Abstract
In this paper, a symmetric cryptosystem has been suggested to increase security of double random phase encoding using superposition technique in fractional Hartley transform (FrHT) and gyrator transform (GT) domains. It uses structured phase mask (SPM) and hybrid mask (HM) deploying equal modulus decomposition (EMD). Related to original phase truncated Fourier transform (PTFT) based cryptosystem, the security of encoding and decoding is upgraded by using the superposition technique. With the usage of SPM we can increase the key space while encoding and can also overcome the axis alignment difficulty. Decoding is just the reversal of the encoding method. The proposed scheme has robustness against common attacks like: noise and occlusion attacks. With the help of numerical simulation results we also show that our cryptosystem is vulnerable to various attacks. Performance of the suggested method is calculated in terms of Mean Square Error (MSE) between original and decoded image and also the sensitivity of the SPM parameters and rotational angles of GT is investigated. The competence of the suggested method includes analysis on EMD, histogram and correlation coefficient. The suggested cryptosystem is also open to the occlusion attack and noise attack to analyze its performance and evenness.
Similar content being viewed by others
References
Abuturab, M.R.: Color image security system using double random structured phase encoding in gyrator transform domain. Appl. Opt. 51, 3006–3016 (2012)
Barrera, J.F., Henao, R., Torroba, R.: Optical encryption method using toroidal zone plates. Opt. Commun. 248, 35–40 (2005a)
Barrera, J.F., Henao, R., Torroba, R.: Fault tolerances using toroidal zone plate encryption. Opt. Commun. 256, 489–494 (2005b)
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), 475–478 (2015)
Carrnicer, A., Montes-Usategui, M., Arcos, S., Juvells, I.: Vulnerability to chosen-ciphertext attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30, 1644–1646 (2005)
Chen, L., Zhao, D.: Optical image encryption with Hartley transforms. Opt. Lett. 31, 3438–3440 (2006)
Dahiya, M., Sukhija, S., Singh, H.: Image encryption using quad phase masks in fractional Fourier domain and case study. In: International Advance Computing Conference, pp. 1048–1053. IEEE (2014)
Davis, J.A., McNamara, D.E., Cottrell, D.M.: Image processing with the radial Hilbert transform: theory and experiments. Opt. Lett. 25, 0146–9592 (2000)
Fatima, A., Mehra, I., Nishchal, N.K.: Optical image encryption using equal modulus decomposition and multiple diffractive imaging. J. Opt. 18(8), 085701 (2016)
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)
Girija, R., Singh, H.: A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition. Opt. Quantum Electr. 50(210), 1–24 (2018a)
Girija, R., Singh, H.: Enahancing security of double random phase encoding based on random S-Box. 3D Res. 9(15), 1–20 (2018b)
Girija, R., Singh, H.: Symmetric cryptosystem based on chaos structured phase masks and equal modulus decomposition using fractional Fourier transform. 3D Res. 9(42), 1–20 (2018c)
Hartley, R.V.L.: A more symmerical Fourier analysis applied to transmission problems. Proc. IRE 30(3), 144–150 (1942)
Hennelly, B.M., Sheridan, J.T.: Random phase and Jigsaw encryption in the Fresnel domain. Opt. Eng. 43(10), 2239–2250 (2004). https://doi.org/10.1117/1.1790502
Javidi, B., et al.: Roadmap on optical security. J. Opt. 18, 1–39 (2016)
Joshi, M., Shakher, C., Singh, K.: Fractional Fourier plane image encryption technique using radial Hilbert and Jigsaw transform. Opt. Laser Eng. 48, 754–759 (2010)
Khurana, M., Singh, H.: Asymmetric optical image encryption using random Hilbert mask based on fast Walsh Hadamard transform. In: International Conference on Computing and Communications Technologies for Smart Nation (IC3TCN), pp. 374–377. IEEE (2017a)
Khurana, M., Singh, H.: Optical image encryption using Fresnel zone plate mask based on fast Walsh Hadamard transform. AIP Conf. Proc. 1953(1), 140043 (2017b)
Khurana, M., Singh, H.: An asymmetric image encryption based on phase truncated hybrid transform. 3D Res. 8(28), 17–28 (2017c)
Kumar, R., Bhaduri, B.: Optical image encryption using Kronecker product and hybrid phase masks. Opt. Laser Technol. 95, 51–55 (2017)
Kumar, P., Joseph, J., Singh, K.: Optical image encryption using a Jigsaw transform for silhoutte removal in inteference based methods and decryption with a single spatial light modulator. Appl. Opt. 50, 1805–1811 (2011)
Mann, P., Singh, H.: Non-linear cryptosystem for image encryption using radial Hilbert mask in fractional Fourier transform domain. 3D Res. 9(53), 1–13 (2018)
Mann, P., Singh, H., Kumari, A.C.: Optical asymmetric cryptosystem based on Kronecker product, hybrid phase mask and Optical vortex phase masks in phase truncated Hybrid transform domain. 3D Res. 10(8), 1–18 (2018)
Matoba, O., Nomura, T., Perez-Cabre, E., Millan, M.S., Javidi, B.: Optical techniques for information security. Proc. IEEE 97, 1128–1148 (2009)
Pei, S.C., Ding, J.J.: Properties, digital implementation, applications and self image phenomena of the gyrator transform. In: Proceedings of 17th European Signal Processing Conference (EURASIP), pp. 441–445 (2009)
