3D Research

, 10:8 | Cite as

Optical Asymmetric Cryptosystem Based on Kronecker Product, Hybrid Phase Mask and Optical Vortex Phase Masks in the Phase Truncated Hybrid Transform Domain

  • Priyanka MaanEmail author
  • Hukum Singh
  • A. Charan Kumari
3DR Express


This research work proposes a novel asymmetric scheme by utilizing the hybrid phase truncated fractional Fourier and Gyrator transform with the secure enhancement by adding Kronecker product as a key. In this cryptosystem, the encryption keys constitute Hybrid Phase Mask along with the Optical Vortex Phase Mask and Kronecker product as the other keys. The Hybrid Phase Mask is formed by the combination of a secondary image and random phase mask. The phase truncated parts during encryption process are reserved as decryption keys with the inverse Kronecker product. The proposed method comprises of more obscure keys for upgraded security and to defend different attacks. In support of the technique proposed, the results under the effect of various attacks are presented. The efficiency and robustness of the presented cryptosystem has been examined and demonstrated by simulation in MATLAB (R2014a) with different performance parameters.


Hybrid phase truncated fractional Fourier and Gyrator transform Kronecker product Hybrid phase mask Optical vortex phase mask 



  1. 1.
    Alfalou, A., & Brosseau, C. (2009). Optical image compression and encryption methods. Advances in Optics and Photonics, 1(3), 589–636.Google Scholar
  2. 2.
    Matoba, O., Nomura, T., Perez-Cabre, E., Millan, M. S., & Javidi, B. (2009). Optical techniques for information security. Proceedings of the IEEE, 97(6), 1128–1148.Google Scholar
  3. 3.
    Chen, W., Javidi, B., & Chen, X. (2014). Advances in optical security systems. Advances in Optics and Photonics, 6(2), 120–155.Google Scholar
  4. 4.
    Javidi, B., Carnicer, A., Yamaguchi, M., Nomura, T., Pérez-Cabré, E., Millán, M. S., et al. (2016). Roadmap on optical security. Journal of Optics, 18(8), 083001.Google Scholar
  5. 5.
    Kumar, P., Joseph, J., & Singh, K. (2016). Double random phase encoding based optical encryption systems using some linear canonical transforms: Weaknesses and countermeasures. In J. J. Healy, M. Alper Kutay, H. M. Ozaktas & J. T. Sheridan (Eds.), Linear canonical transforms (pp. 367–396). New York: Springer.zbMATHGoogle Scholar
  6. 6.
    Maan, P., & Singh, H. (2017) A survey on the applicability of Fourier transform and fractional Fourier transform on various problems of image encryption. In Communication and Computing Systems: Proceedings of the International Conference on Communication and Computing Systems (ICCCS 2016), Gurgaon, India, September 9–11, 2016 (p. 475). CRC Press.Google Scholar
  7. 7.
    Refregier, P., & Javidi, B. (1995). Optical image encryption based on input plane and Fourier plane random encoding. Optics Letters, 20(7), 767–769.Google Scholar
  8. 8.
    Garcia, J., Mas, D., & Dorsch, R. G. (1996). Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm. Applied Optics, 35(35), 7013–7018.Google Scholar
  9. 9.
    Unnikrishnan, G., & Singh, K. (2000). Double random fractional Fourier domain encoding for optical security. Optical Engineering, 39(11), 2853–2860.Google Scholar
  10. 10.
    Unnikrishnan, G., Joseph, J., & Singh, K. (2000). Optical encryption by double-random phase encoding in the fractional Fourier domain. Optics Letters, 25(12), 887–889.Google Scholar
  11. 11.
    Tao, R., Xin, Y., & Wang, Y. (2007). Double image encryption based on random phase encoding in the fractional Fourier domain. Optics Express, 15(24), 16067–16079.Google Scholar
  12. 12.
    Nishchal, N. K., Joseph, J., & Singh, K. (2003). Fully phase encryption using fractional Fourier transform. Optical Engineering, 42(6), 1583–1589.Google Scholar
  13. 13.
    Liu, X., Mei, W., & Du, H. (2014). Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain. Journal of Modern Optics, 61(19), 1570–1577.Google Scholar
  14. 14.
    Singh, H. (2016). Optical cryptosystem of color images using random phase masks in the fractional wavelet transform domain. In AIP conference proceedings (Vol. 1728, 020063-1/4).Google Scholar
  15. 15.
    Dahiya, M., Sukhija, S., & Singh, H. (2014). Image encryption using quad phase masks in fractional Fourier domain and case study. In 2014 IEEE international advance computing conference (IACC) (pp. 1048–1053). IEEE.Google Scholar
  16. 16.
    Situ, G., & Zhang, J. (2004). Double random-phase encoding in the Fresnel domain. Optics Letters, 29(14), 1584–1586.Google Scholar
  17. 17.
    Matoba, O., & Javidi, B. (1999). Encrypted optical memory system using three-dimensional keys in the Fresnel domain. Optics Letters, 24(11), 762–764.Google Scholar
  18. 18.
