JACIII Vol.27 No.2 pp. 292-303
doi: 10.20965/jaciii.2023.p0292

Research Paper:

Synchronization of Hyperchaotic Systems Based on Intermittent Control and its Application in Secure Communication

Jianbin He ORCID Icon, Wenlan Qiu ORCID Icon, and Jianping Cai ORCID Icon

School of Mathematics and Statistics, Minnan Normal University
Zhangzhou , China

Corresponding author

September 26, 2022
December 26, 2022
March 20, 2023
chaos synchronization, intermittent control, secure communication, image encryption

The synchronization of master-slave hyperchaotic systems is investigated by intermittent control and proved by the Lyapunov stable theory. Meanwhile, a new secure communication scheme is designed for the continuous and digital information. The encrypted information is transmitted to receiver through the intermittent controller, which reduces the disturbance to the synchronization of master-slave systems and improves the security and reliability of secure communication. Before transmitting to the receiver, the continuous signal is firstly modulated and masked by the chaotic signals. Furthermore, an encryption algorithm for the digital information of color image is proposed by the pseudo-random sequences of Chen hyperchaotic system, and then the encrypted image is modulated and masked by the variables of the master system. The original image can be decrypted successfully at the receiving end after the slave system is synchronized with the master system. Finally, the feasibility and effectiveness of this scheme are verified by simulation experiments. In addition, the security analysis of the image encryption algorithm is also discussed, such as key sensitivity, correlation coefficient, NIST test, and return map.

