Abstract

A new (to our knowledge) method is proposed in this paper for color image hiding and extracting using the phase retrieval algorithm in the fractional Fourier transform (FRFT) domain and Arnold transform (ART). Based on a cascaded phase iterative FRFT algorithm, the three channels (R, G, and B) of the secret color image permuted by ART are encrypted. Then the encoded information is embedded in the blue channel (B channel) of the enlarged color host image. Using the security enhanced encryption method, not only the random phase mask and the wavelength but also the transform parameters of ART and FRFT are provided as additional keys for decryption. It is shown that the security of information hiding will be enhanced. Computer simulations are performed to show the hiding capacity of the proposed system. Numerical results are presented to verify the validity and efficiency of the proposed method.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2011 (1)

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

2009 (2)

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

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, 22462–22473 (2009).
[CrossRef]

2008 (1)

F. Ge, L. Chen, and D. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281, 4254–4260 (2008).
[CrossRef]

2007 (4)

Z. Liu and S. Liu, “Double image encryption based on iterative fractional fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

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

L. Chen and D. Zhao, “Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography,” Opt. Express 15, 16080–16089 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (2)

G. Situ and J. Zhang, “Image hiding with computer-generated phase codes for optical authentication,” Opt. Commun. 245, 55–65 (2005).
[CrossRef]

H. T. Chang and C. L. Tsan, “Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain,” Appl. Opt. 44, 6211–6219 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (3)

2000 (3)

1997 (1)

B. Javidi, “Security information with optical technology,” Phys. Today 50, 27–32 (1997).
[CrossRef]

1996 (1)

1995 (1)

1982 (1)

Cai, L.

Cai, L. Z.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Cao, L.

Chang, H. T.

Chen, H.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Chen, J. G.

X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
[CrossRef]

Chen, L.

Chen, W.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Cui, Z.

X. Peng, Z. Cui, and T. Tan, “Information encryption with virtual-optics imaging system,” Opt. Commun. 212, 235–245 (2002).
[CrossRef]

Dong, G.

Dong, G. Y.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Dorsch, R.

Fienup, J. R.

Ge, F.

F. Ge, L. Chen, and D. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281, 4254–4260 (2008).
[CrossRef]

He, M.

He, Q.

Javidi, B.

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).
[CrossRef] [PubMed]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

B. Javidi, “Security information with optical technology,” Phys. Today 50, 27–32 (1997).
[CrossRef]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef] [PubMed]

Jin, G.

Joseph, J.

Kishk, S.

Kreske, K.

Kuo, C. J.

Li, P.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Li, Y.

Lin, C.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Liu, S.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Liu, T.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Liu, Z.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Lu, W. C.

Mendlovic, D.

Meng, X.

Meng, X. F.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Nomura, T.

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

Peng, X.

X. Peng, Z. Cui, and T. Tan, “Information encryption with virtual-optics imaging system,” Opt. Commun. 212, 235–245 (2002).
[CrossRef]

Quan, C.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Refregier, P.

Rosen, J.

Shen, X.

Shen, X. X.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Shi, Y.

Singh, K.

Situ, G.

Tan, Q.

Tan, T.

X. Peng, Z. Cui, and T. Tan, “Information encryption with virtual-optics imaging system,” Opt. Commun. 212, 235–245 (2002).
[CrossRef]

Tay, C. J.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Tsan, C. L.

Unnikrishnan, G.

Xu, L.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Xu, X. F.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Yang, X.

Yang, X. L.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Zalevsky, Z.

Zhang, H.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Zhang, J.

Zhao, D.

Zhou, X.

