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A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition

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Abstract

In this paper, an asymmetric cryptosystem has been proposed to enhance the security of DRPE. The traditional DRPE scheme is thus tweaked by using fractional Fourier transform (FrFT), a class of structured phase masks called as deterministic phase masks (DMKs) and deploying singular value decomposition (SVD). In specific, we propose to organise the encryption procedure by using two DMKs and FrFT, additionally deploying SVD. On the decryption front, the input image is recovered by utilising the inverse singular value decomposition (ISVD) and an angular portion of the deterministic phase masks. The use of FrFT for encryption and decryption would enhance the robustness of DRPE scheme. Deployment of SVD on our asymmetric cryptosystem provides three components for cipher image is yet another added feature that hardens the security of DRPE scheme. DMKs are formed by the deviation from conventional rectangular function and limited range values which delivers key components with reduced size, better performance and lower complexity. The capability study of defined method, includes analysis on SVD, histogram and correlation coefficient. Our system is subject to an occlusion attack and noise attack to evaluate its performance and reliability. Computational analysis outputs and security investigation are offered in aspect to determine the security potential of proposed system. Comparative results are shown for values of mean-square-error and peak-signal-to-noise ratio of DRPE schemes.

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References

  • Abuturab, M.R.: Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain. Opt. Laser Technol. 45, 525–532 (2013)

    Article  ADS  Google Scholar 

  • Alfalou, A., Brosseau, C.: Optical image compression and encryption methods. Adv. Opt. Photonics 1, 589–636 (2009)

    Article  Google Scholar 

  • Barrera, J.F., Henao, R., Torroba, R.: Optical encryption method using toroidal zone plates. Opt. Commun. 248, 35–40 (2005a)

    Article  ADS  Google Scholar 

  • Barrera, J.F., Henao, R., Torroba, R.: Fault tolerances using toroidal zone plate encryption. Opt. Commun. 256, 489–494 (2005b)

    Article  ADS  Google Scholar 

  • Chen, W., Chen, X.: Double random phase encoding using phase reservation and compression. J. Opt. 16(2), 025402 (2014). https://doi.org/10.1088/2040-8978/16/2/025402

    Article  ADS  Google Scholar 

  • Chen, L., Zhao, D.: Optical image encryption with Hartley transforms. Opt. Lett. 31, 3438–3440 (2006)

    Article  ADS  Google Scholar 

  • Chen, L., Zhao, D., Ge, F.: Image encryption based on singular value decomposition and Arnold transform in fractional domain. Opt. Commun. 291, 98–103 (2013)

    Article  ADS  Google Scholar 

  • Chen, W., Javidi, B., Chen, X.: Advances in optical security systems. Adv. Opt. Photonics 6(2), 120–155 (2014)

    Article  Google Scholar 

  • Chen, J., Zhang, Y., Li, J., Zhang, L.B.: Security enhancement of double random phase encoding using rear-mounted phase masking. Opt. Lasers Eng. 101, 51–59 (2018)

    Article  Google Scholar 

  • Cheng, X.C., Cai, L.Z., Wang, Y.R., Meng, X.F., Zhang, H., Xu, X.F., Shen, X.X., Dong, G.Y.: Security enhancement of double-random phase encryption by amplitude modulation. Opt. Lett. 33(14), 1575–1577 (2008)

    Article  ADS  Google Scholar 

  • Deng, X., Zhao, D.: Single-channel color image encryption based on asymmetric cryptosystem. Opt. Laser Technol. 44, 136–140 (2012)

    Article  ADS  Google Scholar 

  • Ding, X., Deng, X., Song, K., Chen, G.: Security improvement for asymmetric cryptosystem based on spherical wave illumination. Appl. Opt. 52, 467–473 (2013)

    Article  ADS  Google Scholar 

  • Fan, D., Meng, X., Wang, Y., Yang, X., Peng, X., He, W., Dongc, G., Chen, H.: Optical information encoding and image watermarking scheme based on phase-shifting interferometry and singular value decomposition. J. Mod. Opt. 60(9), 749–756 (2013)

