Application of discrete dynamic systems for security communication channels

Abstract

Dynamic systems with chaotic behavior are currently intensively used and applied in various fields, in particular for cryptographic protection of information. Generators of pseudorandom sequences can be built on the basis of such systems, which are later used for gamification of open text. On the other hand, the dynamic system can be used directly to transform information. A cipher is created on its basis. A necessary condition for unambiguous decryption is the existence of a reverse system. 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 nmnbers 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