M. R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 525–532 (2013).

[CrossRef]

X. Wang and D. Zhao, “Fully phase multiple-image encryption based on superposition principle and the digital holographic technique,” Opt. Commun. 285, 4280–4284 (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]

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]

M. R. Abuturab, “Color image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (2012).

[CrossRef]

M. R. Abuturab, “Color information security system using discrete cosine transform in gyrator transform domain radial-Hilbert phase encoding,” Opt. Lasers Eng. 50, 1209–1216 (2012).

[CrossRef]

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).

[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (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]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284, 4441–4445 (2011).

[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, “Image encoding based on coherent superposition and basic vector operations,” Opt. Commun. 284, 945–951 (2011).

[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]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (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]

N. Singh and A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46, 117–123 (2008).

[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption for twin images in fractional Fourier domain,” Opt. Commun. 281, 5713–5720 (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]

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25, 2608–2617 (2008).

[CrossRef]

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

[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]

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

[CrossRef]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15, 16067–16079 (2007).

[CrossRef]

X. Zhou, S. Yuan, S. W. Wang, and J. Xie, “Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform,” Appl. Opt. 45, 8434–8439 (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, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181–3186 (2006).

[CrossRef]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14, 8552–8560 (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]

K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, 2001).

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]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (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 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, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[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]

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]

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]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).

[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 and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).

[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption for twin images in fractional Fourier domain,” Opt. Commun. 281, 5713–5720 (2008).

[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]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).

[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).

[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).

[CrossRef]

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

[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]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).

[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).

[CrossRef]

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

[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]

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25, 2608–2617 (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]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181–3186 (2006).

[CrossRef]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[CrossRef]

K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, 2001).

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption for twin images in fractional Fourier domain,” Opt. Commun. 281, 5713–5720 (2008).

[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. 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]

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).

[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]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption for twin images in fractional Fourier domain,” Opt. Commun. 281, 5713–5720 (2008).

[CrossRef]

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

[CrossRef]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).

[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]

N. Singh and A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46, 117–123 (2008).

[CrossRef]

N. Singh and A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46, 117–123 (2008).

[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[CrossRef]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).

[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 Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).

[CrossRef]

X. Wang and D. Zhao, “Fully phase multiple-image encryption based on superposition principle and the digital holographic technique,” Opt. Commun. 285, 4280–4284 (2012).

[CrossRef]

X. Wang and D. Zhao, “Image encoding based on coherent superposition and basic vector operations,” Opt. Commun. 284, 945–951 (2011).

[CrossRef]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284, 4441–4445 (2011).

[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]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15, 16067–16079 (2007).

[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).

[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]

K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, 2001).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

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]

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, “Fully phase multiple-image encryption based on superposition principle and the digital holographic technique,” Opt. Commun. 285, 4280–4284 (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]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284, 4441–4445 (2011).

[CrossRef]

X. Wang and D. Zhao, “Image encoding based on coherent superposition and basic vector operations,” Opt. Commun. 284, 945–951 (2011).

[CrossRef]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14, 8552–8560 (2006).

[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]

X. Zhou, S. Yuan, S. W. Wang, and J. Xie, “Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform,” Appl. Opt. 45, 8434–8439 (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]

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]

M. R. Abuturab, “Color image security system using double random-structured phase encoding in gyrator transform domain,” Appl. Opt. 51, 3006–3016 (2012).

[CrossRef]

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

[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 Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).

[CrossRef]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284, 4441–4445 (2011).

[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (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]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption for twin images in fractional Fourier domain,” Opt. Commun. 281, 5713–5720 (2008).

[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (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]

X. Wang and D. Zhao, “Image encoding based on coherent superposition and basic vector operations,” Opt. Commun. 284, 945–951 (2011).

[CrossRef]

X. Wang and D. Zhao, “Fully phase multiple-image encryption based on superposition principle and the digital holographic technique,” Opt. Commun. 285, 4280–4284 (2012).

[CrossRef]

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

[CrossRef]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).

[CrossRef]

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).

[CrossRef]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14, 8552–8560 (2006).

[CrossRef]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181–3186 (2006).

[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]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15, 16067–16079 (2007).

[CrossRef]

M. R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 525–532 (2013).

[CrossRef]

M. R. Abuturab, “Color information security system using discrete cosine transform in gyrator transform domain radial-Hilbert phase encoding,” Opt. Lasers Eng. 50, 1209–1216 (2012).

[CrossRef]

N. Singh and A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46, 117–123 (2008).

[CrossRef]

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

[CrossRef]

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

[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. 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]

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]

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

[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, 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. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, 2001).