Abstract

We present a novel image-encryption algorithm that employs multichannel and multistage fractional Fourier-domain filtering architecture. We perform the encryption and decryption by randomly filtering the spatial frequency of the image and then recombining the information from the algorithm in a multistage fractional Fourier domain with pure random-intensity-encoded masks and their complements in a multichannel scheme. The algorithm can be implemented iteratively in an electro-optical setup. Numerical simulations have verified the validity of the algorithm.

© 2001 Optical Society of America

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References

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  1. B. Javidi, Phys. Today 50(3), 27 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. H. M. Ozaktas and M. A. Kutay, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Chap.  4 and references therein.
  9. B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
    [CrossRef]
  10. See, for instance, A. Menezes, P. van Oorschot, and S. Vanstone , Handbook of Applied Cryptography (CRC, Boca Raton, Fla., 1996); http://www.cacr.math.uwaterloo.ca/hac .
    [CrossRef]
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    [CrossRef]

2001 (1)

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

2000 (3)

1999 (1)

See, for example, the special issue on optical security, Opt. Eng. 38, 8–119 (1999).
[CrossRef]

1997 (3)

1995 (1)

Javidi, B.

Joseph, J.

Kakuta, M.

King, B.

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

Kutay, M. A.

H. M. Ozaktas and M. A. Kutay, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Chap.  4 and references therein.

Lai, S.

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

Li, J.

Liu, S.

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
[CrossRef]

Madjarova, M.

Menezes, A.

See, for instance, A. Menezes, P. van Oorschot, and S. Vanstone , Handbook of Applied Cryptography (CRC, Boca Raton, Fla., 1996); http://www.cacr.math.uwaterloo.ca/hac .
[CrossRef]

Neifeld, M.

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

Ohyama, N.

Ozaktas, H. M.

H. M. Ozaktas and M. A. Kutay, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Chap.  4 and references therein.

Ran, Q.

Réfrégier, P.

Singh, K.

Unnikrishnan, G.

van Oorschot, P.

See, for instance, A. Menezes, P. van Oorschot, and S. Vanstone , Handbook of Applied Cryptography (CRC, Boca Raton, Fla., 1996); http://www.cacr.math.uwaterloo.ca/hac .
[CrossRef]

Vanstone, S.

See, for instance, A. Menezes, P. van Oorschot, and S. Vanstone , Handbook of Applied Cryptography (CRC, Boca Raton, Fla., 1996); http://www.cacr.math.uwaterloo.ca/hac .
[CrossRef]

Yamaguchi, M.

Yu, L.

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

Zhang, G.

Zhu, B.

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
[CrossRef]

Appl. Opt. (1)

Opt. Commun. (2)

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

Opt. Eng. (1)

See, for example, the special issue on optical security, Opt. Eng. 38, 8–119 (1999).
[CrossRef]

Opt. Lett. (4)

Phys. Today (1)

B. Javidi, Phys. Today 50(3), 27 (1997).
[CrossRef]

Other (2)

See, for instance, A. Menezes, P. van Oorschot, and S. Vanstone , Handbook of Applied Cryptography (CRC, Boca Raton, Fla., 1996); http://www.cacr.math.uwaterloo.ca/hac .
[CrossRef]

H. M. Ozaktas and M. A. Kutay, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Chap.  4 and references therein.

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Figures (3)

Fig. 1
Fig. 1

Schematic illustration of the image-encryption algorithm, which uses multichannel and multistage fractional Fourier-domain filtering.

Fig. 2
Fig. 2

Encryption and decryption results with three-stage and three-channel fractional Fourier-domain filtering; α=0.5, α2=0.8, and α3=0.7: (a) original image (Lena); (b) encrypted image; (c), (d) key images; (e) decryption image with incorrect keys, Δα=0.02; (f)  correct decryption.

Fig. 3
Fig. 3

Comparisons of mean-squared errors with the random phase-encoding algorithm: (a) with additive noise, (b)  with multiplicative noise. FRT, fractional Fourier transform.

Equations (4)

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

f0x,y=fx,y,fix,y=Fαifi-1x,yHi,f¯ix,y=Fαifi-1x,yH¯i,
g1x,y=Fαn+1fnx,y.
gkx,y=FαΣkf¯n+2-kx,y,
i=1n+1gix,y=Fαfx,y,

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