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A multimode quantum image representation and its encryption scheme

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Abstract

The research of quantum network will promote the application of quantum image to be more universal and widespread. Quantum image representation model is the basis of quantum image processing. Therefore, we propose a multimode quantum image representation (MQIR) and its preparation. In this representation, the image size can be arbitrary and the color can be in one of several color models, such as Gray, RGB, Lab, HSL. This improves the universality of quantum image applications, and our MQIR requires fewer qubits than other quantum image representations. Furthermore, an MQIR image encryption scheme is presented, which is based on three-dimensional non-equilateral Arnold transformation. We give the MQIR transformation (inverse transformation) algorithm and quantum circuits. Some of the transformation times and the parameters in the scrambling process can be used as the keys in the proposed encryption. Finally, we conduct some simulation experiments on the classical computer to analyze the performance such as histogram analysis, peak signal-to-noise ratio and the correlation coefficients of adjacent pixels between original images and encrypted images. Simulation results show that the proposed quantum image encryption scheme is efficient.

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References

  1. Monroe, C.: Quantum information processing with atoms and photons. Nature 416(6877), 238–46 (2002)

    Article  ADS  Google Scholar 

  2. Monz, T., Kim, K., Hansel, W., Riebe, M., Villar, A.S., Schindler, P., Chwalla, M., Hennrich, M., Blatt, R.: Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett. 102(4), 040501 (2009)

    Article  ADS  Google Scholar 

  3. Melnikov, D., Mironov, A., Mironov, S., Morozov, A., Morozov, A.: Towards topological quantum computer. Nucl. Phys. B 926(C), 491–508 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  4. Figgatt, C., Maslov, D., Landsman, K.A., Linke, N.M., Debnath, S., Monroe, C.: Complete 3-qubit grover search on a programmable quantum computer. Nat. Commun. 8(1), 1–9 (2017)

    Article  Google Scholar 

  5. Ruan, Y., Xue, X., Shen, Y.: Quantum image processing: opportunities and challenges. Math. Probl. Eng. 2021, 1–8 (2021). https://doi.org/10.1155/2021/6671613

  6. Benqiong, H.U., Huang, X.D., Zhou, R.G., Wei, Y.Y., Wan, Q., Pang, C.Y.: A theoretical framework for quantum image representation and data loading scheme. Sci. China. Inf. Sci. 57(3), 1–11 (2014)

    MATH  Google Scholar 

  7. Seyedzadeh, S.M., Norouzi, B., Mosavi, M.R., Mirzakuchaki, S.: A novel color image encryption algorithm based on spatial permutation and quantum chaotic map. Nonlinear Dyn. 81(1–2), 511–529 (2015)

    Article  MathSciNet  Google Scholar 

  8. Hua, T., Chen, J., Pei, D., Zhang, W., Zhou, N.: Quantum image encryption algorithm based on image correlation decomposition. Int. J. Theor. Phys. 54(2), 526–537 (2015)

    Article  Google Scholar 

  9. Zhou, N.R., Hua, T.X., Gong, L.H., Pei, D.J., Liao, Q.H.: Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf. Process. 14(4), 1193–1213 (2015)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  11. Yang, Y.G., Tian, J., Lei, H., Zhou, Y.H., Shi, W.M.: Novel quantum image encryption using one-dimensional quantum cellular automata. Inf. Sci. 345, 257–270 (2016)

    Article  Google Scholar 

  12. Li, C., Luo, G., Qin, K., Li, C.: An image encryption scheme based on chaotic tent map. Nonlinear Dyn. 87(1), 127–133 (2017)

    Article  Google Scholar 

  13. Zhou, N., Yiqun, H., Gong, L., Li, G.: Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations. Quantum Inf. Process. 16(6), 164 (2017)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  16. Ran, Q., Wang, L., Ma, J., Tan, L., Siyuan, Yu.: A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections. Quantum Inf. Process. 17(8), 188 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  17. 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 

  18. Latorre, J.I.: Image compression and entanglement. Computer Science (2005)

  19. 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  Google Scholar 

  20. Zhang, Y., Kai, L., Gao, Y., Wang, M.: Neqr: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zhang, Y., Kai, L., Gao, Y., Kai, X.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3103–3126 (2013)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  24. Sun, B., Le, P.Q., Iliyasu, A.M., Yan, F., Garcia, J.A., Dong, F., Hirota, K.: A multi-channel representation for images on quantum computers using the RGB color space. In: IEEE International Symposium on Intelligent Signal Processing, pp. 1–6 (2011)

