SpringerLink
Log in

Nonlinear image encryption based on phase truncation and phase retrieval operation

  • Research Article
  • Published:
Journal of Optics Aims and scope Submit manuscript

Abstract

In this paper, a nonlinear optical image encryption scheme using a phase retrieval algorithm (PRA) and phase-truncated Fourier transform (PTFT) is proposed. In the scheme, the standard grayscale image is initially encoded into the phase function by using the PRA, which is scrambled by using the pixel scrambling transform and then decomposed digitally into the sign and the amplitude distributions at the Fourier plane. This step increases nonlinearity and complexity of the optical encryption process. The amplitude distribution is processed to produce the ciphertext using the PTFT operation, and the sign distribution is encoded as a binary key. In the system, the encryption keys as the random phase mask (RPM) keys are employed. For decrypting the information, the decryption keys in terms of the binary key and the phase-only mask key are used. Since the encryption keys and the decryption keys are entirely different, the proposed system satisfies the criteria of traditional cryptography. In this work, several operations such as pixel scrambling transform and its inverse are digitally performed, therefore, the proposed system can be suitably implemented using the hybrid optical-digital approach. Numerical-based simulations have been performed to validate the performance and security of the proposed scheme. Simulation results show that the proposed system extends higher security and is robust to different types of attacks.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

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
Fig. 11

Similar content being viewed by others

References

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

    Article  ADS  Google Scholar 

  2. A. Alfalou, C. Brosseau, Recent advances in optical image processing. Prog. Opt. 60, 119–262 (2015)

    Article  Google Scholar 

  3. A. Hazer, R. Yıldırım, A review of single and multiple optical image encryption techniques. J. Opt. 23, 113501 (2021)

    Article  ADS  Google Scholar 

  4. N.K. Nishchal, Optical Cryptosystems (U.K. IOP Publs, Bristol, 2019)

    Book  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. W. Chen, X. Chen, C.J.R. Sheppard, Optical image encryption based on diffractive imaging. Opt. Lett. 35, 3817–3819 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. N. Singh, A. Sinha, Optical image encryption using fractional Fourier transform and chaos. Opt. Lasers Eng. 46, 117–123 (2008)

    Article  Google Scholar 

  10. W. Chen, X. Chen, Double random phase encoding using phase reservation and compression. J. Opt. 16, 025402 (2014)

    Article  ADS  Google Scholar 

  11. X. Peng, P. Zhang, H. Wei, B. Yu, Known-plaintext attack on optical encryption based on double random phase keys. Opt. Lett. 31, 1044–1046 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Y. Frauel, A. Castro, T.J. Naughton, B. Javidi, Resistance of the double random phase encryption against various attacks. Opt. Express 15, 10253–10265 (2007)

    Article  ADS  Google Scholar 

  14. P. Tian, R. Su, A novel virtual optical image encryption scheme created by combining chaotic S-Box with double random phase encoding. Sensors 22, 5325 (2022)

    Article  ADS  Google Scholar 

  15. B. Javidi, N. Takanori, Securing information by use of digital holography. Opt. Lett. 25, 28–30 (2000)

    Article  ADS  Google Scholar 

  16. T. Nomura, B. Javidi, Optical encryption using a joint transform correlator architecture. Opt. Eng. 39, 2031–2035 (2000)

    Article  ADS  Google Scholar 

  17. Y. **ong, J. Gu, R. Kumar, Security analysis on an interference-based optical image encryption scheme. Appl. Opt. 61, 9045–9051 (2022)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. X. Wang, D. Zhao, A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt. Commun. 285, 1078–1081 (2012)

    Article  ADS  Google Scholar 

  20. A. Fatima, N.K. Nishchal, Discussion on comparative analysis and a new attack on optical asymmetric cryptosystem. J. Opt. Soc. Am. A 33, 2034–2040 (2016)

    Article  ADS  Google Scholar 

  21. Y. **ong, A. He, C. Quan, Specific attack and security enhancement to optical image cryptosystem based on two random masks and interference. Opt. Laser Eng. 107, 142–148 (2018)

    Article  ADS  Google Scholar 

  22. Y. **ong, J. Du, C. Quan, Cryptoanalysis on the image encryption scheme based on interference and an amplitude mask. Opt. Commun. 517, 28272 (2022)

    Article  ADS  Google Scholar 

  23. G. Verma, M. Liao, D. Lu, W. He, X. Peng, A. Sinha, An optical asymmetric encryption scheme with biometric keys. Opt. Lasers Eng. 116, 32–40 (2019)

    Article  Google Scholar 

  24. G. Verma, A. Sinha, Securing information using optically generated biometric keys. J. Opt. 18, 115701 (2016)

    Article  ADS  Google Scholar 

  25. W. Chen, Spatial nonlinear optics for securing information. Light Sci. Appl. 11, 11 (2022)

    Article  ADS  Google Scholar 

  26. Z. Liu, S. Li, W. Liu, Y. Wang, S. Liu, Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding. Opt. Lasers Eng. 51, 8–15 (2013)

    Article  Google Scholar 

  27. J. Hou, G. Situ, Image encryption using spatial nonlinear optics. eLight 2, 3 (2022)

    Article  Google Scholar 

  28. W. Liu, Z. Liu, S. Liu, Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm. Opt. Lett. 38, 1651–1653 (2013)

    Article  ADS  Google Scholar 

  29. S.P. Barfungpa, M.R. Abuturab, Asymmetric cryptosystem using coherent superposition and equal modulus decomposition of fractional Fourier spectrum. Opt. Quant. Electron. 48, 520 (2016)

    Article  Google Scholar 

  30. A. Alarifi, M. Amoon, M.H. Aly, W. El-Shafai, Optical PTFT asymmetric cryptosystem-based secure and efficient cancellable biometric recognition system. IEEE Access 8, 221246–221268 (2020)

    Article  Google Scholar 

  31. X. Chang, W. Li, A. Yan, P.W.M. Tsang, T.C. Poon, Asymmetric cryptosystem based on optical scanning cryptography and elliptic curve algorithm. Sci. Rep. 12, 7722 (2022)

    Article  ADS  Google Scholar 

  32. G. Verma, A. Sinha, Optical nonlinear image encryption using biometric phase mask generated by digital holography. Comput. Opt. Sens. Imaging CTu2B.6(2018).

