Abstract

We report an asymmetric optical information hiding method based on a rotating analyzer ellipsometry technique. This asymmetric hiding architecture not only avoids the interception of keys during transmission or distribution but also makes the cyphertext more inconspicuous for attackers. A new kind of one-way optical trapdoor function is constructed based on the fact that the state of polarization (SOP) of elliptical polarized light cannot be recovered with only the knowledge of intensity captured after passing through a linear polarizer. Meanwhile, the SOP of a polarization ellipse could be calculated by rotating the polarizer to record two scenes of intensity after it. Introduction of a quick response code as a container leads to noise-free recovery for original information and enhances practicality of the proposed cryptosystem with versatile key sensitivity and fault tolerance capability. Numerical simulation results that support theoretical analysis are presented. Analysis on the relationship between hiding effect or quality of decryption and parameters of the algorithm also is provided.

© 2014 Optical Society of America

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    [CrossRef]
  2. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).
  3. G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67 (2001).
    [CrossRef]
  4. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
    [CrossRef]
  5. C. Lin and X. Shen, “Multiple images encryption based on Fourier transform hologram,” Opt. Commun. 285, 1023–1028 (2012).
    [CrossRef]
  6. E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
    [CrossRef]
  7. W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
    [CrossRef]
  8. A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
    [CrossRef]
  9. 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]
  10. S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).
    [CrossRef]
  11. B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
    [CrossRef]
  12. Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding by information prechoosing,” Opt. Lett. 33, 542–544 (2008).
    [CrossRef]
  13. X. Peng, H. Wei, and P. Zhang, “Asymmetric cryptography based on wavefront sensing,” Opt. Lett. 31, 3579–3581 (2006).
    [CrossRef]
  14. S. Yuan, X. Zhou, M. S. Alam, X. Lu, and X. Li, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17, 3270–3284 (2009).
  15. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
    [CrossRef]
  16. S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
    [CrossRef]
  17. W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
    [CrossRef]
  18. X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
    [CrossRef]
  19. W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
    [CrossRef]
  20. S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
    [CrossRef]
  21. S. K. Rajput and N. K. Nishchal, “Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain,” Appl. Opt. 52, 4343–4352 (2013).
    [CrossRef]
  22. W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: comment,” Opt. Lett. 38, 4044 (2013).
    [CrossRef]
  23. W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: reply,” Opt. Lett. 38, 4045 (2013).
    [CrossRef]
  24. X. Wang, Y. Chen, C. Dai, and D. Zhao, “Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform,” Appl. Opt. 53, 208–213 (2014).
    [CrossRef]
  25. C. Lin, X. Shen, and Q. Xu, “Optical image encoding based on digital holographic recording on polarization state of vector wave,” Appl. Opt. 52, 6931–6939 (2013).
    [CrossRef]
  26. R. Eriksen, P. Mogensen, and J. Gluckstad, “Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun. 187, 325–336 (2001).
    [CrossRef]
  27. A. Alfalou, M. Elbouz, A. Mansour, and G. Keryer, “New spectral image compression method based on an optimal phase coding and the RMS duration principle,” J. Opt. 12, 115403 (2010).
    [CrossRef]
  28. A. Safrani and I. Abdulhalim, “Liquid-crystal polarization rotator and a tunable polarizer,” Opt. Lett. 34, 1801–1803 (2009).
    [CrossRef]

2014 (1)

2013 (5)

2012 (5)

2011 (1)

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

2010 (3)

2009 (4)

2008 (1)

2006 (2)

2002 (1)

2001 (2)

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67 (2001).
[CrossRef]

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

2000 (2)

1995 (1)

Abdulhalim, I.

Alam, M. S.

Alfalou, A.

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[CrossRef]

A. Alfalou, M. Elbouz, A. Mansour, and G. Keryer, “New spectral image compression method based on an optimal phase coding and the RMS duration principle,” J. Opt. 12, 115403 (2010).
[CrossRef]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).

Brosseau, C.

Chen, W.

W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
[CrossRef]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

Chen, X.

