Skip to main content
SpringerLink
Log in

Image Encryption Application of Chaotic Sequences Incorporating Quantum Keys

  • Research Article
  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

This paper proposes an image encryption algorithm LQBPNN (logistic quantum and back propagation neural network) based on chaotic sequences incorporating quantum keys. Firstly, the improved one-dimensional logistic chaotic sequence is used as the basic key sequence. After the quantum key is introduced, the quantum key is incorporated into the chaotic sequence by nonlinear operation. Then the pixel confused process is completed by the neural network. Finally, two sets of different mixed secret key sequences are used to perform two rounds of diffusion encryption on the confusing image. The experimental results show that the randomness and uniformity of the key sequence are effectively enhanced. The algorithm has a secret key space greater than 2182. The adjacent pixel correlation of the encrypted image is close to 0, and the information entropy is close to 8. The ciphertext image can resist several common attacks such as typical attacks, statistical analysis attacks and differential attacks.

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

Similar content being viewed by others

References

  1. W. L. Guo, M. Z. Mao. Projective lag synchronization and parameter identification of a new hyperchaotic system. International Journal of Automation and Computing, vol. 10, no. 3, pp. 256–259, 2013. DOI: https://doi.org/10.1007/s11633-013-0718-9.

    Article  Google Scholar 

  2. C. J. Xu, Y. S. Wu. Chaos control of a chemical chaotic system via time-delayed feedback control method. International Journal of Automation and Computing, vol. 11, no. 4, pp. 392–398, 2014. DOI: https://doi.org/10.1007/s11633-014-0804-7.

    Article  Google Scholar 

  3. R. Boriga, A. C. Dǎscǎlescu, I. Priescu. A new hyperchaotic map and its application in an image encryption scheme. Signal Processing: Image Communication, vol. 29, no. 8, pp. 887–901, 2014. DOI: https://doi.org/10.1016/j.image.2014.04.001.

    Google Scholar 

  4. E. Yavuz, R. Yazıcı, M. C. Kasapbaşi, E. Yamaç. Enhanced chaotic key-based algorithm for low-entropy image encryption. In Proceedings of the 22nd Signal Processing and Communications Applications Conference, IEEE, Trabzon, Turkey, pp.355–388, 2014. DOI: https://doi.org/10.1109/SIU.2014.6830246.

    Google Scholar 

  5. X. Y. Wang, L. Yang, R. Liu, A. Kadir. A chaotic image encryption algorithm based on perceptron model. Nonlinear Dynamics, vol. 62, no. 3, pp. 615–621, 2010. DOI: https://doi.org/10.1007/s11071-010-9749-8.

    Article  MathSciNet  Google Scholar 

  6. H. J. Liu, X. Y. 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. DOI: https://doi.org/10.1016/j.optcom.2011.04.001.

    Article  Google Scholar 

  7. H. J. Liu, X. Y. Wang, A. Kadir. Image encryption using DNA complementary rule and chaotic maps. Applied Soft Computing, vol. 12, no. 5, pp. 1457–1466, 2012. DOI: https://doi.org/10.1016/j.asoc.2012.01.016.

    Article  Google Scholar 

  8. Z. Y. Liu, T. C. Xia, J. B. Wang. Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem. Chinese Physics B, vol. 27, no. 3, Article number 030502, 2018. DOI: https://doi.org/10.1088/1674-1056/27/3/030502.

    Article  Google Scholar 

  9. J. S. Li, Y. B. Xing, C. Y. Qu, J. X. Zhang. An image encryption method based on tent and Lorenz chaotic systems. In Proceedings of the 6th IEEE International Conference on Software Engineering and Service Science, Beijing, China, pp. 585–586, 2015. DOI: https://doi.org/10.1109/ICSESS.2015.7339125.

  10. M. Mishra, S. Pandit. Image encryption technique based on chaotic system and hash function. In Proceedings of IEEE International Conference on Computer Communication and Systems, Chennai, India, pp. 63–67, 2014. DOI: https://doi.org/10.1109/ICCCS.2014.7068169.

