Abstract

A double-image encryption technique that based on an asymmetric algorithm is proposed. In this method, the encryption process is different from the decryption and the encrypting keys are also different from the decrypting keys. In the nonlinear encryption process, the images are encoded into an amplitude cyphertext, and two phase-only masks (POMs) generated based on phase truncation are kept as keys for decryption. By using the classical double random phase encoding (DRPE) system, the primary images can be collected by an intensity detector that located at the output plane. Three random POMs that applied in the asymmetric encryption can be safely applied as public keys. Simulation results are presented to demonstrate the validity and security of the proposed protocol.

© 2012 OSA

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References

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2012 (1)

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

2011 (5)

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284(1), 148–152 (2011).
[Crossref]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284(19), 4441–4445 (2011).
[Crossref]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284(16-17), 3913–3917 (2011).
[Crossref]

X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50(36), 6645–6651 (2011).
[Crossref] [PubMed]

2010 (4)

2009 (2)

2007 (2)

2006 (2)

2005 (1)

2004 (1)

2003 (1)

2002 (1)

2000 (2)

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]

1995 (1)

1982 (1)

Alfalou, A.

Arcos, S.

Barrera, J. F.

Bolognini, N.

Brosseau, C.

Carnicer, A.

Castro, A.

Chang, H. T.

Chen, W.

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284(16-17), 3913–3917 (2011).
[Crossref]

Chen, X.

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284(16-17), 3913–3917 (2011).
[Crossref]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

Fienup, J. R.

Frauel, Y.

Hennelly, B.

Hwang, H. E.

Javidi, B.

Joseph, J.

Juvells, I.

Kuo, C. J.

Li, D. H.

Lie, W. N.

Lu, W. C.

Montes-Usategui, M.

Naughton, T. J.

Nomura, T.

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

Obi, T.

Ohyama, N.

Peng, X.

Qin, W.

Refregier, P.

Sheridan, J. T.

Singh, K.

Situ, G.

Suzuki, H.

Takeda, M.

Tashima, H.

Tebaldi, M.

Torroba, R.

Unnikrishnan, G.

Vargas, C.

Wang, X.

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284(1), 148–152 (2011).
[Crossref]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284(19), 4441–4445 (2011).
[Crossref]

X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50(36), 6645–6651 (2011).
[Crossref] [PubMed]

Wei, H.

Yachida, M.

Yamaguchi, M.

Yu, B.

Yuan, S.

Zhang, J.

Zhang, P.

Zhao, D.

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284(19), 4441–4445 (2011).
[Crossref]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284(1), 148–152 (2011).
[Crossref]

X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50(36), 6645–6651 (2011).
[Crossref] [PubMed]

Zhou, D. F.

Zhou, X.

Adv. Opt. Photon. (1)

Appl. Opt. (4)

J. Opt. (1)

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

Opt. Commun. (5)

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284(16-17), 3913–3917 (2011).
[Crossref]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

J. F. Barrera and R. Torroba, “One step multiplexing optical encryption,” Opt. Commun. 283(7), 1268–1272 (2010).
[Crossref]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284(1), 148–152 (2011).
[Crossref]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284(19), 4441–4445 (2011).
[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 (4)

Opt. Lett. (8)

Other (1)

W. Stallings, Cryptography and Network Security: Principles and Practice (Prentice Hall, 2003).

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Figures (10)

Fig. 1
Fig. 1

Optical implementation of the decryption process. E(x) is the encoded image, and P 1 (x) , P 2 (u) are two decrypting keys.

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Fig. 2
Fig. 2

Flowchart of the proposed encoding method. R 1 , R 2 and R 3 are three random POMs that used as public keys. P 0 , P 1 are private keys.

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Fig. 3
Fig. 3

(a) Woodstatue, (b) Mudiao, (c) the ciphertext and (d) correct decrypted result.

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Fig. 4
Fig. 4

The two phase keys generated in the encryption process (a) P 1 (x) and (b) P 2 (u) .

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Fig. 5
Fig. 5

Decrypted results using (a) no keys, (b) arbitrarily selected phase keys.

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Fig. 6
Fig. 6

Two fake plain images (a) Office, (b) Spanner. (c) P 1 , and (d) P 2 the generated from (a) and (b). Decrypted results (e) with the phase keys (c) and (d), (f) with two of the encrypting keys.

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Fig. 7
Fig. 7

The relation between the iteration number and the MSE in (a) the first step, (b) the direct attack and (c) the indirect attack.

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Fig. 8
Fig. 8

The decrypted result with the iteration numbers (a) m=500, n 1 =1 ; (b) m=500, n 1 =50 ; (c) m=500, n 2 =1 ; (d) m=500, n 2 =50 .

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Fig. 9
Fig. 9

(a) The ciphertext, (b) the correct decoded image, and (c) the result of indirect specific attack.

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Fig. 10
Fig. 10

The relation between the iteration times and the MSE (a) in the first step, (b) in the second step.

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Equations (9)

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

D(x)=PT{ [E(x)⋅ P 1 (x)]⊗IFT[ P 2 (u)] },
u 0 (x)=[ f 1 (x) R 1 (x)]⊗δ(x− a 1 )+[ f 2 (x) R 2 (x)]⊗δ(x− a 2 ),
g 0 (u)=PT{FT[ u 0 (x)]},
P 0 (u)=PR{FT[ u 0 (x)]}.
u 1 (x)=IFT[ g 0 (u)⋅ R 3 (u)].
E(x)=PT{ u 1 (x)},
P 1 (x)=PR{ u 1 (x)},
P 2 (u)= R 3 ∗ (u)⋅ P 0 (u),
MSE(f, f ′ )= 1 L ∑ i=1 L | f− f ′ | 2 ,

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