Abstract
In this paper, an asymmetric scheme based on double image using phase retrieval algorithms in gyrator domain is reported. The double images are encrypted using QZ synthesis method based on QZ algorithm. The synthesized image is bonded with a random phase mask and undergoes a gyrator transform. The resultant image act as an input for the phase retrieval algorithm. We have tested the scheme with five different phase retrieval algorithms, namely the Gerchberg-Saxton algorithm, modified Gerchberg-Saxton algorithm, input–output algorithm, Yang-Gu mixture amplitude-phase retrieval algorithm, and improved amplitude-phase retrieval algorithm. Simulations are executed to show the performance, feasibility, and robustness of the scheme. The gyrator parameter and private keys are highly sensitive to a small change to their original value. Performance of different phase retrieval algorithms on the scheme is evaluated using multi-attribute decision-making tool: TOPSIS method. Results suggest that the Yang-Gu mixture amplitude-phase retrieval algorithm performs better among phase retrieval algorithms and has ranked 1 in TOPSIS analysis. This has been validated by the figures reported in the paper.
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References
Abuturab, M.R.: Color image security system using double random-structured phase encoding in gyrator transform domain. Appl. Opt. 51(15), 3006–3016 (2012). https://doi.org/10.1364/AO.51.003006
Abuturab, M.R.: Group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform. J. Opt. Soc. Am. 32(10), 1811 (2015). https://doi.org/10.1364/JOSAA.32.001811
Abuturab, M.R.: Securing multiple information using wavelet transform and Yang-Gu mixture amplitude-phase retrieval algorithm. Opt. Lasers Eng. 118, 42–51 (2019). https://doi.org/10.1016/j.optlaseng.2019.01.015
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
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
Chen, S.-J., Hwang, C.-L.: Fuzzy multiple attribute decision making methods, in fuzzy multiple attribute decision making: methods and applications. In: Chen, S.-J., Hwang, C.-L. (eds.) Lecture Notes in Economics and Mathematical Systems, pp. 289–486. Springer, Berlin, Heidelberg (1992). https://doi.org/10.1007/978-3-642-46768-4_5
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), 3913–3913 (2015). https://doi.org/10.1364/OL.40.003913
Deng, X., Zhao, D.: Single-channel color image encryption using a modified Gerchberg–Saxton algorithm and mutual encoding in the Fresnel domain. Appl. Opt. 50(31), 6019–6025 (2011). https://doi.org/10.1364/AO.50.006019
Fienup, J.R.: Reconstruction of an object from the modulus of its Fourier transform. Opt. Lett. 3(1), 27 (1978). https://doi.org/10.1364/OL.3.000027
Fienup, J.R.: Phase retrieval algorithms: a comparison. Appl. Opt. 21(15), 2758 (1982). https://doi.org/10.1364/AO.21.002758
Fienup, J.R.: Phase retrieval algorithms: a personal tour [Invited]. Appl. Opt. 52(1), 45 (2013). https://doi.org/10.1364/AO.52.000045
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
Gaur, K.S., Singh, H., Thakran, S.: Asymmetric cryptosystem using QZ modulation with SPM in Fresnel domain. J. Opt. (2022). https://doi.org/10.1007/s12596-022-00990-1
Gerchberg, R.W., Saxton, W.O.: A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35(2), 237–246 (1972)
Gopinathan, U., Monaghan, D.S., Naughton, T.J., Sheridan, J.T.: A known-plaintext heuristic attack on the fourier plane encryption algorithm. Opt. Express 14(8), 3181–3186 (2006). https://doi.org/10.1364/OE.14.003181
He, Y., Cao, Y., Lu, X.: Color image encryption based on orthogonal composite grating and double random phase encoding technique. Optik 123(17), 1592–1596 (2012). https://doi.org/10.1016/j.ijleo.2011.08.033
He, W., Meng, X., Peng, X.: Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: comment. Opt. Lett. 38(20), 4044 (2013). https://doi.org/10.1364/OL.38.004044
Huang, J.-J.: Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain. Opt. Laser Technol. 44, 2238–2244 (2012). https://doi.org/10.1016/j.optlastec.2012.02.032