  11. Y. G. Yang, P. Xu, J. Tian, H. Zhang. Analysis and improvement of the dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Information Processing, vol. 13, no. 9, pp. 1931–1936, 2014. DOI: https://doi.org/10.1007/s11128-014-0783-1.

    Article  MathSciNet  Google Scholar 

  12. P. C. Li, A. P. Lu. Color image encryption method based on Qubits rotation about axis. Control and Decision, vol. 31, no. 8, pp. 1363–1371, 2016. DOI: https://doi.org/10.13195/j.kzyjc.2015.0782. (in Chinese)

    MATH  Google Scholar 

  13. P. C. Li, Z. Q. Cao. Quantum bits phase based representation and application for color images. Journal of Electronics & Information Technology, vol. 39, no. 2, pp. 489–493, 2017. DOI: https://doi.org/10.11999/JEIT160303. (in Chinese)

    Article  MathSciNet  Google Scholar 

  14. M. E. Goggin, B. Sundaram, P. W. Milonni. Quantum logistic map. Physical Review A, vol. 41, no. 10, pp. 5705–5708, 1990. DOI: https://doi.org/10.1103/PhysRevA.41.5705.

    Article  MathSciNet  Google Scholar 

  15. S. Behnia, P. Ayubi, W. Soltanpoor. Image encryption based on quantum chaotic map and FSM transforms. In Proceedings of the 15th International Telecommunications Network Strategy and Planning Symposium, IEEE, Rome, Italy, pp. 1–6, 2012. DOI: https://doi.org/10.1109/NETWKS.2012.6381669.

    Google Scholar 

  16. P. Kurzyúski, A. Wójcik. Discrete-time quantum walk approach to state transfer. Physical Review A, vol.83, no. 6, Article number 062315, 2011. DOI: https://doi.org/10.1103/PhysRevA.83.062315.

  17. X. Zhan, H. Qin, Z. H. Bian, J. Li, P. Xue. Perfect state transfer and efficient quantum routing: a discrete-time quantum-walk approach. Physical Review A, vol. 90, no. 1, Article number 012331, 2014. DOI: https://doi.org/10.1103/PhysRevA.90.012331.

  18. M. Li, Y. S. Zhang, G. C. Guo. Quantum random walk in periodic potential on a line. Chinese Physics Letters, vol. 30, no. 2, Article number 020304, 2013. DOI: https://doi.org/10.1088/0256-307X/30/2/020304.

    Article  MathSciNet  Google Scholar 

  19. N. Konno. The uniform measure for discrete-time quantum walks in one dimension. Quantum Information Processing, vol. 13, no. 5, pp. 1103–1125, 2014. DOI https://doi.org/10.1007/s11128-013-0714-6.

    Article  MathSciNet  Google Scholar 

  20. H. J. Liu, X. Y. 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. DOI: https://doi.org/10.1016/j.camwa.2010.03.017.

    Article  MathSciNet  Google Scholar 

  21. Y. Q. Zhang, X. Y. Wang. A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice. Information Sciences, vol. 273, pp. 329–351, 2014. DOI: https://doi.org/10.1016/j.ins.2014.02.156.

    Article  Google Scholar 

  22. X. Y. Wang, L. Teng, X. Qin. A novel colour image encryption algorithm based on chaos. Signal Processing, vol. 92, no. 4, pp. 1101–1108, 2012. DOI: https://doi.org/10.1016/j.sigpro.2011.10.023.

    Article  MathSciNet  Google Scholar 

  23. X. Y. Wang, Y. Q. Zhang, X. M. Bao. A novel chaotic image encryption scheme using DNA sequence operations. Optics and Lasers in Engineering, vol. 73, pp. 53–61, 2015. DOI: https://doi.org/10.1016/j.optlaseng.2015.03.022.

