Abstract

The security of important information captured by sensors and cameras is currently a growing concern as information theft via techniques such as side-channel attacks become increasingly more prevalent. Double random phase encoding (DRPE) is an optical encryption method based on optical Fourier transform that is currently being used to implement secure coherent optical systems. In this paper, we propose a new DRPE implementation for incoherent optical systems based on integral photography that can be applied to “encrypted imaging (EI)” to optically encrypt an image before it is captured by an image sensor. Because the proposed incoherent DRPE is constituted from conventional DRPE by rewriting the optical encryption via discretization and Euler’s formula, its security level is the same as that of conventional DRPE. The results of an experiment in which we encrypted a plaintext image optically and then decrypted it numerically demonstrate that our proposed incoherent optical security system is feasible.

© 2014 Optical Society of America

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2013 (4)

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).
[CrossRef]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).
[CrossRef]

J. Zang, Z. Xie, and Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38, 1289–1291 (2013).
[CrossRef]

2011 (3)

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).
[CrossRef]

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).
[CrossRef]

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).
[CrossRef]

2010 (3)

2009 (3)

2008 (1)

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).
[CrossRef]

2007 (2)

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

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15, 16067–16079 (2007).
[CrossRef]

2006 (2)

2005 (1)

2004 (2)

Y. Hayasaki, Y. Matsuba, A. Nagaoka, H. Yamamoto, and N. Nishida, “Hiding an image with a light scattering medium and use of a contrast-discrimination method for readout,” Appl. Opt. 43, 1552–1558 (2004).
[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

2003 (2)

B. M. Hennelly and J. T. Sheridan, “Image encryption and fractional Fourier transform,” Optik 114, 251–265 (2003).
[CrossRef]

S. Kishk and B. Javidi, “3D object watermarking by a 3D hidden object,” Opt. Express 11, 874–888 (2003).
[CrossRef]

2002 (3)

2001 (1)

1999 (2)

1998 (2)

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul 8, 3–30 (1998).
[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

1995 (1)

1992 (1)

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

1990 (1)

1982 (1)

1980 (1)

1977 (1)

1908 (1)

M. G. Lippmann, “Epreuves reversible donnant lasensation du relief,” J. Phys. 7, 821–825 (1908).

Ahouzi, E.

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Alam, M. S.

Arcos, S.

Assawaworrarit, S.

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).
[CrossRef]

Cao, L.

Carnicer, A.

Chen, H.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Chen, W.

Chen, X.

Clemente, P.

Dai, J.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Dias, A. R.

Durán, V.

Gandolfi, K.

K. Gandolfi, C. Mourtel, and F. Olivier, “Electromagnetic analysis: Concrete results,” in Cryptographic Hardware and Embedded Systems (CHES2001) (Springer, 2001), pp. 251–261.

Ge, Q.

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).
[CrossRef]

Gershenfeld, N.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).
[CrossRef]

Glaser, I.

Goodman, J. W.

Hamanaka, K.

Hayasaki, Y.

Y. Hayasaki, Y. Matsuba, A. Nagaoka, H. Yamamoto, and N. Nishida, “Hiding an image with a light scattering medium and use of a contrast-discrimination method for readout,” Appl. Opt. 43, 1552–1558 (2004).
[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

He, M.

He, Q.

Hennelly, B. M.

B. M. Hennelly and J. T. Sheridan, “Image encryption and fractional Fourier transform,” Optik 114, 251–265 (2003).
[CrossRef]

Hiroyuki, H.

Horstmeyer, R.

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).
[CrossRef]

Ishihara, S.

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

Javidi, B.

Jin, G.

Joshi, M.

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).
[CrossRef]

Judkewitz, B.

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).
[CrossRef]

Juvells, I.

Kishimoto, T.

Kishk, S.

Lancis, J.

Li, H.

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).
[CrossRef]

Li, P.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Li, Z.

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).
[CrossRef]

Lippmann, M. G.

M. G. Lippmann, “Epreuves reversible donnant lasensation du relief,” J. Phys. 7, 821–825 (1908).

Liu, S.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

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

Liu, T.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Liu, Z.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

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

Matoba, O.

Matsuba, Y.

Matsumoto, M.

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul 8, 3–30 (1998).
[CrossRef]

Mifune, Y.

Montes-Usategui, M.

Mori, M.

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

Mourtel, C.

K. Gandolfi, C. Mourtel, and F. Olivier, “Electromagnetic analysis: Concrete results,” in Cryptographic Hardware and Embedded Systems (CHES2001) (Springer, 2001), pp. 251–261.

