Abstract

In this paper, we propose a novel input wave front modulation method to enhance the security level of a Mach–Zender interferometer-based Fourier encryption system. The input data is encoded in the two wave fronts propagated in the arms of the interferometer. Both arms contain a 4f setup, and two independent Fourier keys are used to encrypt these wave fronts. During decryption the encrypted wave fronts are propagated through the interferometer. In the case when correct Fourier keys are used for decryption, the reconstructed data page is shown by the interference pattern of the output. We propose a method to synthesize two phase modulated input images for this cryptosystem. The modulation method has a user defined phase parameter. We prove that the security level of the proposed cryptosystem can be significantly improved compared with previous solutions, by using an optimally chosen phase parameter.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46, 5257–5262 (2007).
    [CrossRef]
  8. D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. P. Kumar, J. Joseph, and K. Singh, “Impulse attack-free four random phase mask encryption based on a 4f optical system,” Appl. Opt. 48, 2356–2363 (2009).
    [CrossRef]
  12. X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33, 1575–1577 (2008).
    [CrossRef]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  18. N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009).
    [CrossRef]
  19. B. Yao, Z. Ren, N. Menke, Y. Wang, Y. Zheng, M. Lei, G. Chen, and N. Hampp, “Polarization holographic high-density optical data storage in bacteriorhodopsin film,” Appl. Opt. 44, 7344–7348 (2005).
    [CrossRef]
  20. X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40, 2310–2315 (2001).
    [CrossRef]
  21. M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A 10, 085007 (2008).
    [CrossRef]
  22. J. Joseph and D. A. Waldman, “Homogenized Fourier-transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. 45, 6374–6380 (2006).
    [CrossRef]
  23. P. Koppa, “Phase-to-amplitude data page conversion for holographic storage and optical encryption,” Appl. Opt. 46, 3561–3571 (2007).
    [CrossRef]
  24. T. Sarkadi and P. Koppa, “Optical encryption using pseudorandom complex spatial modulation,” Appl. Opt. 51, 8068–8073 (2012).
    [CrossRef]
  25. J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1975).
  26. H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).
  27. S. B. Wicker and V. K. Bhargava, Reed Solomon Codes and their Applications (IEEE, 1999).

2012 (3)

2011 (1)

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 (2)

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]

H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express 18, 13772–13781 (2010).
[CrossRef]

2009 (2)

2008 (4)

2007 (2)

2006 (4)

2005 (1)

2004 (1)

T. Ujvari, 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. A 6, 401–411 (2004).
[CrossRef]

2001 (1)

2000 (1)

1999 (1)

1995 (1)

Bhargava, V. K.

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

Cai, L. Z.

Chen, G.

Cheng, X. C.

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).

Dong, G. Y.

Gopinathan, U.

Hampp, N.

Ide, M.

Javidi, B.

Joseph, J.

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, P.

Kuroda, K.

Lei, M.

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]

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, J.

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, 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]

Liu, Z.

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. Ujvari, 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. A 6, 401–411 (2004).
[CrossRef]

Lovasz, M.

T. Ujvari, 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. A 6, 401–411 (2004).
[CrossRef]

Mahmud, M. S.

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A 10, 085007 (2008).
[CrossRef]

Matoba, O.

Meng, X. F.

Menke, N.

Monaghan, D. S.

Naughton, T. J.

Naydenova, I.

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A 10, 085007 (2008).
[CrossRef]

Obi, T.

Ohyama, N.

Okada-Shudo, Y.

Peng, X.

Psaltis, D.

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

Refregier, P.

Ren, Z.

Richter, P.

T. Ujvari, 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. A 6, 401–411 (2004).
[CrossRef]

Sajti, S.

T. Ujvari, 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. A 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]

Shen, X. X.

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]

P. Kumar, J. Joseph, and K. Singh, “Impulse attack-free four random phase mask encryption based on a 4f optical system,” Appl. Opt. 48, 2356–2363 (2009).
[CrossRef]

Situ, G.

Suzuki, H.

Takeda, M.

Tan, X.

Tan, X. D.

Tashima, H.

Toal, V.

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A 10, 085007 (2008).
[CrossRef]

Ujvari, T.

T. Ujvari, 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. A 6, 401–411 (2004).
[CrossRef]

Varhegyi, P.

T. Ujvari, 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. A 6, 401–411 (2004).
[CrossRef]

Waldman, D. A.

Wang, B.

Wang, Y.

Wang, Y. R.

Wei, H.

Wicker, S. B.

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

Xie, J.

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]

Xu, X. F.

Yachida, M.

Yamaguchi, M.

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]

Yao, B.

Yu, B.

Zhang, H.

Zhang, P.

Zhang, Y.

Zheng, Y.

Zhu, N.

