Skip to main content
SpringerLink
Log in

Image bit planes approximate reconstruction and encryption based on Gaussian function and multiple parameters chaos

  • Regular Paper
  • Published:
Multimedia Systems Aims and scope Submit manuscript

Abstract

A hybrid image approximate encryption scheme is proposed in this paper. Replacing the full original image with the approximate reconstructed image, the encryption scheme is carried out in the pattern of diffusion, scrambling, and the nonlinear transformation of matrices. A chaotic map with multiple parameters, Gaussian function, and a nonlinear transformation of matrices are composited to form the cryptosystem. Meanwhile, multiple tools and techniques such as dot operation of matrices, random matrix, and sequence rearrangement, etc., are composed to support the scheme. Statistical analysis of the cipher randomness is carried out in the light of international standard SP800 R1a to verify the cryptosystem security, and the encryption simulations are implemented to test the algorithm feasibility and effectiveness. Furthermore, some performance indexes, including key space, key sensitivity, statistical properties, and differential analysis, etc., are taken into account to evaluate the security and robustness of the algorithm. The main contributions of our work includes: different from most full encryption methods, our algorithm is oriented to encrypt the key information of the images; a novel chaos with multiple parameters and Gaussian membership function are introduced to generate the cipher; multiple nonlinear methods are used to implemented the plaintext related technique; the security of the cryptosystem are strictly test by the randomness universal standard. Since the proposed algorithm demonstrates local advantages over the classical ones, it is expected to be applied in practical image encryption.

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
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Zhang, Y.: Chaotic Digital Image Cryptosystem [M]. Tsinghua University Press, Beijing (2016)

    Google Scholar 

  2. Guo, F.M., Tu, L.: Application of Chaos Theory in Cryptography [M]. Beijing Institute of Technology Press, Beijing (2015)

    Google Scholar 

  3. Chai, X., Chen, Y., Broyde, L.: A novel chaos-based image encryption algorithm using DNA sequence operations. Opt. Lasers Eng. 88, 197–213 (2017)

    Article  Google Scholar 

  4. Liu, Y., Jiang, Z., Xu, X., et al.: Optical image encryption algorithm based on hyper-chaos and public-key cryptography. Opt. Laser Technol. 127, 106171 (2020)

    Article  Google Scholar 

  5. Wang, S.C., Wang, C.H., Xu, C.: An image encryption algorithm based on a hidden attractor chaos system and the Knuth-Durstenfeld algorithm. Opt. Lasers Eng. 128, 105995 (2019)

    Article  Google Scholar 

  6. Xue, H., Du, J., Li, S., et al.: Region of interest encryption for color images based on a hyper chaotic system with three positive Lyapunov exponents. Opt. Laser Technol. 106, 506–516 (2018)

    Article  Google Scholar 

  7. Huang, Z.J., Cheng, S., Gong, L.H., et al.: Nonlinear optical multi-image encryption scheme with two-dimensional linear canonical transform. Opt. Lasers Eng. 124, 105821 (2019)

    Article  Google Scholar 

  8. Su, Y., Xu, W., Zhao, J.: Optical image encryption based on chaotic fingerprint phase mask and pattern-illuminated Fourier ptychography. Opt. Lasers Eng. 128, 106020 (2020)

    Article  Google Scholar 

  9. Xu, L., Guo, X., Li, Z., et al.: A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion. Opt. Lasers Eng. 91, 41–52 (2017)

    Article  Google Scholar 

  10. Liang, X., Tan, X., Tao, L., et al.: Image hybrid encryption based on matrix nonlinear operation and generalized Arnold transformation. Int. J. Pattern Recogn. Artif. Intell. 33(6), 19540221–195402217 (2019)

    Article  Google Scholar 

  11. Zhang, Y.: The unified image encryption algorithm based on chaos and cubic S-Box. Inf. Sci. 450, 361–377 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hua, Z., Zhou, Y., Huang, H.: Cosine-transform-based chaotic system for image encryption. Inf. Sci. 480, 403–419 (2019)

    Article  Google Scholar 

  13. Mansouri, A., Wang, X.: A novel one-dimensional sine powered chaotic map and its application in a new image encryption scheme. Inf. Sci. 520, 46–62 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jin, X., Yin, S., Liu, N., Li, X., Zhao, G., Ge, S.: Color image encryption in non-RGB color spaces. Multimed. Tools Appl. 77(12), 15851–15873 (2018)

    Article  Google Scholar 

  15. Zhang, Y., Chen, A., Tang, Y., et al.: Plaintext-related image encryption algorithm based on perceptron-like network. Inf. Sci. 526, 180–202 (2020)

    Article  MathSciNet  Google Scholar 

  16. Preishuber, M., Hütter, T., Katzenbeisser, S.: Depreciating motivation and empirical security analysis of chaos-based image and video encryption. IEEE Trans. Inf. Forensics Secur. 13(9), 2137–2150 (2018)

    Article  Google Scholar 

  17. Jiang, Z.J.: Fuzzy Mathematics Theory & Application [M]. Electronic Industry Press, Beijing (2015)

    Google Scholar 

  18. Contour Detection and Image Segmentation Resources [DB/OL]. https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/resources.html, 2020

  19. 101_ObjectCategories, The Caltech 101 dataset [DB/OL]. http://www.vision.caltech.edu/Image_Datasets/Caltech101/Caltech101.html#Download, 2020

  20. Zhao, B., Chen, M., Zou, F.S., et al.: Proficiency in MATLAB-Science Computation and the Application of Data Statistics [M]. Posts and Telecommunications Press, Beijing (2018)

    Google Scholar 

  21. Liu, Ch.L.: MATLAB Image Processing [M]. Tsinghua University Press, Beijing (2017)

    Google Scholar 

  22. Zhen, P., Zhao, G., Min, L., Jin, X.: Chaos-based image encryption scheme combining DNA coding and entropy. Multimed. Tools Appl. 75(11), 6303–6319 (2016)

    Article  Google Scholar 

  23. Chen, Y.C., Ye, R.S.: A novel image Encryption algorithm based on improved standard mapping. Comput. Sci. Appl. 7(8), 753–773 (2017)

    Google Scholar 

  24. Rukhin, A., Nechvatal, J., Smid M., et al.: A statistical test suite for random and pseudorandom number generator for cryptographic applications. Special Publication 800–22 Revision 1a. National Intitute of Standards and Technology (NIST). https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf, 2020

Download references

Acknowledgements

We express our sincere gratitude to those who have helped us for this work.

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Hangzhou Normal University, Hangzhou, 311121, China

    Xikun Liang, Limin Tao & Bin Hu

Authors
  1. Xikun Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Limin Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xikun Liang.

Additional information

Communicated by A. Sur.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liang, X., Tao, L. & Hu, B. Image bit planes approximate reconstruction and encryption based on Gaussian function and multiple parameters chaos. Multimedia Systems 29, 305–321 (2023). https://doi.org/10.1007/s00530-022-00994-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00530-022-00994-8

Keywords

Search

Navigation