Abstract

Conventional double random phase encoding (DRPE) encrypts plaintext to white noise-like ciphertext which may attract attention of eavesdroppers, and recent research reported that DRPE is vulnerable to various attacks. Here we propose a security enhanced optical encryption system that can hide the existence of secret information by watermarking. The plaintext is encrypted using iterative fractional Fourier transform with random phase key, and ciphertext is randomly permuted with permutation key before watermarking. Cryptanalysis shows that linearity of the security system has been broken and the permutation key prevent the attacker from accessing the ciphertext in various attacks. A series of simulations have shown the effectiveness of this system and the security strength is enhanced for invisibility, nonlinearity and resistance against attacks.

© 2009 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (1)

2008 (3)

2007 (3)

2006 (5)

2005 (1)

2004 (1)

2003 (2)

2002 (2)

2000 (4)

1995 (2)

1992 (1)

G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. Consum. Electron. 38(1), 18–34 (1992).
[CrossRef]

1982 (1)

Arcos, S.

Cai, L. Z.

Carnicer, A.

Castro, A.

Cheng, X. C.

Dong, G. Y.

Dowling, T.

Fienup, J. R.

Frauel, Y.

Glückstad, J.

Gopinathan, U.

Hennelly, B.

Hennelly, B. M.

Javidi, B.

Joseph, J.

Juvells, I.

Kishk, S.

Mait, J. N.

Meng, X. F.

Mifune, Y.

Mogensen, P. C.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Nomura, T.

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[CrossRef] [PubMed]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
[CrossRef]

Peng, X.

Réfrégier, Ph.

Shen, X. X.

Sheridan, J. T.

Shi, Y.

Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

Y. Shi, G. Situ, and J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

Singh, K.

Situ, G.

Takai, N.

Unnikrishnan, G.

Wallace, G. K.

G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. Consum. Electron. 38(1), 18–34 (1992).
[CrossRef]

Wang, Y. R.

Wei, H.

Xu, X. F.

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]

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(2), 257–263 (2007).
[CrossRef]

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(2), 257–263 (2007).
[CrossRef]

X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45(14), 3289–3297 (2006).
[CrossRef] [PubMed]

Yu, B.

Zhang, H.

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]

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(2), 257–263 (2007).
[CrossRef]

Zhang, J.

Zhang, P.

Acta Opt. Sin. (1)

H. Wei and X. Peng, “Known-Plaintext Attack on Optical Cryptosystem Based on Projection-Onto-Constraint-Sets Algorithm and a 4f Correlator,” Acta Opt. Sin. 28(3), 429–434 (2008).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Consum. Electron. (1)

G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. Consum. Electron. 38(1), 18–34 (1992).
[CrossRef]

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

Y. Shi, G. Situ, and J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

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(2), 257–263 (2007).
[CrossRef]

Opt. Eng. (1)

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (12)

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]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31(22), 3261–3263 (2006).
[CrossRef] [PubMed]

Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

Ph. Réfrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[CrossRef] [PubMed]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[CrossRef] [PubMed]

P. C. Mogensen and J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25(8), 566–568 (2000).
[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]

S. Kishk and B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28(3), 167–169 (2003).
[CrossRef] [PubMed]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28(4), 269–271 (2003).
[CrossRef] [PubMed]

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

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]

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]

Other (5)

B. Schneier, Applied Cryptography, 2nd ed. (John Wiley & Sons, 1996).

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

http://www.mathworks.com

http://en.wikipedia.org/wiki/Kerckhoffs'_principle

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (11)

Fig. 1
Fig. 1

System structure of optical encryption and hiding system. VPM, virtual phase mask.

Fig. 2
Fig. 2

Flow chart of iterative phase retrieval algorithm for encryption.

Fig. 3
Fig. 3

(a) Plaintext, (b)overt image, (c)ciphertext, (d)permuted ciphertext, (e)watermarked image, (f)decryption result with correct keys.

Fig. 4
Fig. 4

Convergence curves of MSE in encryption.

Fig. 5
Fig. 5

(a)–(c) are decryption results using 2, 4 and 8 quantization level phase keys, respectively.

Fig. 6
Fig. 6

MSE evolution curves of 2, 4, 8, 16 and 32 quantization level phase keys.

Fig. 7
Fig. 7

Watermarked images attacks and corresponding decryption results.(a) JPEG compression, (b) noise, (c) occlusion, (d) (e) and (f) are decryption results using (a) (b) and (c).

Fig. 8
Fig. 8

(a) (b) Ciphertext 1 and 2, (c) (d) individual decryption results 1 and 2, (e) decryption result with sum of linear combination of two ciphertext, (f) sum of individual decryption results 1 and 2.

Fig. 9
Fig. 9

Amplitude and phase evolutions in KPA. (a) MSE curve, (b) CC curve.

Fig. 10
Fig. 10

Simulation results for known-plaintext attack. (a)attack result for original ciphertext, (b)another plaintext for phase key test, (c)attack result with cracked phase key.

Fig. 11
Fig. 11

Simulation results for chosen-plaintext attack. (a)attack result with cracked phase key in the absence of permutation,(b) another phase key obtained when permutation is applied, (c)attack result using Fig. 8(b).

Tables (1)

Tables Icon

Table 1 The MSE values of decryption results

Equations (12)

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p ( x , y ) = | F -P 1 { F -P 2 [ o ( x , y ) e i c ( x , y ) ] k * ( u , v ) } | ,
o m ( x , y ) e i c m ( x , y ) = F P 2 { F P 1 [ p ( x , y ) e i θ m ( x , y ) ] k ( u , v ) } .
p m ( x , y ) e i θ m ( x , y ) = F -P 1 { F -P 2 [ o ( x , y ) e i c m ( x , y ) ] k * ( u , v ) } .
MSE = 1 M × N i = 1 M j = 1 N [ p m ( i , j ) p ( i , j ) ] 2 ,
o ' ( x , y ) = o ( x , y ) + α P [ c m ( x , y ) ] ,
S { α g + β h } = α S { g } + β S { h } .
o ( x , y ) e i c m ( x , y ) = F P 2 { F P 1 [ p ( x , y ) e i θ m ( x , y ) ] k ( u , v ) } .
c m ( x , y ) = i ln [ o ( x , y ) ] i ln { F P 2 { F P 1 [ p ( x , y ) e i θ m ( x , y ) ] k ( u , v ) } } .
k crack ( u , v ) = F P 1 [ p ( x , y ) e i θ trial ( x , y ) ] / F P 2 [ o ( x , y ) e i c m ( x , y ) ] ,
β δ ( u , v ) = F P 1 [ δ ( x , y ) e i θ m ( x , y ) ] k ( u , v ) = e i θ m ( 0 , 0 ) k ( u , v ) .
k ( u , v ) = e i θ m ( 0 , 0 ) β δ ( u , v ) = e i θ m ( 0 , 0 ) F P 2 [ o ( x , y ) e i c δ ( x , y ) ] ,
p ( x , y ) = | F -P 1 { β ( u , v ) k * ( u , v ) } | .

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