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]

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. 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]

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]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: comment,” Opt. Lett. 38, 4045 (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: reply,” Opt. Lett. 38, 4045 (2013).

[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. 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. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase-amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).

[CrossRef]

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

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]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express 18, 13772–13781 (2010).

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

H. Hwang, H. Chang, and W. Lie, “Multiple-image encryption and multiplexing using modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).

[CrossRef]

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

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

[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]

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

[CrossRef]

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

[CrossRef]

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

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: comment,” Opt. Lett. 38, 4045 (2013).

[CrossRef]

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase-amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).

[CrossRef]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (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]

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

[CrossRef]

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

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” 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]

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

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

[CrossRef]

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

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

[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]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: reply,” Opt. Lett. 38, 4045 (2013).

[CrossRef]

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).

[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: reply,” Opt. Lett. 38, 4045 (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]

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]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: reply,” Opt. Lett. 38, 4045 (2013).

[CrossRef]

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).

[CrossRef]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: comment,” Opt. Lett. 38, 4045 (2013).

[CrossRef]

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase-amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).

[CrossRef]

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

[CrossRef]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: comment,” Opt. Lett. 38, 4045 (2013).

[CrossRef]

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase-amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).

[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]

B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C (Wiley, 1996).

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

[CrossRef]

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

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” 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]

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

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

[CrossRef]

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

[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]

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]

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

[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]

H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express 18, 13772–13781 (2010).

[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]

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. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase-amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).

[CrossRef]

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

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 and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).

[CrossRef]

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

[CrossRef]

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[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]

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).

[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]

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]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: comment,” Opt. Lett. 38, 4045 (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: reply,” Opt. Lett. 38, 4045 (2013).

[CrossRef]

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

[CrossRef]

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

[CrossRef]

H. Hwang, H. Chang, and W. Lie, “Multiple-image encryption and multiplexing using 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]

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

[CrossRef]

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

[CrossRef]

B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C (Wiley, 1996).