Nonlinear Dynamics

, Volume 81, Issue 1–2, pp 511–529 | Cite as

A novel color image encryption algorithm based on spatial permutation and quantum chaotic map

  • Seyed Mohammad SeyedzadehEmail author
  • Benyamin Norouzi
  • Mohammad Reza Mosavi
  • Sattar Mirzakuchaki


In recent years, several algorithms of secure image encryption were studied and developed through chaotic processes. Most of the previous algorithms encrypt color components independently. In this paper, a novel image encryption algorithm based on quantum chaotic map and diffusion–permutation architecture is proposed. First, the new algorithm employs the quantum logistic map to diffuse the relationship of pixels in color components. Next, the keystreams generated by the two-dimensional logistic map are exploited to not only modify the value of diffused pixels, but also spatially permute the pixels of color components at the same time and make the three components affect one another. Finally, the random circular shift operation is applied to the result of the modified and permuted pixels to rearrange bits of each encrypted pixel. In order to achieve the high complexity and the high randomness between these generated keystreams, the two-dimensional logistic map and the quantum chaotic map are independently coupled with nearest-neighboring coupled-map lattices. The results of several experimental analyses about randomness, sensitivity and correlation of the cipher-images show that the proposed algorithm has high security level, high sensitivity and high speed which can be adopted for network security and secure communications.


Image encryption Quantum logistic map Two-dimensional logistic map Nearest-neighboring coupled-map lattices Sensitivity 



The authors would like to thank the Editor and the anonymous Referees for their valuable comments and suggestions to improve this paper.


