Abstract

An improved encoding approach to multiple-image optical encryption based on a cascaded phase retrieval algorithm (CPRA) is proposed. The system consists of several stages of a standard 4-f correlator, in which the keys are not only the phase mask pairs produced by CPRA but also the phase distribution of the output plane of the front stage. The security and the capacity of the system are also discussed. Results indicate that the system can resist known-plaintext attack to some extent, and the encrypted capacity is considerably enhanced. Computer simulations have proved the validity of the proposed idea. The system can be implemented using a pure optical architecture.

© 2009 Optical Society of America

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References

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2009 (2)

2008 (4)

2007 (6)

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane new approaches and critical analysis,” J. Opt. A: Pure and Appl. Opt. 9, 73-80 (2007).
[CrossRef]

X. Meng, L. Cai, and Y. Wang, “Hierarchical optical image encryption based on cascaded phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070-1075(2007).
[CrossRef]

A. Alkholidi, A. Alfalou, and H. Haman, “A new approach for optical colored image compression using the JPEG standards,” Signal Process. 87, 569-583 (2007).
[CrossRef]

B. M. Hennelly, T. J. Naughton, J. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060-1062 (2007).
[CrossRef] [PubMed]

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

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46, 5257-5262 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

2004 (1)

2003 (1)

2002 (1)

2000 (2)

1995 (1)

1993 (1)

1982 (1)

Aflalou, A.

A. Alkholidi, A. Cottour, A. Aflalou, H. Hamam, and G. Keryer, “Real-time optical 2D wavelet transform based on the JPEG2000 standards,” Eur. Phys. J. Appl. Phys. 44, 261-272(2008).
[CrossRef]

Alam, M. S.

Alfalou, A.

A. Alkholidi, A. Alfalou, and H. Haman, “A new approach for optical colored image compression using the JPEG standards,” Signal Process. 87, 569-583 (2007).
[CrossRef]

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane new approaches and critical analysis,” J. Opt. A: Pure and Appl. Opt. 9, 73-80 (2007).
[CrossRef]

Alkholidi, A.

A. Alkholidi, A. Cottour, A. Aflalou, H. Hamam, and G. Keryer, “Real-time optical 2D wavelet transform based on the JPEG2000 standards,” Eur. Phys. J. Appl. Phys. 44, 261-272(2008).
[CrossRef]

A. Alkholidi, A. Alfalou, and H. Haman, “A new approach for optical colored image compression using the JPEG standards,” Signal Process. 87, 569-583 (2007).
[CrossRef]

Cai, L.

X. Meng, L. Cai, and Y. Wang, “Hierarchical optical image encryption based on cascaded phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070-1075(2007).
[CrossRef]

X. Meng, L. Cai, X. Yang, X. Shen, and G. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289-3297(2006).
[CrossRef] [PubMed]

Chang, H. T.

Chung, P. S.

Cottour, A.

A. Alkholidi, A. Cottour, A. Aflalou, H. Hamam, and G. Keryer, “Real-time optical 2D wavelet transform based on the JPEG2000 standards,” Eur. Phys. J. Appl. Phys. 44, 261-272(2008).
[CrossRef]

Dobson, K.

Doh, K.

Doh, K. B.

Dong, G.

Dowling, T.

Fienup, J. R.

Gopinathan, U.

Hamam, H.

A. Alkholidi, A. Cottour, A. Aflalou, H. Hamam, and G. Keryer, “Real-time optical 2D wavelet transform based on the JPEG2000 standards,” Eur. Phys. J. Appl. Phys. 44, 261-272(2008).
[CrossRef]

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane new approaches and critical analysis,” J. Opt. A: Pure and Appl. Opt. 9, 73-80 (2007).
[CrossRef]

Haman, H.

A. Alkholidi, A. Alfalou, and H. Haman, “A new approach for optical colored image compression using the JPEG standards,” Signal Process. 87, 569-583 (2007).
[CrossRef]

Hennelly, B. M.

Javidi, B.

Joseph, J.

Kelly, D. P.

Keryer, G.

A. Alkholidi, A. Cottour, A. Aflalou, H. Hamam, and G. Keryer, “Real-time optical 2D wavelet transform based on the JPEG2000 standards,” Eur. Phys. J. Appl. Phys. 44, 261-272(2008).
[CrossRef]

Kim, T.

Kreske, K.

Kuo, C. J.

Li, X. F.

Li, Y.

Lu, W. C.

Lu, X.

McDonald, J.

