Abstract

Here we present a new approach of multiplexing and simultaneous encoding of target images. Our approach can enhance the encryption level of a classical double random phase (DRP) encryption system by adding a supplementary security layer. The new approach can be divided into two security layers. The first layer is called the multiplexing level, which consists in using iterative Fourier transformations along with several encryption key images. These latter can be a set of biometric images. At the second layer, we use a classical DRP system. The two layers enable us to encode several target images (multi-encryption) and to reduce, at the same time, the requested decoded information (transmitted or storage information).

© 2009 Optical Society of America

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  1. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767-769 (1995).
    [CrossRef] [PubMed]
  2. F. Goudail, F. Bollaro, B. Javidi, and P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629-2638 (1998).
    [CrossRef]
  3. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
    [CrossRef]
  4. S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462-5470(2002).
    [CrossRef] [PubMed]
  5. L. G. Neto and Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459-2463 (1996).
    [CrossRef]
  6. N. Towghi, B. Javidi, and Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915-1927 (1999).
    [CrossRef]
  7. G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51-67 (2001).
    [CrossRef]
  8. B. Javidi and N. Takanori, “Securing information by use of digital holography,” Opt. Lett. 25, 28-30 (2000).
    [CrossRef]
  9. E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
    [CrossRef]
  10. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584-1586 (2004).
    [CrossRef] [PubMed]
  11. O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762-764 (1999).
    [CrossRef]
  12. J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
    [CrossRef]
  13. O. Matoba and B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288-7293 (1999).
    [CrossRef]
  14. J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
    [CrossRef]
  15. L. Cai, M. He, Q. Liu, and X. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43, 3078-3084 (2004).
    [CrossRef] [PubMed]
  16. M. He, L. Cai, Q. Liu, and X. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44, 2600-2606 (2005).
    [CrossRef] [PubMed]
  17. Z. Xin, Y. S. Wei, and X. Jian, “Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform,” Appl. Opt. 45, 8434-8439 (2006).
    [CrossRef] [PubMed]
  18. B. M. Hennelly and J. T. Sheridan, “Image encryption techniques based on fractional Fourier transform,” Proc. SPIE 5202, 76-87 (2003).
    [CrossRef]
  19. Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324-329(2007).
    [CrossRef]
  20. M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29-37 (2005).
    [CrossRef]
  21. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253-10265 (2007).
    [CrossRef] [PubMed]
  22. A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644-1646 (2005).
    [CrossRef] [PubMed]
  23. X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044-1046 (2006).
    [CrossRef] [PubMed]
  24. G. B. Folland, Fourier Analysis and Its Applications (Brooks/Cole, 1992).
  25. M. A. Pinsky, Introduction to Fourier Analysis and Wavelets (Brooks/Cole, 2002).
  26. C. Ioana, A. Mansour, A. Quinquis, and E. Radoi, Digital Signal Processing Using MATLAB (Wiley Science, 2008).
  27. I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase in phase-shifting digital holography,” Appl. Opt. 45, 975-983 (2006).
    [CrossRef] [PubMed]
  28. J. E. Rubio, “The global control of nonlinear diffusion equations,” SIAM J. Cont. Optim. 33, 308-322, 1995).
    [CrossRef]
  29. H. L. Langhaar, Energy Methods in Applied Mechanics (Wiley, 1962).
  30. T. J. Asaki, P. R. Campbell, R. Chartrand, C. E. Powell, K. R. Vixie, and B. Wohlberg, “Abel inversion using total variation regularization: applications,” Inv. Probl. Sci. Eng. 14, 873-885(2006).
    [CrossRef]
  31. J. Van Kan, A. Segal, and F. Vermolen, Numerical Methods in Scientific Computing (VSSD, 2006).
  32. K. Atkinson and W. Han, Theoretical Numerical Analysis (Springer-Verlag, 2001).
  33. A. R. Alghofari, “Problems in analysis related to satellites,” Ph.D. dissertation (The University of New South Wales, 2005).
  34. A. Alfalou and C. Brosseau “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(2009), to be published.
    [CrossRef]
  35. S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane: new approaches and critical analysis,” J. Opt. A Pure Appl. Opt. 9, 73-80 (2007).
    [CrossRef]
  36. A. Alfalou and A. Mansour, “Simultaneous multiplexing and encoding of multiple images based on a double random phase encryption system,” Proc. SPIE 7486, 74860L (2009).
    [CrossRef]

