Abstract

We demonstrate in this paper that the traditional double random phase encoding (DRPE) technique is vulnerable to ciphertext-only attack (COA). In this method, an unauthorized user (or say attacker) is assumed to be able to retrieve the corresponding plaintext from the only ciphertext under some certain condition. The proposed scheme mainly relies on a hybrid iterative phase retrieval (HIPR) algorithm, which combines various phase retrieval algorithms. With an estimation of the number of nonzero pixels (NNP) in the original plaintext, an attacker could recover the plaintext in a large extent. The simulation results show that this method is feasible and validate.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (1)

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

2013 (1)

M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51(3), 317–324 (2013).
[Crossref]

2012 (1)

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44(5), 1203–1206 (2012).
[Crossref]

2011 (1)

Z. Liu, L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49(4), 542–546 (2011).
[Crossref]

2010 (3)

2009 (5)

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282(4), 518–522 (2009).
[Crossref]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282(4), 482–492 (2009).
[Crossref]

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A, Pure Appl. Opt. 11(7), 075402 (2009).
[Crossref]

2008 (2)

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281(23), 5745–5749 (2008).
[Crossref]

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[Crossref] [PubMed]

2007 (5)

2006 (6)

2005 (3)

2004 (3)

2002 (1)

2001 (1)

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187(1), 57–63 (2001).
[Crossref]

2000 (4)

G. Unnikrishnan and K. Singh, “Double random fractional Fourier-domain encoding for optical security,” Opt. Eng. 39(11), 2853–2859 (2000).
[Crossref]

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

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]

B. Zhu, S. Liu, and Q. Ran, “Optical image encryption based on multifractional Fourier transforms,” Opt. Lett. 25(16), 1159–1161 (2000).
[Crossref] [PubMed]

1999 (2)

1995 (1)

1990 (1)

1982 (2)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[Crossref] [PubMed]

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. 30(2), 140–154 (1982).
[Crossref]

Abuturab, M. R.

M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51(3), 317–324 (2013).
[Crossref]

Ahmad, M. A.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Arcos, S.

Bauschke, H. H.

Carnicer, A.

Castro, A.

Chen, L.

Chen, W.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

W. Chen, X. Chen, and C. J. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[Crossref] [PubMed]

Chen, X.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

W. Chen, X. Chen, and C. J. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[Crossref] [PubMed]

Clemente, P.

Combettes, P. L.

Crimmins, T.

Dai, J.

Z. Liu, L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49(4), 542–546 (2011).
[Crossref]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282(4), 518–522 (2009).
[Crossref]

Durán, V.

Fienup, J.

Fienup, J. R.

Frauel, Y.

Gopinathan, U.

Hayes, M. H.

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. 30(2), 140–154 (1982).
[Crossref]

He, H.

He, W.

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44(5), 1203–1206 (2012).
[Crossref]

Javidi, B.

Joseph, J.

Juvells, I.

Koch, C. T.

Lancis, J.

Li, H.

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281(23), 5745–5749 (2008).
[Crossref]

Li, Q.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Lin, C.

Z. Liu, L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49(4), 542–546 (2011).
[Crossref]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

Liu, S.

Z. Liu, L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49(4), 542–546 (2011).
[Crossref]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282(4), 518–522 (2009).
[Crossref]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[Crossref]

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187(1), 57–63 (2001).
[Crossref]

B. Zhu, S. Liu, and Q. Ran, “Optical image encryption based on multifractional Fourier transforms,” Opt. Lett. 25(16), 1159–1161 (2000).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49(4), 542–546 (2011).
[Crossref]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282(4), 518–522 (2009).
[Crossref]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[Crossref]

Luke, D. R.

Matoba, O.

Meng, X.

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44(5), 1203–1206 (2012).
[Crossref]

Millan, M. S.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Nomura, T.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

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

Oszlányi, G.

G. Oszlányi and A. Süto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. A 60(2), 134–141 (2004).
[Crossref] [PubMed]

Peng, X.

