Abstract

A multiple-image encryption scheme is proposed based on the phase retrieval process and phase mask multiplexing in the fractional Fourier transform domain. First, each original gray-scale image is encoded into a phase only function by using the proposed phase retrieval process. Second, all the obtained phase functions are modulated into an interim, which is encrypted into the final ciphertext by using the fractional Fourier transform. From a plaintext image, a group of phase masks is generated in the encryption process. The corresponding decrypted image can be recovered from the ciphertext only with the correct phase mask group in the decryption process. Simulation results show that the proposed phase retrieval process has high convergence speed, and the encryption algorithm can avoid cross-talk; in addition, its encrypted capacity is considerably enhanced.

© 2013 Optical Society of America

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References

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2012 (3)

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, Opt. Laser Technol. 44, 2238 (2012).
[CrossRef]

X. G. Wang and D. M. Zhao, Opt. Commun. 285, 4280 (2012).
[CrossRef]

X. P. Deng and D. M. Zhao, Opt. Laser Technol. 44, 374 (2012).
[CrossRef]

2011 (3)

X. G. Wang and D. M. Zhao, Opt. Commun. 284, 148 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, Appl. Opt. 50, 710 (2011).
[CrossRef]

2009 (3)

2007 (2)

2006 (1)

G. Situ and J. Zhang, J. Opt. A 8, 391 (2006).
[CrossRef]

2005 (1)

Alfalou, A.

Brosseau, C.

Chang, H. T.

Chen, C. M.

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, Opt. Laser Technol. 44, 2238 (2012).
[CrossRef]

Chen, C. Y.

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, Opt. Laser Technol. 44, 2238 (2012).
[CrossRef]

Deng, X. P.

X. P. Deng and D. M. Zhao, Opt. Laser Technol. 44, 374 (2012).
[CrossRef]

Huang, J. J.

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, Opt. Laser Technol. 44, 2238 (2012).
[CrossRef]

Hwang, H. E.

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, Opt. Laser Technol. 44, 2238 (2012).
[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, Appl. Opt. 50, 710 (2011).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, Opt. Lett. 34, 3917 (2009).
[CrossRef]

Lee, C. L.

H. T. Chang, H. E. Hwang, C. L. Lee, and M. T. Lee, Appl. Opt. 50, 710 (2011).
[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

Lee, M. T.

Lie, W. N.

Liu, S.

Z. Liu and S. Liu, Opt. Commun. 275, 324 (2007).
[CrossRef]

Liu, Z.

Z. Liu and S. Liu, Opt. Commun. 275, 324 (2007).
[CrossRef]

Mansour, A.

Shi, Y.

Situ, G.

Wang, X. G.

X. G. Wang and D. M. Zhao, Opt. Commun. 285, 4280 (2012).
[CrossRef]

X. G. Wang and D. M. Zhao, Opt. Commun. 284, 148 (2011).
[CrossRef]

Zhang, J.

Zhao, D. M.

X. G. Wang and D. M. Zhao, Opt. Commun. 285, 4280 (2012).
[CrossRef]

X. P. Deng and D. M. Zhao, Opt. Laser Technol. 44, 374 (2012).
[CrossRef]

X. G. Wang and D. M. Zhao, Opt. Commun. 284, 148 (2011).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

J. Opt. A (1)

G. Situ and J. Zhang, J. Opt. A 8, 391 (2006).
[CrossRef]

Opt. Commun. (4)

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

X. G. Wang and D. M. Zhao, Opt. Commun. 284, 148 (2011).
[CrossRef]

X. G. Wang and D. M. Zhao, Opt. Commun. 285, 4280 (2012).
[CrossRef]

Z. Liu and S. Liu, Opt. Commun. 275, 324 (2007).
[CrossRef]

Opt. Laser Technol. (2)

J. J. Huang, H. E. Hwang, C. Y. Chen, and C. M. Chen, Opt. Laser Technol. 44, 2238 (2012).
[CrossRef]

X. P. Deng and D. M. Zhao, Opt. Laser Technol. 44, 374 (2012).
[CrossRef]

Opt. Lett. (3)

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Figures (5)

Fig. 1.
Fig. 1.

Diagram of iterative process in the FrFT domain.

Fig. 2.
Fig. 2.

Diagram of multiple-image (a) encryption and (b) decryption.

Fig. 3.
Fig. 3.

Optical implementation of (a) encryption and (b) decryption.

Fig. 4.
Fig. 4.

(a) Nine gray-scale images for encryption, (b) ciphertext, and (c) decrypted image “Lena.”

Fig. 5.
Fig. 5.

MSE versus the number of iterations.

Tables (2)

Tables Icon

Table 1. CC and MSE of the Wavelength Multiplexing Algorithm

Tables Icon

Table 2. Number of Iterations and MSE of the Proposed Algorithm

Equations (13)

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hexp(jψ)=Fα2(Fα1(fexp(jϕ))exp(jϕ2))=Fβ2(Fβ1(gexp(jξ1))exp(jξ2)),
Fβ1(Fα2β2(Fα1(fexp(jϕ1))exp(jϕ2))exp(jξ2))=gexp(jξ1).
g^k=Fβ1(Fα2β2(Fα1(fexp(jϕ1k))exp(jϕ2k))exp(jξ2k)).
ξ1k=arg{g^k},gk=|g^k|.
ξ2k+1=arg(Fβ1(gexp(jξ1k))Fα2β2(Fα1(fexp(jϕ1k))exp(jϕ2k))),
ϕ2k+1=arg(Fβ2α2(Fβ1(gexp(jξ1k))exp(jξ2k+1))Fα1(fexp(jϕ1k))),
ϕ1k+1=arg(Fα1(Fβ2α2(Fβ1(gexp(jξ1k))exp(jξ2k+1))exp(jϕ2k+1))).
CC=E[[gE[g]][gkE[gk]]]E[[gE[g]]2]E[[gkE[gk]]2],
MSE=0M10N1[ggk]2M×N,
ϕ1=ϕ1N,ϕ2=ϕ2N,ξ1=ξ1N1,ξ2=ξ2N.
G=exp(ji=1Nξi,1).
ϕi,d=arg(exp(jk=1,kiNξk,1)).
fi=|Fα1(Fβ2α2(Fβ1(Gexp(jϕi,d))exp(jξi,2))exp(iϕi,2))exp(iϕi,1)|.

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