Skip to main content
SpringerLink
Log in

Image encryption algorithm with matrix semi-tensor product

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This article proposed an improved 2D-logistic-adjusted-Sine map, which has better ergodicity, pseudo-randomness, unpredictability and wider chaotic range than many existing 2D-chaotic maps. Utilizing improved 2D-logistic-adjusted-Sine map generates chaotic sequences, where the initial values of the system are assigned based on SHA 512 hash function. Compared with traditional encryption scheme, the size of cipher image is different to plain image, because multiply can be applied between mismatched dimensional matrices through semi-tensor product, and therefore, attackers cannot obtain the size of plain image from encryption image. In order to lighten transmission and storage burden, we reduce the results of semi-tensor product by data process. Keys security, correlation coefficient, information entropy and ability of defending differential attack are analyzed to confirm the security of our encryption scheme. Experimental results confirm that the proposed algorithm can encrypt image effectively and securely.

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. Gan, Z.H., Chai, X.L., Han, D.J.: A chaotic image encryption algorithm based on 3-D bit-plane permutation. Neural Comput. Appl. 31(11), 7111–7130 (2019)

    Article  Google Scholar 

  2. Li, Y.P., Wang, C.H., Chen, H.: A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation. Opt. Lasers Eng. 90, 238–246 (2017)

    Article  Google Scholar 

  3. Zou, C.Y., Zhang, Q., Wei, X.P.: Image encryption based on improved Lorenz system. IEEE Access 8, 75728–75740 (2020)

    Article  Google Scholar 

  4. Khan, M., Masood, F.: A novel chaotic image encryption technique based on multiple discrete dynamical maps. Multimedia Tools Appl. 78(18), 26203–26222 (2019)

    Article  Google Scholar 

  5. Khan, F.A., Ahmed, J., Khan, J.S.: A novel image encryption based on Lorenz equation, Gingerbreadman chaotic map and S-8 permutation. J. Intell. Fuzzy Syst. 33(6), 3753–3765 (2017)

    Article  Google Scholar 

  6. Arshad, U., Batool, S.I., Amin, M.: A novel image encryption scheme based on Walsh compressed quantum spinning chaotic Lorenz system. Int. J. Theor. Phys. 58(10), 3565–3588 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  7. Aqeel-ur-Rehman, Liao, X. F., Hahsmi, M. A.: An efficient mixed inter-intra pixels substitution at 2bits-level for image encryption technique using DNA and chaos. Optik 153: 117–134 (2018).

  8. Wang, X.Y., Gao, S.: Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory. Inf. Sci. 507, 16–36 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  9. Suri, S., Vijay, R.: A Pareto-optimal evolutionary approach of image encryption using coupled map lattice and DNA. Neural Comput. Appl. 32(15), 11859–11873 (2020)

    Article  Google Scholar 

  10. Zhu, S.Q., Zhu, C.X.: Secure image encryption algorithm based on hyperchaos and dynamic DNA coding. Entropy 22(7), 772 (2020)

    Article  MathSciNet  Google Scholar 

  11. Luo, Y.Q., Yu, J., Lai, W.R.: A novel chaotic image encryption algorithm based on improved baker map and logistic map. Multimedia Tools Appl. 78(18), 26203–26222 (2019)

    Article  Google Scholar 

  12. Sui, L.S., Du, C., Tian, A.L.: Double-image encryption based on interference and logistic map under the framework of double random phase encoding. Opt. Lasers Eng. 112, 113–122 (2019)

    Google Scholar 

  13. Wu, J.H., Liao, X.F., Yang, B.: Image encryption using 2D Henon-Sine map and DNA approach. Signal Process. 153, 11–23 (2018)

    Article  Google Scholar 

  14. Jiang, N., Dong, X., Hu, H.: Quantum image encryption based on Henon mapping. Int. J. Theor. Phys. 58(3), 979–991 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lv, X.P., Liao, X.F., Yang, B.: Bit-level plane image encryption based on coupled map lattice with time-varying delay. Modern Phys. Lett. B 32(10), 1850124 (2018)

    Article  MathSciNet  Google Scholar 

  16. Zhang, Y.Q., Wang, X.Y.: A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice. Inf. Sci. 273, 329–351 (2014)

    Article  Google Scholar 

  17. Hua, Z.Y., Zhou, Y.C.: Image encryption using 2D Logistic-adjusted-Sine map. Inf. Sci. 339, 237–253 (2016)

    Article  Google Scholar 

  18. Wang, X.Y., Feng, L., Li, R.: A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model. Nonlinear Dyn. 95(4), 2797–2824 (2019)

    Article  MATH  Google Scholar 

  19. Gu, G.S., Ling, J.: A fast image encryption method by using chaotic 3D cat maps. Optik 125(17), 4700–4705 (2014)

    Article  Google Scholar 

  20. Tang, J., Yu, Z.N., Liu, L.F.: A delay coupling method to reduce the dynamical degradation of digital chaotic maps and its application for image encryption. Multimedia Tools Appl. 78(17), 24765–24788 (2019)

    Article  Google Scholar 

  21. Tutueva, A.V., Nepomuceno, E.G., Karimov, A.I.: Adaptive chaotic maps and their application to pseudo-random numbers generation. Chaos Soliton Fractal 133, 109615 (2020)

