Abstract
In this paper, we have presented an image encryption method in Chirp-Z transform domain using unequal modulus decomposition (UMD) and modified Gerchberg–Saxton (GS) algorithm. The proposed encryption scheme is highly sensitive to the encryption keys and the modified GS algorithm introduces an additional layer of security. The validity of the proposed method is tested with various grayscale and binary images and the numerical simulation results are demonstrated for ‘Cameraman’, ‘Medical’ and Binary ‘CUH’ images. The presented results confirm the robustness of the proposed method against various existing attacks such as, the noise attack, special attack, statistical attack, and brute force attack. A comparative analysis with existing similar methods is also performed and the enhanced security and efficiency of the proposed method is verified.
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References
Abdelfattah, M., Hegazy, S.F., Areed, N.F.F., Obayya, S.S.A.: Compact optical asymmetric cryptosystem based on unequal modulus decomposition of multiple color images. Opt. Lasers Eng. 129, 106063 (2020). https://doi.org/10.1016/j.optlaseng.2020.106063
Agoyi, M., Çelebi, E., Anbarjafari, G.: A watermarking algorithm based on chirp z-transform, discrete wavelet transform, and singular value decomposition. SIViP 9(3), 735–745 (2015). https://doi.org/10.1007/s11760-014-0624-9
Ahouzi, E., Zamrani, W., Azami, N., Lizana, A., Campos, J., Yzuel, M.J.: Optical triple random-phase encryption. Opt. Eng. 56(11), 1 (2017). https://doi.org/10.1117/1.OE.56.11.113114
Anjana, S., Saini, I., Singh, P., Yadav, A.K.: Asymmetric cryptosystem using affine transform in Fourier domain. In: Bhattacharyya, S., Chaki, N., Konar, D., Chakraborty, U.K., Singh, C.T. (eds.) Advanced Computational and Communication Paradigms, vol. 706, pp. 29–37. Springer, Singapore (2018)
Arora, M., Khurana, M.: Secure image encryption technique based on jigsaw transform and chaotic scrambling using digital image watermarking. Opt. Quant. Electron. 52(2), 59 (2020). https://doi.org/10.1007/s11082-019-2130-3
Barfungpa, S.P., Abuturab, M.R.: Asymmetric cryptosystem using coherent superposition and equal modulus decomposition of fractional Fourier spectrum. Opt Quant Electron 48(11), 520 (2016). https://doi.org/10.1007/s11082-016-0786-5
Biryukov, A.: The boomerang attack on 5 and 6-round reduced AES. In: Dobbertin, H., Rijmen, V., Sowa, A. (eds.) Advanced Encryption Standard – AES, vol. 3373, pp. 11–15. Springer, Berlin, Heidelberg (2005)
Cai, J., Shen, X.: Modified optical asymmetric image cryptosystem based on coherent superposition and equal modulus decomposition. Opt Laser Technol 95, 105–112 (2017). https://doi.org/10.1016/j.optlastec.2017.04.018
Cai, J., Shen, X., Lei, M., Lin, C., Dou, S.: Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition. Opt. Lett. 40(4), 475 (2015). https://doi.org/10.1364/OL.40.000475
Cai, J., Shen, X., Lin, C.: Security-enhanced asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition. Opt. Commun. 359, 26–30 (2016). https://doi.org/10.1016/j.optcom.2015.09.058
Chen, W., Javidi, B., Chen, X.: Advances in optical security systems. Adv. Opt. Photon. 6(2), 120 (2014). https://doi.org/10.1364/AOP.6.000120
Chen, H., Du, X., Liu, Z.: Optical spectrum encryption in associated fractional Fourier transform and gyrator transform domain. Opt. Quant. Electron. 48(1), 12 (2015a). https://doi.org/10.1007/s11082-015-0291-2
Chen, H., Du, X., Liu, Z., Yang, C.: Optical color image hiding scheme by using Gerchberg–Saxton algorithm in fractional Fourier domain. Opt. Lasers Eng. 66, 144–151 (2015b). https://doi.org/10.1016/j.optlaseng.2014.09.003
