Abstract

A hybrid encoding method is used to assemble the double-random phase-encoding technique and the binary encoding method. Because the double-random phase-encoding technique is robust for noises and the binary encoding method is free of using external keys, the proposed hybrid encoding method has their advantages. The hybrid encoding method first encodes a covert image to form a complex- number matrix by using the double-random phase-encoding technique, where two random real-number matrices are used to increase the security of the encoding work. Then the elements of the two random real-number matrices and the elements of the complex-number matrix are encoded to form a binary-bit string by using the binary encoding method. Finally, the binary data in the binary-bit string are encoded into a host image to form an overt image with hidden information by using a gray-value modulation method. The decoding work is easy for authorized people, but it is very difficult for unauthorized people. Therefore, the proposed hybrid encoding method is a very useful encoding method.

© 2010 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] [PubMed]
  2. R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
    [CrossRef]
  3. B. Javidi and E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
    [CrossRef]
  4. O. Matoba and B. Javidi, “Secure holographic memory by double-random polarization encryption,” Appl. Opt. 43, 2915–2919 (2004).
    [CrossRef] [PubMed]
  5. M. N. Isiam and M. S. Alam, “Optical encryption and multiplexing of personal identification information using orthogonal code,” Opt. Eng. 45, 098201 (2006).
    [CrossRef]
  6. B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
    [CrossRef]
  7. B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
    [CrossRef]
  8. B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
    [CrossRef]
  9. G. Unnikrishnan, J. Joheph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
    [CrossRef]
  10. B. Wang and C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
    [CrossRef]
  11. N. Takai and Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41, 865–873 (2002).
    [CrossRef] [PubMed]
  12. S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).
    [CrossRef] [PubMed]
  13. X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
    [CrossRef]
  14. X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
    [CrossRef]
  15. R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fraction Fourier domain,” Opt. Express 15, 16067–16079 (2007).
    [CrossRef] [PubMed]
  16. D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
    [CrossRef] [PubMed]
  17. G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
    [CrossRef]
  18. X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).
    [CrossRef] [PubMed]
  19. P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
    [CrossRef]
  20. D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
    [CrossRef]
  21. Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domain,” Opt. Commun. 282, 518–522 (2009).
    [CrossRef]
  22. S. Jun, X. Hong, F. Li, and S. Nong, “Security analysis and improvement on a double-random phase-encoding technique based information hiding method,” Opt. Commun. 282, 2307–2317 (2009).
    [CrossRef]
  23. P. Kumar, J. Joseph, and K. Singh, “Impulse attack-free four random phase mask encryption based on a 4f optical system,” Appl. Opt. 48, 2356–2363 (2009).
    [CrossRef] [PubMed]
  24. Y. L. Xiao, X. Zhou, Q. Liu, and S. Yuan, “An image reconstruction method based on the double-random phase encoding system in the Fresnel domain,” Opt. Laser Technol. 41, 449–453 (2009).
    [CrossRef]
  25. K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447–3453 (2008).
    [CrossRef]
  26. S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).
    [CrossRef]
  27. S. L. Yeh, S. T. Lin, and Y. C. Tu, “A diffusion pattern composed of two-dimensional diffusion dots for encrypting a digital image,” J. Opt. A: Pure Appl. Opt. 10, 115307 (2008).
    [CrossRef]
  28. M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226–239 (1999).
    [CrossRef]
  29. T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image inpaint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia (Association for Computing Machinery, 2003), pp. 102–103.
    [CrossRef]

2009

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domain,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

S. Jun, X. Hong, F. Li, and S. Nong, “Security analysis and improvement on a double-random phase-encoding technique based information hiding method,” Opt. Commun. 282, 2307–2317 (2009).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Impulse attack-free four random phase mask encryption based on a 4f optical system,” Appl. Opt. 48, 2356–2363 (2009).
[CrossRef] [PubMed]

Y. L. Xiao, X. Zhou, Q. Liu, and S. Yuan, “An image reconstruction method based on the double-random phase encoding system in the Fresnel domain,” Opt. Laser Technol. 41, 449–453 (2009).
[CrossRef]

