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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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Multipurpose load-bearing timber hall structure
Matuška, Martin ; Sýkora, Karel (referee) ; Straka, Bohumil (advisor)
This Master’s thesis is focused on the design and structural analysis of load-bearing structure of a multipurpose hall that is strained by the permanent load, working load and climatic load. The hall has the shape of an elliptical dome. Maximum margin of the structure is 60,0m and maximum height is 18,0m. Main carrier elements of the structure are radially arranged curved beams made of glued laminated timber, class SA(GL24).
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Elliptic curve based cryptosystems
Křivka, Petr ; Hajný, Jan (referee) ; Stančík, Peter (advisor)
In this bachelor thesis is examined problems elliptic curve cryptosystems. It is described mathematical underground, which use these systems. In more details is analyzed arithmetic finite fields. An important part of this work is the analysis of elliptical curves in cryptography. Among analyzed algorithms include e.g. ECDH or ECDSA. In conclusion is designed software solution, which helps in the study cryptosystems based elliptic curves. It allows basic operations over prime field.
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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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Rings of endomorphisms of elliptic curves and Mestre's theorem
Szásziová, Lenka ; Hrdina, Jaroslav (referee) ; Kureš, Miroslav (advisor)
Eliptické křivky jsou mocným nástrojem dnešní doby. Jednak přispěly k vyřešení mnoha matematických problémů, ale také nalezly četná uplatnění v aplikacích, jako je například kryptografie založená na eliptických křivkách (ECC). Tato metoda veřejného klíče má velkou budoucnost, neboť v mnohém doplňuje nedostatky známé RSA metody. Jedním z hlavních problémů kryptografie založené na eliptických křivkách je určení řádu eliptické křivky, tedy výpočet počtu bodů eliptické křivky nad prvočíselným polem. Tomuto zásadnímu problému je věnována tato práce. Na určení řádu eliptické křivky existuje řada algoritmů. Pro menší prvočísla (čili pro charakteristiku prvočíselného pole) se užívá metoda založená na přímém výpočtu, tzv. naivní algoritmus. Velkou pomocí v této problematice je Hasseho teorém, který omezuje řád eliptické křivky intervalem. Pro větší prvočísla se s úspěchem používají Shanksův algoritmus a jeho vylepšení Mestreho algoritmus. Oba algoritmy mají dvě části - Baby Step a Giant Step. Shanksův algoritmus je však v určitých případech nepoužitelný a tento problém řeší Mestreho algoritmus, který používá pojem twist eliptické křivky. Díky Mestreho teorému bylo dokázáno, že řád eliptické křivky nad prvočíselným polem muže být spočten pro každé prvočíslo vetší než 457. Důkaz, který spočívá především v isomorfismu okruhu endomorfismů nad eliptickými křivkami a imaginárního kvadratického řádu, je uveden na závěr této práce.
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Electromagnetic analysis
Kolofík, Josef ; Reichert, Pavel (referee) ; Martinásek, Zdeněk (advisor)
This thesis deals with electromagnetic analysis and applications of electromagnetic side channel. The first and second part describes the basics of cryptography, function of cryptographic module and side-channel attacks. The third part discusses the electromagnetic analysis, construction of probe, a description of the laboratory workplace, the electromagnetic emission of PIC16F84A, AES and preparation for laboratory measurements. The fourth part describes specific laboratory measurements and extracting the useful signal. In the fifth part of the thesis presents the results of processing the measured values, the outputs generated by scripts and found the link between measured curves and AES encryption key. In the sixth part of the thesis are analyzed the basics of defense against side channel attack.
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Prestressed membranes above circular and elliptical plan
Juchelková, Pavlína ; Hájek,, Petr (referee) ; Bažant, Zdeněk (referee) ; Fillo,, L´udovít (referee) ; Stráský, Jiří (advisor)
This doctoral thesis deals with suspension cable roof structures above a circular and elliptical plan. The methodology of analysis is based on a basic annular cable roof structure of an external diameter of 70 m. The roof structure is designed as a prestressed membrane from the precast panels made from lightweight structural concrete which are supported with the bearing and prestressing tendons that are radially led between the two peripheral rings. The structural arrangement and the process of construction are described. The static system is specified and the terms like self-anchored system or equilibrium state are also defined. Finally, the results of static analysis are discussed in detail. The main aim of the doctoral thesis is to design a roofing of football stadium terraces using the structures of a basic annular cable roof; and present two alternatives – above circular and elliptical plan. The circular alternative comes directly from basic annulus, only the main dimensions of the new-designed structure are correspondingly extended. The elliptical alternative is an alteration of the circular design. As the radial tendons are anchored to the flexible peripheral curved girders, and the structures form the self-anchored system, the horizontal tendon forces load the peripheral girders radially. Because of that, it is essential to design a state of stress in tendon to prevent the undesirable global bending moments on the peripheral girders, and subsequently large non-uniform horizontal and vertical displacements of structure. Therefore, a study of the optimal load of ellipse is carried out. On the basis of the study, two basic requirements to structural arrangement of the elliptical roof are formulated. To illustrate the importance of a correct design, the optimal and unsuitable structural arrangements are compared. Finally, the results of static analysis of the circular and elliptical roof are again discussed in detail.
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