Abstract

We propose and analyze a compact optical image encoder based on the principle of digital holographic recording on the polarization state of a vector wave. The optical architecture is a Mach–Zehnder interferometer with in-line digital holographic recording mechanism. The original image is represented by distinct polarization states of elliptically polarized light. This state of polarization distribution is scrambled and then recorded by a two-step digital polarization holography method with random phase distributed reference wave. Introduction of a rotation key in the object arm and phase keys in the reference arm can achieve the randomization of plaintext. Statistical property of cyphertext is analyzed from confusion and diffusion point of view. Fault tolerance and key sensitivity of the proposed approach are also investigated. A chosen plaintext attack on the proposed algorithm exhibits its high security level. Simulation results that support the theoretical analysis are presented.

© 2013 Optical Society of America

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2013

C. Lin, X. Shen, and Z. Li, “Cryptographic analysis on the key space of optical phase encryption algorithm based on the design of discrete random phase mask,” Opt. Laser Technol. 49, 108–117 (2013).
[CrossRef]

2012

S. Rajput and N. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

M. Dubreuil, A. Alfalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using the Stokes–Mueller formalism,” J. Opt. 14, 094004 (2012).
[CrossRef]

Y. Kim, J. Jeong, J. Jang, M. W. Kim, and Y. Park, “Polarization holographic microscopy for extracting spatio-temporally resolved Jones matrix,” Opt. Express 20, 9948–9955 (2012).
[CrossRef]

C. Lin and X. Shen, “Analysis and design of impulse attack free generalized joint transform correlator optical encryption scheme,” Opt. Laser Technol. 44, 2032–2036 (2012).
[CrossRef]

2010

2009

2008

Y. Zhu, J. Zhang, T. Yi, and Q. Gong, “Signal and reference wave dually encrypted holographic memory with shift multiplexing,” Opt. Commun. 281, 1450–1454 (2008).
[CrossRef]

Z. Wang, L. J. Millet, M. U. Gillette, and G. Popescu, “Jones phase microscopy of transparent and anisotropic samples,” Opt. Lett. 33, 1270–1272 (2008).
[CrossRef]

2007

2006

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

G. Unnikrishnan, T. Naughton, and J. Sheridan, “Polarization encoding and multiplexing of two-dimensional signals: application to image encryption,” Appl. Opt. 45, 5693–5700 (2006).
[CrossRef]

2005

2004

O. Matoba and B. Javidi, “Secure holographic memory by double-random polarization encryption,” Appl. Opt. 43, 2915–2919 (2004).
[CrossRef]

C. Cheng and M. Chen, “Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 237, 45–52 (2004).
[CrossRef]

2002

2001

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

R. Eriksen, P. Mogensen, and J. Gluckstad, “Elliptical polarization encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun. 187, 325–336 (2001).
[CrossRef]

2000

1995

Alfalou, A.

Barrera, J.

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

Beghuin, D.

Biener, G.

Bolognini, N.

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

Brosseau, C.

Castro, A.

Chen, M.

C. Cheng and M. Chen, “Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 237, 45–52 (2004).
[CrossRef]

Cheng, C.

C. Cheng and M. Chen, “Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 237, 45–52 (2004).
[CrossRef]

Colomb, T.

Cuche, E.

Dahlgren, P.

Depeursinge, C.

Dubreuil, M.

M. Dubreuil, A. Alfalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using the Stokes–Mueller formalism,” J. Opt. 14, 094004 (2012).
[CrossRef]

Eriksen, R.

R. Eriksen, P. Mogensen, and J. Gluckstad, “Elliptical polarization encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun. 187, 325–336 (2001).
[CrossRef]

Frauel, Y.

Gil, S. K.

Gillette, M. U.

Gluckstad, J.

R. Eriksen, P. Mogensen, and J. Gluckstad, “Elliptical polarization encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun. 187, 325–336 (2001).
[CrossRef]

Gong, Q.

Y. Zhu, J. Zhang, T. Yi, and Q. Gong, “Signal and reference wave dually encrypted holographic memory with shift multiplexing,” Opt. Commun. 281, 1450–1454 (2008).
[CrossRef]

Hasman, E.

Henao, R.

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

Ide, M.

Imbe, M.

Jang, J.

Javidi, B.

Jeon, S. H.

Jeong, J.

Kim, M. W.

Kim, Y.

Kleiner, V.

