Abstract
In this paper, a new quantum representation for multiple images (QRMI) is presented, which can save more storage space than the existing representations. Moreover, to improve efficiency and security, a three-layer quantum multi-image encryption scheme is proposed based on QRMI. First, in the position-layer scrambling phase, the 3D non-equilateral Arnold transform is used to scramble the pixel position and sequence number of images, which is equivalent to achieving the 3D pixel position scrambling at one time. Then, in the bit-layer permutation phase, a bit-plane permutation operation is conducted to exchange the bit-plane order. Finally, in the pixel-layer diffusion phase, 3D hyper-chaotic Henon is used to generate three key sequences, and the bit-layer permutated image is XORed with the quantum key image originating from those key sequences to obtain the ciphertext image. The corresponding quantum realization circuits are given, and simulation results show that the proposed quantum multi-image encryption scheme is effective and secure.























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References
Ahmad, J., Khan, M.A., Ahmed, F., Khan, J.S.: A novel image encryption scheme based on orthogonal matrix, skew tent map, and XOR operation. Neural Comput. Appl. 30(12), 3847–3857 (2018)
Kaur, M., Kumar, V.: A comprehensive review on image encryption techniques. Arch. Comput. Methods Eng. 27, 15–43 (2020)
Man, Z., Li, J., Di, X., Sheng, Y., Liu, Z.: Double image encryption algorithm based on neural network and chaos. Chaos Ssolitons Fractals 152, 111318 (2021)
Lai, Q., Hu, G., Erkan, U., Toktas, A.: A novel pixel-split image encryption scheme based on 2D salomon map. Expert Syst. Appl. 213, 118845 (2023)
Gustafson, E., Zhu, Y., Dreher, P., Linke, N.M., Meurice, Y.: Real-time quantum calculations of phase shifts using wave packet time delays. Phys. Rev. D 104, 054507 (2021)
Genoni, M.G., Olivares, S., Paris, M.G.: Optical phase estimation in the presence of phase diffusion. Phys. Rev. Lett. 106(15), 153603 (2011)
Teklu, B., Olivares, S., Paris, M.G.: Bayesian estimation of one-parameter qubit gates. J. Phys. B At. Mol. Opt. Phys. 42(3), 035502 (2009)
Brivio, D., Cialdi, S., Vezzoli, S., Gebrehiwot, B.T., Genoni, M.G., Olivares, S., Paris, M.G.: Experimental estimation of one-parameter qubit gates in the presence of phase diffusion. Phys. Rev. A 81(1), 012305 (2010)
Teklu, B., Genoni, M.G., Olivares, S., Paris, M.G.: Phase estimation in the presence of phase diffusion: the qubit case. Phys. Scr. 2010(T140), 014062 (2010)
Pirandola, S., Andersen, U.L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C., Pereira, J.L., Razavi, M., Shaari, J.S., Tomamichel, M., Usenko, V.C., Vallone, G., Villoresi, P., Wallden, P.: Advances in quantum cryptography. Adv. Opt. Photon. 12(4), 1012–1236 (2020)
Luo, W., Cao, L., Shi, Y., Wan, L., Zhang, H., Li, S., Chen, G., Li, Y., Sijin, L., Wang, Y., Sun, S., Karim, M.F., Cai, H., Kwek, L.C., Liu, A.Q.: Recent progress in quantum photonic chips for quantum communication and internet. Light Sci. Appl. 12(1), 175 (2023)
Chen, Z., Wang, X., Yu, S., Li, Z., Guo, H.: Continuous-mode quantum key distribution with digital signal processing. npj Quantum Inf. 9(1), 28 (2023)
Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Du šek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81(3), 1301–1350 (2009)
Portmann, C., Renner, R.: Security in quantum cryptography. Rev. Mod. Phys. 94(2), 025008 (2022)
Jiang, N., Dong, X., Hu, H., Ji, Z., Zhang, W.: Quantum image encryption based on Henon mapping. Int. J. Theor. Phys. 58(3), 979–991 (2019)
Liu, X., Xiao, D., Huang, W., Liu, C.: Quantum block image encryption based on Arnold transform and sine Chaotification model. IEEE Access 7, 57188–57199 (2019)
Wang, L., Ran, Q., Ding, J.: Quantum color image encryption scheme based on 3D non-equilateral Arnold transform and 3D logistic chaotic map. Int. J. Theor. Phys. 62(2), 36 (2023)
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)
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)
Sun, B., Iliyasu, A., Yan, F., Dong, F., Hirota, K.: An RGB multi-channel representation for images on quantum computers. J. Adv. Comput. Intell. Intell. Inform 17(3), 404 (2013)
Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12, 3103–3126 (2013)
Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quantum Inf. Process. 16(2), 1–14 (2017)
Liu, K., Zhang, Y., Lu, K., Wang, X., Wang, X.: An optimized quantum representation for color digital images. Int. J. Theor. Phys. 57(10), 2938–2948 (2018)
Wang, L., Ran, Q., Ma, J., Yu, S., Tan, L.: QRCI: a new quantum representation model of color digital images. Optics Commun. 438, 147–158 (2019)
