Adaptive synchronization of chaotic systems and its uses in cryptanalysis

This chapter discusses adaptive synchronization of a class of chaotic systems based on a new design of adaptive observer. The design is relied on a linear feedback control scheme and the dynamical minimization algorithm. A linear feedback signal is designed to drive the state estimation errors to zero, while the parametric updating rules are obtained with the dynamical minimization algorithm so that parameter estimation can be achieved at the same time. The success of this approach is illustrated by tackling with some typical synchronization problems found in chaotic systems, where its stability is justified by conditional Lyapunov exponents and local Lyapunov function method. The same design also serves as an effective attack, performing the cryptanalysis for chaos-based communication systems. As demonstrated with our simulation results, the securities of many proposed chaos-based cryptosystems are in fact questionable as the information of their transmitters, including the states and/or system parameters, as well as the transmitting messages, may be revealed by simply observing the transmitted signal.