Kuroda, K.

Li, Z.

C. Lin, X. Shen, and Z. Li, “Cryptographic analysis on the key space of optical phase encryption algorithm based on the design of discrete random phase mask,” Opt. Laser Technol. 49, 108–117 (2013).
[CrossRef]

Lin, C.

C. Lin, X. Shen, and Z. Li, “Cryptographic analysis on the key space of optical phase encryption algorithm based on the design of discrete random phase mask,” Opt. Laser Technol. 49, 108–117 (2013).
[CrossRef]

C. Lin and X. Shen, “Analysis and design of impulse attack free generalized joint transform correlator optical encryption scheme,” Opt. Laser Technol. 44, 2032–2036 (2012).
[CrossRef]

Liu, J.

Marquet, P.

Matoba, O.

Millet, L. J.

Mogensen, P.

R. Eriksen, P. Mogensen, and J. Gluckstad, “Elliptical polarization encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun. 187, 325–336 (2001).
[CrossRef]

Naughton, T.

Naughton, T. J.

Nishchal, N.

Niv, A.

Nomura, T.

Park, Y.

Popescu, G.

Rajput, S.

Refregier, P.

Shen, X.

C. Lin, X. Shen, and Z. Li, “Cryptographic analysis on the key space of optical phase encryption algorithm based on the design of discrete random phase mask,” Opt. Laser Technol. 49, 108–117 (2013).
[CrossRef]

C. Lin and X. Shen, “Analysis and design of impulse attack free generalized joint transform correlator optical encryption scheme,” Opt. Laser Technol. 44, 2032–2036 (2012).
[CrossRef]

Sheridan, J.

Shimura, T.

Shudo, Y.

Tajahuerce, E.

Tan, X.

Tebaldi, M.

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

Terui, Y.

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

Torroba, R.

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

Unnikrishnan, G.

Wang, Y.

Wang, Z.

Xie, J.

Yamaguchi, I.

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

Yi, T.

Y. Zhu, J. Zhang, T. Yi, and Q. Gong, “Signal and reference wave dually encrypted holographic memory with shift multiplexing,” Opt. Commun. 281, 1450–1454 (2008).
[CrossRef]

Yokota, M.

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

Zhang, H.

Zhang, J.

Y. Zhu, J. Zhang, T. Yi, and Q. Gong, “Signal and reference wave dually encrypted holographic memory with shift multiplexing,” Opt. Commun. 281, 1450–1454 (2008).
[CrossRef]

Zhu, N.

Zhu, Y.

Y. Zhu, J. Zhang, T. Yi, and Q. Gong, “Signal and reference wave dually encrypted holographic memory with shift multiplexing,” Opt. Commun. 281, 1450–1454 (2008).
[CrossRef]

Adv. Opt. Photon.

Appl. Opt.

J. Opt.

M. Dubreuil, A. Alfalou, and C. Brosseau, “Robustness against attacks of dual polarization encryption using the Stokes–Mueller formalism,” J. Opt. 14, 094004 (2012).
[CrossRef]

J. Opt. Soc. Korea

Opt. Commun.

C. Cheng and M. Chen, “Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 237, 45–52 (2004).
[CrossRef]

Y. Zhu, J. Zhang, T. Yi, and Q. Gong, “Signal and reference wave dually encrypted holographic memory with shift multiplexing,” Opt. Commun. 281, 1450–1454 (2008).
[CrossRef]

R. Eriksen, P. Mogensen, and J. Gluckstad, “Elliptical polarization encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun. 187, 325–336 (2001).
[CrossRef]

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

Opt. Eng.

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

Opt. Express

Opt. Laser Technol.

C. Lin, X. Shen, and Z. Li, “Cryptographic analysis on the key space of optical phase encryption algorithm based on the design of discrete random phase mask,” Opt. Laser Technol. 49, 108–117 (2013).
[CrossRef]

C. Lin and X. Shen, “Analysis and design of impulse attack free generalized joint transform correlator optical encryption scheme,” Opt. Laser Technol. 44, 2032–2036 (2012).
[CrossRef]

Opt. Lett.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic setup for the proposed optical encoder: L, lens; LP, linear polarizer; WP, wave plate; BS, beam splitter; PBS, polarization beam splitter.

Fig. 2.
Fig. 2.

