Kybernetika 46 no. 1, 1-18, 2010

On the anti-synchronization detection for the generalized Lorenz system and its applications to secure encryption

Volodymyr Lynnyk and Sergej Čelikovský


In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented and tested using the so-called \emph{generalized Lorenz system} (GLS) family making advantage of its special parametrization. Such an implementation relies on the parameter dependent synchronization of several identical copies of the GLS obtained through the observer-based design for nonlinear systems. The purpose of this paper is to study and compare two different methods for the anti-synchronization detection, including further underlying theoretical study of the GLS. Resulting encryption schemes are also compared and analyzed with respect to both the encryption redundancy and the encryption security. Numerical experiments illustrate the results.


synchronization, observer, secure communication, nonlinear system, chaos shift keying, generalized Lorenz system, anti-synchronization


93C10, 37N25