Abstract
In this paper, we propose a new asymmetric optical cryptosystem for phase image encoding with the utilization of speckles generated by scattering the Hermite Gaussian beams (HGBs) through a rough surface. These speckle patterns are unique and almost impossible to clone as one cannot mimic the physical process. The generalized Schur decomposition, named as, QZ decomposition, approach is used to generate unique private keys for decrypting the encoded data. The plaintext image is first phase-encoded and then modulated with the pattern obtained by the convolution of HGBs and random phase masks. The modulated image is then Fresnel propagated for a distance of z1, and the QZ decomposition operation is performed on the complex wavefront to generate the private keys. Afterward, the gyrator transforms with a rotational angle (α), and the phase truncation is used to further process the information. The phase truncation and phase reservation (PT/PR) will result in another phase private key, which will be utilized for decryption. A non-linear power function is introduced to modify the amplitude part after PT/PR operation and the resultant is modulated using an HGB amplitude mask to get an intermediate wavefront. Finally, the encrypted image is obtained by Fresnel propagating the intermediate wavefront with a distance of z2. The effectiveness and validity of the proposed method are tested and verified through numerical simulations. A series of potential attacks such as contamination and plaintext attacks have been tried and tested to further check the robustness of the proposed method. The results confirm the efficacy of the proposed method.
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References
Adlerborn, B., Kågström, B., Kressner, D.: A parallel QZ algorithm for distributed memory HPC systems. SIAM J. Sci. Comput. (2014). https://doi.org/10.1137/140954817
Braman, K., Byers, R., Mathias, R.: The multishift QR algorithm. Part II: Aggressive early deflation. SIAM J. Matrix Anal. Appl. 23(4), 948–973 (2002)
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)
Chen, W., Chen, X.: Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain. Opt. Commun. 284(16–17), 3913–3917 (2011). https://doi.org/10.1016/J.OPTCOM.2011.04.005
Chen, L., Zhao, D.: Optical image encryption based on fractional wavelet transform. Opt. Commun. 254(4–6), 361–367 (2005). https://doi.org/10.1016/J.OPTCOM.2005.05.052
Chen, W., Chen, X., Sheppard, C.J.R.: Optical image encryption based on diffractive imaging. Opt. Lett. 35(22), 3817–3819 (2010). https://doi.org/10.1364/OL.35.003817
Chen, L., He, B., Chen, X., Gao, X., Liu, J.: Optical image encryption based on multi-beam interference and common vector decomposition. Opt. Commun. 361, 6–12 (2016). https://doi.org/10.1016/J.OPTCOM.2015.10.037
Chen, H., Tanougast, C., Liu, Z., Sieler, L.: Asymmetric optical cryptosystem for color image based on equal modulus decomposition in gyrator transform domains. Opt. Lasers Eng. 93, 1–8 (2017). https://doi.org/10.1016/J.OPTLASENG.2017.01.005
Chen, H., Liu, Z.: Recent Advanced in Image Security Technologies: Intelligent Image, Signal, and Video Processing. Springer Nature 2023, (2023). [Online]. Available: http://lib.ugent.be/catalog/ebk01:5700000000347133
Evans, D.J., Yalamov, P.: The QZ orthogonal decomposition method. Parallel Algorithms Appl. 2(4), 263–276 (1994). https://doi.org/10.1080/10637199408915421
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
Goudail, F., Bollaro, F., Javidi, B., Réfrégier, P.: Influence of a perturbation in a double phase-encoding system. J. Opt. Soc. Am. A 15(10), 2629–2638 (1998). https://doi.org/10.1364/JOSAA.15.002629
Hamed, A.M.: Speckle imaging of annular Hermite Gaussian laser beam. Pramana J. Phys. (2021). https://doi.org/10.1007/s12043-021-02231-9
Javidi, B., Sergent, A., Zhang, G., Guibert, L.: Fault tolerance properties of a double phase encoding encryption technique. Opt. Eng. 36, 992–998 (1997)
Jiao, S., Gao, Y., Lei, T., Yuan, X.: Known-plaintext attack to optical encryption systems with space and polarization encoding. Opt. Express 28(6), 8085 (2020). https://doi.org/10.1364/oe.387505
Kagstrom, B.O., Kressner, D.: Multishift variants of the QZ algorithm with aggressive early deflation. SIAM J. Matrix Anal. Appl. 29(1), 199–227 (2006). https://doi.org/10.1137/05064521X
Kumar, R., Bhaduri, B.: Optical image encryption using Kronecker product and hybrid phase masks. Opt. Laser Technol. 95, 51–55 (2017). https://doi.org/10.1016/J.OPTLASTEC.2017.03.041
Kumar, R., Bhaduri, B.: Optical image encryption in Fresnel domain using spiral phase transform. J. Opt. 19, 095701 (2017)
Kumar, R., Bhaduri, B., Nishchal, N.K.: Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition. J. Opt. 20, 015701 (2017)
Li, X., et al.: Designing optical 3D images encryption and reconstruction using monospectral synthetic aperture integral imaging. Opt. Express 26(9), 11084–11099 (2018). https://doi.org/10.1364/OE.26.011084
Lim, W.Q.: Discrete Shearlet Transform : New Multiscale Directional Image Representation’. (2009). Available: https://hal.science/hal-00451791
Liu, S., Guo, C., Sheridan, J.T.: A review of optical image encryption techniques. Opt. Laser Technol. 57, 327–342 (2014). https://doi.org/10.1016/j.optlastec.2013.05.023
