Abstract

In the increasing number of system approaches published in the field of optical encryption, the security level of the system is evaluated by qualitative and empirical methods. To quantify the security of the optical system, we propose to use the equivalent of the key length routinely used in algorithmic encryption. We provide a calculation method of the number of independent keys and deduce the binary key length for optical data encryption. We then investigate and optimize the key length of the combined phase- and amplitude-modulated key encryption in the holographic storage environment, which is one of the promising solutions for the security enhancement of single- and double-random phase-encoding encryption and storage systems. We show that a substantial growth of the key length can be achieved by optimized phase and amplitude modulation compared to phase-only encryption. We also provide experimental confirmation of the model results.

© 2012 Optical Society of America

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References

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    [CrossRef]
  2. T. Nomura and B. Javidi, “Optical encryption system with a binary key code,” Appl. Opt. 39, 4783–4787 (2000).
    [CrossRef]
  3. S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).
    [CrossRef]
  4. B. Javidi, G. S. Zhang, and J. A. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
    [CrossRef]
  5. X. D. Tan, O. Matoba, T. Shimura, and K. Kuroda, “Improvement in holographic storage capacity by use of double-random phase encryption,” Appl. Opt. 40, 4721–4727 (2001).
    [CrossRef]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
    [CrossRef]
  11. B. Javidi, N. Towghi, N. Maghzi, and S. C. Verrall, “Error-reduction techniques and error analysis for fully phase- and amplitude-based encryption,” Appl. Opt. 39, 4117–4130 (2000).
    [CrossRef]
  12. P. Koppa, “Phase-to-amplitude data page conversion for holographic storage and optical encryption,” Appl. Opt. 46, 3561–3571 (2007).
    [CrossRef]
  13. N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
    [CrossRef]
  14. N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117–122 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. A. Kerekes, E. Lorincz, P. S. Ramanujam, and S. Hvilsted, “Light scattering of thin azobenzene side-chain polyester layers,” Opt. Commun. 206, 57–65 (2002).
    [CrossRef]
  24. H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).
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  26. 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]
  27. Z. Gorocs, G. Erdei, T. Sarkadi, F. Ujhelyi, J. Remenyi, P. Koppa, and E. Lorincz, “Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter,” Opt. Lett. 32, 2336–2338 (2007).
    [CrossRef]
  28. J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
    [CrossRef]

2010

2009

2008

2007

2006

2004

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]

2003

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117–122 (2003).
[CrossRef]

2002

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

A. Kerekes, E. Lorincz, P. S. Ramanujam, and S. Hvilsted, “Light scattering of thin azobenzene side-chain polyester layers,” Opt. Commun. 206, 57–65 (2002).
[CrossRef]

2001

2000

1997

1995

1991

J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

Bhargava, V. K.

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

Cai, L. Z.

Cao, L. C.

Cheng, X. C.

Coufal, H. J.

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

Dong, G. Y.

Erdei, G.

Florence, J. M.

J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

Gopinathan, U.

Gorocs, Z.

He, M. Z.

He, Q. S.

Hvilsted, S.

A. Kerekes, E. Lorincz, P. S. Ramanujam, and S. Hvilsted, “Light scattering of thin azobenzene side-chain polyester layers,” Opt. Commun. 206, 57–65 (2002).
[CrossRef]

Javidi, B.

Jin, G. F.

Joseph, J.

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

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117–122 (2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

Juday, R. D.

J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

Kerekes, A.

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

A. Kerekes, E. Lorincz, P. S. Ramanujam, and S. Hvilsted, “Light scattering of thin azobenzene side-chain polyester layers,” Opt. Commun. 206, 57–65 (2002).
[CrossRef]

Kishk, S.

Koppa, P.

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

Z. Gorocs, G. Erdei, T. Sarkadi, F. Ujhelyi, J. Remenyi, P. Koppa, and E. Lorincz, “Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter,” Opt. Lett. 32, 2336–2338 (2007).
[CrossRef]

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]

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

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]

Kumar, P.

Kuroda, K.

Li, J. A.

Lorincz, E.

Z. Gorocs, G. Erdei, T. Sarkadi, F. Ujhelyi, J. Remenyi, P. Koppa, and E. Lorincz, “Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter,” Opt. Lett. 32, 2336–2338 (2007).
[CrossRef]

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]

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

A. Kerekes, E. Lorincz, P. S. Ramanujam, and S. Hvilsted, “Light scattering of thin azobenzene side-chain polyester layers,” Opt. Commun. 206, 57–65 (2002).
[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]

Maghzi, N.

Matoba, O.

Meng, X. F.

Monaghan, D. S.

Naughton, T. J.

