Abstract
In this article, we introduce a multi-channel effective representation of quantum images (MCEQI) based on the improved flexible representation of quantum images (IFRQI) to facilitate the quantum analysis of colored digital images. We use an effective method to encode the intensity value of each pixel of a color digital image into a quantum state vector that yields a highly distinctive probability distribution in response to projective measurements, and thus allows for accurate restoration of the image information. In addition, we propose a high-capacity steganography scheme based on the MCEQI model. We embed the color information of a secret color image in the MCEQI state of a carrier color image by using controlled rotations. The sizes of the secret image and cover image are considered to be \(2^n\times 2^n\) and \(2^{n+1}\times 2^{n+1}\), respectively. We divide the red, green, and blue channel information of the secret image into four planes, each with a depth of 2 bits. For each plane, we construct an array of angle values that encode the color information. The encoded information is then embedded in the MCEQI state of the cover image using controlled rotations determined by the key K, derived from the fractional-order erbium-doped laser chaotic system. The process of extracting the secret image is the inverse of the embedding process and requires the inverse key \(K'\). Finally, we perform the analysis of the embedding capacity, time complexity, and visual effects to establish the effectiveness of the proposed steganography scheme.
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References
Wang, Z., Xu, M., Zhang, Y.: Review of quantum image processing. Arch. Comput. Methods Eng. 29(2), 1–25 (2021)
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)
Sun, B., Iliyasu, A.M., Yan, F., Dong, F., Hirota, K.: An RGB multi-channel representation for images on quantum computers. J. Adv. Comput. Intell. Intell. Informat. 17, 404–417 (2013)
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)
Li, H.-S., Zhu, Q., Zhou, R.-G., Li, M.-C., Song, l., Ian, H.: Multidimensional color image storage, retrieval, and compression based on quantum amplitudes and phases. Inf. Sci. 273, 212–232 (2014)
Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quantum Inf. Process. 16(2), 1–14 (2017)
Khan, R.A.: An improved flexible representation of quantum images. Quantum Inf. Process. 18(7), 1–19 (2019)
Zhu, H.-H., Chen, X.-B., Yang, Y.-X.: Image preparations of multi-mode quantum image representation and their application on quantum image reproduction. Optik 251, 168321 (2022)
Nasr, N., Younes, A., Elsayed, A.: Efficient representations of digital images on quantum computers. Multimed. Tools Appl. 80(25), 34019–34034 (2021)
Amal, R., Kannan, S.: Manifestation of quantum images using unitary matrix encoding. Eur. Phys. J. Plus 137(4), 1–24 (2022)
Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.: Strategies for designing geometric transformations on quantum images. Theor. Comput. Sci. 412(15), 1406–1418 (2011). Theoretical Computer Science Issues in Image Analysis and Processing
Caraiman, S., Manta, V.I.: Quantum image filtering in the frequency domain. Adv. Electr. Comput. Eng. 13(3), 77–85 (2013)
Caraiman, S., Manta, V.I.: Histogram-based segmentation of quantum images. Theor. Comput. Sci. 529, 46–60 (2014)
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)
Jiang, N., Dang, Y., Wang, J.: Quantum image matching. Quantum Inf. Process. 15(9), 3543–3572 (2016)
Jiang, N., Wu, W.-Y., Wang, L.: The quantum realization of Arnold and fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)
Zhou, R.-G., Sun, Y.-J., Fan, P.: Quantum image gray-code and bit-plane scrambling. Quantum Inf. Process. 14(5), 1717–1734 (2015)
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)
Khan, M., Rasheed, A.: Permutation-based special linear transforms with application in quantum image encryption algorithm. Quantum Inf. Process. 18(10), 1–21 (2019)
Khan, M., Rasheed, A.: A fast quantum image encryption algorithm based on affine transform and fractional-order Lorenz-like chaotic dynamical system. Quantum Inf. Process. 21(4), 1–34 (2022)
Jiang, N., Wang, L.: A novel strategy for quantum image steganography based on Moiré pattern. Int. J. Theor. Phys. 54(3), 1021–1032 (2015)
Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Int. J. Theor. Phys. 55(1), 107–123 (2016)
Heidari, S., Farzadnia, E.: A novel quantum LSB-based steganography method using the gray code for colored quantum images. Quantum Inf. Process. 16(10), 1–28 (2017)
Abd El-Latif, A.A., Abd-El-Atty, B., Hossain, M.S., Rahman, M.A., Alamri, A., Gupta, B.B.: Efficient quantum information hiding for remote medical image sharing. IEEE Access 6, 21075–21083 (2018)
Zhou, R.-G., Luo, J., Liu, X., Zhu, C., Wei, L., Zhang, X.: A novel quantum image steganography scheme based on LSB. Int. J. Theor. Phys. 57(6), 1848–1863 (2018)
Qu, Z., Sun, H., Zheng, M.: An efficient quantum image steganography protocol based on improved EMD algorithm. Quantum Inf. Process. 20(2), 1–29 (2021)
Hu, W.-W., Zhou, R.-G., Liu, X.-A., Luo, J., Luo, G.-F.: Quantum image steganography algorithm based on modified exploiting modification direction embedding. Quantum Inf. Process. 19(5), 1–28 (2020)
Wang, M.-X., Yang, H.-M., Jiang, D.-H., Yan, B., Pan, J.-S., Liu, T.: A novel quantum color image steganography algorithm based on turtle shell and LSB. Quantum Inf. Process. 21(4), 1–32 (2022)
Qu, Z., Chen, S., Wang, X.: A secure controlled quantum image steganography algorithm. Quantum Inf. Process. 19(10), 1–25 (2020)
Luo, J., Zhou, R.-G., Hu, W.-W., Luo, G.-F., Liu, G.: Detection of steganography in quantum grayscale images. Quantum Inf. Process. 19(5), 1–17 (2020)
Sun, H., Qu, Z., Sun, L., Chen, X., Xu, G.: High-efficiency quantum image steganography protocol based on double-layer matrix coding. Quantum Inf. Process. 21(5), 1–27 (2022)
Luo, L., Tee, T., Chu, P.: Chaotic behavior in erbium-doped fiber-ring lasers. JOSA B 15(3), 972–978 (1998)
Li, X., Mou, J., Xiong, L., Wang, Z., Xu, J.: Fractional-order double-ring erbium-doped fiber laser chaotic system and its application on image encryption. Opt. Laser Technol. 140, 107074 (2021)
Zhao, S., Yan, F., Chen, K., Yang, H.: Interpolation-based high capacity quantum image steganography. Int. J. Theor. Phys. 60(10), 3722–3743 (2021)
Zeng, Q.-W., Wen, Z.-Y., Fu, J.-F., Zhou, N.-R.: Quantum watermark algorithm based on maximum pixel difference and tent map. Int. J. Theor. Phys. 60(9), 3306–3333 (2021)
Xie, H.-W., Gao, Y.-J., Liu, X.-L., Zhang, J., Zhang, H.: A novel exploiting modification direction scheme and its application in quantum color image steganography. Quantum Inf. Process. 21(7), 249 (2022)
Yao, J.-L., Yang, H.-M., Jiang, D.-H., Yan, B., Pan, J.-S., Wang, M.-X.: A novel quantum image steganography algorithm based on double-layer gray code. Int. J. Theor. Phys. 62(3), 52 (2023)
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Khan, M., Rasheed, A. A secure controlled quantum image steganography scheme based on the multi-channel effective quantum image representation model. Quantum Inf Process 22, 268 (2023). https://doi.org/10.1007/s11128-023-04022-0
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DOI: https://doi.org/10.1007/s11128-023-04022-0