Skip to main content
SpringerLink
Log in

A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, a quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections is proposed. Firstly, in order to enhance the complexity of trajectory, three impulse signals values are injected into coupled hyper-chaotic Lorenz system during iterations. Then, six sequences generated from this system are used to encrypt red, green and blue components of the quantum color original image by XOR operations and right cyclic shift operations. Six initial values and three impulse signals values are used as keys, which could reduce the burden of keys transmission and make the cryptosystem own a key space large enough to resist exhaustive attack, even the attack from a quantum computer. Numerical simulations demonstrate that the proposed encryption scheme has a good feasibility and effectiveness for protecting quantum color images and is more secure in comparison with other encryption algorithms.

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. Liu, Z., Li, S., Liu, W., et al.: Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding. Opt. Laser Eng. 51(1), 8–14 (2013)

    Article  ADS  Google Scholar 

  2. Zhao, T., Ran, Q., Yuan, L., et al.: Image encryption using fingerprint as key based on phase retrieval algorithm and public key cryptography. Opt. Laser Eng. 72, 12–17 (2015)

    Article  Google Scholar 

  3. Kumar, M., Iqbal, A., Kumar, P.: A new RGB image encryption algorithm based on DNA encoding and elliptic curve Diffie–Hellman cryptography. Signal Process. 125, 187–202 (2016)

    Article  Google Scholar 

  4. Zhou, Y., Bao, L., Chen, C.P.: A new 1D chaotic system for image encryption. Signal Process. 97, 172–182 (2014)

    Article  Google Scholar 

  5. Wang, X., Gu, S., Zhang, Y.: Novel image encryption algorithm based on cycle shift and chaotic system. Opt. Laser Eng. 68, 126–134 (2015)

    Article  ADS  Google Scholar 

  6. Zhou, Y., Bao, L., Chen, C.P.: Image encryption using a new parametric switching chaotic system. Signal Process. 93(11), 3039–3052 (2013)

    Article  Google Scholar 

  7. Zhang, Y., Xiao, D., Shu, Y., et al.: A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations. Signal Process. Image 28(3), 292–300 (2013)

    Article  Google Scholar 

  8. Zhang, X., Zhu, H., Yao, H.: Analysis of a new three-dimensional chaotic system. Nonlinear Dyn. 67(1), 335–343 (2012)

    Article  MATH  Google Scholar 

  9. Feng, G., Cao, J.: Master–slave synchronization of chaotic systems with a modified impulsive controller. Adv. Differ. Equs. 2013(1), 1–12 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Löytynoja, T., Li, X., Jänkälä, K., et al.: Quantum mechanics capacitance molecular mechanics modeling of core-electron binding energies of methanol and methyl nitrite on Ag (111) surface. J. Chem. Phys. 145(2), 024703 (2016)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. 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)

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

    Article  MathSciNet  Google Scholar 

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

  17. 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 

  18. 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)

    Article  Google Scholar 

  19. Li, H.S., Zhu, Q.X., Zhou, R.G., Li, M.C., et al.: Multidimensional color image storage, retrieval, and compression based on quantum amplitudes and phases. Inf. Sci. 273, 212–232 (2014)

    Article  Google Scholar 

  20. 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  MathSciNet  MATH  ADS  Google Scholar 

  21. 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  MathSciNet  MATH  ADS  Google Scholar 

  22. Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quantum Inf. Process. 16(2), 42 (2017)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  23. Zhou, R., Wu, Q., Zhang, M., et al.: 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 

  24. 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  MathSciNet  MATH  ADS  Google Scholar 

  25. Yang, Y.G., Jia, X., Sun, S.J., et al.: Quantum cryptographic algorithm for color images using quantum Fourier transform and double random-phase encoding. Inf. Sci. 277(2), 445–457 (2014)

    Article  Google Scholar 

  26. Hua, T.X., Chen, J., Pei, D.J., Zhang, W.Q., Zhou, N.R.: Quantum image encryption algorithm based on image correlation decomposition. Int. J. Theor. Phys. 54(2), 526–537 (2014)

    Article  MATH  Google Scholar 

  27. 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  MathSciNet  MATH  ADS  Google Scholar 

