Skip to main content
Log in

Double chaotic image encryption algorithm based on optimal sequence solution and fractional transform

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

In order to solve the shortcomings of the traditional chaotic encryption and problems of low security, the double chaotic image encryption algorithm based on fractional Fourier transform is proposed. In this algorithm, the optimization algorithm is obtained with the help of Henon mapping and fractional Fourier transforms, then the ciphertext image obtained by the optimization algorithm is taken as input, and according to the sequence of the optimal solution, the logistic chaos is synthesized to obtain the final ciphertext image. This algorithm combines chaotic systems and Fourier transforms, which allows the plaintext to be well hidden, and spatial and frequency domain scrambling is achieved. After experiments, the results show that the improved encryption algorithm achieves better encryption effect. It not only has strong sensitivity and large key space, but also can resist attacks effectively. It has certain application value in image information security.

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

Access this article

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

Similar content being viewed by others

References

  1. Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28, 656–715 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  2. Matthews, R.: On the derivation of a ‘‘chaotic encryption algorithm’’. Cryptologia 13(1), 29–42 (1989)

    Article  MathSciNet  Google Scholar 

  3. Huang, D.M., Geng, X., Wei, L.F.: Secure retrieval schemes for encrypted remote sensing image based on Henon mapping. J. Softw. 27(7), 1729–1740 (2016)

    MathSciNet  Google Scholar 

  4. Zhao, G.M., Li, G.D.: Encryption scheme based on generalized Henon mapping and CNN hyperchaotic system. Acta Sci. Nat. Univ. Sunyatsen J. Nat. Sci. 1, 141–145 (2015)

    MATH  Google Scholar 

  5. Huang, Q.M., Li, G.D.: Application research of image encryption based on hyperchaos of CNN. Jiangxi Mianyang Norm. Univ. 2, 60–66 (2017)

    Google Scholar 

  6. Wang, X., Wang, T.: A novel algorithm for image encryption based on couple chaotic systems. Int. J. Mod. Phys. B 26(30), 1250175–1250183 (2012)

    Article  MATH  Google Scholar 

  7. Ganesan, K., Murali, K.: Image encryption using eight dimensional chaotic cat map. Eur. Phys. J. Spec. Top. 223(8), 1611–1622 (2014)

    Article  Google Scholar 

  8. Cheng, P., Yang, H., Wei, P., Zhang, W.: A fast image encryption algorithm based on chaotic and lookup table. Nonlinear Dyn. 79(3), 2121–2131 (2015)

    Article  Google Scholar 

  9. Xie, G.B., Deng, H.J.: Image encryption algorithm based on quantum chaos and fractional fourier transform. J. Comput. Eng. Appl. (2017). https://doi.org/10.3778/j.issn.1002-8331.1705-0066

    Google Scholar 

  10. Xie, G.B., Jiang, X.H.: Double chaotic image encryption algorithm based on two-dimensional discrete fractional Fourier transform. Comput. Eng. Appl. (2017). https://doi.org/10.3778/j.issn.1002-8331.1609-0147

    Google Scholar 

  11. Yan, S., Cheng, D.: An image encryption algorithm based on dct and chaotic sequences. J. Xuzhou Instit Technol (Nat. Sci. Ed.), (4), pp. 39–43 (2014)

  12. Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024 (1994)

    Article  Google Scholar 

  13. Fei, Shi, Hongmei, Zhang, Xiangli, Zhang: Image encryption algorithm based on chaotic map and DNA coding. Comput. Eng. Appl. 5, 91–95 (2018)

    Google Scholar 

  14. Yang, J., Wu, W.: Color image encryption algorithm based on chaotic system and dynamic DNA coding and operations. Comput. Eng. 44(2), 151–157 (2018)

    Article  Google Scholar 

  15. Pan-Chi, L.I., Ai-Ping, L.U.: Color image encryption method based on qubits rotation about axis. Control Decis 31(8), 1363–1371 (2016)

    Google Scholar 

  16. Yang, Xu, Yingjiu, Huang, Hairong, Li: Research on image encryption algorithm based on quantum logistic mapping. Package Eng. 7, 180–186 (2018)

    Google Scholar 

  17. Yonghong, Zhang, Bo, Zhang: Image encryption algorithm based on logistic chaotic system. J. Comput. Appl. 32(6), 1770–1773 (2015)

    Google Scholar 

  18. Jianguo, Jin, Le, Wang, Mingjun, Wei, et al.: Video encryption of chaotic key modulation DFRFT rotation factor. J. Chin. Pict. Gr. 18(12), 1567–1573 (2013)

    Google Scholar 

  19. Mohindru, P., Khanna, R., Bhatia, S.S.: An improved product theorem for fractional fourier transform. Proc. Natl. Acad. Sci. India 82(4), 343–345 (2012)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is partially supported by Natural resources fund of Xinjiang Uygur autonomous region (2017D01A24); National Natural science foundation of China (11461063); Xinjiang University of finance postgraduate research innovation project (XJUFE2017K006); Xinjiang University of finance postgraduate research innovation project (2018K041).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guo-dong Li.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Gd., Wang, Ll. Double chaotic image encryption algorithm based on optimal sequence solution and fractional transform. Vis Comput 35, 1267–1277 (2019). https://doi.org/10.1007/s00371-018-1574-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-018-1574-y

Keywords

Navigation