Adaptive Synchronization of Lorenz System and Its Uses in Cryptanalysis

This paper addresses the adaptive synchronization problem of Lorenz system even when its system structure is imprecise and some of its parameters are unknown. With only a single observable state, this is accomplished by a newly designed adaptive observer based on linear feedback control, where the estimated parameters are adaptively updated by some dynamical minimization algorithms. As illustrated with the numerical simulations, the observer’s states can asymptotically synchronize with the targeted system, while the unknown parameters can be identified simultaneously in a fast convergence rate. Furthermore, the proposed observer is applied for providing the cryptanalysis of some Lorenz-based chaotic modulation communication systems. It is demonstrated that the covered messages can be easily estimated by such an adaptive attack. Hence, the securities of those systems are challenged. Keywords—Adaptive observer; adaptive synchronization; cryptanalysis; minimization algorithm; secure communica-