Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 713541, 8 pages
http://dx.doi.org/10.1155/2014/713541
Research Article

A Novel Chaotic Map and an Improved Chaos-Based Image Encryption Scheme

1Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong
3College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Received 12 June 2014; Accepted 3 July 2014; Published 20 July 2014

Academic Editor: Qiankun Song

Copyright © 2014 Xianhan Zhang and Yang Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Yoshida, H. Mori, and H. Shigematsu, “Analytic study of chaos of the tent map: band structures, power spectra, and critical behaviors,” Journal of Statistical Physics, vol. 31, no. 2, pp. 279–308, 1983. View at Publisher · View at Google Scholar · View at Scopus
  2. L. Shan, H. Qiang, J. Li, and Z. Wang, “Chaotic optimization algorithm based on Tent map,” Control and Decision, vol. 20, no. 2, pp. 179–182, 2005. View at Google Scholar · View at Scopus
  3. L. Kocarev and G. Jakimoski, “Logistic map as a block encryption algorithm,” Physics Letters A, vol. 289, no. 4-5, pp. 199–206, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. Gutzwiller, “Quantum chaos,” Scientific American, vol. 266, pp. 26–32, 1992. View at Google Scholar
  5. C. Chang-Jian and C. Chen, “Bifurcation and chaos analysis of a flexible rotor supported by turbulent long journal bearings,” Chaos, Solitons and Fractals, vol. 34, no. 4, pp. 1160–1179, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. I. Zelinka, G. Chen, and S. Celikovsky, “Chaos synthesis by evolutionary algorithms,” in Evolutionary Algorithms and Chaotic Systems, pp. 345–382, Springer, 2010. View at Google Scholar
  7. J. Zhang and X. Xiao, “Predicting chaotic time series using recurrent neural network,” Chinese Physics Letters, vol. 17, no. 2, pp. 88–90, 2000. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Han, J. Xi, S. Xu, and F. Yin, “Prediction of chaotic time series based on the recurrent predictor neural network,” IEEE Transactions on Signal Processing, vol. 52, no. 12, pp. 3409–3416, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. M. Ye and X. Wang, “Chaotic time series prediction using least squares support vector machines,” Chinese Physics, vol. 13, no. 4, pp. 454–458, 2004. View at Publisher · View at Google Scholar · View at Scopus
  10. D. S. K. Karunasinghe and S. Liong, “Chaotic time series prediction with a global model: artificial neural network,” Journal of Hydrology, vol. 323, no. 1–4, pp. 92–105, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. W. Zhang, “Global and chaotic dynamics for a parametrically excited thin plate,” Journal of Sound and Vibration, vol. 239, no. 5, pp. 1013–1036, 2001. View at Publisher · View at Google Scholar · View at Scopus
  12. J. G. Lu, “Chaotic dynamics and synchronization of fractional-order Arneodo's systems,” Chaos, Solitons and Fractals, vol. 26, no. 4, pp. 1125–1133, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. O. M. Kwon, J. H. Park, and S. M. Lee, “Secure communication based on chaotic synchronization via interval time-varying delay feedback control,” Nonlinear Dynamics, vol. 63, no. 1-2, pp. 239–252, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. D. Yang, G. Li, and G. Cheng, “On the efficiency of chaos optimization algorithms for global optimization,” Chaos, Solitons and Fractals, vol. 34, no. 4, pp. 1366–1375, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. R. Luo and Y. Wang, “Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication,” Chaos, vol. 22, no. 2, Article ID 023109, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. Cao, “A new hybrid chaotic map and its application on image encryption and hiding,” Mathematical Problems in Engineering, vol. 2013, Article ID 728375, 13 pages, 2013. View at Publisher · View at Google Scholar
  17. J. Guo, Z. Lü, and L. Zhang, “Breaking a chaotic encryption based on henon map,” in Proceedings of the 3rd International Symposium on IEEE Information Processing (ISIP '10), pp. 169–171, Qingdao, China, October 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Naeemabadi, N. Chomachar, M. Zabihi, B. S. Ordoubadi, M. Khalilzadeh, and M. S. Ordoubadi, “Encryption based on variable chaotic key for wireless medical data transmission,” in Proceedings of the 5th International Conference on Application of Information and Communication Technologies (AICT '11), pp. 1–5, IEEE, 2011.
  19. M. T. Rosenstein, J. J. Collins, and C. J. de Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D: Nonlinear Phenomena, vol. 65, no. 1-2, pp. 117–134, 1993. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Kantz, “A robust method to estimate the maximal Lyapunov exponent of a time series,” Physics Letters A, vol. 185, no. 1, pp. 77–87, 1994. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Setare and D. Momeni, “Geodesic stability for Kehagias-Sfetsos black hole in Hořava-lifshitz gravity via Lyapunov exponents,” International Journal of Theoretical Physics, vol. 50, pp. 106–113, 2011. View at Google Scholar
  22. F. Faure, S. Nonnenmacher, and S. de Bièvre, “Scarred eigenstates for quantum cat maps of minimal periods,” Communications in Mathematical Physics, vol. 239, no. 3, pp. 449–492, 2003. View at Publisher · View at Google Scholar · View at Scopus
  23. L. Zhang, X. Liao, and X. Wang, “An image encryption approach based on chaotic maps,” Chaos, Solitons & Fractals, vol. 24, no. 3, pp. 759–765, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. C. Çokal and E. Solak, “Cryptanalysis of a chaos-based image encryption algorithm,” Physics Letters. A, vol. 373, no. 15, pp. 1357–1360, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. S. M. Pincus, “Approximate entropy as a measure of system complexity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 88, no. 6, pp. 2297–2301, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  26. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D: Nonlinear Phenomena, vol. 16, no. 3, pp. 285–317, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  27. E. A. Jackson and A. Hübler, “Periodic entrainment of chaotic logistic map dynamics,” Physica D: Nonlinear Phenomena, vol. 44, no. 3, pp. 407–420, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. S. C. Phatak and S. S. Rao, “Logistic map: a possible random-number generator,” Physical Review E, vol. 51, no. 4, pp. 3670–3678, 1995. View at Publisher · View at Google Scholar · View at Scopus
  29. L. M. Leibowitz, “A simplified binary arithmetic for the Fermat number transform,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 24, no. 5, pp. 356–359, 1976. View at Publisher · View at Google Scholar · View at Scopus
  30. J.-W. Han, C.-S. Park, D.-H. Ryu, and E.-S. Kim, “Optical image encryption based on XOR operations,” Optical Engineering, vol. 38, no. 1, pp. 47–54, 1999. View at Publisher · View at Google Scholar · View at Scopus
  31. W. Yu and J. Cao, “Cryptography based on delayed chaotic neural networks,” Physics Letters A: General, Atomic and Solid State Physics, vol. 356, no. 4-5, pp. 333–338, 2006. View at Publisher · View at Google Scholar · View at Scopus