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A Quantum Image Encryption and Watermarking Algorithm Based on QDCT and Baker map

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Abstract

In many situations, the dual protection of image information transmission security and identity authentication is required. A quantum encryption and watermarking technique combining quantum Baker map (QBM) and quantum discrete cosine transform (QDCT) is presented to address this issue. Firstly, the watermark information used for identity authentication is scrambled by QBM, and the original image is decomposed by two-level quantum Haar wavelet transform (QHWT). To ensure the invisibility and robustness of the watermark, \({\text{HL}}_{1}\) obtained from \({\text{LH}}\) is selected for further segmentation, and then QDCT is applied to \({\text{HL}}_{1}\) sub-block. The obtained matrix is used for watermark embedding. Special pre-processing is applied to the binary image before embedding the identity information, increasing embedding capacity while ensuring robustness and invisibility. Then the watermarked image is encrypted. In the encryption process, QBM is used for block scrambling. A quantum artificial image constructed with chaotic sequences manufactured from 3D Henon hyperchaotic system is utilized to diffuse pixel values. Quantum swap operation is used to achieve further bit-level scrambling, and the ciphertext image containing identity information is obtained. The encrypting security and the invisibility and robustness of watermarking are tested through numerical simulation.

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References

  1. Patterson, C.M., Nurse, J.R.C., Franqueira, V.N.L.: Learning from cyber security incidents: A systematic review and future research agenda. Comput. Secur. 132, 103309 (2023)

    Google Scholar 

  2. Sutradhar, K., Om, H.: Efficient quantum secret sharing without a trusted player. Quantum Inf. Process. 19(2), 73 (2020)

    ADS  MathSciNet  Google Scholar 

  3. Gong, L.H., Pei, J.J., Zhang, T.F, Zhou, N.R.: Quantum convolutional neural network based on variational quantum circuits. Opt. Commun. 550, 129993 (2024)

  4. Gong, C., Zhou, N.R., **a, S.H., Huang, S.Y.: Quantum particle swarm optimization algorithm based on diversity migration strategy. Future Gener. Comp. Sy. 2157, 445–458 (2024).

  5. Sutradhar, K., Om, H.: A generalized quantum protocol for secure multiparty summation. IEEE Trans. Circuits Syst. II Express Briefs 67(12), 2978–2982 (2020)

    Google Scholar 

  6. Sutradhar, K., Venkatesh, R.: A privacy preserving quantum aggregating technique. Quantum Inf. Process. 23(4), 124 (2024)

    MathSciNet  Google Scholar 

  7. Gyongyosi, L., Imre, S.: A Survey on quantum computing technology. Comput. Sci. Rev. 31, 51–71 (2019)

    MathSciNet  Google Scholar 

  8. Wang, Z.B., Xu, M.Z., Zhang, Y.N.: Review of quantum image processing. Arch. Comput. Methods Eng. 29(2), 737–761 (2022)

    MathSciNet  Google Scholar 

  9. Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Quantum Inf. Comput. 5105, 137–147 (2003)

    ADS  Google Scholar 

  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 (2011)

    MathSciNet  Google Scholar 

  11. 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)

    ADS  MathSciNet  Google Scholar 

  12. Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Quantum Inf. Process. 14(11), 4001–4026 (2015)

    ADS  MathSciNet  Google Scholar 

  13. Li, N.Q., Yan, F., Venegas-Andraca, S.E., Hirota, K.: Quantum image scaling with applications to image steganography and fusion. Signal Process.: Image Commun. 117, 117015 (2023)

    Google Scholar 

  14. Li, M.M., Song, X.H., Abd El-Latif, A.A.: EQIRHSI: enhanced quantum image representation using entanglement state encoding in the HSI color model. Quantum Inf. Process. 22(9), 334 (2023)

    ADS  MathSciNet  Google Scholar 

  15. Akhshani, A., Akhavan, A., Lim, S.C., Hassan, Z.: An image encryption scheme based on quantum logistic map. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4653–4661 (2012)

