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Application of discrete dynamic systems for security communication channels

Last modified: 13-11-2023

#### Abstract

This work is based on the method of encryption using forward and reverse systems. Lorentz, Chua, and Ressler systems were used as dynamic chaotic systems. Software implementation of algorithms based on such systems leads to the necessity of transition from differential equations to their finite-difference analogs. However, in this case, if you do not impose restrictions on the length of the numbers used, the problem of a sharp increase in the volume of the encrypted text arises. This is especially true when converting large volumes of data. Therefore, the obtained finite-difference equations were interpreted as equations in finite rings or fields, which in this case are understood as equations defining such a discrete dynamical system as a finite state machine. On the basis of such a transition, an information transformation algorithm is implemented, in which the encrypted sequence is interpreted as a sequence of control actions of a dynamic system, and the sequence of output reactions of the latter is understood as encrypted information. The reverse system is used to decrypt information.

#### Keywords

encryption and data protection; direct and inverse dynamic systems; Lorentz system