    Singh, H., Yadav, A. K., Vashisth, S., & Singh, K. (2015). Optical image encryption using devil’s vortex toroidal lens in the Fresnel transform domain. International Journal of Optics, 926135, 1–13.Google Scholar
  19. 19.
    Rajput, S. K., & Nishchal, N. K. (2014). Fresnel domain nonlinear optical image encryption scheme based on Gerchberg-Saxton phase-retrieval algorithm. Applied Optics, 53(3), 418–425.Google Scholar
  20. 20.
    Singh, H. (2016). Cryptosystem for securing image encryption using structured phase masks in Fresnel wavelet transform domain. 3D Research, 7(4), 1–18.Google Scholar
  21. 21.
    Chen, L., & Zhao, D. (2006). Optical image encryption with Hartley transforms. Optics Letters, 31(23), 3438–3440.Google Scholar
  22. 22.
    Singh, N., & Sinha, A. (2010). Optical image encryption using improper Hartley transforms and chaos. Optik-International Journal for Light and Electron Optics, 121(10), 918–925.Google Scholar
  23. 23.
    Singh, N., & Sinha, A. (2009). Optical image encryption using Hartley transform and logistic map. Optics Communications, 282(6), 1104–1109.Google Scholar
  24. 24.
    Vilardy, J. M., Torres, C. O., & Jimenez, C. J. (2013). Double image encryption method using the Arnold transform in the fractional Hartley domain. Proceedings of SPIE, 8785, 87851R1–87851R5.Google Scholar
  25. 25.
    Liu, Z., Chen, H., Liu, T., Li, P., Xu, L., Dai, J., et al. (2011). Image encryption by using gyrator transform and Arnold transform. Journal of Electronic Imaging, 20(1), 013020.Google Scholar
  26. 26.
    Abuturab, M. R. (2013). Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain. Optics & Laser Technology, 45, 525–532.Google Scholar
  27. 27.
    Singh, P., Yadav, A. K., & Singh, K. (2017). Color image encryption using affine transform in fractional Hartley domain. Optica Applicata, 47(3), 421–433.Google Scholar
  28. 28.
    Zhao, D., Li, X., & Chen, L. (2008). Optical image encryption with redefined fractional Hartley transform. Optics Communications, 281(21), 5326–5329.Google Scholar
  29. 29.
    Singh, P., Yadav, A. K., & Singh, K., (2017). Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition. Optics and Lasers in Engineering91, 187–195.Google Scholar
  30. 30.
    Jimenez, C., Torres, C., & Mattos, L. (2011). Fractional Hartley transform applied to optical image encryption. Journal of Physics: Conference Series, 274(1), 012041.Google Scholar
  31. 31.
    Singh, H. (2017). Nonlinear optical double image encryption using random-optical vortex in fractional Hartley transform domain. Optica Applicata, 47(4), 557–578.Google Scholar
  32. 32.
    Yadav, P. L., & Singh, H. (2018). Optical double image hiding in the fractional Hartley transform using structured phase filter and Arnold transform. 3D Research, 9(2), 20.Google Scholar
  33. 33.
    Rodrigo, J. A., Alieva, T., & Calvo, M. L. (2007). Gyrator transform: Properties and applications. Optics Express, 15(5), 2190–2203.Google Scholar
  34. 34.
    Singh, H., Yadav, A. K., Vashisth, S., & Singh, K. (2014). Fully phase image encryption using double random-structured phase masks in gyrator domain. Applied Optics, 53(28), 6472–6481.Google Scholar
  35. 35.
    Abuturab, M. R. (2012). Color image security system using double random-structured phase encoding in gyrator transform domain. Applied Optics, 51(15), 3006–3016.Google Scholar
  36. 36.
    Liu, Z., Xu, L., Lin, C., Dai, J., & Liu, S. (2011). Image encryption scheme by using iterative random phase encoding in gyrator transform domains. Optics and Lasers in Engineering, 49(4), 542–546.Google Scholar
  37. 37.
    Singh, H., Yadav, A. K., Vashisth, S., & Singh, K. (2015). Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane. Optics and Lasers in Engineering, 67, 145–156.Google Scholar
  38. 38.
    Zhou, N., Wang, Y., & Gong, L. (2011). Novel optical image encryption scheme based on fractional Mellin transform. Optics Communications, 284(13), 3234–3242.Google Scholar
  39. 39.
    Vashisth, S., Singh, H., Yadav, A. K., & Singh, K. (2014). Devil’s vortex phase structure as frequency plane mask for image encryption using the fractional Mellin transform. International Journal of Optics, 728056, 1–9.Google Scholar
  40. 40.
    Zhou, N., Li, H., Wang, D., Pan, S., & Zhou, Z. (2015). Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Optics Communications, 343, 10–21.Google Scholar
  41. 41.
    Maan, P., Singh, H., & Kumari, A. C. (2017). Image encryption based on Walsh Hadamard and fractional fourier transform using Radial Hilbert Mask. In International Conference in Computing and Communication Technologies for Smart Nation (IC3TSN) (pp. 179–183). IEEE.Google Scholar
  42. 42.
