Abstract

A color information cryptosystem based on optical interference principle and spiral phase encoding is proposed. A spiral phase mask (SPM) is used instead of a conventional random phase mask because it contains multiple storing keys in a single phase mask. The color image is decomposed into RGB channels. The decomposed three RGB channels can avoid the interference of crosstalks efficiently. Each channel is encoded into an SPM and analytically generates two spiral phase-only masks (SPOMs). The two SPOMs are then phase-truncated to get two encrypted images and amplitude-truncated to produce two asymmetric phase keys. The two SPOMs and the two asymmetric phase keys can be allocated to four different authorized users. The order, the wavelength, the focal length, and the radius are construction parameters of the SPM (or third SPOM) that can also be assigned to the four other different authorized users. The proposed technique can be used for a highly secure verification system, so an unauthorized user cannot retrieve the original image if only one key out of eight keys is missing. The proposed method does not require iterative encoding or postprocessing of SPOMs to overcome inherent silhouette problems, and its optical setup alleviates stringent alignment of SOPMs. The validity and feasibility of the proposed method are supported by numerical simulation results.

© 2013 Optical Society of America

Full Article  |  PDF Article

Errata

Muhammad Rafiq Abuturab, "Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding: erratum," Appl. Opt. 53, 5064-5064 (2014)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-53-22-5064

References

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  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. S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).
    [CrossRef]
  4. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
    [CrossRef]
  5. X. Meng, L. Cai, X. Yang, X. Shen, and G. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289–3297 (2006).
    [CrossRef]
  6. Z. Liu and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).
    [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. Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(2012).
    [CrossRef]
  9. J.-J. Huang, H.-E. Hwang, C.-Y. Chen, and C.-M. Chen, “Lensless multiple-image optical encryption based on improved phase retrieval algorithm,” Appl. Opt. 51, 2388–2394 (2012).
    [CrossRef]
  10. Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
    [CrossRef]
  11. S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21, 318–323 (1999).
    [CrossRef]
  12. M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
    [CrossRef]
  13. 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]
  14. X. Deng and D. Zhao, “Single-channel color image encryption using a modified Gerchberg–Saxton algorithm and mutual encoding in the Fresnel domain,” Appl. Opt. 50, 6019–6025 (2011).
    [CrossRef]
  15. 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]
  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 image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (2012).
    [CrossRef]
  18. 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]
  19. 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]
  20. M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51, 317–324 (2013).
    [CrossRef]
  21. M. R. Abuturab, “Noise-free recovery of color information using a joint-extended gyrator transform correlator,” Opt. Lasers Eng. 51, 230–239 (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).
    [CrossRef]
  25. X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50, 6645–6651 (2011).
    [CrossRef]
  26. W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
    [CrossRef]
  27. M. R. Abuturab, “Color information cryptosystem based on optical superposition principle and phase-truncated gyrator transform,” Appl. Opt. 51, 7994–8002 (2012).
    [CrossRef]
  28. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  29. 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]
  30. Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A 11, 125406 (2009).
    [CrossRef]
  31. 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]
  32. X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
    [CrossRef]
  33. Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
    [CrossRef]
  34. 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]
  35. A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635–2637 (2007).
    [CrossRef]

2013

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (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]

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

2012

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]

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

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(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]

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]

J.-J. Huang, H.-E. Hwang, C.-Y. Chen, and C.-M. Chen, “Lensless multiple-image optical encryption based on improved phase retrieval algorithm,” Appl. Opt. 51, 2388–2394 (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]

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

2011

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]

X. Deng and D. Zhao, “Single-channel color image encryption using a modified Gerchberg–Saxton algorithm and mutual encoding in the Fresnel domain,” Appl. Opt. 50, 6019–6025 (2011).
[CrossRef]

X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50, 6645–6651 (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]

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).
[CrossRef]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

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]

2010

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (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]

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

2009

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

2008

2007

2006

2004

2002

2000

1999

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

1995

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 image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (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, “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 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]

Cai, L.

Chen, C.-M.

Chen, C.-Y.

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, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

Chen, X.

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

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]

Deng, X.

Di, H.

Dong, G.

Dong, Z.

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

Huang, J.-J.

Hwang, H.-E.

Javidi, B.

Jia, W.

Joseph, J.

Joshi, M.

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

Karim, M. A.

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

Kim, T.

Kim, Y. S.

Kishk, 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, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[CrossRef]

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(2012).
[CrossRef]

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]

Liu, S.

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[CrossRef]

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(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]

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 and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).
[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, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[CrossRef]

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(2012).
[CrossRef]

Liu, Y.

Liu, Z.

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[CrossRef]

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(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]

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 and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).
[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).
[CrossRef]

Peng, X.

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).
[CrossRef]

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

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).
[CrossRef]

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

Refregier, P.

Sakdinawat, A.

Shakher, C.

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

Shen, X.

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]

Unnikrishnan, G.

Wang, B.

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

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

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.

Wang, Y.

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[CrossRef]

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]

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]

Xu, L.

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]

Yang, M.

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(2012).
[CrossRef]

Yang, X.

