Abstract

A novel information authentication system, i.e., an asymmetric optical interference of two beams in the gyrator transform (GT) domain, is proposed. In this algorithm, the input color image is divided into R, G, and B channels. The complex field of each channel is constructed by the inverse Fourier transform of the channel attached with a random phase function. The phase-only mask (POM) and amplitude-only mask (AOM) are analytically derived from the complex field. The POM and AOM are separately gyrator transformed. The two asymmetric phase keys and two encrypted images are obtained by the amplitude truncations and phase truncations of the transform images, respectively. Finally, the encoded image is produced by the interference of two encrypted images. The two asymmetric keys and two angle parameters of the GT are regarded as additional keys for each channel to enhance the security level of the cryptosystem. The noniterative authentication procedure is devoid of any silhouette problem. The proposed system can be implemented digitally or optically, and its architecture is free from optical misalignment problems. The theoretical analysis and numerical simulation results both validate the proposed technique.

© 2013 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. 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]
  3. B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
    [CrossRef]
  4. G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
    [CrossRef]
  5. 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]
  6. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35, 1914–1916 (2010).
    [CrossRef]
  7. H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
    [CrossRef]
  8. S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Technol. Lett. 21, 318–323 (1999).
    [CrossRef]
  9. 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]
  10. M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727 (2009).
    [CrossRef]
  11. Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48, 800–805 (2010).
    [CrossRef]
  12. C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
    [CrossRef]
  13. F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19, 13779–13786 (2011).
    [CrossRef]
  14. Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
    [CrossRef]
  15. M. R. Abuturab, “Color image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (2012).
    [CrossRef]
  16. M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Opt. Lasers Eng. 50, 772–779 (2012).
    [CrossRef]
  17. M. R. Abuturab, “Color information security system using discrete cosine transform in gyrator transform domain radial-Hilbert phase encoding,” Opt. Lasers Eng. 50, 1209–1216 (2012).
    [CrossRef]
  18. M. R. Abuturab, “Securing color image using discrete cosine transform in gyrator transform domain structured-phase encoding,” Opt. Lasers Eng. 50, 1383–1390 (2012).
    [CrossRef]
  19. M. R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 525–532 (2013).
    [CrossRef]
  20. M. R. Abuturab, “Noise-free recovery of color information using a joint-extended gyrator transform correlator,” Opt. Lasers Eng. 51, 230–239 (2013).
    [CrossRef]
  21. M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51, 317–324 (2013).
    [CrossRef]
  22. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
    [CrossRef]
  23. X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
    [CrossRef]
  24. W. Qin, X. Peng, X. F. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt Eng. 50, 080501 (2011).
  25. M. R. Abuturab, “Color information cryptosystem based on optical superposition principle and phase-truncated gyrator transform,” Appl. Opt. 51, 7994–8002 (2012).
    [CrossRef]
  26. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  27. D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
    [CrossRef]
  28. 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]
  29. 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]
  30. Y. J. Han and Y. H. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692 (2010).
    [CrossRef]
  31. B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical streamcipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
    [CrossRef]
  32. W. Jia, F. J. Wen, Y. T. Chow, and C. Zhou, “Binary image encryption based on interference of two phase-only masks,” Appl. Opt. 51, 5253–5258 (2012).
    [CrossRef]
  33. W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
    [CrossRef]
  34. W. He, X. Peng, X. Meng, and X. Liu, “Optical hierarchical authentication based on interference and hash function,” Appl. Opt. 51, 7750–7757 (2012).
    [CrossRef]
  35. X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
    [CrossRef]
  36. Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
    [CrossRef]
  37. M. R. Abuturab, “Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding,” Appl. Opt. 52, 1555–1563 (2013).
    [CrossRef]
  38. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: properties and applications,” Opt. Express 15, 2190–2203 (2007).
    [CrossRef]
  39. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (2007).
    [CrossRef]
  40. Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a non-uniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
    [CrossRef]
  41. Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).
    [CrossRef]
  42. Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
    [CrossRef]
  43. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24, 3500–3507 (2007).
    [CrossRef]

2013 (5)

M. R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 525–532 (2013).
[CrossRef]

M. R. Abuturab, “Noise-free recovery of color information using a joint-extended gyrator transform correlator,” Opt. Lasers Eng. 51, 230–239 (2013).
[CrossRef]

