Abstract

In recent years, optical image encryption has attracted more and more attention in information security due to its unique advantages, such as parallel processing and multiple-parameter characteristics. In this paper, we propose a new method using three-dimensional (3D) processing strategy for interference-based optical image encryption. The plaintext is considered as a series of particles distributed in 3D space, and any one sectional extraction cannot render information about the plaintext during image decryption. In addition, the silhouette problem in the conventional interference-based optical encryption method is effectively suppressed, and the proposed optical cryptosystem can achieve higher security compared with the previous work. A numerical experiment is conducted to demonstrate the feasibility and effectiveness of the proposed method.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef]
  2. B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
    [CrossRef]
  3. B. Javidi, “Securing information with optical technologies,” Phys. Today 50, 27–32 (1997).
    [CrossRef]
  4. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
    [CrossRef]
  5. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
    [CrossRef]
  6. Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
    [CrossRef]
  7. X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10, 41–45 (2002).
  8. N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284, 3234–3242 (2011).
    [CrossRef]
  9. A. Carnicer, M. M. Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
    [CrossRef]
  10. X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
    [CrossRef]
  11. X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).
    [CrossRef]
  12. R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
    [CrossRef]
  13. Y. Li, K. Kreske, and J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).
    [CrossRef]
  14. H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. 41, 4825–4834 (2002).
    [CrossRef]
  15. X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
    [CrossRef]
  16. Y. L. Xiao, X. Zhou, S. Yuan, Q. Liu, and Y. C. Li, “Multiple-image optical encryption: an improved encoding approach,” Appl. Opt. 48, 2686–2692 (2009).
    [CrossRef]
  17. H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).
    [CrossRef]
  18. H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50, 710–716 (2011).
    [CrossRef]
  19. H. T. Chang, H. E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
    [CrossRef]
  20. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  21. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  22. W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
    [CrossRef]
  23. P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
    [CrossRef]
  24. Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A Pure Appl. Opt. 11, 125406 (2009).
    [CrossRef]
  25. B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical stream-cipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
    [CrossRef]
  26. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing (Wiley, 2001).
  27. Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
    [CrossRef]
  28. W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
    [CrossRef]
  29. W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19, 9008–9019 (2011).
    [CrossRef]
  30. B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
    [CrossRef]
  31. N. Zhu, Y. T. Wang, J. Liu, J. H. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009).
    [CrossRef]
  32. C. H. Niu, X. L. Wang, N. G. Lv, Z. H. Zhou, and X. Y. Li, “An encryption method with multiple encrypted keys based on interference principle,” Opt. Express 18, 7827–7834 (2010).
    [CrossRef]
  33. W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
    [CrossRef]
  34. C. F. Ying, H. Pang, C. J. Fan, and W. D. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50, 055802 (2011).
    [CrossRef]
  35. W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
    [CrossRef]
  36. W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (2010).
    [CrossRef]
  37. W. Chen, X. Chen, and C. J. R. Sheppard, “Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating,” Appl. Opt. 50, 5750–5757(2011).
    [CrossRef]
  38. W. Chen and X. Chen, “Optical image encryption using multilevel Arnold transform and noninterferometric imaging,” Opt. Eng. 50, 117001 (2011).
    [CrossRef]

2012 (1)

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[CrossRef]

2011 (10)

W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

C. F. Ying, H. Pang, C. J. Fan, and W. D. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50, 055802 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19, 9008–9019 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50, 710–716 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
[CrossRef]

B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical stream-cipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
[CrossRef]

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284, 3234–3242 (2011).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating,” Appl. Opt. 50, 5750–5757(2011).
[CrossRef]

W. Chen and X. Chen, “Optical image encryption using multilevel Arnold transform and noninterferometric imaging,” Opt. Eng. 50, 117001 (2011).
[CrossRef]

2010 (4)

2009 (6)

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

N. Zhu, Y. T. Wang, J. Liu, J. H. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009).
[CrossRef]

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Y. L. Xiao, X. Zhou, S. Yuan, Q. Liu, and Y. C. Li, “Multiple-image optical encryption: an improved encoding approach,” Appl. Opt. 48, 2686–2692 (2009).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).
[CrossRef]

2008 (1)

2007 (1)

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

2006 (2)

2005 (1)

2004 (1)

2002 (3)

2000 (2)

1997 (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50, 27–32 (1997).
[CrossRef]

1996 (2)

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
[CrossRef]

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

1995 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Arcos, S.

