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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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Measurement of Symmetric Cipher on Low Power Devices for Power Grids
Fujdiak, R.
The symmetric ciphers are often used in low power devices for its low requirements. This article provides a measurement of AES-128 cipher, which should be used for secure communication in power grid (smart grid) networks. We are using as low power devices the microcontroller MSP430 from Texas Instruments. These measurements, deal in this article, should help with implementation of the whole concept of encryption. Concretely, it shows the space left for the other algorithms (as for example elliptic curves algorithm for key distribution, communication protocols etc.)
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The transfer of elliptic curves onto the torus
Bajko, Jaroslav ; Hrdina, Jaroslav (referee) ; Kureš, Miroslav (advisor)
Elliptic curves are an essential part of modern mathematics and play an important role especially in cryptography. The bachelor work focuses on the visualization elliptic curves and group operation in real plane and torus. In the first chapter we will introduce elliptic curves over field of real numbers and above all over prime fields. In order to describe the problematics rigorously the graphical outputs and also the experimental results in the field of discrete elliptic curves will be mentioned. In the next section we will pay a particular attention to topology, functions between topological spaces and to the introduction of the concept of smooth manifold. We will search the suitable functions which can transfer geometrical objects from the real plane onto torus. A software specifically developed for transfering the elliptic curves onto the torus works on the basis of aforementioned functions.
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Qudratic field based cryptography
Straka, Milan ; Žemlička, Jan (referee) ; Stanovský, David (advisor)
Imaginary quadratic fields were first suggested as a setting for public-key cryptography by Buchmann and Williams already in 1988 and more cryptographic schemes followed. Although the resulting protocols are currently not as efficient as those based on elliptic curves, they are comparable to schemes based on RSA and, moreover, their security is believed to be independent of other widely-used protocols including RSA, DSA and elliptic curve cryptography. This work gathers present results in the field of quadratic cryptography. It recapitulates the algebraic theory needed to work with the class group of imaginary quadratic fields. Then it investigates algorithms of class group operations, both asymptotically and practically effective. It also analyses feasible cryptographic schemes and attacks upon them. A library implementing described cryptographic schemes is a part of this work.
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Qudratic field based cryptography
Straka, Milan ; Stanovský, David (advisor)
Imaginary quadratic fields were first suggested as a setting for public-key cryptography by Buchmann and Williams already in 1988 and more cryptographic schemes followed. Although the resulting protocols are currently not as efficient as those based on elliptic curves, they are comparable to schemes based on RSA and, moreover, their security is believed to be independent of other widely-used protocols including RSA, DSA and elliptic curve cryptography. This work gathers present results in the field of quadratic cryptography. It recapitulates the algebraic theory needed to work with the class group of imaginary quadratic fields. Then it investigates algorithms of class group operations, both asymptotically and practically effective. It also analyses feasible cryptographic schemes and attacks upon them. A library implementing described cryptographic schemes is a part of this work.
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