Appl. Opt. (11)

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

X. D. Tan, O. Matoba, T. Shimura, K. Kuroda, and B. Javidi, “Secure optical storage that uses fully phase encryption,” Appl. Opt. 39, 6689–6694 (2000).
[CrossRef]

X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40, 2310–2315 (2001).
[CrossRef]

B. Yao, Z. Ren, N. Menke, Y. Wang, Y. Zheng, M. Lei, G. Chen, and N. Hampp, “Polarization holographic high-density optical data storage in bacteriorhodopsin film,” Appl. Opt. 44, 7344–7348 (2005).
[CrossRef]

J. Joseph and D. A. Waldman, “Homogenized Fourier-transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. 45, 6374–6380 (2006).
[CrossRef]

P. Koppa, “Phase-to-amplitude data page conversion for holographic storage and optical encryption,” Appl. Opt. 46, 3561–3571 (2007).
[CrossRef]

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46, 5257–5262 (2007).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase key in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808–3816 (2008).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Impulse attack-free four random phase mask encryption based on a 4f optical system,” Appl. Opt. 48, 2356–2363 (2009).
[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]

T. Sarkadi and P. Koppa, “Optical encryption using pseudorandom complex spatial modulation,” Appl. Opt. 51, 8068–8073 (2012).
[CrossRef]

J. Opt. A (2)

T. Ujvari, 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. A 6, 401–411 (2004).
[CrossRef]

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A 10, 085007 (2008).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Express (4)

Opt. Lasers Eng. (2)

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]

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]

Opt. Lett. (4)

Other (3)

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 (9)

Fig. 1.
Fig. 1.

Schematics of the optical system: (a) encryption and (b) decryption.

Fig. 2.
Fig. 2.

Complex amplitude diagram of the input image pixels. (a) For Ilow input data the corresponding pixels of the input wave fronts realize destructive interference. (b) In the case of Ihigh input data, phase difference φ is realized between the two corresponding input image pixels, which provide partly constructive interference.

Fig. 3.
Fig. 3.

Point spread function of the joint effect of Fourier encryption and decryption. One-dimensional cross section of the absolute value of the function is plotted on the diagrams. (a) Correct key is used for decryption (κ=0) and (b) incorrect key is used for decryption (κ=0.1).

Fig. 4.
Fig. 4.

Statistical distribution of the Je1=|e1|2 intensity of the error component.

Fig. 5.
Fig. 5.

Intensity of the Js1 signal component (black curve) and the Je1 mean value of the error component intensity (gray curve) as a function of the key distance.

Fig. 6.
Fig. 6.

Complex amplitude diagram of the output wave front. (a) In the case where input data is Ilow, the signal components extinguish each other. The resultant output intensity Jlow originates from the random error components. (b) In the case where input data is Ihigh, the output intensity Jhigh is derived from the sum of the error and signal components.

Fig. 7.
Fig. 7.

Probability density function of the Jlow (black curve) and the Jhigh output intensities (gray curve) at key distance κ=0.05 and phase parameters (a) φ=0, (b) φ=0.25π, and (c) φ=0.4π. Reconstructed output images at partially incorrect reading keys, where key distance is κ=0.05 with phase parameters (d) φ=0, (e) φ=0.25π, and (f), φ=0.4π. Reconstructed output images at correct reading keys (κ=0) with phase parameters (g) φ=0, (h) φ=0.25π, and (i) φ=0.4π.

Fig. 8.
Fig. 8.

Bit error rate of the reconstruction versus key distance at different phase parameters of the input wave front modulation. Points (d), (e), and (f) correspond to the output images shown in Figs. 7(d)7(f), respectively.

Fig. 9.
Fig. 9.

Binary key length of the encryption as a function of the phase parameter of the input wave front modulation. Dotted curve: key lengths of the ideal optical system. Continuous curves: key lengths of realistic optical systems at SNRs 3.9, 5.4, and 8.2.

Equations (20)

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

I(x,y)=|a1(x,y)+a2(x,y)|2,
a1(x,y)=exp(α1(x,y))a2(x,y)=exp(α2(x,y)),
α2=α1+π.
α2=α1+2φ,
o1(x,y)=a1(x,y)PSF1o2(x,y)=a2(x,y)PSF2,
PSF1(x,y)=I(w1(u,v)r1(u,v)A(u,v))PSF2(x,y)=I(w2(u,v)r2(u,v)A(u,v)),
o1(x0,y0)=a1(xx0,yy0)PSF1(x,y)dxdy=s(x0,y0)+e(x0,y0),
s(x0,y0)=Γa1(xx0,yy0)PSF1(x,y)dxdy,
e(x0,y0)=Πa1(xx0,yy0)PSF1(x,y)dxdy.
s(x,y)=s1(x,y)+s2(x,y),
e(x,y)=e1(x,y)+e2(x,y).
J(x,y)=|s(x,y)+e(x,y)|2.
Je(x,y)=Je1(x,y)+Je2(x,y)=2Je1(x,y).
Jlow(x,y)=Je(x,y).
Js(x,y)=|s(x,y)|2=(2|s1(x,y)|cosφ)2.
plow(J)=1Jeexp(JJe),
phigh(J)=1Jeexp(J+JsJe)I0(2(J·Js)1/2Je),
BER=12(0Jtphigh(J)dJ+Jtplow(J)dJ),
L=1/κl.
SNR=μhighμlow(σhigh2+σlow2)1/2,

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