Abstract

In this paper we propose a new (to our knowledge) complex spatial modulation method to encode data pages applicable in double random phase encryption (DRPE) to make the system more resistant to brute-force attack. The proposed modulation method uses data page pixels with random phase and amplitude values with the condition that the intensity of the interference of light from two adjacent pixels should correspond to the encoded information. A differential phase contrast technique is applied to recover the data page at the output of the system. We show that the proposed modulation method can enhance the robustness of the DRPE technique using point spread function analysis. Key space expansion is determined by numeric model calculations.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  7. M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
    [CrossRef]
  8. Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
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  13. J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1975).
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  15. S. B. Wicker and V. K. Bhargava, Reed Solomon Codes and Their Applications (IEEE, 1999).
  16. Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
    [CrossRef]

2012

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358 (2012).
[CrossRef]

T. Sarkadi and P. Koppa, “Quantitative security evaluation of optical encryption using hybrid phase- and amplitude-modulated keys,” Appl. Opt. 51, 745–750 (2012).
[CrossRef]

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

2011

Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

2010

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

2008

M. Singh, A. Kumar, and K. Singh, “Secure optical system that uses fully phase-based encryption and lithium niobate crystal as phase contrast filter for decryption,” Opt. Laser Technol. 40, 619–624 (2008).
[CrossRef]

2007

2004

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

2000

1999

1995

Bhargava, V. K.

S. B. Wicker and V. K. Bhargava, Reed Solomon Codes and Their Applications (IEEE, 1999).

Coufal, H. J.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).

Dai, J.

Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1975).

Gong, M.

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Gopinathan, U.

Javidi, B.

Joshi, M.

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

Koppa, P.

Kumar, A.

M. Singh, A. Kumar, and K. Singh, “Secure optical system that uses fully phase-based encryption and lithium niobate crystal as phase contrast filter for decryption,” Opt. Laser Technol. 40, 619–624 (2008).
[CrossRef]

Kuroda, K.

Li, S.

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358 (2012).
[CrossRef]

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Lin, C.

Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Liu, S.

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358 (2012).
[CrossRef]

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Liu, W.

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358 (2012).
[CrossRef]

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Liu, Z.

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358 (2012).
[CrossRef]

Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Lorincz, E.

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

Lovasz, M.

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

Matoba, O.

Monaghan, D. S.

Naughton, T. J.

Nomura, T.

Psaltis, D.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).

Refregier, P.

Richter, P.

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

Sajti, S.

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

Sarkadi, T.

Shakher, C.

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

Sheridan, J. T.

Shimura, T.

Sincerbox, G. T.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).

Singh, K.

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

M. Singh, A. Kumar, and K. Singh, “Secure optical system that uses fully phase-based encryption and lithium niobate crystal as phase contrast filter for decryption,” Opt. Laser Technol. 40, 619–624 (2008).
[CrossRef]

Singh, M.

M. Singh, A. Kumar, and K. Singh, “Secure optical system that uses fully phase-based encryption and lithium niobate crystal as phase contrast filter for decryption,” Opt. Laser Technol. 40, 619–624 (2008).
[CrossRef]

Tan, X. D.

Ujvári, T.

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

Varhegyi, P.

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

Wicker, S. B.

S. B. Wicker and V. K. Bhargava, Reed Solomon Codes and Their Applications (IEEE, 1999).

Xu, S. L.

Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Yang, M.

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358 (2012).
[CrossRef]

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Appl. Opt.

J. Opt. Pure Appl. Opt.

T. Ujvári, P. Koppa, M. Lovasz, P. Varhegyi, S. Sajti, E. Lorincz, and P. Richter, “A secure data storage system based on phase-encoded thin polarization holograms,” J. Opt. Pure Appl. Opt. 6, 401–411 (2004).
[CrossRef]

Opt. Commun.

