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Elliptic curves and primality testing
Haníková, Adéla ; Drápal, Aleš (advisor) ; Šťovíček, Jan (referee)
The aim of the thesis is to desribe and implement the elliptic curve factorization method using curves in Edwards form. The thesis can be notionally divided into two parts. The first part deals with the theory of Edwards curves especially with properties of elliptic function fields. The second part deals with the factorization algorithm using Edwards form both formally and practically in the way the algorithm is really implemented. The contribution of this thesis is the enclosed implementation of the elliptic curve factorisation algorithm which can be run on a graphic card and which is faster than the state-of-the-art implementation GMP-ECM. Powered by TCPDF (www.tcpdf.org)
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Electronic ID Cards
Mravec, Roman ; Burda, Karel (referee) ; Hajný, Jan (advisor)
This master thesis deals with an implementation of Diffie-Hellman protocol on smart card which is based on MULTOS OS. Defines the smart cards based on MULTOS OS and their usage. Output of this thesis are applications for a smart card and for a client using Diffie-Hellman protocol for establishing of a secret key between two communication sides through unsecured communication channel.
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Primality testing using elliptic curves
Pashchenko, Olha ; Barto, Libor (advisor) ; Šťovíček, Jan (referee)
In the present work we study primality tests. A primality test is an algorithm for determining whether an input number is prime. In the first part of this work we recapitulate the basic definitions and facts about number theory and study Pocklington's algorithm, that based on the group (Z/nZ)∗ . Then we study Generalized Pocklington's primality test and Pépin's primality test for Fermat numbers. In the second part of this work we represent the basic definitions and facts about elliptic curves. Then we study Goldwasser-Killian primality test, that based on elliptic curves. One part of this work is experementation with Goldwasser-Killian primality test. 1
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Post-quantum alternative to secure sockets
Behún, Marek ; Kratochvíl, Miroslav (advisor) ; Kofroň, Jan (referee)
The goal of this thesis is to implement a software library that provides a wrapping of real-time socket- like communication into an cryptographic protocol with purpose similar to SSL or TLS, that is secure against an adversary in possession of a quantum computer. Resulting software utilizes the Supersingular Isogeny Diffie Hellman (SIDH) key-exchange algorithm for achieving this level of security, and is simple, portable and independent on system-specific primitives. The thesis gives a concise introduction to the theory on which SIDH is built, targeting the audience of undergraduate students of Computer Science. Powered by TCPDF (www.tcpdf.org)
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BitCoin Wallet for Windows Phone Platform
Prokop, Tomáš ; Grégr, Matěj (referee) ; Veselý, Vladimír (advisor)
Master's thesis deals with description of a new trading system known as BitCoin. Bitcoin is a unique type of virtual cash in the current world without the influence of large corporations. The system is protected through the use of cryptographic methods that are discussed in detail. The work explains the principles of integrity of transactions exchange transactions and the acquisition of new money through so-called miners. Individual miners services are mediated through software clients including a description of mining. The paper focuses on protocols for communication. It analyzes the different types of software purses for platforms Windows, Linux and Android. Examining reengineering of purses for Android. This document in no small part discusses the implementation own wallets for the Windows Phone platform 8th.
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Parallelization of Integer Factorization from the View of RSA Breaking
Breitenbacher, Dominik ; Henzl, Martin (referee) ; Homoliak, Ivan (advisor)
This paper follows up the factorization of integers. Factorization is the most popular and used method for RSA cryptoanalysis. The SIQS was chosen as a factorization method that will be used in this paper. Although SIQS is the fastest method (up to 100 digits), it can't be effectively computed at polynomial time, so it's needed to look up for options, how to speed up the method as much as possible. One of the possible ways is paralelization. In this case OpenMP was used. Other possible way is optimalization. The goal of this paper is also to show, how easily is possible to use paralelizion and thanks to detailed analyzation the source codes one can reach relatively large speed up. Used method of iterative optimalization showed itself as a very effective tool. Using this method the implementation of SIQS achieved almost 100 multiplied speed up and at some parts of the code even more.
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Modern Asymmetric Cryptosystems
Walek, Vladislav ; Sobotka, Jiří (referee) ; Malina, Lukáš (advisor)
Asymmetric cryptography uses two keys for encryption public key and for decryption private key. The asymmetric cryptosystems include RSA, ElGamal, Elliptic Curves and others. Generally, asymmetric cryptography is mainly used for secure short messages and transmission encryption key for symmetric cryptography. The thesis deals with these systems and implements selected systems (RSA, ElGamal, McEliece, elliptic curves and NTRU) into the application. The application can test the features of chosen cryptosystems. These systems and their performance are compared and evaluated with the measured values. These results can predict the future usage of these systems in modern informatics systems.
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Elliptic curve cryptography in comparison with other representatives of asymmetric cryptography
Stašek, Filip ; Ivánek, Jiří (advisor) ; Palovský, Radomír (referee)
The aim of this thesis is to explain theoretical and mathematical point of view the principle of elliptic curve cryptography, which at present appears as the most petential representative of asymmetric cryptography. The introduction describes basic mathematical assumptions and knowledge which are used in cryptography and in other parts of the thesis we build on them. I visualize elliptic curve cryptosystem, describe the mathematical principle of operation and then show algorithm, which is based cryptosystem. Thesis will continue comparing this cryptosystem with key members of the asymmetric cryptography. These are algorithms RSA and ElGamal. Comparison of these cryptosystems effect mainly from the theoretical point of view and with the help of complexity theory compare time-consuming and subsequently safety aforementioned cryptosystems . Finally, I point to the indisputable benefits of elliptic curve cryptography consisting in the greater security and speed.
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