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X. Deng and D. Zhao, “Multiple-image encryption using phase retrieve algorithm and intermodulation in Fourier domain,” Opt. Laser Technol. 44(2), 374–377 (2012).

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N. Zhou, Y. Wang, and J. Wu, “Image encryption algorithm based on the multi-order discrete fractional Mellin transform,” Opt. Commun. 284(24), 5588–5597 (2011).

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W. Chen and D. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284(16–17), 3913–3917 (2011).

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H. T. Chang, H. E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284(18), 4146–4151 (2011).

[CrossRef]

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50(5), 710–716 (2011).

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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(11), 12033–12043 (2010).

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M. R. Abuturab, “Noise-free recovery of color information using a joint-extended gyrator transform correlator,” Opt. Lasers Eng. 51(3), 230–239 (2013).

[CrossRef]

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik (Stuttg.) 122(11), 1010–1013 (2011).

[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(11), 12033–12043 (2010).

[CrossRef]
[PubMed]

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[PubMed]

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[CrossRef]

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[CrossRef]
[PubMed]

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[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg-Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34(24), 3917–3919 (2009).

[CrossRef]
[PubMed]

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, “Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain,” Opt. Laser Technol. 44(7), 2238–2244 (2012).

[CrossRef]

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, “Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain,” Opt. Laser Technol. 44(7), 2238–2244 (2012).

[CrossRef]

W. Chen and D. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284(16–17), 3913–3917 (2011).

[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain,” Opt. Express 20(4), 3853–3865 (2012).

[CrossRef]
[PubMed]

W. Chen and D. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284(16–17), 3913–3917 (2011).

[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18(26), 27095–27104 (2010).

[CrossRef]
[PubMed]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

X. Deng and D. Zhao, “Multiple-image encryption using phase retrieve algorithm and intermodulation in Fourier domain,” Opt. Laser Technol. 44(2), 374–377 (2012).

[CrossRef]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, “Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain,” Opt. Laser Technol. 44(7), 2238–2244 (2012).

[CrossRef]

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, “Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain,” Opt. Laser Technol. 44(7), 2238–2244 (2012).

[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284(18), 4146–4151 (2011).

[CrossRef]

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50(5), 710–716 (2011).

[CrossRef]
[PubMed]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg-Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34(24), 3917–3919 (2009).

[CrossRef]
[PubMed]

J. Lang, R. Tao, and Y. Wang, “Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function,” Opt. Commun. 283(10), 2092–2096 (2010).

[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284(18), 4146–4151 (2011).

[CrossRef]

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50(5), 710–716 (2011).

[CrossRef]
[PubMed]

H. Li, Y. Wang, H. Yan, L. Li, Q. Li, and X. Zhao, “Double-image encryption by using chaos-based local pixel scrambling technique and gyrator transform,” Opt. Lasers Eng. 51(12), 1327–1331 (2013).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on discrete fractional random transform and chaotic maps,” Opt. Lasers Eng. 49(7), 753–757 (2011).

[CrossRef]

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

[CrossRef]

H. Li and Y. Wang, “Double-image encryption by iterative phase retrieval algorithm in fractional Fourier domain,” J. Mod. Opt. 55(21), 3601–3609 (2008).

[CrossRef]

H. Li, Y. Wang, H. Yan, L. Li, Q. Li, and X. Zhao, “Double-image encryption by using chaos-based local pixel scrambling technique and gyrator transform,” Opt. Lasers Eng. 51(12), 1327–1331 (2013).

[CrossRef]

H. Li, Y. Wang, H. Yan, L. Li, Q. Li, and X. Zhao, “Double-image encryption by using chaos-based local pixel scrambling technique and gyrator transform,” Opt. Lasers Eng. 51(12), 1327–1331 (2013).

[CrossRef]

Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, “Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains,” Opt. Laser Technol. 47, 152–158 (2013).

[CrossRef]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, “Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains,” Opt. Laser Technol. 47, 152–158 (2013).

[CrossRef]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik (Stuttg.) 122(11), 1010–1013 (2011).

[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(11), 12033–12043 (2010).

[CrossRef]
[PubMed]

Z. Liu, H. Zhao, and S. Liu, “A discrete fractional random transform,” Opt. Commun. 255(4-6), 357–365 (2005).

[CrossRef]

B. Zhu, S. Liu, and Q. Ran, “Optical image encryption based on multifractional Fourier transforms,” Opt. Lett. 25(16), 1159–1161 (2000).

[CrossRef]
[PubMed]

Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, “Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains,” Opt. Laser Technol. 47, 152–158 (2013).

[CrossRef]

Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, “Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains,” Opt. Laser Technol. 47, 152–158 (2013).

[CrossRef]

Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, “Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains,” Opt. Laser Technol. 47, 152–158 (2013).

[CrossRef]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik (Stuttg.) 122(11), 1010–1013 (2011).

[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(11), 12033–12043 (2010).

