Abstract

A novel image encryption algorithm is proposed based on the multiple-parameter fractional Fourier transform, which is a generalized fractional Fourier transform, without the use of phase keys. The image is encrypted simply by performing a multiple-parameter fractional Fourier transform with four keys. Optical implementation is suggested. The method has been compared with existing methods and shows superior robustness to blind decryption.

© 2008 Optical Society of America

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References

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  1. B. Hennelly and J. Sheridan, Optik (Stuttgart) 114, 251 (2003).
    [CrossRef]
  2. G. Unnikrishnan, J. Joseph, and K. Singh, Opt. Lett. 25, 887 (2000).
    [CrossRef]
  3. B. Hennelly and J. Sheridan, Opt. Lett. 28, 269 (2003).
    [CrossRef] [PubMed]
  4. B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
    [CrossRef]
  5. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (John Wiley & Sons, 2001).
  6. G. Cariolaro, T. Erseghe, P. Kraniauskas, and N. Laurenti, IEEE Trans. Signal Process. 48, 227 (2000).
    [CrossRef]
  7. C. Shih, Opt. Commun. 48, 495 (1995).
    [CrossRef]

2003 (2)

B. Hennelly and J. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

B. Hennelly and J. Sheridan, Opt. Lett. 28, 269 (2003).
[CrossRef] [PubMed]

2000 (3)

1995 (1)

C. Shih, Opt. Commun. 48, 495 (1995).
[CrossRef]

IEEE Trans. Signal Process. (1)

G. Cariolaro, T. Erseghe, P. Kraniauskas, and N. Laurenti, IEEE Trans. Signal Process. 48, 227 (2000).
[CrossRef]

Opt. Commun. (1)

C. Shih, Opt. Commun. 48, 495 (1995).
[CrossRef]

Opt. Lett. (3)

Optik (Stuttgart) (1)

B. Hennelly and J. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

Other (1)

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (John Wiley & Sons, 2001).

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Figures (3)

Fig. 1
Fig. 1

Results of the proposed algorithm in certain cases of the encryption and decryption.

Fig. 2
Fig. 2

MSE plotted as a function of error in the decryption keys.

Fig. 3
Fig. 3

Optoelectronic hybrid setup of the image encryption and decryption system based on the MPFRFTs.

Equations (4)

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F α [ f ( x ) ] = + f ( x ) A ϕ exp [ i π ( x 2 cot ϕ 2 x x α csc ϕ + x α 2 cot ϕ ) ] d x ,
R M α ( M , N ) [ f ( x ) ] = l = 0 M 1 H l ( α , M , N ) f l ( x ) ,
H l ( α , M , N ) = 1 M k = 0 ( M 1 ) exp { ( 2 π i M ) [ ( m k M + 1 ) α ( k + n k M ) l k ] }
M = ( m 0 , m 1 , , m ( M 1 ) ) Z M , N = ( n 0 , n 1 , , n ( M 1 ) ) Z M .

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