Abstract

We propose a novel optical information encryption and authentication scheme that uses asymmetric keys generated by the phase-truncation approach and the phase-retrieval algorithm. Multiple images bonded with random phase masks are Fourier transformed, and obtained spectra are amplitude- and phase-truncated. The phase-truncated spectra are encoded into a single random intensity image using the phase-retrieval algorithm. Unlike most of the authentication schemes, in this study, only one encrypted reference image is required for verification of multiple secured images. The conventional double random phase encoding and correlation techniques are employed for authentication verification. Computer simulation results and theoretical explanation prove the effectiveness of the proposed scheme.

© 2014 Optical Society of America

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  1. P. Réfrégier and B. Javidi, “Optical image encryption based on input plane encoding and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef]
  2. N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
    [CrossRef]
  3. L. Chen and D. Zhao, “Optical image encryption based on fractional wavelet transform,” Opt. Commun. 254, 361–367 (2005).
    [CrossRef]
  4. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
    [CrossRef]
  5. 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]
  6. J. F. Barrera, A. Mira, and R. Torroba, “Optical encryption and QR codes: secure and noise-free information retrieval,” Opt. Express 21, 5373–5378 (2013).
    [CrossRef]
  7. W. Chen, X. Chen, A. Anand, and B. Javidi, “Optical encryption using multiple intensity samplings in the axial domain,” J. Opt. Soc. Am. A 30, 806–812 (2013).
    [CrossRef]
  8. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Opt. Photon. 1, 589–636 (2009).
    [CrossRef]
  9. A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
    [CrossRef]
  10. A. Alfalou and C. Brosseau, “Implementing compression and encryption of phase-shifting digital holograms for three-dimensional object reconstruction,” Opt. Commun. 307, 67–72 (2013).
    [CrossRef]
  11. A. Carnicer, M. M. Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of the optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
    [CrossRef]
  12. Y. Frauel, A. Castro, T. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
    [CrossRef]
  13. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
    [CrossRef]
  14. S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domains asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
    [CrossRef]
  15. X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated fractional Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
    [CrossRef]
  16. S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
    [CrossRef]
  17. S. K. Rajput and N. K. Nishchal, “Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform,” Appl. Opt. 52, 871–878 (2013).
    [CrossRef]
  18. S. K. Rajput and N. K. Nishchal, “Image encryption using polarized light encoding and amplitude- and phase-truncated Fresnel transform,” Appl. Opt. 52, 4343–4352 (2013).
    [CrossRef]
  19. S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
    [CrossRef]
  20. X. Wang and D. Zhao, “Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier transform-based encryption using a random amplitude mask,” Opt. Lett. 38, 3684–3686 (2013).
    [CrossRef]
  21. X. Wan, Y. Chen, C. Dai, and D. Zhao, “Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform,” Appl. Opt. 53, 208–213 (2014).
    [CrossRef]
  22. S. K. Rajput and N. K. Nishchal, “Fresnel domain nonlinear image encryption scheme based on Gerchberg-Saxton phase-retrieval algorithm,” Appl. Opt. 53, 418–425 (2014).
    [CrossRef]
  23. S. Kishk and B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28, 167–169 (2003).
    [CrossRef]
  24. N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).
    [CrossRef]
  25. Y.-Y. Chen, J.-H. Wang, C.-C. Lin, and H.-E. Hwang, “Lensless optical data hiding system based on phase encoding algorithm in the Fresnel domain,” Appl. Opt. 52, 5247–5257 (2013).
    [CrossRef]
  26. B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  27. D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
    [CrossRef]
  28. S. K. Rajput and N. K. Nishchal, “Image encryption and authentication verification based on nonconventional fractional joint transform correlator,” Opt. Lasers Eng. 50, 1474–1483 (2012).
    [CrossRef]
  29. E. Perez-Cabre, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
    [CrossRef]
  30. M. Cho, A. Mahalanobis, and B. Javidi, “3D passive photon counting automatic target recognition using advanced correlation filters,” Opt. Lett. 36, 861–863 (2011).
    [CrossRef]
  31. E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
    [CrossRef]
  32. M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (2013).
    [CrossRef]
  33. A. Markman and B. Javidi, “Full phase photon counting double-random-phase encryption,” J. Opt. Soc. Am. A 31, 394–403 (2014).
    [CrossRef]
  34. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane,” Optik 35, 237–246 (1972).
  35. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996).
    [CrossRef]
  36. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef]

2014 (3)

2013 (9)

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (2013).
[CrossRef]

Y.-Y. Chen, J.-H. Wang, C.-C. Lin, and H.-E. Hwang, “Lensless optical data hiding system based on phase encoding algorithm in the Fresnel domain,” Appl. Opt. 52, 5247–5257 (2013).
[CrossRef]

