Partial generalized synchronization theorem of discrete systems with applications in encryption scheme

This paper presents a theorem for designing controller to make two independent (chaotic) discrete systems realize directional partial generalized synchronization (PGS). A non-symmetric encryption scheme is introduced based on the theorem. One numerical simulation example is given to illustrate the effectiveness of the proposed theorem and the encryption scheme. The scheme is able successfully to encrypt and decrypt original information without any loss. The analysis of the key space, sensitivity of key parameters show that this scheme has sound security. The key space of the encryption scheme is larger than 1068. It can be expected that our theorem and encryption scheme provide new tools for understanding and studying PGS phenomena and information encryptions.