Robust Synchronization of Chaotic Systems Subject to Noise and Its Application to Secure Communication

This paper attempts to develop a robust synchronization scheme for two different chaotic systems exposed to a bounded noise and their parameters are uncertain. Based on the Lyapunov stability theory and the dead-zone algorithm, a controller that is robust to a bounded noise and independent of the system parameters is proposed to asymptotically synchronize two different chaotic systems. The proposed synchronization controller is embedded in a secure communication scheme, which is not only robust to the channel noise but can also incorporate the noise as part of the encryption key and thus enhance the key security. Numerical simulations for the transmission of the digital image are conducted to evaluate the performance of the proposed secure communication scheme. The results show that the encrypted signal was unable to be recovered without considering the channel noise, and decryption attempts using a slightly incorrect key were unable to recover the original message.