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Goppa codes and their applications
Kotil, Jaroslav ; Drápal, Aleš (advisor) ; Šťovíček, Jan (referee)
Title: Goppa codes and their applications Author: Bc. Jaroslav Kotil Department: Department of algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: In this diploma paper we introduce Goppa codes, describe their para- metres and inclusion in Alternant codes, which are residual Generalized Reed- Solomon codes, and Algebraic-geometry codes. Aftewards we demonstrate deco- ding of Goppa codes and introduce Wild Goppa codes. We also describe post- quantum cryptography member: McEliece cryptosystem for which no effective attacks with quantum computers are known. We outline a usage of this crypto- system with Goppa codes and describe the security of the cryptosystem together with possible attacks of which the most effective ones are based on information- set decoding. Keywords: Goppa codes, Generalized Reed-Solomon codes, Algebraic-geometry codes, Post-quantum cryptography, McEliece cryptosystem 1
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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)
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Post-Quantum Ciphers
Novosadová, Tatiana ; Ricci, Sara (referee) ; Hajný, Jan (advisor)
Národný inštitút pre štandardy a technológie (NIST) zahájil proces na získanie, vyhodnotenie a štandardizáciu jedného alebo viacerých kryptografických algoritmov využívajúcich verejný kľúč prostredníctvom verejnej súťaže. Cieľom tejto dimplomovej práce je naštudovať dostupné postkvantové algoritmy pre ustanovenie kľúča, ktoré boli zverejnené v treťom kole tejto súťaže. Po dôkladnej analýze a porovnaní bol jeden zo študovaných algoritmov implementovaný s využitím knižníc dostupných pre daný algoritmus, následne bol program optimalizovaný a zdokumentovaný.
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Cryptoanalysis of a Post-quantum Cryptography Algorithm
Štumpf, Daniel ; Hojsík, Michal (advisor) ; Příhoda, Pavel (referee)
National Institute of Standards and Technology (NIST) is currently running a stan- dardization process for a post-quantum cryptography primitives. Depending on the al- gorithms building blocks these primitives can be divided into five categories. In the first part of this thesis we described all five categories and compared their characteristics. The most important aspect of the schemes for NIST is security against both classical and quantum adversaries. We chose one of the five categories (namely, we picked lattice- based cryptosystems) for further cryptanalysis. As we think that the security analysis of some of the second round candidates in the NIST standardization project is not suffi- ciently well described in their specification documents and some known attacks are not considered at all, we provide a unified security analysis of these schemes. We described two currently known attacks (primal and dual attacks) against lattice-based schemes, estimated cost of these attacks against the lattice-based candidates in the second round of the NIST standardization project and compared these values with the security claimed by these candidates. In most cases our estimations matches those published in the speci- fication documents and therefore we conclude that the security estimates claimed by the candidates are...
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Securing Narrowband Wireless Communication In Licensed Band
Kolaja, David
With everlasting growth of development of devices in the Internet of Things, there is also a difficulty to keep up with the requirements of security-related topics on such devices. This is no exception for expanding the scale of Low Powered Wide Area Network (LPWAN) devices which communicate over Narrowband IoT. Such devices have constrained computing power. Thus developers of these devices are limited to use as much as possible for the implementation of functions, not having enough space for securing its communication. This article focuses on how to possibly secure these communications.
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Post-quantum cryptography on constrained devices
Matula, Lukáš ; Dzurenda, Petr (referee) ; Malina, Lukáš (advisor)
In recent years, there has been a lot of technological development, which among other things, brings the designs and implementation of quantum computing. Using Shor’s algorithm for quantum computing, it is highly likely that the mathematical problems, which underlie the cryptographic systems, will be computed in polynomial time. Therefore, it is necessary to pay attention to the development of post-quantum cryptography, which is able to secure systems against quantum attacks. This work includes the summary and the comparison of different types of post-quantum cryptography, followed by measuring and analysing its levels of difficulty in order to implement them into limited devices, such as smart cards. The measured values on the PC are used to determine the most suitable implementation on the circuit card and then the verification method itself is implemented on it.
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Securing narrowband wireless communication in licensed band
Kolaja, David ; Brychta, Josef (referee) ; Fujdiak, Radek (advisor)
Contemporary demand for mobile devices and development of devices in the Internet of Things is constantly increasing. This reality also raises concerns about security and privacy of ongoing communication. This is no exception for expanding scale of Low Powered Wide Area Network (LPWAN) devices which communicate over Narrowband IoT and the customer of such devices who has to rely on security of provider’s network to secure customer’s data. This security is effective only in operator’s network while there is no end-to-end encryption enabled. Therefore, this thesis deals with the analysis of NB-IoT communication and its possible end-to-end security proposal, which also provides elements of post-quantum algorithms. Last but not least, this thesis deals with application of this proposal on constrained device and evaluation of its effectivness of time, energy and memory demands.
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A study on ``A New Public-Key Cryptosystem via Mersenne Numbers''
Richter, Filip ; Göloglu, Faruk (advisor) ; El Bashir, Robert (referee)
In 2016 NIST announced a start of a process of development and standardiza- tion of a post-quantum public-key encryption scheme. Mersenne-756839 was one of the proposals. This proposal is described in this thesis, as well as the known attacks against it. The description and the theoretical background behind these attacks are presented in a rigorous way and are accessible to the reader without any previous knowledge about the post-quantum cryptography. New additional ideas for the implementation of the attacks are also presented. Finally, these attacks are implemented and attached to the thesis. 1
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Security and Privacy on Android Devices
Michalec, Pavol ; Dzurenda, Petr (referee) ; Malina, Lukáš (advisor)
The bachelor thesis is about Android security. The main goal is to get acquainted with the security and cryptographic features of Android OS and then implement the knowledge gained into file encryption application. The theoretical part will familiarize readers with the new security mechanisms in Android 6, 7 and 8. We will also be dealing with malware and other forms of Android OS attacks. In the practical part, we will evaluate the cryptographic capabilities of Android as well as compare several libraries and applications for cryptography. Finally, we create our own cryptographic application with support for symmetric, asymetric and post-quantum cryptography.
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