Abstract

A double-random-phase optical encryption system that uses a binary key code is proposed. The key code is generated as a binary computer-generated hologram. The binary key code can be displayed on a binary spatial light modulator (SLM) such as a ferroelectric liquid-crystal display. The use of a binary SLM enables us to renew the key at high speed. A joint transform correlator based on a photorefractive crystal in the Fourier domain is used to perform shift-invariant encryption and decryption. Computer simulations of the effects of using a binary encoded key code instead of a complex amplitude key code are shown. Preliminary optical experimental results are presented to demonstrate the effectiveness of the proposed system.

© 2000 Optical Society of America

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References

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1999 (1)

Special issue on optical security, Opt. Eng. 38, 8–119 (1999).

1998 (2)

1997 (1)

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

1996 (1)

Special issue on optical security, Opt. Eng. 35, 2451–2541 (1996).

1995 (1)

1994 (1)

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

1993 (1)

1967 (1)

1966 (1)

Bollaro, F.

Brown, B. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Goudail, F.

Guilbert, L.

B. Javidi, A. Sergent, G. Zhang, L. Guilbert, “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]

Itoh, M.

Javidi, B.

F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

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

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

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

Li, H.-Y. S.

Lohmann, A. W.

Paek, E. G.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

Paris, D. P.

Psaltis, D.

Qiao, Y.

Réfrégier, P.

Sergent, A.

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

Watson, C. I.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

Wilson, C. L.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

Yatagai, T.

Yoshikawa, N.

Zhang, G.

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

Appl. Opt. (3)

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

Opt. Eng. (4)

Special issue on optical security, Opt. Eng. 35, 2451–2541 (1996).

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

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

Special issue on optical security, Opt. Eng. 38, 8–119 (1999).

Opt. Lett. (2)

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Optical double-random phase encryption with binary encoded key code. (a) Encryption. (b) Decryption. 2D, two dimensional.

Fig. 2
Fig. 2

Image with a spatial carrier frequency to be encrypted.

Fig. 3
Fig. 3

Portion of the binary key code used in the computer simulations.

Fig. 4
Fig. 4

Reconstructed Fourier phase mask with a computer simulation. (a) Amplitude distribution. (b) Phase distribution.

Fig. 5
Fig. 5

Histograms of both the amplitude and the phase mask generated by a CGH binary key code.

Fig. 6
Fig. 6

Image decrypted with computer simulations. (a) Correct binary key code. (b) Incorrect key code.

Fig. 7
Fig. 7

Experimental setup for a JTC with a photorefractive crystal: BE, beam expander; CL, collimating lens; Ar+, argon-ion; P, plane; S, shutter; L, lens; f c (x, y), image to be encrypted with a spatial carrier frequency; α(x, y), input phase code; h c (x, y), binary key code.

Fig. 8
Fig. 8

Input images consisting of the original image to be encrypted and the binary key code represented by a CGH for optical experiments.

Fig. 9
Fig. 9

Input images observed through the photorefractive crystal with optical experiments.

Fig. 10
Fig. 10

Decrypted images with correct binary encoded key codes with optical experiments.

Fig. 11
Fig. 11

Decrypted image with incorrect binary encoded key codes with optical experiments.

Tables (1)

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Table 1 SNR of the Decrypted Image

Equations (13)

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fcx, y=fx, ycos2πv0y,
hcx, y=hx, ycos2πv0y.
gx, y=fx, yαx, y,
gcx, y=fcx, yαx, y=gx, ycos2πv0y.
Gcu, v=1/2Gu, v * δv-v0+δv+v0,
Hcu, v=1/2Hu, v * δv-v0+δv+v0,
Gcu, v=Gu, v * δv-v0=Gu, v-v0,
Hcu, v=Hu, v * δv-v0=Hu, v-v0,
Eu, v=|Gcu, v|2+|Hcu, v|2+Gcu, v×Hc*u, v+Gc*u, vHcu, v,
Du, v=Hcu, vEu, v=Hu, v-v0|Gu, v-v0|2+Hu, v-v0+Gu, v-v0+H2u, v-v0G*u, v-v0,
dx, y=hcx, y * gcx, y  gc*x, y+hcx, y+gcx, y+hcx, y * gcx, y  hcx, y,
gcx, y=gx, yexpj2πv0y=fx, yαx, yexpj2πv0y.
SNR=x,yfex, y2x,yfex, y-fdx, y2,

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