J. Wu, L. Zhang, and N. Zhou, “Image encryption based on the multiple-order discrete fractional cosine transform,” Opt. Commun. 283(9), 1720–1725 (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(3), 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48(7-8), 800–805 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282(4), 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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).

[CrossRef]

Y. Sheng, Z. Xin, M. S. Alam, L. Xi, and L. Xiao-Feng, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17(5), 3270–3284 (2009).

[CrossRef]
[PubMed]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17(16), 13418–13424 (2009).

[CrossRef]
[PubMed]

W. Liu, G. Yang, and H. Xie, “A hybrid heuristic algorithm to improve known-plaintext attack on Fourier plane encryption,” Opt. Express 17(16), 13928–13938 (2009).

[CrossRef]
[PubMed]

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281(23), 5745–5749 (2008).

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).

[CrossRef]

M. Joshi, K. Chandrashakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279(1), 35–42 (2007).

[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: properties and applications,” Opt. Express 15(5), 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(16), 10253–10265 (2007).

[CrossRef]
[PubMed]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24(10), 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(24), 16067–16079 (2007).

[CrossRef]
[PubMed]

L. Chen and D. Zhao, “Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography,” Opt. Express 15(24), 16080–16089 (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(8), 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(10), 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(22), 3261–3263 (2006).

[CrossRef]
[PubMed]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).

[CrossRef]

C. Jeffries and J. Perez, “Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator,” Phys. Rev. A 26(4), 2117–2122 (1982).

[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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).

[CrossRef]

J. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24(10), 3135–3139 (2007).

[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: properties and applications,” Opt. Express 15(5), 2190–2203 (2007).

[CrossRef]
[PubMed]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: properties and applications,” Opt. Express 15(5), 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(10), 3135–3139 (2007).

[CrossRef]

M. Joshi, K. Chandrashakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279(1), 35–42 (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(3), 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(3), 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48(7-8), 800–805 (2010).

[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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 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(4), 518–522 (2009).

[CrossRef]

C. Jeffries and J. Perez, “Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator,” Phys. Rev. A 26(4), 2117–2122 (1982).

[CrossRef]

M. Joshi, K. Chandrashakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279(1), 35–42 (2007).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281(23), 5745–5749 (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(3), 035407 (2010).

[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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).

[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(3), 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48(7-8), 800–805 (2010).

[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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 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(4), 518–522 (2009).

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (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(3), 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(3), 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48(7-8), 800–805 (2010).

[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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 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(4), 518–522 (2009).

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).

[CrossRef]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31(22), 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(8), 1044–1046 (2006).

[CrossRef]
[PubMed]

C. Jeffries and J. Perez, “Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator,” Phys. Rev. A 26(4), 2117–2122 (1982).

[CrossRef]

M. Joshi, K. Chandrashakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279(1), 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(12), 887–889 (2000).

[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(3), 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48(7-8), 800–805 (2010).

[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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 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(4), 518–522 (2009).

[CrossRef]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).

[CrossRef]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17(16), 13418–13424 (2009).

[CrossRef]
[PubMed]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281(23), 5745–5749 (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(24), 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(22), 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(8), 1044–1046 (2006).

[CrossRef]
[PubMed]

J. Wu, L. Zhang, and N. Zhou, “Image encryption based on the multiple-order discrete fractional cosine transform,” Opt. Commun. 283(9), 1720–1725 (2010).

[CrossRef]

J. Wu, L. Zhang, and N. Zhou, “Image encryption based on the multiple-order discrete fractional cosine transform,” Opt. Commun. 283(9), 1720–1725 (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(22), 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(8), 1044–1046 (2006).

[CrossRef]
[PubMed]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).

[CrossRef]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).

[CrossRef]

J. Wu, L. Zhang, and N. Zhou, “Image encryption based on the multiple-order discrete fractional cosine transform,” Opt. Commun. 283(9), 1720–1725 (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(3), 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282(4), 518–522 (2009).

[CrossRef]

M. Joshi, K. Chandrashakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279(1), 35–42 (2007).

[CrossRef]

J. Wu, L. Zhang, and N. Zhou, “Image encryption based on the multiple-order discrete fractional cosine transform,” Opt. Commun. 283(9), 1720–1725 (2010).

[CrossRef]

Y. Zhang, C.-H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).

[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 1D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281(23), 5745–5749 (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(24), 16067–16079 (2007).

[CrossRef]
[PubMed]

W. Liu, G. Yang, and H. Xie, “A hybrid heuristic algorithm to improve known-plaintext attack on Fourier plane encryption,” Opt. Express 17(16), 13928–13938 (2009).

[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(16), 10253–10265 (2007).

[CrossRef]
[PubMed]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17(16), 13418–13424 (2009).

[CrossRef]
[PubMed]

Y. Sheng, Z. Xin, M. S. Alam, L. Xi, and L. Xiao-Feng, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17(5), 3270–3284 (2009).

[CrossRef]
[PubMed]

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009).

[CrossRef]

L. Chen and D. Zhao, “Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography,” Opt. Express 15(24), 16080–16089 (2007).

[CrossRef]
[PubMed]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: properties and applications,” Opt. Express 15(5), 2190–2203 (2007).

[CrossRef]
[PubMed]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Lasers Eng. 48(7-8), 800–805 (2010).

[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).

[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).

[CrossRef]
[PubMed]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28(4), 269–271 (2003).

[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(10), 1414–1416 (2006).

[CrossRef]
[PubMed]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).

[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(22), 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(8), 1044–1046 (2006).

[CrossRef]
[PubMed]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30(11), 1306–1308 (2005).

[CrossRef]
[PubMed]

C. Jeffries and J. Perez, “Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator,” Phys. Rev. A 26(4), 2117–2122 (1982).

[CrossRef]