Abstract

We present a technique of nonlinear image encryption by use of virtual optics. The image to be encrypted is superposed on a random intensity image. And this superposed image propagates through a nonlinear medium and a 4-f system with single phase key. The image is encrypted to a stationary white noise. The decryption process is sensitive to the parameters of the encryption system and the phase key in 4-f system. This sensitivity makes attackers hard to access the phase key. In nonlinear medium, optically-induced potentials, which depend on intensity of optical wave, make the superposition principle frustrated. This nonlinearity based on optically induced potentials highly improves the secrecy level of image encryption. Resistance against attacks based on the phase retrieval technique proves that it has the high secrecy level. This nonlinear image encryption based on optically induced potentials is proposed and demonstrated for the first time.

© 2011 OSA

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References

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  1. C. Barsi and J. W. Fleischer, “Digital reconstruction of optically-induced potentials,” Opt. Express 17(25), 23338–23343 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-23338 .
    [CrossRef] [PubMed]
  2. C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
    [CrossRef]
  3. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [CrossRef] [PubMed]
  4. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. 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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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-1-41 .
    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. 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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2009

2008

2007

2006

2005

2004

2002

2000

1997

1995

1978

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals 1. Steady-state,” Ferroelectrics 22(1), 949–960 (1978).
[CrossRef]

Arcos, S.

Barsi, C.

Cai, L.

Cai, L. Z.

Cao, L.

Carnicer, A.

Castro, A.

Cheng, X. C.

Dong, G. Y.

Fleischer, J. W.

Frauel, Y.

Guo, B.

He, M.

He, Q.

Javidi, B.

Jin, G.

Jing, F.

Joseph, J.

Juvells, I.

Kim, D. H.

Kim, H.

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals 1. Steady-state,” Ferroelectrics 22(1), 949–960 (1978).
[CrossRef]

Lee, W. K.

Lee, Y.

Liu, W.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals 1. Steady-state,” Ferroelectrics 22(1), 949–960 (1978).
[CrossRef]

Meng, X. F.

Montes-Usategui, M.

Naughton, T. J.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals 1. Steady-state,” Ferroelectrics 22(1), 949–960 (1978).
[CrossRef]

Peng, X.

Refregier, P.

She, W. L.

Shen, X. X.

Singh, K.

Situ, G.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals 1. Steady-state,” Ferroelectrics 22(1), 949–960 (1978).
[CrossRef]

Tan, Q.

Unnikrishnan, G.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals 1. Steady-state,” Ferroelectrics 22(1), 949–960 (1978).
[CrossRef]

Wan, W.

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[CrossRef]

Wang, X.

Wang, Y. R.

Wei, H.

Wei, X.

Xie, H.

Xu, C. C.

Xu, X. F.

Yamaguchi, I.

Yang, G.

Yang, X. L.

Yu, B.

Yu, L.

Zhang, H.

Zhang, J.

Zhang, P.

Zhang, T.

Zhao, D.

Ferroelectrics

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals 1. Steady-state,” Ferroelectrics 22(1), 949–960 (1978).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[CrossRef]

Opt. Express

W. Liu, G. Yang, and H. Xie, “A hybrid heuristic algorithm to improve known-plaintext attack on Fourier plane encryption,” Opt. Express 17(16), 13928–13938 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13928 .
[CrossRef] [PubMed]

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22462 .
[CrossRef] [PubMed]

C. Barsi and J. W. Fleischer, “Digital reconstruction of optically-induced potentials,” Opt. Express 17(25), 23338–23343 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-23338 .
[CrossRef] [PubMed]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15(16), 10253–10265 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-102532 .
[CrossRef] [PubMed]

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics,” Opt. Express 14(4), 1476–1486 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1476 .
[CrossRef] [PubMed]

X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-1-41 .
[PubMed]

H. Kim, D. H. Kim, and Y. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4912 .
[CrossRef] [PubMed]

Opt. Lett.

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]

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

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[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]

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

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33(14), 1575–1577 (2008).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Optical setup for optically-induced-potential-based image encryption system. NLM stands for nonlinear medium, RPM stands for random phase mask.

Fig. 2
Fig. 2

Encryption and decryption. (a) Lena image as the plaintext, (b)/(c) real-part/image-part of output field from the nonlinear medium in plane P1, (d)/(e) real-part/image-part of ciphertext in plane P3, (f) decrypted image with correct keys and correct parameters.

Fig. 3
Fig. 3

Decryption results with incorrect parameters. (a) /(b) /(c) the decrypted image while the parameter of γeff with a deviation of 0.0001%/0.0005%/0.001%, (d)/(e)/ (f) the decrypted image while the wavelength λ in linear process with a deviation of 0.0001%/0.0005%/0.001%.

Fig. 4
Fig. 4

(a) Dependence of CC on deviation of nonlinear coefficient γ, (b) Dependence of CC on deviation of wavelength in linear diffraction process.

Fig. 5
Fig. 5

Decryption results with noise-added phase keys in the presence and absence of the nonlinear medium. (a)/ (b)/ (c)/ (d) the decrypted image in the presence of nonlinear medium while a random noise with amplitude of 10−7/5*10−7/1*10−6/5*10−6 is superimposed on the phase mask M, (e)/ (f)/ (g)/ (h) the decrypted image in the absence of the nonlinear medium while the phase mask M a random noise with amplitude of 0.01/0.05/0.1/0.5 is superimposed on the phase mask M.

Fig. 6
Fig. 6

Nonlinearity analysis of the system. (a) ciphertext 1, (b) corresponding decrypted image with (a), (c) ciphertext 2, (d) corresponding decrypted image with (c), (e) decrypted result with the sum of the two ciphertexts with weights of 0.5, (f) linear superposition of the two individual decrypted images.

Fig. 7
Fig. 7

Resistance against known plaintext attack. (a) original ciphertext, (b) corresponding plaintext of (a), (c) attack result using ciphertext (a) by hybrid input–output algorithm, (d) another ciphertext to be test, (e) decrypted result with the retrieved phase keys, (f) decrypted result with correct keys.

Equations (10)

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

ψ z =[i 1 2nk 2 +ikΔn( | ψ | 2 )]ψ=[D+N( | ψ | 2 )]ψ,
Δn( | ψ | 2 )= 1 2 n e 3 γ eff E pv I s I s +1 ,
ψ(z+dz) e dzD e dzN( | ψ | 2 ) ψ(z).
ψ( z 1 )=ψ( z 0 ) e dzD e dz N 0 ( | ψ | 2 ) e dzD e dz N 1 ( | ψ | 2 ) e dzD e dz N m ( | ψ | 2 ) ,
g(x,y)=FT{ FT{ ψ( z 1 ) } ×exp[ j2πp(x,y) ] },
ψ( z 1 )=IFT{ IFT{ g(x,y) } ×exp[ j2πp(x,y) ] },
ψ(z) e dzD e dzN( | ψ | 2 ) ψ(z+dz).
ψ( z 0 )=ψ( z 1 ) e dzD e dz N m ( | ψ | 2 ) e dzD e dz N m1 ( | ψ | 2 ) e dzD e dz N 0 ( | ψ | 2 ) .
im(x,y)=ψ( z 0 )r(x,y).
γ= 1 2 k n e 3 γ eff E pv = π λ n e 3 γ eff E pv .

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