2008

K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447–3453 (2008).
[CrossRef]

S. L. Yeh, S. T. Lin, and Y. C. Tu, “A diffusion pattern composed of two-dimensional diffusion dots for encrypting a digital image,” J. Opt. A: Pure Appl. Opt. 10, 115307 (2008).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
[CrossRef] [PubMed]

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).
[CrossRef] [PubMed]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

2007

X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
[CrossRef]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fraction Fourier domain,” Opt. Express 15, 16067–16079 (2007).
[CrossRef] [PubMed]

2006

S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).
[CrossRef]

X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
[CrossRef]

M. N. Isiam and M. S. Alam, “Optical encryption and multiplexing of personal identification information using orthogonal code,” Opt. Eng. 45, 098201 (2006).
[CrossRef]

2004

2002

2001

B. Wang and C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[CrossRef]

2000

1999

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226–239 (1999).
[CrossRef]

1998

B. Javidi and E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

1997

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

1996

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (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

Ahouzi, E.

B. Javidi and E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Alam, M. S.

M. N. Isiam and M. S. Alam, “Optical encryption and multiplexing of personal identification information using orthogonal code,” Opt. Eng. 45, 098201 (2006).
[CrossRef]

Cai, L. Z.

Chang, R. C.

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image inpaint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia (Association for Computing Machinery, 2003), pp. 102–103.
[CrossRef]

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, J. G.

X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
[CrossRef]

Cheng, X. C.

Dai, J.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domain,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Dong, G. Y.

Gopinathan, U.

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
[CrossRef] [PubMed]

Guibert, L.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Hong, X.

S. Jun, X. Hong, F. Li, and S. Nong, “Security analysis and improvement on a double-random phase-encoding technique based information hiding method,” Opt. Commun. 282, 2307–2317 (2009).
[CrossRef]

Hu, J. P.

X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
[CrossRef]

Isiam, M. N.

M. N. Isiam and M. S. Alam, “Optical encryption and multiplexing of personal identification information using orthogonal code,” Opt. Eng. 45, 098201 (2006).
[CrossRef]

Javidi, B.

O. Matoba and B. Javidi, “Secure holographic memory by double-random polarization encryption,” Appl. Opt. 43, 2915–2919 (2004).
[CrossRef] [PubMed]

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).
[CrossRef] [PubMed]

B. Javidi and E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (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] [PubMed]

Joheph, J.

Joseph, J.

P. Kumar, J. Joseph, and K. Singh, “Impulse attack-free four random phase mask encryption based on a 4f optical system,” Appl. Opt. 48, 2356–2363 (2009).
[CrossRef] [PubMed]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

Jun, S.

S. Jun, X. Hong, F. Li, and S. Nong, “Security analysis and improvement on a double-random phase-encoding technique based information hiding method,” Opt. Commun. 282, 2307–2317 (2009).
[CrossRef]

Kishk, S.

Kumar, P.

P. Kumar, J. Joseph, and K. Singh, “Impulse attack-free four random phase mask encryption based on a 4f optical system,” Appl. Opt. 48, 2356–2363 (2009).
[CrossRef] [PubMed]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

Kutter, M.

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226–239 (1999).
[CrossRef]

Lai, D.

X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
[CrossRef]

Li, D. H.

X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
[CrossRef]

Li, F.

S. Jun, X. Hong, F. Li, and S. Nong, “Security analysis and improvement on a double-random phase-encoding technique based information hiding method,” Opt. Commun. 282, 2307–2317 (2009).
[CrossRef]

Li, J.

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Lin, K. T.

K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447–3453 (2008).
[CrossRef]

Lin, S. T.

S. L. Yeh, S. T. Lin, and Y. C. Tu, “A diffusion pattern composed of two-dimensional diffusion dots for encrypting a digital image,” J. Opt. A: Pure Appl. Opt. 10, 115307 (2008).
[CrossRef]

Liu, Q.

