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Robustness and Security of H∞-Synchronizer in Chaotic Communication System

In recent years, a large amount of work on chaos-based cryptosystems has been published (Kocarev (2001); Millerioux et al. (2008)). A general methodology for designing chaotic and hyperchaotic cryptosystems has been developed using the control systems theory (Grassi et al. (1999); Liao et al. (1999); Yang et al. (1997a;b)). The chaotic communication system is closely related to the concept of chaos synchronization. An overview of chaotic secure communication systems can be found in (Yang (2004)). He classified the continuous-time chaotic secure communication systems into four generations. In the third generation, the combination of the classical cryptographic technique and chaotic synchronization is used to enhance the degree of security. Specifically, Yang et al. proposed a new chaos-based secure communication scheme in an attempt to thwart the attacks (Yang et al. (1997a;b)). They have combined both conventional cryptographic method and synchronization of chaotic systems. Their cryptographic method consists of an encryption function (the multi-shift cipher), a decryption function (the inverse of the encryption function), a chaotic encrypter that generates the key signal for the encryption function, and a decrypter that estimates the key signal. The approach has a limitation since the cryptosystem design may fail if different chaotic circuits are utilized. So far, this generation has the highest security in all the chaotic communication systems had been proposed and has not yet broken. From the control theoretic perspective, the transmitter and the receiver in the chaotic communication system can be considered as the nonlinear plant and its observer, respectively. Grassi et al. proposed a nonlinear-observer-based decrypter to reconstruct the state of the encrypter (Grassi et al. (1999); Liao et al. (1999)). They extended the Chua’s oscillator to the observer-based decrypter. The cryptosystem does not require initial conditions of the encrypter and the decrypter belonging to the same basin of attraction. If we can design a decrypter without the knowledge of the parameters of the encrypter, the chaos-based secure communication systems are not secure, because the parameters of the encrypter is selected as static secret keys in the cryptosystem. Parameter identification and adaptive synchronization methods may be effective for intruders in building reconstruction mechanisms, even when a synchronizing system is not available. Therefore, it is important for secure issues to investigate whether adaptive identifiers without the system information of encrypter can be constructed or not. We have recently designed an observer-based chaotic communication system combining the cryptosystems proposed by Grassi et al. (Grassi et al. (1999)) and by Liao et al. (Liao et al. (1999)) that allows us to assign the relative degree and the zeros of its encrypter system (Matsuo et al. (2004)). Specifically, we constructed three cryptosystems based on a Chua’s circuit by assigning its relative degree and zeros. The cryptosystem consists of 20