    Singh, H. (2016). Optical cryptosystem of color images based on fractional-, Wavelet transform domains using random phase masks. Indian Journal of Science and Technology, 9S(1), 1–15.Google Scholar
  43. 43.
    Peng, X., Zhang, P., Wei, H., & Yu, B. (2006). Known-plaintext attack on optical encryption based on double random phase keys. Optics Letters, 31(8), 1044–1046.Google Scholar
  44. 44.
    Rajput, S. K., & Nishchal, N. K. (2013). Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem. Optics Communications, 309, 231–235.Google Scholar
  45. 45.
    Carnicer, A., Montes-Usategui, M., Arcos, S., & Juvells, I. (2005). Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. Optics Letters, 30(13), 1644–1646.Google Scholar
  46. 46.
    Frauel, Y., Castro, A., Naughton, T. J., & Javidi, B. (2007). Resistance of the double random phase encryption against various attacks. Optics Express, 15(16), 10253–10265.Google Scholar
  47. 47.
    Qin, W., & Peng, X. (2010). Asymmetric cryptosystem based on phase-truncated Fourier transforms. Optics Letters, 35(2), 118–120.Google Scholar
  48. 48.
    Wang, X., & Zhao, D. (2011). Security enhancement of a phase-truncation based image encryption algorithm. Applied Optics, 50(36), 6645–6651.Google Scholar
  49. 49.
    Wang, Q., Guo, Q., & Zhou, J. (2013). Color image hiding based on phase-truncation and phase retrieval technique in the fractional Fourier domain. Optik-International Journal for Light and Electron Optics, 124(12), 1224–1229.Google Scholar
  50. 50.
    Cai, J., Shen, X., Lei, M., Lin, C., & Dou, S. (2015). Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition. Optics Letters, 40(4), 475–478.Google Scholar
  51. 51.
    Barrera, J. F., Henao, R., & Torroba, R. (2005). Optical encryption method using toroidal zone plates. Optics Communications, 248(1–3), 35–40.Google Scholar
  52. 52.
    Abuturab, M. R. (2012). Securing color image using discrete cosine transform in gyrator transform domain structured-phase encoding. Optics and Lasers in Engineering, 50(10), 1383–1390.Google Scholar
  53. 53.
    Liu, Z., Li, S., Liu, W., Liu, W., & Liu, S. (2013). Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains. Optics and Laser Technology, 45, 198–203.Google Scholar
  54. 54.
    Tebaldi, M., Furlan, W. D., Torroba, R., & Bolognini, N. (2009). Optical-data storage-readout technique based on fractal encrypting masks. Optics Letters, 34(3), 316–318.Google Scholar
  55. 55.
    Vashisth, S., Singh, H., Yadav, A. K., & Singh, K. (2014). Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval. Optik-International Journal for Light and Electron Optics, 125(18), 5309–5315.Google Scholar
  56. 56.
    Zamrani, W., Ahouzi, E., Lizana, A., Campos, J., & Yzuel, M. J. (2016). Optical image encryption technique based on deterministic phase masks. Optical Engineering, 55(10), 103108.Google Scholar
  57. 57.
    Girija, R., & Singh, H. (2018). A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition. Optical and Quantum Electronics, 50(5), 210.Google Scholar
  58. 58.
    Khurana, M., & Singh, H. (2018). Asymmetric optical image triple masking encryption based on Gyrator and Fresnel transforms to remove silhouette problem. 3D Research, 9(3), 38.Google Scholar
  59. 59.
    Liansheng, S., Bei, Z., Xiaojuan, N., & Ailing, T. (2016). Optical multiple-image encryption based on the chaotic structured phase masks under the illumination of a vortex beam in the gyrator domain. Optics Express, 24(1), 499–515.Google Scholar
  60. 60.
    Kumar, R., & Bhaduri, B. (2017). Optical image encryption using Kronecker product and hybrid phase masks. Optics & Laser Technology, 95, 51–55.Google Scholar
  61. 61.
    Zhang, H., & Ding, F. (2013). On the Kronecker products and their applications. Journal of Applied Mathematics, 296185, 1–8.MathSciNetzbMATHGoogle Scholar
  62. 62.
    Van Loan, C. F. (2000). The ubiquitous Kronecker product. Journal of computational and applied Mathematics, 123(1–2), 85–100.MathSciNetzbMATHGoogle Scholar
  63. 63.
    Maan, P., & Singh, H. (2018). Non-linear cryptosystem for image encryption using radial Hilbert mask in fractional Fourier transform domain. 3D Research, 9(4), 53.Google Scholar
  64. 64.
    Singh, H. (2018). Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain. Journal of Modern Optics, 65(18), 2065–2078.MathSciNetGoogle Scholar
  65. 65.
    Khurana, M., & Singh, H. (2017). An asymmetric image encryption based on phase truncated hybrid transform. 3D Research, 8(3), 28.Google Scholar

Copyright information

© 3D Display Research Center, Kwangwoon University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringThe NorthCap UniversityGurugramIndia
  2. 2.Department of Applied SciencesThe NorthCap UniversityGurugramIndia

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