Discrete-time chaotic systems: Applications in secure communications

The general design for dead-beat and asymptotic synchronizers for a large c lass of discrete time chaotic systems is proposed. According to whether the form of the transmitter output (drive signal) is linear, nonlinear or the sum of two, different system structures for synchronization discussions are held. Secure communications is then applied taking into consideration to w hich state in the transmitter masks the message. Examples of different secu re communication schemes are discussed, with a comparison given of the vari ous schemes based on the performance of the receivers ability to recover th e message. To accomodate the uncertainty existing in the transmitter parame ters, an extended Kalman filter (EKF) algorithm is utilized to estimate bot h the parameters and states when the message is already embedded. To overco me the problem of high error rates of recovered messages while simultaneous ly estimating parameters, two alternative methods, namely linear output sch eme and indirect scheme, are presented to improve the performance. Numerica l simulations for secure communications illustrate a binary signal as the m essage is recovered and recognizable at the receiver's end.