Skip to main content
SpringerLink
Log in

Adaptive LSB quantum image watermarking algorithm based on Haar wavelet transforms

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, a novel scheme for quantum image watermarking based on novel enhanced quantum representation of digital images (NEQR) is proposed which can embed a \({{\text {2}}^{n-1}}\times {{\text {2}}^{n-1}}\) binary watermark image into a \({\text {2}^{n}}\times {{\text {2}}^{n}}\) grayscale carrier image. Since only the least significant bits of the diagonal details of the carrier image are embedded with the watermark information, the embedded image is highly consistent with the carrier image after restoration. Again by reversing the embedding, the copyright owner can simply extract the watermarked image. The simulation technique confirms the invisibility and robustness of the proposed watermarking method. The embedded watermarked image and the carrier image are highly relevant, with peak signal-to-noise ratio (PSNR) above 48 dB, structural similarity index metric (SSIM) above 0.997 and correlation coefficient (R) above 0.994. The robustness of the proposal is demonstrated by checking the bit error rate (BER) count and R after it has been attacked. Through the above embedding method, the watermarked image can ensure its robustness and achieve better visual effects.

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
Fig. 16

Similar content being viewed by others

Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Iliyasu, A.M.: Towards realising secure and efficient image and video processing applications on quantum computers[J]. Entropy 15(8), 2874–2974 (2013)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  2. Yan, F., Iliyasu, A.M., Le, P.Q.: Quantum image processing: a review of advances in its security technologies[J]. Int. J. Quant. Inf. 15(03), 1730001 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Stajic, J.: The future of quantum information processing[J]. Science 339(6124), 1163–1163 (2013)

    Article  ADS  Google Scholar 

  4. Venegas-Andraca, S.E., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics[C]. In: Quantum information and computation, pp. 137–147. SPIE (2003)

    Chapter  Google Scholar 

  5. Latorre J.I.: Image compression and entanglement[J]. arXiv preprint arXiv: quant-ph/0510031, (2005)

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

    Article  MathSciNet  Google Scholar 

  7. Zhang, Y., Lu, K., Gao, Y., et al.: NEQR: a novel enhanced quantum representation of digital images[J]. Quant. Inf. Process. 12(8), 2833–2860 (2013)

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, H.S., Zhu, Q., Li, M.C., et al.: Multidimensional color image storage, retrieval, and compression based on quantum amplitudes and phases[J]. Inf. Sci. 273, 212–232 (2014)

    Article  Google Scholar 

  10. Şahin, E., Yilmaz, I.: QRMW: quantum representation of multi wavelength images[J]. Turk. J. Electr. Eng. Comput. Sci. 26(2), 768–779 (2018)

    Article  Google Scholar 

  11. Wang, L., Ran, Q., Ma, J., et al.: QRCI: a new quantum representation model of color digital images[J]. Opt. Commun. 438, 147–158 (2019)

    Article  ADS  Google Scholar 

  12. Wang, B., Hao, M., Li, P., et al.: Quantum representation of indexed images and its applications[J]. Int. J. Theor. Phys. 59(2), 374–402 (2020)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  13. Li, H.S., Fan, P., Xia, H.Y., et al.: Quantum implementation circuits of quantum signal representation and type conversion[J]. IEEE Trans. Circuits Syst. I Regular Pap. 66(1), 341–354 (2018)

    Article  ADS  Google Scholar 

  14. Wang, Z., Xu, M., Zhang, Y.: Review of quantum image processing[J]. Arch. Comput. Methods Eng. 29(2), 737–761 (2022)

    Article  MathSciNet  Google Scholar 

  15. Laurel, C.O., Dong, S.H., Cruz-Irisson, M.: Steganography on quantum pixel images using Shannon entropy[J]. Int. J. Quant. Inf. 14(05), 1650021 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Heidari, S., Naseri, M.: A novel LSB based quantum watermarking[J]. Int. J. Theor. Phys. 55(10), 4205–4218 (2016)

    Article  MATH  Google Scholar 

  17. Yan, F., Iliyasu, A.M., Sun, B., et al.: A duple watermarking strategy for multi-channel quantum images[J]. Quant. Inf. Process. 14(5), 1675–1692 (2015)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  18. Naseri, M., Heidari, S., Baghfalaki, M., et al.: A new secure quantum watermarking scheme[J]. Optik 139, 77–86 (2017)

    Article  ADS  Google Scholar 

  19. Heidari, S., Naseri, M., Gheibi, R., et al.: A new quantum watermarking based on quantum wavelet transforms[J]. Commun. Theor. Phys. 67(6), 732 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  20. Zhou, R.G., Hu, W., Fan, P.: Quantum watermarking scheme through Arnold scrambling and LSB steganography[J]. Quant. Inf. Process. 16(9), 1–21 (2017)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  21. Atta, R., Ghanbari, M.: A high payload steganography mechanism based on wavelet packet transformation and neutrosophic set[J]. J. Vis. Commun. Image Represent. 53, 42–54 (2018)

