The application of fractal functions for data encryption in information security systems

DOI: 10.31673/2412-4338.2020.011524

Authors

  • О. В. Свинчук, (Svynchuk О. V.) State University of Telecommunications, Kyiv
  • О. В. Барабаш, (Barabash O. V.) State University of Telecommunications, Kyiv
  • Ю. І. Олімпієва, (Olimpiyeva Yu. I.) State University of Telecommunications, Kyiv
  • О. Ю. Ільїн, (Ilin O. Yu.) State University of Telecommunications, Kyiv

Abstract

Information security is an important issue nowadays. Data should be protected from unauthorized users. At present, there are many different text and image encryption methods aimed at providing a high level of security. Fractals, which have an interesting chaotic structure, can be used to develop new document security methods. In the encryption theory, fractal functions are used as reliable detectors for pseudorandom sequences that turn input character sets into a numerical sequence. It is almost impossible to analyse this sequence. However, knowing the initial function and its initial parameters makes it easy to restore the original character set. Fractal objects also help to improve the tools for increasing the quality of printed products protection by means of creating fractal nets that cannot be reproduced with regular copying. This article deals with the development and implementation of a new mathematical model for data encryption based on a class of singular Cantor-type functions. The values of initial sets of these functions are randomly generated. The inverse solution is impossible, because finding the initial digits in the argument image is time-consuming. The algorithm of graphing, the key properties of functions and their use in creating a cryptographic key are investigated. The dependence between the information transmission through the communication channels and the initial numerical function sets and its effect on the increase in the information security are analyzed. The cryptographic stability of the obtained algorithm based on fractal functions and the development of new classes of functions that will give the minimum key size with the maximum stability of the encryption system are the subjects of further research.

Keywords: fractal, fractal functions, singular functions of Cantor type, fractal analysis, data encryption, information security.

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Published

2020-08-02

Issue

No. 1 (2020)

Section

Articles