Cai, L.

Cai, L. Z.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Carnicer, A.

Chang, H. T.

Chatwin, C.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Chen, W.

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating,” Appl. Opt. 50, 5750–5757(2011).
[CrossRef]

W. Chen and X. Chen, “Optical image encryption using multilevel Arnold transform and noninterferometric imaging,” Opt. Eng. 50, 117001 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19, 9008–9019 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (2010).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Chen, X.

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating,” Appl. Opt. 50, 5750–5757(2011).
[CrossRef]

W. Chen and X. Chen, “Optical image encryption using multilevel Arnold transform and noninterferometric imaging,” Opt. Eng. 50, 117001 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19, 9008–9019 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (2010).
[CrossRef]

Cheng, X. C.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Dong, G. Y.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Dong, Z.

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

Fan, C. J.

C. F. Ying, H. Pang, C. J. Fan, and W. D. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50, 055802 (2011).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gong, L.

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284, 3234–3242 (2011).
[CrossRef]

Hwang, H. E.

Javidi, B.

B. Javidi, “Securing information with optical technologies,” Phys. Today 50, 27–32 (1997).
[CrossRef]

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
[CrossRef]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

Joseph, J.

Juvells, I.

Kippelen, B.

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
[CrossRef]

Kreske, K.

Kumar, P.

Kuo, C. J.

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing (Wiley, 2001).

Lee, C. L.

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50, 710–716 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
[CrossRef]

Lee, M. T.

Li, X. Y.

Li, Y.

Li, Y. C.

Lie, W. N.

Lin, C.

Liu, J.

Liu, Q.

Liu, S.

Liu, Z.

Lu, W. C.

Lv, N. G.

Meerholz, K.

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
[CrossRef]

Meng, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Niu, C. H.

Ozaktas, H. M.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing (Wiley, 2001).

Pang, H.

C. F. Ying, H. Pang, C. J. Fan, and W. D. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50, 055802 (2011).
[CrossRef]

Peng, X.

Peyghambarian, N.

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
[CrossRef]

Quan, C.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Refregier, P.

Rosen, J.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Shen, X. X.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Sheppard, C. J. R.

Singh, K.

Situ, G.

Tanno, N.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Tay, C. J.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Unnikrishnan, G.

Usategui, M. M.

Volodin, B. L.

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
[CrossRef]

Wang, B.

B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical stream-cipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
[CrossRef]

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
[CrossRef]

Wang, R. K.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Wang, X. L.

Wang, Y.

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284, 3234–3242 (2011).
[CrossRef]

Wang, Y. R.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Wang, Y. T.

Watson, I. A.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Wei, H.

Xiao, Y. L.

Xie, J. H.

Xu, L.

Xu, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Yang, B.

Yang, X. L.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Ying, C. F.

C. F. Ying, H. Pang, C. J. Fan, and W. D. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50, 055802 (2011).
[CrossRef]

Yu, B.

Yu, L.

Yuan, S.

Zalevsky, Z.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing (Wiley, 2001).

Zhang, H.

N. Zhu, Y. T. Wang, J. Liu, J. H. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Zhang, J.

Zhang, P.

Zhang, Y.

B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical stream-cipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
[CrossRef]

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
[CrossRef]

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Zheng, C. H.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Zhou, N.

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284, 3234–3242 (2011).
[CrossRef]

Zhou, W. D.

C. F. Ying, H. Pang, C. J. Fan, and W. D. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50, 055802 (2011).
[CrossRef]

Zhou, X.

Zhou, Z. H.

Zhu, N.

