over a field and examine their structure. Applying the executed general ob- servations on the specific case of the formal Laurent series we get to efficient Reed-Solomon decoding algorithm. Without complete proofs we also men- tion other two decoding algorithms that are based on solving the key equation as well, namely Berlekamp-Massey and Euclidean algorithm. In the end we show the equivalence of these three algorithms.
Binární znaménkové reprezentace celých čísel v kryptoanalýze hashovacích funkcí
Vábek, Jiří ; Tůma, Jiří (advisor) ; Kůrka, Petr (referee) ; Holub, Štěpán (referee)
Title: Binary Signed Digit Representations of Integers in Cryptanalysis of Hash Functions Author: Jiří Vábek Department: Department of Algebra Supervisor: doc. RNDr. Jiří Tůma, DrSc., Department of Algebra Abstract: The work summarizes two main papers, A New Type of 2-block Colli- sions in MD5 and On the Number of Binary Signed Digit Representations of a Given Weight, while containing also the wider introduction to the topic of crypt- analysis of MD5 and binary signed digit representations (BSDR's). In the first paper we have implemented and applied Stevens algorithm to the newly proposed initial message differences and constructed a new type of collisions in MD5. In the second paper we have introduced and proved a new improved bound for the number of optimal BSDR's and also a new recursive bound for the number of BSDR's of a given integer with a given overweight. In addition to the results in mentioned papers, the generalized result is stated with the new bound for the number of optimal D-representations of natural numbers with D = {0, 1, 3}. Keywords: hash function, MD5, binary signed digit representation (BSDR), non- adjacent form (NAF) 1
Structure of equality sets
Hadravová, Jana ; Holub, Štěpán (advisor) ; Currie, James (referee) ; Masáková, Zuzana (referee)
Title: Structure of equality sets Author: Jana Hadravová Department: Department of Algebra Supervisor: doc. Mgr. Štěpán Holub, Ph.D., Dept. of Algebra Abstract: Binary equality set of two morphisms g, h : ⌃⇤ ! A⇤ is a set of all words w over two-letter alphabet ⌃ satisfying g(w) = h(w). Elements of this set are called binary equality words. One of the important results of research on binary equality sets is the proof of the fact that each binary equality set is generated by at most two words provided that both morphisms g and h are non-periodic. Moreover, if a binary equality set is generated by exactly two words, then the structure of both generators, and therefore of the whole set, is uniquely given. This work presents the results of our research on the structure of binary equality sets with a single generator. Importantly, these generators can be decomposed into simpler structures. Generators which can not be further decomposed are called simple equality words. First part of the presented work describes the structure of simple equality words and introduces their detailed classification. The main result of the first part is a precise characterisation of su ciently large simple equality words. In the second part, the work describes the iterative process which transforms a general generator of a binary...
Correlation attacks
Mařák, David ; Hojsík, Michal (advisor) ; Holub, Štěpán (referee)
This bachelor thesis decribes Correlation attacks on stream ciphers combination generator type. The reader is briefly acquainted with the basic definitions of cryptographic theory which is necessary to understand the text. Afterwards, the thesis describes the original article that presented this type of attack, and which was the inspiration for further improvements and modifications. These improvements are then described in more details, namely the group called "Fast correlation attacks" which are more efficient and fully replaced the original attack. Finally, there are described some modifications of Fast correlation attacks. Powered by TCPDF (www.tcpdf.org)
Biautomata
Klouček, Miloš ; Holub, Štěpán (advisor) ; Kozlík, Andrew (referee)
This paper is focused on finite automata and their ability to recognize certain significant classes of regular languages. First of all we define core terms of the theory of finite automata, then we proceed to provide an overview of their properties. Thereafter we focus on extending finite automata into biautomata by equipping them by an extra "backwards" transformation function and on examining properties of such structures. While doing so we especially focus on comparing similar properties of automata and biautomata. In the second part of this paper we demonstrate the utility of biautomata by providing an improved proof of famous Simon's theorem, which characterizes piecewise testable languages. This proof is a slightly modified version of the result of O. Klíma a L. Polák. Powered by TCPDF (www.tcpdf.org)
Discrete Channel Capacity
Butora, Jan ; Holub, Štěpán (advisor) ; Žemlička, Jan (referee)
Title: Discrete Channel Capacity Author: Jan Butora Department: Department of Algebra Supervisor: doc. Mgr. Štěpán Holub, Ph.D. et Ph.D., Department of Algebra Abstract: This Bachelor thesis introduces and examines C.E. Shannon's discrete channel capacity theory, which was first published in 1948 as one of the founding studies in the field of mathematical information theory. In the first place, possible way of information measurement is presented and communication systems are described. Additionally, emphasis is given to discrete noiseless channel and the theorem on calculating the capacity of such channels is examined and proven. Shannon's proof is examined in detail as it contains several non-trivial results in finite differences. Finally, calculation of channel capacity using the theorem is shown in practice. Keywords: difference equations, generating function, channel capacity
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
Testování náhodnosti a použití statistických testů v kryptografii
Nižnanský, Petr ; Růžička, Pavel (advisor) ; Holub, Štěpán (referee)
Pseudorandom generators belong to the primary focus of cryptology. The key to every cipher has to be generated at random, otherwise the security of the whole cipher is threatened. Another point of importance is the pseudorandom generators' close relationship to the stream ciphers. In this work, we first introduce statistical theory related to randomness testing. Then, we describe 8 classical statistical tests. We introduce a concept of next bit testing and derive variants of previous tests. Moreover, with this new battery of tests we examine the randomness of SHA-3 second round candidates and present the results. Also a sensitivity of tests is investigated and several useful transformations are shown. Powered by TCPDF (www.tcpdf.org)
A polynomial algorithm for the binary PCP
Kuřinová, Petra ; Holub, Štěpán (advisor) ; Růžička, Pavel (referee)
The Post correspondence problem, introduced in 1946 by Emil Post, is an important example of undecidable problem. Therefore PCP figures in pro- ofs of some results in theory of formal languages, matrix theory and other. The decidability of the Post correspondence problem proved Ehrenfeucht, Karhumäki and Rozenberg in the 1980s and Halava, Harju and Hirvensalo in 2002 ended the proof. Eight years later was verified that the solution can be found even in polynomial time. The main goal of this diploma thesis is to describe this algorithm in detail and to implement it in a web application. The thesis also introduces basics of com- binatorics on words and some facts about PCP and produces some interesting examples of instances of PCP. Keywords: Post correspondence problem, generalized Post correspondence problem, binary PCP, polynomial algorithms on words, successors of morphisms 1

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