    Article  ADS  Google Scholar 

  • Garcia, J., Mas, D., Dorsch, R.G.: Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm. Appl. Opt. 35, 7013–7018 (1996)

    Article  ADS  Google Scholar 

  • Goodman, J.W.: Introduction to Fourier Optics, 2nd edn. McGraw-Hill, New York (1996)

    Google Scholar 

  • Hennelly, B.M., Sheridan, J.T.: Image encryption and the fractional Fourier transform. Optik 114, 251–265 (2003)

    Article  ADS  Google Scholar 

  • Javidi, B. (ed.): Optical and Digital Techniques for Information Security. Springer, Berlin (2005)

    Google Scholar 

  • Javidi, B., et al.: Roadmap on optical security. J. Opt. 18(8), 083001-1–083001-39 (2016)

    Article  Google Scholar 

  • Khurana, M., Singh, H.: An asymmetric image encryption based on phase truncated hybrid transform. 3D Res. 8, 28-1–28-17 (2017)

    Article  Google Scholar 

  • Kumar, P., Joseph, J., Singh, K.: Double random phase encoding based optical encryption systems using some linear canonical transforms: weaknesses and countermeasures. In: Healy, J.J., Alper Kutay, M., Ozaktas, H.M., Sheridan J.T. (eds.) Linear Canonical Transforms, pp. 367–396. Springer, New York (2016)

    Chapter  Google Scholar 

  • Lee, I.H., Cho, M.: Double random phase encryption based orthogonal encoding technique for color images. J. Opt. Soc. Korea 18(2), 129–133 (2014)

    Article  Google Scholar 

  • Lee, I.H., Cho, M.: Security enhancement for double-random phase encryption using orthogonally encoded image and electronically synthesized key data. Chin. Opt. Lett. 13(1), 010603-1–010603-5 (2015)

    ADS  Google Scholar 

  • Lin, C., Shen, X.: Design of reconfigurable and structured spiral phase mask for optical security system. Opt. Commun. 370, 127–134 (2016)

    Article  ADS  Google Scholar 

  • Lin, C., Shen, X., Lei, M.: Generation of plaintext-independent private key based on conditional decomposition strategy. Opt. Lasers Eng. 86, 303–308 (2016)

    Article  Google Scholar 

  • Liu, S., Guo, C., Sheridan, J.T.: A review of optical image encryption techniques. Opt. Laser Technol. 57, 327–342 (2014)

    Article  ADS  Google Scholar 

  • Matoba, O., Nomura, T., Perez-Cabre, E., Millan, M.S., Javidi, B.: Optical techniques for information security. Proc. IEEE 97, 1128–1148 (2009)

    Article  Google Scholar 

  • Mehra, I., Rajput, S.K., Nishchal, N.K.: Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification. Opt. Eng. 52, 028202-1–028202-6 (2013)

    ADS  Google Scholar 

  • Qian, S.X., Li, Y., Kong, L.J., Li, S.M., Ren, Z.C., Tu, C., Wang, H.T.: Security enhancement of double-random phase encryption by iterative algorithm. J. Opt. 16(8), 085401-1–085401-7 (2014)

    Article  ADS  Google Scholar 

  • Qin, W., Peng, X.: Asymmetric cryptosystem based on phase-truncated Fourier transform. Opt. Lett. 35, 118–120 (2010)

    Article  ADS  Google Scholar 

  • Qin, W., Peng, X., Meng, X., Gao, B.: Universal and special keys based on phase-truncated Fourier transform. Opt. Eng. 50, 080501-1–080501-3 (2011)

    ADS  Google Scholar 

  • Rajput, S.K., Nishchal, N.K.: Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask. Appl. Opt. 51, 5377–5786 (2012)

    Article  ADS  Google Scholar 

  • Rajput, S.K., Nishchal, N.K.: Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain. Appl. Opt. 52, 4343–4352 (2013)