  1. 1.
    Li, S., Chen, G., Zheng, X.: Multimedia Security Handbook. CRC Press, Boca Raton (2005)Google Scholar
  2. 2.
    Seyedzade, S.M., Mirzakuchaki, S., Atani, R.E.: A novel image encryption algorithm based on hash function, 6th International conference on Machine Vision and Image Processing (MVIP), pp. 1–6 (2010)Google Scholar
  3. 3.
    Norouzi, B., Seyedzadeh, S., Mirzakuchaki, S., Mosavi, M.: A novel image encryption based on hash function with only two-round diffusion process. Multimed. Syst. 20, 45–64 (2014)CrossRefGoogle Scholar
  4. 4.
    Cheng, H., Li, X.: Partial encryption of compressed images and videos. IEEE Trans. Signal Process. 48, 2439–2451 (2000)CrossRefGoogle Scholar
  5. 5.
    Lafe, O.: Data compression and encryption using cellular automata transform. Eng. Appl. Artif. Intell. 10, 581–591 (1998)CrossRefGoogle Scholar
  6. 6.
    Chen, R.-J., Lai, J.-L.: Image security system using recursive cellular automata substitution. Pattern Recognit. 40, 1621–1631 (2007)zbMATHCrossRefGoogle Scholar
  7. 7.
    Dyson, F.J., Falk, H.: Period of a discrete cat mapping. Am. Math. Mon. 99, 603–614 (1992)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Chen, W., Chen, X.: Space-based optical image encryption. Opt. Expr. 18, 27095–27104 (2010)CrossRefGoogle Scholar
  9. 9.
    Guo, Q., Liu, Z., Liu, S.: Color image encryption by using arnold and discrete fractional random transforms in ihs space. Opt. Lasers Eng. 48, 1174–1181 (2010)CrossRefGoogle Scholar
  10. 10.
    Chen, W., Quan, C., Tay, C.: Optical color image encryption based on arnold transform and interference method. Opt. Commun. 282, 3680–3685 (2009)CrossRefGoogle Scholar
  11. 11.
    Liu, Z., Xu, L., Chen, H., Lin, C., et al.: Color image encryption by using arnold transform and color-blend operation in discrete cosine transform domains. Opt. Commun. 284, 123–128 (2011)CrossRefGoogle Scholar
  12. 12.
    Abuturab, M.: Securing color information using arnold transform in gyrator transform domain. Opt. Lasers Eng. 50, 772–779 (2012)CrossRefGoogle Scholar
  13. 13.
    Chen, W., Chen, X.: Optical image encryption using multilevel arnold transform and noninterferometric imaging. Opt. Eng. 50, 117001–117005 (2011)CrossRefGoogle Scholar
  14. 14.
    Lio, H., Wang, X., Kadir, A.: Image encryption using dna complementary rule and chaotic maps. Appl. Soft Comput. 12, 1457–1466 (2012)CrossRefGoogle Scholar
  15. 15.
    Matthew, R.: One the derivation of a chaotic encryption algorithm. Cryptologia 8, 29–42 (1989)CrossRefGoogle Scholar
  16. 16.
    Baptista, M.: Cryptography with chaos. Phys. Lett. A 240, 50–54 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Fridrich, J.: Symmetric ciphers based on two dimensional chaotic maps. Int. J. Bifurc. Chaos 8, 1259–1284 (1998)Google Scholar
  18. 18.
    Zhang, G., Liu, Q.: A novel image encryption method based on total shuffling scheme. Opt. Commun. 284, 2775–2780 (2011)CrossRefGoogle Scholar
  19. 19.
    Eslami, Z., Bakhshandeh, A.: An improvement over an image encryption method based on total shuffling. Opt. Commun. 286, 51–55 (2012)CrossRefGoogle Scholar
  20. 20.
    Tong, X., Cui, M.: Image encryption with compound chaotic sequence cipher shifting dynamically. Image Vis. Comput. 26, 843–850 (2008)CrossRefGoogle Scholar
  21. 21.
    Li, C., Li, S., Chen, G., Halang, W.A.: Cryptanalysis of an image encryption scheme based on a compound chaotic sequence. Image Vis. Comput. 27, 1035–1039 (2009)CrossRefGoogle Scholar
  22. 22.
    Tong, X., Cui, M.: Image encryption scheme based on 3d baker with dynamical compound chaotic sequence cipher generator. Signal Process. 89, 480–491 (2009)zbMATHCrossRefGoogle Scholar
  23. 23.
    Pareek, N., Patidar, V., Sud, K.: Image encryption using chaotic logistic map. Image Vis. Comput. 24, 926–934 (2006)CrossRefGoogle Scholar
  24. 24.
    Mazloom, S., Eftekhari-Moghadam, A.: Color image encryption based on coupled nonlinear chaotic map. Chaos Solitons Fractals 42, 1745–1754 (2009)zbMATHCrossRefGoogle Scholar
  25. 25.
    Seyedzadeh, S.M., Mirzakuchaki, S.: A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map. Signal Process. 92, 1202–1215 (2012)CrossRefGoogle Scholar
  26. 26.
    Norouzi, B., Mirzakuchaki, S., Seyedzadeh, S.M., Mosavi, M.R.: A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Multimed. Tools Appl. 71, 1469–1497 (2014)CrossRefGoogle Scholar
  27. 27.