Meng, X.

X. Meng, L. Cai, and Y. Wang, “Hierarchical optical image encryption based on cascaded phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070-1075(2007).
[CrossRef]

X. Meng, L. Cai, X. Yang, X. Shen, and G. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289-3297(2006).
[CrossRef] [PubMed]

Monaghan, D. S.

Naughton, T. J.

Peng, X.

Poon, T. -C.

Poon, T.-C

Refregier, P.

Rosen, J.

Shen, X.

Sheridan, J. T.

Shi, Y.

Singh, K.

Situ, G.

Soualmi, S.

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane new approaches and critical analysis,” J. Opt. A: Pure and Appl. Opt. 9, 73-80 (2007).
[CrossRef]

Unnikrishnan, G.

Wang, S. W.

Wang, Y.

X. Meng, L. Cai, and Y. Wang, “Hierarchical optical image encryption based on cascaded phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070-1075(2007).
[CrossRef]

Wei, H.

Xie, J.

Yang, X.

Yu, B.

Yuan, S.

Zhang, J.

Zhang, P.

Zhou, X.

Appl. Opt. (8)

Eur. Phys. J. Appl. Phys. (1)

A. Alkholidi, A. Cottour, A. Aflalou, H. Hamam, and G. Keryer, “Real-time optical 2D wavelet transform based on the JPEG2000 standards,” Eur. Phys. J. Appl. Phys. 44, 261-272(2008).
[CrossRef]

J. Opt. A: Pure and Appl. Opt. (1)

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane new approaches and critical analysis,” J. Opt. A: Pure and Appl. Opt. 9, 73-80 (2007).
[CrossRef]

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

X. Meng, L. Cai, and Y. Wang, “Hierarchical optical image encryption based on cascaded phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070-1075(2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Opt. Lett. (9)

Signal Process. (1)

A. Alkholidi, A. Alfalou, and H. Haman, “A new approach for optical colored image compression using the JPEG standards,” Signal Process. 87, 569-583 (2007).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Architecture of optical encryption system based on a 4 - f correlator.

Fig. 2
Fig. 2

(a) Lena, (b) baboon, (c) the real part of RPM1, and (d) the real part of RPM2.

Fig. 3
Fig. 3

Variation of CC with iterative number.

Fig. 4
Fig. 4

Architecture of the multiple-image optical encryption system.

Fig. 5
Fig. 5

(a) Input gray image; (b), (c), (d) the target gray images.

Fig. 6
Fig. 6

(a), (b), (c) Decrypted gray images; (d) the ultimate approximate gray image.

Fig. 7
Fig. 7

(a) Input binary image; (b), (c), (d) the target binary images.

Fig. 8
Fig. 8

(a), (b), (c) Decrypted binary images; (d) the ultimate approximate binary image.

Fig. 9
Fig. 9

CC variation of the gray and the binary images.

Equations (8)

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g k ( x , y ) · exp [ i ϕ k ( x , y ) ] = FT 1 ( F T { f ( x , y ) exp [ i θ k ( x , y ) ] } × exp [ i φ k ( u , v ) ] ) ,
φ k + 1 ( u , v ) = angle ( FT { g ( x , y ) exp [ i ϕ k ( x , y ) ] } FT { f ( x , y ) exp [ i θ k ( x , y ) ] } ) ,
θ k + 1 ( x , y ) = angle [ FT 1 ( FT { g ( x , y ) exp [ i ϕ k ( x , y ) ] } × exp [ i φ k + 1 ( u , v ) ] ) ] ,
CC = cov [ g ( x , y ) , g k ( x , y ) ] σ g σ g k ,
g 0 n + 1 k exp ( i ϕ n ) = FT 1 { FT [ g 0 n k exp ( i θ n ) ] exp ( i φ n ) } .
g 0 n + 1 k exp ( i ϕ n ) = FT 1 { FT [ g 0 n k exp ( i ϕ n 1 ) × exp ( i ϕ n 1 ) exp ( i θ n ) ] exp ( i φ n ) } .
g 0 n + 1 k exp ( i ϕ n ) = FT 1 [ FT { g 0 n k exp ( i ϕ n 1 ) × exp [ i ( θ n ϕ n 1 ) ] } exp ( i φ n ) ] .
g 0 n k exp i ( ϕ n 1 ) = FT 1 { FT [ g 0 n + 1 k exp ( i ϕ n ) ] × exp ( i φ n ) } exp [ i ( θ n ϕ n 1 ) ] .

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