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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 7683687, 15 pages
http://dx.doi.org/10.1155/2016/7683687
Research Article

A Novel 1D Hybrid Chaotic Map-Based Image Compression and Encryption Using Compressed Sensing and Fibonacci-Lucas Transform

School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China

Received 31 December 2015; Revised 17 April 2016; Accepted 18 April 2016

Academic Editor: Zhen-Lai Han

Copyright © 2016 Tongfeng Zhang et al. 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. C. Schwartz, “A new graphical method for encryption of computer data,” Cryptologia, vol. 15, no. 1, pp. 43–46, 2010. View at Publisher · View at Google Scholar
  2. N. Bourbakis and C. Alexopoulos, “Picture data encryption using SCAN pattern,” Pattern Recognition, vol. 25, no. 6, pp. 567–581, 1992. View at Publisher · View at Google Scholar · View at Scopus
  3. R. Matthews, “On the derivation of a “chaotic” encryption algorithm,” Cryptologia, vol. 13, no. 1, pp. 29–42, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 8, no. 6, pp. 1259–1284, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. G. Chen, Y. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos, Solitons and Fractals, vol. 21, no. 3, pp. 749–761, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. X. Huang, “Image encryption algorithm using chaotic Chebyshev generator,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2411–2417, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. N. K. Pareek, V. Patidar, and K. K. Sud, “Image encryption using chaotic logistic map,” Image and Vision Computing, vol. 24, no. 9, pp. 926–934, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. T. Gao and Z. Chen, “Image encryption based on a new total shuffling algorithm,” Chaos, Solitons & Fractals, vol. 38, no. 1, pp. 213–220, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Lian, J. Sun, and Z. Wang, “A block cipher based on a suitable use of the chaotic standard map,” Chaos, Solitons and Fractals, vol. 26, no. 1, pp. 117–129, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. G. Alvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 8, pp. 2129–2151, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. R. Brown and L. O. Chua, “Clarifying chaos: examples and counterexamples,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 6, no. 2, pp. 219–249, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. V. Patidar, N. K. Pareek, and K. K. Sud, “A new substitution-diffusion based image cipher using chaotic standard and logistic maps,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 3056–3075, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Wang, K.-W. Wong, X. Liao, and T. Xiang, “A block cipher with dynamic S-boxes based on tent map,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 3089–3099, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. H. S. Kwok and W. K. S. Tang, “A fast image encryption system based on chaotic maps with finite precision representation,” Chaos, Solitons & Fractals, vol. 32, no. 4, pp. 1518–1529, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Optics Communications, vol. 284, no. 16-17, pp. 3895–3903, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. O. Mirzaei, M. Yaghoobi, and H. Irani, “A new image encryption method: parallel sub-image encryption with hyper chaos,” Nonlinear Dynamics, vol. 67, no. 1, pp. 557–566, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. Y. Zhang and D. Xiao, “Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform,” Optics and Lasers in Engineering, vol. 51, no. 4, pp. 472–480, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Mazloom and A. M. Eftekhari-Moghadam, “Color image encryption based on coupled nonlinear chaotic map,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1745–1754, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Zhou, L. Bao, and C. L. Philip Chen, “A new 1D chaotic system for image encryption,” Signal Processing, vol. 97, pp. 172–182, 2014. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. Zhou, Z. Hua, C.-M. Pun, and C. L. Philip Chen, “Cascade chaotic system with applications,” IEEE Transactions on Cybernetics, vol. 45, no. 9, pp. 2001–2012, 2015. View at Publisher · View at Google Scholar · View at Scopus
  21. N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Optics Communications, vol. 343, pp. 10–21, 2015. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Zhao, L. Wang, W. Liang, W. Cheng, and L. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Optics Communications, vol. 353, pp. 90–95, 2015. View at Publisher · View at Google Scholar · View at Scopus
  23. N. Zhou, J. Yang, C. Tan, S. Pan, and Z. Zhou, “Double-image encryption scheme combining DWT-based compressive sensing with discrete fractional random transform,” Optics Communications, vol. 354, pp. 112–121, 2015. View at Publisher · View at Google Scholar · View at Scopus
  24. N. Rawat, R. Kumar, and B.-G. Lee, “Implementing compressive fractional Fourier transformation with iterative kernel steering regression in double random phase encoding,” Optik, vol. 125, no. 18, pp. 5414–5417, 2014. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Liu, D. Xiao, Y. Liu, and Y. Zhang, “Securely compressive sensing using double random phase encoding,” Optik, vol. 126, no. 20, pp. 2663–2670, 2015. View at Publisher · View at Google Scholar · View at Scopus
  26. V. Cambareri, M. Mangia, F. Pareschi, R. Rovatti, and G. Setti, “On known-plaintext attacks to a compressed sensing-based encryption: a quantitative analysis,” IEEE Transactions on Information Forensics and Security, vol. 10, no. 10, pp. 2182–2195, 2015. View at Publisher · View at Google Scholar · View at Scopus
  27. L.-B. Zhang, Z.-L. Zhu, B.-Q. Yang, W.-Y. Liu, H.-F. Zhu, and M.-Y. Zou, “Medical image encryption and compression scheme using compressive sensing and pixel swapping based permutation approach,” Mathematical Problems in Engineering, vol. 2015, Article ID 940638, 9 pages, 2015. View at Publisher · View at Google Scholar · View at Scopus
  28. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on Information Theory, vol. 53, no. 12, pp. 4655–4666, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for l1-minimization with applications to compressed sensing,” SIAM Journal on Imaging Sciences, vol. 1, no. 1, pp. 143–168, 2008. View at Publisher · View at Google Scholar
  32. M. Mishra, P. Mishra, M. C. Adhikary, and S. Kumar, “Image encryption using fibonacci-lucas transformation,” International Journal on Cryptography and Information Security, vol. 2, no. 3, pp. 131–141, 2012. View at Google Scholar
  33. Y. Wang, K.-W. Wong, X. Liao, T. Xiang, and G. Chen, “A chaos-based image encryption algorithm with variable control parameters,” Chaos, Solitons & Fractals, vol. 41, no. 4, pp. 1773–1783, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. C. E. Shannon, “Communication theory of secrecy systems,” Bell System Technical Journal, vol. 28, no. 4, pp. 656–715, 1949. View at Publisher · View at Google Scholar · View at MathSciNet