Abstract

An image cryptosystem based on multiple phase-only masks is proposed. The proposed cryptosystem is a hierarchical security system that can use multiple phase keys to retrieve different amounts of data. In addition to the sequential order of the phase keys, the distance parameters among the phase keys are introduced to increase the system security. Even when an illegal user steals all the phase keys, the system cannot be broken without the correct sequential order and the distance parameters. However, the proposed system can verify the identities of the persons by the cascaded structure for the phase keys to generate different verification images. Simulation results are further demonstrated to verify the proposed method.

© 2002 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. R. K. Wang, I. A. Watson, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
    [CrossRef]
  3. Y. Li, K. Kreske, J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).
    [CrossRef]
  4. J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on XOR operation,” Opt. Eng. 37, 47–54 (1999).
    [CrossRef]
  5. T. S. Chen, C. C. Chang, M. S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process. 7, 1485–1488 (1998).
    [CrossRef]
  6. N. Towghi, B. Javidi, Z. Luo, “Fully phase encryption image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
    [CrossRef]
  7. M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-30, 140–154 (1982).
    [CrossRef]
  8. C. J. Kuo, M. H. Tsai, Three dimensional holographic imaging (Wiley, New York, 2002).
    [CrossRef]
  9. A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. 22, 735–742 (1975).
    [CrossRef]
  10. G. Strang, Introduction to Applied Mathematics (Wellesley, Cambridge, Mass., 1986).
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    [CrossRef]
  12. R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).
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    [CrossRef]
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    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996) Chap. 4.
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    [CrossRef]
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    [CrossRef] [PubMed]
  18. S. Lai, M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178, 283–289 (2000).
    [CrossRef]
  19. L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Optical Commun. 203, 67–77 (2002).
    [CrossRef]
  20. E. Tajahuerce, O. Matoba, S. C. Verall, B. Javidi, “Optoelectronic information encryption using phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
    [CrossRef]
  21. A. D. Poularilcas, S. Seely, Signals and Systems (PWS-KENT, Boston, Mass., 1991).

2002 (1)

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Optical Commun. 203, 67–77 (2002).
[CrossRef]

2000 (3)

1999 (2)

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on XOR operation,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

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

1998 (1)

T. S. Chen, C. C. Chang, M. S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process. 7, 1485–1488 (1998).
[CrossRef]

1996 (1)

R. K. Wang, I. A. Watson, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

1995 (1)

1993 (1)

1988 (1)

1982 (2)

J. R. Fienup, “Phase retrieval algorithms: A comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-30, 140–154 (1982).
[CrossRef]

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–306 (1980).
[CrossRef]

1975 (1)

A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. 22, 735–742 (1975).
[CrossRef]

1974 (1)

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Bryngdahl, O.

Cai, L.

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Optical Commun. 203, 67–77 (2002).
[CrossRef]

Chang, C. C.

T. S. Chen, C. C. Chang, M. S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process. 7, 1485–1488 (1998).
[CrossRef]

Chen, T. S.

T. S. Chen, C. C. Chang, M. S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process. 7, 1485–1488 (1998).
[CrossRef]

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: A comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–306 (1980).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996) Chap. 4.

Han, J. W.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on XOR operation,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Hayes, M. H.

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-30, 140–154 (1982).
[CrossRef]

Hwang, M. S.

T. S. Chen, C. C. Chang, M. S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process. 7, 1485–1488 (1998).
[CrossRef]

Javidi, B.

Kim, E. S.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on XOR operation,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Kreske, K.

Kuo, C. J.

C. J. Kuo, M. H. Tsai, Three dimensional holographic imaging (Wiley, New York, 2002).
[CrossRef]

Lai, S.

S. Lai, M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178, 283–289 (2000).
[CrossRef]

Li, Y.

Luo, Z.

Matoba, O.

Neifeld, M. A.

S. Lai, M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178, 283–289 (2000).
[CrossRef]

Papouli, A.

A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. 22, 735–742 (1975).
[CrossRef]

Park, C. S.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on XOR operation,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Peng, X.

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Optical Commun. 203, 67–77 (2002).
[CrossRef]

Poularilcas, A. D.

A. D. Poularilcas, S. Seely, Signals and Systems (PWS-KENT, Boston, Mass., 1991).

Refregier, P.

Rosen, J.

Ryu, D. H.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on XOR operation,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Seely, S.

A. D. Poularilcas, S. Seely, Signals and Systems (PWS-KENT, Boston, Mass., 1991).

Strang, G.

G. Strang, Introduction to Applied Mathematics (Wellesley, Cambridge, Mass., 1986).

Tajahuerce, E.

