Synchronization of chaotic-type delayed neural networks and its application

  • M. Kalpana
  • K. Ratnavelu
  • P. Balasubramaniam
  • M. Z. M. Kamali
Original Paper
  • 34 Downloads

Abstract

Our proposed image encryption is based on synchronization of chaotic fuzzy cellular neural networks (FCNNs) with different time delays and uses sampled-data controller. (i) It is known that the chaotic system plays a vital role in secure communication. (ii) FCNNs are more suitable for image processing due to its local connectedness. (iii) There are some results derived on theory part for the problem of synchronization of chaotic delayed FCNNs. (iv) We raise the following question: Is it possible to utilize these obtained chaotic values via FCNNs to image encryption? (v) Finally, we tried the above and succeed. Moreover, numerical instance and comparison results show that the proposed scheme works well and is resistant to differential attack.

Keywords

Chaos Encryption Fuzzy cellular neural networks Leakage delay Linear matrix inequality Sampled-data controller 

Notes

Acknowledgements

This effort was assisted by the Fundamental Research Grant Scheme (FRGS) from MoHE under Grant No. FP051-2016. Dr. M. Kalpana is working as a Post-doctoral Research Fellow at the University of Malaya.

Compliance with ethical standards

Conflict of interest

The authors have no conflicts of interest to declare.