    Seyedzadeh, S.M., Moosavi, S.M.S., Mirzakuchaki, S.: Using self-adaptive coupled piecewise nonlinear chaotic map for color image encryption scheme, 19th Iranian Conference on Electrical Engineering (ICEE) pp. 1–6 (2011)Google Scholar
  28. 28.
    Norouzi, B., Mirzakuchaki, S.: A fast color image encryption algorithm based on hyper-chaotic systems. Nonlinear Dynamics 78, 995–1015 (2014)Google Scholar
  29. 29.
    Liu, S., Sun, J., Xu, Z.: An improved image encryption algorithm based on chaotic system. J. Comput. 4, 1091–1100 (2009)Google Scholar
  30. 30.
    Akhshani, A., Akhavan, A., Lim, S.-C., Hassan, Z.: An image encryption scheme based on quantum logistic map. Commun. Nonlinear Sci. Numer. Simul. 17, 4653–4661 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  31. 31.
    Wang, X., Teng, L., Qin, X.: A novel colour image encryption algorithm based on chaos. Signal Process. 92, 1101–1108 (2012)CrossRefGoogle Scholar
  32. 32.
    Li, C., Zhang, Y., Ou, R., Wong, K.W.: Breaking a novel colour image encryption algorithm based on chaos. Nonlinear Dyn. 70, 2383–2388 (2012)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Kaneko, K.: Pattern dynamics in spatiotemporal chaos: pattern selection, diffusion of defect and pattern competition intermettency. Phys. D Nonlinear Phenom. 34, 1–41 (1989)zbMATHCrossRefGoogle Scholar
  34. 34.
    Zhang, Q., Guo, L., Wei, X.: Image encryption using dna addition combining with chaotic maps. Math. Comput. Model. 52, 2028–2035 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  35. 35.
    El-Latif, A.A.A., Li, L., Wang, N., Han, Q., Niu, X.: A new approach to chaotic image encryption based on quantum chaotic system, exploiting color spaces. Signal Process. 93, 2986–3000 (2013)CrossRefGoogle Scholar
  36. 36.
    Goggin, M., Sundaram, B., Milonni, P.: Quantum logistic map. Phys. Rev. A 41, 5705–5708 (1990)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Ding, M., Yang, W.: Stability of synchronous chaos and on-off intermittency in coupled map lattices. Phys. Rev. E 56, 4009–4016 (1997)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Wang, Y., Liao, X., Xiao, D., Wong, K.-W.: One-way hash function construction based on 2d coupled map lattices. Inf. Sci. 178, 1391–1406 (2008)zbMATHCrossRefGoogle Scholar
  39. 39.
    Standard, NIST-FIPS: Announcing the advanced encryption standard (AES), Federal Information Processing Standards Publication 197 (2001)Google Scholar
  40. 40.
    Seyedzadeh, S.M., Hashemi, Y.: Image encryption algorithm based on choquet fuzzy integral with self-adaptive pseudo-random number generator, 11th International Conference on Intelligent Systems Design and Applications (ISDA) pp. 642–647 (2011)Google Scholar
  41. 41.
    Seyedzadeh, S.M., Norouzi, B., Mirzakuchaki, S.: Rgb color image encryption based on choquet fuzzy integral. J. Syst. Softw. 97, 128–139 (2014)CrossRefGoogle Scholar
  42. 42.
    Schneier, B.: Applied cryptography: protocols, algorithms, and source code in C, 2nd edn. Wiley, New York (1996)zbMATHGoogle Scholar
  43. 43.
    Norouzi, B., Seyedzadeh, S.M., Mirzakuchaki, S., Mosavi, M.R.: A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos. Multimedia Tools and Applications (2013)Google Scholar
  44. 44.
    Seyedzadeh, S.M., Mirzakuchaki, S.: Image encryption scheme based on choquet fuzzy integral with pseudo-random keystream generator. International Symposium on Artificial Intelligence and Signal Processing (AISP) pp. 101–106 (2011)Google Scholar
  45. 45.
    Walker, J.: ENT Test suite. (1998)
  46. 46.
    Rukhin, A., et al.: A Statistical test suite for random and pseudorandom number generators for cryptographic applications, NIST Special Publication pp. 800–22, (2001).
  47. 47.
    G. Marsaglia, Diehard, A battery of tests for random number generators (1997).
  48. 48.
    Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of applied cryptography. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  49. 49.
    Goldreich, O.: Foundations of cryptography. Weizmann Institute of Science, Rehovot (1995)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Seyed Mohammad Seyedzadeh
    • 1
    Email author
  • Benyamin Norouzi
    • 2
  • Mohammad Reza Mosavi
    • 2
  • Sattar Mirzakuchaki
    • 2
  1. 1.Department of Computer ScienceUniversity of PittsburghPittsburghUSA
  2. 2.Department of Electrical EngineeringIran University Science and TechnologyNarmakIran

Personalised recommendations