LSBs-based quantum color images watermarking algorithm in edge region

  • WenWen Hu
  • Ri-Gui ZhouEmail author
  • Jia Luo
  • BiYing Liu


Based on the NEQR representation for quantum color and binary images, an enhanced quantum watermarking scheme is investigated through Gray code transform and least significant bit (LSB) steganography, which embeds a quantum binary image (i.e., watermark image) into the edge region of a quantum color image (i.e., carrier image) LSB and second LSB. The size of the carrier and watermark images are assumed to be \( 2^{n} \times 2^{n} \) and \( 2^{n - 1} \times 2^{n - 1} \), respectively. At first, the watermark image is resized into an appropriate size image with 4-qubit grayscale based on the nearest neighbor interpolation method, which is of the same size with the preselected edge region in carrier image. To enhance the security of the watermark image, the binary code of 4-qubit grayscale of watermark image is transformed into the corresponding Gray code, and one 3-Controlled-NOT gate is utilized to generate a quantum binary image \( \left| {K1} \right\rangle \). To further scatter the watermark image qubits that are embedded into the LSB and second LSB of carrier image, the quantum image \( \left| {K1} \right\rangle \) is employed to choose any two channels from the color image among the three channels of R, G and B (i.e., R, G or R, B channels would be chosen as the embedding channels). Furthermore, a quantum binary image \( \left| {K2} \right\rangle \) is generated through XOR operation decided by the quantum image \( \left| {K1} \right\rangle \), which is used to determine the embedding order of watermark image qubits. The extraction process is the inverse operation of embedding, which also needs the two quantum binary key images \( \left| {K1} \right\rangle \) and \( \left| {K2} \right\rangle \). Finally, the experiment results are simulated under the classical computer software MATLAB 2016(b), which illustrates that our investigated LSBs-based quantum watermarking has a better visual effect than some related works in terms of PSNR value.


Quantum watermarking Gray code transform Least significant bit Nearest neighbor interpolation 



This work is supported by the National Key R&D Plan under Grant Nos. 2018YFC1200200 and 2018YFC1200205, National Natural Science Foundation of China under Grant No. 61463016 and “Science and technology innovation action plan” of Shanghai in 2017 under Grant No. 17510740300.


