Abstract

We present a protocol for the amplification and distribution of a one-time-pad cryptographic key over a point-to-multipoint optical network based on computational ghost imaging (GI) and compressed sensing (CS). It is shown experimentally that CS imaging can perform faster authentication and increase the key generation rate by an order of magnitude compared with the scheme using computational GI alone. The protocol is applicable for any number of legitimate user, thus, the scheme could be used in real intercity networks where high speed and high security are crucial.

© 2013 Optical Society of America

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    [CrossRef]
  5. H. K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
    [CrossRef]
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2013 (1)

2012 (2)

D. J. Guan, Y. J. Wang, and E. S. Zhang, “Quantum key evolution and its applications,” Int. J. Quantum Inform. 10, 1250044 (2012).
[CrossRef]

M. Tanha, R. Kheradmand, and S. Ahmadi-Kandjani, “Gray-scale and color optical encryption based on computational ghost imaging,” Appl. Phys. Lett. 101, 101108 (2012).
[CrossRef]

2011 (1)

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

2010 (2)

2009 (1)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

2008 (4)

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802R (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

2006 (1)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

2005 (2)

D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
[CrossRef]

H. K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
[CrossRef]

2004 (1)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

1998 (1)

W. Y. Hwang, I. G. Koh, and Y. D. Han, “Quantum cryptography without public announcement of bases,” Phys. Rev. A 244, 489–494 (1998).

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef]

1992 (3)

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[CrossRef]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

C. H. Bennett, G. Brassard, and A. Ekert, “Quantum cryptography,” Sci. Am. 267, 50–57 (1992).
[CrossRef]

Ahmadi-Kandjani, S.

M. Tanha, R. Kheradmand, and S. Ahmadi-Kandjani, “Gray-scale and color optical encryption based on computational ghost imaging,” Appl. Phys. Lett. 101, 101108 (2012).
[CrossRef]

Ardehali, M.

H. K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
[CrossRef]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, and A. Ekert, “Quantum cryptography,” Sci. Am. 267, 50–57 (1992).
[CrossRef]

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[CrossRef]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

C. H. Bennett and G. Brassard, “Quantum cryptography: public-key distribution and coin tossing,” in Proc. ICCSSP, Bangalore, India, 1984, pp. 175–179.

Berchera, I. R.

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Bessette, F.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[CrossRef]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

Brassard, G.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[CrossRef]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

C. H. Bennett, G. Brassard, and A. Ekert, “Quantum cryptography,” Sci. Am. 267, 50–57 (1992).
[CrossRef]

C. H. Bennett and G. Brassard, “Quantum cryptography: public-key distribution and coin tossing,” in Proc. ICCSSP, Bangalore, India, 1984, pp. 175–179.

Brida, G.

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Bromberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Candès, E. J.

E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematics (European Mathematical Society, 2006), Vol. 3, p. 1433.

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Chau, H. F.

H. K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
[CrossRef]

Chekhova, M. V.

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Chen, X. H.

Clemente, P.

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Durán, V.

Ekert, A.

C. H. Bennett, G. Brassard, and A. Ekert, “Quantum cryptography,” Sci. Am. 267, 50–57 (1992).
[CrossRef]

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Fornaro, G. A.

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

Genovese, M.

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Guan, D. J.

D. J. Guan, Y. J. Wang, and E. S. Zhang, “Quantum key evolution and its applications,” Int. J. Quantum Inform. 10, 1250044 (2012).
[CrossRef]

Han, Y. D.

W. Y. Hwang, I. G. Koh, and Y. D. Han, “Quantum cryptography without public announcement of bases,” Phys. Rev. A 244, 489–494 (1998).

Hwang, W. Y.

W. Y. Hwang, I. G. Koh, and Y. D. Han, “Quantum cryptography without public announcement of bases,” Phys. Rev. A 244, 489–494 (1998).

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Kheradmand, R.

M. Tanha, R. Kheradmand, and S. Ahmadi-Kandjani, “Gray-scale and color optical encryption based on computational ghost imaging,” Appl. Phys. Lett. 101, 101108 (2012).
[CrossRef]

Koh, I. G.

