International Journal of Theoretical Physics

, Volume 54, Issue 2, pp 526–537 | Cite as

Quantum Image Encryption Algorithm Based on Image Correlation Decomposition

  • Tianxiang Hua
  • Jiamin Chen
  • Dongju Pei
  • Wenquan Zhang
  • Nanrun ZhouEmail author


A novel quantum gray-level image encryption and decryption algorithm based on image correlation decomposition is proposed. The correlation among image pixels is established by utilizing the superposition and measurement principle of quantum states. And a whole quantum image is divided into a series of sub-images. These sub-images are stored into a complete binary tree array constructed previously and then randomly performed by one of the operations of quantum random-phase gate, quantum revolving gate and Hadamard transform. The encrypted image can be obtained by superimposing the resulting sub-images with the superposition principle of quantum states. For the encryption algorithm, the keys are the parameters of random phase gate, rotation angle, binary sequence and orthonormal basis states. The security and the computational complexity of the proposed algorithm are analyzed. The proposed encryption algorithm can resist brute force attack due to its very large key space and has lower computational complexity than its classical counterparts.


Image correlation decomposition Quantum computation Quantum image encryption Information security 



This work is supported by the National Natural Science Foundation of China (grant no. 61262084), the Natural Science Foundation of Jiangxi Province, China (grant no. 20122BAB201031), the Foundation for Young Scientists of Jiangxi Province (Jinggang Star) (grant no. 20122BCB23002), the Research Foundation of the Education Department of Jiangxi Province (grant nos. GJJ14138 and GJJ13057), the Open Project of Key Laboratory of Photoeletronics & Telecommunication of Jiangxi Province (grant no. 2013003), and the Innovation Project of Jiangxi Graduate Education (grant no. YC2012-S009).


  1. 1.
    Javidi, B., Zhang, G., Li, J.: Opt. Eng. 35, 2506 (1996)ADSCrossRefGoogle Scholar
  2. 2.
    Peng, X., Zhang, P., Wei, H., Yu, B.: Opt. Lett. 31, 1044 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    Tao, R., Xin, Y., Wang, Y.: Opt. Express 15, 16067 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    Maity, S.P., Kundu, M.K.: Inform. Sci. 181, 450 (2011)CrossRefGoogle Scholar
  5. 5.
    Aung, A., Ng, B.P., Rahardja, S.: J. Signal Process. Sys. 64, 319 (2011)CrossRefGoogle Scholar
  6. 6.
    Zhou, N.R., Wang, Y.X., Gong, L.H.: Opt. Commun. 284, 3234 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Solak, E., Rhouma, R., Belghith, S.: Opt. Commun. 283, 232 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    Rhouma, R., Solak, E., Belghith, S.: Commun. Nonlinear Sci. Numer. Simulat. 15, 1887 (2010)Google Scholar
  9. 9.
    Zhang, Y., Xiao, D.: Nonlinear Dynam. 72, 751 (2013)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Li, C., Liu, Y., Zhang, L.Y., Chen, M.Z.: Int. J. Bifurcat. Chaos 23, 1350075 (2013)CrossRefGoogle Scholar
  11. 11.
    Nielsen, M.A., Chuang, I.L.: Cambridge University Press (2010)Google Scholar
  12. 12.
    Venegas-Andraca, S.E., Bose, S.: Conference on Quantum Information and Computation, Orlando. Fl. 5105, 137 (2003)Google Scholar
  13. 13.
    Venegas-Andraca, S.E., Ball, J.L.: Quantum Inf. Process. 9, 1 (2010)Google Scholar
  14. 14.
    Latorre, J.I.: Quantum Phys. 0510031 (2005)Google Scholar
  15. 15.
    Le, P.Q., Dong, F.Y., Hirota, K.: Quantum Inf. Process. 10, 63 (2011)Google Scholar
  16. 16.
    Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.I.: JACIII 15, 698 (2011)CrossRefGoogle Scholar
  17. 17.
    Sun, B., Le, P.Q., Iliyasu, A.M., Yan, F., Garcia, J.A., Dong, F., Hirota, K.: Intelligent Signal Processing (WISP), 2011 IEEE 7th International Symposium on. Floriana 1 (2011)Google Scholar
  18. 18.
    Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: IAENG Int. J. Apl. Math. 40, 113 (2010)Google Scholar
  19. 19.
    Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: Theor. Comput. Sci. 412, 1406 (2011)CrossRefGoogle Scholar
  20. 20.
    Iliyasu, A.M., Le, P.Q., Dong, F.Y., Hirota, K.: Inform. Sci. 186, 126 (2012)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Le, P.Q., Iliyasu, A.M., Garcia, J.A., Dong, F., Hirota, K.: JACIII 16, 631 (2012)CrossRefGoogle Scholar
  22. 22.
    Goldin, M.A., Francisco, D., Ledesma, S.: Opt. Commun. 284, 2089 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: Quantum Inf. Process. 12, 2833 (2013)Google Scholar
  24. 24.
    Zhang, Y., Lu, K., Gao, Y.H., Xu, K.: Quantum Inf. Process. 12, 3101 (2013)Google Scholar
  25. 25.
    Li, H.S., Zhu, Q.X., Song, L., Shen, C.Y., Zhou, R.G., Mo, J.: Quantum Inf. Process. 12, 2269 (2013)Google Scholar
  26. 26.
    Akhshani, A., Akhavan, A., Lim, S.C., Hassan, Z.: Commun. Nonlinear Sci. Numer. Simulat. 17, 4653 (2012)Google Scholar
  27. 27.
    Zhou, R.G., Wu, Q., Zhang, M.Q., Shen, C.Y.: Int. J. Theor. Phys. 52, 1802 (2013)Google Scholar
  28. 28.
    Zhang, W.W., Gao, F., Liu, B., Wen, Q.Y., Chen, H.: Quantum Inf. Process. 12, 793 (2013)Google Scholar
  29. 29.
    Abd El-Latif, A.A., Li, L., Wang, N., Han, Q., Niu, X.M.: Sig. Process. 93, 2986 (2013)Google Scholar
  30. 30.
    Yang, Y.G., Xia, J., Jia, X., Zhang, H.: Quantum Inf. Process. 12, 3477 (2013)ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    Song, X.H., Wang, S., Abd El-Latif, A.A., Niu, X.M.: Multimedia Syst. 20, 379 (2014)Google Scholar
  32. 32.
    Alvarez, G., Li, S.J.: Int. J. Bifurcat. Chaos 16, 2129 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Tianxiang Hua
    • 1
  • Jiamin Chen
    • 2
  • Dongju Pei
    • 3
  • Wenquan Zhang
    • 1
  • Nanrun Zhou
    • 1
    • 4
    Email author
  1. 1.Department of Electronic Information EngineeringNanchang UniversityNanchangChina
  2. 2.Department of PhysicsNanchang UniversityNanchangChina
  3. 3.School of Computer and Information EngineeringJiangxi Agricultural UniversityNanchangChina
  4. 4.Key Laboratory of Photoeletronics & Telecommunication of Jiangxi ProvinceNanchangChina

Personalised recommendations