    Article  Google Scholar 

  22. Atta, R., Ghanbari, M., Elnahry, I.: Advanced image steganography based on exploiting modification direction and neutrosophic set[J]. Multim. Tools Appl. 80(14), 21751–21769 (2021)

    Article  Google Scholar 

  23. Luo, G., Zhou, R.G., Hu, W.W., et al.: Enhanced least significant qubit watermarking scheme for quantum images[J]. Quant. Inf. Process. 17(11), 1–19 (2018)

    Article  MATH  ADS  Google Scholar 

  24. Luo, G., Zhou, R.G., Luo, J., et al.: Adaptive LSB quantum watermarking method using tri-way pixel value differencing[J]. Quant. Inf. Process. 18(2), 1–20 (2019)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  25. Luo, J., Zhou, R.G., Luo, G.F., et al.: Traceable quantum steganography scheme based on pixel value differencing[J]. Sci. Rep. 9(1), 1–12 (2019)

    Article  ADS  Google Scholar 

  26. Zeng, Q.W., Wen, Z.Y., Fu, J.F., et al.: Quantum watermark algorithm based on maximum pixel difference and tent map[J]. Int. J. Theor. Phys. 60(9), 3306–3333 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  27. Wu, D.C., Tsai, W.H.: A steganographic method for images by pixel-value differencing[J]. Pattern Recognit. Lett. 24(9–10), 1613–1626 (2003)

    Article  MATH  ADS  Google Scholar 

  28. Iranmanesh, S., Atta, R., Ghanbari, M.: Implementation of a quantum image watermarking scheme using NEQR on IBM quantum experience[J]. Quant. Inf. Process. 21(6), 1–40 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  29. Taubman, D.S., Marcellin, M.W., Rabbani, M.: JPEG2000: image compression fundamentals, standards and practice. J. Electron. Imag. 11, 286–287 (2002)

    Article  ADS  Google Scholar 

  30. Nanmaran, R., Nagarajan, S., Sindhuja, R., et al.: Wavelet transform based multiple image watermarking technique[C]. In: IOP conference series: materials science and engineering. IOP Publishing p. 012167 (2020)

  31. Hu, W.W., Zhou, R.G., El-Rafei, A., et al.: Quantum image watermarking algorithm based on haar wavelet transform[J]. IEEE Access 7, 121303–121320 (2019)

    Article  Google Scholar 

  32. IBM Q Experience. https://quantumexperience.ng.bluemix.net/qx/experience

  33. Al-Haj, A.: Combined DWT-DCT digital image watermarking[J]. J. Comput. Sci. 3(9), 740–746 (2007)

    Article  Google Scholar 

  34. Sudibyo, U., Eranisa, F., Rachmawanto, E.H., et al. A secure image watermarking using Chinese remainder theorem based on haar wavelet transform[C]. In: 2017 4th International Conference on Information Technology, Computer, and Electrical Engineering (ICITACEE). IEEE, pp. 208–212 (2017)

  35. Fijany, A., Williams, C.P.: Quantum wavelet transforms: Fast algorithms and complete circuits[C]. In: NASA international conference on quantum computing and quantum communications, pp. 10–33. Springer, Berlin, Heidelberg (1999)

    Chapter  MATH  Google Scholar 

  36. Abraham, H., et al.: Qiskit: an open-source framework for quantum computing. https://github.com/Qiskit/qiskit

  37. Yan, F., Le, P.Q., Iliyasu, A.M.: Assessing the similarity of quantum images based on probability measurements[C]. In: IEEE Congress on Evolutionary Computation. IEEE pp. 1–6 (2012)

  38. Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm[J]. International Journal of Theoretical Physics 55(1), 107–123 (2016)

    Article  MATH  ADS  Google Scholar 

Download references

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 61772295), Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2021MF049, ZR2019YQ01) and Project of Shandong Provincial Natural Science Foundation Joint Fund Application (ZR202108020011).

Author information

Authors and Affiliations

  1. School of Science, Qingdao University of Technology, Qingdao, Shandong Province, China

    Yiming Yu & Shumei Wang

  2. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, Shandong Province, China

    Jie Gao & Xiaoyi Mu

Authors
  1. Yiming Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoyi Mu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shumei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shumei Wang.

Ethics declarations

Conflict of interest

All authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, Y., Gao, J., Mu, X. et al. Adaptive LSB quantum image watermarking algorithm based on Haar wavelet transforms. Quantum Inf Process 22, 180 (2023). https://doi.org/10.1007/s11128-023-03926-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-03926-1

Keywords

Search

Navigation