An observer based approach for multi-scroll chaotic system synchronization and secure communication with multi-shift ciphering

In this paper, a nonlinear observer based approach for multi-scroll chaotic system synchronization and information recovery with multi-shift ciphering is presented. The approach is based on using differential mean value theorem based observer design technique for chaotic system synchronization purpose. Here, by using a differential mean value theorem, nonlinear observer estimation error dynamics is transformed into a linear parameter varying system and sufficient condition for error convergence is derived using a quadratic Lyapunov function which is nonlinear matrix inequality with time varying parameters. The derived sufficient condition is then reformulated as a set of linear matrix inequalities using convexity principle and solved with MATLAB LMI toolbox. In the proposed scheme, security is enhanced by using multi-shift ciphering for information encryption and the key used for ciphering is one of the states of a chaotic system. The estimate of key is obtained by using differential mean value theorem based observer and used to recover encrypted data at the receiver side. An example of multi-scroll Chen system synchronization along with information encryption and decryption with simulation results is given to show the efficacy of the proposed approach.