Skip to main content
SpringerLink
Log in

Cryptanalysis for double-image encryption using the DTLM in frequency plane with QR decomposition and gyrator transform

  • Regular Paper
  • Published:
Optical Review Aims and scope Submit manuscript

Abstract

To enhance the security in optical image encryption scheme and to safeguard it from the invaders, this paper proposes a new scheme using devil’s toroidal lens masks (DTLMs) and QR decomposition in gyrator transform (GT) domain. The proposed cryptosystem utilizes DTLMs which are the complex phase masks designed using the combination of a phases of devil’s mask (\({\rm DM})\) and toroidal mask \(\left({\rm TM}\right)\). QR is an operation used to decompose the matrix and is utilized to supersede the phase-truncation (PT) task in the traditional phase-truncated Fourier transform (PTFT). Hence, the proposed method is immune to the attacks to which the PTFT-based cryptosystems are vulnerable. The cryptosystem is asymmetric as both the encryption and decryption processes are different along with different encryption and decryption keys. The private keys produced during the encryption method are utilized in the decryption process to retrieve the original image. The decryption process can be realized with both the digital and the modified optical architecture. Recommended scheme strengthens the safety of DRPE by growing the key capacity and the number of parameters for safety and vigorous against diverse protection.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

References

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

    ADS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  4. Millan, M.S., Perez-Cabre, E.: Optical data encryption, optical and digital image processing: fundamentals and applications. In: Cristobal, G., Schelkens, P., Thienpont, H. (eds). Wiley, 739–767

  5. Schneier, B.: Applied Cryptography, 2nd edn. Wiley, New York (1996)

    MATH  Google Scholar 

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

    Google Scholar 

  7. Voelz, D.G.: Computational Fourier Optics A MATLAB(R) Tutorial. SPIE Press, USA (2011)

    Google Scholar 

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

    Google Scholar 

  9. Yadav, A.K., Vashisth, S., Singh, H., Singh, K.: Optical cryptography and watermarking using some Fractional canonical transforms, and structured masks. In: Advances in optical and Eng.: Proc. IEM Optronix 2014, Springer 25–36 (2015)

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

    ADS  Google Scholar 

  11. Dahiya, M., Sukhija, S., Singh, H.: Image encryption using quad masks in fractional fourier domain and case study. In: IEEE International Advance Computing Conference (IACC), 1048–1053 (2014)

  12. Singh, H.: Optical cryptosystem of color images using random phase masks in the fractional wavelet transform domain. In: AIP conf. Proc. 1728: 020063–1/4 (2016).

  13. Singh, H.: Optical cryptosystem of color images based on fractional-, wavelet transform domains using random phase masks. Ind. J. Sci. Technol. 9S(1), 1–15 (2016)

    Google Scholar 

  14. Maan, P., Singh, H.: Non-linear cryptosystem for image encryption using radial Hilbert mask in fractional Fourier transform domain. 3D Res. 9, 53 (2018). https://doi.org/10.1007/s13319-018-0205-8

    Article  Google Scholar 

  15. Girija, R., Singh, H.: A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition. Opt. Quantum Electron. 50, 210 (2018)

    Google Scholar 

  16. Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 49, 1584–1586 (2004)

    ADS  Google Scholar 

  17. 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 (2015)

    Google Scholar 

  18. Singh, H.: Cryptosystem for securing image encryption using structured phase masks in Fresnel wavelet transform domain. 3D Res 7, 34 (2016). https://doi.org/10.1007/s13319-016-0110-y

    Article  Google Scholar 

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

    ADS  Google Scholar 

  20. 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’l. J. Opt. 2014, 1–9 (2014)

    Google Scholar 

  21. 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)

    ADS  Google Scholar 

  22. Singh, H.: Watermarking image encryption using deterministic phase mask and singular value decomposition in fractional Mellin transform domain. IET Image Proc. 12(11), 1994–2001 (2018)

    Google Scholar 

  23. Rodrigo, J.A., Alieva, T., Calvo, M.L.: Gyrator transform: properties and applications. Opt. Express 15, 2190–2203 (2007)

    ADS  Google Scholar 

  24. 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)

    ADS  Google Scholar 

  25. 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 (2015)

    Google Scholar 

  26. Singh, H.: Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain. J. Mod Opt. 65(18), 2065–2078 (2018)

    ADS  MathSciNet  Google Scholar 

  27. Khurana, M., Singh, H.: Asymmetric optical image triple masking encryption based on gyrator and Fresnel transforms to remove silhouette problem. 3D Res. 9, 38 (2018). https://doi.org/10.1007/s13319-018-0190-y

    Article  Google Scholar 

  28. Khurana, M., Singh, H.: A spiral-phase rear mounted triple masking for secure optical image encryption based on gyrator transform. Recent Patents Comput. Sci. 12(2), 80–84 (2019)

    Google Scholar 

  29. Singh, H.: Devil’s vortex Fresnel lens phase masks on an asymmetric cryptosystem based on phase-truncated in gyrator wavelet transform. Opt. Lasers Eng. 81, 125–139 (2016)

    Google Scholar 

  30. Mehra, I., Fatima, A., Nishchal, N.K.: Gyrator wavelet transform. IET Image Proc. 12(3), 432–437 (2017)

    Google Scholar 

  31. Carnicer, A., Montes-Usategui, M., Arcos, S., Juvells, I.: Vulnerability to chosen-cypher text attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30(13), 1644–1646 (2005)

    ADS  Google Scholar 

  32. 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)

