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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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Alternative methods in cryptology
Hampl, Dalibor ; Doležel, Radek (referee) ; Hajný, Jan (advisor)
In the first part of this thesis explains, what is generally cryptography, generally analyze the problem of the current encryption methods. These include asymmetric, symmetric and hybrid encryption methods. The second part focuses on the theory of lattices and their main mathematical problems, then the shortest vector problem, the closest vector problem, the approximate shortest vector problem and the approximate closest vector problem. Mathematically difficult problems of lattice are used in an encryption method GGH for asymmetrically encrypted communications method and GGH for digital signatures. It explains mathematical methods, which use these encryption methods. Another part of this thesis deals with the encryption method and the establishment of XTR on Diffie-Hellman protocol, thus XTR-DH. It explains mathematical methods, which use methods XTR, XTR-DH and Diffie-Hellman protocol. There are shown the main mathematical problems for this part of thesis DHP (Diffie-Hellman problem) and DLP (discrete logarithm problem). The fourth part focuses on a program designed to demonstrate the GGH encryption method for asymmetrically encrypted communications. Describes the structure, functionality, graphical part of the program and shows to a user interface. Students can test how the GGH encryption method behave when entering different input values. During the work with the program, the user should obtain sufficient information to understand the principles of this encryption method.
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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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Electronic geocaching
Pavel, Lukáš ; Babnič, Patrik (referee) ; Burda, Karel (advisor)
The goal is to design and implement a concept of electronic geocaching with contactless smart card and cell phone with NFC interface. In the first chapter I describe geocaching and try to familiarize the reader with this game. The second chapter deals with the issue of smart cards, I describe here the contact and contactless cards and their security. In the third chapter, I describe use and security of radio communication interface NFC. In the fourth chapter, I describe the principles of symmetric and asymmetric cryptography and selected cryptographic techniques. In the fifth chapter is description of proposed solution for electronic geocaching with digital signature. The last chapter describes all created applications.
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Digital certificates and certificate authorities
Lepa, Ondřej ; Hajný, Jan (referee) ; Člupek, Vlastimil (advisor)
This diploma thesis deals with certification and certification authorities, certification path PKI and principles of its validation and security. Also deals with structure of certificate itself and possible misuse of included information. Moreover, possibility of misues of third party certificates and proclamation of untrusted certificate to client's system.
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Efficient Digital Signature Schemes
Varga, Ondrej ; Sobotka, Jiří (referee) ; Malina, Lukáš (advisor)
Digital signatures, which take the properties of classical signatures, are used to secure the actual content of documents, which can be modified during transmission over an insecure channel. The problems of security and protection of communicating participants are solved by cryptographic techniques. Identity verification, message integrity, credibility, the ownership of documents, and the secure transmission of information over an unsecured channel, are all dealt with in secure communications - Public Key Infrastructure, which uses digital signatures. Nowadays digital signatures are often used to secure data in communication over an unsecured channel. The aim of the following master’s thesis is to familiarize readers with the necessary technological aspects of digital signatures, as well as their advantages and disadvantages. By the time digital signatures are being used they will have to be improved and modified to be secure against more sophisticated attacks. In this paper, proposals of new efficient digital signature schemes and their comparison with current ones are described. Also are examined their implications for computationally weak devices, or deployment in low speed channel transmission systems. After an explanation of cryptography and a description of its basic subjects, digital signatures are introduced. The first chapter describes the possible formatting and architecture of the digital signature. The second part of this master’s thesis is about current digital signature schemes and their properties. Chapter 3 describes some proposals of new efficient digital signature schemes and their comparison to those currently in use. In the practical part, the implementations (in the environment .NET in C#) of two effective digital signature schemes as part of a client-server application are presented and described (Chapter 4). In the last chapter the comparison and analysis of the implemented signature schemes are provided.
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Digital signature
Vaverka, Aleš ; Lambertová, Petra (referee) ; Zeman, Václav (advisor)
Digital signature, the subject of this semester paper, is nowadays very up-to-date. The still rising capabilities of the internet and the vision of lowering the amounts of paper documentation made it necessary to develop a way of signing documents which are transferred through the internet. This is supposed to be equally safe and unassailable as the handwritten signature. This method is called the digital signature. The paper focuses on the explanation of the essential terms connected to digital signature, such as certificate, certification authority, authentication, but in particular on the elementary cryption algorithms, further on applications that make use of digital signature, e.g. post services and electronic banking. In the final chapter, the positive and negative aspects of the electronic signature are discussed.
