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Web application on pairing-based cryptography
Mogrovics, Alexander ; Dzurenda, Petr (oponent) ; Ricci, Sara (vedoucí práce)
The aim of this thesis is to shed some light on elliptic curve cryptography via web application. It follows mathematical and algebraic principles of establishing elliptic curves over finite fields, performing computations over them and establishing bilinear pairings. It also describes the architecture and implementation of the web application, which uses website template with embedded SageMathCell in order to minimize required space. This application allows the user to preform computation of points on elliptic curve over finite field and their plot, plot of an elliptic curve over real numbers, operations over points of elliptic curves, to establish bilinear pairing, to establish 3-way Diffie--Hellman key exchange and to conduct a MOV attack.
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End-to-end encryption protocol for IEEE 802.15.4
Bača, Jaromír ; Člupek, Vlastimil (oponent) ; Krajsa, Ondřej (vedoucí práce)
This thesis explores the topic of encryption of communication between low-voltage de-vices that are controlled by microcontrollers. Two deRFnod development boards wereused in the work, which were equipped with AVR ATmega 128 RFA1 chips, which en-able wireless communication. The application was developed and tested on these devices.The final output of the work is the design of an application for asymmetric key exchange,which is based on elliptic curves. This application is implanted in Atmel LightWeight,where the issue of mutual communication between communicating points is also ad-dressed. The generated key is also used to propagate communication using the AESencryption algorithm, which is already implemented in the used LightWeigt protocol.This encryption allows not only encryption of endpoints, but also of the communicationtunnel. Such protection provides users with anonymity of data and makes it impossibleor very difficult for potential attackers to physically locate devices based on knowledgeof data routing on the network.
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Benchmarks With Points On Elliptic Curves
Brychta, Josef
This paper deals with benchmarks of generating random points and arithmetic operations with points on elliptic curves. These benchmarks were implemented on the hardware platforms Raspberry Pi Zero/1/2/3. The primary goal was to measure usage of the system resources and energetic consumption of that hardware platform. Specifically, it was memory and time consumption of Raspberry. In total, 48 elliptic curves of standards NIST, BRAINPOOL, GOST and FRP were measured.
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Kryptografie na výkonově omezených zařízeních
Hlinka, Jan ; Dzurenda, Petr (oponent) ; Hajný, Jan (vedoucí práce)
Tato práce popisuje implementaci strany ověřovatele, revokační autority a vydavatele pro atributovou autentizaci pomocí čipové karty a terminálu v podobě výkonově omezeného zařízení. Vybrané schéma, RKVAC, slouží k realizaci atributové autentizace, tedy autentizace se záměrem ochránit citlivá osobní data uživatele. Schéma vyhovuje principům Privacy by Design a Privacy by Default, které jsou součástí nařízení, jako je například GDPR (General Data Protection Regulation) a eIDAS (Electronic Identification and Trust Services).
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Cryptographic Protection of Digital Identity
Dzurenda, Petr ; Švenda,, Petr (oponent) ; Castella-Roca, Jordi (oponent) ; Hajný, Jan (vedoucí práce)
The doctoral thesis deals with privacy-preserving cryptographic schemes in access control and data collection areas. Currently, card-based physical access control systems are used by most people on a daily basis, for example, at work, in public transportation and at hotels. However, these systems have often very poor cryptographic protection. For instance, user identifiers and keys can be easily eavesdropped and counterfeited. Furthermore, privacy-preserving features are almost missing and, therefore, user’s movement and behavior can by easily tracked. Service providers (and even eavesdroppers) can profile users, know what they do, where they go, and what they are interested in. In order to improve this state, we propose four novel cryptographic schemes based on efficient zero-knowledge proofs and elliptic curve cryptography. In particular, the thesis presents three novel privacy-friendly authentication schemes for access control and one for data collection application scenarios. The first scheme supports distributed multi-device authentication with multiple Radio-Frequency IDentification (RFID) user’s devices. This feature is particularly important in applications for controlling access to dangerous areas where the presence of protective equipment is checked during each access control session. The other two presented schemes use attribute-based approach to protect user’s privacy, i.e. these schemes allow users to anonymously prove the ownership of their attributes, such as age, citizenship, and gender. While one of our scheme brings efficient revocation and identification mechanisms, the other one provides the fastest authentication phase among the current state of the art solutions. The last (fourth) proposed scheme is a novel short group signature scheme for data collection scenarios. Data collection schemes are used for secure and reliable data transfer from multiple remote nodes to a central unit. With the increasing importance of smart meters in energy distribution, smart house installations and various sensor networks, the need for secure data collection schemes becomes very urgent. Such schemes must provide standard security features, such as confidentiality and authenticity of transferred data, as well as novel features, such as strong protection of user’s privacy and identification of malicious users. The proposed schemes are provably secure and provide the full set of privacy-enhancing features, namely anonymity, untraceability and unlinkability of users. Besides the full cryptographic specification and security analysis, we also show the results of our implementations on devices commonly used in access control and data collection applications.
