Abstract

An approach for multiple-image encryption based on interference and position multiplexing is proposed. In the encryption process, multiple images are analytically hidden into three phase-only masks (POMs). The encryption algorithm for this method is quite simple and does not need iterative encoding. For decryption, both the digital method and optical method could be employed. Also, we analyze the multiplexing capacity through the correlation coefficient. In addition, the silhouette problem that exists in previous interference-based encryption methods with two POMs can be eliminated during the generation procedure of POMs based on the interference principle. Simulation results are presented to verify the validity of the proposed approach.

© 2013 Optical Society of America

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References

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  1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).
    [CrossRef]
  2. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef]
  3. 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]
  4. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
    [CrossRef]
  5. X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
    [CrossRef]
  6. X. Peng, H. Q. Tang, and J. D. Tian, “Ciphertext only attack on double random phase encoding optical encryption system,” Acta. Phys. Sin. 56, 2629–2636 (2007).
  7. H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. 41, 4825–4834 (2002).
    [CrossRef]
  8. Y. Li, K. Kreske, and J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).
    [CrossRef]
  9. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  10. X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
    [CrossRef]
  11. G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
    [CrossRef]
  12. G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
    [CrossRef]
  13. D. Amaya, M. Tebaldi, R. Torroba, and N. Bolognini, “Wavelength multiplexing encryption using joint transform correlator architecture,” Appl. Opt. 48, 2099–2104 (2009).
    [CrossRef]
  14. H. Hwang, H. T. Chang, and W. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).
    [CrossRef]
  15. B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
    [CrossRef]
  16. W. Chen and X. Chen, “Optical multiple-image encryption based on multi-plane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
    [CrossRef]
  17. D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
    [CrossRef]
  18. Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A 11, 125406 (2009).
    [CrossRef]
  19. P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
    [CrossRef]

2012 (1)

2011 (1)

W. Chen and X. Chen, “Optical multiple-image encryption based on multi-plane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

2010 (1)

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

2009 (5)

2008 (1)

2007 (1)

X. Peng, H. Q. Tang, and J. D. Tian, “Ciphertext only attack on double random phase encoding optical encryption system,” Acta. Phys. Sin. 56, 2629–2636 (2007).

2006 (2)

2005 (1)

2004 (1)

2002 (1)

2000 (2)

1999 (1)

D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

1995 (1)

Alfalou, A.

Amaya, D.

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Bolognini, N.

Brosseau, C.

Chang, H. T.

Chen, W.

W. Chen and X. Chen, “Optical multiple-image encryption based on multi-plane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

Chen, X.

W. Chen and X. Chen, “Optical multiple-image encryption based on multi-plane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

Dong, Z.

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A 11, 125406 (2009).
[CrossRef]

Ferreria, C.

D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Garcia, J.

D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Hwang, H.

Javidi, B.

Joseph, J.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[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]

Kreske, K.

Kumar, P.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

Kuo, C. J.

Li, Y.

Lie, W.

Lu, W. C.

Marinho, F.

D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Mas, D.

D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Peng, X.

X. Peng, H. Q. Tang, and J. D. Tian, “Ciphertext only attack on double random phase encoding optical encryption system,” Acta. Phys. Sin. 56, 2629–2636 (2007).

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
[CrossRef]

Refregier, P.

Rosen, J.

Singh, K.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[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]

Situ, G.

Tang, H. Q.

X. Peng, H. Q. Tang, and J. D. Tian, “Ciphertext only attack on double random phase encoding optical encryption system,” Acta. Phys. Sin. 56, 2629–2636 (2007).

Tebaldi, M.

Tian, J. D.

X. Peng, H. Q. Tang, and J. D. Tian, “Ciphertext only attack on double random phase encoding optical encryption system,” Acta. Phys. Sin. 56, 2629–2636 (2007).

Torroba, R.

Unnikrishnan, G.

Wang, B.

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A 11, 125406 (2009).
[CrossRef]

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

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
[CrossRef]

Wang, X.

Wei, H.

Yu, B.

Zhang, J.

Zhang, P.

Zhang, Y.

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A 11, 125406 (2009).
[CrossRef]

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

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
[CrossRef]

Zhao, D.

Acta. Phys. Sin. (1)

X. Peng, H. Q. Tang, and J. D. Tian, “Ciphertext only attack on double random phase encoding optical encryption system,” Acta. Phys. Sin. 56, 2629–2636 (2007).

Adv. Opt. Photon. (1)

Appl. Opt. (4)

J. Opt. (2)

W. Chen and X. Chen, “Optical multiple-image encryption based on multi-plane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

J. Opt. A (2)

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A 11, 125406 (2009).
[CrossRef]

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
[CrossRef]

Opt. Commun. (2)

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

D. Mas, J. Garcia, C. Ferreria, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Opt. Lett. (7)

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the optical decryption system. f, plaintexts; g, the intermediate function; λ, wavelength; M, extracted POMs; BS, beam splitter.

Fig. 2.
Fig. 2.

Encryption results of the proposal. (a)–(d) are the four original images and (e)–(g) are the ciphertexts, M1, M2, and M3.

Fig. 3.
Fig. 3.

Decryption results by the use of the correct POMs (a)–(d), the wrong POMs (e)–(h), and the correct POMs with filtering (i)–(l).

Fig. 4.
Fig. 4.

Decrypted images obtained by using only the POM M1 (a)–(d), M2 (e)–(h), and M3 (i)–(l).

Fig. 5.
Fig. 5.

Behavior of CC versus N.

Equations (13)

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

fk(xo,yo)=fk(xo,yo)exp[j2πrand(xo,yo)],
gk(x,y)=FrTλ[fk(xo,yo);dk],
g(x,y)=k=1Ngk(x,y).
g(x,y)={[M1(xi,yi)+M2(xi,yi)]M3(xi,yi)}*h(xi,yi,l),
h(xi,yi,l)=exp(j2πl/λ)jλlexp[jπ(xi2+yi2)/λl]
[M1(xi,yi)+M2(xi,yi)]M3(xi,yi)=D,
[M1(xi,yi)][M1(xi,yi)]*=[M2(xi,yi)][M2(xi,yi)]*=1,
m1(xi,yi)=θ(xi,yi)arccos[M(xi,yi)/2],
m2(xi,yi)=arg[M(xi,yi)exp(jm1(xi,yi))],
m3(xi,yi)=θ(xi,yi)φ(xi,yi),
f^k(xo,yo)=fk(xo,yo)+nk(xo,yo),
nk(xo,yo)=qknq(xo,yo)=qkFrTλ{FrTλ[fq(xo,yo);dq];dk}
CC=E{[fE(f)][|f^k|E(|f^k|)]}E{[fE(f)]2}E{[|f^k|E(|f^k|)]2},

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