Abstract

In this paper, a new multiple-image encryption and decryption technique that utilizes the compressive sensing (CS) concept along with a double-random phase encryption (DRPE) has been proposed. The space multiplexing method is employed for integrating multiple-image data. The method, which results in a nonlinear encryption system, is able to overcome the vulnerability of classical DRPE. The CS technique and space multiplexing are able to provide additional key space in the proposed method. A numerical experiment of the proposed method is implemented and the results show that the proposed method has good accuracy and is more robust than classical DRPE. The proposed system is also employed against chosen-plaintext attacks and it is found that the inclusion of compressive sensing enhances robustness against the attacks.

© 2014 Optical Society of America

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    [CrossRef]
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2014 (3)

2013 (5)

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform,” Appl. Opt. 52, 871–878 (2013).
[CrossRef]

Q. Gong, X. Liu, G. Li, and Y. Qin, “Multiple-image encryption and authentication with sparse representation by space multiplexing,” Appl. Opt. 52, 7486–7493 (2013).
[CrossRef]

P. Lu, Z. Xu, X. Lu, and X. Liu, “Digital image information encryption based on compressive sensing and double random-phase encoding technique,” Optik 124, 2514–2518 (2013).
[CrossRef]

X. Liu, Y. Cao, P. Lu, X. Lu, and Y. Li, “Optical image encryption technique based on compressed sensing and Arnold transformation,” Optik 124, 6590–6593 (2013).
[CrossRef]

W. Chen, X. Chen, A. Stern, and B. Javidi, “Phase-modulated optical system with sparse representation for information encoding and authentication,” IEEE Photon. J. 5, 6900113 (2013).
[CrossRef]

2012 (2)

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt. 14, 045401 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

2011 (3)

2010 (1)

2009 (2)

2008 (2)

2007 (2)

2005 (2)

1999 (1)

D. Weber and J. Trolinger, “Novel implementation of nonlinear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

1995 (1)

1994 (1)

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Abdallah, N.

Alfalou, A.

Arcos, S.

Becker, S.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[CrossRef]

Bobin, J.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[CrossRef]

Brosseau, C.

Cai, L. Z.

Candès, E.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[CrossRef]

E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process Mag. 25(2), 21–30 (2008).

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

Cao, Y.

X. Liu, Y. Cao, P. Lu, X. Lu, and Y. Li, “Optical image encryption technique based on compressed sensing and Arnold transformation,” Optik 124, 6590–6593 (2013).
[CrossRef]

Carnicer, A.

Castro, A.

Chen, W.

W. Chen, X. Chen, A. Stern, and B. Javidi, “Phase-modulated optical system with sparse representation for information encoding and authentication,” IEEE Photon. J. 5, 6900113 (2013).
[CrossRef]

Chen, X.

W. Chen, X. Chen, A. Stern, and B. Javidi, “Phase-modulated optical system with sparse representation for information encoding and authentication,” IEEE Photon. J. 5, 6900113 (2013).
[CrossRef]

Chen, Y.

Cheng, X. C.

Cho, M.

Dai, C.

Dong, G. Y.

Frauel, Y.

Gong, Q.

Horner, J. L.

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Huang, R.

R. Huang and K. Sakurai, “A robust and compression-combined digital image encryption method based on compressive sensing,” in Seventh International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) (IEEE, 2011, Vol. 53, pp. 105–108.

Javidi, B.

Joseph, J.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt. 14, 045401 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase function,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

Jridi, M.

Juvells, I.

Kumar, A.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase function,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

Kumar, P.

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt. 14, 045401 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase function,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

Li, G.

Li, Y.

X. Liu, Y. Cao, P. Lu, X. Lu, and Y. Li, “Optical image encryption technique based on compressed sensing and Arnold transformation,” Optik 124, 6590–6593 (2013).
[CrossRef]

Liu, X.

X. Liu, Y. Cao, P. Lu, X. Lu, and Y. Li, “Optical image encryption technique based on compressed sensing and Arnold transformation,” Optik 124, 6590–6593 (2013).
[CrossRef]

Q. Gong, X. Liu, G. Li, and Y. Qin, “Multiple-image encryption and authentication with sparse representation by space multiplexing,” Appl. Opt. 52, 7486–7493 (2013).
[CrossRef]

P. Lu, Z. Xu, X. Lu, and X. Liu, “Digital image information encryption based on compressive sensing and double random-phase encoding technique,” Optik 124, 2514–2518 (2013).
[CrossRef]

Lu, P.

P. Lu, Z. Xu, X. Lu, and X. Liu, “Digital image information encryption based on compressive sensing and double random-phase encoding technique,” Optik 124, 2514–2518 (2013).
[CrossRef]

X. Liu, Y. Cao, P. Lu, X. Lu, and Y. Li, “Optical image encryption technique based on compressed sensing and Arnold transformation,” Optik 124, 6590–6593 (2013).
[CrossRef]

Lu, X.

