Valeriy Osipyan
Kirill Litvinov
ABSTRACT
This paper shows the objective necessity of improving the information security systems (ISS) under the development of information and telecommunication technologies. The paper also shows the theorems that describe properties of the parametric solutions of multi-degree systems of Diophantine equations (MSDE) necessary for development of the mathematical models of the information security systems (ISS) based on MSDE solutions. The Frolov’s theorem is generalized, and the author’s theorem is given that allows developing the mathematical model of ISS containing Diophantine difficulties and the author’s mathematical model of alphabetic cryptosystem in the form of tuple.
A new approach to the development of dissymmetric bigram cryptosystem (DBC) is proposed based on two-parameter and three-parameter solutions, it generalizes the principle of building the public key cryptosystems. It is proposed to implement direct and inverse transformations based on the parametric solution, previously divided into two parts: one part - for direct transformation, and the other part - for inverse transformation. A new concept of equivalence of the ordered sets of numbers or parameters of given dimension and order is introduced. The described mathematical models demonstrate the potential of using Diophantine equations and systems of Diophantine equations for development of ISS with a high degree of reliability.
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Index Terms
- Development of the mathematic model of disymmetric bigram cryptosystem based on a parametric solution family of multi-degree system of Diophantine equations✱
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