2009

A. Alfalou and C. Brosseau “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(2009), to be published.
[CrossRef]

A. Alfalou and A. Mansour, “Simultaneous multiplexing and encoding of multiple images based on a double random phase encryption system,” Proc. SPIE 7486, 74860L (2009).
[CrossRef]

2008

C. Ioana, A. Mansour, A. Quinquis, and E. Radoi, Digital Signal Processing Using MATLAB (Wiley Science, 2008).

2007

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane: new approaches and critical analysis,” J. Opt. A Pure Appl. Opt. 9, 73-80 (2007).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324-329(2007).
[CrossRef]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253-10265 (2007).
[CrossRef] [PubMed]

2006

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044-1046 (2006).
[CrossRef] [PubMed]

T. J. Asaki, P. R. Campbell, R. Chartrand, C. E. Powell, K. R. Vixie, and B. Wohlberg, “Abel inversion using total variation regularization: applications,” Inv. Probl. Sci. Eng. 14, 873-885(2006).
[CrossRef]

J. Van Kan, A. Segal, and F. Vermolen, Numerical Methods in Scientific Computing (VSSD, 2006).

I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase in phase-shifting digital holography,” Appl. Opt. 45, 975-983 (2006).
[CrossRef] [PubMed]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

Z. Xin, Y. S. Wei, and X. Jian, “Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform,” Appl. Opt. 45, 8434-8439 (2006).
[CrossRef] [PubMed]

2005

M. He, L. Cai, Q. Liu, and X. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44, 2600-2606 (2005).
[CrossRef] [PubMed]

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644-1646 (2005).
[CrossRef] [PubMed]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29-37 (2005).
[CrossRef]

A. R. Alghofari, “Problems in analysis related to satellites,” Ph.D. dissertation (The University of New South Wales, 2005).

2004

L. Cai, M. He, Q. Liu, and X. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43, 3078-3084 (2004).
[CrossRef] [PubMed]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584-1586 (2004).
[CrossRef] [PubMed]

2003

B. M. Hennelly and J. T. Sheridan, “Image encryption techniques based on fractional Fourier transform,” Proc. SPIE 5202, 76-87 (2003).
[CrossRef]

2002

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462-5470(2002).
[CrossRef] [PubMed]

M. A. Pinsky, Introduction to Fourier Analysis and Wavelets (Brooks/Cole, 2002).

2001

K. Atkinson and W. Han, Theoretical Numerical Analysis (Springer-Verlag, 2001).

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51-67 (2001).
[CrossRef]

2000

B. Javidi and N. Takanori, “Securing information by use of digital holography,” Opt. Lett. 25, 28-30 (2000).
[CrossRef]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
[CrossRef]

1999

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

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

O. Matoba and B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288-7293 (1999).
[CrossRef]

1998

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

1996

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

1995

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

J. E. Rubio, “The global control of nonlinear diffusion equations,” SIAM J. Cont. Optim. 33, 308-322, 1995).
[CrossRef]

1992

G. B. Folland, Fourier Analysis and Its Applications (Brooks/Cole, 1992).

1962

H. L. Langhaar, Energy Methods in Applied Mechanics (Wiley, 1962).

Alfalou, A.