Li, H.S., Chen, X., Xia, H., Liang, Y., Zhou, Z.: A quantum image representation based on bitplanes. IEEE access 6, 62396–62404 (2018)
Chen, X., Liu, Z., Chen, H., Xu, C.: QIPC: A novel quantum representation model for polar coordinate images. Quantum Inf. Process. 21(5), 174 (2022)
Zhou, N., Yan, X., Liang, H., Tao, X., Li, G.: Multi-image encryption scheme based on quantum 3D Arnold transform and scaled Zhongtang chaotic system. Quantum Inf. Process. 17(12), 1–36 (2018)
Wang, L., Ran, Q., Ma, J.: Double quantum color images encryption scheme based on DQRCI. Multimedia Tools Appl. 79(9), 6661–6687 (2020)
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)
Liang, H.R., Tao, X.Y., Zhou, N.R.: Quantum image encryption based on generalized affine transform and logistic map. Quantum Inf. Process. 15(7), 2701–2724 (2016)
Gong, L.H., He, X.T., Cheng, S., Hua, T.X., Zhou, N.R.: Quantum image encryption algorithm based on quantum image XOR operations. Int. J. Theor. Phys. 55(7), 3234–3250 (2016)
Zhou, N., Hu, Y., Gong, L., Li, G.: Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations. Quantum Inf. Process. 16(6), 1–23 (2017)
Wang, J., Geng, Y.C., Han, L., Liu, J.Q.: Quantum image encryption algorithm based on quantum key image. Int. J. Theor. Phys. 58(1), 308–322 (2019)
Song, X., Chen, G., Abd El-Latif, A.A.: Quantum color image encryption scheme based on geometric transformation and intensity channel diffusion. Mathematics 10(17), 3038 (2022)
Liu, X., Liu, C.: Quantum image encryption scheme using independent bit-plane permutation and baker map. Quantum Inf. Process. 22(6), 262 (2023)
Jiang, Z., Liu, X.: Image encryption algorithm based on discrete quantum baker map and chen hyperchaotic system. Int. J. Theor. Phys. 62(2), 22 (2023)
Wang, S., Song, X., Niu, X.: A novel encryption algorithm for quantum images based on quantum wavelet transform and diffusion. In: Intelligent Data Analysis and its Applications, vol. II, pp. 243–250. Springer, Cham (2014)
Hu, W.W., Zhou, R.G., Luo, J., Jiang, S.X., Luo, G.F.: Quantum image encryption algorithm based on Arnold scrambling and wavelet transforms. Quantum Inf. Process. 19, 1–29 (2020)
Gong, L.H., He, X.T., Tan, R.C., Zhou, Z.H.: Single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform. Int. J. Theor. Phys. 57(1), 59–73 (2018)
Li, X.Z., Chen, W.W., Wang, Y.Q.: Quantum image compression-encryption scheme based on quantum discrete cosine transform. Int. J. Theor. Phys. 57(9), 2904–2919 (2018)
Li, Y.K., Feng, Q.S., Zhou, F., Li, Q.: 2-D arnold transformation and non-equilateral image scrambling transformation. Comput. Eng. Design 30(13) (2009)
Ma, Y., Zhou, N.R.: Quantum color image compression and encryption algorithm based on Fibonacci transform. Quantum Inf. Process. 22(1), 39 (2023)
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(8), 1–13 (2020)
Anandkumar, R., Kalpana, R.: Designing a fast image encryption scheme using fractal function and 3D Henon map. J. Inf. Secur. Appl. 49, 102390 (2019)
Khorrampanah, M., Houshmand, M., Lotfi Heravi, M.M.: New method to encrypt RGB images using quantum computing. Opt. Quant. Electron. 54(4), 1–16 (2022)
Ran, Q., Wang, L., Ma, J., Tan, L., Yu, S.: A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections. Quantum Inf. Process. 17(8), 1–30 (2018)
Wang, X., Su, Y., Luo, C., Nian, F., Teng, L.: Color image encryption algorithm based on hyperchaotic system and improved quantum revolving gate. Multimed. Tools Appl. 81(10), 13845–13865 (2022)
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)
Gao, Y.J., Xie, H.W., Zhang, J., Zhang, H.: A novel quantum image encryption technique based on improved controlled alternated quantum walks and hyperchaotic system. Phys. A Stat. Mech. Appl. 598, 127334 (2022)
Liu, X.: Quantum image encryption based on baker map and DNA circular shift operation. Phys. Scr. 98(11), 115112 (2023)
Yu, F.F., Dai, J.Y., Liu, S.H., Gong, L.H.: Visually meaningful quantum color image encryption scheme based on measured alternate quantum walks and quantum logistic mixed linear-nonlinear coupled mapping lattices. Int. J. Theor. Phys. 62(2), 33 (2023)
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Ling Wang was involved in conceptualization, methodology and software. Qiwen Ran was responsible for supervision and validation. Junrong Ding contributed to formal analysis and writing–reviewing and editing.
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Wang, L., Ran, Q. & Ding, J. A three-layer quantum multi-image encryption scheme. Quantum Inf Process 23, 123 (2024). https://doi.org/10.1007/s11128-024-04327-8
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DOI: https://doi.org/10.1007/s11128-024-04327-8