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Software support of education in cryptography based on integer factorization
Vychodil, Petr ; Martinásek, Zdeněk (referee) ; Burda, Karel (advisor)
This thesis deals with new teaching software, which supports asymmetric encryption algorithms based on the issue of large numbers´ factorization. A model program was created. It allows to carry out operations related to encryption and decryption with an interactive control. There is a simple way to understand the principle of the RSA encryption method with its help. The encryption of algorithms is generally analysed in chapters 1,2. Chapters 3 and 4 deals with RSA encryption algorithm in much more details, and it also describes the principles of the acquisition, management and usage of encryption keys. Chapters 5 suggest choosing of appropriate technologies for the creation of the final software product, which allow an appropriate way to present the characteristics of the extended RSA encryption algorithm. The final software product is the java applet. Aplet is described in the chaprers 6 and 7. It is divided into a theoretical and practical part. The theoretical part presents general information about the RSA encryption algorithm. The practical part allows the users of the program to have a try at tasks connected with the RSA algorthm in their own computers. The last part of Java applet deals with the users´ work results. The information obtained by the user in the various sections of the program are satisfactory enough to understand the principle of this algorithm´s operations.
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Application for digital signature and timestamping
Remiaš, Miroslav ; Burda, Karel (referee) ; Lambertová, Petra (advisor)
In general, the Internet represents an unsecured medium of data transfer. Besides the rising popularity of the Internet, the matters of safety are getting to the foreground of importance. Anybody would be able to gain access to the computer network or to other valuable information if no algorithm of verifying the genuineness of identity were used. It is necessary to secure not only the access to the documents but also the content itself, which could be modified during the transfer through an unsecured medium. Last but not least, without the discretion provided by cryptography, the information may become literally public. To provide security and protection for the communicating participants the problems mentioned above are solved with the help of cryptographic techniques. The verification of the identity and the integrity of messages, the credibility of document’s ownership and safe data transfer through an unsecured medium are all the aspects, which the field of communication security on the Internet, thus the public key infrastructure, deals with. The electronic signature, as a part of the security area, is one of many advertised themes nowadays in Czech Republic. The aim of this master’s thesis is to acquaint the reader with the necessary technological procedures of digital signature, such as cryptographic techniques, public key infrastructure and timestamp. The practical part of this thesis consists of a suggested implementation of a web application in the programming language ASP.NET, which forms a certification authority with an opportunity of claiming a timestamp to authorize timestamps. After the problematic of cryptography was explained in the first chapter, the term of electronic signature has been introduced in the second chapter. Very important information, as far as the electronic signature of documents is concerned, is the time of the document’s creation and the subsequent signature verification by an appropriate authority. So the following part of the thesis is dedicated to the timestamp and to the authority of its verification. The fourth section deals with the large scale of public key infrastructure. The fifth part focuses on the description of the support for the whole problem mentioned so far using Microsoft’s programming language ASP.NET. The final sixth chapter represents the practical part of the thesis, namely the web application itself, where the individual modules of the application with its functions are described.
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Lab of public key infrastructure
Slavík, Petr ; Lambertová, Petra (referee) ; Burda, Karel (advisor)
The aim of this thesis is to study and describe the theme of Public Key Infrastructure (PKI). Within the scope of minute PKI characterization there is a gradual depiction of particular structural elements, which are above all represented by cryptographic operations (asymetric and symetric cryptography, hash function and digital signature); then, there are also individual PKI subjects that are dealt with, like eg. certification authority, certificates, security protocols, secure heap etc. Last but not least there are a few complete Public Key Infrastructure implementation solutions described (OpenSSL, Microsft CA). The practical part of the thesis, a lab exercise, gives potential students the knowledge of installing OpenSSL system based certification authority. The next task educate students how to secure web server with certificate signed with own CA and also how to secure web server users‘ access control through certificates signed by the previously installed CA.
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