X. Liu, Y. Cao, P. Lu, X. Lu, and Y. Li, “Optical image encryption technique based on compressed sensing and Arnold transformation,” Optik 124, 6590–6593 (2013).
[CrossRef]

P. Lu, Z. Xu, X. Lu, and X. Liu, “Digital image information encryption based on compressive sensing and double random-phase encoding technique,” Optik 124, 2514–2518 (2013).
[CrossRef]

Mehra, I.

I. Mehra and N. K. Nishchal, “Asymmetric cryptosystem for securing multiple images using two beam interference phenomenon,” Opt. Laser Technol. 60, 1–7 (2014).
[CrossRef]

I. Mehra and N. K. Nishchal, “Image fusion using wavelet transform and its application to asymmetric cryptosystem and hiding,” Opt. Express 22, 5474–5482 (2014).
[CrossRef]

Meng, X. F.

Montes-Usategui, M.

Naughton, T. J.

Nesterov, Y.

Y. Nesterov, “Smooth minimization of non-smooth functions,” Math. Program. 103, 127–152 (2005).
[CrossRef]

Nishchal, N. K.

Pérez-Cabré, E.

Qin, Y.

Rajput, S. K.

Refregier, P.

Rivenson, Y.

Romberg, J.

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

Sakurai, K.

R. Huang and K. Sakurai, “A robust and compression-combined digital image encryption method based on compressive sensing,” in Seventh International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) (IEEE, 2011, Vol. 53, pp. 105–108.

Shen, X. X.

Singh, K.

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt. 14, 045401 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase function,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

Stern, A.

W. Chen, X. Chen, A. Stern, and B. Javidi, “Phase-modulated optical system with sparse representation for information encoding and authentication,” IEEE Photon. J. 5, 6900113 (2013).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double random phase encoding,” Opt. Express 18, 15094–15103 (2010).
[CrossRef]

Trolinger, J.

D. Weber and J. Trolinger, “Novel implementation of nonlinear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

Wakin, M.

E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process Mag. 25(2), 21–30 (2008).

Wang, X.

Wang, Y. R.

Weber, D.

D. Weber and J. Trolinger, “Novel implementation of nonlinear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

Xu, X. F.

Xu, Z.

P. Lu, Z. Xu, X. Lu, and X. Liu, “Digital image information encryption based on compressive sensing and double random-phase encoding technique,” Optik 124, 2514–2518 (2013).
[CrossRef]

Zhang, H.

Zhao, D.

Adv. Opt. Photon. (1)

Appl. Opt. (3)

IEEE Photon. J. (1)

W. Chen, X. Chen, A. Stern, and B. Javidi, “Phase-modulated optical system with sparse representation for information encoding and authentication,” IEEE Photon. J. 5, 6900113 (2013).
[CrossRef]

IEEE Signal Process Mag. (1)

E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process Mag. 25(2), 21–30 (2008).

Inverse Probl. (1)

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

J. Opt. (1)

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt. 14, 045401 (2012).
[CrossRef]

Math. Program. (1)

Y. Nesterov, “Smooth minimization of non-smooth functions,” Math. Program. 103, 127–152 (2005).
[CrossRef]

Opt. Eng. (2)

D. Weber and J. Trolinger, “Novel implementation of nonlinear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Opt. Express (4)

Opt. Laser Technol. (1)

I. Mehra and N. K. Nishchal, “Asymmetric cryptosystem for securing multiple images using two beam interference phenomenon,” Opt. Laser Technol. 60, 1–7 (2014).
[CrossRef]

Opt. Lasers Eng. (1)

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

Opt. Lett. (5)

Optik (2)

P. Lu, Z. Xu, X. Lu, and X. Liu, “Digital image information encryption based on compressive sensing and double random-phase encoding technique,” Optik 124, 2514–2518 (2013).
[CrossRef]

X. Liu, Y. Cao, P. Lu, X. Lu, and Y. Li, “Optical image encryption technique based on compressed sensing and Arnold transformation,” Optik 124, 6590–6593 (2013).
[CrossRef]

SIAM J. Imaging Sci. (1)

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[CrossRef]

Other (1)

R. Huang and K. Sakurai, “A robust and compression-combined digital image encryption method based on compressive sensing,” in Seventh International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) (IEEE, 2011, Vol. 53, pp. 105–108.

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Figures (10)

Fig. 1.
Fig. 1.

Proposed encryption setup.

Fig. 2.
Fig. 2.

Proposed decryption setup.

Fig. 3.
Fig. 3.

Simulated results using the proposed method. (a1)–(a4) Images before encryption (256×256). (b1)–(b4) Sampled image data after compressive sampling (128×128). (c) Single synthesized image after space multiplexing (256×256). (d) Encrypted image after DRPE (256×256). (e1)–(e4) Decrypted images (256×256) with (e1) PSNR=31.48dB, normalized correlation NC=0.9933; (e2) PSNR=32.08dB, NC=0.9968; (e3) PSNR=42.81dB, NC=1.0; and (e4) PSNR=24.01dB, NC=0.9951.

Fig. 4.
Fig. 4.

