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Kódování a efektivita LDPC kódů
Kozlík, Andrew ; Drápal, Aleš (advisor) ; Holub, Štěpán (referee)
Low-density parity-check (LDPC) codes are linear error correcting codes which are capable of performing near channel capacity. Furthermore, they admit efficient decoding algorithms that provide near optimum performance. Their main disadvantage is that most LDPC codes have relatively complex encoders. In this thesis, we begin by giving a detailed discussion of the sum-product decoding algorithm, we then study the performance of LDPC codes on the binary erasure channel under sum-product decoding to obtain criteria for the design of codes that allow reliable transmission at rates arbitrarily close to channel capacity. Using these criteria we show how such codes are designed. We then present experimental results and compare them with theoretical predictions. Finally, we provide an overview of several approaches to solving the complex encoder problem.
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Audio steganography and IP telephony
Hrinčárová, Monika ; Drápal, Aleš (advisor) ; Kozlík, Andrew (referee)
Steganography is a technique which hides secret information. In this work, we will hide a secret information in the packets which are produced during a Skype call. Skype is one of the best known and the most widely used VoIP applications. We will propose, describe and implement a steganography method by which we will send the secret message during the Skype call. For embedding the message into packets and extracting them, we will use steganographic method called matrix encoding. To avoid packet loss, we will increase the robustness of this method by error-correcting and self-synchronising codes. As error-correcting codes, we will use the binary Hamming (7, 4) -codes and for the self-synchronising, we will use T-codes. 1
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Designs and their algebraic theory
Kozlík, Andrew
It is well known that for any Steiner triple system (STS) one can define a binary operation · upon its base set by assigning x·x = x for all x and x·y = z, where z is the third point in the block containing the pair {x, y}. The same can be done for Mendelsohn triple systems (MTS), directed triple systems (DTS) as well as hybrid triple systems (HTS), where (x, y) is considered to be ordered. In the case of STSs and MTSs the operation yields a quasigroup, however this is not necessarily the case for DTSs and HTSs. A DTS or an HTS which induces a quasigroup is said to be Latin. The quasigroups associated with STSs and MTSs satisfy the flexible law x · (y · x) = (x · y) · x but those associated with Latin DTSs and Latin HTSs need not. A DTS or an HTS is said to be pure if when considered as a twofold triple system it contains no repeated blocks. This thesis focuses on the study of Latin DTSs and Latin HTSs, in particular it aims to examine flexibility, purity and other related properties in these systems. Latin DTSs and Latin HTSs which admit a cyclic or a rotational automorphism are also studied. The existence spectra of these systems are proved and enumeration results are presented. A smaller part of the thesis is then devoted to examining the size of the centre of a Steiner loop and the connection to...
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Cryptanalytic attacks on lightweight ciphers
Rabas, Tomáš ; Göloglu, Faruk (advisor) ; Kozlík, Andrew (referee)
In 2016 the National Institute of Standards and Technology (NIST) started the stan- dardization process for lightweight cryptography (LWC). We provide a broad introduc- tion to lightweight cryptography together with a survey of current design trends and lightweight cryptography standards, with special attention to this competition. In the second part, we present a description and cryptoanalysis of three lightweight ciphers: SIV-Rijndael256, CLX, and Limdolen. 1
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Audio steganography and IP telephony
Hrinčárová, Monika ; Drápal, Aleš (advisor) ; Kozlík, Andrew (referee)
Steganography is a technique which hides secret information. In this work, we will hide a secret information in the packets which are produced during a Skype call. Skype is one of the best known and the most widely used VoIP applications. We will propose, describe and implement a steganography method by which we will send the secret message during the Skype call. For embedding the message into packets and extracting them, we will use steganographic method called matrix encoding. To avoid packet loss, we will increase the robustness of this method by error-correcting and self-synchronising codes. As error-correcting codes, we will use the binary Hamming (7, 4) -codes and for the self-synchronising, we will use T-codes. 1
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Designs and their algebraic theory
Kozlík, Andrew ; Drápal, Aleš (advisor) ; Donovan, Diane (referee) ; Lindner, Charles Curtis (referee)
It is well known that for any Steiner triple system (STS) one can define a binary operation · upon its base set by assigning x·x = x for all x and x·y = z, where z is the third point in the block containing the pair {x, y}. The same can be done for Mendelsohn triple systems (MTS), directed triple systems (DTS) as well as hybrid triple systems (HTS), where (x, y) is considered to be ordered. In the case of STSs and MTSs the operation yields a quasigroup, however this is not necessarily the case for DTSs and HTSs. A DTS or an HTS which induces a quasigroup is said to be Latin. The quasigroups associated with STSs and MTSs satisfy the flexible law x · (y · x) = (x · y) · x but those associated with Latin DTSs and Latin HTSs need not. A DTS or an HTS is said to be pure if when considered as a twofold triple system it contains no repeated blocks. This thesis focuses on the study of Latin DTSs and Latin HTSs, in particular it aims to examine flexibility, purity and other related properties in these systems. Latin DTSs and Latin HTSs which admit a cyclic or a rotational automorphism are also studied. The existence spectra of these systems are proved and enumeration results are presented. A smaller part of the thesis is then devoted to examining the size of the centre of a Steiner loop and the connection to...
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Designs and their algebraic theory
Kozlík, Andrew
It is well known that for any Steiner triple system (STS) one can define a binary operation · upon its base set by assigning x·x = x for all x and x·y = z, where z is the third point in the block containing the pair {x, y}. The same can be done for Mendelsohn triple systems (MTS), directed triple systems (DTS) as well as hybrid triple systems (HTS), where (x, y) is considered to be ordered. In the case of STSs and MTSs the operation yields a quasigroup, however this is not necessarily the case for DTSs and HTSs. A DTS or an HTS which induces a quasigroup is said to be Latin. The quasigroups associated with STSs and MTSs satisfy the flexible law x · (y · x) = (x · y) · x but those associated with Latin DTSs and Latin HTSs need not. A DTS or an HTS is said to be pure if when considered as a twofold triple system it contains no repeated blocks. This thesis focuses on the study of Latin DTSs and Latin HTSs, in particular it aims to examine flexibility, purity and other related properties in these systems. Latin DTSs and Latin HTSs which admit a cyclic or a rotational automorphism are also studied. The existence spectra of these systems are proved and enumeration results are presented. A smaller part of the thesis is then devoted to examining the size of the centre of a Steiner loop and the connection to...
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Audio steganography and IP telephony
Hrinčárová, Monika ; Drápal, Aleš (advisor) ; Kozlík, Andrew (referee)
Steganography is a technique which hides secret information. In this work, we will hide a secret information in the packets which are produced during a Skype call. Skype is one of the best known and the most widely used VoIP applications. We will propose, describe and implement a steganography method by which we will send the secret message during the Skype call. For embedding the message into packets and extracting them, we will use steganographic method called matrix encoding. To avoid packet loss, we will increase the robustness of this method by error-correcting and self-synchronising codes. As error-correcting codes, we will use the binary Hamming (7, 4) -codes and for the self-synchronising, we will use T-codes. 1
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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)
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