M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51, 317–324 (2013).
[CrossRef]

Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
[CrossRef]

M. R. Abuturab, “Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding,” Appl. Opt. 52, 1555–1563 (2013).
[CrossRef]

2012 (12)

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
[CrossRef]

H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
[CrossRef]

M. R. Abuturab, “Color image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (2012).
[CrossRef]

W. Jia, F. J. Wen, Y. T. Chow, and C. Zhou, “Binary image encryption based on interference of two phase-only masks,” Appl. Opt. 51, 5253–5258 (2012).
[CrossRef]

W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
[CrossRef]

W. He, X. Peng, X. Meng, and X. Liu, “Optical hierarchical authentication based on interference and hash function,” Appl. Opt. 51, 7750–7757 (2012).
[CrossRef]

M. R. Abuturab, “Color information cryptosystem based on optical superposition principle and phase-truncated gyrator transform,” Appl. Opt. 51, 7994–8002 (2012).
[CrossRef]

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

M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Opt. Lasers Eng. 50, 772–779 (2012).
[CrossRef]

M. R. Abuturab, “Color information security system using discrete cosine transform in gyrator transform domain radial-Hilbert phase encoding,” Opt. Lasers Eng. 50, 1209–1216 (2012).
[CrossRef]

M. R. Abuturab, “Securing color image using discrete cosine transform in gyrator transform domain structured-phase encoding,” Opt. Lasers Eng. 50, 1383–1390 (2012).
[CrossRef]

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
[CrossRef]

2011 (6)

W. Qin, X. Peng, X. F. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt Eng. 50, 080501 (2011).

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

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

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19, 13779–13786 (2011).
[CrossRef]

2010 (7)

2009 (4)

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]

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]

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]

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727 (2009).
[CrossRef]

2008 (1)

2007 (3)

2005 (1)

2003 (1)

2000 (1)

1999 (1)

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Technol. Lett. 21, 318–323 (1999).
[CrossRef]

1995 (1)

Abuturab, M. R.

M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51, 317–324 (2013).
[CrossRef]

M. R. Abuturab, “Noise-free recovery of color information using a joint-extended gyrator transform correlator,” Opt. Lasers Eng. 51, 230–239 (2013).
[CrossRef]

M. R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 525–532 (2013).
[CrossRef]

M. R. Abuturab, “Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding,” Appl. Opt. 52, 1555–1563 (2013).
[CrossRef]

M. R. Abuturab, “Color image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (2012).
[CrossRef]

M. R. Abuturab, “Color information cryptosystem based on optical superposition principle and phase-truncated gyrator transform,” Appl. Opt. 51, 7994–8002 (2012).
[CrossRef]

M. R. Abuturab, “Securing color image using discrete cosine transform in gyrator transform domain structured-phase encoding,” Opt. Lasers Eng. 50, 1383–1390 (2012).
[CrossRef]

M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Opt. Lasers Eng. 50, 772–779 (2012).
[CrossRef]

M. R. Abuturab, “Color information security system using discrete cosine transform in gyrator transform domain radial-Hilbert phase encoding,” Opt. Lasers Eng. 50, 1209–1216 (2012).
[CrossRef]

Ahmad, M. A.

Alfalou, A.

Alieva, T.

Arrizón, V.

Barrera, J. F.

Bolognini, N.

Brosseau, C.

Calvo, M. L.

Carrada, R.

Chang, H. T.

Chen, H.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Chen, W.

W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
[CrossRef]

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (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.

Chin, C.

Chow, Y. T.

Dai, J.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48, 800–805 (2010).
[CrossRef]

Di, H.

Fu, Y.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

Gao, B.

W. Qin, X. Peng, X. F. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt Eng. 50, 080501 (2011).

González, L. A.

Guo, Q.

Han, Y. J.

Y. J. Han and Y. H. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692 (2010).
[CrossRef]

He, W.

Hennelly, B.

Hwang, H.-E.

Javidi, B.

Jia, W.

Joseph, J.

Joshi, M.

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727 (2009).
[CrossRef]

Karim, M. A.

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Technol. Lett. 21, 318–323 (1999).
[CrossRef]

Kim, T.

Kim, Y. S.

Kumar, P.

Lam, E. Y.

Li, P.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Li, S.

Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
[CrossRef]

Lie, W.-N.

Lin, C.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Liu, J.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[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]

Liu, S.

Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
[CrossRef]

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

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

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

Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a non-uniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48, 800–805 (2010).
[CrossRef]

Liu, T.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Liu, W.

Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
[CrossRef]

Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
[CrossRef]

Liu, X.

Liu, Z.

Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
[CrossRef]

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

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48, 800–805 (2010).
[CrossRef]

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

Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a non-uniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
[CrossRef]

Meng, X.

Meng, X. F.

W. Qin, X. Peng, X. F. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt Eng. 50, 080501 (2011).

Mosso, F.

Peng, X.

Poon, T.-C.

Qin, W.

W. Qin, X. Peng, X. F. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt Eng. 50, 080501 (2011).

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[CrossRef]

Quan, C.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (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]

Refregier, P.

Rodrigo, J. A.

Ruiz, U.

Shakher, C.

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727 (2009).
[CrossRef]

Sheridan, J. T.

Singh, K.

Situ, G.

Sun, X.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48, 800–805 (2010).
[CrossRef]

Tay, C. J.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (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]

Tebaldi, M.

Torroba, R.

Unnikrishnan, G.

Wang, B.

Wang, Q.

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
[CrossRef]

Wang, X.

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

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
[CrossRef]

Wang, Y.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[CrossRef]

Wang, Y. T.

Wen, F. J.

Weng, D.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[CrossRef]

Xie, J.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[CrossRef]

Xie, J. H.

Xu, L.

Yang, B.

Zhang, H.

Zhang, J.

Zhang, S. Q.

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Technol. Lett. 21, 318–323 (1999).
[CrossRef]

Zhang, X.

Zhang, Y.

Zhang, Y. H.

Y. J. Han and Y. H. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692 (2010).
[CrossRef]

Zhao, D.

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

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
[CrossRef]

Zheng, K.

Zhou, C.

Zhu, N.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[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]

Appl. Opt. (10)

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
[CrossRef]

H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
[CrossRef]

M. R. Abuturab, “Color image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (2012).
[CrossRef]

W. Jia, F. J. Wen, Y. T. Chow, and C. Zhou, “Binary image encryption based on interference of two phase-only masks,” Appl. Opt. 51, 5253–5258 (2012).
[CrossRef]

W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
[CrossRef]

W. He, X. Peng, X. Meng, and X. Liu, “Optical hierarchical authentication based on interference and hash function,” Appl. Opt. 51, 7750–7757 (2012).
[CrossRef]

M. R. Abuturab, “Color information cryptosystem based on optical superposition principle and phase-truncated gyrator transform,” Appl. Opt. 51, 7994–8002 (2012).
[CrossRef]

M. R. Abuturab, “Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding,” Appl. Opt. 52, 1555–1563 (2013).
[CrossRef]

Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a non-uniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
[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]

J. Opt. Soc. Am. A (2)

Microwave Opt. Technol. Lett. (1)

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Technol. Lett. 21, 318–323 (1999).
[CrossRef]

Opt Commun. (1)

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]

Opt Eng. (1)

W. Qin, X. Peng, X. F. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt Eng. 50, 080501 (2011).

Opt. Commun. (5)

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[CrossRef]

Y. J. Han and Y. H. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692 (2010).
[CrossRef]

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

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

Opt. Express (5)

Opt. Laser Technol. (3)

M. R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 525–532 (2013).
[CrossRef]

Z. Liu, S. Li, W. Liu, W. Liu, and S. Liu, “Image hiding scheme by use of rotating squared sub-image in the gyrator transform domains,” Opt. Laser Technol. 45, 198–203 (2013).
[CrossRef]

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

Opt. Lasers Eng. (7)

M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Opt. Lasers Eng. 50, 772–779 (2012).
[CrossRef]

M. R. Abuturab, “Color information security system using discrete cosine transform in gyrator transform domain radial-Hilbert phase encoding,” Opt. Lasers Eng. 50, 1209–1216 (2012).
[CrossRef]

M. R. Abuturab, “Securing color image using discrete cosine transform in gyrator transform domain structured-phase encoding,” Opt. Lasers Eng. 50, 1383–1390 (2012).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727 (2009).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48, 800–805 (2010).
[CrossRef]

M. R. Abuturab, “Noise-free recovery of color information using a joint-extended gyrator transform correlator,” Opt. Lasers Eng. 51, 230–239 (2013).
[CrossRef]

M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51, 317–324 (2013).
[CrossRef]

Opt. Lett. (8)

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 (7)

Fig. 1.
Fig. 1.

