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Gröbner basis, Zhuang-Zi algorithm and attacks of multivariable cryptosystems
Doktorová, Alice ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This diploma thesis is devoted to the multivariate cryptosystems. It includes an overview of commutative algebra with emphasis on Gröbner bases. Of all algorithms, especially the ones using Gröbner bases are studied, i.e. Buchberger's algorithm, which is already implemented in Wolfram Mathematica, and F4 algorithm, for which a program package has been created in the Wolfram Mathematica environment. Also Zhuang-Zi algorithm is described. To simplify its steps a program to compute the Lagrange interpolation polynomial has been created in Python.
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Algorithms of the interpolation by multivariate polynomials
Doktorová, Alice ; Čermák, Libor (referee) ; Kureš, Miroslav (advisor)
This bachelor's work concerns to algorithms of the multivariate interpolation. The problem of the interpolation over the plane is studied in the first part of this work. In the next section, the multivariate Lagrange interpolation is described and the polynomial degree is discussed. A Mathematica program package was developed, by this, the multivariate interpolation over an arbitrary field can be solved.
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Gröbner basis, Zhuang-Zi algorithm and attacks of multivariable cryptosystems
Doktorová, Alice ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This diploma thesis is devoted to the multivariate cryptosystems. It includes an overview of commutative algebra with emphasis on Gröbner bases. Of all algorithms, especially the ones using Gröbner bases are studied, i.e. Buchberger's algorithm, which is already implemented in Wolfram Mathematica, and F4 algorithm, for which a program package has been created in the Wolfram Mathematica environment. Also Zhuang-Zi algorithm is described. To simplify its steps a program to compute the Lagrange interpolation polynomial has been created in Python.
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|
|
Algorithms of the interpolation by multivariate polynomials
Doktorová, Alice ; Čermák, Libor (referee) ; Kureš, Miroslav (advisor)
This bachelor's work concerns to algorithms of the multivariate interpolation. The problem of the interpolation over the plane is studied in the first part of this work. In the next section, the multivariate Lagrange interpolation is described and the polynomial degree is discussed. A Mathematica program package was developed, by this, the multivariate interpolation over an arbitrary field can be solved.
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