ABSTRACT
In this chapter, the authors illustrate the discrete-time cryptography by chaos based on the inclusion method (DCCIM), with the background of observability normal forms and observability bifurcation analysis. The purpose is to give examples of encoding method based on the use of chaotic systems and the Inclusion method. The chapter presents an example of chaotic synchronization, which is a capital phenomenon in the realization of a cryptographic application using chaotic processes and the description of the transmission scheme for the DCCIM. It focuses on the basis of the Mandelbrot map. Although its strength for use in cryptographic type security is under debate, it has been shown that communications privacy can be enhanced by masking signals with chaotic carriers. The authors measure the speed of exponential divergence of some nearby trajectories which stem from slightly different initial conditions. They discuss the efficiency of the observability bifurcations in a secured communication.
