Skip to main content
SpringerLink
Log in

Quantum Image Encryption Based on Henon Mapping

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Quantum image processing has great significance as a branch of quantum computing. This paper gives a quantum image encryption based on Henon mapping, which breaks away from the restriction of classical computers and does the work in quantum computers end to end, including the generation of the chaos sequence, the encryption and the decryption. The algorithm is based on the GQIR quantum image representation model and the two-dimensional Henon chaotic mapping. However, the decimal sequence generated by Henon mapping can not be directly applied to quantum computers. Hence, we reform the Henon mapping by binary shift. The quantum image is encrypted by being XORed with the quantum Henon mapping. Simulation experiments indicate that the encrypted image has good radomness and the pixel values are evenly distributed. Since the chaotic sequence itself is suitable for image encryption, coupled with its own quantum confidentiality, the encryption method of this paper is safe, convenient and reliable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Fridrich, J.: Image encryption based on chaotic maps. IEEE Int. Conf. Syst. 2, 1105–1110 (1997)

    Google Scholar 

  2. Luo, Y.L., Du, M.H.: Image encryption algorithm based on quantum logistic map in wavelet domain. J. South China Univ. Technol. (Nat. Sci. Edn.) 41(6), 53–62 (2013)

    Google Scholar 

  3. Zhou, R.G., Wu, Q., Zhang, M.Q., Shen, C.Y.: A quantum image encryption algorithm based on quantum image geometric transformations. Int. J. Theor. Phys. 52 (6), 480–487 (2012)

    MathSciNet  Google Scholar 

  4. Song, X.H., Wang, S., El-Latif, A.A.A., Niu, X.M.: Quantum image encryption based on restricted geometric and color transformations. Quantum Inf. Process 13(8), 1765–1787 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Zhou, N.R., Hua, T.X., Gong, L.H., Pei, D.J., Liao, Q.H.: Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quant. Inf. Process. 14(4), 1193–1213 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Hua, T., Chen, J., Pei, D., Zhang, W., Zhou, N.: Quantum image encryption algorithm based on image correlation decomposition. Int. J. Theor. Phys. 54(2), 526–537 (2015)

    Article  MATH  Google Scholar 

  7. Zheng, F., Tian, X.J., Fan, W.H., Li, X.Y., Gao, B.: Image encryption based on Henon map. J. Beijing Univ. Posts Telecommun. 31(1), 66–70 (2008)

    Google Scholar 

  8. 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(11), 2986–3000 (2013)

    Article  Google Scholar 

  9. Cao, G., Zhou, J., Zhang, Y.: Quantum chaotic image encryption with one time running key. Int. J. Secur. Appl. 8(4), 77–88 (2014)

    Google Scholar 

  10. Seyedzadeh, S.M., Norouzi, B., Mosavi, M.R., Mirzakuchaki, S.: A novel color image encryption algorithm based on spatial permutation and quantum chaotic map. Nonlin. Dyn. 81(1–2), 511–529 (2015)

    Article  MathSciNet  Google Scholar 

  11. Liang, H.R., Tao, X.Y., Zhou, N.R.: Quantum image encryption based on generalized affine transform and logistic map. Quantum Inf. Process 15(7), 2701–2724 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Tan, R.C., Lei, T., Zhao, Q.M., Gong, L.H., Zhou, Z.H.: Quantum color image encryption algorithm based on a hyper-chaotic system and quantum fourier transform. Int. J. Theor. Phys. 55(12), 1–17 (2016)

    Article  MATH  Google Scholar 

  13. Wang, H., Wang, J., Geng, Y.C., Song, Y., Liu, J.Q.: Quantum image encryption based on iterative framework of frequency-spatial domain transforms. Int. J. Theor. Phys. 56(8), 1–21 (2017)

    MathSciNet  MATH  Google Scholar 

  14. Li, L., Abd-El-Atty, B., El-Latif, A.A.A., Ghoneim, A.: Quantum color image encryption based on multiple discrete chaotic systems. IEEE Comput. Sci. Inf. Sys., 555–559 (2017)

  15. Zhou, N., Chen, W., Yan, X., Wang, Y.: Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system. Quantum Inf. Process 17(6), 137 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Wang, J., Geng, Y.C., Han, L., Liu, J.Q.: Quantum image encryption algorithm based on quantum key image. International Journal of Theoretical Physics, published online (2018)

  17. Wang, J., Wang, H., Song, Y.: Quantum endpoint detection based on QRDA. Int. J. Theor. Phys. 56(10), 3257–3270 (2017)

    Article  MATH  Google Scholar 

  18. Chen, X.M., Zhou, P.: Tracking control and synchronization for two-dimension discrete chaotic systems. J. Chin. Univ. Posts Telecommun. 9(3), 7–10 (2002)

    Google Scholar 

  19. Pareek, N.K., Patidar, V., Sud, K.K.: Image encryption using chaotic Logistic map. Image Vis. Comput. 24(9), 926–934 (2006)

    Article  Google Scholar 

  20. Henon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50(1), 69–77 (1976)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Al-Hazaimeh, O.M., Al-Jamal, M.F., Alhindawi, N., Omari, A.: Image encryption algorithm based on Lorenz chaotic map with dynamic secret keys. Neural Comput. Appl., 1–11 (2017)

  22. Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Kluwer Acad. Publ. 14(11), 1–26 (2015)

    MathSciNet  MATH  Google Scholar 

  23. Vedral, V.V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Phys. Rev. A 54(1), 147 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  24. Lu, X.W., Jiang, N., Hu, H., Ji, Z.X.: Quantum adder for superposition states. Int. J. Theor. Phys. 57(9), 2575–2584 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kotiyal, S., Thapliyal, H., Ranganathan, N.: Circuit for reversible quantum multiplier based on binary tree optimizing ancilla and garbage bits. In: IEEE International Conference on VLSI Design and 2014 International Conference on Embedded Systems, pp. 545–550 (2014)

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grants No. 61502016 and 61771230, the Joint Open Fund of Information Engineering Team in Intelligent Logistics under Grants No. LDXX2017KF152, and Shandong Provincial Key Research and Development Program under Grants No. 2017CXGC0701.

Author information

Authors and Affiliations

  1. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Nan Jiang, Xuan Dong, Hao Hu & Zhuoxiao Ji

  2. School of Information Science and Technology, Linyi University, Linyi, 276000, China

    Nan Jiang & Wenyin Zhang

  3. Beijing Key Laboratory of Trusted Computing, Beijing, 100124, China

    Nan Jiang

  4. National Engineering Laboratory for Critical Technologies of Information Security Classified Protection, Beijing, 100124, China

    Nan Jiang

Authors
  1. Nan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xuan Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hao Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhuoxiao Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wenyin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nan Jiang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, N., Dong, X., Hu, H. et al. Quantum Image Encryption Based on Henon Mapping. Int J Theor Phys 58, 979–991 (2019). https://doi.org/10.1007/s10773-018-3989-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-018-3989-7

Keywords

Search

Navigation