Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication

Secure communication by the synchronization of coupled chaotic systems may be destroyed by channel noise and inaccurate estimation of system parameters. This paper attempts to develop a robust synchronization scheme for two different chaotic systems which are 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 both the continuous signal and the digital image are conducted to evaluate the performance of the proposed secure communication scheme. The comparison of schemes with and without a noise assumption, and the sensitivity analysis of the decryption key are carried out as well. The results show that the encrypted signal or picture 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.