J. F. Barrera, A. Mira, and R. Torroba, “Optical encryption and QR codes: secure and noise-free information retrieval,” Opt. Express 21, 5373–5378 (2013).
[CrossRef]

W. Chen, X. Chen, A. Anand, and B. Javidi, “Optical encryption using multiple intensity samplings in the axial domain,” J. Opt. Soc. Am. A 30, 806–812 (2013).
[CrossRef]

A. Alfalou and C. Brosseau, “Implementing compression and encryption of phase-shifting digital holograms for three-dimensional object reconstruction,” Opt. Commun. 307, 67–72 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform,” Appl. Opt. 52, 871–878 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption using polarized light encoding and amplitude- and phase-truncated Fresnel transform,” Appl. Opt. 52, 4343–4352 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
[CrossRef]

X. Wang and D. Zhao, “Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier transform-based encryption using a random amplitude mask,” Opt. Lett. 38, 3684–3686 (2013).
[CrossRef]

2012 (5)

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domains asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[CrossRef]

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

S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption and authentication verification based on nonconventional fractional joint transform correlator,” Opt. Lasers Eng. 50, 1474–1483 (2012).
[CrossRef]

2011 (4)

E. Perez-Cabre, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

M. Cho, A. Mahalanobis, and B. Javidi, “3D passive photon counting automatic target recognition using advanced correlation filters,” Opt. Lett. 36, 861–863 (2011).
[CrossRef]

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).
[CrossRef]

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

2010 (3)

2009 (1)

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Opt. Photon. 1, 589–636 (2009).
[CrossRef]

2007 (2)

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[CrossRef]

Y. Frauel, A. Castro, T. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
[CrossRef]

2005 (2)

2003 (1)

2001 (1)

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

1989 (1)

1972 (1)

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

Abookasis, D.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Abril, H. C.

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

Alfalou, A.

A. Alfalou and C. Brosseau, “Implementing compression and encryption of phase-shifting digital holograms for three-dimensional object reconstruction,” Opt. Commun. 307, 67–72 (2013).
[CrossRef]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[CrossRef]

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]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Opt. Photon. 1, 589–636 (2009).
[CrossRef]

Alieva, T.

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[CrossRef]

Anand, A.

Arazi, O.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Arcos, S.

Barrera, J. F.

Brosseau, C.

A. Alfalou and C. Brosseau, “Implementing compression and encryption of phase-shifting digital holograms for three-dimensional object reconstruction,” Opt. Commun. 307, 67–72 (2013).
[CrossRef]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[CrossRef]

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]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Opt. Photon. 1, 589–636 (2009).
[CrossRef]

Calvo, M. L.

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[CrossRef]

Carnicer, A.

Castro, A.

Chen, L.

L. Chen and D. Zhao, “Optical image encryption based on fractional wavelet transform,” Opt. Commun. 254, 361–367 (2005).
[CrossRef]

Chen, W.

Chen, X.

Chen, Y.

Chen, Y.-Y.

Cho, M.

Dai, C.

Dorsch, R. G.

Frauel, Y.

Gerchberg, R. W.

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

Horner, J. L.

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Hwang, H.-E.

Javidi, B.

A. Markman and B. Javidi, “Full phase photon counting double-random-phase encryption,” J. Opt. Soc. Am. A 31, 394–403 (2014).
[CrossRef]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (2013).
[CrossRef]

W. Chen, X. Chen, A. Anand, and B. Javidi, “Optical encryption using multiple intensity samplings in the axial domain,” J. Opt. Soc. Am. A 30, 806–812 (2013).
[CrossRef]

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

E. Perez-Cabre, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

M. Cho, A. Mahalanobis, and B. Javidi, “3D passive photon counting automatic target recognition using advanced correlation filters,” Opt. Lett. 36, 861–863 (2011).
[CrossRef]

Y. Frauel, A. Castro, T. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
[CrossRef]

S. Kishk and B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28, 167–169 (2003).
[CrossRef]

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

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

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef]

Juvells, I.

Kishk, S.

Lin, C.-C.

Mahalanobis, A.

Markman, A.

Mendlovic, D.

Millan, M. S.

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

Mira, A.

Naughton, T.

Naughton, T. J.

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

Nishchal, N. K.

S. K. Rajput and N. K. Nishchal, “Fresnel domain nonlinear image encryption scheme based on Gerchberg-Saxton phase-retrieval algorithm,” Appl. Opt. 53, 418–425 (2014).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption using polarized light encoding and amplitude- and phase-truncated Fresnel transform,” Appl. Opt. 52, 4343–4352 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform,” Appl. Opt. 52, 871–878 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domains asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption and authentication verification based on nonconventional fractional joint transform correlator,” Opt. Lasers Eng. 50, 1474–1483 (2012).
[CrossRef]

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).
[CrossRef]

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

Peng, X.