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44(5), 1203–1206 (2012).
[Crossref]

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A, Pure Appl. Opt. 11(7), 075402 (2009).
[Crossref]

H. Tang, X. Peng, and J. Tian, “Ciphertext-only attack on double random phase encoding optical encryption system,” Wuli Xuebao 56(5), 2629–2636 (2007).

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]

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]

Perez-Cabre, E.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Qin, W.

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A, Pure Appl. Opt. 11(7), 075402 (2009).
[Crossref]

Ran, Q.

Refregier, P.

Sheppard, C. J.

Sheridan, J. T.

Singh, K.

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]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier-domain encoding for optical security,” Opt. Eng. 39(11), 2853–2859 (2000).
[Crossref]

Situ, G.

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282(4), 482–492 (2009).
[Crossref]

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A, Pure Appl. Opt. 8(5), 391–397 (2006).
[Crossref]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30(11), 1306–1308 (2005).
[Crossref] [PubMed]

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

Spence, J. C. H.

J. S. Wu and J. C. H. Spence, “Reconstruction of complex single-particle images using charge-flipping algorithm,” Acta Crystallogr. A 61(2), 194–200 (2005).
[Crossref] [PubMed]

J. S. Wu, U. Weierstall, J. C. H. Spence, and C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29(23), 2737–2739 (2004).
[Crossref] [PubMed]

Sun, X.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282(4), 518–522 (2009).
[Crossref]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Süto, A.

G. Oszlányi and A. Süto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. A 60(2), 134–141 (2004).
[Crossref] [PubMed]

Tajahuerce, E.

Tang, H.

H. Tang, X. Peng, and J. Tian, “Ciphertext-only attack on double random phase encoding optical encryption system,” Wuli Xuebao 56(5), 2629–2636 (2007).

Tao, R.

Thelen, B.

Tian, J.

H. Tang, X. Peng, and J. Tian, “Ciphertext-only attack on double random phase encoding optical encryption system,” Wuli Xuebao 56(5), 2629–2636 (2007).

Torres-Company, V.

Unnikrishnan, G.

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]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier-domain encoding for optical security,” Opt. Eng. 39(11), 2853–2859 (2000).
[Crossref]

Wang, B.

Wang, Y.

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281(23), 5745–5749 (2008).
[Crossref]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15(24), 16067–16079 (2007).
[Crossref] [PubMed]

Wei, H.

Weierstall, U.

Wu, J. S.

J. S. Wu and J. C. H. Spence, “Reconstruction of complex single-particle images using charge-flipping algorithm,” Acta Crystallogr. A 61(2), 194–200 (2005).
[Crossref] [PubMed]

J. S. Wu, U. Weierstall, J. C. H. Spence, and C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29(23), 2737–2739 (2004).
[Crossref] [PubMed]

Xin, Y.

Xu, L.

Z. Liu, L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49(4), 542–546 (2011).
[Crossref]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
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Figures (11)

Fig. 1
Fig. 1 Schematic diagrams of double random phase encryption scheme.
Fig. 2
Fig. 2 Flow chart of iterative phase retrieval with NNP constraint in the nth iteration.
Fig. 3
Fig. 3 Visualization of alternating projections in 3-dimention real vector space. (a) The comparison: alternating projection with support constraint and NNP constraint. (b) The comparison: projection algorithm (ER), over projection algorithm (CF), and HIO algorithm.
Fig. 4
Fig. 4 Flow chart of the COA process of DRPE based on HIPR algorithm
Fig. 5
Fig. 5 (a) The original gray-scale plaintext ‘dog’, (b) amplitude distribution of the corresponding ciphertext of (a), (c) the support of autocorrelation of plaintext (a), (d) recovered plaintext from (b) by use our proposed attack scheme, (e) the original binary plaintext ‘SZU’, (f) amplitude distribution of the corresponding ciphertext of (e), (g) the support of autocorrelation of plaintext (e), (d) recovered plaintext from (f) by using our proposed attack scheme.
Fig. 6
Fig. 6 Recovered plaintext with 5 estimated NNP parameter. The NNP’s percentages are (a) 8%, (b) 9%, (c) 10%, (d) 11%, and (e) 12%.
Fig. 7
Fig. 7 (a) The R factors as a function of iteration number for both gray-scale image and binary image respectively. (b) Reconstructed gray-scale image after 1000th iteration. (c) Reconstructed binary image after 1000th iteration.
Fig. 8
Fig. 8 The correlation coefficient (cc) as a function of iteration number for both gray-scale image and binary image respectively.
Fig. 9
Fig. 9 Decryption result of the subsequent ciphertext with the cracked keys. (a) The original Lena image. (b) The ciphertext corresponding to (a). (c) Decryption result by unmodified key. (d) Decryption result by modified key.
Fig. 10
Fig. 10 The comparison of simulation result by using different COA methods. (a), (b), (c) The estimated support of “dog”, recovered plaintext and decrypted subsequent Lena image by using the approach proposed in [30] and [43], respectively. (d), (e), (f) The estimated support of “dog”, recovered plaintext and decrypted subsequent Lena image by our approach respectively.
Fig. 11
Fig. 11 (a) The original gray-scale plaintext ‘tree’, (b) amplitude distribution of the corresponding ciphertext of (a), (c) the recovered support of plaintext (a), (d) recovered plaintext from (b) by use our proposed attack scheme, (e) The R factors as a function of iteration number. (f) The correlation coefficient as a function of iteration number.

