Abstract

In this article, a multiple-image encryption method based on the optical interference principle and phase-only mask (POM) multiplexing is proposed. During the encryption process, each secret image is encoded into two analytically obtained POMs and one computer-generated random POM, in which no iterative computation is required. The analytically obtained POMs taken from different secret images are then synthesized by POM multiplexing and further encoded into two complex ciphertext images. The silhouette problem that exists in the earlier interference principle-based encryption approaches is totally resolved by the proposal. Both digital and optical means can be used for decryption. The crosstalk effect between the secret images will not appear in the decrypted results by using the proposed system. Numerical simulations have been given to verify the performance and feasibility of the proposal. We also discuss briefly the influence of information compression on the quality of decrypted images.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmanns second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
    [CrossRef]
  5. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
    [CrossRef]
  6. A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
    [CrossRef]
  7. 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]
  8. X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).
    [CrossRef]
  9. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  10. Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A 11, 125406 (2009).
    [CrossRef]
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    [CrossRef]
  12. P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
    [CrossRef]
  13. X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
    [CrossRef]
  14. Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
    [CrossRef]
  15. G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
    [CrossRef]
  16. G. Situ and J. Zhang, “Position multiplexing for multiple image encryption,” J. Opt. A 8, 391–397 (2006).
    [CrossRef]
  17. D. Amaya, M. Tebaldi, R. Torroba, and N. Bolognini, “Wavelength multiplexing encryption using joint transform correlator architecture,” Appl. Opt. 48, 2099–2104 (2009).
    [CrossRef]
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    [CrossRef]
  20. H. T. Chang, H.-E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
    [CrossRef]
  21. 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]
  22. Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32, 1914–1916 (2007).
    [CrossRef]
  23. D. Kong, X. Shen, Q. Xu, W. Xin, and H. Guo, “Multiple-image encryption scheme based on cascaded fractional Fourier transform,” Appl. Opt. 52, 2619–2625 (2013).
    [CrossRef]
  24. B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
    [CrossRef]
  25. W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane phase retrieval and interference,” J. Opt. 13, 115401 (2011).
    [CrossRef]
  26. Y. Qin and Q. Gong, “Interference-based multiple-image encryption with silhouette removal by position multiplexing,” Appl. Opt. 52, 3987–3992 (2013).
    [CrossRef]

2013

2012

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51, 686–691 (2012).
[CrossRef]

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
[CrossRef]

2011

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
[CrossRef]

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

H. T. Chang, H.-E. Hwang, C. L. Lee, and M.-T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50, 710–716 (2011).
[CrossRef]

H. T. Chang, H.-E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
[CrossRef]

2010

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

2009

2008

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmanns second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

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

2007

2006

2005

2004

2000

1995

Alfalou, A.

Amaya, D.

Arcos, S.

Bolognini, N.

Brosseau, C.

Carnicer, A.

Chang, H. T.

Chen, L. F.

Chen, W.

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

Chen, X.

W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane 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]

Gong, Q.

Guo, H.

Hwang, H.

Hwang, H.-E.

H. T. Chang, H.-E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
[CrossRef]

H. T. Chang, H.-E. Hwang, C. L. Lee, and M.-T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50, 710–716 (2011).
[CrossRef]

Javidi, B.

Joseph, J.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (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]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmanns second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[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]

Juvells, I.

Kong, D.

Kumar, P.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (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]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmanns second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

Lee, C. L.

H. T. Chang, H.-E. Hwang, C. L. Lee, and M.-T. Lee, “Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain,” Appl. Opt. 50, 710–716 (2011).
[CrossRef]

H. T. Chang, H.-E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
[CrossRef]

Lee, M.-T.

Lie, W.

Montes-Usategui, M.

Peng, X.

Qin, Y.

Refregier, P.

Shen, X.

Shi, Y.

Singh, K.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (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]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmanns second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[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.

Tebaldi, M.

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, Q.

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
[CrossRef]

Wang, X.

Wei, H.

Xin, W.

Xu, Q.

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.

Zhao, D. M.

Adv. Opt. Photon.

