Abstract

In this paper, we propose a novel method for image encryption by employing the diffraction imaging technique. This method is in principle suitable for most diffractive-imaging-based optical encryption schemes, and a typical diffractive imaging architecture using three random phase masks in the Fresnel domain is taken for an example to illustrate it. The encryption process is rather simple because only a single diffraction intensity pattern is needed to be recorded, and the decryption procedure is also correspondingly simplified. To achieve this goal, redundant data are digitally appended to the primary image before a standard encrypting procedure. The redundant data serve as a partial input plane support constraint in a phase retrieval algorithm, which is employed for completely retrieving the plaintext. Simulation results are presented to verify the validity of the proposed approach.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. 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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2014 (2)

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photon. 6, 120–155 (2014).
[CrossRef]

2013 (2)

2011 (1)

2010 (3)

2009 (2)

2008 (1)

2006 (2)

2005 (1)

2004 (1)

2000 (2)

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]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

1995 (1)

1994 (1)

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Alfalou, A.

Anand, A.

Arcos, S.

Brosseau, C.

Carnicer, A.

Chang, H. T.

Chen, W.

Chen, X.

Gao, Q.

Guo, C.

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Horner, J. L.

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Hwang, H. E.

Javidi, B.

Joseph, J.

Juvells, I.

Li, H.

Li, T.

Lie, W. N.

Liu, S.

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Montes-Usategui, M.

Nomura, T.

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

Paganin, D. M.

R. P. Yu and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

Peng, X.

Qin, W.

Refregier, P.

Sheppard, C. J. R.

Sheridan, J. T.

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Shi, Y.

Singh, K.

Situ, G.

Unnikrishnan, G.

Wang, B.

Wang, Y.

Wei, H.

Yu, B.

Yu, R. P.

R. P. Yu and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

Zhang, J.

Zhang, P.

Zhang, S.

Zhang, Y.

Adv. Opt. Photon. (2)

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

New J. Phys. (1)

R. P. Yu and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

Opt. Eng. (2)

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Opt. Lett. (10)

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

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[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]

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

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]

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]

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-ciphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Schematic optical setup for the proposed optical security system. U, plaintext; M, phase only mask; CCD, charge-coupled device.

Fig. 2.
Fig. 2.

(a) Original image. (b) Original image with redundant data. (c) Support constraint formed by the redundant data.

Fig. 3.
Fig. 3.

Phase-only masks: (a) M1, (b) M2, and (c) M3. (d) Diffraction intensity pattern recorded by CCD camera.

Fig. 4.
Fig. 4.

(a) Decrypted plaintext. (b) Retrieved primary image after removing the redundant data from (a). (b) Corresponding relationship between the number of iterations and iterative errors

Fig. 5.
Fig. 5.

Decrypted image (a) after 2000 iterations by using wrong M1. (b) Corresponding dependence of CC on iteration number.

Fig. 6.
Fig. 6.

Decrypted images after 2000 iterations by using (a) wrong wavelength and (b) wrong d1, and the dependences of CC on iteration number [(b) and (d)] corresponding to (a) and (c).

Fig. 7.
Fig. 7.

(a) 6.5% occluded ciphertext; the decrypted image (b) obtained after 2000 iterations and the dependence of CC on iteration number corresponding to (a); (d) 13% occluded ciphertext; decrypted image (e) obtained after 2000 iterations and the dependence of CC on iteration number corresponding to (d).

Fig. 8.
Fig. 8.

Noise robustness tests. Contaminated images [(a), (d)], decryption results [(b), (e)], and the correlation outputs [(c), (f)] for verification with white noise distributed within [0; α]. (a), (b), (c) α=0.01; (d), (e), (f) α=0.1.

Fig. 9.
Fig. 9.

Relationship between CC and iteration number when ρ takes different values.

Equations (10)

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U(η,ξ)=exp(j2πd1/λ)jλd1U(x,y)M1(x,y)×exp[jπ[(xη)2+(yξ)2]/λd1]dxdy,
U(η,ξ)=FrTλ[U(x,y)M1(x,y);d1].
I(μ,ν)=|FrTλ[FrTλ{FrTλ[U(x,y)M1(x,y);d1]×M2(η,ξ);d2}M3(p,q);d3]|2,
ρ=Quantity of the redundant data(Pixels)Quantity of the original image(Pixels).
Un(μ,ν)=FrTλ[FrTλ{FrTλ[Tn(x,y)M1(x,y);d1]×M2(η,ξ);d2}M3(p,q);d3].
Un(μ,ν)¯=I(μ,ν)1/2Un(μ,ν)/|Un(μ,ν)|.
Tn(x,y)¯=|FrTλ[FrTλ{FrTλ[Un(μ,ν)¯;d3]×M3*(p,q);d2}M2*(η,ξ);d1]|2,
Tn+1(x,y)=RD[(x,y);ρ]Tn(x,y)¯,
Error=[|Tn(x,y)||Tn+1(x,y)|]2.
CC=E{[UoE(Uo)][UrE(Ur)]}E{[UoE(Uo)]2}E{[UrE(Ur)]2},

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