  1. 1.
    Yan, F., Iliyasu, A.M., Le, P.Q.: Quantum image processing: a review of advances in its security technologies. Int. J. Quantum Inf. 15, 1730001 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Recent advances and new insights into quantum image processing. (2017)
  3. 3.
    Yan, F., Iliyasu, A.M., Venegas-Andraca, S.E.: A survey of quantum image representations. Quantum Inf. Process. 15, 1–35 (2016)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Venegas-Andraca S.E., Bose S.: Storing, processing, and retrieving an image using quantum mechanics. In: Proceedings of SPIE Conference of Quantum Information and Computation, vol. 5105, pp. 134–147 (2003)Google Scholar
  5. 5.
    Latorre, J.: Image compression and entanglement (2005). arXiv:quant-ph/0510031
  6. 6.
    Le, P., Dong, F., Hitora, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10, 63–84 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Sun, B., Iliyasu, A., Yan, F., et al.: An RGB multi-channel representation for images on quantum computers. J. Adv. Comput. Intell. Intell. Inform. 17, 404–417 (2013)CrossRefGoogle Scholar
  8. 8.
    Zhang, Y., Lu, K., Gao, Y., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12, 2833–2860 (2013)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12, 3103–3126 (2013)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Yuan, S.Z., Mao, X., Xue, Y.L., et al.: SQR: a simple quantum representation of infrared images. Quantum Inf. Process. 13, 1353–1379 (2014)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Abdolmaleky, M., et al.: Red–Green–Blue multi-channel quantum representation of digital images. Opt. Int. J. Light Electron Opt. 128, 121–132 (2017)CrossRefGoogle Scholar
  12. 12.
    Sang, J.Z., Wang, S., Li, Q.: A novel quantum representation for color digital images. Quantum Inf. Process. 16, 42 (2017)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Li, H.S., Chen, X., Xia, H.Y., et al.: A quantum image representation based on bitplanes. IEEE Access. (2018). CrossRefGoogle Scholar
  14. 14.
    Li, H.S., Fan, P., Xia, H.Y., et al.: Quantum implementation circuits of quantum signal representation and type conversion. IEEE Trans. Circuits Syst. I Regul. Pap. (2018). CrossRefGoogle Scholar
  15. 15.
    Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13, 1223–1236 (2014)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int. J. Theor. Phys. 53, 2463–2484 (2014)CrossRefGoogle Scholar
  17. 17.
    Zhou, R.G., Sun, Y.J., Fan, P.: Quantum image Gray-code and bit-plane scrambling. Quantum Inf. Process. 14, 1717–1734 (2015)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Zhang, W., Gao, F., Liu, B., Jia, H.: A quantum watermark protocol. Int. J. Theor. Phys. 52, 504–513 (2013)MathSciNetCrossRefGoogle Scholar
  19. 19.
    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, 2765–2769 (2013)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Yang, Y.G., Xu, P., Ju, T.J., Zhang, H.: Analysis and improvement of the dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 13, 1931–1936 (2014)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    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. 22, 271–272 (2016)CrossRefGoogle Scholar
  22. 22.
    Jiang, N., Wang, L.: A novel strategy for quantum image steganography based on Moir pattern. Int. J. Theor. Phys. 54, 1021–1032 (2015)CrossRefGoogle Scholar
  23. 23.
    Wang, S., et al.: Least significant qubit (LSQb) information hiding algorithm for quantum image. Measurement 73, 352–359 (2015)CrossRefGoogle Scholar
  24. 24.
    Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Int. J. Theor. Phys. 55, 107–123 (2016)CrossRefGoogle Scholar
  25. 25.
    Miyake, S., Nakamae, K.: A quantum watermarking scheme using simple and small-scale quantum circuits. Quantum Inf. Process. 15, 1849–1864 (2016)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Heidari, S., Naseri, M.: A novel LSB based quantum image watermarking. Int. J. Theor. Phys. 55, 4205–4218 (2016)CrossRefGoogle Scholar
  27. 27.
    Sang, J., Wang, S., Li, Q.: Least significant qubit algorithm for quantum images. Quantum Inf. Process. 15, 4441–4460 (2016)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Li, P.C., Zhao, Y., Xiao, H., Cao, M.J.: An improved quantum watermarking scheme using small-scale quantum circuits and color scrambling. Quantum Inf. Process. 16, 127 (2017)ADSCrossRefGoogle Scholar
  29. 29.
    Naseri, M., Heidari, S., et al.: A new secure quantum watermarking scheme. Opt. Int. J. Light Electron Opt. 139, 77–86 (2017)CrossRefGoogle Scholar
  30. 30.
    Zhou, R.G., Hu, W.W., Fan, P.: Quantum watermarking scheme through Arnold scrambling and LSB steganography. Quantum Inf. Process. 16, 212 (2017)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Heidari, S., Pourarian, M.R., Gheibi, R., et al.: Quantum red–green–blue image steganography. Int. J. Quantum Inf. 15(7), 1750039 (2017)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Heidari, S., Farzadnia, E.: A novel quantum LSB-based steganography method using the Gray code for colored quantum images. Quantum Inf. Process. 16, 242 (2017)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Zhou, R.G., Luo, J., Liu, X.A., et al.: A novel quantum image steganography scheme based on LSB. Int. J. Theor. Phys. 57, 1–16 (2018)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Li, P.C., Liu, X.D.: A novel quantum steganography scheme for color images. Int. J. Quantum Inf. 16(9), 1850020 (2018)CrossRefGoogle Scholar
  35. 35.
    Luo, G.F., Zhou, R.G., Hu, W.W., et al.: Enhanced least significant qubit watermarking scheme for quantum images. Quantum Inf. Process. 17, 299 (2018). ADSCrossRefzbMATHGoogle Scholar
  36. 36.
    Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14, 1559–1571 (2015)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Tirkel A.Z., Rankin G.A., VanSchyndel R.M., et al.: Electronic watermark. In: Proceedings of Digital Image Computing: Techniques and Applications, pp. 666–672. Macquarie University (1993)Google Scholar
  38. 38.
    Gray, F.: Pulse code communication. United States patent 2632058, Mar 1953Google Scholar
  39. 39.
    Barenco, A., Bennett, C.H., et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3488 (1995)ADSCrossRefGoogle Scholar
  40. 40.
    Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Information EngineeringShanghai Maritime UniversityShanghaiChina
  2. 2.College of Economics and ManagementShanghai Maritime UniversityShanghaiChina

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