    Article  MathSciNet  Google Scholar 

  22. Nepomuceno, E.G., Lima, A.M., Arias-Garcia, J.: Minimal digital chaotic system. Chaos, Soliton Fractal 120, 62–66 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang, X.Y., Gao, S.: Application of matrix semi-tensor product in chaotic image encryption. J. Franklin Inst. Eng. Appl. Math. 356(18), 11638–11667 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang, J. M., Wang, J., Jiang, Y. J.: Image encryption algorithm based on the semi-tensor product. Journal of Image and Graphics 21(3), 282–296 (2016)

  25. Wang, J.M., Ye, S.P., Xu, Z.Y.: Low storage space of random measurement matrix for compressed sensing with semi-tensor product. ACTA Electr. Sinica 46(4), 797–804 (2018)

    Google Scholar 

  26. Wang, X.Y., Feng, L., Zhao, H.Y.: Fast image encryption algorithm based on parallel computing system. Inf. Sci. 486, 340–358 (2019)

    Article  MATH  Google Scholar 

  27. Wang, X.Y., Zhang, Y.Q., Bao, X.M.: A novel chaotic image encryption scheme using DNA sequence operations. Opt. Lasers Eng. 73, 53–61 (2015)

    Article  Google Scholar 

  28. Cheng, D.Z., Qi, H.S.: Principle and range of possible applications of semi-tensor product of matrices. Syst. Sci. Math. 32(12), 1488–1496 (2012)

    MathSciNet  MATH  Google Scholar 

  29. May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261(5560), 459–467 (1976)

    Article  MATH  Google Scholar 

  30. Wu, Y., Yang, G.L., Jin, H.X.: Image encryption using the two-dimensional logistic chaotic map. J. Electr. Imaging 20(1), 013014 (2012)

    Article  Google Scholar 

  31. Hua, Z.Y., Zhou, Y.C., Pun, C.M.: 2D Sine Logistic modulation map for image encryption. Inf. Sci. 297, 80–94 (2015)

    Article  Google Scholar 

  32. Hua, Z.Y., Zhou, Y.C.: Image encryption using 2D Logistic-adjusted-Sine map. Inf. Sci. 339, 237–253 (2016)

    Article  Google Scholar 

  33. Cardoso, V., Miranda, A.S., Berti, E.: Geodesic stability, Lyapunov exponents, and quasinormal modes. Phys. Rev. D 79(6), 064016 (2009)

    Article  MathSciNet  Google Scholar 

  34. Pincus, S.M.: Approximate entropy as a measure of system-complexity. Proc. Natl. Acad. Sci. USA 88(6), 2297–2301 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  35. Alvarez, G., Li, S.J.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos 18(6), 2129–2151 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wang, Y., Wong, K.W., Liao, X.F.: A new chaos-based fast image encryption algorithm. Appl. Soft Comput. 11(1), 514–522 (2011)

    Article  Google Scholar 

  37. Wen, W.Y., Hong, Y.K., Fang, Y.M.: A visually secure image encryption scheme based on semi-tensor product compressed sensing. Signal Process. 173, 107580 (2020)

    Article  Google Scholar 

  38. Seyedzadeh, S.M., Mirzakuchaki, S.: A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map. Signal Process. 92(5), 1202–1215 (2012)

    Article  Google Scholar 

  39. Wang, T., Wang, M.H.: Hyperchaotic image encryption algorithm based on bit-level permutation and DNA encoding. Opt. Laser Technol. 132, 106355 (2020)

    Article  Google Scholar 

  40. Asgari-Chenaghlu, M., Feizi-Derakhshi, M.R., Nikzad-Khasmakhi, N.: C-y: Chaotic yolo for user intended image encryption and sharing in social media. Inf. Sci. 542, 212–227 (2021)

    Article  Google Scholar 

  41. Abbasi, A.A., Mazinani, M., Hosseini, R.: Chaotic evolutionary-based image encryption using RNA codons and amino acid truth table. Opt. Laser Technol. 132, 106465 (2020)

    Article  Google Scholar 

  42. Kaur, G., Agarwal, R., Patidar, V.: Chaos based multiple order optical transform for 2D image encryption. Eng. Sci. Technol. Int. J. Jestech 23(5), 998–1014 (2020)

    Google Scholar 

  43. Hua, Z.Y., Jin, F., Xu, B.X.: 2D Logistic-Sine-coupling map for image encryption. Signal Process. 149, 148–161 (2018)

    Article  Google Scholar 

  44. Diaconu, A.V.: Circular inter-intra pixels bit-level permutation and chaos-based image encryption. Inf. Sci. 355, 314–327 (2016)

    Article  Google Scholar 

  45. Wang, X.Y., Liu, C.M., Xu, D.H.: Image encryption scheme using chaos and simulated annealing algorithm. Nonlinear Dyn. 84(3), 1417–1429 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No: 61672124) and the Password Theory Project of the 13th Five-Year. Plan National Cryptography Development Fund (No: MMJJ20170203).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China

    Chengye Zou

  2. School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Xingyuan Wang

  3. School of Software, Dalian University of Technology, Dalian, 116024, China

    Haifeng Li

Authors
  1. Chengye Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingyuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haifeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chengye Zou.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zou, C., Wang, X. & Li, H. Image encryption algorithm with matrix semi-tensor product. Nonlinear Dyn 105, 859–876 (2021). https://doi.org/10.1007/s11071-021-06542-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06542-9

Keywords

Search

Navigation