    ADS  MathSciNet  Google Scholar 

  16. Zhou, N.R., Chen, W.W., Yan, X.Y., Wang, Y.Q.: Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system. Quantum Inf. Process. 17(6), 137 (2018)

    ADS  MathSciNet  Google Scholar 

  17. Song, X.H., Wang, H.Q., Venegas-Andraca, S.E., El-Latif, A.: Quantum video encryption based on qubit-planes controlled-XOR operations and improved logistic map. Phys. A Stat. Mech. Appl. 537, 122660 (2020)

    MathSciNet  Google Scholar 

  18. Wang, X.Y., Su, Y.N., Luo, C., Nian, F.Z., Teng, L.: Color image encryption algorithm based on hyperchaotic system and improved quantum revolving gate. Multimed. Tools Appl. 81(10), 13845–13865 (2022)

    Google Scholar 

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

    Google Scholar 

  20. Kasana, G., Kasana, S.S.: Reference based semi blind image watermarking scheme in wavelet domain. Optik-Int. J. Light Electron Opt. 142, 191–204 (2017)

    Google Scholar 

  21. Haribabu, K., Deepak, M., Subrahmanyam, R.K., Sai, G.: Exploring the learning capabilities of convolutional neural networks for robust image watermarking. Comput. Secur. 65, 247–268 (2017)

    Google Scholar 

  22. Najafi, E.: A robust embedding and blind extraction of image watermarking based on discrete wavelet transform. Math. Sci. 11, 307–318 (2017)

    MathSciNet  Google Scholar 

  23. Anand, A., Singh, A.K.: An improved DWT-SVD domain watermarking for medical information security. Comput. Commun. 152, 72–80 (2020)

    Google Scholar 

  24. Chai, X.L., Fu, J.Y., Gan, Z.H., Lu, Y., Zhang, Y.S.: An image encryption scheme based on multi-objective optimization and block compressed sensing. Nonlinear Dyn. 108(3), 2671–2704 (2022)

    Google Scholar 

  25. Gong, L.H., Luo, H.X.: Dual color images watermarking scheme with geometric correction based on quaternion FrOOFMMs and LS-SVR. Opt. Laser Technol. 167, 109665 (2023)

    Google Scholar 

  26. Mohammed, A.O., Hussein, H.I., Mstafa, R.J., Abdulazeez, A.M.: A blind and robust color image watermarking scheme based on DCT and DWT domains. Multimed. Tools Appl. 82(21), 32855–32881 (2023)

    Google Scholar 

  27. 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)

    ADS  MathSciNet  Google Scholar 

  28. Wang, S., Song, X.H., Niu, X.M.: Quantum cosine transform based watermarking scheme for quantum images. Chin. J. Electron. 24(2), 321–325 (2015)

    Google Scholar 

  29. Zhou, R.G., Hu, W., Fan, P.: Quantum watermarking scheme through Arnold scrambling and LSB steganography. Quantum Inf. Process. 16(9), 212 (2017)

    ADS  MathSciNet  Google Scholar 

  30. Luo, G.F., Zhou, R.G., Hu, W.W., Luo, J., Liu, X.A., Hou, L.: Enhanced least significant qubit watermarking scheme for quantum images. Quantum Inf. Process. 17(11), 299 (2018)

    ADS  Google Scholar 

  31. Iranmanesh, S., Atta, R., Ghanbari, M.: Implementation of a quantum image watermarking scheme using NEQR on IBM quantum experience. Quantum Inf. Process. 21(6), 194 (2022)

    ADS  MathSciNet  Google Scholar 

  32. Sun, J.Y., Wang, W.T., Hao, Z., Jun, Z.: Color image quantum steganography scheme and circuit design based on DWT+DCT+SVD. Phys. A Stat. Mech. Appl. 617, 128688 (2023)

    MathSciNet  Google Scholar 

  33. Ren, N., Tong, D.Y., Cui, H.C., Zhu, C.Q., Zhou, Q.F.: Congruence and geometric feature-based commutative encryption-watermarking method for vector maps. Comput. Geosci. 159, 105009 (2022)