W. Y. Hwang, I. G. Koh, and Y. D. Han, “Quantum cryptography without public announcement of bases,” Phys. Rev. A 244, 489–494 (1998).

Lanci, J.

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Li, C. B.

C. B. Li, “An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing,” Masters of Science thesis (Rice University, 2010).

Li, S.

Lo, H. K.

H. K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
[CrossRef]

Lopaeva, E. D.

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Mermin, N. D.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef]

Salvail, L.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[CrossRef]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef]

Shapiro, J. H.

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802R (2008).
[CrossRef]

Shih, Y. H.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef]

Silberberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Smolin, J.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef]

Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Tajahuerce, E.

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Tanha, M.

M. Tanha, R. Kheradmand, and S. Ahmadi-Kandjani, “Gray-scale and color optical encryption based on computational ghost imaging,” Appl. Phys. Lett. 101, 101108 (2012).
[CrossRef]

Torres-Company, V.

Walker, J.

J. Walker, “Ent: a pseudorandom number sequence test program,” Tech. Rep. (1998), http://www.fourmilab.ch/random .

Wang, Y. J.

D. J. Guan, Y. J. Wang, and E. S. Zhang, “Quantum key evolution and its applications,” Int. J. Quantum Inform. 10, 1250044 (2012).
[CrossRef]

Wu, L. A.

Yao, X. R.

Yu, W. K.

Zhai, G. J.

Zhai, Y. H.

Zhang, D.

Zhang, E. S.

D. J. Guan, Y. J. Wang, and E. S. Zhang, “Quantum key evolution and its applications,” Int. J. Quantum Inform. 10, 1250044 (2012).
[CrossRef]

Appl. Phys. Lett. (3)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

M. Tanha, R. Kheradmand, and S. Ahmadi-Kandjani, “Gray-scale and color optical encryption based on computational ghost imaging,” Appl. Phys. Lett. 101, 101108 (2012).
[CrossRef]

IEEE Signal Process. Mag. (1)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Int. J. Quantum Inform. (1)

D. J. Guan, Y. J. Wang, and E. S. Zhang, “Quantum key evolution and its applications,” Int. J. Quantum Inform. 10, 1250044 (2012).
[CrossRef]

J. Cryptol. (2)

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[CrossRef]

H. K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (5)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802R (2008).
[CrossRef]

W. Y. Hwang, I. G. Koh, and Y. D. Han, “Quantum cryptography without public announcement of bases,” Phys. Rev. A 244, 489–494 (1998).

Phys. Rev. Lett. (3)

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

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Sci. Am. (1)

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[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Diagrammatic representation of a secure communication network of users in two cities.

Fig. 2.
Fig. 2.

Experimental setup.

Fig. 3.
Fig. 3.

(a) Image of the original mask. (b)–(d) Images of the letter “A” reconstructed experimentally by: (b) DGI, with M=1000, (c) DGI, with M=13500, (d) CS, using the same experimental data as in (b), and MSE=4.642×102.

Fig. 4.
Fig. 4.

Images reconstructed experimentally by DGI for different regions. (a), (b), (c), (d), and (e): reconstructed DGI images of the letters “C”, “A”, “S”, “CA”, and “CAS”, respectively.

Fig. 5.
Fig. 5.

(a) DGI image recovered from the correct start key. (b) DGI image recovered with one bit of the start key incorrect. (c) and (d) The keys obtained from (a) and (b), respectively. (e) CS image retrieved from the correct start key. (f) CS image retrieved with 19 bits of the measured intensity incorrect.

Tables (2)

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Table 1. ENT Randomness Test Results for Different Numbers of Frames

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Table 2. ENT Randomness Test Results for Different Letter Images

Equations (5)

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

y=Ax+e,x=Ψx,
minx12yAΨx22+τx1,
GDGI(m,n)=yiai(m,n)yiBai(m,n)B,
B=c=1md=1nai(c,d).
MSE=1mn·c=1md=1n(Xori(c,d)GDGI(c,d))2.

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