  28. Yang, Y.G., Pan, Q.X., Sun, S.J., Xu, P.: Novel image encryption based on quantum walks. Sci. Rep. UK 5, 7784 (2015)

    Article  Google Scholar 

  29. Zhou, N., Hua, T., Gong, L., et al.: Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf. Process. 14(4), 1193–1213 (2015)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  30. Yang, Y.G., Tian, J., Lei, H., et al.: Novel quantum image encryption using one-dimensional quantum cellular automata. Inf. Sci. 345, 257–270 (2016)

    Article  Google Scholar 

  31. Gong, L.H., He, X.T., Cheng, S., Hua, T.X., Zhou, N.R.: Quantum image encryption algorithm based on quantum image XOR operations. Int. J. Theor. Phys. 55(7), 3234–3250 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhou, N., Hu, Y., Gong, L., et al.: Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations. Quantum Inf. Process. 16(6), 1–23 (2017)

    MathSciNet  MATH  ADS  Google Scholar 

  33. Tan, R.C., Lei, T., Zhao, Q.M., et al.: Quantum color image encryption algorithm based on a hyper-chaotic system and quantum Fourier transform. Int. J. Theor. Phys. 55(12), 5368–5384 (2016)

    Article  MATH  Google Scholar 

  34. Li, P., Zhao, Y.: A simple encryption algorithm for quantum color image. Int. J. Theor. Phys. 56(6), 1961–1982 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  35. Grassi, G., Severance, F.L., Miller, D.A.: Multi-wing hyperchaotic attractors from coupled lorenz systems. Chaos Solitons Fractals 41(1), 284–291 (2009)

    Article  MATH  ADS  Google Scholar 

  36. Kempe, J., Bacon, D., Lidar, D.A., et al.: Theory of decoherence-free fault-tolerant universal quantum computation. Phys. Rev. A 63(4), 392–396 (2000)

    Google Scholar 

  37. Cabello, A.: Six-qubit permutation-based decoherence-free orthogonal basis. Phys. Rev. A 75(2), 441–445 (2007)

    Article  MathSciNet  Google Scholar 

  38. Maniscalco, S., Francica, F., Zaffino, R.L., et al.: Protecting entanglement via the quantum Zeno effect. Phys. Rev. Lett. 100(9), 090503 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  39. Paz-Silva, G.A., Rezakhani, A.T., Dominy, J.M., et al.: Zeno effect for quantum computation and control. Phys. Rev. Lett. 108(8), 080501 (2012)

    Article  ADS  Google Scholar 

  40. Viola, L., Knill, E., Lloyd, S.: Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82(12), 2417–2421 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  41. Souza, A.M., lvarez, G.A., Suter, D.: Robust dynamical decoupling for quantum computing and quantum memory. Phys. Rev. Lett. 106(24), 240501 (2011)

    Article  ADS  Google Scholar 

  42. Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54(2), 1098–1105 (1995)

    Article  ADS  Google Scholar 

  43. Steane, A.: Multiple-particle interference and quantum error correction. Proc. R. Soc. Lond. A 452(1954), 2551–2577 (1996)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  44. Devitt, S.J., Munro, W.J., Nemoto, K.: Quantum error correction for beginners. Rep. Prog. Phys. 76(7), 076001 (2013)

    Article  ADS  Google Scholar 

  45. Yap, W.S., Phan, R.C.W., Goi, B.M., et al.: On the effective subkey space of some image encryption algorithms using external key. J. Vis. Commun. Image R 40, 51–57 (2016)

    Article  Google Scholar 

  46. Wang, L.Y., Song, H.J., Liu, P.: A novel hybrid color image encryption algorithm using two complex chaotic systems. Opt. Laser Eng. 77, 118–125 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support from the National Natural Science Foundation of China (61671179) and the National Key Basic Research Program of China (2013CB329003).

Author information

Authors and Affiliations

  1. State Key Laboratory of Tunable Laser Technology Research, Institute of Optic-Electronics, Harbin Institute of Technology, Harbin, 150001, China

    Qiwen Ran, Ling Wang, Jing Ma, Liying Tan & Siyuan Yu

Authors
  1. Qiwen Ran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ling Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jing Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Liying Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Siyuan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ling Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ran, Q., Wang, L., Ma, J. et al. A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections. Quantum Inf Process 17, 188 (2018). https://doi.org/10.1007/s11128-018-1958-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1958-y

Keywords

Search

Navigation