Abstract

In previous diffractive-imaging-based optical encryption schemes, it is impossible to totally retrieve the plaintext from a single diffraction pattern. In this paper, we proposed a new method to achieve this goal. The encryption procedure can be completed by proceeding only one exposure, and the single diffraction pattern is recorded as ciphertext. For recovering the plaintext, a novel median-filtering-based phase retrieval algorithm, including two iterative cycles, has been developed. This proposal not only extremely simplifies the encryption and decryption processes, but also facilitates the storage and transmission of the ciphertext, and its effectiveness and feasibility have been demonstrated by numerical simulations.

© 2014 Optical Society of America

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References

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    [Crossref]
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2014 (4)

2013 (4)

2012 (1)

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on coherent diffractive imaging using multiple wavelengths,” Opt. Commun. 285(3), 225–228 (2012).
[Crossref]

2011 (3)

2010 (4)

2009 (1)

2006 (3)

2005 (1)

2004 (1)

2003 (1)

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42(6), 1583–1588 (2003).
[Crossref]

2000 (1)

1997 (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

1995 (1)

Ahmad, M. A.

Alfalou, A.

Anand, A.

Arcos, S.

Barrera, J. F.

Brosseau, C.

Carnicer, A.

Chen, W.

Chen, X.

Cho, M.

Dong, T.

N. Zhou, T. Dong, and J. Wu, “Novel image encryption algorithm based on multiple-parameter discrete fractional random transform,” Opt. Commun. 283(15), 3037–3042 (2010).
[Crossref]

Gao, Q.

Gong, L.

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284(13), 3234–3242 (2011).
[Crossref]

Gong, Q.

Gopinathan, U.

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]

Guo, Q.

Javidi, B.

Joseph, J.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42(6), 1583–1588 (2003).
[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] [PubMed]

Juvells, I.

Li, H.

Li, T.

Liu, S.

Liu, W.

Liu, Z.

Mira, A.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Nishchal, N. K.

S. K. Rajput and N. K. Nishchal, “Fresnel domain nonlinear image encryption scheme based on Gerchberg-Saxton phase retrieval algorithm,” Appl. Opt. 53(3), 418–425 (2014).

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42(6), 1583–1588 (2003).
[Crossref]

Peng, X.

Pérez-Cabré, E.

Qin, Y.

Rajput, S. K.

Refregier, P.

Sheppard, C. J. R.

Sheridan, J. T.

Shi, Y.

Singh, K.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42(6), 1583–1588 (2003).
[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] [PubMed]

Situ, G.

Torroba, R.

Unnikrishnan, G.

Wang, Y.

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

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284(13), 3234–3242 (2011).
[Crossref]

Wang, Z.

Wei, H.

Wu, J.

N. Zhou, T. Dong, and J. Wu, “Novel image encryption algorithm based on multiple-parameter discrete fractional random transform,” Opt. Commun. 283(15), 3037–3042 (2010).
[Crossref]

Xu, L.

Yu, B.

Zhang, J.

Zhang, P.

Zhang, S.

Zhou, N.

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284(13), 3234–3242 (2011).
[Crossref]

N. Zhou, T. Dong, and J. Wu, “Novel image encryption algorithm based on multiple-parameter discrete fractional random transform,” Opt. Commun. 283(15), 3037–3042 (2010).
[Crossref]

Adv. Opt. Photon. (2)

Appl. Opt. (3)

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

Opt. Commun. (3)

N. Zhou, T. Dong, and J. Wu, “Novel image encryption algorithm based on multiple-parameter discrete fractional random transform,” Opt. Commun. 283(15), 3037–3042 (2010).
[Crossref]

N. Zhou, Y. Wang, and L. Gong, “Novel optical image encryption scheme based on fractional Mellin transform,” Opt. Commun. 284(13), 3234–3242 (2011).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on coherent diffractive imaging using multiple wavelengths,” Opt. Commun. 285(3), 225–228 (2012).
[Crossref]

Opt. Eng. (1)

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42(6), 1583–1588 (2003).
[Crossref]

Opt. Express (3)

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. (11)

