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]

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]

P. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (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]

X. Deng and D. Zhao, “Single channel color image encryption based on asymmetric cryptosystem,” Opt. Laser Technol. 44, 136–140 (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. Chen and X. Chen, “Optical color image encryption based on asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).

[CrossRef]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (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]

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. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimentional space-based model,” J. Opt. 13, 075404 (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]

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]

P. Clemente, V. Durán, V. T. Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35, 2391–2393 (2010).

[CrossRef]

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[CrossRef]

W. Chen, X. Chen, and J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).

[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (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]

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

[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]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[CrossRef]

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

[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]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (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]

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]

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]

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[CrossRef]

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[CrossRef]

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, “Optical image encryption based on polarization encoding by liquid crystal spatial light modulator,” J. Opt. A 6, 524–528 (2004).

[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]

G. Unnikrishnan, M. Pohit, and K. Singh, “A polarization encoded optical system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).

[CrossRef]

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

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

[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]

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

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[CrossRef]

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

[CrossRef]

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, “Optical image encryption based on polarization encoding by liquid crystal spatial light modulator,” J. Opt. A 6, 524–528 (2004).

[CrossRef]

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

[CrossRef]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimentional space-based model,” J. Opt. 13, 075404 (2011).

[CrossRef]

W. Chen, X. Chen, and J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).

[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (2010).

[CrossRef]

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

[CrossRef]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimentional space-based model,” J. Opt. 13, 075404 (2011).

[CrossRef]

W. Chen, X. Chen, and J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).

[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (2010).

[CrossRef]

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, “Optical image encryption based on polarization encoding by liquid crystal spatial light modulator,” J. Opt. A 6, 524–528 (2004).

[CrossRef]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[CrossRef]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[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]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).

[CrossRef]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (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]

O. Matoba and B. Javidi, “Secure holographic memory by double random polarization encryption,” Appl. Opt. 43, 2915–2919 (2004).

[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]

P. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).

[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]

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]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).

[CrossRef]

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

[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).

[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]

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

[CrossRef]

O. Matoba and B. Javidi, “Secure holographic memory by double random polarization encryption,” Appl. Opt. 43, 2915–2919 (2004).

[CrossRef]

X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40, 2310–2315 (2001).

[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. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[CrossRef]

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

[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]

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]

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, “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 domain 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]

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]

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]

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 Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).

[CrossRef]

G. Unnikrishnan, M. Pohit, and K. Singh, “A polarization encoded optical system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (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]

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]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. 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]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).

[CrossRef]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).

[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. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).

[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]

G. Unnikrishnan, M. Pohit, and K. Singh, “A polarization encoded optical system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).

[CrossRef]

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

[CrossRef]

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, “Optical image encryption based on polarization encoding by liquid crystal spatial light modulator,” J. Opt. A 6, 524–528 (2004).

[CrossRef]

G. Unnikrishnan, M. Pohit, and K. Singh, “A polarization encoded optical system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).

[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]

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]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).

[CrossRef]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[CrossRef]

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

[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]

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]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).

[CrossRef]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[CrossRef]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).

[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]

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]

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

[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. Deng and D. Zhao, “Single channel color image encryption based on asymmetric cryptosystem,” Opt. Laser Technol. 44, 136–140 (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]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).

[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]

X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40, 2310–2315 (2001).

[CrossRef]

O. Matoba and B. Javidi, “Secure holographic memory by double random polarization encryption,” Appl. Opt. 43, 2915–2919 (2004).

[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 based on interference that uses fractional Fourier domain 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. Ding, X. Deng, K. Song, and G. Chen, “Security improvement for asymmetric cryptosystem based on spherical wave illumination,” Appl. Opt. 52, 467–473 (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]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. 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]

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]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimentional space-based model,” J. Opt. 13, 075404 (2011).

[CrossRef]

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, “Optical image encryption based on polarization encoding by liquid crystal spatial light modulator,” J. Opt. A 6, 524–528 (2004).

[CrossRef]

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

[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).

[CrossRef]

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

[CrossRef]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (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]

G. Unnikrishnan, M. Pohit, and K. Singh, “A polarization encoded optical system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).

[CrossRef]

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

[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]

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

[CrossRef]

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