Skip to main content
Log in

A Secret Sharing Scheme for Quantum Gray and Color Images Based on Encryption

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

This paper is concerned with the better security of quantum image secret sharing (QISS) algorithm. The improved QISS (IQISS) scheme is implemented on both quantum gray image (FRQI) and quantum color image (MCQI). The new IQISS scheme comprises efficient sharing process and recovering process. The core idea of the sharing process is to combine encryption and measurement for two types of quantum secret images to acquire the quantum shadow images. In the recovering process, strip operation is firstly utilized on the shadow images. Afterwards, the decryption algorithm is used to recover the original quantum secret image. Experiments demonstrate that significant improvements in the security are in favor of the proposed approach.

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.

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. 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. Lond. 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. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P.W., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. Part A 52, 3457 (1995)

    Article  ADS  Google Scholar 

  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. Monz, T., Kim, K., Hansel, W., Riebe, M., Villar, A.S., Schindler, P., Chwalla, M., Hennrich, M., Blatt, R.: Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett. 102, 040501 (2009)

    Article  ADS  Google Scholar 

  8. Abal, G., Donangelo, R., Fort, H.: Conditional strategies in iterated quantum games. Physica A 387, 5326–5332 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  9. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of 35th Annual Symposium Foundations of 751 Computer Science, pp. 124–134. IEEE Computer Society Press, Los Almitos (1994)

  10. Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression and processing operations. Quantum Inf. Process. 10(1), 63–84 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR, a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  13. Song, X., Wang, S., Niu, X.: Multi-channel quantum image representation based on phase transform and elementary transformations. J. Inf. Hiding Multimed. Signal Process. 5(4), 574–585 (2014)

    Google Scholar 

  14. Yan, F., Iliyasu Abdullah, M., Venegas-Andraca Salvador, E.: A survey of quantum image representations. Quantum Inf. Process. 15(1), 1–35 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Le, P., Iliyasu, A., Dong, F., Hirota, K.: Fast geometric transformations on quantum images. IAENG Int. J. Appl. Math. 40(3), 113–123 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Le, P., Iliyasu, A., Dong, F., Hirota, K.: Efficient colour transformations on quantum image. J. Adv. Comput. Intell. Intell. Inf. 15(6), 698–706 (2011)

    Article  Google Scholar 

  17. Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process. 14(5), 1589–1604 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Sun, B., Iliyasu, A., Yan, F., Garcia, J., Dong, F., Al-Asmari, A., Hirota, K.: Multi-channel information operations on quantum images. J. Adv. Comput. Intell. Intell. Inf. 18(4) (2014)

  19. Jiang, N., Wu, W., 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 

  20. Zhou, R., Wu, Q., Zhang, M., Shen, C.: Quantum image encryption and decryption algorithms based on quantum image geometric transformations. Int. J. Theor. Phys. 52(6), 1802–1817 (2013)

    Article  MathSciNet  Google Scholar 

  21. Zhou, N., Hua, T., Gong, L., Liao, Q.: 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 

  22. Liang, H., Tao, X., Zhou, N.: Quantum image encryption based on generalized affine transform and logistic map. Quantum Inf. Process. 15(7), 2701–2724 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Yang, Y., Xu, P., Yang, R., Zhou, Y., Shi, W.: Quantum hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption. Sci. Rep. 6, 19788 (2016)

    Article  ADS  Google Scholar 

  24. Zhou, N., Yan, X., Liang, H., Tao, X., Li, G.: Multi-image encryption scheme based on quantum 3D Arnold transform and scaled Zhongtang chaotic system. Quantum Inf. Process. 17, 338 (2018)

    Article  ADS  MATH  Google Scholar 

  25. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  26. Blakley, G.R.: Safeguarding cryptographic keys. Proc. Natl. Comput. Conf. 48, 313–317 (1979)

    Google Scholar 

  27. Naor, M., Shamir, A.: Visual cryptography. In: Proceedings of EUROCRYPT 94, Berlin, Germany, vol. 950, pp. 1–12 (1995)

  28. Luo, H., Yu, F., Pan, J.-S., Lu, Z.-M.: Robust and progressive color image visual secret sharing cooperated with data hiding. In: Eighth International Conference on Intelligent Systems Design and Applications, ISDA08, vol. 3, pp. 431–436 (2008)

  29. Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648–651 (1999)

    Article  ADS  Google Scholar 

  30. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  31. Guo, G.P., Guo, G.C.: Quantum secret sharing without entanglement. Phys. Lett. A 310(4), 247–251 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)

    Article  ADS  Google Scholar 

  33. Song, X., Wang, C.S., Sang, C.J., Yan, C.X., Niu, C.X.: Flexible quantum image secret sharing based on measurement and strip. In: The Tenth IEEE International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIHMSP), pp. 215–218 (2014)

  34. Iliyasu, A.M., Le, P.Q., Dong, F., et al.: A framework for representing and producing movies on quantum computers[J]. Int. J. Quantum Inf. 9(6), 1459–1497 (2011)

    Article  MATH  Google Scholar 

  35. Abd El-Latif, A.A., Li, L., Wang, N., Han, Q., Niu, X.M.: A New approach to chaotic image encryption based on quantum chaotic systems, exploiting color spaces. Signal Process. 93(11), 2986–3000 (2013)

    Article  Google Scholar 

  36. Song, X.H., Wang, S., Abd El-Latif, A.A., et al.: Quantum image encryption based on restricted geometric and color transformations. Quantum Inf. Process. 13, 1765 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (61501148), the Natural Science Foundation of Heilongjiang Province (QC2017075), the Postdoctoral Research Foundation of China (2018M631914) and the Heilongjiang Provincial Postdoctoral Science Foundation (CN) (LBH-Z17042) and the Training Program for Young Creative Talents of Ordinary Universities in Heilongjiang (UNPYSCT-2017078).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xian-Hua Song.

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

Wang, HQ., Song, XH., Chen, LL. et al. A Secret Sharing Scheme for Quantum Gray and Color Images Based on Encryption. Int J Theor Phys 58, 1626–1650 (2019). https://doi.org/10.1007/s10773-019-04057-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-019-04057-z

Keywords

Navigation