Generalized Synchronization Theorem for Undirectional Discrete Systems with Application in Encryption Scheme

This paper establishes a theorem of generalized chaos synchronization (GCS) for bidirectional discrete systems. Based on this theorem, one can construct new chaotic sys- tems which can achieve GCS among some of the state vari- ables. As a first application, a four dimensional bidirectional GCS discrete system (BGCSDS) is introduced, whose pro- totype is the Sinai map. Numerical simulation shows that two pair variables of the BGCSDS achieve GCS via a pre- designed transform H. Based on the BGCSDS an encryption scheme is intro- duced. This scheme has the functions of the authentication of the data, and the one-time-pad. The scheme is able to en- crypt and decrypt information without any loss. The analy- sis of the key space and sensitivity of key parameters shows that this scheme has sound security. The key space of the scheme is larger than 2300. It can be expected that our the- orem and scheme provide new tools for understanding and studying the GS phenomena and information encryption.