    Article  Google Scholar 

  24. X. Y. Wang, L. T. Liu, Y. Q. Zhang. A novel chaotic block image encryption algorithm based on dynamic random growth technique. Optics and Lasers in Engineering, vol. 66, pp. 10–18, 2015. DOI: https://doi.org/10.1016/j.optlaseng.2014.08.005.

    Article  Google Scholar 

  25. S. Amina, F. K. Mohamed. An efficient and secure chaotic cipher algorithm for image content preservation. Communications in Nonlinear Science and Numerical Simulation, vol. 60, pp. 12–32, 2018. DOI: https://doi.org/10.1016/j.cnsns.2017.12.017.

    Article  Google Scholar 

  26. A. Souyah, K. M. Faraoun. An image encryption scheme combining chaos-memory cellular automata and weighted histogram. Nonlinear Dynamics, vol. 86, no. 1, pp. 639–653, 2016. DOI: https://doi.org/10.1007/s11071-016-2912-0.

    Article  MathSciNet  Google Scholar 

  27. Y. Q. Zhang, X. Y. Wang. A new image encryption algorithm based on non-adjacent coupled map lattices. Applied Soft Computing, vol. 26, pp. 10–20, 2015. DOI: https://doi.org/10.1016/j.asoc.2014.09.039.

    Article  Google Scholar 

  28. Y. Liu, X. J. Tong, J. Ma. Image encryption algorithm based on hyper-chaotic system and dynamic S-box. Multimedia Tools and Applications, vol. 75, no. 13, pp. 7739–7759, 2016. DOI: https://doi.org/10.1007/s11042-015-2691-5.

    Article  Google Scholar 

  29. G. Bhatnagar, Q. M. J. Wu, B. Raman. Image and video encryption based on dual space-filling curves. The Computer Journal, vol. 55, no. 6, pp. 667–685, 2018. DOI: https://doi.org/10.1093/comjnl/bxs009.

    Article  Google Scholar 

  30. Q. Lin, Y. J. Wang, J. Wang. The image encryption scheme with optional dynamic state variables based on hyperchaotic system. Scientia Sinica Technologica, vol. 46, no. 9, pp. 910–918, 2016. DOI: https://doi.org/10.1360/N092016-00115. (in Chinese)

    Article  Google Scholar 

  31. E. Yavuz, R. Yazıcı, M. C. Kasapbaşı, E. Yamaç. A chaos-based image encryption algorithm with simple logical functions. Computers & Electrical Engineering, vol. 54, pp. 471–483, 2016. DOI: https://doi.org/10.1016/j.compeleceng.2015.11.008.

    Article  Google Scholar 

  32. Y. Wu, J. P. Noonan, S. Agaian. NPCR and UACI randomness tests for image encryption. Cyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications, vol. 2, pp. 31–38, 2011.

    Google Scholar 

  33. D. Ravichandran, P. Praveenkumar, J. B. Balaguru Rayappan, R. Amirtharajan. Chaos based crossover and mutation for securing DICOM image. Computers in Biology and Medicine, vol. 72, pp. 170–184, 2016. DOI: https://doi.org/10.1016/j.compbiomed.2016.03.020.

    Article  Google Scholar 

  34. Y. Wu, Y. C. Zhou, G. Saveriades, S. Agaian, J. P. Noonan, P. Natarajan. Local Shannon entropy measure with statistical tests for image randomness. Information Sciences, vol. 222, pp. 323–342, 2013. DOI: https://doi.org/10.1016/j.ins.2012.07.049.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 61402012) and Doctor Foundation of Anhui University of Science and Technology.

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, Anhui University of Science and Technology, Huainan, 232001, China

    Bin Ge & Hai-Bo Luo

Authors
  1. Bin Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hai-Bo Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hai-Bo Luo.

Additional information

Recommended by Associate Editor Zhi-Jie Xu

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ge, B., Luo, HB. Image Encryption Application of Chaotic Sequences Incorporating Quantum Keys. Int. J. Autom. Comput. 17, 123–138 (2020). https://doi.org/10.1007/s11633-019-1173-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-019-1173-z

Keywords

Search

Navigation