References

  1. 1.
    Kaur, R., Singh, E.K.: Image encryption techniques: a selected review. J. Comput. Eng. (IOSR-JCE) 9, 80–83 (2013)CrossRefGoogle Scholar
  2. 2.
    Feng, G.: Principle and Network Security Technology. Science Press, Beijing (2003)Google Scholar
  3. 3.
    Yu, L., Wang, Z., Wang, W.: The application of hybrid encryption algorithm in software security. In: 4th IEEE International Conference on Computational Intelligence and Communication Networks, pp. 762-765 (2012)Google Scholar
  4. 4.
    Enayatifar, R., Sadaei, H.J., Abdullah, A.H., Lee, M., Isnin, I.F.: A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata. Opt. Lasers Eng. 71, 33–41 (2015)CrossRefGoogle Scholar
  5. 5.
    Carroll, T.L., Pecora, L.M.: Synchronization chaotic circuits. IEEE Trans. Circuits Syst. 38, 453–456 (1991)CrossRefGoogle Scholar
  6. 6.
    Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Kwon, O.M., Park, J.H., Lee, S.M.: Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn. 63, 239–252 (2011)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Moskalenko, O.I., Koronovskii, A.A., Hramov, A.E.: Generalized synchronization of chaos for secure communication: remarkable stability to noise. Phys. Lett. A 374, 2925–2931 (2010)CrossRefMATHGoogle Scholar
  9. 9.
    Wang, H., Han, Z., Zhang, W., Xie, Q.: Chaotic synchronization and secure communication based on descriptor observer. Nonlinear Dyn. 57, 69–73 (2009)CrossRefMATHGoogle Scholar
  10. 10.
    Niyat, A.Y., Moattar, M.H., Torshiz, M.N.: Color image encryption based on hybrid hyper-chaotic system and cellular automata. Opt. Lasers Eng. 90, 225–237 (2017)CrossRefGoogle Scholar
  11. 11.
    Wang, Z., Huang, L.: Synchronization analysis of linearly coupled delayed neural networks with discontinuous activations. Appl. Math. Model. 39, 7427–7441 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Assad, S.E., Farajallah, M.: A new chaos-based image encryption system. Signal Process. Image Commun. 41, 144–157 (2016)CrossRefGoogle Scholar
  13. 13.
    Zhao, J., Wang, S., Chang, Y., Li, X.: A novel image encryption scheme based on an improper fractional-order chaotic system. Nonlinear Dyn. 80, 1721–1729 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Xie, E.Y., Li, C., Yu, S., Lü, J.: On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Process. 132, 150–154 (2017)CrossRefGoogle Scholar
  15. 15.
    Özkaynak, F.: Brief review on application of nonlinear dynamics in image encryption. Nonlinear Dyn. 1–9 (2018)Google Scholar
  16. 16.
    Yang, T., Yang, L.B., Wu, C.W., Chua, L.O.: Fuzzy cellular neural networks: theory. In: Proceedings of the IEEE International Workshop on Cellular Neural Networks and Applications, pp. 181–186 (1996)Google Scholar
  17. 17.
    Yang, T., Yang, L.B., Wu, C.W., Chua, L.O.: Fuzzy cellular neural networks: applications. In: Proceedings of the IEEE International Workshop on Cellular Neural Networks and Applications, pp. 225–230 (1996)Google Scholar
  18. 18.
    Wen, S., Zeng, Z., Huang, T., Meng, Q., Yao, W.: Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans. Neural Netw. Learn. Syst. 26, 1493–1502 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Chen, L., Wu, R., Pan, D.: Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays. Expert Syst. Appl. 38, 6294–6299 (2011)CrossRefGoogle Scholar
  20. 20.
    Liu, Z., Zhang, H., Wang, Z.: Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays. Neurocomputing 72, 1056–1064 (2009)CrossRefGoogle Scholar
  21. 21.
    Balasubramaniam, P., Kalpana, M., Rakkiyappan, R.: Stationary oscillation of interval fuzzy cellular neural networks with mixed delays under impulsive perturbations. Neural Comput. Appl. 22, 1645–1654 (2013)CrossRefGoogle Scholar
  22. 22.
    Li, X., Rakkiyappan, R., Balasubramaniam, P.: Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J. Frankl. Inst. 348, 135–155 (2011)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Balasubramaniam, P., Kalpana, M., Rakkiyappan, R.: Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Math. Comput. Model. 53, 839–853 (2011)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Balasubramaniam, P., Kalpana, M., Rakkiyappan, R.: Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst. Signal Process. 30, 1595–1616 (2011)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Mathematics and Its Applications, vol. 74. Springer, Dordrecht (1992)CrossRefMATHGoogle Scholar
  26. 26.
    Gan, Q., Xu, R., Yang, P.: Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control. Commun. Nonlinear Sci. Numer. Simul. 17, 433–443 (2012)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Yu, J., Hu, C., Jiang, H., Teng, Z.: Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control. Math. Comput. Simul. 82, 895–908 (2012)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Lu, J., Hill, D.J.: Global asymptotical synchronization of chaotic Lur’e systems using sampled data: a linear matrix inequality approach. IEEE Trans. Circuits Syst. II(55), 586–590 (2008)Google Scholar
  29. 29.
    Gan, Q., Liang, Y.: Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. J. Frankl. Inst. 349, 1955–1971 (2012)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Li, N., Zhang, Y., Hu, J., Nie, Z.: Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74, 805–811 (2011)CrossRefGoogle Scholar
  31. 31.
    Li, C., Lin, D., Lü, J.: Cryptanalyzing an image-scrambling encryption algorithm of pixel bits. IEEE MultiMed. 24, 64–71 (2017)CrossRefGoogle Scholar
  32. 32.
    Li, C., Liu, Y., Xie, T., Chen, M.Z.Q.: Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlinear Dyn. 73, 2083–2089 (2013)MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Dang, P.P., Chau, P.M.: Image encryption for secure Internet multimedia applications. IEEE Trans. Consum. Electron. 46, 395–403 (2000)CrossRefGoogle Scholar
  34. 34.
    Fridman, E., Seuret, A., Richard, J.P.: Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40, 1441–1446 (2004)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)CrossRefMATHGoogle Scholar
  36. 36.
    Sanchez, E.N., Perez, J.P.: Input-to-state stability (ISS) analysis for dynamic neural networks. IEEE Trans. Circuits Syst. I(46), 1395–1398 (1999)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Yang, T., Yang, L.B.: Global stability of fuzzy cellular neural network. IEEE Trans. Circuits Syst. I(43), 880–883 (1996)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE Conference on Decision and Control Sydney, Australia, pp. 2805-2810 (2000)Google Scholar
  39. 39.
    Li, T., Fei, S., Zhu, Q.: Design of exponential state estimator for neural networks with distributed delays. Nonlinear Anal. Real World Appl. 10, 1229–1242 (2009)MathSciNetCrossRefMATHGoogle Scholar
  40. 40.
    Boeing, G.: Visual analysis of nonlinear dynamical systems: chaos, fractals, self-similarity and the limits of prediction. Systems 4, 37–54 (2016)CrossRefGoogle Scholar
  41. 41.
    Liu, H., Kadir, A.: Asymmetric color image encryption scheme using 2D discrete-time map. Signal Process. 113, 104–112 (2015)CrossRefGoogle Scholar
  42. 42.
    Dong, C.: Color image encryption using one-time keys and coupled chaotic systems. Signal Process. Image Commun. 29, 628–640 (2014)CrossRefGoogle Scholar
  43. 43.
    Wei, X., Guo, L., Zhang, Q., Zhang, J., Lian, S.: A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J. Syst. Softw. 85, 290–299 (2012)CrossRefGoogle Scholar
  44. 44.
    Wang, X., Zhao, Y., Zhang, H., Guo, K.: A novel color image encryption scheme using alternate chaotic mapping structure. Opt. Lasers Eng. 82, 79–86 (2016)CrossRefGoogle Scholar
  45. 45.
    Wang, X., Zhang, H.: A color image encryption with heterogeneous bit-permutation and correlated chaos. Opt. Commun. 342, 51–60 (2015)CrossRefGoogle Scholar
  46. 46.
    Wu, X., Kan, H., Kurths, J.: A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps. Appl. Soft Comput. 37, 24–39 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • M. Kalpana
    • 1
  • K. Ratnavelu
    • 1
  • P. Balasubramaniam
    • 2
  • M. Z. M. Kamali
    • 3
  1. 1.Institute of Mathematical Sciences, Faculty of ScienceUniversity of MalayaKuala LumpurMalaysia
  2. 2.Department of MathematicsGandhigram Rural Institute - Deemed UniversityGandhigramIndia
  3. 3.Centre for Foundation Studies in ScienceUniversity of MalayaKuala LumpurMalaysia

Personalised recommendations