Abstract

The performance of fully phase- and amplitude-based encryption processors is analyzed. The effects of noise perturbations on the encrypted information are considered. A thresholding method of decryption that further reduces the mean-squared error (MSE) for the fully phase- and amplitude-based encryption processes is provided. The proposed thresholding scheme significantly improves the performance of fully phase- and amplitude-based encryption, as measured by the MSE metric. We obtain analytical MSE bounds when thresholding is used for both decryption methods, and we also present computer-simulation results. These results show that the fully phase-based method is more robust. We also give a formal proof of a conjecture about the decrypted distribution of distorted encrypted information. This allows the analytical bounds of the MSE to be extended to more general non-Gaussian, nonadditive, nonstationary distortions. Computer simulations support this extension.

© 2000 Optical Society of America

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  1. Special Issue on Optical Security, Opt. Eng.35, 2451–2541 (1996).
  2. Special Issue on Optical Security, Opt. Eng.38, 1–119 (1999).
  3. B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  4. P. Réfrégier, B. Javidi, “Optical image encryption using input and Fourier plane random phase encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef]
  5. Q. Huang, J. Caulfield, “Wave guide holography and its applications,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 303–312 (1991).
  6. 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]
  7. K. H. Fielding, J. L. Horner, C. K. Makekau, “Optical fingerprint identification by binary joint transform correlation,” Opt. Eng. 30, 1958–1961 (1991).
    [CrossRef]
  8. H.-Y. Li, Y. Qiao, D. Psaltis, “Optical network for real-time face recognition,” Appl. Opt. 32, 5026–5035 (1993).
    [CrossRef] [PubMed]
  9. B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34, 1752–1756 (1995).
    [CrossRef]
  10. J. Rodolfo, H. Rajbenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
    [CrossRef]
  11. C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. Casasent, T. H. Chao, eds., Proc. SPIE3073, 373–382 (1997).
  12. N. Riza, M. Howlader, “Photonics security system using spatial codes and remote coded coherent optical communications,” Opt. Eng. 35, 2487–2498 (1996).
    [CrossRef]
  13. M. Drake, M. Lid, M. A. Fiddy, “Wave guide hologram fingerprint entry device,” Opt. Eng. 35, 2499–2505 (1996).
    [CrossRef]
  14. 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]
  15. J. Campello, J. T. Gill, M. Morf, M. J. Flynn, “Smart photonic networks and computer security for image data,” in Multimedia Networks: Security, Displays, Terminals, and Gateways, B. Derryberry, C. R. Holliday, L. S. Lome, V. Markandey, B. Vasudev, M. V. Bove, A. G. Tescher, eds., Proc. SPIE3228, 272–279 (1998).
  16. H. F. Heanue, M. C. Bashaw, L. Hesselink, “Encrypted holographic data storage based on orthogonal-phase-code multiplexing,” Appl. Opt. 34, 6012–6015 (1995).
    [CrossRef] [PubMed]
  17. O. Matoba, B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
    [CrossRef]
  18. B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to xor encryption,” Opt. Eng. 38, 9–19 (1999).
    [CrossRef]
  19. L. O’Gorman, I. Rabinovich, “Secure identification documents via pattern recognition and public-key cryptography,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 1097–1102 (1998).
    [CrossRef]
  20. N. Towghi, B. Javidi, Z. Luo, “Fully phase encrypted optical processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
    [CrossRef]
  21. V. Gnedenko, The Theory of Probability (Mir, Moscow, 1976).
  22. B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding technique,” Opt. Eng. 36, 992–998 (1997).
    [CrossRef]
  23. I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).

1999 (4)

Special Issue on Optical Security, Opt. Eng.38, 1–119 (1999).

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to xor encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

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

O. Matoba, B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[CrossRef]

1998 (2)

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]

L. O’Gorman, I. Rabinovich, “Secure identification documents via pattern recognition and public-key cryptography,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 1097–1102 (1998).
[CrossRef]

1997 (1)

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

1996 (4)

Special Issue on Optical Security, Opt. Eng.35, 2451–2541 (1996).