Mandapati, V.C., et al.: Multi-user nonlinear optical cryptosystem based on polar decomposition and fractional vortex speckle patterns. Photonics (2023). https://doi.org/10.3390/photonics10050561
Matoba, O., Javidi, B.: Encrypted optical memory system using three-dimensional keys in the Fresnel domain. Opt. Lett. 24(11), 762–764 (1999). https://doi.org/10.1364/OL.24.000762
Matoba, O., Nomura, T., Perez-Cabre, E., Millan, M.S., Javidi, B.: Optical techniques for information security. Proc. IEEE 97(6), 1128–1148 (2009). https://doi.org/10.1109/JPROC.2009.2018367
Mehra, I., Nishchal, N.K.: Image fusion using wavelet transform and its application to asymmetric cryptosystem and hiding. Opt. Express 22(5), 5474–5482 (2014)
Moler, C.B., Stewart, G.W.: An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10(2), 241–256 (1973). https://doi.org/10.1137/0710024
Muniraj I., Sheridan, J.T.: Optical Encryption and Decryption’, Optical Encryption and Decryption, (2019), [Online]. Available: https://api.semanticscholar.org/CorpusID:88488859
Nishchal, N.K., Joseph, J., Singh, K.: Securing information using fractional Fourier transform in digital holography. Opt. Commun. 235(4–6), 253–259 (2004). https://doi.org/10.1016/j.optcom.2004.02.052
Niu, C.-H., Wang, X.-L., Lv, N.-G., Zhou, Z.-H., Li, X.-Y.: An encryption method with multiple encrypted keys based on interference principle. Opt. Express 18(8), 7827–7834 (2010). https://doi.org/10.1364/OE.18.007827
Peng, X., Zhang, P., Wei, H., Yu, B.: Known-plaintext attack on optical encryption based on double random phase keys. Opt. Lett. 31(8), 1044–1046 (2006). https://doi.org/10.1364/OL.31.001044
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), 118–120 (2010)
Rafiq Abuturab, M.: 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
Rajput, S.K., Matoba, O.: Optical voice encryption based on digital holography. Opt. Lett. 42(22), 4619–4622 (2017). https://doi.org/10.1364/OL.42.004619
Rajput, S.K., Nishchal, N.K.: Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain. Appl. Opt. 52(18), 4343–4352 (2013)
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.: Experimental implementation of the gyrator transform. J. Opt. Soc. Am. A Opt. Image Sci. vis. 24(10), 3135–3139 (2007a)
Rodrigo, J.A., Alieva, T., Calvo, M.L., Ozaktas, H.M. Zalevsky, Z., Alper Kutay, M.: Fourier transforms; (120.4820) Optical systems; (200.4740) Optical processing; (140.3300) Laser beam shaping (2007)
Rosales-Guzmán, C., Forbes, A.: How to shape Light with Spatial Light Modulators. SPIE PRESS (2017). https://doi.org/10.1117/3.2281295
Salla, G.R., Perumangattu, C., Prabhakar, S., Anwar, A., Singh, R.P.: Recovering the vorticity of a light beam after scattering. Appl. Phys. Lett. (2015). https://doi.org/10.1063/1.4926913
Shen, X., Dou, S., Lei, M., Chen, Y.: ‘Optical image encryption based on a joint Fresnel transform correlator with double optical wedges. Appl. Opt. 55(30), 8513–8522 (2016)
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
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), 13772–13781 (2010)
Topuzoski3’, S., Janicijevic3 L., Stoyanov, L., Dreischuh, A.: Transformation of HG(l,0) and HG(1,1) Modes into Beams with Multiple Vortices by the Fork-Shaped Grating (2018)
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
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
Weng, D., Zhu, N., Wang, Y., Xie, J., Liu, J.: Experimental verification of optical image encryption based on interference. Opt. Commun. 284(10–11), 2485–2487 (2011). https://doi.org/10.1016/J.OPTCOM.2011.01.039
Wu, J., Liu, W., Liu, Z., Liu, S.: Cryptanalysis of an & #x201C;asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition”. Appl. Opt. 54(30), 8921–8924 (2015). https://doi.org/10.1364/AO.54.008921
Xin-Xin, L., Dao-Mu, Z.: Optical image encryption with simplified fractional hartley transform. Chin. Phys. Lett. 25(7), 2477 (2008)
Zea, A.V., Barrera, J.F., Torroba, R.: ‘Experimental optical encryption of grayscale information. Appl. Opt. 56(21), 5883–5889 (2017)
Zhang, Y., Wang, B.: Optical image encryption based on interference. Opt. Lett. 33(21), 2443–2445 (2008). https://doi.org/10.1364/OL.33.002443
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RK would like to acknowledge the support from the Science and Engineering Research Board (SERB), the Government of India, under the SERB-SURE research grant (File No. SUR/2022/000910). SGR would like to acknowledge the support from SRM University-AP for seed research grants under SRMAP/URG/CG/2022-23/006 and SRMAP/URG/E&PP/2022-23/003.
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RK Conceptualized the idea and methodology, HV and Sakshi did the validation, formal analysis, and investigations. SGR, IM, and RK provided the resources ad software, HV and Sakshi wrote the original draft of manuscript, SGR and RK acquired the funding; supervised the project. All authors have reviewed and agreed to the published version of the manuscript
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Vardhan, H., Sakshi, Reddy, S.G. et al. A symmetric optical cryptosystem based on QZ decomposition and Hermite Gaussian beam speckles. Opt Quant Electron 56, 885 (2024). https://doi.org/10.1007/s11082-024-06740-w
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DOI: https://doi.org/10.1007/s11082-024-06740-w