Chen, L., Gao, X., Chen, X., He, B., Liu, J., Li, D.: A new optical image cryptosystem based on two-beam coherent superposition and unequal modulus decomposition. Opt. Laser Technol. 78, 167–174 (2016). https://doi.org/10.1016/j.optlastec.2015.11.009
Chen, H., Zhu, L., Liu, Z., Tanougast, C., Liu, F., Blondel, W.: Optical single-channel color image asymmetric cryptosystem based on hyperchaotic system and random modulus decomposition in Gyrator domains. Opt. Lasers Eng. 124, 105809 (2020). https://doi.org/10.1016/j.optlaseng.2019.105809
Deng, X.: Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition: comment. Opt. Lett. 40(16), 3913 (2015). https://doi.org/10.1364/OL.40.003913
Fatima, A., Mehra, I., Nishchal, N.K.: Optical image encryption using equal modulus decomposition and multiple diffractive imaging. J. Opt. 18(8), 085701 (2016). https://doi.org/10.1088/2040-8978/18/8/085701
Fienup, J.R.: Phase retrieval algorithms: a comparison. Appl. Opt. 21(15), 2758 (1982). https://doi.org/10.1364/AO.21.002758
Frauel, Y., Castro, A., Naughton, T.J., Javidi, B.: Security analysis of optical encryption. Bruges, Belgium, p. 598603 (2005). https://doi.org/10.1117/12.633677.
Javidi, B.: Fault tolerance properties of a double phase encoding encryption technique. Opt. Eng 36(4), 992 (1997). https://doi.org/10.1117/1.601144
Javidi, B., Nomura, T.: Securing information by use of digital holography. Opt. Lett. 25(1), 28 (2000). https://doi.org/10.1364/OL.25.000028
Javidi, B., et al.: Roadmap on optical security. J. Opt. 18(8), 083001 (2016). https://doi.org/10.1088/2040-8978/18/8/083001
Kishk, S., Javidi, B.: Information hiding technique with double phase encoding. Appl. Opt. 41(26), 5462 (2002). https://doi.org/10.1364/AO.41.005462
Kumar, R., Quan, C.: Asymmetric multi-user optical cryptosystem based on polar decomposition and Shearlet transform. Opt. Lasers Eng. 120, 118–126 (2019a). https://doi.org/10.1016/j.optlaseng.2019.03.024
Kumar, R., Quan, C.: Optical colour image encryption using spiral phase transform and chaotic pixel scrambling. J. Mod. Opt. 66(7), 776–785 (2019b). https://doi.org/10.1080/09500340.2019.1572807
Kumar, R., Bhaduri, B., Hennelly, B.: QR code-based non-linear image encryption using Shearlet transform and spiral phase transform. J. Mod. Opt. 65(3), 321–330 (2018a). https://doi.org/10.1080/09500340.2017.1395486
Kumar, J., Singh, P., Yadav, A.K., Kumar, A.: Asymmetric cryptosystem for phase images in fractional Fourier domain using LU-decomposition and Arnold transform. Procedia Comput. Sci. 132, 1570–1577 (2018b). https://doi.org/10.1016/j.procs.2018.05.121
Kumar, J., Singh, P., Yadav, A.K., Kumar, A.: Asymmetric image encryption using Gyrator transform with singular value decomposition. In: Ray, K., Sharan, S.N., Rawat, S., Jain, S.K., Srivastava, S., Bandyopadhyay, A. (eds.) Engineering Vibration, Communication and Information Processing, vol. 478, pp. 375–383. Springer, Singapore (2019a)
Kumar, R., Zhong, F., Quan, C.: Optical voice information hiding using enhanced iterative algorithm and computational ghost imaging. J. Opt. 21(6), 065704 (2019b). https://doi.org/10.1088/2040-8986/ab1e32
Lai, C.S., et al.: A robust correlation analysis framework for imbalanced and dichotomous data with uncertainty. Inf. Sci. 470, 58–77 (2019). https://doi.org/10.1016/j.ins.2018.08.017
Liu, L., Shan, M., Zhong, Z., Liu, B.: Asymmetric image encryption based on optical interference using modified error-reduction phase retrieval algorithm. Laser Phys. Lett. 17(3), 035204 (2020). https://doi.org/10.1088/1612-202X/ab6856
