Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Quantum image encryption based on generalized affine transform and logistic map

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum circuits of the generalized affine transform are devised based on the novel enhanced quantum representation of digital images. A novel quantum image encryption algorithm combining the generalized affine transform with logistic map is suggested. The gray-level information of the quantum image is encrypted by the XOR operation with a key generator controlled by the logistic map, while the position information of the quantum image is encoded by the generalized affine transform. The encryption keys include the independent control parameters used in the generalized affine transform and the logistic map. Thus, the key space is large enough to frustrate the possible brute-force attack. Numerical simulations and analyses indicate that the proposed algorithm is realizable, robust and has a better performance than its classical counterpart in terms of computational complexity.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  2. Deutsch, D.: Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. London A400, 97–117 (1985)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  4. Venegas-Andraca, S. E., Bose, S.: Quantum computation and image processing: new trends in artificial intelligence. In: Proceedings of the International Conference on Artificial Intelligence IJCAI-03, pp. 1563-1564 (2003)

  5. Lanzagorta, M., Uhlmann, J.: Quantum algorithmic methods for computational geometry. Math. Struct. Comput. Sci. 20(6), 1117–1125 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Trugenberger, C.: Probabilistic quantum memories. Phys. Rev. Lett. 87, 067901 (2001)

    Article  ADS  Google Scholar 

  7. Trugenberger, C.: Phase transitions in quantum pattern recognition. Phys. Rev. Lett. 89, 277903 (2002)

    Article  ADS  Google Scholar 

  8. Mastriani, M.: Optimal Estimation of States in Quantum Image Processing. arXiv:1406.5121 [quant-ph] (2014)

  9. Caraiman, Simona, Manta, V.I.: Image segmentation on a quantum computer. Quantum Inf. Process. 14(5), 1693–1715 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. In: Proceedings of the SPIE Conference on Quantum Information and Computation, pp. 137-147 (2003)

  11. Latorre, J.I.: Image compression and entanglement. arXiv:quant-ph/0510031 (2005)

  12. Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)

    Article  MathSciNet  Google Scholar 

  13. Le, P.Q., Dong, F.Y., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression and processing operations. Quantum Inf. Process. 10(1), 63–84 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sun, B., Iliyasu, A.M., Yan, F., Dong, F.Y., Hirota, K.: An RGB multi-channel representation for images on quantum computers. J. Adv. Comput. Intell. Intell. Inf. 17(3), 404–417 (2013)

    Google Scholar 

  15. Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(12), 2833–2860 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Zhang, Y., Lu, K., Gao, Y.H., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3103–3126 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Li, H.S., Zhu, Q., Song, L., et al.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum Inf. Process. 12(9), 2269–2290 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Li, H.S., Zhu, Q.X., Zhou, R.G., Lan, S., Yang, X.J.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quantum Inf. Process. 13(4), 991–1011 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Mastriani, M.: Quantum Boolean image denoising. Quantum Inf. Process. 14(5), 1647–1673 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Akhshani, A., Akhavan, A., Lim, S.C., Hassan, Z.: An image encryption scheme based on quantum logistic map. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4653–4661 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Yuan, S.Z., Mao, X., Li, T., Xue, Y.L., Chen, L.J., Xiong, Q.X.: Quantum morphology operations based on quantum representation model. Quantum Inf. Process. 14(5), 1625–1645 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Yan, F., Iliyasu, A.M., Sun, B., Venegas-Andraca, S.E., Dong, F.Y., Hirota, K.: A duple watermarking strategy for multi-channel quantum images. Quantum Inf. Process. 14(5), 1675–1692 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Zhou, N., Liu, Y., Zeng, G., Xiong, J., Zhu, F.: Novel qubit block encryption algorithm with hybrid keys. Phys. A. 375(2), 693–698 (2007)

    Article  Google Scholar 

  24. Abd El-Latif, 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 

  25. Song, X., Wang, S., El-Latif, A.A.A., Niu, X.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimedia Syst. 20(4), 379–388 (2014)

    Article  Google Scholar 

  26. Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int. J. Theor. Phys. 53(7), 2463–2484 (2014)

    Article  MATH  Google Scholar 

  27. Yang, Y.G., Xia, J., Jia, X., Zhang, H.: Novel image encryption/decryption based on quantum Fourier transform and double phase encoding. Quantum Inf. Process. 12(11), 3477–3493 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Song, X.H., Wang, S., Abd El-Latif, 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 

  29. Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Jiang, N., Wang, L.: Analysis and improvement of the quantum Arnold image scrambling. Quantum Inf. Process. 13(7), 1545–1551 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. 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. Quantum Inf. Process. 14(4), 1193–1213 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Devaney, R.L.: An Introduction to Chaotic Dynamical Systems. Westview Press, Boulder (2003)

    MATH  Google Scholar 

  33. Vlatko, V., Adriano, B., Artur, E.: Quantum networks for elementary arithmetic operations. Phys. Rev. A 54(1), 147–153 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  34. Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dynam. 77(4), 1191–1207 (2014)

    Article  Google Scholar 

  35. Ahmed, H., Kalash, H., Allah, O.: Implementation of rc5 block cipher algorithm for image cryptosystems. Int. J. Inf. Technol. 3(4), 245–250 (2007)

    Google Scholar 

  36. Enayatifar, R.: Image encryption via logistic map function and heap tree. Int. J. Phys. Sci. 6(2), 221–228 (2011)

    Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61462061, 61561033 and 61262084), the Natural Science Foundation of Jiangxi Province, China (Grant No. 20151BAB207002), the Research Foundation of the Education Department of Jiangxi Province (Grant No. GJJ14138) and the Open Project of Key Laboratory of Photoelectronics and Telecommunication of Jiangxi Province (Grant No. 2013003).

Author information

Authors and Affiliations

  1. Key Laboratory of Photoelectronics and Telecommunication of Jiangxi Province, Jiangxi Normal University, Nanchang, 330022, China

    Hao-Ran Liang & Xiang-Yang Tao

  2. Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031, China

    Hao-Ran Liang & Nan-Run Zhou

Authors
  1. Hao-Ran Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiang-Yang Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nan-Run Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nan-Run Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liang, HR., Tao, XY. & Zhou, NR. Quantum image encryption based on generalized affine transform and logistic map. Quantum Inf Process 15, 2701–2724 (2016). https://doi.org/10.1007/s11128-016-1304-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-016-1304-1

Keywords

Search

Navigation