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.

[1]  K.Murali,et al.  Secure communication using a compound signal from generalized synchronizable chaotic systems , 1997, chao-dyn/9709025.

[2]  Cynthia A. Phillips,et al.  A graph-based system for network-vulnerability analysis , 1998, NSPW '98.

[3]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[4]  Sushil Jajodia,et al.  Efficient minimum-cost network hardening via exploit dependency graphs , 2003, 19th Annual Computer Security Applications Conference, 2003. Proceedings..

[5]  Paul Ammann,et al.  A host-based approach to network attack chaining analysis , 2005, 21st Annual Computer Security Applications Conference (ACSAC'05).

[6]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[7]  Sushil Jajodia,et al.  Managing attack graph complexity through visual hierarchical aggregation , 2004, VizSEC/DMSEC '04.

[8]  Richard H. Mogford,et al.  Mental Models and Situation Awareness in Air Traffic Control , 1997 .

[9]  C. Chui,et al.  A symmetric image encryption scheme based on 3D chaotic cat maps , 2004 .

[10]  Leon O. Chua,et al.  Reconstruction and Synchronization of hyperchaotic Circuits via One State Variable , 2002, Int. J. Bifurc. Chaos.

[11]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[12]  Chai Wah Wu,et al.  A Simple Way to Synchronize Chaotic Systems with Applications to , 1993 .

[13]  Mica R. Endsley,et al.  Design and Evaluation for Situation Awareness Enhancement , 1988 .

[14]  L. Chua,et al.  Generalized synchronization of chaos via linear transformations , 1999 .

[15]  Leon O. Chua,et al.  Transmission of Digital signals by Chaotic Synchronization , 1992, Chua's Circuit.

[16]  J. Yorke,et al.  Differentiable generalized synchronization of chaos , 1997 .

[17]  Akiko Nakata,et al.  Situation awareness in air traffic control : enhanced displays for advanced operations , 2000 .

[18]  David N. Hogg,et al.  Development of a situation awareness measure to evaluate advanced alarm systems in nuclear power plant control rooms , 1995 .

[19]  Somesh Jha,et al.  Automated generation and analysis of attack graphs , 2002, Proceedings 2002 IEEE Symposium on Security and Privacy.

[20]  Dennis K. Leedom,et al.  Training Situational Awareness Through Pattern Recognition in a Battlefield Environment , 1991 .

[21]  Paul Ammann,et al.  Using model checking to analyze network vulnerabilities , 2000, Proceeding 2000 IEEE Symposium on Security and Privacy. S&P 2000.

[22]  Mica R. Endsley,et al.  Measurement of Situation Awareness in Dynamic Systems , 1995, Hum. Factors.

[23]  Sushil Jajodia,et al.  Understanding complex network attack graphs through clustered adjacency matrices , 2005, 21st Annual Computer Security Applications Conference (ACSAC'05).

[24]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II: The Mapping Approach , 1983 .

[25]  Guanrong Chen,et al.  Secure synchronization of a class of chaotic systems from a nonlinear observer approach , 2005, IEEE Transactions on Automatic Control.