  33. M.R. Abuturab, Asymmetric multiple information cryptosystem based on chaotic spiral phase mask and random spectrum decomposition. Opt. Laser Technol. 98, 298–308 (2018)

    Article  ADS  Google Scholar 

  34. I. Mehra, N.K. Nishchal, Fingerprint image encryption using phase retrieval algorithm in gyrator wavelet transform domain using QR decomposition. Opt. Commun. 533, 129265 (2023)

    Article  Google Scholar 

  35. Z. Liu, Q. Guo, L. Xu, M.A. Ahmad, S. Liu, Double image encryption by using iterative random binary encoding in gyrator domains. Opt. Express 18, 12033–12043 (2010)

    Article  ADS  Google Scholar 

  36. S. Liansheng, C. Yin, W. Zhanmin, T. Ailing, A.K. Asundi, Single-pixel correlated imaging with high-quality reconstruction using iterative phase retrieval algorithm. Opt. Laser Eng. 111, 108–113 (2018)

    Article  Google Scholar 

  37. G. Verma, W. He, D. Lu, M. Lao, X. Peng, J. Healy, J. Sheridan, Securing multiple information using bio-chaotic keys. IEEE Photon J. 13, 1–17 (2021)

    Article  Google Scholar 

  38. G. Verma, M. Liao, D. Lu, W. He, X. Peng, A novel optical two-factor face authentication scheme. Opt. Lasers Eng. 123, 28–36 (2019)

    Article  Google Scholar 

  39. M.R. Abuturab, Securing multiple information using wavelet transform and Yang-Gu mixture amplitude-phase retrieval algorithm. Opt. Lasers Eng. 118, 42–51 (2019)

    Article  Google Scholar 

  40. N. Saini, A. Sinha, Biometrics based key management of double random phase encoding scheme using error control codes. Opt. Lasers Eng. 5, 1014–1022 (2013)

    Article  Google Scholar 

  41. T. Zhao, Q. Ran, L. Yuan, Y. Chi, J. Ma, Image encryption using fingerprint as key based on phase retrieval algorithm and public key cryptography. Opt. Lasers Eng. 72, 12–17 (2015)

    Article  Google Scholar 

  42. Q. Chen, X. Shen, Y. Cheng, C. Lin, Y. Liu, B. Zhou, A security-enhanced joint transform correlator optical encryption system with crop** operation. Optik 245, 167654 (2021)

    Article  ADS  Google Scholar 

  43. I.M. Qasim, E.A. Mohammed, Optical image encryption based on linear canonical transform with sparse representation. Opt. Commun. 533, 129262 (2023)

    Article  Google Scholar 

  44. H.E. Hwang, H.T. Chang, W.N. Lie, Multiple-image encryption and multiplexing using a modifified gerchberg saxton algorithm and phase modulation in Fresnel-transform domain. Opt. Lett. 34, 3917–3919 (2009)

    Article  ADS  Google Scholar 

  45. Z. Liu, S. Liu, Double image encryption based on iterative fractional Fourier transform. Opt. Commun. 275, 324–329 (2007)

    Article  ADS  Google Scholar 

  46. G. Verma, W. He, X. Peng, A novel four image encryption approach in sparse domain based on biometric keys. Multimed. Tools Appl. 82, 22889–22904 (2023)

    Article  Google Scholar 

  47. X. Wang, D. Zhao, Y. Chen, Double-image encryption without information disclosure using phase-truncation Fourier transforms and a random amplitude mask. Appl. Opt. 53, 5100–5108 (2014)

    Article  ADS  Google Scholar 

  48. G. Verma, A. Sinha, Optical image encryption system using nonlinear approach based on biometric authentication. J. Mod. Opt. 64, 1321–1329 (2017)

    Article  ADS  Google Scholar 

  49. P. Kumar, N.K. Nishchal, Enhanced exclusive-OR and quick response code-based image encryption through incoherent illumination. Appl. Opt. 58, 1408–1412 (2019)

    Article  ADS  Google Scholar 

  50. A. Shikder, N.K. Nishchal, Image encryption using binary polarization states of light beam. Sci. Rep. 13, 14028 (2023)

    Article  ADS  Google Scholar 

  51. L.Y. Chen, Y.N. Zhao, L.S. Chen, C. Wang, C. Ren, D. Cao, Color ghost imaging based on optimized random speckles and truncated singular value decomposition. Opt. Laser Tech. 169, 110007 (2024)

    Article  Google Scholar 

Download references

Funding

The authors did not receive support from any organization for the submitted work.

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, B K Birla Institute of Engineering and Technology, Pilani, Rajasthan, India

    Gaurav Verma

Authors
  1. Gaurav Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gaurav Verma.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in 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

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Verma, G. Nonlinear image encryption based on phase truncation and phase retrieval operation. J Opt (2023). https://doi.org/10.1007/s12596-023-01499-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12596-023-01499-x

Keywords

Search

Navigation