    ADS  Google Scholar 

  33. Peng, X., Wei, H., Zhang, P.: Chosen-plaintext attack on lens-less double-random phase encoding in the Fresnel domain. Opt. Lett. 31(22), 3261–3263 (2006)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  35. 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)

    ADS  Google Scholar 

  36. Mitra, P., Gunjan, R., Gaur, M.S.: Coutourlet transform based image watermarking using QR decomposition. In: Proc. of SPIE,8760, 87601F-1/8 (2013)

  37. Su, Q., Niu, Y., Wang, G., Jia, S., Yue, J.: Color image blind watermarking scheme based on QR decomposition. Signal Process. 94, 219–235 (2014)

    Google Scholar 

  38. Abuturab, M.R.: Single-channel color information security system using LU decomposition in gyrator transform domains. Opt. Commun. 323, 100–109 (2014)

    ADS  Google Scholar 

  39. Abuturab, M.R.: Multiple color-image authentication system using HIS color space and QR decomposition in gyrator domains. J. Mod. Opt. 63(11), 1035–1050 (2016)

    ADS  Google Scholar 

  40. Xiong, Y., Quan, C.: Hybrid attack free optical cryptosystem based on two random masks and lower upper decomposition with partial pivoting. Opt. Laser Technol. 109, 456–464 (2019)

    ADS  Google Scholar 

  41. 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)

    Google Scholar 

  42. Rakheja, P., Singh, P., Vig, R.: An asymmetric image encryption mechanism using QR decomposition in hybrid multi-sesolution wavelet domain. Opt. Lasers Eng. 134, 106177 (2020)

    Google Scholar 

  43. Furlan, W.D., Gimenez, F., Calatayud, A., Monsoriu, J.A.: Devil’s vortex-lenses. Opt. Express 17, 21891–21896 (2009)

    ADS  Google Scholar 

  44. Calatayud, A., Monsoriu, J.A., Mendoza-Yero, O., Furlan, W.D.: Polyadic devil’s lenses. J. Opt. Soc. Am. A 26, 2532–2537 (2009)

    ADS  Google Scholar 

  45. Furlan, W.D., Gimenez, F., Calatayud, A., Remon L., Monsoriu J.A.: Volumetric multiple optical traps produced by Devil’s lenses. J. Europ. Opt. Soc. Rapid Publ. 5,100375–1/5(2010).

  46. Barrera, J.F., Tebaldi, M., Ammaya, D., Furlan, W.D., Monsoriu, J.A., Bolognini, N., Torroba, R.: Multiplexing of encrypted data using fractal masks. Opt. Lett. 37, 2895–2897 (2012)

    ADS  Google Scholar 

  47. Calatayud, A., Rodrigo, J.A., Tremon, L., Furlan, W.D., Cristobal, G., Monsoriu, J.A.: Experimental generation and characterization of Devil’s vortex-lenses. Appl. Phys. B 106, 915–919 (2012)

    ADS  Google Scholar 

  48. Mitry, M., Doughty, D.C., Chaloupka, J.L., Anderson, M.E.: Experimental realization of the devil’s vortex Fresnel lens with a programmable spatial light modulator. Appl. Opt. 51, 4103–4108 (2012)

    ADS  Google Scholar 

  49. Calabuig, A., Sanchez-Ruiz, S., Martinez-Leon, L., Tajahuerce, E., Fernandez-Alonso, M., Furlan, W.D., Monsoriu, J.A., Pons-Marti, A.: Generation of programmable 3D optical vortex structures through devil’s vortex-lens arrays. Appl Opt 52, 5822–5829 (2013)

    ADS  Google Scholar 

  50. Yadav, A.K., Vashisth, S., Singh, H., Singh, K.: A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask. Opt Commun 344, 172–180 (2015)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  53. Strang, G.: Linear Algebra and Its Applications, 4th edn. Thomson Learning Inc., Belmont (2006)

    MATH  Google Scholar 

  54. Girija, R., Singh, H.: Triple-level cryptosystem using deterministic masks and modified Gerchberg–Saxton iterative algorithm in fractional Hartley domain by positioning singular value decomposition. Optik 187, 238–257 (2019)

    ADS  Google Scholar 

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

    Google Scholar 

  56. Anshula, Singh, H.: , Security enrichment of an asymmetric optical image encryption-based devil’s vortex Fresnel lens phase mask and lower upper decomposition with partial pivoting in gyrator transform domain, Optical. Quant. Electron. 53(4), 1–23 (2021)

    Google Scholar 

  57. Sangwan, A., Singh, H.: A secure asymmetric optical image encryption based on phase truncation and singular value decomposition in linear canonical transform domain . Int. J. Opt. 5510125(2021), 1–19 (2021)

    Google Scholar 

Download references

Acknowledgements

All authors have made substantial contributions to the work reported in the manuscript (e.g., technical help, writing and editing assistance, general support). The authors wish to thank the management of The NorthCap University, Gurugram, for their encouragement and support of various research facilities.

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, The NorthCap University, Sector 23-A, Gurugram, 122 017, India

    Anshula

  2. Department of Applied Sciences, The NorthCap University, Sector 23-A, Gurugram, 122 017, India

    Hukum Singh

Authors
  1. Anshula
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hukum Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hukum Singh.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anshula, Singh, H. Cryptanalysis for double-image encryption using the DTLM in frequency plane with QR decomposition and gyrator transform. Opt Rev 28, 596–610 (2021). https://doi.org/10.1007/s10043-021-00705-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10043-021-00705-0

Keywords

Search

Navigation