X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
[CrossRef]

Appl. Opt. (6)

J. Mod. Opt. (1)

X. Zhou and J. G. Chen, “Information hiding based on double-random phase encoding technology,” J. Mod. Opt. 53, 1777–1783 (2006).
[CrossRef]

Opt. Commun. (7)

F. Ge, L. Chen, and D. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281, 4254–4260 (2008).
[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

X. Peng, Z. Cui, and T. Tan, “Information encryption with virtual-optics imaging system,” Opt. Commun. 212, 235–245 (2002).
[CrossRef]

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

G. Situ and J. Zhang, “Image hiding with computer-generated phase codes for optical authentication,” Opt. Commun. 245, 55–65 (2005).
[CrossRef]

Opt. Eng. (1)

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Phys. Today (1)

B. Javidi, “Security information with optical technology,” Phys. Today 50, 27–32 (1997).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Numerical experimental diagram of the proposed method: (a) image encryption, (b) the optical realization of the encryption and extraction.

Fig. 2
Fig. 2

(a) Host image, (b) image to be hidden, (c) blue channel of the host image, (d) RPM2.

Fig. 3
Fig. 3

Results after ART permutation with iterative number equal to 5: (a) red channel, (b) green channel, (c) blue channel. Phase components of the encoded results by phase iterative algorithm: (d) red channel, (e) green channel, (f) blue channel.

Fig. 4
Fig. 4

MSE for the R, G, and B channels of the recovered hidden image and those of the original secret image versus number of iterations.

Fig. 5
Fig. 5

(a) Watermarked host image with α = 0.01 ; decrypted result with (b) all correct keys, (c) wrong phase key RPM2, (d) ART iterative number R = B = 5 , G = 20 (wrong), (e)  R = 5 , B = G = 20 , (f)  R = G = B = 20 .

Fig. 6
Fig. 6

Effect of occlusion: (a) watermarked image occlusion, with the image recovered for occlusions of sizes (b) 25%, (c) 40%, and (d) 70%.

Fig. 7
Fig. 7

Noise attack: the watermarked host image with (a) Gaussian noise, (b) salt and pepper noise; (c) recovered result from (a); (d) recovered hidden result from (b).

Tables (1)

Tables Icon

Table 1 MSE for the Decrypted Results

Equations (9)

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( x y ) = ( 1 1 1 2 ) ( x y ) ( mod N ) ,
c ( x , y ) = g k ( x , y ) e i R k ( x , y ) = F p 2 { F p 1 { f R ( x , y ) · φ k ( x , y ) } · h ( u , v ) } ,
g k ( x , y ) = P [ c ( x , y ) ] = g ( x , y ) e i R k ( x , y ) ,
o ( x , y ) = f k ( x , y ) e i θ k ( x , y ) = F p 1 { F p 2 { g k ( x , y ) } · h * ( u , v ) } ,
f R ( x , y ) · φ k + 1 ( x , y ) = P [ o ( x , y ) ] = f R ( x , y ) e i θ k ( x , y ) ,
MSE = 1 M N x = 1 N y = 1 M [ I ( x , y ) I k ( x , y ) ] 2 ,
E i ( 2 m 1 , 2 n - 1 ) = g i ( m , n ) , E i ( 2 m 1 , 2 n ) = g i ( m , n ) , E i ( 2 m , 2 n 1 ) = g i ( m , n ) , E i ( 2 m , 2 n ) = g i ( m , n ) ,
E B ( 2 m - 1 , 2 n 1 ) = E B ( 2 m 1 , 2 n 1 ) + α · R k ( m , n ) , E B ( 2 m 1 , 2 n ) = E B ( 2 m 1 , 2 n ) + α · G k ( m , n ) , E B ( 2 m , 2 n 1 ) = E B ( 2 m , 2 n 1 ) + α · B k ( m , n ) , E B ( 2 m , 2 n ) = E B ( 2 m , 2 n ) ,
α R k ( m , n ) = E B ( 2 m - 1 , 2 n 1 ) - E B ( 2 m , 2 n ) , α G k ( m , n ) = E B ( 2 m 1 , 2 n ) E B ( 2 m , 2 n ) , α B k ( m , n ) = E B ( 2 m , 2 n 1 ) E B ( 2 m , 2 n ) .

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