N. Riza, M. Howlader, “Photonics security system using spatial codes and remote coded coherent optical communications,” Opt. Eng. 35, 2487–2498 (1996).
[CrossRef]

M. Drake, M. Lid, M. A. Fiddy, “Wave guide hologram fingerprint entry device,” Opt. Eng. 35, 2499–2505 (1996).
[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]

1995 (4)

B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34, 1752–1756 (1995).
[CrossRef]

J. Rodolfo, H. Rajbenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

H. F. Heanue, M. C. Bashaw, L. Hesselink, “Encrypted holographic data storage based on orthogonal-phase-code multiplexing,” Appl. Opt. 34, 6012–6015 (1995).
[CrossRef] [PubMed]

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

1994 (1)

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

1993 (1)

1991 (1)

K. H. Fielding, J. L. Horner, C. K. Makekau, “Optical fingerprint identification by binary joint transform correlation,” Opt. Eng. 30, 1958–1961 (1991).
[CrossRef]

Bashaw, M. C.

Bernard, L.

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to xor encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

Bollaro, F.

Campello, J.

J. Campello, J. T. Gill, M. Morf, M. J. Flynn, “Smart photonic networks and computer security for image data,” in Multimedia Networks: Security, Displays, Terminals, and Gateways, B. Derryberry, C. R. Holliday, L. S. Lome, V. Markandey, B. Vasudev, M. V. Bove, A. G. Tescher, eds., Proc. SPIE3228, 272–279 (1998).

Caulfield, J.

Q. Huang, J. Caulfield, “Wave guide holography and its applications,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 303–312 (1991).

Drake, M.

M. Drake, M. Lid, M. A. Fiddy, “Wave guide hologram fingerprint entry device,” Opt. Eng. 35, 2499–2505 (1996).
[CrossRef]

Fiddy, M. A.

M. Drake, M. Lid, M. A. Fiddy, “Wave guide hologram fingerprint entry device,” Opt. Eng. 35, 2499–2505 (1996).
[CrossRef]

Fielding, K. H.

K. H. Fielding, J. L. Horner, C. K. Makekau, “Optical fingerprint identification by binary joint transform correlation,” Opt. Eng. 30, 1958–1961 (1991).
[CrossRef]

Flynn, M. J.

J. Campello, J. T. Gill, M. Morf, M. J. Flynn, “Smart photonic networks and computer security for image data,” in Multimedia Networks: Security, Displays, Terminals, and Gateways, B. Derryberry, C. R. Holliday, L. S. Lome, V. Markandey, B. Vasudev, M. V. Bove, A. G. Tescher, eds., Proc. SPIE3228, 272–279 (1998).

Gikhman, I. I.

I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).

Gill, J. T.

J. Campello, J. T. Gill, M. Morf, M. J. Flynn, “Smart photonic networks and computer security for image data,” in Multimedia Networks: Security, Displays, Terminals, and Gateways, B. Derryberry, C. R. Holliday, L. S. Lome, V. Markandey, B. Vasudev, M. V. Bove, A. G. Tescher, eds., Proc. SPIE3228, 272–279 (1998).

Gnedenko, V.

V. Gnedenko, The Theory of Probability (Mir, Moscow, 1976).

Goudail, F.

Guibert, L.

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

Heanue, H. F.

Hesselink, L.

Horner, J. L.

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

K. H. Fielding, J. L. Horner, C. K. Makekau, “Optical fingerprint identification by binary joint transform correlation,” Opt. Eng. 30, 1958–1961 (1991).
[CrossRef]

Howlader, M.

N. Riza, M. Howlader, “Photonics security system using spatial codes and remote coded coherent optical communications,” Opt. Eng. 35, 2487–2498 (1996).
[CrossRef]

Huang, Q.

Q. Huang, J. Caulfield, “Wave guide holography and its applications,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 303–312 (1991).

Huignard, J.-P.

J. Rodolfo, H. Rajbenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

Javidi, B.