Y. L. Xiao, X. Zhou, Q. Liu, and S. Yuan, “An image reconstruction method based on the double-random phase encoding system in the Fresnel domain,” Opt. Laser Technol. 41, 449–453 (2009).
[CrossRef]

Liu, S.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domain,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Liu, Z.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domain,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Lu, L. C.

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image inpaint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia (Association for Computing Machinery, 2003), pp. 102–103.
[CrossRef]

Matoba, O.

Meng, X. F.

Mifune, Y.

Monaghan, D. S.

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
[CrossRef] [PubMed]

Naughton, T. J.

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
[CrossRef] [PubMed]

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

Nong, S.

S. Jun, X. Hong, F. Li, and S. Nong, “Security analysis and improvement on a double-random phase-encoding technique based information hiding method,” Opt. Commun. 282, 2307–2317 (2009).
[CrossRef]

Osten, W.

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

Pedrini, G.

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

Petitcolas, F. A. P.

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226–239 (1999).
[CrossRef]

Refregier, P.

Sergent, A.

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Shen, X. X.

Sheridan, J. T.

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
[CrossRef] [PubMed]

Shih, T. K.

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image inpaint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia (Association for Computing Machinery, 2003), pp. 102–103.
[CrossRef]

Singh, K.

Situ, G.

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
[CrossRef] [PubMed]

Sun, C. C.

B. Wang and C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[CrossRef]

Sun, X.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domain,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Takai, N.

Tao, R.

Tu, Y. C.

S. L. Yeh, S. T. Lin, and Y. C. Tu, “A diffusion pattern composed of two-dimensional diffusion dots for encrypting a digital image,” J. Opt. A: Pure Appl. Opt. 10, 115307 (2008).
[CrossRef]

Unnikrishnan, G.

Wang, B.

B. Wang and C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[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, Y.

Wang, Y. R.

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]

Xiao, Y. L.

Y. L. Xiao, X. Zhou, Q. Liu, and S. Yuan, “An image reconstruction method based on the double-random phase encoding system in the Fresnel domain,” Opt. Laser Technol. 41, 449–453 (2009).
[CrossRef]

Xin, Y.

Xu, X. F.

Yeh, S. L.

S. L. Yeh, S. T. Lin, and Y. C. Tu, “A diffusion pattern composed of two-dimensional diffusion dots for encrypting a digital image,” J. Opt. A: Pure Appl. Opt. 10, 115307 (2008).
[CrossRef]

S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).
[CrossRef]

Yuan, S.

Y. L. Xiao, X. Zhou, Q. Liu, and S. Yuan, “An image reconstruction method based on the double-random phase encoding system in the Fresnel domain,” Opt. Laser Technol. 41, 449–453 (2009).
[CrossRef]

X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
[CrossRef]

Zhang, G.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Zhang, H.

Zhou, X.

Y. L. Xiao, X. Zhou, Q. Liu, and S. Yuan, “An image reconstruction method based on the double-random phase encoding system in the Fresnel domain,” Opt. Laser Technol. 41, 449–453 (2009).
[CrossRef]

X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
[CrossRef]

X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

S. L. Yeh, S. T. Lin, and Y. C. Tu, “A diffusion pattern composed of two-dimensional diffusion dots for encrypting a digital image,” J. Opt. A: Pure Appl. Opt. 10, 115307 (2008).
[CrossRef]

Opt. Commun.

K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447–3453 (2008).
[CrossRef]

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122–5125 (2008).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domain,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

S. Jun, X. Hong, F. Li, and S. Nong, “Security analysis and improvement on a double-random phase-encoding technique based information hiding method,” Opt. Commun. 282, 2307–2317 (2009).
[CrossRef]

Opt. Eng.

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

B. Wang and C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[CrossRef]

M. N. Isiam and M. S. Alam, “Optical encryption and multiplexing of personal identification information using orthogonal code,” Opt. Eng. 45, 098201 (2006).
[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

Opt. Express

Opt. Laser Technol.

