Abstract

A method for optical image hiding and for optical image encryption and hiding in the Fresnel domain via completely optical means is proposed, which encodes original object image into the encrypted image and then embeds it into host image in our modified Mach-Zehnder interferometer architecture. The modified Mach-Zehnder interferometer not only provides phase shifts to record complex amplitude of final encrypted object image on CCD plane but also introduces host image into reference path of the interferometer to hide it. The final encrypted object image is registered as interference patterns, which resemble a Fresnel diffraction pattern of the host image, and thus the secure information is imperceptible to unauthorized receivers. The method can simultaneously realize image encryption and image hiding at a high speed in pure optical system. The validity of the method and its robustness against some common attacks are investigated by numerical simulations and experiments.

© 2014 Optical Society of America

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    [CrossRef]
  31. W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
    [CrossRef]
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    [CrossRef]
  33. Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
    [CrossRef] [PubMed]

2014 (1)

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

2013 (6)

2012 (2)

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

W. Chen, X. Chen, 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]

2011 (2)

2010 (2)

2009 (2)

2008 (3)

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

Y. Zhang, B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[CrossRef] [PubMed]

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

2007 (2)

2006 (2)

2005 (2)

2003 (1)

2002 (2)

2000 (2)

1999 (1)

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

1995 (1)

Abdallah, N.

Alfalou, A.

Anderson, R. J.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Brosseau, C.

Cai, L. Z.

Chang, H. T.

Chen, L. F.

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

Chen, W.

Chen, X.

Chen, X. D.

Chen, Y. L.

C. H. Chuang, Y. L. Chen, “Steganographic optical image encryption system based on reversible data hiding and double random phase encoding,” Opt. Eng. 52(2), 028201 (2013).
[CrossRef]

Chuang, C. H.

C. H. Chuang, Y. L. Chen, “Steganographic optical image encryption system based on reversible data hiding and double random phase encoding,” Opt. Eng. 52(2), 028201 (2013).
[CrossRef]

Dong, G. Y.

Gao, Q.

Ge, F.

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

He, M. Z.

Javidi, B.

Joseph, J.

Jridi, M.

Kishk, S.

Kuhn, M. G.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Kumar, P.

Li, H.

Li, J.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Li, R.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Li, T.

Liu, J.

Liu, Q.

Liu, Q. Z.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Liu, S.

Liu, W.

Liu, Z.

Ma, K.

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Meng, X. F.

Mifune, Y.

Nomura, T.

Petitcolas, F. A. P.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Refregier, P.

Shen, X. X.

Sheppard, C. J. R.

Shi, Y.

Singh, K.

Singh, N.

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

Sinha, A.

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

Situ, G.

Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

Y. Shi, G. Situ, J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

Takai, N.

Tao, R.

Tsan, C. L.

Unnikrishnan, G.

Wang, B.

Wang, Y.

Wang, Y. R.

Wang, Y. T.

Xiao, D.

Y. S. Zhang, 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]

Xie, J. H.

Xie, Z.

Xin, Y.

Xu, X. F.

Yang, X. L.

Yu, N.

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Zang, J.

Zhang, H.

Zhang, J.

Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

Y. Shi, G. Situ, J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

Zhang, S.

Zhang, W. M.

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Zhang, Y.

Zhang, Y. S.

Y. S. Zhang, 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]

Zhao, D. M.

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

Zheng, T.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Zhu, N.

Adv. Opt. Photon. (1)

Appl. Opt. (5)

J. Opt. A, Pure Appl. Opt. (1)

Y. Shi, G. Situ, J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

Opt. Commun. (2)

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Opt. Eng. (1)

C. H. Chuang, Y. L. Chen, “Steganographic optical image encryption system based on reversible data hiding and double random phase encoding,” Opt. Eng. 52(2), 028201 (2013).
[CrossRef]

Opt. Express (5)

Opt. Lasers Eng. (2)

Y. S. Zhang, 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]

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

Opt. Lett. (12)

W. Chen, X. D. Chen, C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[CrossRef] [PubMed]

Y. Zhang, B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[CrossRef] [PubMed]

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

B. Javidi, T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[CrossRef] [PubMed]

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

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006).
[CrossRef] [PubMed]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[CrossRef] [PubMed]

J. Zang, Z. Xie, Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38(8), 1289–1291 (2013).
[CrossRef] [PubMed]

W. Liu, Z. Liu, S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38(10), 1651–1653 (2013).
[CrossRef] [PubMed]

A. Alfalou, C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010).
[CrossRef] [PubMed]

S. Kishk, B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28(3), 167–169 (2003).
[CrossRef] [PubMed]

Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

Proc. IEEE (1)

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Signal Process. (1)

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Other (2)

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Academic, 2001).