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to xor encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

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

O. Matoba, B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[CrossRef]

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. Guibert, “Fault tolerance properties of a double phase encoding 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]

B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34, 1752–1756 (1995).
[CrossRef]

P. Réfrégier, B. Javidi, “Optical image encryption using input and Fourier plane random phase 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.

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]

B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34, 1752–1756 (1995).
[CrossRef]

Lid, M.

M. Drake, M. Lid, M. A. Fiddy, “Wave guide hologram fingerprint entry device,” Opt. Eng. 35, 2499–2505 (1996).
[CrossRef]

Luo, Z.

Makekau, C. K.

K. H. Fielding, J. L. Horner, C. K. Makekau, “Optical fingerprint identification by binary joint transform correlation,” Opt. Eng. 30, 1958–1961 (1991).
[CrossRef]

Matoba, O.

Morf, M.

J. Campello, J. T. Gill, M. Morf, M. J. Flynn, “Smart photonic networks and computer security for image data,” in Multimedia Networks: Security, Displays, Terminals, and Gateways, B. Derryberry, C. R. Holliday, L. S. Lome, V. Markandey, B. Vasudev, M. V. Bove, A. G. Tescher, eds., Proc. SPIE3228, 272–279 (1998).

O’Gorman, L.

L. O’Gorman, I. Rabinovich, “Secure identification documents via pattern recognition and public-key cryptography,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 1097–1102 (1998).
[CrossRef]

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. Casasent, T. H. Chao, eds., Proc. SPIE3073, 373–382 (1997).

Psaltis, D.

Qiao, Y.

Rabinovich, I.

L. O’Gorman, I. Rabinovich, “Secure identification documents via pattern recognition and public-key cryptography,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 1097–1102 (1998).
[CrossRef]

Rajbenbach, H.

J. Rodolfo, H. Rajbenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

Réfrégier, P.

Riza, N.

N. Riza, M. Howlader, “Photonics security system using spatial codes and remote coded coherent optical communications,” Opt. Eng. 35, 2487–2498 (1996).
[CrossRef]

Rodolfo, J.

J. Rodolfo, H. Rajbenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

Sergent, A.

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

Skorokhod, A. V.

I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).

Tang, Q.

B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34, 1752–1756 (1995).
[CrossRef]

Towghi, N.

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

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to xor encryption,” Opt. Eng. 38, 9–19 (1999).
[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. Casasent, T. H. Chao, eds., Proc. SPIE3073, 373–382 (1997).

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. Casasent, T. H. Chao, eds., Proc. SPIE3073, 373–382 (1997).

Zhang, G.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding 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. (3)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. O’Gorman, I. Rabinovich, “Secure identification documents via pattern recognition and public-key cryptography,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 1097–1102 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (10)

N. Riza, M. Howlader, “Photonics security system using spatial codes and remote coded coherent optical communications,” Opt. Eng. 35, 2487–2498 (1996).
[CrossRef]

M. Drake, M. Lid, M. A. Fiddy, “Wave guide hologram fingerprint entry device,” Opt. Eng. 35, 2499–2505 (1996).
[CrossRef]

J. Rodolfo, H. Rajbenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[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]

K. H. Fielding, J. L. Horner, C. K. Makekau, “Optical fingerprint identification by binary joint transform correlation,” Opt. Eng. 30, 1958–1961 (1991).
[CrossRef]

Special Issue on Optical Security, Opt. Eng.35, 2451–2541 (1996).

Special Issue on Optical Security, Opt. Eng.38, 1–119 (1999).

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

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

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to xor encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

Opt. Lett. (2)

Other (5)

J. Campello, J. T. Gill, M. Morf, M. J. Flynn, “Smart photonic networks and computer security for image data,” in Multimedia Networks: Security, Displays, Terminals, and Gateways, B. Derryberry, C. R. Holliday, L. S. Lome, V. Markandey, B. Vasudev, M. V. Bove, A. G. Tescher, eds., Proc. SPIE3228, 272–279 (1998).

V. Gnedenko, The Theory of Probability (Mir, Moscow, 1976).

Q. Huang, J. Caulfield, “Wave guide holography and its applications,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 303–312 (1991).

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

I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).

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