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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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Smart's algorithm
Sladovník, Tomáš ; Příhoda, Pavel (advisor) ; Šťovíček, Jan (referee)
The discrete logarithm problem is one of the most common trap- door functions in asymmetric cryptography and the use of elliptic curves over a finite field with prime characteristics seems to be a very efficient platform. This paper addresses the solution of a special type of elliptic curves where the number of points is equal to the characteristic of a field. Our goal is to construct a linear algorithm in goup operations and prove correctness. In order to create the algorithm, we will implement p-adic numbers, introduce the theory of formal groups and the formal logarithm and subgroups of an elliptic curve over the field of p-adic numbers. We will show that this type of curves is absolutely useless for cryptography because these curves are not safe. 1
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Generic algorithms
Snítilá, Jitka ; Příhoda, Pavel (advisor) ; Jedlička, Přemysl (referee)
This thesis focuses on the lower bounds for generic algorithms for discrete logarithms problem and Diffie-Hellman's problems. This thesis introduces two diffrent models of Black-Box for that purpose. On these models thesis approxi- mates and compares success probability of generic algorithms for given problems including Maurer's reduction. This reduction solves discrete logarithms problem using a appropriate elliptic curve and a Diffie-Hellman's oracle. This thesis also researches generic algorithm for identifiaction schemes, that are based on discrete logarithms problem. 1
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Smart's algorithm
Sladovník, Tomáš ; Příhoda, Pavel (advisor) ; Šťovíček, Jan (referee)
The discrete logarithm problem is one of the most common trap- door functions in asymmetric cryptography and the use of elliptic curves over a finite field with prime characteristics seems to be a very efficient platform. This paper addresses the solution of a special type of elliptic curves where the number of points is equal to the characteristic of a field. Our goal is to construct a linear algorithm in goup operations and prove correctness. In order to create the algorithm, we will implement p-adic numbers, introduce the theory of formal groups and the formal logarithm and subgroups of an elliptic curve over the field of p-adic numbers. We will show that this type of curves is absolutely useless for cryptography because these curves are not safe. 1
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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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