Robustness check of the proposed system against occlusion. (a) 1/8 image occluded (lower right triangular region). (b) 1/8 image occluded (upper left rectangular region). (c) 1/4 image occluded (right quarter). (d) 1/4 image occluded (upper left quarter). (e) Decrypted image from (a) PSNR=10.59dB, NC=0.7631. (f) Decrypted image from (b) PSNR=11.57dB, NC=0.7591. (g) Decrypted image from (c) PSNR=9.51dB, NC=0.6158. (h) Decrypted image from (d) PSNR=9.52dB, NC=0.6135. (i) Plot showing correlation against percentage of occlusion of encrypted image.

Fig. 5.
Fig. 5.

Robustness check of the proposed system against random noise. (a) Decrypted image with Gaussian noise of 0.1 variance, PSNR=31.19dB, NC=0.9933. (b) Decrypted image with Gaussian noise of 1 variance, PSNR=30.65dB, NC=0.9932.

Fig. 6.
Fig. 6.

Robustness check of the proposed system against deployment of wrong DRPE keys. (a1)–(a4) Decrypted images with wrong first phase mask key: (a1) PSNR=6.95dB, NC=0.0198; (a2) PSNR=8.29dB, NC=0.0286; (a3) PSNR=13.35dB, NC=0.0123; and (a4) PSNR=6.83dB, NC=0.0132. (b1)–(b4) Decrypted images with wrong second phase mask key: (b1) PSNR=6.86dB, NC=0.0049; (b2) PSNR=8.04dB, NC=0.0044; (b3) PSNR=13.52dB, NC=0.0071; and (b4) PSNR=6.83dB, NC=0.0045.

Fig. 7.
Fig. 7.

Decrypted images with wrong binary keys used. (a) PSNR=9.95dB, NC=0.0397; (b) PSNR=11.46dB, NC=0.044; (c) PSNR=9.99dB, NC=0.0059; and (d) PSNR=9.62dB, NC=0.0243. (e) Plot showing correlation value against resemblance percentage of the partially incorrect binary keys used with correct binary masks.

Fig. 8.
Fig. 8.

Robustness check of the proposed system against use of wrong sampling operators. (a1)–(a4) Decrypted images: (a1) PSNR=12.65dB, NC=0.0829; (a2) PSNR=12.43dB, NC=0.2576; (a3) PSNR=14.02dB, NC=0.2539; and (a4) PSNR=10.91dB, NC=0.0944. (b1)–(b4) Scrambled images of Figs. 3(a1)3(a4). (c1)–(c4) Decrypted images of (b1)–(b4) using the sampling operators in Figs. 3(a1)3(a4): (c1) PSNR=12.87dB, NC=0.016; (c2) PSNR=11.65dB, NC=0.0589; (c3) PSNR=14.12dB, NC=0.2121; and (c4) PSNR=11.94dB, NC=0.0272.

Fig. 9.
Fig. 9.

Effect of sampling ratio on decrypted images. (a1)–(a4) Decrypted images for sampling ratio 16.66%: (a1) PSNR=29.08dB, NC=0.9891; (a2) PSNR=31.16dB, NC=0.9947; (a3) PSNR=31.52dB, NC=0.9984; and (a4) PSNR=24.35dB, NC=0.9926. (b1)–(b4) Decrypted images for sampling ratio 10%: (b1) PSNR=27.11dB, NC=0.9826; (b2) PSNR=27.38dB, NC=0.9912; (b3) PSNR=25.02dB, NC=0.9919; and (b4) PSNR=23.65dB, NC=0.9884. (c1)–(c4) Decrypted images for sampling ratio 4%: (c1) PSNR=22.63dB, NC=0.9668; (c2) PSNR=22.42dB, NC=0.9796; (c3) PSNR=18.67dB, NC=0.9610; and (c4) PSNR=20.70dB, NC=0.9756. (d) Plot showing correlation against sampling ratio R. (e) Plot showing PSNR against sampling ratio R.

Fig. 10.
Fig. 10.

Robustness of the proposed system against plaintext attacks. (a) Plain text P1. (b) Plain text P2. (c) Cipher text C1. (d) Cipher text C2. (e) Difference between cipher texts C1 and C2. (f) Actual (Fourier) phase mask used for encryption. (g) Decrypted image using an incorrect plaintext attack key: PSNR=7.34dB, NC=0.0024. (h) Encrypted Dirac Delta function using the proposed method.

Equations (14)

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

B=Ω·F·X.
Si(u,v)=Ωi(u,v).F[fi(x,y)],
si(x,y)=F1[Si(u,v)].
u(x,y)=[m(x,y)×M1(x,y)]*F[M2(u,v)],
m(x,y)=[u(x,y)×M1c(x,y)]*F1[M2c(u,v)],
si(x,y)=nonzeros(bi(x,y)×m(x,y)).
yk=argminxQpL2xxk22+f(xk),xxk,
zk=argminxQpLσppp(x)+i=0kαif(xk),xxk,
xk=τkzk+(1+τk)yk,
P1(x,y)P2(x,y)=Δ.
C1(x,y)=λ·P1(x,y),
C2(x,y)=λ·P2(x,y).
C1(x,y)C2(x,y)=λ·(P1(x,y)P2(x,y)),
C1(x,y)C2(x,y)=λ·Δ.

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