Perez-Cabre, E.

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

E. Perez-Cabre, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

Qin, W.

Rajput, S. K.

Réfrégier, P.

Rodrigo, J. A.

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[CrossRef]

Rosen, J.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Saxton, W. O.

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

Torroba, R.

Usategui, M. M.

Wan, X.

Wang, J.-H.

Wang, X.

X. Wang and D. Zhao, “Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier transform-based encryption using a random amplitude mask,” Opt. Lett. 38, 3684–3686 (2013).
[CrossRef]

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

Zalevsky, Z.

Zhao, D.

Appl. Opt. (8)

J. Opt. (1)

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

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

Opt. Commun. (6)

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

L. Chen and D. Zhao, “Optical image encryption based on fractional wavelet transform,” Opt. Commun. 254, 361–367 (2005).
[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
[CrossRef]

A. Alfalou and C. Brosseau, “Implementing compression and encryption of phase-shifting digital holograms for three-dimensional object reconstruction,” Opt. Commun. 307, 67–72 (2013).
[CrossRef]

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

Opt. Eng. (3)

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

S. K. Rajput and N. K. Nishchal, “Image encryption and authentication verification based on nonconventional fractional joint transform correlator,” Opt. Lasers Eng. 50, 1474–1483 (2012).
[CrossRef]

Opt. Lett. (11)

E. Perez-Cabre, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

M. Cho, A. Mahalanobis, and B. Javidi, “3D passive photon counting automatic target recognition using advanced correlation filters,” Opt. Lett. 36, 861–863 (2011).
[CrossRef]

S. Kishk and B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28, 167–169 (2003).
[CrossRef]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[CrossRef]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (2013).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996).
[CrossRef]

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

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]

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

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

X. Wang and D. Zhao, “Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier transform-based encryption using a random amplitude mask,” Opt. Lett. 38, 3684–3686 (2013).
[CrossRef]

Opt. Photon. (1)

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Opt. Photon. 1, 589–636 (2009).
[CrossRef]

Optik (1)

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

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Figures (7)

Fig. 1.
Fig. 1.

Block diagram of key generator. PT, phase truncation; AT, amplitude truncation; RPM, random phase mask; FT, Fourier transform; FT1, inverse FT; P1n and P2n, phase values for nth image; RII, random intensity image.

Fig. 2.
Fig. 2.

Schematic diagram of authentication system. SLM, spatial light modulator; L, lens; f, focal length; CF, correlation filters; CCD, charge-coupled device camera.

Fig. 3.
Fig. 3.

Simulation results for first gray-scale image: (a) an input image to be verified, (b) RII, (c) relation showing matching of random intensity image with PTV, and (d) retrieved input image obtained in verification plane. PTV, phase-truncated value.

Fig. 4.
Fig. 4.

(a) Auto-correlation peak, (b) cross-correlation peak when RII is wrong, and (c) cross-correlation peak when keys are wrong.

Fig. 5.
Fig. 5.

Simulation results for another gray-scale image: (a) an image of cameraman to be verified, (b) relation showing matching of random intensity image with PTV, (c) retrieved input image obtained in verification plane, (d) auto-correlation peak, (e) cross-correlation peak when keys are wrong, and (f) cross-correlation peak when RII is wrong.

Fig. 6.
Fig. 6.

Plot between cumulative average of MSE for multiple images and number of images. MSE, mean square error; AMSE, average of MSE.

Fig. 7.
Fig. 7.

Attack results for first gray-scale image: (a) plot between MSE and number of iterations during generations of first asymmetric key, (b) plot between MSE and number of iterations during generations of second asymmetric key, and (c) corresponding decrypted image.

Equations (12)

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Fn(u,v)=I[fn(x,y)×exp{i2πr1n(x,y)}].
An(u,v)=PT{Fn(u,v)},
Pn(u,v)=AT{Fn(u,v)}.
A(n)m+1(x,y)=I1[Anm(u,v)]=|A(n)m+1(x,y)|×exp{iφnm(x,y)}.
A(n)m+1(u,v)=I[A(n)m+1(x,y)]=|A(n)m+1(u,v)|×exp{iφ(n)m(u,v)}.
MSE=x=0N1y=0N1{|R(x,y)||A(n)m+1(x,y)|}2N×N.
K1n(u,v)=Pn(u,v)×exp{ir2(n)m+1(u,v)},
K2n(x,y)=exp{iφnm(x,y)}.
dn(x,y)=I1[I{Rn(x,y)×K2n(x,y)}×K1n(u,v)].
Cn(x,y)=I1[Q1×Q2],
Q1=|I{dn(x,y)}×[I{fn(x,y)}]|t,
Q2=exp{iarg[I{dn(x,y)}]arg[I{fn(x,y)}]}.

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