Nagaoka, A.

Nakano, K.

K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).
[CrossRef]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

Nemoto, H.

Nishchal, N. K.

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).
[CrossRef]

Nishida, N.

Nishimura, T.

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul 8, 3–30 (1998).
[CrossRef]

Obi, T.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).
[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

Ohyama, N.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).
[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

Oikawa, M.

Okuda, E.

Olivier, F.

K. Gandolfi, C. Mourtel, and F. Olivier, “Electromagnetic analysis: Concrete results,” in Cryptographic Hardware and Embedded Systems (CHES2001) (Springer, 2001), pp. 251–261.

Pappu, R.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).
[CrossRef]

Peng, X.

Recht, B.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).
[CrossRef]

Refregier, P.

Rosen, J.

Sergent, A.

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Sheng, Y.

Sheppard, C. J. R.

Sheridan, J. T.

B. M. Hennelly and J. T. Sheridan, “Image encryption and fractional Fourier transform,” Optik 114, 251–265 (2003).
[CrossRef]

Singh, K.

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).
[CrossRef]

Sun, X.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Suzuki, H.

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).
[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

Tajahuerce, E.

Takai, N.

Takeda, M.

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).
[CrossRef]

K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).
[CrossRef]

Tan, Q.

Tao, R.

Tashima, H.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).
[CrossRef]

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

Taylor, J.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).
[CrossRef]

Tohyama, I.

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

Torres-Company, V.

Vellekoop, I. M.

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).
[CrossRef]

Wang, X.

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).
[CrossRef]

Wang, Y.

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).
[CrossRef]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15, 16067–16079 (2007).
[CrossRef]

Wei, H.

Woody, L. M.

Xi, L.

Xiao-feng, L.

Xie, Z.

Xin, Y.

Xin, Z.

Yachida, M.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).
[CrossRef]

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Figures (15)

Fig. 1.
Fig. 1.

Conceptual depiction of the incoherent optical system in incoherent DRPE.

Fig. 2.
Fig. 2.

Encryption process for incoherent optical system.

Fig. 3.
Fig. 3.

Decryption process for incoherent optical system.

Fig. 4.
Fig. 4.

Plaintext image (N2=3×3 checkered pattern).

Fig. 5.
Fig. 5.

Simple incoherent DRPE optical system.

Fig. 6.
Fig. 6.

Encryption mask (4×N2×N2).

Fig. 7.
Fig. 7.

Element images focused onto the ground glass.

Fig. 8.
Fig. 8.

Encryption masked image (4×N2×N2).

Fig. 9.
Fig. 9.

Intensity ratios Ri for the element images.

Fig. 10.
Fig. 10.

Correct masked image (4×N2×N2).

Fig. 11.
Fig. 11.

Summation of masked element images.

Fig. 12.
Fig. 12.

Summed image of the masked element images (4×N2).

Fig. 13.
Fig. 13.

Encrypted image (2×N2).

Fig. 14.
Fig. 14.

(a) Correct and (b) incorrect decryption keys used in the experiment.

Fig. 15.
Fig. 15.

(a) Correctly and (b) incorrectly decrypted images.

Equations (19)

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c(x,y)=IF{F{f(x,y)·exp[jRRP(x,y)]}·exp[jREKP(μ,ν)]},
ID(x,y)=|IF{F{c(x,y)}·exp[jRDKP(μ,ν)]}|,
cc=REKPcWDFTcRRPcf,
gc=(WDFTc)tRDKPccc,
f^k=|gkexp[jθ^k]|=gk.
b=Ka,
K=KR+jKI,a=aR+jaI,
[bRbI]=[KRKIKIKR][aRaI],
cr=REKPrTRRPrf=REKPrWDFTrRRPrf=Ef,
rk,lRP={cos2παlfor1kN,k=lsin2παlforN+1k2N,kN=l,0otherwise
rk,lKP={cos2πβl1kN,k=lsin2πβlN1kN,k+N=lsin2πβlN+1k2N,kN=lcos2πβlNN+1k2N,k=l0otherwise,
g=TtRDKPrcr=Dcr,
f^k=(gRk2+gIk2)1/2.
K=KR+KR+KI+KI,a=aR+aR+aI+aI,
bR+=KR+aR++KRaR+KI+aI+KIaI+.
E=REKPrWDFTrRRPr,
Ri=IiImax,i=1,2,2×N2×N2,
w^i=wiRi,white,b^i=biRi,black,i=1,2,,2×N2×N2,
d=ftf^f^tf^·ftf.

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