Peng, X., Zhang, P., Wei, H., Yu, B.: Known plaintext attack on optical encryption based on double random phase keys. Opt. Lett. 31, 1044–1046 (2006)
Qin, W., Peng, X.: Asymmetric cryptosystem based on phase truncated Fourier transforms. Opt. Lett. 35, 118–120 (2010)
Rajput, S.K., Nischal, N.K.: Image encryption based on interference that uses fractional Fourier domain asymmetric keys. Appl. Opt. 51(10), 1446–1452 (2012)
Rajput, S.K., Nischal, N.K.: Fresnel domain nonlinear optical encryption scheme based on Gerchberg–Saxton phase retreival algorithm. Appl. Opt. 53, 418–425 (2014)
Rajput, S.K., Nishchal, N.: Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask. Appl. Opt. 51, 5377–5786 (2012)
Rajput, S.K., Nishchal, N.K.: Known plaintext attack on encryption domain independent optical Asymmetric cryptosystem. Opt. Commun. 309, 231–235 (2013)
Refregier, P., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20, 767–769 (1995)
Rodrigo, J.A., Alieva, T., Calvo, M.L.: Gyrator transform: properties and applications. Opt. Express 15, 2190–2203 (2007a)
Rodrigo, J.A., Alieva, T., Calvo, M.L.: Applications of gyrator transform for image processing. Opt. Commun. 278, 279–284 (2007b)
Singh, H.: Cryptosystem for securing image encryption using structured phase masks in Fresnel Wavelet transform domain. 3D Res. 7(34), 1–18 (2016a)
Singh, H.: Optical cryptosystems of color images using random phase masks in fractional wavelet transform domain. AIP Conf. Proc. 1728, 020063 (2016b)
Singh, H.: Devil's vortex Fresnel lens phase masks on an asymmetric cryptosystem based on phase-truncation in gyrator wavelet transform domain. Opt. Lasers Eng. 81, 125–139 (2016c)
Singh, H.: Non linear optical double image encryption using random- optical vortex in fractional Hartley domain. Opt. Appl. 47(4), 557–578 (2017)
Singh, H.: Watermarking image encryption using deterministic phase mask and singular value decomposition in fractional Mellin transform domain. IET Image Process. 12(11), 1994–2001 (2018)
Singh, N., Sinha, A.: Optical image encryption using improper Hartley transforms and chaos. Optik 121, 918–925 (2010)
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)
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. 926135, 1–13 (2015a)
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)
Singh, P., Yadav, A.K., Singh, K.: Color image encryption using affine transform in fractional Hartley domain. Opt. Appl. 47(3), 421–433 (2017)
Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 29, 1584–1586 (2004)
Sui, L., Cheng, Y., Wang, Z., Tian, A., Anand, A.K.: Single-pixel correlated imaging with high-quality reconstruction using iterative phase retrieval algorithm. Opt. Laser Eng. 111, 108–113 (2018)
Sui, L., Zhang, X., Huang, C., Tian, A., Anand, A.K.: Silhouette-free interfernce-based multiple-image encryption using cascaded fractional Fourier transforms. Opt. Laser Eng. 113, 29–37 (2019a)
Sui, L., Zhang, X., Zhao, X., Tian, A., Anand, A.K.: An optical multiple-image authentication based on transport of intensity equation. Opt. Laser Eng. 116, 116–124 (2019b)
Towghi, N., Javidi, B., Luo, Z.: Fully phase encrypted image processor. J. Opt. Soc. Am. A 16, 1915–1917 (1999)
Unnikrishnan, G., Singh, K.: Double random fractional Fourier domain encoding for optical security. Opt. Eng. 39(11), 2853–2859 (2000)
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. 728056, 1–9 (2014)
Vilardy, J.M., Torres, C.O., Jimenez, C.J.: Double image encryption method using the Arnold transform in the fractional Hartley domain. Proc. SPIE 8785, 87851R (2013)
Wu, J., Zhang, L., Zhou, N.: Image encryption based on the multiple order discrete fractional cosine transform. Opt. Commun. 283(9), 1720–1725 (2010)
Yadav, P.L., Singh, H.: Optical asymmetric cryptosystem centered on fractional Fourier domain using Hilbert phase mask. In: International Conference on Computing and Communications Technologies for Smart Nation (IC3TCN), pp. 173–178. IEEE (2017)
Yadav, P.L., Singh, H.: Optical double image hiding in fractional Hartley transform using structured phase filter and Arnold transform. 3D Res. 9(20), 1–20 (2018)
Zhang, Y., Wang, B.: Optical image encryption based on interference. Opt. Lett. 33, 2443–2445 (2008)
Zhao, D., Li, X., Chen, L.: Optical image encryption with redefined fractional Hartley transform. Opt. Commun. 281, 5326–5329 (2008)
Zhou, N., Dong, T., Wu, J.: Novel image encryption algorithm based on multiple - parameter discrete fractional random transform. Opt. Commun. 283(15), 3037–3042 (2010)
Zhou, N.R., Wang, Y., Gong, L.: Novel Optical image encryption scheme based on fractional Mellin transform. Opt. Commun. 284, 3234–3242 (2011)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yadav, P.L., Singh, H. Security enrichment of optical image cryptosystem based on superposition technique using fractional Hartley and gyrator transform domains deploying equal modulus decomposition. Opt Quant Electron 51, 140 (2019). https://doi.org/10.1007/s11082-019-1854-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-019-1854-4