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Modern Asymmetric Cryptosystems
Walek, Vladislav ; Sobotka, Jiří (referee) ; Malina, Lukáš (advisor)
Asymmetric cryptography uses two keys for encryption public key and for decryption private key. The asymmetric cryptosystems include RSA, ElGamal, Elliptic Curves and others. Generally, asymmetric cryptography is mainly used for secure short messages and transmission encryption key for symmetric cryptography. The thesis deals with these systems and implements selected systems (RSA, ElGamal, McEliece, elliptic curves and NTRU) into the application. The application can test the features of chosen cryptosystems. These systems and their performance are compared and evaluated with the measured values. These results can predict the future usage of these systems in modern informatics systems.
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Software support for cryptography system training based on discrete logarithm
Kříž, Jiří ; Zeman, Václav (referee) ; Burda, Karel (advisor)
Current needs of human communication came to status, when most of transferred messages are considered as private and transition over non-secured communication lines in open form is not possible. That originated a lot of different methods for securing of messages and transfers in ciphered form. Two mainstreams were established, symmetric cryptography and asymmetric cryptography. Second of mentioned groups is based on usage of two information – keys, when one of then is broadly known and is public and second, well protected and private. Using a public key it is possible to establish a cryptogram of message, but for deciphering it is necessary to know private key. Asymmetric methods are based on mathematical problems, for which there is not an effective computing algorithm. This thesis are focused for asymmetric cryptosystems based on discrete logarithm problem, where ciphering of message using public key is very easy and quick, but deciphering without knowledge of private key is extremely time consuming process. Work describes a mathematical base of discrete logarithm problem, its’ properties and methods developed for solving of this problem. Descriptions of particular cryptosystems are given, i.e. ElGamal cryptosystem, Diffie-Hellman protocol and DSA. Second part of thesis is focused for web application developed as study support of discrete logarithm problem and of cryptosystems using this problem. It describes functional and graphical interface, work with it and options given to user working with application. Mentions also lessons for user which should help with understanding of described problems and practicing.
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Comparison of public key cryptography algorithms
Mareš, Jiří ; Stanovský, David (advisor) ; Žemlička, Jan (referee)
In the present work we study comparison of basic public key encryption algorithms - RSA, Rabin and ElGamel method. We derive theoretic complexity of encrypting / decrypting of one block and we derive an expected model of its behavior with the key of double size. We also take practical measurements of speed of each algorithm using keys sized 64 - 4096 bits and we statistically analyze the results. We also mention special cases of some algorithms and discuss the advantages and disadvantages of their practical usage. At the end of this thesis we make a comparison of the speed of algorithms and we also compare the measured data with theoretical hypothesis.
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Comparing Groups of Public-Key Ciphers
Lukáš, Martin ; Ivánek, Jiří (advisor) ; Palovský, Radomír (referee)
In this thesis, I introduce several groups of public-key algorithms, the groups being factori-zation problem, discrete logarithm problem, and other problems. I choose one representa-tive algorithm from each group and describe it in-depth, also mentioning certain aspects used in real world implementations and most important attacks. other problems. The objec-tives of this thesis are to compare these groups as well as algorithms in them according to their operational speed, key lengths and resistance against quantum cryptanalysis.
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Comparison of public key cryptography algorithms
Mareš, Jiří ; Stanovský, David (advisor) ; Žemlička, Jan (referee)
In the present work we study comparison of basic public key encryption algorithms - RSA, Rabin and ElGamel method. We derive theoretic complexity of encrypting / decrypting of one block and we derive an expected model of its behavior with the key of double size. We also take practical measurements of speed of each algorithm using keys sized 64 - 4096 bits and we statistically analyze the results. We also mention special cases of some algorithms and discuss the advantages and disadvantages of their practical usage. At the end of this thesis we make a comparison of the speed of algorithms and we also compare the measured data with theoretical hypothesis.
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Modern Asymmetric Cryptosystems
Walek, Vladislav ; Sobotka, Jiří (referee) ; Malina, Lukáš (advisor)
Asymmetric cryptography uses two keys for encryption public key and for decryption private key. The asymmetric cryptosystems include RSA, ElGamal, Elliptic Curves and others. Generally, asymmetric cryptography is mainly used for secure short messages and transmission encryption key for symmetric cryptography. The thesis deals with these systems and implements selected systems (RSA, ElGamal, McEliece, elliptic curves and NTRU) into the application. The application can test the features of chosen cryptosystems. These systems and their performance are compared and evaluated with the measured values. These results can predict the future usage of these systems in modern informatics systems.
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|
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Software support for cryptography system training based on discrete logarithm
Kříž, Jiří ; Zeman, Václav (referee) ; Burda, Karel (advisor)
Current needs of human communication came to status, when most of transferred messages are considered as private and transition over non-secured communication lines in open form is not possible. That originated a lot of different methods for securing of messages and transfers in ciphered form. Two mainstreams were established, symmetric cryptography and asymmetric cryptography. Second of mentioned groups is based on usage of two information – keys, when one of then is broadly known and is public and second, well protected and private. Using a public key it is possible to establish a cryptogram of message, but for deciphering it is necessary to know private key. Asymmetric methods are based on mathematical problems, for which there is not an effective computing algorithm. This thesis are focused for asymmetric cryptosystems based on discrete logarithm problem, where ciphering of message using public key is very easy and quick, but deciphering without knowledge of private key is extremely time consuming process. Work describes a mathematical base of discrete logarithm problem, its’ properties and methods developed for solving of this problem. Descriptions of particular cryptosystems are given, i.e. ElGamal cryptosystem, Diffie-Hellman protocol and DSA. Second part of thesis is focused for web application developed as study support of discrete logarithm problem and of cryptosystems using this problem. It describes functional and graphical interface, work with it and options given to user working with application. Mentions also lessons for user which should help with understanding of described problems and practicing.
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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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