CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
MATHEMATICAL MODELING OF THE DATA PROTECTION SYSTEMS BASED ON DIOPHANTINE EQUATIONS
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Read | Osipyan Valeriy O. MATHEMATICAL MODELING OF THE DATA PROTECTION SYSTEMS BASED ON DIOPHANTINE EQUATIONS // Caspian journal : management and high technologies. — 2018. — №1. — pp. 152-160. |
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Osipyan Valeriy O. - Doct. Sci. (Physics and Mathematics), Associate Professor, Kuban State University, 149 Stavropolskaya St., Krasnodar, 350040, Russian Federation, v.osippyan@gmail.com
The objective need for improving data protection systems in conditions of information and telecommunication technologies development is showed. Mathematical models of the DPS developed on the basis of linear inhomogeneous and square homogeneous Diophantine equations are presented. A solution to the given Diophantine equations serves as the original message and the ciphertext is its right part. The problem of finding the Diophantine representation of the given set with the entire numerical components. The authors present the theorems, which let describe the characteristics of the Diophantine equations parameter solutions, necessary for data protection systems mathematical models development on their basis. The cryptanalysis of the described mathematical models, despite their vulnerability, demonstrates the potential of applying Diophantine equations for the development of data protection systems with a high degree of reliability. In particular, such models allow to build both symmetrical data protection systems and systems with an open key. Such systems admit the existence of numerous equi-probable keys, as the corresponding Diophantine set of a given dimension consists of enumerable quantity of numeric elements.
Key words: системы защиты информации, информационные технологии, шифрование информации, симметричная криптосистема, криптосистема с открытым ключом, линейное диофантово уравнение, диофантовы трудности, диофантово множество, data protection systems, information techn