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Two types of septic trinomials and their use in hyperelliptic cryptography
Felcmanová, Adéla ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This thesis deals with two types of septic trinomials and genus three hyperelliptic curves constructed from them. It includes an introduction to the theory of hyperelliptic curves and divisors, as well as terms and algorithms necessary for their implementation in hyperelliptic cryptosystems. The principle of the hyperelliptic curve cryptography is presented along with two examples of cryptosystems. It also contains several exercises, some of which were programmed in Python language.
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Two types of septic trinomials and their use in hyperelliptic cryptography
Felcmanová, Adéla ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This thesis deals with two types of septic trinomials and genus three hyperelliptic curves constructed from them. It includes an introduction to the theory of hyperelliptic curves and divisors, as well as terms and algorithms necessary for their implementation in hyperelliptic cryptosystems. The principle of the hyperelliptic curve cryptography is presented along with two examples of cryptosystems. It also contains several exercises, some of which were programmed in Python language.
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Point Counting on Elliptic and Hyperelliptic Curves
Vácha, Petr ; Šťovíček, Jan (advisor) ; Drápal, Aleš (referee)
In present work we study the algorithms for point counting on elliptic and hy- perelliptic curves. At the beginning we describe a few simple and ineffective al- gorithms. Then we introduce more complex and effective ways to determine the point count. These algorithms(especially the Schoof's algorithm) are important for the cryptography based on discrete logarithm in the group of points of an el- liptic or hyperelliptic curve. The point count is important to avoid the undesirable cases where the cryptosystem is easy to attack. 1
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Point Counting on Elliptic and Hyperelliptic Curves
Vácha, Petr ; Šťovíček, Jan (advisor) ; Drápal, Aleš (referee)
In present work we study the algorithms for point counting on elliptic and hy- perelliptic curves. At the beginning we describe a few simple and ineffective al- gorithms. Then we introduce more complex and effective ways to determine the point count. These algorithms(especially the Schoof's algorithm) are important for the cryptography based on discrete logarithm in the group of points of an el- liptic or hyperelliptic curve. The point count is important to avoid the undesirable cases where the cryptosystem is easy to attack. 1
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