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]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35(13), 2185–2187 (2010).
[Crossref] [PubMed]

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

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
[Crossref] [PubMed]

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] [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]

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

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30(13), 1644–1646 (2005).
[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. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[Crossref] [PubMed]

W. Liu, Z. Liu, and 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]

Phys. Today (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 A schematic setup for the proposed optical image encryption based on coherent diffractive imaging.
Fig. 2
Fig. 2 (a)The original image; (b) the ciphertext(diffraction pattern); (c) the relationship between CC values and iterative number by use of Chen’s method; (d) the corresponding decrypted plaintext after 1000 times.
Fig. 3
Fig. 3 Flow chart for illustrating cycle A.
Fig. 4
Fig. 4 Flow chart for illustrating cycle B.
Fig. 5
Fig. 5 (a) The phase-only masks (a) M1, (b) M2 and (c) M3.
Fig. 6
Fig. 6 The decrypted image (a) with our proposal and the corresponding dependence of CC on iteration number (b); the dependence of CC on iteration number corresponding to the first iterative procedure (c) and the second iterative procedure (d).
Fig. 7
Fig. 7 The decrypted image (a) after 1000 iterations with incorrect M1 and the corresponding dependence of CC on iteration number (b); the decrypted image (c) after 1000 iterations with incorrect d1 and the corresponding dependence of CC on iteration number (d); the decrypted image (e) after 1000 iterations with incorrect wavelength and the corresponding dependence of CC on iteration number (f).
Fig. 8
Fig. 8 The contaminated ciphertext (a), the decryption results (b), and the corresponding dependence of CC value on the iteration number; (d) 10% occluded ciphertext; (e) the decrypted image obtained after 1000 iterations and (f) the dependence of CC on iteration number corresponding to (d).

Equations (13)

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U( η,ξ )= exp( j2π d 1 /λ ) jλ d 1 U( x,y ) M 1 ( x,y )exp[ jπ[ ( x-η ) 2 + ( y-ξ ) 2 ] / λ d 1 ]dxdy
U( η,ξ ) =FrT λ [ U( x,y ) M 1 ( x,y );λ; d 1 ]
I( μ,ν )= | FrT λ [ FrT λ { FrT λ [ U( x,y ) M 1 ( x,y ); d 1 ] M 2 ( η,ξ ); d 2 } M 3 ( p,q ); d 3 ] | 2
CC= E{ [ U o E( U o ) ][ U r E( U r ) ] } E{ [ U o E( U o ) ] 2 }E{ [ U r E( U r ) ] 2 }
U n ( μ,ν ) =FrT λ [ FrT λ { FrT λ [ T n ( x,y ) M 1 ( x,y ); d 1 ] M 2 ( η,ξ ); d 2 } M 3 ( p,q ); d 3 ].
U n ( μ,ν ) ¯ =I ( μ,ν ) 1/2 U n ( μ,ν ) / | U n ( μ,ν ) | .
T n ( x,y ) ¯ = | FrT λ [ FrT λ { FrT λ [ U n ( μ,ν ) ¯ ; d 3 ] M 3 ( p,q ); d 2 } M 2 ( η,ξ ); d 1 ] | 2 ,
T n ( x,y ) ¯ =LPFilter[ T n ( x,y ) ¯ ],
Error 1 = [ | T n ( x,y ) || T n1 ( x,y ) | ] 2 ,
U n ( μ,ν ) =FrT λ [ FrT λ { FrT λ [ T n ( x,y ) M 1 ( x,y ); d 1 ] M 2 ( η,ξ ); d 2 } M 3 ( p,q ); d 3 ],
U n ( μ,ν ) ¯ =I ( μ,ν ) 1/2 U n ( μ,ν ) / | U n ( μ,ν ) | .
T n ( x,y ) ¯ = | FrT λ [ FrT λ { FrT λ [ U n ( μ,ν ) ¯ ; d 3 ] M 3 ( p,q ); d 2 } M 2 ( η,ξ ); d 1 ] | 2 .
Error 2 = [ | T n ( x,y ) ¯ || T n-1 ( x,y ) ¯ | ] 2

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