Abstract

We technically investigate the robustness of an image encryption technique that uses a virtual phase image and a joint transform correlator (JTC) in the frequency domain. An encrypted image is obtained by the Fourier transform of the product of a virtual phase image, which camouflages the original image, and a random phase image. The resulting image is then decrypted by use of a decrypting key made from the proposed phase assignment rule in order to enhance the level of security. We demonstrate that the encrypted image generated by the proposed JTC-based decryption technique is robust to data loss and image shift.

© 2004 Optical Society of America

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  1. B. Javidi, J. L. Horner, “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. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  3. B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (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]
  6. P. C. Mogensen, J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40, 1226–1235 (2001).
    [CrossRef]
  7. H. T. Chang, “Image encryption using separable amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
    [CrossRef]
  8. B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
    [CrossRef]
  9. B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
    [CrossRef]
  10. B. Wang, C. C. Sun, W. C. Su, A. E. T. Chiou, “Shift-tolerance property of an optical double-random phase-encoding encryption system,” Appl. Opt. 39, 4788–4793 (2000).
    [CrossRef]
  11. B. Wang, C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
    [CrossRef]
  12. T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
    [CrossRef]
  13. T. Nomura, B. Javidi, “Optical encryption system with a binary key code,” Appl. Opt. 39, 4783–4787 (2000).
    [CrossRef]
  14. M. Yamazaki, J. Ohtsubo, “Optimization of encrypted holograms in optical security systems,” Opt. Eng. 40, 132–137 (2001).
    [CrossRef]
  15. J. Ohtsubo, A. Fujimoto, “Practical image encryption and decryption by phase-coding technique for optical security systems,” Appl. Opt. 41, 4848–4855 (2002).
    [CrossRef] [PubMed]

2002 (1)

2001 (4)

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

H. T. Chang, “Image encryption using separable amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

B. Wang, C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[CrossRef]

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

2000 (3)

1999 (1)

1998 (2)

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

1997 (1)

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

1996 (1)

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

1995 (1)

1994 (1)

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

Ahouzi, E.

B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Chang, H. T.

H. T. Chang, “Image encryption using separable amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

Chiou, A. E. T.

Fujimoto, A.

Glückstad, J.

Guibert, L.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Horner, J. L.

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

Javidi, B.

T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

T. Nomura, B. Javidi, “Optical encryption system with a binary key code,” Appl. Opt. 39, 4783–4787 (2000).
[CrossRef]

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

B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef] [PubMed]

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

Li, J.

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Luo, Z.

Mogensen, P. C.

Nomura, T.

T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

T. Nomura, B. Javidi, “Optical encryption system with a binary key code,” Appl. Opt. 39, 4783–4787 (2000).
[CrossRef]

Ohtsubo, J.

J. Ohtsubo, A. Fujimoto, “Practical image encryption and decryption by phase-coding technique for optical security systems,” Appl. Opt. 41, 4848–4855 (2002).
[CrossRef] [PubMed]

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

Réfrégier, P.

Sergent, A.

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Su, W. C.

Sun, C. C.

B. Wang, C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[CrossRef]

B. Wang, C. C. Sun, W. C. Su, A. E. T. Chiou, “Shift-tolerance property of an optical double-random phase-encoding encryption system,” Appl. Opt. 39, 4788–4793 (2000).
[CrossRef]

Towghi, N.

Wang, B.

B. Wang, C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[CrossRef]

B. Wang, C. C. Sun, W. C. Su, A. E. T. Chiou, “Shift-tolerance property of an optical double-random phase-encoding encryption system,” Appl. Opt. 39, 4788–4793 (2000).
[CrossRef]

Yamazaki, M.

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

Zhang, G.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. A (1)

Opt. Eng. (8)

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

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

H. T. Chang, “Image encryption using separable amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Wang, C. C. Sun, “Enhancement of signal-to-noise ratio of a double random phase encoding encryption system,” Opt. Eng. 40, 1502–1506 (2001).
[CrossRef]

T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

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

Opt. Lett. (1)

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Figures (7)

Fig. 1
Fig. 1

Scheme of the JTC architecture: L1, Fourier-transform lens; P1, plane; f, focal length; λ/2, half-wave plate.

Fig. 2
Fig. 2

Images used for simulations: (a) original image, (b) virtual image, (c) Fourier decrypting key |D(u, v)|, and (d) encrypted data |E(u, v)|.

Fig. 3
Fig. 3

Reconstructed images: (a) the intensity image of Eq. (7) and (b) the reconstructed image that is digitally obtained by the inversion of even-numbered pixels along the x axis in (a).

Fig. 4
Fig. 4

Modified images used for the encryption and the corresponding results: (a) modified encrypted image |E m (u, v)|, (b) modified decrypting key |D m (u, v)|, (c) reconstructed image, and (d) inversion of (c).

Fig. 5
Fig. 5

MSE for the reconstructed images when the encrypted image is blocked along the u axis.

Fig. 6
Fig. 6

Decrypted results when the encrypted image is shifted (a) 1, (b) 3, and (c) 5 pixels from the matching position in Fourier space.

Fig. 7
Fig. 7

Decrypted results when the encrypted image with a constant phase shift π/2 is shifted (a) 1, (b) 3, and (c) 5 pixels from the matching position in Fourier space. (d) The compensated image for stripes.

Equations (16)

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expjπfx, y=expjπvx, y+2rx, y-dAx, y,
ex, y=expjπvx, y+2rx, y.
expjπdAx, y=expjπvx, y+2rx, y-fx, y.
expjπfx, y=expjπfx, y±2n,expjπdAx, y=expjπdAx, y±2n,
expjπdx, y=expjπdAx, y+2-1dAx, y<0expjπdAx, y0dAx, y<2expjπdAx, y-22dAx, y3,
Ou, v=Eu-u0, v+Du+u0, v.
|ox, y|2=2+2 cosπfx, y-4πu0x,
Δd=12fx0,x=kΔd=k LNx,u=k 1Δd=k NxL,
|ox, y|2=2+2 cosπfx, y-4π14ΔdkxΔd=2+2 cosπfx, y-πkx=2+2 cosπfx, ykx=2n2-2 cosπfx, ykx=2n+1,
Emu, v=emx, y=ex, yexp-j2πu0x,Dmu, v=dmx, y=expjπdx, yexpj2πu0x,
|ox, y|2=2+2 cosπfx, y-2πkx=2+2 cosπfx, y,
Ou, v=Emu-u0-α, v+Dmu+u0, v.
|ox, y|2=2+2 cosπfx, y-2παx.
|ocx, y|2=2-2 sinπfx, y-2παx.
fx, y=arccosI1-22cos2παx-I2-22sin2παxπ,
MSE=E1N×Mx=0N-1y=0M-1fox, y|-|fdx, y2,

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