Towghi, N.

Tsai, M. H.

C. J. Kuo, M. H. Tsai, Three dimensional holographic imaging (Wiley, New York, 2002).
[CrossRef]

Verall, S. C.

Wang, R. K.

R. K. Wang, I. A. Watson, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Watson, I. A.

R. K. Wang, I. A. Watson, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Wyrowski, F.

Yu, L.

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Optical Commun. 203, 67–77 (2002).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Acoust. Speech Signal Proc. (1)

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-30, 140–154 (1982).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. 22, 735–742 (1975).
[CrossRef]

IEEE Trans. Image Process. (1)

T. S. Chen, C. C. Chang, M. S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process. 7, 1485–1488 (1998).
[CrossRef]

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

Opt. Acta (1)

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

Opt. Commun. (1)

S. Lai, M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178, 283–289 (2000).
[CrossRef]

Opt. Eng. (3)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–306 (1980).
[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on XOR operation,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

R. K. Wang, I. A. Watson, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Opt. Lett. (2)

Optical Commun. (1)

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Optical Commun. 203, 67–77 (2002).
[CrossRef]

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Other (4)

G. Strang, Introduction to Applied Mathematics (Wellesley, Cambridge, Mass., 1986).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996) Chap. 4.

C. J. Kuo, M. H. Tsai, Three dimensional holographic imaging (Wiley, New York, 2002).
[CrossRef]

A. D. Poularilcas, S. Seely, Signals and Systems (PWS-KENT, Boston, Mass., 1991).

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Figures (15)

Fig. 1
Fig. 1

Data-access control in a hierarchical security system.

Fig. 2
Fig. 2

Optical setup of the basic architecture.

Fig. 3
Fig. 3

Block diagram of the POCS algorithm.

Fig. 4
Fig. 4

Optical setup of the advanced architecture.

Fig. 5
Fig. 5

Schematic and operation representation of the space distance d i .

Fig. 6
Fig. 6

Three test images in levels one, two, and three.

Fig. 7
Fig. 7

Phase distribution of three optimized phase-only masks P 1, P 2, P 3 generated by the POCS algorithm.

Fig. 8
Fig. 8

Phase distribution of the three phase keys P I,1, P I,2, P I,3 in the basic architecture.

Fig. 9
Fig. 9

Retrieved images of the basic architecture in levels one, two, and three.

Fig. 10
Fig. 10

Phase distribution of the three phase keys P I,1, P I,2, P I,3 in the advanced architecture.

Fig. 11
Fig. 11

Retrieved images of the advanced architecture in levels one, two, and three.

Fig. 12
Fig. 12

Retrieved image without the second phase key P 2 in the basic architecture.

Fig. 13
Fig. 13

Retrieved images with incorrect distance parameters (d 1 = 6 mm, d 2 = 9 mm, and d 3 = 16 mm) in the advanced architecture.

Fig. 14
Fig. 14

Correlation results of retrieved images obtained by the phase key that was shifted different distances from its correct position.

Fig. 15
Fig. 15

Retrieved images with different correlation values.

Tables (1)

Tables Icon

Table 1 Correlation Comparisona

Equations (8)

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

UIx, y=AIx, yPIx, y=AI expjϕIx, y, PIx, y=expjϕIx, y,
UOfx, fy=AOfx, fyPOfx, fy=AO expjϕOfx, fy, POfx, fy=expjϕOfx, fy,
UOx, y=-- UIx, yGx, y×expj 2πλLxfx+yfydxdy.
Ki=PI,ix, yPI,i-1x, y=expjϕI,ix, y-ϕI,i-1x, y.
UO,nfx, fy=FTK1×K2××Kn, =FTexpjϕI,1x, y-ϕI,0x, y+ϕI,2x, y-ϕI,1x, y++ϕI,nx, y-ϕI,n-1x, y, =FTexpjϕI,nx, y, =FTPI,nx, y,
UI,ixi, yi= Ux, yexpj k2dix-xi2+y-yi2dxdy, =Ux, yexpj k2dixi2+yi2,
K1=K1h-d1, K2=K2h-d1K1¯h-d2-d1, K3=K3h-d1K1¯h-d2-d1×K2¯h-d3-d2, = Kn=Knh-d1K1¯h-d2-d1K2¯h-d3-d2×Kn-1¯h-dn-dn-1,
UO,ifx, fy=FTKihdi-di-1×Ki-1hdi-1-di-2×K1hd1, =FTKi, =FTexpjϕI,ix, y, =FTPI,i(x, y,

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