Abstract
In modern civilization information, security is a crucial problem. Image encryption and watermarking can effectively protect information from unauthorized access. This paper introduces a new vigorous symmetric optical image encryption and watermarking technique. This technique depends on a novel dynamic delay chaotic hopping pattern (DDCHP) combined with double random phase encoding (DRPE). To get a robust watermark image, the plain image is first watermarked with a binary secret message using a new chaotic hopping pattern (CHP) and then encrypted using a DRPE system that is controlled by double random independent keys generated with double DDCHP. In this symmetric cryptosystem, three different chaotic maps are used to enlarge the key space of the proposed cryptosystem against brute-force attack and overcome the linearity and vulnerable of the classical DRPE. The system keys are hypersensitive and their initial parameters are selected carefully. Security scrutiny proves the efficiency of the suggested cryptosystem. Therefore, the obtained simulation results prove that the cryptosystem is robust enough against the known attacks, such as statistical attack (uniform histograms of different encrypted images, correlation coefficients between the plain and the encrypted image is as low as 5.46 × 10−6), differential attack (99.99% NPCR and 38.6% UACI), brute force attack (large enough key space), and entropy attack. Moreover, the robustness of the watermark (secret message) is proved due to the solidity of CHP. The proposed approach can be used in different implementations like secure military communications, e-finance, e-healthcare, authenticated multimedia broadcasting, etc.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abuturab, M.R.: Asymmetric multiple information cryptosystem based on chaotic spiral phase mask and random spectrum decomposition. Opt. Laser Technol. 98, 298–308 (2018). https://doi.org/10.1016/j.optlastec.2017.08.010
Arnold, B.C., Coelho, C.A., Marques, F.J.: The distribution of the product of powers of independent uniform random variables: a simple but useful tool to address and better understand the structure of some distributions. J. Multivar. Anal. 113, 19–36 (2013). https://doi.org/10.1016/j.jmva.2011.04.006
Azoug, S.E., Bouguezel, S.: A non-linear preprocessing for opto-digital image encryption using multiple-parameter discrete fractional Fourier transform. Opt. Commun. 359, 85–94 (2016). https://doi.org/10.1016/j.optcom.2015.09.054
Bisht, A., Dua, M., Dua, S.: A novel approach to encrypt multiple images using multiple chaotic maps and chaotic discrete fractional random transform. J. Ambient Intell. Humanized Comput. (2018). https://doi.org/10.1007/s12652-018-1072-0
Carnicer, A., Montes-Usategui, M., Arcos, S., Juvells, I.: Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30(13), 1644–1646 (2005). https://doi.org/10.1364/OL.30.001644
Chai, Z., Liang, S., Hu, G., Zhang, L., Wu, Y.G., Cao, C.: Periodic characteristics of the Josephus ring and its application in image scrambling. Springer Open Access 2018(162), 1–11 (2018). https://doi.org/10.1186/s13638-018-1167-5
Chen, J., Bao, N., Li, J., Zhu, Z.-L., Zhang, L.Y.: Cryptanalysis of optical ciphers integrating double random phase encoding with permutation. IEEE Access 5, 16124–16129 (2017). https://doi.org/10.1109/access.2017.2735420
Dettmann, C.P., Georgiou, O.: Product of independent uniform random variables. Stat. Probab. Lett. 79(24), 2501–2503 (2009). https://doi.org/10.1016/j.spl.2009.09.004
Diab, H.: An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations. IEEE Access 6, 42227–42244 (2018). https://doi.org/10.1109/2858839
Frauel, Y., Castro, A., Naughton, T.J., Javidi, B.: Resistance of the double random phase encryption against various attacks. Opt. Express 15(16), 10253–10265 (2007). https://doi.org/10.1364/oe.15.010253
Fu, X.-Q., Liu, B.-C., Xie, Y.-Y., Li, W., Liu, Y.: Image encryption-then-transmission using DNA encryption algorithm and the double chaos. IEEE Photon. J. 10(3), 1–16 (2018). https://doi.org/10.1109/jphot.2018.2827165
Girija, R., Singh, H.: Symmetric cryptosystem based on chaos structured phase masks and equal modulus decomposition using fractional fourier transform. 3D Res. 9(42), 1–20 (2018a). https://doi.org/10.1007/s13319-018-0192-9
Girija, R., Singh, H.: A cryptosystem based on deterministic phase masks and fractional Fourier Transform deploying singular value decomposition. Opt. Quantum Electron. 50(210), 1–24 (2018b). https://doi.org/10.1007/s11082-018-1472-6
Han, C.: An image encryption algorithm based on modified logistic chaotic map. Optik 181, 779–785 (2019). https://doi.org/10.1016/j.ijleo.2018.12.178
Han, F., Liao, X., Yang, B., Zhang, Y.: A hybrid scheme for self-adaptive double color-image encryption. Multimed. Tools Appl. 77(11), 14285–14304 (2018). https://doi.org/10.1007/s11042
Huang, H., Yang, S.: Image encryption technique combining compressive sensing with double random-phase encoding. Math. Probl. Eng. 2018, 1–10 (2018). https://doi.org/10.1155/2018/6764052
Huo, D., Zhou, X., Zhang, L.: Multiple-image encryption scheme via compressive sensing and orthogonal encoding based on double random phase encoding. J. Mod. Opt. 65(18), 2093–2102 (2018). https://doi.org/10.1080/09500340
