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Ciphertext-only attacks on the double random phase encryption based on redundancy vulnerability

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Abstract

The double random phase encoding techniques have received considerable attention from researchers in recent years because of their advantages of parallel and high-speed processing capability. Meanwhile, the security of the cryptosystem is also one of the major concerns. We experimentally showed the ciphertext redundancy vulnerability of the coherent double random phase encryption (DRPE) system. Based on the statistical ergodicity of speckles and the consistency of the energy spectral density (ESD), we have proved that the method can retrieve the most plaintext information from partial ciphertext alone. We performed the simulation and experimental results to verify whether the algorithm is effective. The ciphertext redundancy of the DRPE system is analyzed from the results of the ciphertext occlusion test. There is a risk of plaintext leakage in this scheme, as long as the average ESD can be estimated from the sub-images. The results will further our understanding of the limitation of current optical security techniques. The DRPE system has potential redundancy risk. This vulnerability allows a cryptanalyst to estimate the plaintext information with only a half or less ciphertext.

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References

  1. Alfalou, C.: Brosseau: optical image compression and encryption methods. Adv. Opt. Photonics 1(3), 589–636 (2009). https://doi.org/10.1364/AOP.1.000589

    Article  ADS  Google Scholar 

  2. Millán, M.S.: Advanced optical correlation and digital methods for pattern matching-50th anniversary of Vander Lugt matched filter. J. Opt. A-Pure Appl. Op. 14(10), 103001 (2012). https://doi.org/10.1088/2040-8978/14/10/103001

    Article  Google Scholar 

  3. Chen, W., Javidi, B., Chen, X.: Advances in optical security systems. Adv. Opt. Photonics 6(2), 120–155 (2014). https://doi.org/10.1364/AOP.6.000120

    Article  ADS  Google Scholar 

  4. 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

    Article  ADS  Google Scholar 

  5. Javidi, A., Carnicer, M., Yamaguchi, T., Nomura, E., Pérez-Cabré, M.S., Millán, N.K., Nishchal, R., Torroba, J.F., Barrera, W., He, X., Peng, A., Stern, Y., Rivenson, A., Alfalou, C., Brosseau, C., Guo, J.T., Sheridan, G., Situ, M., Naruse, T., Matsumoto, I., Juvells, E., Tajahuerce, J., Lancis, W., Chen, X., Chen, P.W.H., Pinkse, A.P., Mosk, A.: Markman: Roadmap on optical security. J. Opt. A-Pure Appl. Op. 18(8), 083001–083039 (2016). https://doi.org/10.1088/2040-8978/18/8/083001

    Article  Google Scholar 

  6. 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, 103 (2020). https://doi.org/10.1007/s11082-020-2219-8

    Article  Google Scholar 

  7. Mohamed, A., Salem, F.H., Nihal, F.F.A., Salah, S.A.O.: 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

    Article  Google Scholar 

  8. Su, Y., Xu, W., Zhao, J.: Optical image encryption based on chaotic fingerprint phase mask and pattern-illuminated Fourier ptychography. Opt. Lasers Eng. 128, 106042 (2020). https://doi.org/10.1016/j.optlaseng.2020.106042

    Article  Google Scholar 

  9. Zhao, H., Zhong, Z., Fang, W., Xie, H., Zhang, Y., Shan, M.: Double-image encryption using chaotic maps and nonlinear non-DC joint fractional Fourier transform correlator. Opt. Eng. 55(9), 0931091–0931097 (2016). https://doi.org/10.1117/1.OE.55.9.093109

    Article  Google Scholar 

  10. Vaish, Kumar, M.: Color image encryption using MSVD, DWT and Arnold transform in fractional Fourier domain. Optik 145, 273–283 (2017). https://doi.org/10.1016/j.ijleo.2017.07.041

    Article  ADS  Google Scholar 

  11. Jaramillo, J., Barrera, F., Zea, A.V., Torroba, R.: Fractional optical cryptographic protocol for data containers in a noise-free multiuser environment. Opt. Lasers Eng. 102, 119–125 (2018). https://doi.org/10.1016/j.optlaseng.2017.10.008