(a) Plaintext. (b), (c) Cyphertexts in vertical and horizontal directions when inserting LP2. (d), (e) Cyphertexts in vertical and horizontal directions when inserting 1/4WP. (f) Decrypted image with correct keys.

Fig. 3.
Fig. 3.

Histograms of cyphertexts. (a)–(d) Histograms of Figs. 2(b)2(e), respectively. (e) Histogram of cyphertext encrypted with DRPE algorithm. (f) Histogram of cyphertext encrypted with double random polarization encoding algorithm. (g) Histogram of cyphertext encrypted with the dual encryption scheme using polarized light.

Fig. 4.
Fig. 4.

Wrongly decrypted images: (a), (b) phase keys are wrong with 0.006% and 0.34% pixels, respectively, (c) rotation and input keys are wrong in the central section, (d) orientation of LP2 is wrong with 0.09 rad, (e) fast axis orientation of 1/4WP is wrong with 0.09 rad, and (f) Fresnel diffraction distances are wrong with 1 mm, respectively.

Fig. 5.
Fig. 5.

(a) Relationship curve of CCs and Fresnel diffraction distances when Fresnel diffraction distance is wrong during decryption. (b) Variation between CC and orientation angle of LP2. (c) Variation between CC and fast axis orientation angle of 1/4WP.

Fig. 6.
Fig. 6.

(a)–(c) Decrypted images when Fresnel diffraction distances are wrong with 0.5, 2, and 10 mm, respectively. (d)–(f) Decrypted images when orientation angles of LP2 are wrong with 0.01, 0.05, and 0.1 rad, respectively. (g)–(i) Decrypted images when fast axis orientation angles of 1/4WP are wrong with 0.01, 0.05, and 0.1 rad, respectively.

Fig. 7.
Fig. 7.

Cyphertext sensitivity depicted with relationship between error percentage of pixel number and CC.

Equations (17)

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Oin(x,y)=f(x,y)2+g(x,y),
Oout(x,y)=(cos[πr(x,y)]sin[πr(x,y)]sin[πr(x,y)]cos[πr(x,y)])×(cos[πOin(x,y)]isin[πOin(x,y)]isin[πOin(x,y)]cos[πOin(x,y)])×Jo.
Oout(x,y)=(isin[πOin(x,y)]cos[πr(x,y)]+sin[πr(x,y)]cos[πOin(x,y)]isin[πOin(x,y)]sin[πr(x,y)]+cos[πOin(x,y)]cos[πr(x,y)]).
Rout1(x,y)=(cos2θpsinθpcosθpsinθpcosθpsin2θp)×(R1(x,y)0)=(cos2θpR1(x,y)sinθpcosθpR1(x,y)).
Ix1(x,y)=cos2θpR1(x,y)Ooutx*(x,y)+cos2θpR1*(x,y)Ooutx(x,y),
Iy1(x,y)=sinθpcosθpR1(x,y)Oouty*(x,y)+sinθpcosθpR1*(x,y)Oouty(x,y),
Rout2(x,y)=1/2(1+icos2θcisin2θcisin2θc1icos2θc)×(R2(x,y)0)=1/2((1+icos2θc)R2(x,y)isin2θcR2(x,y)).
Ix2(x,y)=1/2(1+icos2θc)R2(x,y)Ooutx*(x,y)+1/2(1icos2θc)R2*(x,y)Ooutx(x,y),
Iy2(x,y)=1/2(isin2θc)R2(x,y)Oouty*(x,y)+1/2(isin2θc)R2*(x,y)Oouty(x,y).
Ooutx=1/2(1+icos2θc)R2Ix1cos2θpR1Ix21/2(1+icos2θc)cos2θpR1*R21/2(1icos2θc)cos2θpR1R2*,
Oouty=1/2(isin2θc)R2Iy1sinθpcosθpR1Iy21/2(isin2θc)sinθpcosθpR1*R2+1/2(isin2θc)sinθpcosθpR1R2*.
cc=|f(x,y)||φ(x,y)|dxdy|f(x,y)|2dxdy|φ(x,y)|2dxdy.
H=i=1Lpilog2pi.
Oouthamp=sin2(πOin)cos2(πr)+sin2(πr)cos2(πOin),
Oouthpha=arctan[tan(πOin)tan(πr)],
Ooutvamp=sin2(πOin)sin2(πr)+cos2(πr)cos2(πOin),
Ooutvpha=arctan[tan(πOin)tan(πr)].

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