A. Alfalou and C. Brosseau “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(2009), to be published.
[CrossRef]

A. Alfalou and A. Mansour, “Simultaneous multiplexing and encoding of multiple images based on a double random phase encryption system,” Proc. SPIE 7486, 74860L (2009).
[CrossRef]

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane: new approaches and critical analysis,” J. Opt. A Pure Appl. Opt. 9, 73-80 (2007).
[CrossRef]

Alghofari, A. R.

A. R. Alghofari, “Problems in analysis related to satellites,” Ph.D. dissertation (The University of New South Wales, 2005).

Arcos, S.

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644-1646 (2005).
[CrossRef] [PubMed]

Asaki, T. J.

T. J. Asaki, P. R. Campbell, R. Chartrand, C. E. Powell, K. R. Vixie, and B. Wohlberg, “Abel inversion using total variation regularization: applications,” Inv. Probl. Sci. Eng. 14, 873-885(2006).
[CrossRef]

Atkinson, K.

K. Atkinson and W. Han, Theoretical Numerical Analysis (Springer-Verlag, 2001).

Barrera, J. F.

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

Bollaro, F.

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

Bolognini, N.

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

Brosseau, C.

A. Alfalou and C. Brosseau “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(2009), to be published.
[CrossRef]

Cai, L.

M. He, L. Cai, Q. Liu, and X. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44, 2600-2606 (2005).
[CrossRef] [PubMed]

L. Cai, M. He, Q. Liu, and X. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43, 3078-3084 (2004).
[CrossRef] [PubMed]

Cai, L. Z.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29-37 (2005).
[CrossRef]

Campbell, P. R.

T. J. Asaki, P. R. Campbell, R. Chartrand, C. E. Powell, K. R. Vixie, and B. Wohlberg, “Abel inversion using total variation regularization: applications,” Inv. Probl. Sci. Eng. 14, 873-885(2006).
[CrossRef]

Carnicer, A.

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644-1646 (2005).
[CrossRef] [PubMed]

Castro, A.

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253-10265 (2007).
[CrossRef] [PubMed]

Chartrand, R.

T. J. Asaki, P. R. Campbell, R. Chartrand, C. E. Powell, K. R. Vixie, and B. Wohlberg, “Abel inversion using total variation regularization: applications,” Inv. Probl. Sci. Eng. 14, 873-885(2006).
[CrossRef]

Folland, G. B.

G. B. Folland, Fourier Analysis and Its Applications (Brooks/Cole, 1992).

Frauel, Y.

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253-10265 (2007).
[CrossRef] [PubMed]

Goudail, F.

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

Hamam, H.

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane: new approaches and critical analysis,” J. Opt. A Pure Appl. Opt. 9, 73-80 (2007).
[CrossRef]

Han, W.

K. Atkinson and W. Han, Theoretical Numerical Analysis (Springer-Verlag, 2001).

He, M.

M. He, L. Cai, Q. Liu, and X. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44, 2600-2606 (2005).
[CrossRef] [PubMed]

L. Cai, M. He, Q. Liu, and X. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43, 3078-3084 (2004).
[CrossRef] [PubMed]

He, M. Z.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29-37 (2005).
[CrossRef]

Henao, R.

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

Hennelly, B. M.

B. M. Hennelly and J. T. Sheridan, “Image encryption techniques based on fractional Fourier transform,” Proc. SPIE 5202, 76-87 (2003).
[CrossRef]

Ioana, C.

C. Ioana, A. Mansour, A. Quinquis, and E. Radoi, Digital Signal Processing Using MATLAB (Wiley Science, 2008).

Javidi, B.

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253-10265 (2007).
[CrossRef] [PubMed]

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462-5470(2002).
[CrossRef] [PubMed]

B. Javidi and N. Takanori, “Securing information by use of digital holography,” Opt. Lett. 25, 28-30 (2000).
[CrossRef]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

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

O. Matoba and B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288-7293 (1999).
[CrossRef]

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

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

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

Jian, X.

Z. Xin, Y. S. Wei, and X. Jian, “Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform,” Appl. Opt. 45, 8434-8439 (2006).
[CrossRef] [PubMed]

Joseph, J.