Lyda, R., Hamrock, J.: Using entropy analysis to find encrypted and packed malware. IEEE Secur. Priv. Mag. 5(2), 40–45 (2007). https://doi.org/10.1109/MSP.2007.48
Midoun, M.A., Wang, X., Talhaoui, M.Z.: A sensitive dynamic mutual encryption system based on a new 1D chaotic map. Opt. Lasers Eng. 139, 106485 (2021). https://doi.org/10.1016/j.optlaseng.2020.106485
Mosso, E., Bolognini, N.: Dynamic multiple-image encryption based on chirp z-transform. J. Opt. 21(3), 035704 (2019). https://doi.org/10.1088/2040-8986/ab015f
Mosso, E., Suárez, O., Bolognini, N.: Asymmetric multiple-image encryption system based on a chirp z-transform. Appl. Opt. 58(21), 5674 (2019). https://doi.org/10.1364/AO.58.005674
Peng, X., Zhang, P., Wei, H., Yu, B.: Known-plaintext attack on optical encryption based on double random phase keys. Opt. Lett. 31(8), 1044 (2006). https://doi.org/10.1364/OL.31.001044
Rakheja, P., Vig, R., Singh, P., Kumar, R.: An iris biometric protection scheme using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain. Opt. Quant. Electron. 51(6), 204 (2019a). https://doi.org/10.1007/s11082-019-1921-x
Rakheja, P., Vig, R., Singh, P.: An asymmetric hybrid cryptosystem using equal modulus and random decomposition in hybrid transform domain. Opt. Quant. Electron. 51(2), 54 (2019b). https://doi.org/10.1007/s11082-019-1769-0
Rakheja, P., Vig, R., Singh, P.: An asymmetric hybrid cryptosystem using hyperchaotic system and random decomposition in hybrid multi resolution wavelet domain. Multimed. Tools Appl. 78(15), 20809–20834 (2019c). https://doi.org/10.1007/s11042-019-7406-x
Rakheja, P., Vig, R., Singh, P.: An asymmetric watermarking scheme based on random decomposition in hybrid multi-resolution wavelet domain using 3D Lorenz chaotic system. Optik 198, 163289 (2019d). https://doi.org/10.1016/j.ijleo.2019.163289
Rakheja, P., Vig, R., Singh, P.: Double image encryption using 3D Lorenz chaotic system, 2D non-separable linear canonical transform and QR decomposition. Opt. Quant. Electron. 52(2), 103 (2020a). https://doi.org/10.1007/s11082-020-2219-8
Rakheja, P., Singh, P., Vig, R., Kumar, R.: Double image encryption scheme for iris template protection using 3D Lorenz system and modified equal modulus decomposition in hybrid transform domain. J. Mod. Opt. 67(7), 592–605 (2020b). https://doi.org/10.1080/09500340.2020.1760384
Refregier, P., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20(7), 767 (1995). https://doi.org/10.1364/OL.20.000767
Singh, H., Yadav, A.K., Vashisth, S., Singh, K.: Fully phase image encryption using double random-structured phase masks in gyrator domain. Appl. Opt. 53(28), 6472 (2014). https://doi.org/10.1364/AO.53.006472
Singh, P., Yadav, A.K., Singh, K., Saini, I.: Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition. AIP Conference Proceedings 1802, 020017 (2017a). https://doi.org/10.1063/1.4973267
Singh, P., Yadav, A.K., Singh, K.: Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition. Opt. Lasers Eng. 91, 187–195 (2017b). https://doi.org/10.1016/j.optlaseng.2016.11.022
Singh, P., Yadav, A.K., Singh, K., Saini, I.: Asymmetric watermarking scheme in fractional Hartley domain using modified equal modulus decomposition. J. Optoelectron. Adv. Mater. 21, 484–491 (2019)
Singh, P., Yadav, A.K., Singh, K.: Known-plaintext attack on cryptosystem based on fractional hartley transform using particle swarm optimization algorithm. In: Ray, K., Sharan, S.N., Rawat, S., Jain, S.K., Srivastava, S., Bandyopadhyay, A. (eds.) Engineering Vibration, Communication and Information Processing, vol. 478, pp. 317–327. Springer, Singapore (2019b)
