Abstract

We propose a novel nonlinear image-encryption scheme based on a Gerchberg–Saxton (G-S) phase-retrieval algorithm in the Fresnel transform domain. The decryption process can be performed using conventional double random phase encoding (DRPE) architecture. The encryption is realized by applying G-S phase-retrieval algorithm twice, which generates two asymmetric keys from intermediate phases. The asymmetric keys are generated in such a way that decryption is possible optically with a conventional DRPE method. Due to the asymmetric nature of the keys, the proposed encryption process is nonlinear and offers enhanced security. The cryptanalysis has been carried out, which proves the robustness of proposed scheme against known-plaintext, chosen-plaintext, and special attacks. A simple optical setup for decryption has also been suggested. Results of computer simulation support the idea of the proposed cryptosystem.

© 2014 Optical Society of America

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  1. P. Refregier and B. Javidi, “Optical image encryption based on input plane encoding and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef]
  2. O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
    [CrossRef]
  3. 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]
  4. B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
    [CrossRef]
  5. N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
    [CrossRef]
  6. G. Situ and J. Zhang, “Double random phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
    [CrossRef]
  7. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
    [CrossRef]
  8. 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]
  9. X. Peng, P. Chang, H. Wei, and B. Yu, “Known plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
    [CrossRef]
  10. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
    [CrossRef]
  11. X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double random phase encoding in Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).
    [CrossRef]
  12. W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. 11, 075402 (2009).
    [CrossRef]
  13. P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double random-phase encryption scheme with randomized lens-phase function,” Opt. Lett. 34, 331–333 (2009).
    [CrossRef]
  14. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  15. A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
    [CrossRef]
  16. M. Dubreuil, A. Aflalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using Stokes-Mueller formalism,” J. Opt. 14, 094004 (2012).
    [CrossRef]
  17. M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (2013).
    [CrossRef]
  18. Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
    [CrossRef]
  19. K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
    [CrossRef]
  20. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
    [CrossRef]
  21. X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284, 148–152 (2011).
    [CrossRef]
  22. 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]
  23. 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]
  24. 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]
  25. 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]
  26. 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]
  27. I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
    [CrossRef]
  28. I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
    [CrossRef]
  29. S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
    [CrossRef]
  30. W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
    [CrossRef]
  31. 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]
  32. 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]
  33. 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]
  34. A. Alfalou and A. Mansour, “Double random phase encryption scheme to multiplex and simultaneous encode multiple image,” Appl. Opt. 48, 5933–5947, (2009).
    [CrossRef]
  35. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Opt. Photon. 1, 589–636 (2009).
    [CrossRef]

2014 (1)

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
[CrossRef]

2013 (9)

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (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]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (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]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38, 1651–1653 (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]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (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 (4)

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, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (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]

M. Dubreuil, A. Aflalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using Stokes-Mueller formalism,” J. Opt. 14, 094004 (2012).
[CrossRef]

2011 (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]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284, 148–152 (2011).
[CrossRef]

2010 (2)

2009 (5)

2008 (1)

2007 (2)

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

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

2006 (2)

2005 (1)

2004 (1)

2003 (1)

2000 (1)

1999 (1)

1996 (1)

1995 (1)

Aflalou, A.

M. Dubreuil, A. Aflalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using Stokes-Mueller formalism,” J. Opt. 14, 094004 (2012).
[CrossRef]

Alfalou, A.

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]

Arcos, S.

Brosseau, C.

M. Dubreuil, A. Aflalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using Stokes-Mueller formalism,” J. Opt. 14, 094004 (2012).
[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, “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.

Chang, H. T.

Chang, P.

Cho, M.

Dorsch, R. G.

Dubreuil, M.

M. Dubreuil, A. Aflalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using Stokes-Mueller formalism,” J. Opt. 14, 094004 (2012).
[CrossRef]

Frauel, Y.

Gao, Q.

Hennelly, B.

Hwang, H.-E.

Javidi, B.

Joseph, J.

Juvells, I.

Kumar, A.

Kumar, P.

Li, H.

Li, T.

Lie, W.-N.

Liu, S.

Liu, W.

Liu, Z.

Mansour, A.

Matoba, O.

Mehra, I.

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
[CrossRef]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[CrossRef]

Mendlovic, D.

Nakano, K.

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

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]

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

Nishchal, N. K.

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (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-based optical cryptosystem using phase-truncated Fresnel transform,” Appl. Opt. 52, 871–878 (2013).
[CrossRef]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (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, “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]

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.

Qin, W.

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

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. 11, 075402 (2009).
[CrossRef]

Rajput, S. K.

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
[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]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[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, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

Refregier, 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]

Sheridan, J. T.

Shi, Y.

Singh, K.

Situ, G.

Suzuki, H.

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

Takeda, M.

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

Unnikrishnan, G.

Usategui, M. M.

Wang, B.

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]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284, 148–152 (2011).
[CrossRef]

Wang, Y.

Wei, H.

Yamaguchi, M.

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

Yu, B.

Zalevsky, Z.

Zhang, J.

Zhang, P.

Zhang, S.

Zhang, Y.

Zhao, D.

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]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284, 148–152 (2011).
[CrossRef]

Appl. Opt. (5)

J. Opt. (2)

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. 11, 075402 (2009).
[CrossRef]

M. Dubreuil, A. Aflalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using Stokes-Mueller formalism,” J. Opt. 14, 094004 (2012).
[CrossRef]

Opt. Commun. (6)

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (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]

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

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, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284, 148–152 (2011).
[CrossRef]

Opt. Eng. (1)

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
[CrossRef]

Opt. Lett. (18)

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]

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

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[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]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
[CrossRef]

G. Situ and J. Zhang, “Double random phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[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. Peng, P. Chang, H. Wei, and B. Yu, “Known plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
[CrossRef]

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

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

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double random-phase encryption scheme with randomized lens-phase function,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

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

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[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. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[CrossRef]

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

Opt. Photon. (1)

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

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