Abstract

Conventional double-random phase encoding is vulnerable to a chosen or known plaintext attack owing to the linearity of the system. We introduce a technique to break down this linearity with an undercover amplitude modulation in the encryption scheme. As an additional key, this operation can significantly enhance the security of the system. A series of computer simulations have shown the effectiveness of this method and its resistance against the known plaintext attack. The design and parameter choice of the amplitude modulator is also discussed.

© 2008 Optical Society of America

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References

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2007

2006

2005

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

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, Proc. SPIE 5986, 25 (2005).

2004

2003

B. Zhu, H. Zhao, and S. Liu, Optik (Jena) 114, 95 (2003).

2002

2000

1995

1982

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, 25 (2005).

Fienup, J. R.

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, 25 (2005).

Gopinathan, U.

He, M. Z.

Javidi, B.

Joseph, J.

Juvells, I.

Liu, Q.

Liu, S.

B. Zhu, H. Zhao, and S. Liu, Optik (Jena) 114, 95 (2003).

Matoba, O.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Peng, X.

Réfrégier, P.

Sheridan, J. T.

Singh, K.

Situ, G.

Unnikrishnan, G.

Wei, H.

Yang, X. L.

Yu, B.

Zhang, J.

Zhang, P.

Zhao, H.

B. Zhu, H. Zhao, and S. Liu, Optik (Jena) 114, 95 (2003).

Zhu, B.

B. Zhu, H. Zhao, and S. Liu, Optik (Jena) 114, 95 (2003).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the DRPAE with an amplitude modulator.

Fig. 2
Fig. 2

(a) Lena image to be encrypted, (b) amplitude modulator with k = 0.01 and p = 0.126 , (c) ciphertext with the AM, (d) ciphertext without the AM, (e) decrypted image from (c) with the use of D ( α , β ) , (f) decrypted image from (c) with no use of D ( α , β ) .

Fig. 3
Fig. 3

Relation between the parameters k and p of the AM and CCs for grayscale images.

Fig. 4
Fig. 4

Resistance of DRPAE against a known plaintext attack. (a) Pepper image, (b) ciphertext corresponding to (a), (c) decrypted image with the ciphertext in Fig. 2c and the retrieved phase masks obtained by using (a) and (b).

Equations (7)

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U ( α , β ) = FT { g ( x , y ) exp [ j p 1 ( x , y ) ] } exp [ j p 2 ( α , β ) ] ,
U ( α , β ) = FT { g ( x , y ) exp [ j p 1 ( x , y ) ] } exp [ j p 2 ( α , β ) ] D ( α , β ) .
D ( m , n ) = { 1 if ( m , n ) γ k if ( m , n ) γ } ,
u ( x , y ) = FT { FT { g ( x , y ) exp [ j p 1 ( x , y ) ] } exp [ j p 2 ( α , β ) ] D ( α , β ) } .
D ( m , n ) = { k if ( m , n ) γ 1 if ( m , n ) γ } .
U ( α , β ) = k FT { g ( x , y ) exp [ j p 1 ( x , y ) ] } exp [ j p 2 ( α , β ) ] .
CC ( g , g 0 ) = cov ( g , g 0 ) σ g σ g 0 ,

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