CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
METHOD OF PARAMETRIZATION OF DIOPHANTINE EQUATIONS AND MATHEMATICAL MODELING OF DATA PROTECTION SYSTEMS ON THEIR BASIS
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Read | Osipyan Valeriy O., Grigoryan Evelina S. METHOD OF PARAMETRIZATION OF DIOPHANTINE EQUATIONS AND MATHEMATICAL MODELING OF DATA PROTECTION SYSTEMS ON THEIR BASIS // Caspian journal : management and high technologies. — 2019. — №1. — pp. 164-172. |
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Osipyan Valeriy O. - Doct. Sci. (Physics and Mathematics), Associate Professor, ORCID 0000-0001-6558-7998, Kuban State University, 149 Stavropolskaya St., Krasnodar, 350040, Russian Federation, v.osippyan@gmail. Com
Grigoryan Evelina S. - bachelor, Kuban State University, 149 Stavropolskaya St., Krasnodar, 350040, Russian Federation, EvoGrigoryan@mail.ru
The method of parametrization of homogeneous and other multi-degree Diophantine equations of the second degree of a special type is given and mathematical models of symmetric and asymmetric information protection systems are developed on their basis. An original hybrid method (SO method) for the development of information protection systems, generalizing the principle of construction of public key cryptosystems, based on NP-complete problem of non-standard backpack and the problem of numerical solutions of Diophantine equations of a given dimension and degree, is proposed. The numerical equivalents of the elementary messages of these systems are the numerical solutions of a given Diophantine equation. Cryptanalysis of the described mathematical models demonstrates the potential of applying Diophantine equations for the development of GIS with a high degree of reliability. Unlike classical asymmetric cryptosystems, this type of mathematical model of asymmetric cryptosystem shares a secret according to a given algorithm. In particular, such models of systems admit the existence of a set of equally probable keys, since the corresponding Diophantine set of a given dimension consists of a countable number of numerical elements.
Key words: система защиты информации, информационная технология, прямое и обратное преобразование данных, симметричная криптосистема, криптосистема с открытым ключом, многостепенное диофантово уравнение, параметризация диофантова уравнения, диофантовы трудности, мат