Abstract

We demonstrate experimentally that the traditional double random phase encoding (DPRE) technique is vulnerable to the cyphertext-only attack (COA). With the statistical ergodic property of the speckle, we show that the plaintext image can be recovered from the cyphertext alone owing to the fact that their energy spectral density functions are identical. Our result reveals the most serious security issue with the DRPE as it suggests that even the one-time-pad does not guarantee its security. This will open up new inside understanding of current optical security techniques.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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2017 (1)

M. Liao, W. He, D. Lu, and X. Peng, “Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium,” Sci. Rep. 7, 41789 (2017).
[Crossref] [PubMed]

2016 (2)

X. Xu, Q. Wu, J. Liu, and G. Situ, “Decryption with incomplete cyphertext and multiple-information encryption in phase space,” Opt. Express 24, 1734–1746 (2016).
[Crossref] [PubMed]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

2015 (3)

2014 (1)

Ori Katz, Pierre Heidmann, Mathias Fink, and Sylvain Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photon. 8, 784–790 (2014).
[Crossref]

2013 (1)

2009 (1)

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

2007 (3)

2006 (1)

2005 (1)

2001 (1)

1996 (1)

L. G. Neto and Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[Crossref]

1995 (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] [PubMed]

P. Refregier and B. Javidi, “Optical image encryption using input plane and Fourier plane random encoding,” Proc. SPIE.,  2565, 62–68 (1995).
[Crossref]

1990 (1)

I. Freund, “Correlation imaging through multiply scattering media,” Phys. Lett. A 147, 502–506 (1990).
[Crossref]

1989 (1)

1987 (1)

1982 (2)

Alfalou, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Arcos, S.

Barrera, J. F.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Brosseau, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Carnicer, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[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] [PubMed]

Castro, A.

Chapman, H. N.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Sig. Proc. Mag.May, 87–109 (2015).
[Crossref]

Chen, W.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Chen, X.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Cohen, O.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Sig. Proc. Mag.May, 87–109 (2015).
[Crossref]

Eldar, Y. C.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Sig. Proc. Mag.May, 87–109 (2015).
[Crossref]

Fienup, J. R.

Fink, Mathias

Ori Katz, Pierre Heidmann, Mathias Fink, and Sylvain Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photon. 8, 784–790 (2014).
[Crossref]

Frauel, Y.

Freund, I.

I. Freund, “Correlation imaging through multiply scattering media,” Phys. Lett. A 147, 502–506 (1990).
[Crossref]

Gigan, Sylvain

Ori Katz, Pierre Heidmann, Mathias Fink, and Sylvain Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photon. 8, 784–790 (2014).
[Crossref]

Gonglewski, J. D.

Goodman, R. S.

Gopinathan, U.

Guo, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

C. Guo, S. Liu, and J. T. Sheridan, “Iterative phase retrieval algorithms. Part II: Attacking optical encryption systems,” Appl. Opt. 54, 4709–4718 (2015).
[Crossref] [PubMed]

Hagler, M. O.

He, W.

M. Liao, W. He, D. Lu, and X. Peng, “Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium,” Sci. Rep. 7, 41789 (2017).
[Crossref] [PubMed]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Heidmann, Pierre

Ori Katz, Pierre Heidmann, Mathias Fink, and Sylvain Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photon. 8, 784–790 (2014).
[Crossref]

Idell, P. S.

Javidi, B.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
[Crossref] [PubMed]

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

P. Refregier and B. Javidi, “Optical image encryption using input plane and Fourier plane random encoding,” Proc. SPIE.,  2565, 62–68 (1995).
[Crossref]

Juvells, I.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[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] [PubMed]

Katz, Ori

Ori Katz, Pierre Heidmann, Mathias Fink, and Sylvain Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photon. 8, 784–790 (2014).
[Crossref]

Knopp, J.

Kral, E. L.

Lancis, J.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Liao, M.

M. Liao, W. He, D. Lu, and X. Peng, “Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium,” Sci. Rep. 7, 41789 (2017).
[Crossref] [PubMed]

Liu, J.

Liu, S.

Lu, D.

M. Liao, W. He, D. Lu, and X. Peng, “Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium,” Sci. Rep. 7, 41789 (2017).
[Crossref] [PubMed]

Markman, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Matoba, O.

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Matsumoto, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Miao, J.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Sig. Proc. Mag.May, 87–109 (2015).
[Crossref]

Millán, M. S.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Monaghan, D. S.

Montes-Usategui, M.

