A cascading method for constructing new discrete chaotic systems with better randomness

The randomness of chaos comes from its sensitivity to initial conditions, which can be used for cryptosystems and secure communications. The Lyapunov exponent is a typical measure of this sensitivity. In this paper, for a given discrete chaotic system, a cascading method is presented for constructing a new discrete chaotic system, which can significantly enlarge the maximum Lyapunov exponent and improve the complex dynamic characteristics. Conditions are derived to ensure the cascading system is chaotic. The simulation results demonstrate that proper cascading can significantly enlarge the system parameter space and extend the full mapping range of chaos. These new features have good potential for better secure communications and cryptography.