Nishchal, N. K.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117–122 (2003).
[CrossRef]

Nomura, T.

Obi, T.

Ohyama, N.

Psaltis, D.

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

Ramanujam, P. S.

A. Kerekes, E. Lorincz, P. S. Ramanujam, and S. Hvilsted, “Light scattering of thin azobenzene side-chain polyester layers,” Opt. Commun. 206, 57–65 (2002).
[CrossRef]

Refregier, P.

Remenyi, J.

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]

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

Sarkadi, T.

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.

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

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117–122 (2003).
[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]

Situ, G.

Suzuki, H.

Szarvas, G.

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

Takeda, M.

Tan, Q. F.

Tan, X. D.

Tashima, H.

Towghi, N.

Ujhelyi, F.

Z. Gorocs, G. Erdei, T. Sarkadi, F. Ujhelyi, J. Remenyi, P. Koppa, and E. Lorincz, “Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter,” Opt. Lett. 32, 2336–2338 (2007).
[CrossRef]

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[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]

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

Verrall, S. C.

Waldman, D. A.

Wang, Y. R.

Wicker, S. B.

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

Xu, X. F.

Yachida, M.

Yamaguchi, M.

Zhang, G. S.

Zhang, H.

Appl. Opt.

T. Nomura and B. Javidi, “Optical encryption system with a binary key code,” Appl. Opt. 39, 4783–4787 (2000).
[CrossRef]

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

B. Javidi, G. S. Zhang, and J. A. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
[CrossRef]

X. D. Tan, O. Matoba, T. Shimura, and K. Kuroda, “Improvement in holographic storage capacity by use of double-random phase encryption,” Appl. Opt. 40, 4721–4727 (2001).
[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]

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]

B. Javidi, N. Towghi, N. Maghzi, and S. C. Verrall, “Error-reduction techniques and error analysis for fully phase- and amplitude-based encryption,” Appl. Opt. 39, 4117–4130 (2000).
[CrossRef]

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

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

Appl. Phys. B

P. Varhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lorincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397–402 (2003).
[CrossRef]

J. Opt. A

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]

Opt. Commun.

A. Kerekes, E. Lorincz, P. S. Ramanujam, and S. Hvilsted, “Light scattering of thin azobenzene side-chain polyester layers,” Opt. Commun. 206, 57–65 (2002).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117–122 (2003).
[CrossRef]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Analysis of phase encoding for optical encryption,” Opt. Commun. 282, 482–492 (2009).
[CrossRef]

Opt. Eng.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

Opt. Express

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. Lett.

Proc. SPIE

J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

Other

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 (7)

Fig. 1.
Fig. 1.

Schematic diagram of the modeled optical setup. BS, beam splitter; SLM, spatial light modulator; OW, object wave; RW, reference wave; SF, low-pass spatial filter; H, hologram; BR, birefringent crystal; CCD, camera.

Fig. 2.
Fig. 2.

BER of hologram reading in Fourier-encrypted data storage system as a function of reading key error for phase-only modulation and combined phase–amplitude modulation (BER statistic on 218bits).

Fig. 3.
Fig. 3.

Typical diagram of e normalized number of error bits in an arbitrary output data block as the function of κ reading key error at parameters c=0.3, q=0.3, and N=642 (gray plus symbols). The BER(κ) function calculated on 218bit data volume (black curve).

Fig. 4.
Fig. 4.

Encryption key lengths as a function of amplitude contrast at different fill factor values q in azobenzene polyester film holographic material. Computer model results.

Fig. 5.
Fig. 5.

Longest available key length as a function of the signal-to-noise ratio of the hologram reading. A circle shows the case of azobenzene polyester material used in our measurement setup.

Fig. 6.
Fig. 6.

Parts of the hybrid-modulated keys and the object beam wavefronts. (a) Writing key: gray scale symbolizes the binary amplitude modulation; the 0 and π represents the phase modulation. Amplitude modulation parameters: c=6, q=0.4. (b) Phase-modulated input data page after phase-to-amplitude conversion. (c) Correct reading key: amplitude distribution is the inverse of the writing reference. (d) Reconstructed data using the correct key. (e) Random incorrect key. (f) Output wavefront of the same hologram used in image c, reconstructed by incorrect key. Key error κ=0.5.

Fig. 7.
Fig. 7.

Composition of experimental and computer model results. BER versus key error values for phase-only and phase–amplitude-modulated encryption key.

Equations (5)

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

η=KIobjIref[1+F(Iobj+Iref)]2,
e=EN,
BER=limNEN.
P(e+(κ)<e(κ))=ε,
P(e(κ)>e(κ))=ε,

Metrics