Abstract
Driven by the growing significance of information security, the field of image encryption is attracting increasing interest. This work solves an image encryption issue of experiencing actual chaotic mapping via an optical neural network, extending our knowledge of image encryption based on chaos theory. In this paper, we first construct an optical neural network that is a four-channel signal injection optical reservoir computing (ORC) system relied on an optical dynamics system of the mutually coupled quantum dot spin-polarized vertical cavity surface emitting lasers (MCQD spin-VCSELs) subject to external optical injection, the dynamics of which is analyzed. Then, a secure and general image encryption scheme based on the ORC system is newly developed. The encryption process first requires the image to undergo an ORC-based actual chaotic mapping that achieves a transformation from the original image domain to the chaos domain. Then, one important role of the ORC system outputs is to create secret keys related to plain image combining with chaotic keys derived from the optical chaotic system, and the other one is to act as a transitional medium, being scrambled and diffused by the obtained plaintext-related keys, which further increase the security of our scheme, and finally obtaining the cipher-image. The simulation and analysis results demonstrate that the proposed image encryption scheme is effective and highly secure. Moreover, this study provides an important practical implication that brings the inspiration for future similar research into information security and will help other researchers design new encryption techniques based on chaos theory using neural networks.
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References
Erkan, U., Toktas, A., Toktas, F., Alenezi, F.: 2D e\(\pi \)-map for image encryption. Inf. Sci. 589, 770–789 (2022)
Chen, J., Chen, L., Zhou, Y.: Cryptanalysis of a DNA-based image encryption scheme. Inf. Sci. 520, 130–141 (2020)
Ma, Y., Li, N., Zhang, W., Wang, S., Ma, H.: Image encryption scheme based on alternate quantum walks and discrete cosine transform. Opt. Express 29(18), 28338–28351 (2021)
Ye, G., Pan, C., Dong, Y., Shi, Y., Huang, X.: Image encryption and hiding algorithm based on compressive sensing and random numbers insertion. Signal Process. 172, 107563 (2020)
Zhou, Y., Hua, Z., Pun, C., Chen, C.P.: Cascade chaotic system with applications. IEEE Trans. Cybern. 45(9), 2001–2012 (2014)
Wang, X., Teng, L., Qin, X.: A novel colour image encryption algorithm based on chaos. Signal Process. 92(4), 1101–1108 (2012)
Wu, J., Liao, X., Yang, B.: Image encryption using 2D Hénon-sine map and DNA approach. Signal Process. 153, 11–23 (2018)
Wang, X., Xue, W., An, J.: Image encryption algorithm based on tent-dynamics coupled map lattices and diffusion of household. Chaos Solitons Fractals 141, 110309 (2020)
Kang, X., Ming, A., Tao, R.: Reality-preserving multiple parameter discrete fractional angular transform and its application to color image encryption. IEEE Trans. Circuits Syst. Video Technol. 29(6), 1595–1607 (2018)
Khalil, N., Sarhan, A., Alshewimy, M.A.: An efficient color/grayscale image encryption scheme based on hybrid chaotic maps. Opt. Laser Technol. 143, 107326 (2021)
Zhou, W., Wang, X., Wang, M., Li, D.: A new combination chaotic system and its application in a new Bit-level image encryption scheme. Opt. Lasers Eng. 149, 106782 (2022)
Liu, X., Tong, X., Wang, Z., Zhang, M.: Uniform non-degeneracy discrete chaotic system and its application in image encryption. Nonlinear Dyn. 108(1), 653–682 (2022)
Li, H., Li, C., Ouyang, D., Nguang, S.K.: Impulsive synchronization of unbounded delayed inertial neural networks with actuator saturation and sampled-data control and its application to image encryption. IEEE Trans. Neural Netw. Learn. Syst. 32(4), 1460–1473 (2020)
Wang, J., Ji, Z., Zhang, H., Wang, Z., Meng, Q.: Synchronization of generally uncertain Markovian inertial neural networks with random connection weight strengths and image encryption application. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3131512
Ding, Y., Tan, F., Qin, Z., Cao, M., Choo, K.K.R., Qin, Z.: Deepkeygen: a deep learning-based stream cipher generator for medical image encryption and decryption. IEEE Trans. Neural Netw. Learn. Syst. pp. 1–15 (2021)
Lai, Q., Wan, Z., Zhang, H., Chen, G.: Design and analysis of multiscroll memristive hopfield neural network with adjustable memductance and application to image encryption. IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3146570
Jiang, X., Xiao, Y., Xie, Y., Liu, B., Ye, Y., Song, T., Chai, J., Liu, Y.: Exploiting optical chaos for double images encryption with compressive sensing and double random phase encoding. Opt. Commun. 484, 126683 (2021)
Dong, W., Li, Q., Tang, Y.: Image encryption-then-transmission combining random sub-block scrambling and loop DNA algorithm in an optical chaotic system. Chaos Solitons Fractals 153, 111539 (2021)
Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., Garcia Ojalvo, J., Mirasso, C.R., Pesquera, L., Shore, K.A.: Chaos-based communications at high bit rates using commercial Fibre-optic links. Nature 438(7066), 343–346 (2005)