Jahanshahloo, G.R., Lotfi, F.H., Izadikhah, M.: An algorithmic method to extend TOPSIS for decision-making problems with interval data. Appl. Math. Comput. 175(2), 1375–1384 (2006). https://doi.org/10.1016/j.amc.2005.08.048
Kumar, R., Quan, C.: Asymmetric multi-user optical cryptosystem based on polar decomposition and Shearlet transform. Opt. Lasers Eng. 120, 118–126 (2019). https://doi.org/10.1016/j.optlaseng.2019.03.024
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, pp. 375–383. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-1642-5_34
Liu, Z., et al.: Fast algorithm of discrete gyrator transform based on convolution operation. Optik 122(10), 864–867 (2011). https://doi.org/10.1016/j.ijleo.2010.06.010
Liu, X., Cao, Y., Lu, P., Lu, X., Li, Y.: Optical image encryption technique based on compressed sensing and Arnold transformation. Optik 124(24), 6590–6593 (2013). https://doi.org/10.1016/j.ijleo.2013.05.092
Liu, W., Liu, Z., Liu, S.: Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm. Opt. Lett. 38(10), 1651–1653 (2013a). https://doi.org/10.1364/OL.38.001651
Liu, W., Liu, Z., Liu, S.: Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: reply. Opt. Lett. 38(20), 4045 (2013b). https://doi.org/10.1364/OL.38.004045
Liu, X., Wu, J., He, W., Liao, M., Zhang, C., Peng, X.: Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding. Opt. Express 23(15), 18955 (2015). https://doi.org/10.1364/OE.23.018955
Mehra, I., Nishchal, N.K.: Fingerprint image encryption using phase retrieval algorithm in gyrator wavelet transform domain using QR decomposition. Opt. Commun. 533, 129265 (2023). https://doi.org/10.1016/j.optcom.2023.129265
Nishchal, N.K.: Optical Cryptosystems. (IOP), Bristol, UK (2019). https://doi.org/10.1088/978-0-7503-2220-1
Peng, X., Wei, H., Zhang, P.: Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain. Opt. Lett. 31(22), 3261–3263 (2006). https://doi.org/10.1364/OL.31.003261
Qin, W., Peng, X.: Asymmetric cryptosystem based on phase-truncated fourier transforms. Opt. Lett. 35(2), 118 (2010). https://doi.org/10.1364/OL.35.000118
Rajput, S.K., Nishchal, N.K.: Optical asymmetric cryptosystem based on photon counting and phase-truncated Fresnel transforms. J. Mod. Opt. 64(8), 878–886 (2017). https://doi.org/10.1080/09500340.2016.1265677
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 (2019). https://doi.org/10.1016/j.ijleo.2019.163289
Rakheja, P., Yadav, S., Tobria, A.: A novel image encryption mechanism based on umbrella map and Yang-Gu algorithm. Optik 271, 170152 (2022). https://doi.org/10.1016/j.ijleo.2022.170152
Refregier, P., Javidi, B.: Optical image encryption based on input plane and fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995). https://doi.org/10.1364/OL.20.000767
Rodrigo, J.A., Alieva, T., Calvo, M.L.: Gyrator transform: properties and applications. Opt. Express 15(5), 2190 (2007). https://doi.org/10.1364/OE.15.002190
Sachin, A., Singh, P.: Cascaded unequal modulus decomposition in Fresnel domain based cryptosystem to enhance the image security. Opt. Lasers Eng. 137, 106399–106411 (2021). https://doi.org/10.1016/j.optlaseng.2020.106399
Sachin, A., Singh, P.: Asymmetric watermarking scheme for color images using cascaded unequal modulus decomposition in fourier domain. J. Mod. Opt. 68(20), 1–14 (2021b). https://doi.org/10.1080/09500340.2021.1977404
Shen, Y., Tang, C., Xu, M., Lei, Z.: Optical asymmetric single-channel cryptosystem based on QZ synthesis for color images. Opt. Laser Technol. 153, 108254 (2022). https://doi.org/10.1016/j.optlastec.2022.108254
Singh, H.: Watermarking image encryption using deterministic phase mask and singular value decomposition in fractional Mellin transform domain. IET Image Proc. 12(11), 1994–2001 (2018). https://doi.org/10.1049/iet-ipr.2018.5399
Singh, P., Yadav, A.K., Singh, K.: Color image encryption using affine transform in fractional Hartley domain. Opt. Appl. XLVII, 421–433 (2017). https://doi.org/10.5277/oa170308
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(7–8), 848–491 (2019)
Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 29(14), 1584–1586 (2004). https://doi.org/10.1364/OL.29.001584
Su, Q., Wang, G., Zhang, X., Lv, G., Chen, B.: A new algorithm of blind color image watermarking based on LU decomposition. Multidimens. Syst. Signal Process. 29(3), 1055–1074 (2018). https://doi.org/10.1007/s11045-017-0487-7