Appl. Opt.

J. Opt.

W. Chen and X. Chen, “Optical multiple-image encryption based on multiplane 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

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

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

Opt. Commun.

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285, 4294–4301 (2012).
[CrossRef]

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

H. T. Chang, H.-E. Hwang, and C. L. Lee, “Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 284, 4146–4151 (2011).
[CrossRef]

Opt. Eng.

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmanns second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[CrossRef]

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
[CrossRef]

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]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).
[CrossRef]

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

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]

Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32, 1914–1916 (2007).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Optical implementation scheme for decryption.

Fig. 2.
Fig. 2.

Secret images: (a) Lena, (b) Baboon (c) Cameraman, and (d) Livingroom.

Fig. 3.
Fig. 3.

(a) Phase distribution of M3(x,y); (b), (d) amplitude components, (c), (e) phase components of ciphertexts C1(ξ,η) and C2(ξ,η), and (f), (g) phase distributions of decryption POMs φ11(x,y) and φ12(x,y) for Lena.

Fig. 4.
Fig. 4.

(a)–(d) Decrypted images retrieved with corresponding correct decryption POMs and correct parameter of Fresnel transforms. (e)–(h) Decrypted images retrieved with wrong POM M3(x,y). (i)–(l) Decrypted images retrieved with incorrect ciphertext C1(ξ,η) while other keys were correctly used. The numbers shown in the left-hand top corners are the corresponding RE values.

Fig. 5.
Fig. 5.

(a)–(d) Corresponding recovered images obtained with incorrect synthetic decryption POMs applied for decryption. (e)–(h) Recovered results obtain with wrong illumination wavelength or (i)–(l) wrong distance d1. The numbers shown in the lefthand top corners are the corresponding RE values.

Fig. 6.
Fig. 6.

Dependence of RE on the change of (a) λ, (b) d1, and (c) d2.

Fig. 7.
Fig. 7.

(a)–(d) Recovered results when only the first group of POM keys Mi1(x,y) were used. (e)–(l) Recovered results when (e)–(h) only the combination of Mi1(x,y) and Mi2(x,y) or (i)–(l) only the combination of Mi1(x,y) and M3(x,y) was used for decoding. The numbers shown in the left-hand top corners are the corresponding RE values.

Fig. 8.
Fig. 8.

Recovered Baboon images when pixel values of ciphertexts and decryption keys are encoded on (a) 6, (b) 8, (c) 10, and (d) 12 bits. The numbers shown in the left-hand top corners are the corresponding RE values.

Equations (14)

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

O(u,v)=O(u,v)R(u,v)=O(u,v)exp[j2πrand(u,v)],
D(x,y)=FRλ,d1{O(u,v)}=M1(x,y)+M2(x,y)+M3(x,y),
p(x,y)=FRλ,d1{P(u,v)}=F1{F{P(u,v)}F{h(x,y,d,λ)}},
h(x,y,d,λ)=exp(j2πd/λ)jdλexp[jπdλ(x2+y2)].
P(u,v)=FRλ,d{p(x,y)}=F1{F{p(x,y)}F{h(x,y,d,λ)}},
m1=θ(x,y)arcos{|D(x,y)|/2},
m2=θ(x,y)+arcos{|D(x,y)|/2}.
Di(x,y)=FRλ,d11{fi(u,v)exp[j2πrand(u,v)]}=Mi1(x,y)+Mi2(x,y)+M3(x,y).
Gk(x,y)=exp[ji=1Nmik(x,y)],k=1,2,
φik(x,y)=arg{exp[jl=1,liNmlk(x,y)]}.
Ck(ξ,η)=FRλ,d21{Gk(x,y)},k=1,2.
Mik(x,y)=FRλ,d2{Ck(ξ,η)}exp[jφik(x,y)]=Gk(x,y)exp[jφik(x,y)],
fi=|FRλ,d1{Mi1(x,y)+Mi2(x,y)+M3(x,y)}|2.
RE=m=1Mn=1NR(m,n)||O(m,n)2m=1Mn=1N|O(m,n)|2,

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