Malica, T., Bouchez, G., Wolfersberger, D., Sciamanna, M.: Spatiotemporal complexity of chaos in a phase-conjugate feedback laser system. Opt. Lett. 45(4), 819–822 (2020)
Zhao, A., Jiang, N., Zhang, Y., Peng, J., Liu, S., Qiu, K., Deng, M., Zhang, Q.: Semiconductor laser-based multi-channel wideband chaos generation using optoelectronic hybrid feedback and parallel filtering. J. Lightwave Technol. 40(3), 751–761 (2022)
Liansheng, S., Meiting, X., Ailing, T.: Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain. Opt. Lett. 38(11), 1996–1998 (2013)
Mehra, I., Nishchal, N.K.: Optical asymmetric image encryption using gyrator wavelet transform. Opt. Commun. 354, 344–352 (2015)
Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 29(14), 1584–1586 (2004)
Luan, G., Li, A., Zhang, D., Wang, D.: Asymmetric image encryption and authentication based on equal modulus decomposition in the Fresnel transform domain. IEEE Photonics J. 11(1), 1–7 (2018)
Li, N., Susanto, H., Cemlyn, B., Henning, I., Adams, M.: Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs. Opt. Express 26(11), 14636–14649 (2018)
Jiang, X., Xie, Y., Liu, B., Ye, Y., Song, T., Chai, J., Tang, Q.: Dynamics of mutually coupled quantum dot spin-VCSELs subject to key parameters. Nonlinear Dyn. 105(4), 3659–3671 (2021)
Deng, Y., Fan, Z., Zhao, B., Wang, X., Zhao, S., Wu, J., Grillot, F., Wang, C.: Mid-infrared hyperchaos of interband cascade lasers. Light Sci. Appl. 11(1), 1–10 (2022)
Martinenghi, R., Rybalko, S., Jacquot, M., Chembo, Y.K., Larger, L.: Photonic nonlinear transient computing with multiple-delay wavelength dynamics. Phys. Rev. Lett. 108(24), 244101 (2012)
Brunner, D., Soriano, M.C., Mirasso, C.R., Fischer, I.: Parallel photonic information processing at gigabyte per second data rates using transient states. Nat. Commun. 4(1), 1–7 (2013)
Katumba, A., Freiberger, M., Laporte, F., Lugnan, A., Sackesyn, S., Ma, C., Dambre, J., Bienstman, P.: Neuromorphic computing based on silicon photonics and reservoir computing. IEEE J. Sel. Top. Quantum Electron. 24(6), 1–10 (2018)
Guo, X.X., Xiang, S.Y., Zhang, Y.H., Lin, L., Wen, A.J., Hao, Y.: Polarization multiplexing reservoir computing based on a VCSEL with polarized optical feedback. IEEE J. Sel. Top. Quantum Electron. 26(1), 1–9 (2019)
Huang, Y., Zhou, P., Yang, Y., Chen, T., Li, N.: Time-delayed reservoir computing based on a two-element phased laser array for image identification. IEEE Photonics J. 13(5), 1–9 (2021)
Nguimdo, R.M., Verschaffelt, G., Danckaert, J., Van der Sande, G.: Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics. Opt. Express 22(7), 8672-8686 (2014)
Hou, Y., Xia, G., Yang, W., Wang, D., Jayaprasath, E., Jiang, Z., Hu, C., Wu, Z.: Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection. Opt. Express 26(8), 10211–10219 (2018)
Weigend, A.S.: Time Series Prediction: Forecasting the Future and Understanding the Past. Routledge, Milton Park (2018)
Chen, G., Mao, Y., Chui, C.K.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fractals 21(3), 749–761 (2004)
Wu, H., Zhu, H., Ye, G.: Public key image encryption algorithm based on pixel information and random number insertion. Phys. Scr. 96(10), 105202 (2021)
Lin, F.Y., Liu, J.M.: Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback. IEEE J. Quantum Electron. 39(4), 562–568 (2003)
Zhang, Y., He, Y., Li, P., Wang, X.: A new color image encryption scheme based on 2DNLCML system and genetic operations. Opt. Lasers Eng. 128, 106040 (2020)
Zhou, J., Zhou, N., Gong, L.: Fast color image encryption scheme based on 3D orthogonal Latin squares and matching matrix. Opt. Laser Technol. 131, 106437 (2020)
Chai, X., Zhi, X., Gan, Z., Zhang, Y., Chen, Y., Fu, J.: Combining improved genetic algorithm and matrix semi-tensor product (STP) in color image encryption. Signal Process. 183, 108041 (2021)
Teng, L., Wang, X., Yang, F., Xian, Y.: Color image encryption based on cross 2D hyperchaotic map using combined cycle shift scrambling and selecting diffusion. Nonlinear Dyn. 105(2), 1859–1876 (2021)
Duan, C., Zhou, J., Gong, L., Wu, J., Zhou, N.: New color image encryption scheme based on multi-parameter fractional discrete Tchebyshev moments and nonlinear fractal permutation method. Opt. Lasers Eng. 150, 106881 (2022)
Funding
This work was supported in part by the Innovation Research 2035 Pilot Plan of Southwest University and Fundamental Research Funds for the Central Universities under Grant SWU-XDPY22013; in part by the Chongqing Talent Plan under Grant cstc2022ycjh-bgzxm0165; in part by the Special funds for Postdoctoral research of Chongqing under Grant 2010010004713415; and in part by the Chongqing Normal University Ph.D. Startup Fund under Grant 21XLB035.
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Jiang, X., Xie, Y., Liu, B. et al. Image encryption based on actual chaotic mapping using optical reservoir computing. Nonlinear Dyn 111, 15531–15555 (2023). https://doi.org/10.1007/s11071-023-08666-6
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DOI: https://doi.org/10.1007/s11071-023-08666-6