    Article  Google Scholar 

  12. Wang, J., Song, L., Liang, X., Liu, Y., Liu, P.: Secure and noise-free nonlinear optical cryptosystem based on phase-truncated Fresnel diffraction and QR code. Opt. Quant. Electron. 48(11), 523 (2016). https://doi.org/10.1007/s11082-016-0796-3

    Article  Google Scholar 

  13. 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). https://doi.org/10.1364/AO.55.008513

    Article  ADS  Google Scholar 

  14. Zhang, W.H., Wu, J., Peng, X.: Optical cryptosystem based on phase-truncated Fresnel diffraction and transport of intensity equation. Opt. Express 23(7), 8845–8854 (2015). https://doi.org/10.1364/OE.23.008845

    Article  ADS  Google Scholar 

  15. Li, X., Meng, X., Yang, X., Wang, Y., Yin, Y., Peng, X., He, W., Dong, G., Chen, H.: Multiple-image encryption via lifting wavelet transform and XOR operation based on compressive ghost imaging scheme. Opt. Lasers Eng. 102, 106–111 (2018). https://doi.org/10.1007/s10043-017-0390-3

    Article  Google Scholar 

  16. Liu, Q., Wang, Y., Wang, J., Wang, Q.-H.: Optical image encryption using chaos-based compressed sensing and phase-shifting interference in fractional wavelet domain. Opt. Rev. 25(1), 46–55 (2017). https://doi.org/10.1007/s10043-017-0390-3

    Article  Google Scholar 

  17. Liu, J., Xu, X., Wu, Q., Sheridan, J.T., Situ, G.: Information encryption in phase space. Opt. Lett. 40(6), 859–862 (2015). https://doi.org/10.1364/OL.40.000859

    Article  ADS  Google Scholar 

  18. Xu, X., Wu, Q., Liu, J., Situ, G.: Decryption with incomplete cyphertext and multiple-information encryption in phase space. Opt. Express 24(2), 1734–1746 (2016). https://doi.org/10.1364/OE.24.001734

    Article  ADS  Google Scholar 

  19. Monaghan, S., Gopinathan, U., Naughton, T.J., Sheridan, J.T.: Key-space analysis of double random phase encryption technique. Appl. Opt. 46(26), 6641–6647 (2007). https://doi.org/10.1364/AO.46.006641

    Article  ADS  Google Scholar 

  20. 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

    Article  ADS  Google Scholar 

  21. Situ, G., Gopinathan, U., Monaghan, D.S., Sheridan, J.T.: Cryptanalysis of optical security systems with significant output images. Appl. Opt. 46(22), 5257–5262 (2007). https://doi.org/10.1364/AO.46.005257

    Article  ADS  Google Scholar 

  22. Frauel, Y., Castro, A., Naughton, T.J., Javidi, B.: Resistance of the double random phase encryption against various attacks. Opt. Express 15(6), 10253–10265 (2007). https://doi.org/10.1364/OE.15.010253

    Article  ADS  Google Scholar 

  23. Carnicer, M.M.-U., 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

    Article  ADS  Google Scholar 

  24. Guo, S., Liu, J., Sheridan, T.: Iterative phase retrieval algorithms. Part II: attacking optical encryption systems. Appl. Opt. 54(15), 4709–4718 (2015). https://doi.org/10.1364/AO.54.004709

    Article  ADS  Google Scholar 

  25. Zhou, L., Xiao, Y., Chen, W.: Vulnerability to machine learning attacks of optical encryption based on diffractive imaging. Opt. Lasers Eng. 125, 105858 (2020). https://doi.org/10.1016/j.optlaseng.2019.105858

    Article  Google Scholar 

  26. 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

    Article  ADS  Google Scholar 

  27. Liao, M., He, W., Lu, D., Peng, X.: Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium. Sci. Rep. 7, 41789 (2017). https://doi.org/10.1038/srep41789

    Article  ADS  Google Scholar 

  28. Li, T., Miao, Z., Shi, Y.: Ciphertext-only attack on phase-shifting interferometry-based encryption. IEEE Photonics J. 9(5), 1–8 (2017). https://doi.org/10.1109/JPHOT.2017.2743060

    Article  Google Scholar 

  29. 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 (2018). https://doi.org/10.1364/JOSAA.35.0000A1

