Application of nonlinear discrete maps to construct pseudo-chaotic cryptosystems.
DOI:
https://doi.org/10.15276/opu.2.70.2024.19Keywords:
pseudo-chaotic sequences, image encryption, cryptosystems, protection of information from unauthorized access, hardware-software platform, statistical analysis, discrete dynamical systems, unstable periodic orbits, stabilization of periodic orbitsAbstract
The article is devoted to the application of nonlinear discrete dynamical systems in computer cryptography. The basis of many stream encryption schemes is pseudo-chaotic sequences, which are generated using a certain selected trajectory of a discrete dynamical system. The main problem with using pseudo-chaotic dynamical systems in computer calculations is that the number of all possible states in a computer is finite, therefore, every constructed trajectory is periodic, and the period length can be small. In addition, different platforms (hardware and software) use different algorithms for calculating mathematical functions and store intermediate results with different precision, so the results obtained on different platforms can differ significantly. To overcome these problems, it is proposed to use a new dynamical system, namely the generalized Tent map with control, which stabilizes cycles of a given length. These cycles depend on the system parameters and the initial value; these values are a short key (seed) for generating a long pseudo-chaotic sequence. The article provides a simple statistical analysis to check the uncorrelation of the key sequence, as well as a graphical test. The experiments show the absence of significant correlation. The sensitivity of the elements of the key sequence to the variation of the key parameters was also investigated. As an example of the algorithm’s operation, the problem of image encryption is considered.
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