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

Volodymyr Lynnyk; Sergej Čelikovský

Kybernetika (2010)

  • Volume: 46, Issue: 1, page 1-18
  • ISSN: 0023-5954

Abstract

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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 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.

How to cite

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Lynnyk, Volodymyr, and Čelikovský, Sergej. "On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption." Kybernetika 46.1 (2010): 1-18. <http://eudml.org/doc/37707>.

@article{Lynnyk2010,
abstract = {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 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.},
author = {Lynnyk, Volodymyr, Čelikovský, Sergej},
journal = {Kybernetika},
keywords = {nonlinear system; observer; chaos shift keying; generalized Lorenz system; synchronization; anti-synchronization; secure communication; synchronization; observer; secure communication; nonlinear system; chaos shift keying; generalized Lorenz system; anti-synchronization},
language = {eng},
number = {1},
pages = {1-18},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption},
url = {http://eudml.org/doc/37707},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Lynnyk, Volodymyr
AU - Čelikovský, Sergej
TI - On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 1
SP - 1
EP - 18
AB - 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 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.
LA - eng
KW - nonlinear system; observer; chaos shift keying; generalized Lorenz system; synchronization; anti-synchronization; secure communication; synchronization; observer; secure communication; nonlinear system; chaos shift keying; generalized Lorenz system; anti-synchronization
UR - http://eudml.org/doc/37707
ER -

References

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  1. Stability of observer-based chaotic communication for a class of Lur’e systems, Internat. J. Bifurcation Chaos 7 (2002), 1605–1618. 
  2. Cryptographic requirements for chaotic secure communications, arXiv: nlin. CD/0311039, 2003. 
  3. Cascading synchronized chaotic systems, Physica D 67 (1993), 126–140. 
  4. Observer form of the hyperbolic-type generalized Lorenz system and its use for chaos synchronization, Kybernetika 40 (2004), 6, 649–664. MR2120388
  5. On a generalized Lorenz canonical form of chaotic systems, Internat. J. Bifurcation Chaos 12 (2002), 1789–1812. MR1927413
  6. Secure synchronization of chaotic systems from a nonlinear observer approach, IEEE Trans. Automat. Control 50 (2005), 76–82. MR2110810
  7. Anti-synchronization chaos shift keying method based on generalized Lorenz system, In: Proc. The 1st IFAC Conference on Analysis and Control of Chaotic Systems. CHAOS’06, 2006, pp. 333–338. 
  8. Observer-based chaos sychronization in the generalized chaotic Lorenz systems and its application to secure encryption, In: Proc. The 45th IEEE Conference on Decision and Control, 2006, pp. 3783–3788. 
  9. Anti-synchronization chaos shift keying method: Error derivative detection improvement, In: Proc. The 2st IFAC Conference on Analysis and Control of Chaotic Systems. CHAOS ’09, pp. 1-6. 
  10. Bilinear systems and chaos, Kybernetika 30 (1994), 403–424. 
  11. Circuit implementation of synchronized chaos with application to communications, Physical Rev. Lett. 71 (1993),1, 65–68. 
  12. Synchronization of Lorenz-based chaotic circuits with applications to communications, IEEE Trans. Circuits and Systems II 40 (1993), 626–633. 
  13. Chaos and cryptography, IEEE Trans. Circuits and Systems I 48 (2001), 1498–1509. MR1873100
  14. 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. 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. Synchronization of the unified chaotic system and application in secure communication, Communications in Nonlinear Science and Numerical Simulation 14 (2009), 6, 2793–2806. MR2483887
  17. General approach for chaotic synchronization with applications to communications, Phys. Rev. Lett. 74 (1995), 25, 5028–5031. 
  18. Chaos-based cryptography: a brief overview, Circuits Systems Magazine 1 (2001), 6–21. 
  19. Method for secure data transmission based on generalized synchronization, BRAS: Physics. 72 (2008), 1, 131–135. 
  20. Synchronization with message embedded for generalized Lorenz chaotic circuits and its error analysis, IEEE Trans. Circuits Systems I 47 (2000), 1418–1424. MR1803664
  21. Encoding messages using chaotic synchronization, Phys. Rev. E. 53 (1996), 4351–4361. 
  22. Transmission of digital signals by chaotic synchronization, Internat. J. Bifur. Chaos 2 (1992), 973–977. 
  23. Use of chaotic dynamical systems in cryptography, J. Franklin Inst. 338 (2001), 4, 429–441. Zbl0979.94038MR1833969
  24. Control Systems: From Linear Analysis to Synthesis of Chaos, Prentice-Hall, London 1996. MR1481725
  25. 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. 

Citations in EuDML Documents

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  1. Xiaobing Zhou, Murong Jiang, Yaqun Huang, Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification
  2. Zhi-cai Ma, Yong-zheng Sun, Hong-jun Shi, Finite-time outer synchronization between two complex dynamical networks with time delay and noise perturbation
  3. Hassan Saberi Nik, Ping He, Sayyed Taha Talebian, Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
  4. Jie Wu, Zhi-cai Ma, Yong-zheng Sun, Feng Liu, Finite-time synchronization of chaotic systems with noise perturbation

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