Jiao, S., Jin, Z., Zhou, C., Zou, W., Li, X.: Is QR code an optimal data container in optical encryption systems from an error-correction coding perspective? J. Opt. Soc. Am. A 35, A23–A29 (2018a). https://doi.org/10.1364/josaa.35.000a23
Jiao, S., Li, G., Zhou, C., Zou, W., Li, X.: Special ciphertext-only attack to double random phase encryption by plaintext shifting with speckle correlation. J. Opt. Soc. Am. A 35(1), A1–A6 (2018b). https://doi.org/10.1364/josaa.35.0000a1
Jiao, S., Zhoua, C., Shib, Y., Zoua, W., Lia, X.: Review on optical image hiding and watermarking techniques. Opt. Laser Technol. 109, 370–380 (2019). https://doi.org/10.1016/j.optlastec.2018.08.011
Khurana, M., Singh, H.: Asymmetric optical image triple masking encryption based on Gyrator and Fresnel transforms to remove silhouette problem. 3D Res. 9(38), 1–17 (2018). https://doi.org/10.1007/s13319-018-0190-y
Li, C., Hai, W.: Image encryption scheme based on amplitude modulation of chaotic signals. J. Softw. 13(8), 421–436 (2018). https://doi.org/10.17706/jsw.13.8.421-436
Li, G., Yang, W., Li, D., Situ, G.: Cyphertext-only attack on the double random-phase encryption: experimental demonstration. Opt. Express 25(8), 8690–8697 (2017). https://doi.org/10.1364/OE.25.008690
Li, C., Feng, B., Lu, J.: Cryptanalysis of a chaotic image encryption algorithm based on information entropy. IEEE Access 4, 1–9 (2018). arXiv:1803.10024v2
Liu, L., Miao, S.: An image encryption algorithm based on Baker map with varying parameter. Multimedia Tools Appl. 76(15), 16511–16527 (2017). https://doi.org/10.1007/s11042-016-3925-x
Luo, Y., Yu, J., Lai, W., Liu, L.: A novel chaotic image encryption algorithm based on improved baker map and logistic map. Multimedia Tools Appl. (2019). https://doi.org/10.1007/s11042-019-7453-3
Qin, Y., Zhang, Y.: Information encryption in ghost imaging with customized data container and XOR operation. IEEE Photon. J. 9(2), 1–9 (2017). https://doi.org/10.1109/jphot.2017.2690314
Refregier, P., Javidi, B.: Optical image encryption based on input plane Fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995). https://doi.org/10.1364/ol.20.000767
Ren, G., Han, J., Fu, J., Shan, M.: Asymmetric image encryption using phase-truncated discrete multiple-parameter fractional Fourier transform. Opt. Rev. 25(6), 701–707 (2018). https://doi.org/10.1007/s10043
Sharma, N., Saini, I., Yadav, A.K., Singh, P.: Phase-image encryption based on 3D-Lorenz chaotic system and double random phase encoding. 3D Res. 8(39), 1–17 (2017). https://doi.org/10.1007/s13319-017-0149-4
Shuming, J., Zou, W., Li, X.: Noise removal for optical holographic encryption from telecommunication engineering perspective. J. Opt. Soc. Am. A (2017). https://doi.org/10.1364/dh.2017.th2a.5
Singh, H., Girija, R.: Enhancing security of double random phase encoding based on random S-Box. 3D Research 9(15), 1–20 (2018). https://doi.org/10.1007/s13319
Vaishi, A., Kumar, M.: Color image encryption using singular value decomposition in discrete cosine Stockwell transform domain. Opt. Appl. 48, 25–38 (2018). https://doi.org/10.5277/oa180103
Wang, J., Wang, Q.-H., Hu, Y.: Image encryption using compressive sensing and Detour cylindrical diffraction. IEEE Photon. J. 10(3), 1–15 (2018a). https://doi.org/10.1109/access.2017.2735420
Wang, J., Wang, Q.-H., Hu, Y.: Asymmetric color image cryptosystem using Detour cylindrical-diffraction and phase reservation and truncation. IEEE Access 6, 53976–53983 (2018b). https://doi.org/10.1109/ACCESS.2018.2871102
Wang, X., Zhu, X., Zhang, Y.: An image encryption algorithm based on Josephus traversing and mixed chaotic map. IEEE Access 6, 23733–23746 (2018c). https://doi.org/10.1109/access.2018.2805847
Wu, G.-C., Baleanu, D.: Discrete fractional logistic map and its chaos. Nonlinear Dyn. 75(2), 283–287 (2014). https://doi.org/10.1007/s11071
Wu, X., Zhu, B., Hu, Y., Ran, Y.: A novel color image encryption scheme using rectangular transform-enhanced chaotic tent maps. IEEE Access 5, 6429–6436 (2017). https://doi.org/10.1109/access.2017.2692043
Xu, Z.G., Tian, Q., Tian, L.: Theorem to generate independently and uniformly distributed chaotic key stream via topologically conjugated maps of tent map. Math. Probl. Eng. 2012, 619257 (2012). https://doi.org/10.1155/2012/619257
Yao, H., Liu, X., Tang, Z., Qin, C.: An improved image camouflage technique using color difference channel transformation and optimal prediction-error expansion. IEEE Access 6, 40569–40584 (2018). https://doi.org/10.1109/2858858
Zhang, D., Liao, X., Yang, B., Zhang, Y.: A fast and efficient approach to color-image encryption based on compressive sensing and fractional Fourier transform. Multimedia Tools Appl. 77(2), 2191–2208 (2018). https://doi.org/10.1007/s1104
Zhu, H., Zhao, Y., Song, Y.: 2D logistic-modulated-sine-coupling-logistic chaotic map for image encryption. IEEE Access 7, 14081–14098 (2019). https://doi.org/10.1109/ACCESS.2019.2893538
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bhnassy, M.A., Hagras, E.A.A., El-Badawy, ES.A. et al. Image encryption and watermarking combined dynamic chaotic hopping pattern with double random phase encoding DRPE. Opt Quant Electron 51, 246 (2019). https://doi.org/10.1007/s11082-019-1961-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-019-1961-2