(a) Optoelectronic setup for proposed encryption system. (b) Proper rotation with angles ϕ1 and ϕ2 of the generalized lenses L1 and L2. (c) Optoelectronic setup for proposed decryption system.

Fig. 2.
Fig. 2.

Simulation results of the proposed scheme: (a) Original color image with 512×512 pixels and 24 bits, (b) real part of the POM, (c) real part of the AOM; (d) real part of the first asymmetric phase key; (e) real part of the second asymmetric phase key; (f) encrypted POM; (g) encrypted AOM; (h) encrypted image by interference of two masks with all correct keys.

Fig. 3.
Fig. 3.

Reconstruction results: (a) without only first asymmetric phase key, (b) without only second asymmetric phase key, (c) without only POM, (d) without only AOM, (e) the transformation angle for each channel of POM is shifted by 0.002° but all other parameters are correct, (f) the transformation angle for each channel of AOM is shifted by 0.002° but all other parameters are correct, (g) normalized difference between original image and decrypted image, (h) decrypted image with all exact keys.

Fig. 4.
Fig. 4.

Histogram analysis: (a) histogram of the original color image [as shown in Fig. 2(a)], (b) histogram of the encrypted image [as shown in Fig. 2(h)].

Fig. 5.
Fig. 5.

(a) MSE against variation in transformation angle for each channel of POM, (b) MSE against variation in transformation angle for each channel of AOM.

Fig. 6.
Fig. 6.

Robustness test: (a) encrypted image with a 25% occlusion, (b) corresponding recovered image from (a) with all the correct keys, (c) encrypted image with a 50% occlusion, (d) corresponding retrieved image from (c) with all the correct keys, (e) encrypted image with 0.3 density Gaussian noise, (f) corresponding reconstructed image from (e) with all the accurate keys, (g) encrypted image with 0.2 density speckle-noise, (h) corresponding decrypted image from (g) with all the exact keys.

Fig. 7.
Fig. 7.

(a) MSE against variation in the Gaussian noise attack on the encrypted R, G, and B channels, and their corresponding reconstructed images; (b) MSE against variation in the speckle noise attack on the encrypted R, G, and B channels, and their corresponding recovered images.

Equations (19)

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

fo(xo,yo)=Gα[fi(xi,yi)](xo,yo)=1|sinα|+fi(xi,yi)exp(i2π(xoyo+xiyi)cosα(xiyo+xoyi)sinα)dxidyi,
Ir(xi,yi)=fr(xi,yi)exp[i2πφr(xi,yi)],
Ir(xi,yi)=F[exp[iMr1(x,y)]]+F[Mr2(x,y)],
exp[iMr1(x,y)]+Mr2(x,y)=F1[Ir(xi,yi)]=Er(x,y),
Im[exp[iMr1(x,y)]]=Im[Er(x,y)],
Re[exp[iMr1(x,y)]]+Mr2(x,y)=Re[Er(x,y)],
Mr1(x,y)=arg[i{Im[Er(x,y)]}1{Im[Er(x,y)]}2],
Mr2(x,y)=Re[Er(x,y)]+1{Im[Er(x,y)]}2,
Er1(xo,yo)=Gαr1{exp[iMr1(x,y)]},
Er2(xo,yo)=Gαr2[Mr2(x,y)].
Er1(xo,yo)=PT[Er1(xo,yo)],
Er2(xo,yo)=PT[Er2(xo,yo)].
kr1(xo,yo)=AT[Er1(xo,yo)],
kr2(xo,yo)=AT[Er2(xo,yo)].
Dr1(x,y)=Gαr1[Er1(xo,yo)kr1(xo,yo)],
Dr2(x,y)=Gαr2[Er2(xo,yo)kr2(xo,yo)],
fr(xi,yi)=PT{F[Dr1(x,y)+Dr2(x,y)]}.
sin2ϕ1=cot(α/2),sin2ϕ2=(sinα)/2.
MSE=1M×Ni=1Mj=1N|Io(m,n)Id(m,n)|2,

Metrics