Abstract

The Fourier plane encryption algorithm is subjected to a known-plaintext attack. The simulated annealing heuristic algorithm is used to estimate the key, using a known plaintext-ciphertext pair, which decrypts the ciphertext with arbitrarily low error. The strength of the algorithm is tested by using this estimated key to decrypt a different ciphertext which was also encrypted using the same original key. We assume that the plaintext is amplitude-encoded real-valued image, and analyze only the mathematical algorithm rather than a real optical system that can be more secure. The Fourier plane encryption algorithm is found to be susceptible to a known-plaintext heuristic attack.

© 2006 Optical Society of America

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References

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2005

2004

T.J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
[CrossRef]

2003

2000

1999

1998

1995

1988

1983

S. Kirkpatrick, C. D. Gellatt and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 771-680 (1983).
[CrossRef]

Arcos, S.

Carnicer, A.

Castro, A.

Y. Frauel, A. Castro, T.J. Naughton, and B. Javidi, "Security analysis of optical encryption," Proc. SPIE 5986, 25-34 (2005).

Frauel, Y.

Y. Frauel, A. Castro, T.J. Naughton, and B. Javidi, "Security analysis of optical encryption," Proc. SPIE 5986, 25-34 (2005).

Fuentes, J. F.

Gellatt, C. D.

S. Kirkpatrick, C. D. Gellatt and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 771-680 (1983).
[CrossRef]

Glckstad, J.

Hennelly, B. M.

Javidi, B.

Joseph, J.

Juvells, I.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gellatt and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 771-680 (1983).
[CrossRef]

Matoba, O.

Mogensen, P. C.

Montes-Usategui, M.

Naughton, T.J.

Y. Frauel, A. Castro, T.J. Naughton, and B. Javidi, "Security analysis of optical encryption," Proc. SPIE 5986, 25-34 (2005).

T.J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
[CrossRef]

Navarro, R.

Nieto-Vesperinas, M.

Nomura, T.

R´, Ph.

Sheridan, J. T.

Singh, K.

Tajahuerce, E.

Unnikrishnan, G.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gellatt and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 771-680 (1983).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

T.J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
[CrossRef]

Opt. Lett.

Proc. SPIE

Y. Frauel, A. Castro, T.J. Naughton, and B. Javidi, "Security analysis of optical encryption," Proc. SPIE 5986, 25-34 (2005).

Science

S. Kirkpatrick, C. D. Gellatt and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 771-680 (1983).
[CrossRef]

Other

W. Stallings, Cryptography and Network Security, Third edition, (Prentice Hall, 2004).

B. Javidi, ed. Optical and Digital Techniques for Information Security, (Springer Verlag, 2005).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Time taken to estimate the key which would decrypt the encrypted image of A with an NRMS error of 0.1. Results of 50 trials, 25 each for cases when plaintext is a 32×32 pixel image and 64×64 pixel image.

Fig. 2.
Fig. 2.

NRMS error to decrypt the encrypted image of B. The key used was the one found to decrypt the encrypted image of A with NRMS error of 0.1. A and B are encrypted using the same set of keys. Results of 50 trials, 25 each for cases when plaintext is a 32×32 pixel image and 64×64 pixel image.

Fig. 3.
Fig. 3.

(a) Images from the 64×64 pixel trials: (a) the plaintext A, (b) the real part and (c) the imaginary part of the complex-valued encrypted image of A, (d) the decrypted image with an NRMS error of 0.1, (e) the plaintext B, (f) the real part and (g) the imaginary part of the complex-valued encrypted image of B, (h) the decrypted image B with an NRMS error of 0.4, and (i) the decrypted image B in trial 3 with an NRMS error of 0.8.

Equations (3)

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ψ = [ f ( . ) R 1 ] * R ̂ 2 ( . )
f ˜ 2 = ψ ( . ) * R ̂ 3 ( . ) 2
NRMS = i = 1 N j = 1 N I d i j I i j 2 i = 1 N j = 1 N I i j 2

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