Zhang, J.

Zhang, S. Q.

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

Zhang, X.

Zhang, Y.

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

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

Zhao, D.

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]

Appl. Opt.

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]

X. Deng and D. Zhao, “Single-channel color image encryption using a modified Gerchberg–Saxton algorithm and mutual encoding in the Fresnel domain,” Appl. Opt. 50, 6019–6025 (2011).
[CrossRef]

X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50, 6645–6651 (2011).
[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]

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]

J.-J. Huang, H.-E. Hwang, C.-Y. Chen, and C.-M. Chen, “Lensless multiple-image optical encryption based on improved phase retrieval algorithm,” Appl. Opt. 51, 2388–2394 (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]

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

X. Meng, L. Cai, X. Yang, X. Shen, and G. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289–3297 (2006).
[CrossRef]

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

J. Opt. A

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

Microw. Opt. Technol. Lett.

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

Opt. Commun.

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[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]

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

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

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]

Opt. Eng.

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).
[CrossRef]

Opt. Lasers Eng.

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. 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]

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, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358(2012).
[CrossRef]

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[CrossRef]

Opt. Lett.

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Figures (8)

Fig. 1.
Fig. 1.

Optical setup for interference-based color image decryption system.

Fig. 2.
Fig. 2.

Simulation results of the proposed system: (a) Original color image with 512×512 pixels and 24 bits. (b) SPM as SPOM 3, the phase distributions of (c) SPOM 1 and (d) SPOM 2. (e) Real part of phase key for SPOM 1, (f) real part of phase key for SPOM 2, (g) encrypted image with all right keys, and (h) decrypted image with all correct keys.

Fig. 3.
Fig. 3.

Decryption results of the SPM (as SPOM 3) with error only in (a) m=0.005, (b) λ=0.2nm, (c) f=0.0004cm, and (d) r=0.00002mm.

Fig. 4.
Fig. 4.

Recovered images without (a) SPOM 1, (b) SPOM 2, (c) first asymmetric phase key, and (d) second asymmetric phase key.

Fig. 5.
Fig. 5.

Histogram analysis of the proposed algorithm (a) histogram of the plain image shown in Fig. 2(a) and (b) histogram of the encrypted image shown in Fig. 2(g).

Fig. 6.
Fig. 6.

(a) MSE versus deviation in order of RGB channels of SPM (as SPOM 3). (b) MSE versus deviation in wavelength of RGB channels of SPM (as SPOM 3). (c) MSE versus deviation in focal length of RGB channels of SPM (as SPOM 3). (d) MSE versus deviation in radius of RGB channels of SPM (as SPOM 3).

Fig. 7.
Fig. 7.

Robustness test of the proposed method: (a) occluded encrypted image with a 25% occlusion, (b) corresponding reconstructed image with all the right keys from (a), (c) occluded encrypted image with a 75% occlusion, (d) corresponding recovered image with all the correct keys from (c), (e) occluded encrypted image with a 90% occlusion, (f) corresponding retrieved image with all the right keys from (e), (g) Gaussian-noised encrypted image with a 0.1 density, and (h) corresponding decrypted image with all the correct keys from (g).

Fig. 8.
Fig. 8.

(a) MSE versus deviation in the occlusion part on the encrypted RGB channels and their corresponding recovered images. (b) MSE versus deviation in the Gaussian noise attack on the encrypted RGB channels, and their corresponding decrypted images.

Equations (20)

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Sr(r,θ)=H(r,θ)Z(r,θ)=exp(imθ)exp(iπλfr2)=exp[imθiπλfr2],
Ir(xi,yi)=fr(xi,yi)Sr(r,θ).
Ir(xi,yi)=F[Sr1(x,y)+Sr2(x,y)+Sr3(x,y)],
Sr1(x,y)+Sr2(x,y)+Sr3(x,y)=F1[Ir(xi,yi)]=Er(x,y),
Sr1(x,y)=exp[isr1(x,y)],
Sr2(x,y)=exp[isr2(x,y)],
Sr3(x,y)=Sr(r,θ).
[Er(x,y)Sr1(x,y)][Er(x,y)Sr1(x,y)]*=1,
sr1(x,y)=arg[Er(x,y)]arccos[|Er(x,y)/2|],
sr2(x,y)=arg[Er(x,y)]+arccos[|Er(x,y)/2|],
Er1(x,y)=PT[Sr1(x,y)],
Er2(x,y)=PT[Sr2(x,y)],
kr1(x,y)=AT[Er1(x,y)],
kr2(x,y)=AT[Er2(x,y)],
Dr1(x,y)=Er1(x,y)kr1(x,y),
Dr2(x,y)=Er2(x,y)kr2(x,y),
fr(xi,yi)=PT{F[Dr1(x,y)+Dr2(x,y)+Sr3(x,y)]}.
MSE=1M×Ni=1Mj=1N|Io(m,n)Id(m,n)|2,
S=Sm×Sλ×Sf×Sr.
S=(628)512×512×(7)512×512×(3928)512×512×(78571)512×512,

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