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
[CrossRef]

Juvells, I.

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644-1646 (2005).
[CrossRef] [PubMed]

Kishk, S.

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462-5470(2002).
[CrossRef] [PubMed]

Langhaar, H. L.

H. L. Langhaar, Energy Methods in Applied Mechanics (Wiley, 1962).

Liu, Q.

M. He, L. Cai, Q. Liu, and X. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44, 2600-2606 (2005).
[CrossRef] [PubMed]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29-37 (2005).
[CrossRef]

L. Cai, M. He, Q. Liu, and X. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43, 3078-3084 (2004).
[CrossRef] [PubMed]

Liu, S.

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324-329(2007).
[CrossRef]

Liu, Z.

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324-329(2007).
[CrossRef]

Luo, Z.

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

Mansour, A.

A. Alfalou and A. Mansour, “Simultaneous multiplexing and encoding of multiple images based on a double random phase encryption system,” Proc. SPIE 7486, 74860L (2009).
[CrossRef]

C. Ioana, A. Mansour, A. Quinquis, and E. Radoi, Digital Signal Processing Using MATLAB (Wiley Science, 2008).

Matoba, O.

O. Matoba and B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288-7293 (1999).
[CrossRef]

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

Meng, X. F.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29-37 (2005).
[CrossRef]

Mills, G. A.

I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase in phase-shifting digital holography,” Appl. Opt. 45, 975-983 (2006).
[CrossRef] [PubMed]

Montes-Usategui, M.

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644-1646 (2005).
[CrossRef] [PubMed]

Naughton, T. J.

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253-10265 (2007).
[CrossRef] [PubMed]

Neto, L. G.

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

Peng, X.

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044-1046 (2006).
[CrossRef] [PubMed]

Pinsky, M. A.

M. A. Pinsky, Introduction to Fourier Analysis and Wavelets (Brooks/Cole, 2002).

Powell, C. E.

T. J. Asaki, P. R. Campbell, R. Chartrand, C. E. Powell, K. R. Vixie, and B. Wohlberg, “Abel inversion using total variation regularization: applications,” Inv. Probl. Sci. Eng. 14, 873-885(2006).
[CrossRef]

Quinquis, A.

C. Ioana, A. Mansour, A. Quinquis, and E. Radoi, Digital Signal Processing Using MATLAB (Wiley Science, 2008).

Radoi, E.

C. Ioana, A. Mansour, A. Quinquis, and E. Radoi, Digital Signal Processing Using MATLAB (Wiley Science, 2008).

Refregier, P.

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

Réfrégier, P.

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

Rubio, J. E.

J. E. Rubio, “The global control of nonlinear diffusion equations,” SIAM J. Cont. Optim. 33, 308-322, 1995).
[CrossRef]

Segal, A.

J. Van Kan, A. Segal, and F. Vermolen, Numerical Methods in Scientific Computing (VSSD, 2006).

Sheng, Y.

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I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase in phase-shifting digital holography,” Appl. Opt. 45, 975-983 (2006).
[CrossRef] [PubMed]

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G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584-1586 (2004).
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X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044-1046 (2006).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288-7293 (1999).
[CrossRef]

L. Cai, M. He, Q. Liu, and X. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43, 3078-3084 (2004).
[CrossRef] [PubMed]

M. He, L. Cai, Q. Liu, and X. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44, 2600-2606 (2005).
[CrossRef] [PubMed]

Z. Xin, Y. S. Wei, and X. Jian, “Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform,” Appl. Opt. 45, 8434-8439 (2006).
[CrossRef] [PubMed]

Inv. Probl. Sci. Eng.