X. Zhou, D. Lai, S. Yuan, D. H. Li, and J. P. Hu, “A method for hiding information utilizing double-random phase-encoding technique,” Opt. Laser Technol. 39, 1360–1363 (2007).
[CrossRef]

Y. L. Xiao, X. Zhou, Q. Liu, and S. Yuan, “An image reconstruction method based on the double-random phase encoding system in the Fresnel domain,” Opt. Laser Technol. 41, 449–453 (2009).
[CrossRef]

Opt. Lett.

Proc. SPIE

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226–239 (1999).
[CrossRef]

Other

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image inpaint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia (Association for Computing Machinery, 2003), pp. 102–103.
[CrossRef]

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 (6)

Fig. 1
Fig. 1

Example matrices: (a) host matrix H , (b) matrix T , (c) matrix H , and (d) overt image H * .

Fig. 2
Fig. 2

Covert images for tests: (a) 64 × 64 binary image and (b) 64 × 64 256-gray-level image.

Fig. 3
Fig. 3

512 × 512 host image used to form different overt images.

Fig. 4
Fig. 4

Element values of the random real-number matrices (a) a and (b) b . (Pixels with the gray value 0 denote “0,” and pixels with the gray value 255 denote “1.”)

Fig. 5
Fig. 5

Matrix T for Fig. 2a.

Fig. 6
Fig. 6

Matrix T for Fig. 2b.

Tables (1)

Tables Icon

Table 1 PSNR Values of Original Covert Images and Decoded Covert Images

Equations (22)

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

D ( x , y ) = F { F { C ( x , y ) exp [ ( 1 ) 1 / 2 2 π a ( x , y ) ] } exp [ ( 1 ) 1 / 2 2 π b ( ξ , η ] } ,
C ( x , y ) = F 1 { F 1 { D ( x , y ) exp [ ( 1 ) 1 / 2 2 π b ( ξ , η ) ] } exp [ ( 1 ) 1 / 2 2 π a ( x , y ] } ,
k = i = 1 T k i 2 i 1 + k 0 .
G a ( ( ( m 1 ) c + n ) u + i ) = a i ( m , n ) ,
G b ( ( ( m 1 ) c + n ) v + i ) = b i ( m , n ) .
E ( ( r 1 ) c + c ) = D ( r , c ) ,
G D ( i + ( n + m ) ( k 1 ) ) = A i ( k ) , ( for     1 i n ) ,
G D ( i + n + ( n + m ) ( k 1 ) ) = p i ( k ) , ( for     1 i m ) ,
H ( u , v ) = 2 floor ( H ( u , v ) / 2 ) ,
H * ( u , v ) = T ( u , v ) + H ( u , v ) .
T ( m , n ) = H * ( m , n ) 2 × floor ( H * ( m , n ) / 2 ) ,
G a ( k ) = G ( k ) (for     k = 1 u × r × c ) ,
G b ( k ) = G ( k u × r × c ) , ( for     k = u × r × c + 1 ( u + v ) × r × c ) ,
G D ( k ) = G ( k ( u + v ) × r × c ) , (for   k =( u + v ) × r × c + 1 ( u + v + m + n ) × r × c ) .
a ( m , n ) = 1 s i = 1 u G a ( ( ( m 1 ) c + n ) u + i ) 2 i 1 .
b ( m , n ) = 1 f i = 1 v G b ( ( ( m 1 ) c + n ) v + i ) 2 i 1 .
A ( k ) = 10 d n = 1 n G ( ( n + m ) ( k 1 ) + n ) 2 n n ,
θ ( k ) = 2 π p m = 1 m G ( ( n + m ) ( k 1 ) + n + m ) 2 m m ,
E ( k ) = A ( k ) exp ( ( 1 ) 1 / 2 θ ( k ) ) .
D ( r , c ) = E ( ( r 1 ) c + c ) .
PSNR = 10 × log ( M × N MSE ) ,
MSE = 1 M × N i = 1 M j = 1 N [ H ( i , j ) H * ( i , j ) ] 2 .

Metrics