Abstract

Security of the conventional Fourier-based double-random-phase encryption (DRPE) technique is prone to impulse attacks, as the Fourier transform (FT) of a delta function results in a unity function. To negate such an attack, the phase factors of the lenses are modified by multiplying these with random-phase functions. Owing to this modification of the FT as a result of the randomized lens phase function, a modified FT (MFTLR) gives the random output for a delta function input. Employing MFTLR in the DRPE technique enhances the security features and makes the encryption system safer from the impulse attack. Numerical and experimental results are given for the validation of the proposed technique.

© 2009 Optical Society of America

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References

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B.Javidi, ed., Optical and Digital Techniques for Information Security (Springer-Verlag, 2005).
[CrossRef]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, Proc. SPIE 5986, 598603 (2005).
[CrossRef]

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, Opt. Lett. 30, 1644 (2005).
[CrossRef] [PubMed]

2003

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

2000

1998

1995

Arcos, S.

Cai, L. Z.

Carnicer, A.

Castro, A.

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, Opt. Express 15, 10253 (2007).
[CrossRef] [PubMed]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, Proc. SPIE 5986, 598603 (2005).
[CrossRef]

Cheng, X. C.

Dong, G. Y.

Feng, S.

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, Proc. SPIE 6837, 683703 (2007).
[CrossRef]

Frauel, Y.

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, Opt. Express 15, 10253 (2007).
[CrossRef] [PubMed]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, Proc. SPIE 5986, 598603 (2005).
[CrossRef]

Gao, B. Z.

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, Proc. SPIE 6837, 683703 (2007).
[CrossRef]

Gopinathan, U.

Javidi, B.

Jing, F.

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

Joseph, J.

Juvells, I.

Liu, H.

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, Proc. SPIE 6837, 683703 (2007).
[CrossRef]

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

Mao, H.

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

Meng, X. F.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Peng, X.

Poon, T. C.

T. C. Poon, Optical Scanning Holography With MATLAB (Springer, 2007).
[CrossRef]

Refregier, P.

Shen, X. X.

Sheridan, J. T.

Singh, K.

Situ, G.

Unnikrishnan, G.

Wang, Y. R.

Wei, H.

Wei, X.

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

Xu, X. F.

Yu, B.

Zhang, H.

Zhang, P.

Zhao, D.

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

Zhu, Q.

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

Appl. Opt.

Opt. Commun.

D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, Opt. Commun. 227, 213 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, Proc. SPIE 6837, 683703 (2007).
[CrossRef]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, Proc. SPIE 5986, 598603 (2005).
[CrossRef]

Other

T. C. Poon, Optical Scanning Holography With MATLAB (Springer, 2007).
[CrossRef]

B.Javidi, ed., Optical and Digital Techniques for Information Security (Springer-Verlag, 2005).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Randomized lens-phase-function-based Fourier transform, i.e., MFT LR of an impulse function.

Fig. 2
Fig. 2

Schematic for the proposed scheme.

Fig. 3
Fig. 3

(a) Image of LENA, (b) encrypted image with the proposed technique, (c) decrypted image.

Fig. 4
Fig. 4

Decryption under different conditions. (a) Decryption with the Fourier plane mask obtained from the FT of the impulse encrypted image, (b) decryption with correct mask R 2 and FT, and (c) decryption with R 2 and MFT LR b when MFT LR a is replaced with FT.

Fig. 5
Fig. 5

Experimental setup for the proposed scheme. BE: beam expander; BS: beam splitter; M: mirror; I: image, R 1 and R 2 : random phase masks; L Ra and L Rb : lenses with randomized phase functions; L 1 : imaging lens; and Li N b O 3 : photorefractive crystal.

Fig. 6
Fig. 6

Experimental results (a) image to be encrypted, (b) encrypted image, (c) correctly decrypted image, and (d) decryption with lateral shift of 0.01 mm in lens L Rb and (e) decrypted image with lateral shift of 0.01 mm in lens L Ra .

Equations (10)

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E ( x , y ) = FT 1 [ ( FT [ I ( x , y ) R 1 ( x , y ) ] ) R 2 ( u , v ) ] .
E ( x , y ) = FT 1 [ ( FT [ δ ( 0 , 0 ) R 1 ( x , y ) ] ) R 2 ( u , v ) ] .
E 1 ( x , y ) = FT 1 [ ( FT [ I 1 ( x , y ) R 1 ( x , y ) ] ) R 2 ( u , v ) ] ,
E 2 ( x , y ) = FT 1 [ ( FT [ I 2 ( x , y ) R 1 ( x , y ) ] ) R 2 ( u , v ) ] .
E 1 ( x , y ) E 2 ( x , y ) = FT 1 [ ( FT [ δ ( 0 , 0 ) R 1 ( x , y ) ] ) R 2 ( u , v ) ] .
ψ m ( x , y ; f ) = { [ t ( x , y ) h ( x , y ; f ) ] [ ϕ modified ( x , y ) ] } h ( x , y ; f ) ,
ψ m ( u , v ) = MFT LR [ t ( x , y ) ] .
E ( x , y ) = MFT LR b [ ( MFT LR a [ I ( x , y ) R 1 ( x , y ) ] ) R 2 ( u , v ) ] .
E ( x , y ) = MFT LR b [ ( MFT LR a [ δ ( 0 , 0 ) R 1 ( x , y ) ] ) R 2 ( u , v ) ] .
E ( x , y ) = MFT LR b [ ( MFT LR a [ { I 1 ( x , y ) I 2 ( x , y ) } R 1 ( x , y ) ] ) R 2 ( u , v ) ] .

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