Mosk, A. P.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Naruse, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Naughton, T. J.

Neto, L. G.

L. G. Neto and Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[Crossref]

Nishchal, N. K.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Nomura, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Peng, X.

M. Liao, W. He, D. Lu, and X. Peng, “Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium,” Sci. Rep. 7, 41789 (2017).
[Crossref] [PubMed]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Pérez-Cabré, E.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Pinkse, P. W. H.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Refregier, P.

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

P. Refregier and B. Javidi, “Optical image encryption using input plane and Fourier plane random encoding,” Proc. SPIE.,  2565, 62–68 (1995).
[Crossref]

Rivenson, Y.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Segev, M.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Sig. Proc. Mag.May, 87–109 (2015).
[Crossref]

Shechtman, Y.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Sig. Proc. Mag.May, 87–109 (2015).
[Crossref]

Sheng, Y.

L. G. Neto and Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[Crossref]

Sheridan, J. T.

Situ, G.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

X. Xu, Q. Wu, J. Liu, and G. Situ, “Decryption with incomplete cyphertext and multiple-information encryption in phase space,” Opt. Express 24, 1734–1746 (2016).
[Crossref] [PubMed]

J. Liu, X. Xu, Q. Wu, J. T. Sheridan, and G. Situ, “Information encryption in phase space,” Opt. Lett. 40, 859–862 (2015).
[Crossref] [PubMed]

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46, 5257–5262 (2007).
[Crossref] [PubMed]

Stallings, W.

W. Stallings, Cryptography and Network Security (Prentice Hall, 2004).

Stern, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Su, W.-C.

Sun, C.-C.

Tajahuerce, E.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Torroba, R.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Voelz, D. G.

Walkup, J. F.

Wu, Q.

Xie, Z.

Xu, X.

Yamaguchi, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Zang, J.

Zhang, Y.

Appl. Opt. (6)

IEEE Sig. Proc. Mag. (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Sig. Proc. Mag.May, 87–109 (2015).
[Crossref]

J. Opt. (1)

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Nat. Photon. (1)

Ori Katz, Pierre Heidmann, Mathias Fink, and Sylvain Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photon. 8, 784–790 (2014).
[Crossref]

Opt. Eng. (1)

L. G. Neto and Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[Crossref]

Opt. Express (3)

Opt. Lett. (6)

Phys. Lett. A (1)

I. Freund, “Correlation imaging through multiply scattering media,” Phys. Lett. A 147, 502–506 (1990).
[Crossref]

Proc. IEEE (1)

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Proc. SPIE. (1)

P. Refregier and B. Javidi, “Optical image encryption using input plane and Fourier plane random encoding,” Proc. SPIE.,  2565, 62–68 (1995).
[Crossref]

Sci. Rep. (1)

M. Liao, W. He, D. Lu, and X. Peng, “Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium,” Sci. Rep. 7, 41789 (2017).
[Crossref] [PubMed]

Other (1)

W. Stallings, Cryptography and Network Security (Prentice Hall, 2004).

Cited By

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Figures (5)

Fig. 1
Fig. 1

The schematic flowchart of the proposed COA algorithm.

Fig. 2
Fig. 2

Simulation demonstration. (a) the original plaintext image, (b) the cyphertext image generated by using Eq. (1). (c) The speckle obtained in the Fourier plane according to Eq. (2), (d) the averaging of the autocorrelations of the subimages, (e) the estimated ESD, and (f) the recovered plaintext image by the proposed COA algorithm. Note that the hot colormap was used to render the gray-scale images for impression sake.

Fig. 3
Fig. 3

Cyphertext-only attack to the single random phase encoding method. (a) Experimental setup. (b) Reconstructed plaintext image.

Fig. 4
Fig. 4

Experimental setup of the double random-phase encoding system.

Fig. 5
Fig. 5

Cyphertext-only attack on the double random-phase encryption. First row: reconstructed images. Second row: primary plaintext images.

Equations (3)

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g ( r ) = { { f ( r ) exp [ i R 1 ( r ) ] } exp [ i R 2 ( u ) ] } ,
I ( u ) = | 1 { g ( r ) ( u ) } | 2 = | { f ( r ) exp [ i R 1 ( r ) ] } ( u ) | 2 .
lim N N 1 n = 1 N P ( u ) Δ I n ( u ) P ( u + Δ u ) Δ I n ( u + Δ u ) d u = | Γ ( Δ u ) | 2 H ( Δ u ) ,

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