Sui, L., Liu, B., Wang, Q., Li, Y., Liang, J.: Double-image encryption based on Yang-Gu mixture amplitude-phase retrieval algorithm and high dimension chaotic system in gyrator domain. Optics Communications 354, 184–196 (2015a). https://doi.org/10.1016/j.optcom.2015.05.071
Sui, L., Liu, B., Wang, Q., Li, Y., Liang, J.: Color image encryption by using Yang-Gu mixture amplitude-phase retrieval algorithm in gyrator transform domain and two-dimensional Sine logistic modulation map. Opt. Lasers Eng. 75, 17–26 (2015b). https://doi.org/10.1016/j.optlaseng.2015.06.005
Tzeng, G.-H., Huang, J.-J.: Multiple attribute decision making: methods and applications. CRC Press, Boca Raton (2011)
Unnikrishnan, G., Joseph, J., Singh, K.: Optical encryption by double-random phase encoding in the fractional fourier domain. Opt. Lett. 25(12), 887–889 (2000). https://doi.org/10.1364/OL.25.000887
Vashisth, S., Singh, H., Yadav, A.K., Singh, K.: Devil’s vortex phase structure as frequency plane mask for image encryption using the fractional Mellin transform. Int. J. Opt. 2014, 1–9 (2014). https://doi.org/10.1155/2014/728056
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, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004). https://doi.org/10.1109/TIP.2003.819861
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), 208–213 (2014a). https://doi.org/10.1364/AO.53.000208
Wang, X., Zhao, D., Chen, Y.: Double-image encryption without information disclosure using phase-truncation Fourier transforms and a random amplitude mask. Appl. Opt. 53(23), 5100 (2014b). https://doi.org/10.1364/AO.53.005100
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), 6874–6881 (2015). https://doi.org/10.1364/AO.54.006874
Wang, Y., Quan, C., Tay, C.J.: Asymmetric optical image encryption based on an improved amplitude–phase retrieval algorithm. Opt. Lasers Eng. 78, 8–16 (2016). https://doi.org/10.1016/j.optlaseng.2015.09.008
Wei, H., Wang, X.: Optical multiple-image authentication and encryption based on phase retrieval and interference with sparsity constraints. Opt. Laser Technol. 142, 107257 (2021). https://doi.org/10.1016/j.optlastec.2021.107257
Xiong, Y., Quan, C.: Hybrid attack free optical cryptosystem based on two random masks and lower upper decomposition with partial pivoting. Opt. Laser Technol. 109, 456–464 (2019). https://doi.org/10.1016/j.optlastec.2018.08.033
Xu, H., Xu, W., Wang, S., Wu, S.: Phase-only asymmetric optical cryptosystem based on random modulus decomposition. J. Mod. Opt. 65(10), 1245–1252 (2018). https://doi.org/10.1080/09500340.2018.1431314
Zhou, N., Liu, X., Zhang, Y., Yang, Y.: Image encryption scheme based on fractional Mellin transform and phase retrieval technique in fractional fourier domain. Opt. Laser Technol. 47, 341–346 (2013). https://doi.org/10.1016/j.optlastec.2012.08.033
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This work was supported by award reference number 1172(CSIR-UGC NET DEC.2018) from University Grants Commission, Ministry of Human Resource Development.
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Archana Tobria contributed to methodology, validation and writing original draft; Phool Singh contributed to formal analysis, writing-review and editing. The authors have read and approved the final manuscript.
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Appendix
Appendix
The decision matrix, normalized decision matrix, weighted normalized decision matrix, positive and negative ideal solution matrix of both images such as Peppers and Cameraman for the proposed scheme are depicted here. Herein, \(CC3\) and \(CC4\) represents the \(CC\) value of another set of grayscale images Airplane and Boat.
See Tables 3,4, 5, 6, 7, 8, 9 and 10.
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Tobria, A., Singh, P. A comparative analysis of phase retrieval algorithms in asymmetric double image cryptosystem in gyrator domain. Opt Quant Electron 56, 33 (2024). https://doi.org/10.1007/s11082-023-05524-y
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DOI: https://doi.org/10.1007/s11082-023-05524-y