[CrossRef]
[PubMed]

Z. Liu, H. Zhao, and S. Liu, “A discrete fractional random transform,” Opt. Commun. 255(4-6), 357–365 (2005).

[CrossRef]

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieve algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

[CrossRef]

L. Sui, H. Lu, Z. Wang, and Q. Sun, “Double-image encryption using discrete fractional random transform and logistic maps,” Opt. Lasers Eng. 56, 1–12 (2014).

[CrossRef]

J. Wu, X. Luo, and N. Zhou, “Four-image encryption method based on spectrum truncation, chaos and the MODFrFT,” Opt. Laser Technol. 45, 571–577 (2013).

[CrossRef]

Z. Liu, M. Gong, Y. Dou, F. Liu, S. Lin, A. A. Muhammad, J. Dai, and S. Liu, “Double image encryption by using Arnold transform and discrete fractional angular transform,” Opt. Lasers Eng. 50(2), 248–255 (2012).

[CrossRef]

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieve algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

[CrossRef]

N. Singh and A. Sinha, “Chaos based multiple image encryption using multiple canonical transforms,” Opt. Laser Technol. 42(5), 724–731 (2010).

[CrossRef]

N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009).

[CrossRef]

N. Singh and A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008).

[CrossRef]

N. Singh and A. Sinha, “Chaos based multiple image encryption using multiple canonical transforms,” Opt. Laser Technol. 42(5), 724–731 (2010).

[CrossRef]

N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009).

[CrossRef]

N. Singh and A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008).

[CrossRef]

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A, Pure Appl. Opt. 8(5), 391–397 (2006).

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

L. Sui, H. Lu, Z. Wang, and Q. Sun, “Double-image encryption using discrete fractional random transform and logistic maps,” Opt. Lasers Eng. 56, 1–12 (2014).

[CrossRef]

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieve algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

[CrossRef]

L. Sui, H. Lu, Z. Wang, and Q. Sun, “Double-image encryption using discrete fractional random transform and logistic maps,” Opt. Lasers Eng. 56, 1–12 (2014).

[CrossRef]

J. Lang, R. Tao, and Y. Wang, “Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function,” Opt. Commun. 283(10), 2092–2096 (2010).

[CrossRef]

X. Wang and D. Zhao, “Double images encryption method with resistance against the specific attack based on an asymmetric algorithm,” Opt. Express 20(11), 11994–12003 (2012).

[CrossRef]
[PubMed]

X. Wang and D. Zhao, “Fully phase multiple-image encryption based on superposition principle and the digital holographic technique,” Opt. Commun. 285(21–22), 4280–4284 (2012).

[CrossRef]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284(1), 148–152 (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(19), 4441–4445 (2011).

[CrossRef]

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieve algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

[CrossRef]

Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, “Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains,” Opt. Laser Technol. 47, 152–158 (2013).

[CrossRef]

H. Li, Y. Wang, H. Yan, L. Li, Q. Li, and X. Zhao, “Double-image encryption by using chaos-based local pixel scrambling technique and gyrator transform,” Opt. Lasers Eng. 51(12), 1327–1331 (2013).

[CrossRef]

N. Zhou, Y. Wang, and J. Wu, “Image encryption algorithm based on the multi-order discrete fractional Mellin transform,” Opt. Commun. 284(24), 5588–5597 (2011).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on discrete fractional random transform and chaotic maps,” Opt. Lasers Eng. 49(7), 753–757 (2011).

[CrossRef]

J. Lang, R. Tao, and Y. Wang, “Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function,” Opt. Commun. 283(10), 2092–2096 (2010).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption by iterative phase retrieval algorithm in fractional Fourier domain,” J. Mod. Opt. 55(21), 3601–3609 (2008).

[CrossRef]

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

[CrossRef]

L. Sui, H. Lu, Z. Wang, and Q. Sun, “Double-image encryption using discrete fractional random transform and logistic maps,” Opt. Lasers Eng. 56, 1–12 (2014).

[CrossRef]

J. Wu, X. Luo, and N. Zhou, “Four-image encryption method based on spectrum truncation, chaos and the MODFrFT,” Opt. Laser Technol. 45, 571–577 (2013).

[CrossRef]

N. Zhou, Y. Wang, and J. Wu, “Image encryption algorithm based on the multi-order discrete fractional Mellin transform,” Opt. Commun. 284(24), 5588–5597 (2011).

[CrossRef]

Y. Zhang and D. Xiao, “Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform,” Opt. Lasers Eng. 51(4), 472–480 (2013).

[CrossRef]

H. Li, Y. Wang, H. Yan, L. Li, Q. Li, and X. Zhao, “Double-image encryption by using chaos-based local pixel scrambling technique and gyrator transform,” Opt. Lasers Eng. 51(12), 1327–1331 (2013).

[CrossRef]

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A, Pure Appl. Opt. 8(5), 391–397 (2006).

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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