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 Optical Society of America

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References

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  1. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
    [Crossref] [PubMed]
  2. 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]
  3. 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]
  4. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
    [Crossref] [PubMed]
  5. H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14(5), 1755–1766 (2006).
    [Crossref] [PubMed]
  6. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589–636 (2009).
    [Crossref]
  7. J. F. Barrera and R. Torroba, “One step multiplexing optical encryption,” Opt. Commun. 283(7), 1268–1272 (2010).
    [Crossref]
  8. T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
    [Crossref]
  9. H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. 41(23), 4825–4834 (2002).
    [Crossref] [PubMed]
  10. H. E. Hwang, H. T. Chang, and W. N. Lie, “Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems,” Opt. Express 17(16), 13700–13710 (2009).
    [Crossref] [PubMed]
  11. J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35(21), 3553–3555 (2010).
    [Crossref] [PubMed]
  12. 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]
  13. 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]
  14. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15(16), 10253–10265 (2007).
    [Crossref] [PubMed]
  15. H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express 18(13), 13772–13781 (2010).
    [Crossref] [PubMed]
  16. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
    [Crossref] [PubMed]
  17. W. Stallings, Cryptography and Network Security: Principles and Practice (Prentice Hall, 2003).
  18. 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]
  19. 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]
  20. W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
    [Crossref]
  21. 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]
  22. 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]
  23. X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50(36), 6645–6651 (2011).
    [Crossref] [PubMed]
  24. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [Crossref] [PubMed]
  25. S. Yuan, X. Zhou, D. H. Li, and D. F. Zhou, “Simultaneous transmission for an encrypted image and a double random-phase encryption key,” Appl. Opt. 46(18), 3747–3753 (2007).
    [Crossref] [PubMed]

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

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]

2010 (4)

2009 (2)

2007 (2)

2006 (2)

2005 (1)

2004 (1)

2003 (1)

2002 (1)

2000 (2)

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]

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

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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