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Generování eliptických křivek pro kryptografický protokol
Herbrych, Daniel ; Hajný, Jan (oponent) ; Fujdiak, Radek (vedoucí práce)
Tato práce má za cíl vytvořit generátor eliptických křivek pro kryptografický protokol. Je k tomu použita knihovna MIRACL a jazyk C++. Jedním ze stěžejních problémů je určení řádu grupy eliptické křivky. Pro toto se používá algoritmus SEA (Schoof Elkies Atkin), dle toho je tak metoda napříč zdroji zvána jako metoda počítání bodů na křivce, SEA metoda, případně i jinak. Druhou metodou pro generování je metoda komplexního násobení (complex multiplication, zkráceně CM). Obě jsou v generátoru k dispozici. Byla měřena závislost rychlosti základních operací nad eliptickou křivkou na velikosti křivky a také na jednotlivých parametrech křivky. Bylo implementováno hybridní schéma ECIES jako praktické ověření funkčnosti generátoru. Dále byly měřeny rychlosti ECIES šifrování a dešifrování v závislosti na různých parametrech, např. velikost křivky, jakou metodou byla křivka vygenerována, velikost zprávy a další.
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Side-channel analysis
Novosadová, Tatiana ; Lieskovan, Tomáš (oponent) ; Gerlich, Tomáš (vedoucí práce)
This thesis deals with an issue of side channels, elliptic curves and their implementation in algorithms. Theoretical part is aimed at describing the basic concepts and various possibilities of side-channel attacks, with a more detailed focus on power analysis. The second theoretical part is focused on describing methods of elliptic curves and different elliptic curves-based protocols. The practical part deals with implementation of such cryptosystem on smart card, using the experimental environment to measure power consumption and analysis of this consumption.
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Proposal Of Cryptographic Elliptic Curves
Generator
Herbrych, Daniel
This paper deals with creation of elliptic curves generator. The purpose is generating disposable elliptic curves for cryptographic protocol. Miracl library is used. The most important issue is to determine the order of the elliptic curve group. SEA algorithm (Schoof–Elkies–Atkin) is used for this purpose. The second goal is to find suitable elliptic curves for the cryptographic purposes.
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Eliptické křivky nad konečnými tělesy
Beran, Adam ; Šťovíček, Jan (vedoucí práce) ; Žemlička, Jan (oponent)
V této práci se zabýváme teorií eliptických křivek, zvláštní pozornost věnujeme eliptickým křivkám nad konečnými tělesy. Představíme základní teorii, zohled- níme přitom několik technických aspektů (singularita křivky, vliv charakteristiky tělesa na rovnici křivky). Algebraicky odvodíme a zformulujeme grupový zákon neboli definici operace sčítání na množině bodů na eliptické křivce. Dále zpracu- jeme důkaz známého faktu, že množina bodů na eliptické křivce spolu s operací sčítání tvoří komutativní grupu. K důkazu přistoupíme elementárně, některé vý- počty z důvodu jejich náročnosti provedeme v počítačovém programu Mathema- tica. Nakonec studujeme endomorfismy eliptických křivek nad konečnými tělesy (homomorfismy na množině bodů eliptické křivky, jež jsou zadané racionálními funkcemi). Pomocí získaných výsledků dokážeme Hasseho větu, která poskytuje odhad na řád grupy bodů na eliptické křivce nad konečným tělesem. 1
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