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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 728375, 13 pages
http://dx.doi.org/10.1155/2013/728375
Research Article

A New Hybrid Chaotic Map and Its Application on Image Encryption and Hiding

College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Received 4 June 2013; Accepted 27 September 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 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. N. Doraswamy and D. Harkins, Ipsec: the New Security Standard For the Internet, Intranet and Virtual Private Network, Prentice Hall, New York, NY, USA, 2003.
  2. B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C, John Wiley & Sons, New York, NY, USA, 2007.
  3. J. K. Su, F. Hartung, and B. Girod, “Digital watermarking of text, image, and video documents,” Computers and Graphics, vol. 22, no. 6, pp. 687–695, 1998. View at Publisher · View at Google Scholar · View at Scopus
  4. M. Hénon, “A two-dimensional mapping with a strange attractor,” Communications in Mathematical Physics, vol. 50, no. 1, pp. 69–77, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Uhl and A. Pommer, Image and Video Encryption: From Digital Rights Management to Secured Personal Communication, vol. 15, Springer, New York, NY, USA, 2004.
  6. L. Kocarev and S. Lian, Chaos-Based Cryptography: Theory, Algorithms and Applications, vol. 354, Springer, New York, NY, USA, 2011.
  7. P. Stavroulakis and M. Stamp, Handbook of Information and Communication Security, Springer, New York, NY, USA, 2010.
  8. M. E. Smid and D. K. Branstad, “Data encryption standard: past and future,” Proceedings of the IEEE, vol. 76, pp. 550–559, 1988. View at Publisher · View at Google Scholar
  9. S. William, Cryptography and Network Security, 4/E, Pearson Education, New Delhi, India, 2006.
  10. J. L. Freitas and R. R. Oliveira, “Implementação, comparação e análise dos algoritmos IDEA e DES,” in I Encontro Regional em Modelagem e Análise Computacional de Sistemas (ERMACS '04), Goiânia, Brazil, 2004.
  11. J. Daemen and V. Rijmen, The Design of Rijndael: AES-the Advanced Encryption Standard, Springer, New York, NY, USA, 2002. View at MathSciNet
  12. 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
  13. K.-W. Wong, B. S.-H. Kwok, and W.-S. Law, “A fast image encryption scheme based on chaotic standard map,” Physics Letters A, vol. 372, no. 15, pp. 2645–2652, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. C. K. Huang and H. H. Nien, “Multi chaotic systems based pixel shuffle for image encryption,” Optics Communications, vol. 282, no. 11, pp. 2123–2127, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Behnia, A. Akhshani, S. Ahadpour, H. Mahmodi, and A. Akhavan, “A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps,” Physics Letters A, vol. 366, no. 4-5, pp. 391–396, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. X.-Y. Wang, L. Yang, R. Liu, and A. Kadir, “A chaotic image encryption algorithm based on perceptron model,” Nonlinear Dynamics, vol. 62, no. 3, pp. 615–621, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. M. S. Baptista, “Cryptography with chaos,” Physics Letters A, vol. 240, no. 1-2, pp. 50–54, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. G. Álvarez, F. Montoya, M. Romera, and G. Pastor, “Cryptanalysis of an ergodic chaotic cipher,” Physics Letters A, vol. 311, no. 2-3, pp. 172–179, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. A. Kiani-B, K. Fallahi, N. Pariz, and H. Leung, “A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 3, pp. 863–879, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. G. C. Wu and D. Baleanu, “Discrete fractional logistic map and its chaos,” Nonlinear Dynamics, 2013. View at Publisher · View at Google Scholar
  21. N. K. Pareek, V. Patidar, and K. K. Sud, “Cryptography using multiple one-dimensional chaotic maps,” Communications in Nonlinear Science and Numerical Simulation, vol. 10, no. 7, pp. 715–723, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. 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
  23. G. Álvarez, F. Montoya, M. Romera, and G. Pastor, “Cryptanalysis of a discrete chaotic cryptosystem using external key,” Physics Letters A, vol. 319, no. 3-4, pp. 334–339, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. C. Li, S. Li, M. Asim, J. Nunez, G. Alvarez, and G. Chen, “On the security defects of an image encryption scheme,” Image and Vision Computing, vol. 27, no. 9, pp. 1371–1381, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. S. Li, X. Mou, Y. Cai, Z. Ji, and J. Zhang, “On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision,” Computer Physics Communications, vol. 153, no. 1, pp. 52–58, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  27. H. Liu and X. Wang, “Color image encryption based on one-time keys and robust chaotic maps,” Computers & Mathematics with Applications, vol. 59, no. 10, pp. 3320–3327, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. P. F. Verhulst, “Recherches mathématiques sur la loi d’accroissement de la population,” Nouveaux Mémoires de l’académie Royale des Sciences et Belles-Lettres de Bruxelles, vol. 18, pp. 3–38, 1845. View at Google Scholar
  29. R. M. May, “Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos,” Science, vol. 186, no. 4164, pp. 645–647, 1974. View at Publisher · View at Google Scholar · View at Scopus
  30. K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Optics Communications, vol. 30, no. 2, pp. 257–261, 1979. View at Publisher · View at Google Scholar · View at Scopus
  31. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D, vol. 16, no. 3, pp. 285–317, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. G. Elert, The Chaos Hypertextbook: Measuring Chaos, vol. 10, 2003.
  33. K. Mahmoud, S. Datta, and J. Flint, Frequency Domain Watermarking: An Overview, 2003.
  34. C. E. Shannon, “A mathematical theory of communication,” ACM SIGMOBILE Mobile Computing and Communications Review, vol. 5, pp. 3–55, 2001. View at Google Scholar
  35. Q. Huynh-Thu and M. Ghanbari, “Scope of validity of PSNR in image/video quality assessment,” Electronics Letters, vol. 44, no. 13, pp. 800–801, 2008. View at Publisher · View at Google Scholar · View at Scopus
  36. A. Cilardo, L. Coppolino, N. Mazzocca, and L. Romano, “Elliptic curve cryptography engineering,” Proceedings of the IEEE, vol. 94, no. 2, pp. 395–405, 2006. View at Publisher · View at Google Scholar · View at Scopus
  37. Y. Wu, J. P. Noonan, and S. Agaian, “NPCR and UACI randomness tests for image encryption,” Cyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications, pp. 31–38, 2011. View at Google Scholar