    Article  ADS  Google Scholar 

  30. Shechtman, Y., Eldar, Y.C., Cohen, O., Chapman, H.N., Miao, J., Segev, M.: Phase retrieval with application to optical imaging: a contemporary overview. IEEE Sig. Proc. 32(3), 87–109 (2015). https://doi.org/10.1109/MSP.2014.2352673

    Article  Google Scholar 

  31. Xiong, Y., Kumar, R., Quan, C.: Security analysis on an optical encryption and authentication scheme based on phase-truncation and phase-retrieval algorithm. IEEE Photonics J. 11(5), 1–14 (2019). https://doi.org/10.1109/JPHOT.2019.2936236

    Article  Google Scholar 

  32. Katz, O., Heidmann, P., Fink, M., et al.: Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations. Nat. Photon. 8, 784–790 (2014). https://doi.org/10.1038/nphoton.2014.189

    Article  ADS  Google Scholar 

  33. Zea, A.V., Barrera, J.F., Torroba, R.: Experimental optical encryption of grayscale information. Appl. Opt. 56(21), 5883–5889 (2017). https://doi.org/10.1364/AO.56.005883

    Article  ADS  Google Scholar 

  34. Ahouzi, E., Zamrani, W., Azami, N., Lizana, A., Campos, J., Yzuel, M.J.: Optical triple random-phase encryption. Opt. Eng. 56(11), 113114 (2017). https://doi.org/10.1117/1.OE.56.11.113114

    Article  ADS  Google Scholar 

  35. Zea, A.V., Barrera, J.F., Torroba, R.: Cryptographic salting for security enhancement of double random phase encryption schemes. J. Opt. 19(10), 105703 (2017). https://doi.org/10.1088/2040-8986/aa8738

    Article  ADS  Google Scholar 

  36. Ma, L., Jin, W.: Symmetric and asymmetric hybrid cryptosystem based on compressive sensing and computer generated holography. Opt. Commun. 407, 51–56 (2018). https://doi.org/10.1016/j.optcom.2017.08.047

    Article  ADS  Google Scholar 

  37. Xiong, Y., He, A., Quan, C.: Hybrid attack on an optical cryptosystem based on phase-truncated Fourier transforms and a random amplitude mask. Appl. Opt. 57(21), 6010–6016 (2018). https://doi.org/10.1364/AO.57.006010

    Article  ADS  Google Scholar 

  38. Liansheng, S., Cong, D., Xiao, Z., Ailing, T., Anand, A.: Double-image encryption based on interference and logistic map under the framework of double random phase encoding. Opt. Lasers Eng. 122, 113–122 (2019). https://doi.org/10.1016/j.optlaseng.2019.06.005

    Article  Google Scholar 

  39. Idell, P.S., Fienup, J.R., Goodman, R.S.: Image synthesis from nonimaged laser-speckle patterns. Opt. Lett. 12(11), 858 (1987). https://doi.org/10.1364/OL.12.000858

    Article  ADS  Google Scholar 

  40. Idell, P.S., Knopp, J., Gonglewski, J.D., Voelz, D.G.: Image synthesis from nonimaged laser-speckle patterns: experimental verification. Opt. Lett. 14, 154–156 (1989). https://doi.org/10.1364/OL.14.000154

    Article  ADS  Google Scholar 

  41. 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

    Article  ADS  Google Scholar 

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Acknowledgements

This research was funded by Open Foundation of The Suzhou Smart City Research Institute, Suzhou University of Science and Technology, grant number SZSCR2019008; Suzhou Key Industry Technology Innovation Plan, grant number SYG202013; PAPD, USTS Cooperative Innovation Center, and Suzhou Key Laboratory for Low Dimensional Optoelectronic Materials and Devices, grant number SZS201611. We also thank anonymous reviewers for their helpful comments on an earlier draft of this paper.

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  1. Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application, School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009, People’s Republic of China

    Xingzhi Wu, Liwei Zhang, Haobo Chen, Wenqing Sun & Quanying Wu

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  1. Xingzhi Wu
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Wu, X., Zhang, L., Chen, H. et al. Ciphertext-only attacks on the double random phase encryption based on redundancy vulnerability. Opt Rev 28, 589–595 (2021). https://doi.org/10.1007/s10043-021-00703-2

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