X. P. Zhang, Reversible data hiding in encrypted image,” IEEE Signal Proc. Let. 18, 255–258 (2011). http://www.sciencedirect.com/science/article/pii/S0165168413002417 - item1#item1

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Figures (12)

Fig. 1
Fig. 1

Scheme of optical image encryption and hiding. BE, beam expander; L, lens; BS, beam splitter; M, mirror; NDF, neutral density filters; R, random phase plate; PZT, piezoelectric transducer mirror; Oe, object image; Oh, host image.

Fig. 2
Fig. 2

Experimental results. (a) One of the interferograms of the host image and (b) one of the interferograms from when the hidden image has been embedded into the host image; (c) retrieved image from when the phase information ϕ h of the host image is used; and (d) the larger version of (c).

Fig. 3
Fig. 3

Interferograms after performing optical image encryption and hiding with different embedded levels and host image. (a) The interferogram when the light amplitude ratio of the object beam and reference beam is 0.00001:1; (b) the interferogram when the light amplitude ratio of the object beam and reference beam is 0.000001:1;(c) host image.

Fig. 4
Fig. 4

Results with a binary image. (a) Binary image; (b) one of three interferograms for (a) after performing optical image encryption and hiding; (c) retrieved image only using the phase information ϕ h (ξ,η) of the host image; (d) retrieved image when the phase information ϕ h (ξ,η) of the host image is not used; (e) retrieved image when the amplitude A(ξ,η) and phase information ϕ(ξ,η) are all used to recover the original image.

Fig. 5
Fig. 5

Similar results as in Fig. 4 but with a gray-level image.

Fig. 6
Fig. 6

Robustness of this method against occlusion attack. (a) One of the three interferograms cut by 25% for Fig. 5(a); (b) the corresponding retrieved object image.

Fig. 7
Fig. 7

Robustness of this method against noise attack. (a) One of the three interferograms for Fig. 5(a) distorted by zero-mean white additive Gaussian noise with a standard deviation of 0.1; (b) the corresponding retrieved object image.

Fig. 8
Fig. 8

Robustness of this method against low-pass filter attack. (a) One of the three interferograms for Fig. 5(a) filtered by a low-pass Gaussian filter with 3×3 window size and a standard deviation of 0.5; (b) the corresponding retrieved object image.

Fig. 9
Fig. 9

Robustness of this method against high-pass Gaussian filter attack. (a) One of the three interferograms for Fig. 5(a) filtered by a high-pass Gaussian filter with 3×3 window size and a standard deviation of 0.5; (b) the corresponding retrieved object image.

Fig. 10
Fig. 10

Robustness of this method against JPEG compression attack. (a) One of the three interferograms for Fig. 5(a) compressed with the compression ratio parameter q = 99%; (b) the corresponding retrieved object image.

Fig. 11
Fig. 11

Robustness of this method against rotation attack. (a) One of the three interferograms for Fig. 5(a) rotated anticlockwise by 0.2 degree; (b) the corresponding recovered object image.

Fig. 12
Fig. 12

The curves of CCs versus different intensity of some common image distortions and attacks. (a) Low-pass Gaussian filter attack; (b) high-pass Gaussian filter attack; (c) JPEG compression attack; (d) rotation attack.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ψ 0 (ξ,η)=A(ξ,η)exp(iϕ(ξ,η)) =Fr t Z 2 { Fr t Z 1 { C 1 ×O( x 0 , y 0 )×exp[i2πp( x 0 , y 0 )] }×exp[i2πq( x 1 , y 1 )] },
ψ h (ξ,η; ϕ R )= A h (ξ,η)exp[i ϕ h (ξ,η)]exp(i ϕ R ) =Fr t Z 3 { C 2 exp(i ϕ R )h( x 0 ' , y 0 ' ) } ( ϕ R =0, π 2 ,π),
I(ξ,η; ϕ R )= | ψ 0 (ξ,η)+ ψ h (ξ,η; ϕ R ) | 2 =A (ξ,η) 2 + A h (ξ,η) 2 +2A(ξ,η) A h (ξ,η)cos[ ϕ h (ξ,η)+ ϕ R -ϕ(ξ,η)].
ϕ(ξ,η)= tan 1 2I(ξ,η;π/ 2)I(ξ,η;0)I(ξ,η;π) I(ξ,η;0)I(ξ,η;π) + ϕ h (ξ,η),
A(ξ,η)= { [I(ξ,η;0)I(ξ,η;π)] 2 +[2I(ξ,η;π/ 2)I(ξ,η;0)I(ξ,η;π) ] 2 } 1/2 4 A h (ξ,η) ,
O ' ( x 0 , y 0 )=IFr t Z 1 { IFr t Z 2 { A(ξ,η)exp(jϕ(ξ,η) }×exp[i2πq( x 1 , y 1 )] }×exp[i2πp( x 0 , y 0 )],
CC= COV[O'( x 0 , y 0 ),O( x 0 , y 0 )] σ O σ O' ,

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