Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

Z. Liu and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).

[CrossRef]
[PubMed]

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

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

[CrossRef]

X. Wang and D. Zhao, “Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry,” Opt. Commun. 268, 240–244 (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]
[PubMed]

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

[CrossRef]
[PubMed]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).

[CrossRef]
[PubMed]

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]
[PubMed]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).

[CrossRef]

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

[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain” Opt. Lett. 24, 762–764 (1999).

[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).

[CrossRef]

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).

[CrossRef]

S. Zhang and R. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).

[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).

[CrossRef]

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

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).

[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

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

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).

[CrossRef]

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).

[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).

[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain” Opt. Lett. 24, 762–764 (1999).

[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

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]

S. Zhang and R. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).

[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).

[CrossRef]

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).

[CrossRef]

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).

[CrossRef]

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

[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).

[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

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

[CrossRef]

Z. Liu and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

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

[CrossRef]

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

[CrossRef]
[PubMed]

Z. Liu and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).

[CrossRef]
[PubMed]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).

[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).

[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).

[CrossRef]

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

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

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

[CrossRef]

X. Wang and D. Zhao, “Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry,” Opt. Commun. 268, 240–244 (2006).

[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).

[CrossRef]

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

[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

S. Zhang and R. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).

[CrossRef]

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

[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).

[CrossRef]
[PubMed]

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, “Stream cipher based on pseudorandom number generation with optical affine transformation,” Appl. Opt. 39, 2340–2346 (2000).

[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]

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

[CrossRef]

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

[CrossRef]

X. Wang and D. Zhao, “Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry,” Opt. Commun. 268, 240–244 (2006).

[CrossRef]

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

[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).

[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).

[CrossRef]

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).

[CrossRef]

S. Zhang and R. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).

[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).

[CrossRef]
[PubMed]

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]
[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]

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

[CrossRef]
[PubMed]

Z. Liu and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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]

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]

M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).

[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain” Opt. Lett. 24, 762–764 (1999).

[CrossRef]

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