Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

G. Situ, G. Pedrini, and W. Osten, “Strategy for cryptanalysis of optical encryption in the Fresnel domain,” Appl. Opt. 49, 457–462 (2010).

[CrossRef]
[PubMed]

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).

[CrossRef]
[PubMed]

S. Yuan, X. Zhou Xin, S. A. Mohammed, X. Lu, and X.-F. Li, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17, 3270–3284(2009).

[CrossRef]

W. Liu, G. Yang, and H. Xie, “A hybrid heuristic algorithm to improve known-plaintext attack on Fourier plane encryption,” Opt. Express 17, 13928–13938 (2009).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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

[CrossRef]

Z. Liu, M. A. Ahmad, and S. Liu, “Image encryption scheme based on the commutation and anti-commutation rules,” Opt. Commun. 279, 285–290 (2007).

[CrossRef]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: Properties and applications,” Opt. Express 15, 2190–2203(2007).

[CrossRef]
[PubMed]

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]
[PubMed]

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).

[CrossRef]
[PubMed]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (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]
[PubMed]

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]
[PubMed]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416 (2006).

[CrossRef]
[PubMed]

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]
[PubMed]

L. Chen and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31, 3438–3440 (2006).

[CrossRef]
[PubMed]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).

[CrossRef]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).

[CrossRef]
[PubMed]

Z. Liu, M. A. Ahmad, and S. Liu, “Image encryption scheme based on the commutation and anti-commutation rules,” Opt. Commun. 279, 285–290 (2007).

[CrossRef]

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

[CrossRef]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (2007).

[CrossRef]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: Properties and applications,” Opt. Express 15, 2190–2203(2007).

[CrossRef]
[PubMed]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: Properties and applications,” Opt. Express 15, 2190–2203(2007).

[CrossRef]
[PubMed]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (2007).

[CrossRef]

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

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749(2008).

[CrossRef]

H. Li and Y. Wang, “Information security system based on iterative multiple-phase retrieval in gyrator domain,” Opt. Laser Technol. 40, 962–966 (2008).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).

[CrossRef]
[PubMed]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, M. A. Ahmad, and S. Liu, “Image encryption scheme based on the commutation and anti-commutation rules,” Opt. Commun. 279, 285–290 (2007).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).

[CrossRef]
[PubMed]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, M. A. Ahmad, and S. Liu, “Image encryption scheme based on the commutation and anti-commutation rules,” Opt. Commun. 279, 285–290 (2007).

[CrossRef]

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).

[CrossRef]
[PubMed]

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]
[PubMed]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).

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]
[PubMed]

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]
[PubMed]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (2007).

[CrossRef]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: Properties and applications,” Opt. Express 15, 2190–2203(2007).

[CrossRef]
[PubMed]

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

[CrossRef]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749(2008).

[CrossRef]

H. Li and Y. Wang, “Information security system based on iterative multiple-phase retrieval in gyrator domain,” Opt. Laser Technol. 40, 962–966 (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]
[PubMed]

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]
[PubMed]

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]
[PubMed]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).

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]
[PubMed]

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]
[PubMed]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).

[CrossRef]

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

G. Situ, G. Pedrini, and W. Osten, “Strategy for cryptanalysis of optical encryption in the Fresnel domain,” Appl. Opt. 49, 457–462 (2010).

[CrossRef]
[PubMed]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, M. A. Ahmad, and S. Liu, “Image encryption scheme based on the commutation and anti-commutation rules,” Opt. Commun. 279, 285–290 (2007).

[CrossRef]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).

[CrossRef]

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

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749(2008).

[CrossRef]

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).

[CrossRef]
[PubMed]

S. Yuan, X. Zhou Xin, S. A. Mohammed, X. Lu, and X.-F. Li, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17, 3270–3284(2009).

[CrossRef]

W. Liu, G. Yang, and H. Xie, “A hybrid heuristic algorithm to improve known-plaintext attack on Fourier plane encryption,” Opt. Express 17, 13928–13938 (2009).

[CrossRef]
[PubMed]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: Properties and applications,” Opt. Express 15, 2190–2203(2007).

[CrossRef]
[PubMed]

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]
[PubMed]

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]
[PubMed]

H. Li and Y. Wang, “Information security system based on iterative multiple-phase retrieval in gyrator domain,” Opt. Laser Technol. 40, 962–966 (2008).

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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]
[PubMed]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416 (2006).

[CrossRef]
[PubMed]

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]
[PubMed]

L. Chen and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31, 3438–3440 (2006).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).