Appl. Opt. (7)

J. Opt. (2)

W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[CrossRef]

J. Opt. A Pure Appl. Opt. (2)

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Nature (1)

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383, 58–60 (1996).
[CrossRef]

Opt. Commun. (5)

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284, 3234–3242 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

Opt. Eng. (3)

C. F. Ying, H. Pang, C. J. Fan, and W. D. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50, 055802 (2011).
[CrossRef]

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

W. Chen and X. Chen, “Optical image encryption using multilevel Arnold transform and noninterferometric imaging,” Opt. Eng. 50, 117001 (2011).
[CrossRef]

Opt. Express (6)

Opt. Lett. (9)

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).
[CrossRef]

A. Carnicer, M. M. Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
[CrossRef]

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

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).
[CrossRef]

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

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[CrossRef]

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Phys. Today (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50, 27–32 (1997).
[CrossRef]

Other (1)

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing (Wiley, 2001).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

(a) Schematic experimental setup for conventional interference-based optical image encryption [2123]. (b) Schematic experimental setup for the proposed optical cryptosystem in 3D space: M, phase-only mask; CBS, cube beam splitter. Lens parameters, such as lens positions, are simultaneously adjusted in the two optical paths for each particle as indicated in Fig. 1(b).

Fig. 2.
Fig. 2.

Flow chart for the proposed phase retrieval algorithm during image encryption.

Fig. 3.
Fig. 3.

Conventional interference-based optical encoding: (a) an input image or a plaintext, (b) extracted phase-only mask M1, (c) extracted phase-only mask M2, and (d) a decrypted image using correct security keys and extracted phase-only masks.

Fig. 4.
Fig. 4.

Conventional interference-based optical encoding: (a) a decrypted image based on a single optical path using the extracted phase-only mask M1 and (b) a decrypted image based on a single optical path using the extracted phase-only mask M2.

Fig. 5.
Fig. 5.

Proposed 3D interference-based optical cryptosystem: (a) the fixed phase-only mask M2, and (b) the phase-only mask M1 extracted by using the phase retrieval algorithm during image encryption.

Fig. 6.
Fig. 6.

(a) Relationship between the number of iterations and IEs during image encryption and (b) the relationship with a natural logarithmic scale corresponding to (a).

Fig. 7.
Fig. 7.

(a) Decrypted image obtained by using correct security keys and the phase-only masks, and decrypted images obtained at one section of the image plane obtained by using one FrFT function order of (b) 0.1, (c) 0.5, or (d) 0.95.

Fig. 8.
Fig. 8.

Decrypted images obtained at one section just using the extracted phase-only mask M1 with one FrFT function order of (a) 0.1, (b) 0.5, or (c) 0.95; and decrypted images obtained at one section just using the phase-only mask M2 with one FrFT function order of (d) 0.1, (e) 0.5, or (f) 0.95.

Fig. 9.
Fig. 9.

Assuming that the 3D particle distribution (i.e., principal key) is correct during image decryption, (a) a decrypted image based on a single optical path just using the extracted phase-only mask M1 and (b) a decrypted image based on a single optical path just using the phase-only mask M2.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

O(ξ,η)exp[jH(ξ,η)]=FrFTa,a{exp[jM1(x,y)]}+FrFTa,a{exp[jM2(x,y)]},
FrFTa{exp[jM1(x)]}=+{exp[jM1(x)]}Pa(ξ,x)dx,
Pa(ξ,x)={Texp{jπ[ξ2cot(aπ/2)+x2cot(aπ/2)2ξxcsc(aπ/2)]}ifa2mδ(ξx)ifa=4mδ(ξ+x)ifa=4m±2,
M1(x,y)=angle(FrFTa,a{O(ξ,η)exp[jH(ξ,η)]})arccos{[abs(FrFTa,a{O(ξ,η)exp[jH(ξ,η)]})]/2},
M2(x,y)=angle(FrFTa,a{O(ξ,η)exp[jH(ξ,η)]}exp[jM1(x,y)]),
O(ξi,ηi)¯={[2Ω|O(ξi,ηi)||O(ξi,ηi)|]O(ξi,ηi)/|O(ξi,ηi)|if(ξi,ηi)WO(ξi,ηi)if(ξi,ηi)W,
IE=(ξN,ηN)W[|O(ξN,ηN)|O(ξN,ηN)]2.
O(ξ,η)¯=I(ξi,ηi),i=1,N|FrFTai,ai{exp[jM1(x,y)]}+FrFTai,ai{exp[jM2(x,y)]}|2,
CC=[cov(O,O¯)]/(σO×σO¯),

Metrics