  25. Li, H.-S., Chen, X., Xia, H., Liang, Y., Zhou, Z.: A quantum image representation based on bitplanes. IEEE Access 6, 62396–62404 (2018)

    Article  Google Scholar 

  26. Li, H.-S., Song, S., Fan, P., Peng, H., Xia, H., Liang, Y.: Quantum vision representations and multi-dimensional quantum transforms. Inf. Sci. 502, 42–58 (2019)

    Article  MathSciNet  Google Scholar 

  27. Li, H.-S., Fan, P., Xia, H.-Y., Peng, H., Song, S.: Quantum implementation circuits of quantum signal representation and type conversion. IEEE Trans. Circuits Syst. I Regul. Pap. 66(1), 341–354 (2018)

    Article  Google Scholar 

  28. Zhang, W.-W., Gao, F., Liu, B., Jia, H.-Y., Wen, Q.-Y., Chen, H.: A quantum watermark protocol. Int. J. Theor. Phys. 52(2), 504–513 (2013)

    Article  MathSciNet  Google Scholar 

  29. Wei, Z.H., Chen, X.B., Xu, S.J., Niu, X.X., Yang, Y.X.: A spatial domain quantum watermarking scheme. Commun. Theor. Phys. 66(1), 66–76 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  30. Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  31. Jiang, N., Wang, L.: Analysis and improvement of the quantum Arnold image scrambling. Quantum Inf. Process. 13(7), 1545–1551 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  32. Jiang, N., Wang, L., Wu, W.Y.: Quantum hilbert image scrambling. Int. J. Theor. Phys. 53(7), 2463–2484 (2014)

    Article  Google Scholar 

  33. Zhou, R.G., Sun, Y.J., Fan, P.: Quantum image gray-code and bit-plane scrambling. Quantum Inf. Process. 14(5), 1–18 (2015)

    MathSciNet  MATH  Google Scholar 

  34. Abd, A.A., El-Latif, B.A.-E.-A., Talha, M.: Robust encryption of quantum medical images. IEEE Access 6, 1073–1081 (2018)

    Article  Google Scholar 

  35. Liu, X., Xiao, D., Liu, C.: Three-level quantum image encryption based on Arnold transform and logistic map. Quantum Inf. Process. 20(1), 1–22 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  36. Zhu, H.-H., Chen, X.-B., Yang, Y.-X.: A quantum image dual-scrambling encryption scheme based on random permutation. Sci. China Inf. Sci. 62(12), 229501 (2019)

    Article  Google Scholar 

  37. Yong-Kui, L.I., Feng, Q.S., Zhou, F., Qiang, L.I.: 2-D Arnold transformation and non-equilateral image scrambling transformation. Comput. Eng. Des. 30(13), 3133–3135 (2009)

    Google Scholar 

  38. Li, H.-S., Fan, P., Xia, H., Peng, H., Long, G.-L.: Efficient quantum arithmetic operation circuits for quantum image processing. Sci. China Phys. Mech. Astron. 63, 1–13 (2020)

    Article  Google Scholar 

  39. Chengmao, W., Tian, X.: 3-dimensional non-equilateral Arnold transformation and its application in image scrambling. J. Comput.-Aid. Des. Comput. Graph. 22(10), 1831–1840 (2010)

    Google Scholar 

  40. Wen, C.-C., Wang, Q., Ding, H., Miao, X.-N., Tao, C.-S.: Image scrambling algorithm based on three-dimensional affine transformations. J. Univ. Sci. Technol. Beijing 34(12), 1478–1482 (2012)

    Google Scholar 

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Acknowledgements

This work was supported by the Fund of the Fundamental Research Funds for the Central Universities (No. 2019XD-A02).

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Correspondence to Xiu-Bo Chen.

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Zhu, HH., Chen, XB. & Yang, YX. A multimode quantum image representation and its encryption scheme. Quantum Inf Process 20, 315 (2021). https://doi.org/10.1007/s11128-021-03255-1

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