Sukhoy, V., Stoytchev, A.: Generalizing the inverse FFT off the unit circle. Sci. Rep. 9(1), 14443 (2019). https://doi.org/10.1038/s41598-019-50234-9
Tashima, H., Takeda, M., Suzuki, H., Obi, T., Yamaguchi, M., Ohyama, N.: Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack. Opt. Express 18(13), 13772 (2010). https://doi.org/10.1364/OE.18.013772
Unnikrishnan, G., Joseph, J., Singh, K.: Optical encryption by double-random phase encoding in the fractional Fourier domain. Opt. Lett. 25(12), 887 (2000). https://doi.org/10.1364/OL.25.000887
Vandana, A., Sachin, S., Singh, P.: Cascaded unequal modulus decomposition in Fresnel domain based cryptosystem to enhance the image security. Opt. Lasers Eng. 137, 12 (2021). https://doi.org/10.1016/j.optlaseng.2020.106399
Wang, X., Zhao, D.: A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt. Commun. 285(6), 1078–1081 (2012). https://doi.org/10.1016/j.optcom.2011.12.017
Wang, X., Chen, Y., Dai, C., Zhao, D.: Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform. Appl. Opt. 53(2), 208 (2014). https://doi.org/10.1364/AO.53.000208
Wang, Y., Quan, C., Tay, C.J.: Optical color image encryption without information disclosure using phase-truncated Fresnel transform and a random amplitude mask. Opt. Commun. 344, 147–155 (2015a). https://doi.org/10.1016/j.optcom.2015.01.045
Wang, Y., Quan, C., Tay, C.J.: Improved method of attack on an asymmetric cryptosystem based on phase-truncated Fourier transform. Appl. Opt. 54(22), 6874 (2015b). https://doi.org/10.1364/AO.54.006874
Wang, Y., Quan, C., Tay, C.J.: New method of attack and security enhancement on an asymmetric cryptosystem based on equal modulus decomposition. Appl. Opt. 55(4), 679 (2016). https://doi.org/10.1364/AO.55.000679
Wu, J., Liu, W., Liu, Z., Liu, S.: Cryptanalysis of an asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition. Appl. Opt. 54(30), 8921 (2015). https://doi.org/10.1364/AO.54.008921
Xiong, Y., Kumar, R., Quan, C.: Security analysis on an optical encryption and authentication scheme based on phase-truncation and phase-retrieval algorithm. IEEE Photon. J. 11(5), 1–14 (2019a). https://doi.org/10.1109/JPHOT.2019.2936236
Xiong, Y., Du, J., Quan, C.: Single-channel optical color image cryptosystem using two-step phase-shifting interferometry and random modulus decomposition. Opt. Laser Technol. 119, 105580 (2019b). https://doi.org/10.1016/j.optlastec.2019.105580
Xu, H., Xu, W., Wang, S., Wu, S.: Asymmetric optical cryptosystem based on modulus decomposition in Fresnel domain. Opt. Commun. 402, 302–310 (2017). https://doi.org/10.1016/j.optcom.2017.05.035
Yadav, A.K., Singh, P., Singh, K.: Cryptosystem based on devil’s vortex Fresnel lens in the fractional Hartley domain. J Opt 47(2), 208–219 (2018). https://doi.org/10.1007/s12596-017-0435-9
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This work was funded by award reference Number 09/1152(0012)/2019-EMR-1 from Council of Scientific & Industrial Research (CSIR), India, a premier national R&D organization. The contents of the publication are solely the responsibility of the authors and do not necessarily represent the official views of the Council of Scientific & Industrial Research.
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Sachin, S., Kumar, R. & Singh, P. Unequal modulus decomposition and modified Gerchberg Saxton algorithm based asymmetric cryptosystem in Chirp-Z transform domain. Opt Quant Electron 53, 254 (2021). https://doi.org/10.1007/s11082-021-02908-w
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DOI: https://doi.org/10.1007/s11082-021-02908-w