W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
[CrossRef]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

Chen, Y.

Dai, C.

Elbouz, M.

A. Alfalou, M. Elbouz, A. Mansour, and G. Keryer, “New spectral image compression method based on an optimal phase coding and the RMS duration principle,” J. Opt. 12, 115403 (2010).
[CrossRef]

Eriksen, R.

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

Gluckstad, J.

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

He, W.

Javidi, B.

Joseph, J.

Keryer, G.

A. Alfalou, M. Elbouz, A. Mansour, and G. Keryer, “New spectral image compression method based on an optimal phase coding and the RMS duration principle,” J. Opt. 12, 115403 (2010).
[CrossRef]

Kishk, S.

Li, X.

Lin, C.

C. Lin, X. Shen, and Q. Xu, “Optical image encoding based on digital holographic recording on polarization state of vector wave,” Appl. Opt. 52, 6931–6939 (2013).
[CrossRef]

C. Lin and X. Shen, “Multiple images encryption based on Fourier transform hologram,” Opt. Commun. 285, 1023–1028 (2012).
[CrossRef]

Liu, S.

Liu, W.

Liu, Z.

Lu, X.

Mansour, A.

A. Alfalou, M. Elbouz, A. Mansour, and G. Keryer, “New spectral image compression method based on an optimal phase coding and the RMS duration principle,” J. Opt. 12, 115403 (2010).
[CrossRef]

Meng, X.

Mogensen, P.

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

Naughton, T.

Nishchal, N. K.

Peng, X.

Qin, W.

Rajput, S. K.

Refregier, P.

Safrani, A.

Shen, X.

C. Lin, X. Shen, and Q. Xu, “Optical image encoding based on digital holographic recording on polarization state of vector wave,” Appl. Opt. 52, 6931–6939 (2013).
[CrossRef]

C. Lin and X. Shen, “Multiple images encryption based on Fourier transform hologram,” Opt. Commun. 285, 1023–1028 (2012).
[CrossRef]

Sheridan, J.

Shi, Y.

Singh, K.

Situ, G.

Tajahuerce, E.

Unnikrishnan, G.

Wang, B.

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

Wang, X.

X. Wang, Y. Chen, C. Dai, and D. Zhao, “Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform,” Appl. Opt. 53, 208–213 (2014).
[CrossRef]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
[CrossRef]

Wei, H.

Xu, Q.

Yuan, S.

Zhang, J.

Zhang, P.

Zhang, Y.

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

Zhao, D.

X. Wang, Y. Chen, C. Dai, and D. Zhao, “Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform,” Appl. Opt. 53, 208–213 (2014).
[CrossRef]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
[CrossRef]

Zhou, X.

Adv. Opt. Photon. (1)

Appl. Opt. (9)

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]

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

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
[CrossRef]

W. Chen and X. Chen, “Interference-based optical image encryption using three-dimensional phase retrieval,” Appl. Opt. 51, 6076–6083 (2012).
[CrossRef]

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

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain,” Appl. Opt. 52, 4343–4352 (2013).
[CrossRef]

X. Wang, Y. Chen, C. Dai, and D. Zhao, “Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform,” Appl. Opt. 53, 208–213 (2014).
[CrossRef]

C. Lin, X. Shen, and Q. Xu, “Optical image encoding based on digital holographic recording on polarization state of vector wave,” Appl. Opt. 52, 6931–6939 (2013).
[CrossRef]

J. Opt. (1)

A. Alfalou, M. Elbouz, A. Mansour, and G. Keryer, “New spectral image compression method based on an optimal phase coding and the RMS duration principle,” J. Opt. 12, 115403 (2010).
[CrossRef]

Opt. Commun. (6)

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

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67 (2001).
[CrossRef]

C. Lin and X. Shen, “Multiple images encryption based on Fourier transform hologram,” Opt. Commun. 285, 1023–1028 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (10)

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[CrossRef]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[CrossRef]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
[CrossRef]

Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding by information prechoosing,” Opt. Lett. 33, 542–544 (2008).
[CrossRef]

