Development of mathematical models of systems of protection data on the basis of the multistage systems of diophantine equations

Authors

  • Osipyan V.O. Kuban State University, Krasnodar, Russian Federation
  • Litvinov K.I. Kuban State University, Krasnodar, Russian Federation
  • Zhuk A.S. Kuban State University, Krasnodar, Russian Federation

UDC

519.72+004

EDN

TDXIMZ

DOI:

10.31429/vestnik-16-3-6-15

Abstract

The objective necessity of improvement of information security systems (SPI) in the conditions of development of information and telecommunication technologies is shown. Theorems which allow to describe the properties of parametric solutions of multistage systems of Diophantine equations necessary for the development of mathematical models of SPI on their basis are given. The theorem generalizing the known Frolov's theorem is presented, and the author's theorem on the basis of which the mathematical model of SPI containing Diophantine difficulties is developed is given.

A new approach to the development of SPI generalizing the principle of construction of public key cryptosystems is proposed. One part of the conditional identity is used for the direct transformation of the original message, and the other part - for the inverse transformation. A new concept of equivalence of ordered sets of numbers or parameters with a given dimension and degree is introduced.

Mathematical models of cryptosystems developed on the basis of two-parameter solutions of multistage systems of Diophantine equations, in particular, - equations of the fifth degree with the number of variables equal to twelve are presented. The described mathematical models demonstrate the potential of using Diophantine equations for the development of SPI with a high degree of reliability. These models allow to build asymmetric GIS, and the system public key. Such systems contain Diophantine difficulties admitting the existence of a countable set of equally probable keys.

Keywords:

information technologies, information security system, information encryption, symmetric cryptosystem, public key cryptosystem, multi-level system of Diophantine equations, Diophantine difficulties, Diophantine set, Diophantine representation

Funding information

Работа выполнена при финансовой поддержке гранта РФФИ (проект 19-01-00596).

Authors info

  • Valery O. Osipyan

    д-р физ.-мат. наук, доцент, профессор кафедры информационных технологий Кубанского государственного университета

  • Kirill I. Litvinov

    аспирант кафедры информационных технологий Кубанского государственного университета

  • Arseny S. Zhuk

    старший преподаватель кафедры вычислительных технологий Кубанского государственного университета

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Issue

Vol. 16 (2019) No. 3

Pages

6-15

Section

Mathematics

Dates

Submitted

August 22, 2019

Accepted

September 3, 2019

Published

September 30, 2019

How to Cite

[1]
Osipyan, V.O., Litvinov, K.I., Zhuk, A.S., Development of mathematical models of systems of protection data on the basis of the multistage systems of diophantine equations. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2019, т. 16, № 3, pp. 6–15. DOI: 10.31429/vestnik-16-3-6-15

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Copyright (c) 2019 Осипян В.О., Литвинов К.И., Жук А.С.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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