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

Z. Liu, M. Yang, W. Liu, S. Li, M. Gong, W. Liu, and S. Liu, “Image encryption algorithm based on the random local phase encoding in gyrator transform domains,” Opt. Commun. 285, 3921–3925 (2012).
[CrossRef]

Opt. Laser Technol.

M. Singh, A. Kumar, and K. Singh, “Secure optical system that uses fully phase-based encryption and lithium niobate crystal as phase contrast filter for decryption,” Opt. Laser Technol. 40, 619–624 (2008).
[CrossRef]

Opt. Lasers Eng.

Z. Liu, S. Li, M. Yang, W. Liu, and S. Liu, “Image encryption based on the random rotation operation in the fractional Fourier transform domains,” Opt. Lasers Eng. 50, 1352–1358 (2012).
[CrossRef]

Z. Liu, S. L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Opt. Lett.

Other

J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1975).

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).

S. B. Wicker and V. K. Bhargava, Reed Solomon Codes and Their Applications (IEEE, 1999).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of the cryptosystem. Encryption: px,y, complex input image; ϕx,y, object phase mask; L, Fourier lenses; φu,v, Fourier phase mask; C, encrypted page. Decryption: L, Fourier lenses; φu,v, Fourier phase mask; ϕx,y, object phase mask; B, birefringent crystal; P, polarizer; Ix,y, decrypted page.

Fig. 2.
Fig. 2.

Point spread function (PSF) of the encryption system for different Fourier keys. (a) Correct Fourier key is applied for decryption (κ=0), (b) PSF using an incorrect Fourier key (κ=5%). Γ and Π denote the integration ranges used in Eq. (7). (c) PSF using an incorrect Fourier key (κ=30%).

Fig. 3.
Fig. 3.

Generation method of the complex amplitudes p14 input pixels to encode I14 intensity values.

Fig. 4.
Fig. 4.

(a) Pixels of the binary data page have Ilow and Ihigh intensities; (b) intensity pattern of the pseudorandom complex input image that encodes the data page in (a); (c) intensity histogram of the wavefront in (b).

Fig. 5.
Fig. 5.

Average intensity of the error component of the output page as a function of the mean intensity Iλ when the same PSF is applied to the different input images. Both intensities are measured in ID units.

Fig. 6.
Fig. 6.

Bit error rate (BER) of the output data pages as a function of key error rate of the Fourier key. BER profiles of pseudorandom input images are plotted at two differential Iλ values. The curve corresponding to the conventional binary phase encoded data page is also displayed.

Fig. 7.
Fig. 7.

Calculated key length of the encryption as a function of parameter Iλ of the pseudorandom input wavefront at three different signal-to-noise ratio values.

Fig. 8.
Fig. 8.

(a) Grayscale input image encrypted with DRPE and decrypted by the correct Fourier key, (b) Same encrypted image used in (a), recovered by a half-known Fourier phase key, (c) input image encoded into a pseudorandom complex wavefront then encrypted with DRPE and recovered by the correct phase key, (d) Same encrypted pseudorandom complex wave used in (c), recovered by a half-known Fourier phase key.

Equations (12)

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

PSFϕ=δx0,y0·ϕx,y,
PSFφ=I(φu,v),
PSFenc=δx0,y0·ϕx,yI(φu,v).
PSFdec=I(φu,v)(δx0,y0·ϕx,y+δxd,y0·ϕxd,y),
PSF=PSFencPSFdec=δx0,y0·ϕx,yI(φu,v·φu,v)(δx0,y0·ϕx,y+δxd,y0·ϕxd,y).
ax,y=PSFu,v·pux,vydudv,
ax,y=s+e=ΓPSFu,v·pux,vydudv+ΠPSFu,v·pux,vydudv,
s=γ(p1+p2),
Is=|s|2,
I=|s+e|2.
In=|pn+pn1|2.
Ii*Io=E((IiE(Ii))(IoE(Io)))σiσo,

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