Abstract

A discussion and a cryptanalysis of the optical phase-truncated Fourier-transform-based cryptosystem are presented in this paper. The concept of an optical asymmetric cryptosystem, which was introduced into the optical image encryption scheme based on phase-truncated Fourier transforms in 2010, is suggested to be retained in optical encryption. A new method of attack is also proposed to simultaneously obtain the main information of the original image, the two decryption keys from its cyphertext, and the public keys based on the modified amplitude-phase retrieval algorithm. The numerical results illustrate that the computing efficiency of the algorithm is improved and the number of iterations is much less than that by the specific attack, which has two iteration loops.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2013

2012

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
[CrossRef]

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, 1203–1206 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Laser Technol. 50, 1196–1201 (2012).

2011

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13, 075404 (2011).
[CrossRef]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

2010

2009

2008

2007

2006

2005

2004

2000

1995

Alfalou, A.

Arcos, S.

Barrera, J. F.

Brosseau, C.

Cai, L.

Carnicer, A.

Castro, A.

Chang, H.

Chen, G.

Chen, W.

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13, 075404 (2011).
[CrossRef]

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

Chen, X.

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13, 075404 (2011).
[CrossRef]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

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

Cheng, X.

Cho, M.

Deng, X.

Ding, X.

Dong, G.

Frauel, Y.

He, W.

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: comment,” Opt. Lett. 38, 4045 (2013).
[CrossRef]

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, 1203–1206 (2012).
[CrossRef]

Hwang, H.

Javidi, B.

Joseph, J.

Juvells, I.

Kumar, A.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Laser Technol. 50, 1196–1201 (2012).

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

Kumar, P.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Laser Technol. 50, 1196–1201 (2012).

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

Lie, W.

Liu, S.

Liu, W.

Liu, Z.

Meng, X.

Mira, A.

Montes-Usategui, M.

Naughton, T. J.

Nishchal, N. K.

Obi, T.

Ohyama, N.

Peng, X.

Pérez-Cabré, E.

Qin, W.

Rajput, S. K.

Refregier, P.

Schneier, B.

B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C (Wiley, 1996).

Shen, X.

Sheppard, C. J. R.

Singh, K.

Situ, G.

Song, K.

Suzuki, H.

Takeda, M.

Tashima, H.

Torroba, R.

Unnikrishnan, G.

Wang, X.

Wang, Y.

Wei, H.

Xu, X.

Yamaguchi, M.

Yu, B.

Zhang, H.

Zhang, J.

Zhang, P.

Zhao, D.

Adv. Opt. Photon.

Appl. Opt.

J. Opt.

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13, 075404 (2011).
[CrossRef]

Opt. Commun.

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
[CrossRef]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

Opt. Express

Opt. Laser Technol.

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, 1203–1206 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Laser Technol. 50, 1196–1201 (2012).

Opt. Lett.

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
[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]

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

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, 1644–1646 (2005).
[CrossRef]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
[CrossRef]

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

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[CrossRef]

X. Wang and D. Zhao, “Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask,” Opt. Lett. 38, 3684–3686 (2013).
[CrossRef]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: comment,” Opt. Lett. 38, 4045 (2013).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm: reply,” Opt. Lett. 38, 4045 (2013).
[CrossRef]

X. Cheng, L. Cai, Y. Wang, X. Meng, H. Zhang, X. Xu, X. Shen, and G. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

H. Hwang, H. Chang, and W. Lie, “Multiple-image encryption and multiplexing using modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).
[CrossRef]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[CrossRef]

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

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

Other

B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C (Wiley, 1996).

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Figures (5)

Fig. 1.
Fig. 1.

Flowchart of the new attack method based on modified amplitude-phase retrieval algorithm.

Fig. 2.
Fig. 2.

(a) Gray-scale image to be encrypted, (b) binary image to be encrypted, (c) RPM1, (d) RPM2, (e) encrypted result from (a), and (f) encrypted result from (b).

Fig. 3.
Fig. 3.

Recovered images corresponding to different numbers of iterations. (a) 10, (b) 100, (c) 250, (d) 10, (e) 100, and (f) 300.

Fig. 4.
Fig. 4.

Behavior of MSE versus number of iterations for the decryption of (a) gray-scale image and (b) binary image.

Fig. 5.
Fig. 5.

(a) Behavior of MSE versus number of iterations in the second step for the gray-scale image decryption, (b) recovered image with the minimum value of MSE, (c) behavior of MSE versus number of iterations in the second step for the binary image decryption, and (d) recovered image after 200 iterations.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

C(x,y)=PT{IFT[g(u,υ)R2(u,υ)]},
g(u,υ)=PT{FT[f(x,y)R1(x,y)]},
K1(u,υ)=PR{FT[f(x,y)R1(x,y)]},
K2(x,y)=PR{IFT[g1(u,υ)R2(u,υ)]},
gk(u,υ)=PT{FT[Ik1(x,y)R1(x,y)]},
Pk(u,υ)=PR{FT[Ik1(x,y)R1(x,y)]},
Ck(x,y)=PT{IFT[gk(u,υ)R2(u,υ)]},
Pk(x,y)=PR{IFT[gk(u,υ)R2(u,υ)]}.
gk(u,υ)=PT{FT[C(x,y)Pk(x,y)]}.
Ik(x,y)=PT{IFT[gk(u,υ)Pk(u,υ)]}.
MSE(Ck,C)=1M×Ni=1Mj=1N|Ck(i,j)C(i,j)|2,

Metrics