Skip to main content
SpringerLink
Log in

A quantum watermarking scheme using simple and small-scale quantum circuits

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

A new quantum gray-scale image watermarking scheme by using simple and small-scale quantum circuits is proposed. The NEQR representation for quantum images is used. The image sizes for carrier and watermark are assumed to be \(2n \times 2n\) and \(n \times n\), respectively. At first, a classical watermark with \(n \times n\) image size and 8 bits gray scale is expanded to an image with \(2n \times 2n\) image size and 2 bits gray scale. Then the expanded image is scrambled to be a meaningless image by the SWAP gates that controlled by the keys only known to the operator. The scrambled image is embedded into the carrier image by the CNOT gates (XOR operation). The watermark is extracted from the watermarked image by applying operations in the reverse order. Simulation-based experimental results show that our proposed scheme is excellent in terms of three items, visual quality, robustness performance under noises, and 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

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. Gea-Banacloche, J.: Hiding messages in quantum data. J. Math. Phys. 43(9), 4531–4536 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Martin, K.: Secure communication without encryption? IEEE Secur. Priv. 5(2), 68–71 (2007)

    Article  Google Scholar 

  3. Mogos, G.: A quantum way to data hiding. Int. J. Multimed. Ubiquitous Eng. 4(2), 13–20 (2009)

    Google Scholar 

  4. Iliyasu, A.M., Le, P.Q., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186(1), 126–149 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Iliyasu, A.M., Le, Q.P., HIROTA, K., et al.: Restricted geometric transformation and their applications for quantum image watermarking and authentication. In: Asian Conference on Quantum Information Science 2010 (AQIS2010), pp. 96–97 (2010)

  6. Shaw, B.A., Brun, T.A.: Quantum steganography with noisy quantum channels. Phys. Rev. A 83(2), 022310-1–022310-8 (2011)

    Article  ADS  Google Scholar 

  7. Williams, C.P.: Explorations in Quantum Computing, 2nd edn. Springer, London (2011)

    Book  MATH  Google Scholar 

  8. 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 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, Y., Lu, K., Gao, Y., 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 

  10. Zhang, W.W., Gao, F., Liu, B., Wen, Q.Y., Chen, H.: A watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12(2), 793–803 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Song, X.H., Wang, S., Liu, S., El-Latif, A.A.A., Niu, X.M.: A dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 12(12), 3689–3706 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  13. Yang, Y.G., Jia, X., Xu, P., Tian, J.: Analysis and improvement of the watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12(8), 2765–2769 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Yang, Y.G., Xu, P., Tian, J., Zhang, H.: Analysis and improvement of the dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 13(9), 1931–1936 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Yang, Y.G., Wang, Y., Zhao, Q.Q.: Letter to the Editor regarding Dynamic watermarking scheme for quantum images based on Hadamard transform by Song et al. Multimed. Syst. 20(4), 379–388 (2014)

  16. Jiang, N., Wang, L.: A novel strategy for quantum image steganography based on Moiré pattern. Int. J. Theor. Phys. 54, 1021–1032 (2015)

    Article  MATH  Google Scholar 

  17. Gottesman, D.: Stabilizer Codes and Quantum Error Correction. Ph.D. Thesis, California, Institute of Technology, Pasadena, California (1997). arXiv:quant-ph/9705052

Download references

Author information

Authors and Affiliations

  1. Information Science and Technology, Osaka University, Suita, Japan

    S. Miyake & K. Nakamae

Authors
  1. S. Miyake
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Nakamae
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Nakamae.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Miyake, S., Nakamae, K. A quantum watermarking scheme using simple and small-scale quantum circuits. Quantum Inf Process 15, 1849–1864 (2016). https://doi.org/10.1007/s11128-016-1260-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-016-1260-9

Keywords

Search

Navigation