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The Botanical Pavillion in Brno
Rusoňová, Nikola ; Hron, Lukáš (referee) ; Šmak, Milan (advisor)
Master´s thesis describes the design and check of the construction of botanical pavillion in Brno. The structure has an elliptical ground plan with dimensions 34 x 20 m, height of 9 m. The supporting structure consists of 16 support curved ribs which are braced at the top of the elliptical steel ring. Between the ribs are inserted purlins which support the perimeter cladding. The supporting structure is designed as an alternative system as girders of glued laminated timber and as system of steel truss girders.
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Elliptic curves in cryptography
Geyer, Lukáš ; Burda, Karel (referee) ; Lambertová, Petra (advisor)
The objective of this bachelor thesis is to decribe the role of the elliptic curves in modern cryptosystems, explain the mathematical fundamentals upon which the elliptic curves are based along with their advantages and disadvantages, followed by application in the digital signature. The project is concluded by a software solution demonstrating the use of elliptic curves in digital signature scheme ECDSA
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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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Efektivní aritmetika eliptických křivek nad konečnými tělesy
Skalický, Jakub ; Krhovják, Jan (advisor) ; Drápal, Aleš (referee)
The thesis deals with arithmetics of elliptic curves over finite fields and methods to improve those calculations. In the first part, algebraic geometry helps to define elliptic curves and derive their basic properties including the group law. The second chapter seeks ways to speed up these calculations by means of time-memory tradeoff, i.e. adding redundancy. At last, the third part introduces a wholly new curve form, which is particularly effective for such purposes.
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Cryptographic schemes based on the discrete logarithm problem
Kadlček, Tomáš ; Holub, Štěpán (advisor) ; Růžička, Pavel (referee)
In the paper we try to give a view of the discrete logarithm problem, especially of related problems that appear in literature since 2001. These problems are based on a computation of Weil and Tate pairing on eliptic curves. We give a view of these problems including some reductions. We mention some chosen schemes based on these problems that are iteresting because of their practical parametrs, primaci of security proofs or because these schemes introduced the new problem. We try to cover precisely the most important definitions in this sector of cryptography because these definition are omitted in the literature and it is often left up to reader to presume details by himself.
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Software support of education in cryptography area based on elliptic curves
Szturc, Jakub ; Sobotka, Jiří (referee) ; Burda, Karel (advisor)
The master‘s thesis is focusing on cryptography based on elliptical curves consists of four main parts. The first part provides an overview of the basic cryptographic and mathematical concepts. A key element of this work is the second part which are described in detail the mechanisms of counting two points on elliptic curve and counting point to themselves over the various fields. On this mechanism is based almost the entire issue. In the third section provides the best-known algorithms and protocols for key exchange, encryption and digital signature. The goal of this paper is to devise software to support teaching. This material is created as a web presentation, which described the theoretical foundations and the main characteristics of cryptosystems based on elliptical curves. The whole issue is supported by practical examples of calculations examples, there are also examples for independent work. Additionally, java applets are prepared that allow an interactive opportunity to try the basic parameters of curves, or verify the calculations.
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Latest trends in public-key cryptography
Tvaroh, Tomáš ; Ivánek, Jiří (advisor) ; Palovský, Radomír (referee)
The goal of this thesis is to describe principles of public-key cryptography, introduce and compare latest algorithms for asymmetric encryption and point out their advantages over the most popular cryptosystem - RSA. At the beginning, this thesis describes the evolution of public-key cryptography, its differences compared to symmetric-key cryptography and possibilities of using it for data encryption and digital signature. Mathematical background as well as principles of RSA are described afterwards. At the end, this thesis focuses on the latest algorithms on the basis of eliptic curves and their advantages over the most common algorithms are pointed out. The comparison is then summarized and a recommendation for the best cryptosystem is offered.
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Modern access control system
Vomáčka, Martin ; Hajný, Jan (referee) ; Malina, Lukáš (advisor)
The thesis describes the design of scheme for access system with user authentication via smart cards. The first chapter explains various types of identification items used for authentication of users and different types of readers and terminals, followed by chapter 2 with a deeper insight on smart cards with focus on their types, what internal structure and principle of communication with card readers are used, etc. with primary focus on Java cards. The third chapter describes Java Card cryptography - especially elliptic curve cryptography used on this platform. The fourth part focuses on PACE protocol with subsections dedicated to the individual parts of the protocol and its applicability to smart cards environment. Chapter 5 explains the proposed design of the authentication scheme elaborated in the thesis, including a detailed description of specific parts, their funcionality and exemplary usage in the created applications.
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