X. Peng, H. Wei, and P. Zhang, “Asymmetric cryptography based on wavefront sensing,” Opt. Lett. 31, 3579–3581 (2006).
[CrossRef]

A. Safrani and I. Abdulhalim, “Liquid-crystal polarization rotator and a tunable polarizer,” Opt. Lett. 34, 1801–1803 (2009).
[CrossRef]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: comment,” Opt. Lett. 38, 4044 (2013).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: reply,” Opt. Lett. 38, 4045 (2013).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Schematic setup for the proposed asymmetric optical cryptosystem: BS, beam splitter; LP, linear polarizer; WP, wave plate; SLM, spatial light modulator; MLP, matrix of linear polarizers; LCR, liquid crystal retarder.

Fig. 2.
Fig. 2.

Flow chart of proposed asymmetric information hiding cryptosystem.

Fig. 3.
Fig. 3.

(a) Information coded into original QR code. (b) Original QR code. (c) Host image QR code. (d) Information coded into host QR code. (e) Public key (known as parameter of MLP1). (f) Private key (known as parameter of MLP2). (g) Cyphertext in horizontal direction. (h) Cyphertext in vertical direction. (i) Intensity transmittance T2. (j) Decrypted QR code when all keys are right.

Fig. 4.
Fig. 4.

Variation curves. (a) and (b) CC and PSNR between hidden image and host image versus coefficient a. (c) and (d) CC and PSNR between hidden image and host image versus coefficient b. (e)–(f) CC and PSNR between decrypted image and original image versus coefficient a. (g)–(h) CC and PSNR between decrypted image and original image versus coefficient b.

Fig. 5.
Fig. 5.

Variation curves for CC and PSNR between hidden image and host image varies with both coefficient a and coefficient b.

Fig. 6.
Fig. 6.

Decrypted QR codes assuming that orientation angle distribution of MLP1 and MLP2 is globally or partially wrong. (a)–(c) Decrypted images when errors are 0.01, 0.05, and 0.1 rad globally, respectively. (d)–(f) Error percentages are 3.9% for (d) and 12.5% for (e) and (f).

Equations (15)

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

(Ox(i,j)Oy(i,j))=(exp(iπ·fg(i,j)/4)00exp(iπ·fg(i,j)/4))×(cos(π·r(i,j))sin(π·r(i,j))sin(π·r(i,j))cos(π·r(i,j)))×(01).
(Ooutx(i,j)Oouty(i,j))=(cos2θ1(i,j)12sin2θ1(i,j)12sin2θ1(i,j)sin2θ1(i,j))×(Ox(i,j)Oy(i,j)),
T1=Iout1Iin=14sin22θ1+cos4θ1+Ar2sin4θ1+Arsin2θ1cosPd1+Ar2.
χ=EyEx=|Ey||Ex|ej(δyδx).
T=(T11T12T21T22).
χout=T22χin+T21T12χin+T11.
T2=Iout2Iin=14sin22θ2+cos4θ2+Ar2sin4θ2+Arsin2θ2cosPd1+Ar2.
Ar2=sin2θ2(cos2θ1Iout1Iin)+sin2θ1(Iout2Iincos2θ2)sin2θ2(Iout1Iinsin2θ1)+sin2θ1(sin2θ2Iout2Iin),
cosPd=Iout1Iin(1+Ar2)cos2θ1Ar2sin2θ1Arsin2θ1.
(Ox(i,j)Oy(i,j))=(sin(π·r(i,j))exp(iπ·fg(i,j)/4)cos(π·r(i,j))exp(iπ·fg(i,j)/4)),
fg(i,j)=2Pdπ.
V=(1cos2θ11)H.
Pd=fg×πb,
Ar=sin2θ1cosPd±(sin2θ1cosPd)24(T1sin2θ1)(T1cos2θ1)2(T1sin2θ1).
Eout=(cosδ2/2cosδ1/2cosδ2/2sinδ1/2sinδ2/2cosδ1/2sinδ2/2sinδ1/2)Ein,

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