Discrete-time chaotic systems: Applications in secure communications

The general design for dead-beat and asymptotic synchronizers for a large class 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 which state in the transmitter masks the message. Examples of different secure communication schemes are discussed, with a comparison given of the various schemes based on the performance of the receivers ability to recover the message. To accomodate the uncertainty existing in the transmitter parameters, an extended Kalman filter (EKF) algorithm is utilized to estimate both the parameters and states when the message is already embedded. To overcome the problem of high error rates of recovered messages while simultaneously estimating parameters, two alternative methods, namely linear output scheme and indirect scheme, are presented to improve the performance. Numerical simulations for secure communications illustrate a binary signal as the message is recovered and recognizable at the receiver's end.