    Google Scholar 

  34. Sheng, Q.X., Fu, C., Lin, Z.N., Tie, M., Chen, J.X., Sham, C.W.: A one-time-pad-like chaotic image encryption scheme using data steganography. J. Inf. Secur. Appl. 78, 103592 (2023)

    Google Scholar 

  35. Dai, J.Y., Ma, Y., Zhou, N.R.: Quantum multi-image compression-encryption scheme based on quantum discrete cosine transform and 4D hyper-chaotic Henon map. Quantum Inf. Process. 20(7), 246 (2021)

    ADS  MathSciNet  Google Scholar 

  36. Zhou, N.R., Hu, L.L., Huang, Z.W., Wang, M.M., Lou, G.S.: Novel multiple color images encryption and decryption scheme based on a bit-level extension algorithm. Expert Syst. Appl. 238, 122052 (2024)

    Google Scholar 

  37. Yu, Y.M., Gao, J., Mu, X.Y., Wang, S.M.: Adaptive LSB quantum image watermarking algorithm based on Haar wavelet transforms. Quantum Inf. Process. 22(5), 180 (2023)

    ADS  MathSciNet  Google Scholar 

  38. Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcation Chaos 8(6), 1259–1284 (1998)

    ADS  MathSciNet  Google Scholar 

  39. Jiang, Z.Y., Liu, X.B.: Image encryption algorithm based on discrete quantum Baker map and Chen hyperchaotic system. Int. J. Theor. Phys. 62(2), 22 (2023)

    MathSciNet  Google Scholar 

  40. Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swap**-based confusion approach. Nonlinear Dyn. 77(4), 1191–1207 (2014)

    Google Scholar 

  41. Zhou, N.R., Yan, X.Y., Liang, H.R., Tao, X.Y., Gong, L.H.: Multi-image encryption scheme based on quantum 3D Arnold transform and scaled Zhongtang chaotic system. Quantum Inf. Process. 17(12), 338 (2018)

    ADS  Google Scholar 

  42. Liang, Q., Zhu, C.X.: A new one-dimensional chaotic map for image encryption scheme based on random DNA coding. Opt. Laser Technol. 160, 109033 (2023)

    Google Scholar 

  43. Wang, H., Wang, J., Geng, Y.C., Song, Y., Liu, J.Q.: Quantum image encryption based on iterative framework of frequency-spatial domain transforms. Int. J. Theor. Phys. 56(10), 3029–3049 (2017)

    MathSciNet  Google Scholar 

  44. Ralph, T.C., Resch, K.J., Gilchrist, A.: Efficient Toffoli gates using qubits. Phys. Rev. A 75(2), 022313 (2007)

    ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 62202252 and 61861029), and the Science & Technology Planning Project of Shanghai (Grant No. 23010501800).

Funding

This work was supported by National Natural Science Foundation of China, 61861029, 62202252, Science & Technology Planning Project of Shanghai, 23010501800.

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Authors and Affiliations

  1. School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Nan-Run Zhou, Ming-Xuan Chen & Meng-Meng Wang

  2. Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031, China

    Jia-Wen Wu

  3. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, 266033, China

    Meng-Meng Wang

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  1. Nan-Run Zhou
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Contributions

Nan-Run Zhou: Supervision, Funding acquisition, Project administration, Resources. Jia-Wen Wu: Writing-review & editing. Ming-Xuan Chen: Conceptualization, Formal analysis, Validation, Resources, Writing & original draft. Meng-Meng Wang: Supervision, Methodology, Investigation, Visualization, Writing & review & editing. All authors reviewed the manuscript.

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Correspondence to Meng-Meng Wang.

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Zhou, NR., Wu, JW., Chen, MX. et al. A Quantum Image Encryption and Watermarking Algorithm Based on QDCT and Baker map. Int J Theor Phys 63, 100 (2024). https://doi.org/10.1007/s10773-024-05630-x

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