Abstract

A method of image encryption and decryption is proposed for optical security systems. A phase-coded image to be encrypted together with a random phase pattern is Fourier transformed and the result of the complex-valued data is used as an encrypted pattern. The decryption is simply performed by an inverse-Fourier transform for the addition of the encrypted pattern and the Fourier transform of the random phase. The intensity of the inverse-Fourier transformed image gives the exact result for the decryption. Further, the binarization of the encrypted pattern is performed for the easiness of the optical and electronic readout of the images, and it also gives rise to the enhancement of the degree of security for the encryption. The binary pattern is optimized by a statistical iteration technique and an excellent decryption image is obtained by the optimization.

© 2002 Optical Society of America

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References

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  1. B. Javidi, J. L. Hoener, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  2. P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 90, 767–769 (1995).
    [CrossRef]
  3. L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
    [CrossRef]
  4. B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
    [CrossRef]
  5. N. Towghi, B. Javidi, Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
    [CrossRef]
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    [CrossRef]
  7. P. C. Mogensen, J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (2000).
    [CrossRef]
  8. P. C. Mogensen, J. Glückstad, “Phase-only optical encryption of a fixed mask,” Appl. Opt. 40, 1226–1235 (2001).
    [CrossRef]
  9. H. G. Yan, E. S. Kim, “Practical image encryption scheme by real-valued data,” Opt. Eng. 35, 2473–2478 (1996).
    [CrossRef]
  10. M. Yamazaki, J. Ohtsubo, “Optimization of encrypted holograms in optical security systems,” Opt. Eng. 40, 132–137 (2001).
    [CrossRef]
  11. S. J. Park, J. Y. Kim, J. K. Bae, S. J. Kim, “Fourier-plane encryption technique based on removing the effect of phase terms in a joint transform correlator,” Opt. Rev. 8, 413–415 (2001).
    [CrossRef]
  12. Y. Kobayashi, H. Toyoda, “Development of an optical joint transform correlation system for fingerprint recognition,” Opt. Eng. 38, 1205–1210 (1999).
    [CrossRef]

2001

M. Yamazaki, J. Ohtsubo, “Optimization of encrypted holograms in optical security systems,” Opt. Eng. 40, 132–137 (2001).
[CrossRef]

S. J. Park, J. Y. Kim, J. K. Bae, S. J. Kim, “Fourier-plane encryption technique based on removing the effect of phase terms in a joint transform correlator,” Opt. Rev. 8, 413–415 (2001).
[CrossRef]

P. C. Mogensen, J. Glückstad, “Phase-only optical encryption of a fixed mask,” Appl. Opt. 40, 1226–1235 (2001).
[CrossRef]

2000

1999

N. Towghi, B. Javidi, Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
[CrossRef]

Y. Kobayashi, H. Toyoda, “Development of an optical joint transform correlation system for fingerprint recognition,” Opt. Eng. 38, 1205–1210 (1999).
[CrossRef]

1998

1996

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

H. G. Yan, E. S. Kim, “Practical image encryption scheme by real-valued data,” Opt. Eng. 35, 2473–2478 (1996).
[CrossRef]

1995

P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 90, 767–769 (1995).
[CrossRef]

1994

B. Javidi, J. L. Hoener, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Ahouzi, E.

Bae, J. K.

S. J. Park, J. Y. Kim, J. K. Bae, S. J. Kim, “Fourier-plane encryption technique based on removing the effect of phase terms in a joint transform correlator,” Opt. Rev. 8, 413–415 (2001).
[CrossRef]

Glückstad, J.

Hoener, J. L.

B. Javidi, J. L. Hoener, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Javidi, B.

Kim, E. S.

H. G. Yan, E. S. Kim, “Practical image encryption scheme by real-valued data,” Opt. Eng. 35, 2473–2478 (1996).
[CrossRef]

Kim, J. Y.

S. J. Park, J. Y. Kim, J. K. Bae, S. J. Kim, “Fourier-plane encryption technique based on removing the effect of phase terms in a joint transform correlator,” Opt. Rev. 8, 413–415 (2001).
[CrossRef]

Kim, S. J.

