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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2001

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

2000

1999

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

1997

1995

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.

Opt. Commun.

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.

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

Opt. Lett.

Phys. Today

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

Other

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.

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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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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