    Article  ADS  Google Scholar 

  • Refregier, P., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20, 767–769 (1995)

    Article  ADS  Google Scholar 

  • Rodrigo, J.A., Alieva, T., Calvo, M.L.: Applications of gyrator transform for image processing. Opt. Commun. 278, 279–284 (2007)

    Article  ADS  Google Scholar 

  • Singh, H.: Optical cryptosystem of color images using random phase masks in the fractional wavelet transform domain. In: AIP Conference Proceedings, vol. 1728, p. 020063 (2016)

  • Singh, H.: Nonlinear optical double image encryption using random-optical vortex in fractional Hartley transform domain. Opt. Appl. 47(4), 557–578 (2017)

    Google Scholar 

  • 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, 6472–6481 (2014)

    Article  ADS  Google Scholar 

  • Singh, H., Yadav, A.K., Vashisth, S., Singh, K.: Optical image encryption using devil’s vortex toroidal lens in the Fresnel transform domain. Int. J. Opt. 2015, 1–13 (2015a)

    Article  Google Scholar 

  • Singh, H., Yadav, A.K., Vashisth, S., Singh, K.: Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane. Opt. Lasers Eng. 67, 145–156 (2015b)

    Article  Google Scholar 

  • 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 (2017)

    Article  Google Scholar 

  • Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 29(14), 1584–1586 (2004)

    Article  ADS  Google Scholar 

  • Unnikrishnan, G., Singh, K.: Double random fractional Fourier-domain encoding for optical security. Opt. Eng. 39, 2853–2859 (2000)

    Article  ADS  Google Scholar 

  • Unnikrishnan, G., Joseph, J., Singh, K.: Optical encryption by double-random phase encoding in the fractional Fourier domain. Opt. Lett. 25, 887–889 (2000)

    Article  ADS  Google Scholar 

  • Vashisth, S., Singh, H., Yadav, A.K., Singh, K.: Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval. Optik 125, 5309–5315 (2014)

    Article  ADS  Google Scholar 

  • Vashisth, S., Yadav, A.K., Singh, H., Singh, K.: Watermarking in gyrator domain using an asymmetric cryptosystem. In: Proceedings of SPIE, 9654 96542E-1/8 (2015)

  • Vilardy, J.M., Millán, M.S., Pérez-Cabré, E.: Nonlinear optical security system based on a joint transform correlator in the Fresnel domain. Appl. Opt. 53, 1674–1682 (2014)

    Article  ADS  Google Scholar 

  • Xi, S., Wang, X., Song, L., Zhu, Z., Zhu, B., Huang, S., Yu, N., Wang, H.: Experimental study on optical image encryption with asymmetric double random phase and computer-generated hologram. Opt. Express 25(7), 8212–8222 (2017)

    Article  ADS  Google Scholar 

  • Zamrani, W., Ahouzi, E., Lizana, A., Campos, J., Yzuel, M.J.: Optical image encryption technique based on deterministic phase masks. Opt. Eng. 55, 103108-1–103108-9 (2016)

    Article  ADS  Google Scholar 

  • 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 

  • Zhou, N., Dong, T., Wu, J.: Novel image encryption algorithm based on multiple-parameter discrete fractional random transform. Opt. Commun. 283, 3037–3042 (2010)

    Article  ADS  Google Scholar 

  • Zhou, N., Wang, Y., Gong, L.: Novel optical image encryption scheme based on fractional Mellin transform. Opt. Commun. 284, 3234–3242 (2011)

    Article  ADS  Google Scholar 

  • Zhou, N., Li, H., Wang, D., Pan, S., Zhou, Z.: Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Opt. Commun. 343, 10–21 (2015)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The NorthCap University, Gurugram, India

    R. Girija

  2. Department of Applied Sciences, The NorthCap University, Gurugram, India

    Hukum Singh

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  1. R. Girija
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Girija, R., Singh, H. A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition. Opt Quant Electron 50, 210 (2018). https://doi.org/10.1007/s11082-018-1472-6

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