S. J. Park, J. Y. Kim, J. K. Bae, S. J. Kim, “Fourier-plane encryption technique based on removing the effect of phase terms in a joint transform correlator,” Opt. Rev. 8, 413–415 (2001).
[CrossRef]

Kobayashi, Y.

Y. Kobayashi, H. Toyoda, “Development of an optical joint transform correlation system for fingerprint recognition,” Opt. Eng. 38, 1205–1210 (1999).
[CrossRef]

Kuroda, K.

Luo, Z.

Matoba, O.

Mogensen, P. C.

Neto, L. G.

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

Ohtsubo, J.

M. Yamazaki, J. Ohtsubo, “Optimization of encrypted holograms in optical security systems,” Opt. Eng. 40, 132–137 (2001).
[CrossRef]

Park, S. J.

S. J. Park, J. Y. Kim, J. K. Bae, S. J. Kim, “Fourier-plane encryption technique based on removing the effect of phase terms in a joint transform correlator,” Opt. Rev. 8, 413–415 (2001).
[CrossRef]

Réfrégier, P.

P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 90, 767–769 (1995).
[CrossRef]

Sheng, Y.

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

Shimura, T.

Tan, X.

Towghi, N.

Toyoda, H.

Y. Kobayashi, H. Toyoda, “Development of an optical joint transform correlation system for fingerprint recognition,” Opt. Eng. 38, 1205–1210 (1999).
[CrossRef]

Yamazaki, M.

M. Yamazaki, J. Ohtsubo, “Optimization of encrypted holograms in optical security systems,” Opt. Eng. 40, 132–137 (2001).
[CrossRef]

Yan, H. G.

H. G. Yan, E. S. Kim, “Practical image encryption scheme by real-valued data,” Opt. Eng. 35, 2473–2478 (1996).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

H. G. Yan, E. S. Kim, “Practical image encryption scheme by real-valued data,” Opt. Eng. 35, 2473–2478 (1996).
[CrossRef]

M. Yamazaki, J. Ohtsubo, “Optimization of encrypted holograms in optical security systems,” Opt. Eng. 40, 132–137 (2001).
[CrossRef]

B. Javidi, J. L. Hoener, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Y. Kobayashi, H. Toyoda, “Development of an optical joint transform correlation system for fingerprint recognition,” Opt. Eng. 38, 1205–1210 (1999).
[CrossRef]

Opt. Lett.

P. C. Mogensen, J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (2000).
[CrossRef]

P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 90, 767–769 (1995).
[CrossRef]

Opt. Rev.

S. J. Park, J. Y. Kim, J. K. Bae, S. J. Kim, “Fourier-plane encryption technique based on removing the effect of phase terms in a joint transform correlator,” Opt. Rev. 8, 413–415 (2001).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Encryption and decryption of a binary image by the proposed method. (a) Original image f 0(x, y), (b) encryption key r 0(x, y), (c) real part of the encrypted pattern Re[G(u, v)], (d) imaginary part of the encrypted pattern Im[G(u, v)], (e) decrypted image |h(x, y)|2.

Fig. 2
Fig. 2

Encryption (a) and decryption (b) for gray-scale fingerprint image.

Fig. 3
Fig. 3

Decryption with real-valued patterns. (a) Original image. The fingerprint image is inverted and the gray scale of each pixel is nonlinearly transformed by an arccosine function [compare it with Fig. 2(a)]. (b) Encryption key, (c) real part of the encrypted pattern, (d) real part of the decryption key, (e) decrypted image.

Fig. 4
Fig. 4

Decryption with the binarized patterns of the encryption pattern and the decryption key. (a) Binarized encryption pattern, (b) binarized decryption key, (c) decrypted image. The patterns are binarized according to the signs of the real part values.

Fig. 5
Fig. 5

Optimization of the encrypted pattern. (a) Optimized pattern for the binary-encryption pattern of Fig. 4(a) and 4(b) the decryption of it.

Fig. 6
Fig. 6

Normalized cost function for the optimization in Fig. 5.

Equations (3)

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

gx, y=expiπf0x, yexpiπr0x, y,
Hu, v=Gu, v+Ru, v,
|hx, y|2=|gx, y|2+|rx, y|2+gx, yr*x, y+g*x, yrx, y =2+2 cosπf0x, y.

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