Secure Communication Using IFS: Almost Sure and Mean Square Stability Approaches

A new secure communication system is presented in this paper. The main idea is based on the use of a certain class of jump linear system (JLS), namely random iterated functions system (RIFS). The security algorithm is enhanced by random switching rules between several linear and affine subsystems. The synchronization between the sender and the receiver is assured by two systematic procedures that evolve second moment and the almost sure stability. An example is given in the end of the paper to illustrate the efficiency of the developed theory.