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

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

[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain 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]

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

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]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).

[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]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Signal Process. Lett. 16, 853–856 (2009).

[CrossRef]

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

[CrossRef]

A. Alfalou and A. Mansour, “Double random phase encryption scheme to multiplex and simultaneous encode multiple images,” Appl. Opt. 48, 5933–5947 (2009).

[CrossRef]

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

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (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]

X. Peng, P. Zhang, 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 the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).

[CrossRef]

U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Polarization encoding and multiplexing of two-dimensional signals: application to image encryption,” Appl. Opt. 45, 5693–5700 (2006).

[CrossRef]

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. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).

[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549–1554 (2000).

[CrossRef]

B. Javidi and T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).

[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]

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

[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]

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,” Adv. Opt. Photon. 1, 589–636 (2009).

[CrossRef]

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

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

[CrossRef]

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

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

[CrossRef]

P. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).

[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]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).

[CrossRef]

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. 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]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).

[CrossRef]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Signal Process. Lett. 16, 853–856 (2009).

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).

[CrossRef]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Signal Process. Lett. 16, 853–856 (2009).

[CrossRef]

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

[CrossRef]

P. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).

[CrossRef]

B. Javidi and T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).

[CrossRef]

W. Qin, X. Peng, X. 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]

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

[CrossRef]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).

[CrossRef]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Signal Process. Lett. 16, 853–856 (2009).

[CrossRef]

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

[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]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).

[CrossRef]

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]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Signal Process. Lett. 16, 853–856 (2009).

[CrossRef]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Signal Process. Lett. 16, 853–856 (2009).

[CrossRef]

X. Peng, P. Zhang, 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 the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).

[CrossRef]

X. Peng, P. Zhang, 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 the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).

[CrossRef]

H. Chang, W. Lu, and C. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. 41, 4825–4834 (2002).

[CrossRef]

A. Alfalou and A. Mansour, “Double random phase encryption scheme to multiplex and simultaneous encode multiple images,” Appl. Opt. 48, 5933–5947 (2009).

[CrossRef]

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

[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]

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

[CrossRef]

Q. Wang, Q. Guo, L. Lei, and J. Zhou, “Multiple-image encryption based on interference principle and phase-only mask multiplexing in Fresnel transform domain,” Appl. Opt. 52, 6849–6857 (2013).

[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549–1554 (2000).

[CrossRef]

U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Polarization encoding and multiplexing of two-dimensional signals: application to image encryption,” Appl. Opt. 45, 5693–5700 (2006).

[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain,” Appl. Opt. 52, 4343–4352 (2013).

[CrossRef]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Signal Process. Lett. 16, 853–856 (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]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).

[CrossRef]

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

[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]

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]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).

[CrossRef]

P. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).

[CrossRef]

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

[CrossRef]

B. Javidi and T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).

[CrossRef]

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]

S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).

[CrossRef]

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

[CrossRef]

X. Peng, P. Zhang, 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 the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).

[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]

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).