Synchronizing Cascade-Connected Chaotic Systems with Uncertainties and Breaking Chaotic Cryptosystems via a Novel Adaptive Control Scheme

This paper deals with synchronization problems of chaotic systems by applying a new adaptive variable structure control (AVSC) scheme. On the basis of Lyapunov synthesis method and Barbalat's Lemma, the proposed control law is shown to render the slave system asymptotically synchronized with the master system even though the parameters of the master system are unknown. A robust adaptive control scheme is presented to guarantee the robustness of the synchronization against bounded disturbances. Even for the case that the slave and master chaotic systems are not of the same type, the proposed AVSC may approximately null the synchronization error. We used an uncertain Rossler system, an uncertain Chua's circuit and an uncertain Duffing–Holmes oscillator as examples to illustrate the controller design. Both theoretical and simulation results strongly suggest that chaotic cryptosystems could be broken by the proposed adaptive control method. This reveals the fact that chaos-based cryptosystems may fail to achieve the secure communication.