T. J. Asaki, P. R. Campbell, R. Chartrand, C. E. Powell, K. R. Vixie, and B. Wohlberg, “Abel inversion using total variation regularization: applications,” Inv. Probl. Sci. Eng. 14, 873-885(2006).
[CrossRef]

J. Opt. A Pure Appl. Opt.

S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane: new approaches and critical analysis,” J. Opt. A Pure Appl. Opt. 9, 73-80 (2007).
[CrossRef]

J. Opt. Soc. Am. A

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

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[CrossRef]

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[CrossRef]

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[CrossRef]

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G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
[CrossRef]

B. Javidi and N. Takanori, “Securing information by use of digital holography,” Opt. Lett. 25, 28-30 (2000).
[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584-1586 (2004).
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Figures (16)

Fig. 1
Fig. 1

Synoptic diagram of classical DRP encrypted system: “Mono-encryption DRP system”.

Fig. 2
Fig. 2

Synoptic diagram of our multi-encryption approach.

Fig. 3
Fig. 3

DRP encryption system enforced by two encryption levels.

Fig. 4
Fig. 4

Outcomes of our algorithm applied on positive speech signals: (a) first positive signal; (b) target positive signal; (c) first encrypted signal; (d) second encrypted signal.

Fig. 5
Fig. 5

Convergence of the mean square error (MSE).

Fig. 6
Fig. 6

Proposed multiplexing algorithm used in the first level of our multi-encryption scheme.

Fig. 7
Fig. 7

Two input images (a target image and a key image): (a) black and white image; (b) a gray-scale image of “Lena”.

Fig. 8
Fig. 8

MSEs with respect to iteration numbers.

Fig. 9
Fig. 9

Outcomes of the first stage of our encryption algorithm: (a) origin target image ( I 0 ); (b) known key image ( I 1 ); (c) first level output image MSE = 0.0014 (using 25 iterations); (d) first level output image MSE = 1.2869 × 10 4 (using 500 iterations).

Fig. 10
Fig. 10

Final encrypted image I c e i φ c after 500 iterations.

Fig. 11
Fig. 11

Synoptic diagram of the decryption system.

Fig. 12
Fig. 12

Outcomes of the encryption—decryption algorithm: (a) input target image ( I 0 ); (b) known key image ( I 1 ); (c) encrypted image at the output of our two-level encrypted system [ T c e { I φ c } ]; (d) decrypted image with a MSE = 0.0173 .

Fig. 13
Fig. 13

Pirated image.

Fig. 14
Fig. 14

Encryption of a multiple target images using a DRP system: (a) using the same key images; (b) using a different key for each target image.

Fig. 15
Fig. 15

Synoptic diagram of multi-encryption-DRP system.

Fig. 16
Fig. 16

Main ideas of our algorithm.

Tables (3)

Tables Icon

Table 1 Outcomes of Our Multi-Encryption Approach: Multiplexed, Encrypted, Decrypted, and Demultiplexed Images

Tables Icon

Table 2 Comparison Between Two Encryption Techniques: Successive Classical DRP and the Proposed Multi-Encryption DRP

Tables Icon

Table 3 Simulation Results

Equations (6)

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

I 1 e i φ 1 n = FT n ( I 0 e i φ 0 n ) ,
for   i = 1 : T , X 1 ( f ) = F T ( x ( t ) exp ( j φ 1 ( t ) ) ) , φ S ( f ) = angle ( X 1 ( f ) ) , y ( t ) = F T 1 ( Y ( f ) exp ( j φ S ( f ) ) ) , φ 1 ( t ) = angle ( y ( t ) ) , end .
Min φ ( t ) E | | F T 1 ( Y ( f ) exp ( j φ ( f ) ) ) | x ( t ) | 2 .
MSE = 1 M × N i N j M | ρ 1 ( i , j ) I 1 ( i , j ) | 2 .
I 0 e i φ 0 n I 1 e i φ 1 n ; I 1 e i φ 1 n = FT ( I 0 e i φ 0 n ) .
C R = ( 1 256 × 256 × 2 N 256 × 256 × 2 8 ) × 100.

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