On the anti-synchronization detection for the generalized Lorenz system and its applications to secure encryption. (English) Zbl 1190.93038

Summary: 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 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 studying 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.


93C10 Nonlinear systems in control theory
37N25 Dynamical systems in biology
94A60 Cryptography
Full Text: EuDML Link


[1] J. Alvarez, H. Puebla, and I. Cervantes: Stability of observer-based chaotic communication for a class of Lur’e systems. Internat. J. Bifurcation Chaos 7 (2002), 1605-1618.
[2] G. Alvarez and S. Li: Cryptographic requirements for chaotic secure communications. arXiv: nlin. CD/0311039, 2003.
[3] T. L. Carroll and L. M. Pecora: Cascading synchronized chaotic systems. Physica D 67 (1993), 126-140. · Zbl 0800.94100
[4] S. Čelikovský: Observer form of the hyperbolic-type generalized Lorenz system and its use for chaos synchronization. Kybernetika 40 (2004), 6, 649-664. · Zbl 1249.93090
[5] S. Čelikovský and G. Chen: On a generalized Lorenz canonical form of chaotic systems. Internat. J. Bifurcation Chaos 12 (2002), 1789-1812. · Zbl 1043.37023
[6] S. Čelikovský and G. Chen: Secure synchronization of chaotic systems from a nonlinear observer approach. IEEE Trans. Automat. Control 50 (2005), 76-82. · Zbl 1365.93384
[7] S. Čelikovský, V. Lynnyk, and M. Šebek: Anti-synchronization chaos shift keying method based on generalized Lorenz system. Proc. The 1st IFAC Conference on Analysis and Control of Chaotic Systems. CHAOS’06, 2006, pp. 333-338.
[8] S. Čelikovský, V. Lynnyk, and M. Šebek: Observer-based chaos sychronization in the generalized chaotic Lorenz systems and its application to secure encryption. Proc. The 45th IEEE Conference on Decision and Control, 2006, pp. 3783-3788.
[9] S. Čelikovský and V. Lynnyk: Anti-synchronization chaos shift keying method: Error derivative detection improvement. Proc. The 2st IFAC Conference on Analysis and Control of Chaotic Systems. CHAOS ’09, pp. 1-6.
[10] S. Čelikovský and A. Vaněček: Bilinear systems and chaos. Kybernetika 30 (1994), 403-424. · Zbl 0823.93026
[11] K. M. Cuomo and A. V. Oppenheim: Circuit implementation of synchronized chaos with application to communications. Physical Rev. Lett. 71 (1993),1, 65-68.
[12] K. Cuomo, A. Oppenheim, and S. Strogatz: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits and Systems II 40 (1993), 626-633.
[13] F. Dachselt and W. Schwartz: Chaos and cryptography. IEEE Trans. Circuits and Systems I 48 (2001), 1498-1509. · Zbl 0999.94030
[14] H. Dedieu, M. P. Kennedy, and M. Hasler: Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuit. IEEE Trans. Circuits and Systems II 40 (1993), 634-642.
[15] L. Gamez-Guzman, R. M. Cruz-Hernandez, Lopez-Gutierrez, and E. E. Garcia-Guerrero: Synchronization of Chua’s circuits with multi-scroll attractors: Application to communication. Communications in Nonlinear Science and Numerical Simulation 14 (2009), 6, 2765-2775.
[16] J. M. V. Grzybowski, M. Rafikov, and J. M. Balthazar: Synchronization of the unified chaotic system and application in secure communication. Communications in Nonlinear Science and Numerical Simulation 14 (2009), 6, 2793-2806. · Zbl 1221.94047
[17] L. Kocarev and U. Parlitz: General approach for chaotic synchronization with applications to communications. Phys. Rev. Lett. 74 (1995), 25, 5028-5031.
[18] L. Kocarev: Chaos-based cryptography: a brief overview. Circuits Systems Magazine 1 (2001), 6-21.
[19] A. A. Koronovskii, O. I. Moskalenko, P. V. Popov, and A. E. Hramov: Method for secure data transmission based on generalized synchronization. BRAS: Physics. 72 (2008), 1, 131-135.
[20] K. Lian and P. Liu: Synchronization with message embedded for generalized Lorenz chaotic circuits and its error analysis. IEEE Trans. Circuits Systems I 47 (2000), 1418-1424. · Zbl 1011.94033
[21] U. Parlitz, L. Kocarev, T. Stojanovski, and H. Preckel: Encoding messages using chaotic synchronization. Phys. Rev. E. 53 (1996), 4351-4361.
[22] U. Parlitz, L. O. Chua, L. Kocarev, K. S. Halle, and A. Shang: Transmission of digital signals by chaotic synchronization. Internat. J. Bifur. Chaos 2 (1992), 973-977. · Zbl 0870.94011
[23] R. Schmitz: Use of chaotic dynamical systems in cryptography. J. Franklin Inst. 338 (2001), 4, 429-441. · Zbl 0979.94038
[24] A. Vaněček and S. Čelikovský: Control Systems: From Linear Analysis to Synthesis of Chaos. Prentice-Hall, London 1996. · Zbl 0874.93006
[25] A. R. Volkovskii and N. Rulkov: Synchronouns chaotic response of a nonlinear oscillating system as a principle for the detection of the information component of chaos. Tech. Phys. Lett. 19 (1993), 97-99.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.