Cite this article as:
J. He, W. Qiu, and J. Cai, “Synchronization of Hyperchaotic Systems Based on Intermittent Control and its Application in Secure Communication,” J. Adv. Comput. Intell. Intell. Inform., Vol.27 No.2, pp. 292-303, 2023.
Data files:
  1. [1] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett., Vol.64, pp. 821-824, 1990.
  2. [2] X. Shi and Z. Wang, “Adaptive synchronization of the energy resource systems with mismatched parameters via linear feedback control,” Nonlinear Dynamics, Vol.69, pp. 993-997, 2012.
  3. [3] M. Ma, H. Zhang, J. Cai, and J. Zhou, “Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch,” Kybernetika, Vol.49, No.4, pp. 539-553, 2013.
  4. [4] Z.-M. Ge and J.-K. Lee, “Chaos synchronization and parameter identification for gyroscope system,” Applied Mathematics and Computation, Vol.163, No.2, pp. 667-682, 2005.
  5. [5] J. Huang, C. Li, T. Huang, and Q. Han, “Lag quasisynchronization of coupled delayed systems with parameter mismatch by periodically intermittent control,” Nonlinear Dynamics, Vol.71, pp. 469-478, 2013.
  6. [6] J. Cai and M. Ma, “Synchronization between two non-autonomous chaotic systems via intermittent control of sinusoidal state error feedback,” Optik, Vol.130, pp. 455-463, 2017.
  7. [7] Ö. Morgül and M. Feki, “Synchronization of chaotic systems by using occasional coupling,” Physical Review E, Vol.55, pp. 5004-5010, 1997.
  8. [8] T. Huang, C. Li, W. Yu, and G. Chen, “Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback,” Nonlinearity, Vol.22, No.3, pp. 569-584, 2009.
  9. [9] M. Żochowski, “Intermittent dynamical control,” Physica D: Nonlinear Phenomena, Vol.145, Nos.3-4, pp. 181-190, 2000.
  10. [10] Z.-L. Zhu, W. Zhang, K.-W. Wong, and H. Yu, “A chaos-based symmetric image encryption scheme using a bit-level permutation,” Information Sciences, Vol.181, No.6, pp. 1171-1186, 2011.
  11. [11] Y. Wang, K.-W. Wong, X. Liao, and G. Chen, “A new chaos-based fast image encryption algorithm,” Applied Soft Computing, Vol.11, No.1, pp. 514-522, 2011.
  12. [12] M. K. Mandal, G. D. Banik, D. Chattopadhyay, and D. Nandi, “An Image Encryption Process Based on Chaotic Logistic Map,” IETE Technical Review, Vol.29, No.5, pp. 395-404, 2012.
  13. [13] X.-Y. Wang and T. Wang, “A novel algorithm for image encryption based on couple chaotic systems,” Int. J. of Modern Physics B, Vol.26, No.30, Article No.1250175, 2012.
  14. [14] T. Gao and Z. Chen, “A new image encryption algorithm based on hyper-chaos,” Physics Letters A, Vol.372, No.4, pp. 394-400, 2008.
  15. [15] J. He, S. Yu, and J. Cai, “A method for image encryption based on fractional-order hyperchaotic systems,” J. of Applied Analysis and Computation, Vol.5, No.2, pp. 197-209, 2015.
  16. [16] J. Cai and J. He, “A new hyperchaotic system generated by an external periodic excitation and its image encryption application,” J. Adv. Comput. Intell. Intell. Inform., Vol.26, No.3, pp. 418-430, 2022.
  17. [17] S. Banerjee, D. Ghosh, A. Ray, and A. R. Chowdhury, “Synchronization between two different time-delayed systems and image encryption,” Europhysics Letters, Vol.81, No.2, Article No.20006, 2007.
  18. [18] M. K. Shukla and B. B. Sharma, “Secure communication and image encryption scheme based on synchronisation of fractional order chaotic systems using backstepping,” Int. J. of Simulation and Process Modelling, Vol.13, No.5, pp. 473-485, 2018.
  19. [19] J. He, J. Cai, and J. Lin, “Synchronization of hyperchaotic systems with multiple unknown parameters and its application in secure communication,” Optik, Vol.127, No.5, pp. 2502-2508, 2016.
  20. [20] T. Yang and L. O. Chua, “Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication,” IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications, Vol.44, No.10, pp. 976-988, 1997.
  21. [21] H. Zhang, X. Liu, X. S. Shen, and J. Liu, “Intermittent Impulsive Synchronization of Hyperchaos with Application to Secure Communication,” Asian J. of Control, Vol.15, No.6, pp. 1686-1699, 2013.
  22. [22] L. Zhou and F. Tan, “A chaotic secure communication scheme based on synchronization of double-layered and multiple complex networks,” Nonlinear Dynamics, Vol.96, pp. 869-883, 2019.
  23. [23] F. Aliabadi, M.-H. Majidi, and S. Khorashadizadeh, “Chaos synchronization using adaptive quantum neural networks and its application in secure communication and cryptography,” Neural Computing and Applications, Vol.34, pp. 6521-6533, 2022.
  24. [24] Q. D. Nguyen, V. N. Giap, D.-H. Pham, and S.-C. Huang, “Fast speed convergent stability of T-S fuzzy sliding-mode control and disturbance observer for a secure communication of chaos-based system,” IEEE Access, Vol.10, pp. 95781-95790, 2022.
  25. [25] Q. D. Nguyen, V. N. Giap, V. H. Tran, D.-H. Pham, and S.-C. Huang, “A novel disturbance rejection method based on robust sliding mode control for the secure communication of chaos-based system,” Symmetry, Vol.14, No.8, Article No.1668, 2022.
  26. [26] N. V. Giap, H. S. Vu, Q. D. Nguyen, and S.-C. Huang, “Disturbance and uncertainty rejection-based on fixed-time sliding-mode control for the secure communication of chaotic systems,” IEEE Access, Vol.9, pp. 133663-133685, 2021.
  27. [27] V. N. Giap, Q. D. Nguyen, and S.-C. Huang, “Synthetic adaptive fuzzy disturbance observer and sliding-mode control for chaos-based secure communication systems,” IEEE Access, Vol.9, pp. 23907-23928, 2021.
  28. [28] J. He and J. Cai, “Parameter modulation for secure communication via the synchronization of Chen hyperchaotic systems,” Systems Science & Control Engineering, Vol.2, No.1, pp. 718-726, 2014.
  29. [29] Y. Li, W. K. S. Tang, and G. Chen, “Generating hyperchaos via state feedback control,” Int. J. of Bifurcation and Chaos, Vol.15, No.10, pp. 3367-3375, 2005.
  30. [30] G. Giorgi and S. Komlósi, “Dini derivatives in optimization – Part I,” Rivista di Matematica per le Scienze Economiche e Sociali, Vol.15, No.1, pp. 3-30, 1992.
  31. [31] R. A. Horn and C. R. Johnson, “Matrix analysis,” Cambridge University Press, Cambridge, 2012.
  32. [32] R. Guesmi and M. A. B. Farah, “A new efficient medical image cipher based on hybrid chaotic map and DNA code,” Multimedia Tools and Appl., Vol.80, pp. 1925-1944, 2021.
  33. [33] L. E. Bassham, A. L. Rukhin, J. Soto, J. R. Nechvatal, M. E. Smid, S. D. Leigh, M. Levenson, M. Vangel, N. A. Heckert, and D. L. Banks, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22, 2010.
  34. [34] G. Pérez and H. A. Cerdeira, “Extracting messages masked by chaos,” Phys. Rev. Lett., Vol.74, pp. 1970-1973, 1995.

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