Equations (19)

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ψ ( x , y ) = FT 1 { FT { f ( x , y ) exp [ i 2 π n ( x , y ) ] } exp [ i 2 π b ( u , v ) ] }
Ψ ( u , v ) = FT { ψ ( x , y ) } = FT { f ( x , y ) exp [ i 2 π n ( x , y ) ] } exp [ i 2 π b ( u , v ) ]
Ψ ( u , v ) = FT { f ( x , y ) } exp [ i 2 π b ( u , v ) ] = F ( u , v ) exp [ i 2 π b ( u , v ) ]
| Ψ ( u , v ) | = | F ( u , v ) |
g n + 1 ( x ) = { g n ( x ) x S n g n ( x ) β g n ( x ) x S n
g n + 1 ( x ) = { g n ( x ) x S n g n ( x ) x S n
g n + 1 ( x ) = { g n ( x ) x S n 0 x S n
M = { g : | FT { g } | = F }
N = { g : g 0 = K }
FT { f ( x , y ) f ( x , y ) } = | F ( u , v ) | 2
R = i = 1 , j = 1 M , N | | G n ( u i , v j ) | F ( u i , v j ) | i = 1 , j = 1 M , N F ( u i , v j )
G ( u , v ) = FT { g ( x , y ) } = exp [ j 2 π ( u x 0 + v y 0 ) ] F ( u , v )
φ ^ ( u , v ) = Ψ ( u , v ) G ( u , v ) = exp [ j 2 π ( u x 0 + v y 0 ) ] exp [ j b ( u , v ) ]
f ^ s ( x , y ) = | FT 1 { FT { ψ s ( u , v ) } φ ^ * } | = | FT 1 { FT { f s ( x , y ) exp [ j n ( x , y ) ] } exp [ j b ( α , β ) ] φ ^ * } | = | FT 1 { FT { f s ( x , y ) exp [ j n ( x , y ) ] } exp [ j 2 π ( u x 0 + v y 0 ) ] } | = f s ( x x 0 , y y 0 )
φ ( u , v ) = φ ^ ( u , v ) exp [ j 2 π ( u x 0 + v y 0 ) ]
G ( u , v ) = FT { g ( x , y ) } = exp [ j 2 π ( u x 0 + v y 0 ) ] F * ( u , v )
F ( u , v ) = G * ( u , v ) exp [ j 2 π ( u x 0 + v y 0 ) ]
φ ( u , v ) = Ψ ( u , v ) F ( u , v ) = Ψ ( u , v ) G * ( u , v ) exp [ j 2 π ( u x 0 + v y 0 ) ]
c c = i = 1 , j = 1 M , N ( f i , j f m e a n ) ( f ^ i , j f ^ m e a n ) ( i = 1 , j = 1 M , N ( f i , j f m e a n ) 2 ) ( i = 1 , j = 1 M , N ( f ^ i , j f ^ m e a n ) 2 )

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