Abstract

Random Phase Encoding (RPE) techniques for image encryption have drawn increasing attention during the past decades. We demonstrate in this contribution that the RPE-based optical cryptosystems are vulnerable to the chosen-plaintext attack (CPA) with deep learning strategy. A deep neural network (DNN) model is employed and trained to learn the working mechanism of optical cryptosystems, and finally obtaining a certain optimized DNN that acts as a decryption system. Numerical simulations were carried out to verify its feasibility and reliability of not only the classical Double RPE (DRPE) scheme but also the security-enhanced Tripe RPE (TRPE) scheme. The results further indicate the possibility of reconstructing images (plaintexts) outside the original data set.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  24. Z. Zhang, Q. Liu, and Y. Wang, “Road extraction by deep residual u-net,” inProceedings of IEEE Geoscience and Remote Sensing Letters (IEEE, 2018), 749–753.
  25. H. Xiao, K. Rasul, and R. Vollgraf, “Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms,” arXiv, 1708, 07747 (2017).
  26. L. Deng, “The MNIST database of handwritten digit images for machine learning research,” in Proceedings of IEEE Signal Processing Magazine (IEEE, 2012), 141–142.
    [Crossref]
  27. B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35(9), 2506–2512 (1996).
    [Crossref]

2018 (5)

2017 (5)

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
[Crossref]

Y. Rivenson, Z. Gorocs, H. Günaydın, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
[Crossref]

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

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(1), 41789 (2017).
[Crossref] [PubMed]

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

2010 (1)

2008 (1)

2006 (2)

2004 (2)

1996 (1)

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35(9), 2506–2512 (1996).
[Crossref]

1995 (1)

Azami, N.

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

Badrinarayanan, V.

V. Badrinarayanan, A. Kendall, and R. Cipolla, “A deep convolutional encoder-decoder architecture for image segmentation,” inProceedings of IEEE transactions on pattern analysis and machine intelligence (IEEE, 2017), 2481–2495.
[Crossref]

Barbastathis, G.

Cai, L. Z.

Campos, J.

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

Chan, T. H.

T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma, “PCANet: A simple deep learning baseline for image classification,” inProceedings of IEEE transactions on image processing (IEEE, 2015), 5017–5032.
[Crossref]

Chen, J.

J. Chen, Y. Zhang, J. Li, and L. B. Zhang, “Security enhancement of double random phase encoding using rear-mounted phase masking,” Opt. Eng. 101(2), 51–59 (2018).
[Crossref]

Chen, N.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

Cheng, X. C.

Cipolla, R.

V. Badrinarayanan, A. Kendall, and R. Cipolla, “A deep convolutional encoder-decoder architecture for image segmentation,” inProceedings of IEEE transactions on pattern analysis and machine intelligence (IEEE, 2017), 2481–2495.
[Crossref]

Deng, L.

L. Deng, “The MNIST database of handwritten digit images for machine learning research,” in Proceedings of IEEE Signal Processing Magazine (IEEE, 2012), 141–142.
[Crossref]

Dong, G. Y.

Esmail, A.

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

Gao, S.

T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma, “PCANet: A simple deep learning baseline for image classification,” inProceedings of IEEE transactions on image processing (IEEE, 2015), 5017–5032.
[Crossref]

Gorocs, Z.

Gunaydin, H.

Günaydin, H.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Y. Rivenson, Z. Gorocs, H. Günaydın, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
[Crossref]

He, K.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2016), 770–778.

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(1), 41789 (2017).
[Crossref] [PubMed]

Javidi, B.

Jia, K.

T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma, “PCANet: A simple deep learning baseline for image classification,” inProceedings of IEEE transactions on image processing (IEEE, 2015), 5017–5032.
[Crossref]

Kendall, A.

V. Badrinarayanan, A. Kendall, and R. Cipolla, “A deep convolutional encoder-decoder architecture for image segmentation,” inProceedings of IEEE transactions on pattern analysis and machine intelligence (IEEE, 2017), 2481–2495.
[Crossref]

Lam, E. Y.

Lee, J.

Li, G.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

Li, J.

J. Chen, Y. Zhang, J. Li, and L. B. Zhang, “Security enhancement of double random phase encoding using rear-mounted phase masking,” Opt. Eng. 101(2), 51–59 (2018).
[Crossref]

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35(9), 2506–2512 (1996).
[Crossref]

Li, S.

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(1), 41789 (2017).
[Crossref] [PubMed]

Lin, X.

Liu, Q.

Z. Zhang, Q. Liu, and Y. Wang, “Road extraction by deep residual u-net,” inProceedings of IEEE Geoscience and Remote Sensing Letters (IEEE, 2018), 749–753.

Lizana, A.

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

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(1), 41789 (2017).
[Crossref] [PubMed]

Lu, J.

T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma, “PCANet: A simple deep learning baseline for image classification,” inProceedings of IEEE transactions on image processing (IEEE, 2015), 5017–5032.
[Crossref]

Lyu, M.

Ma, Y.

T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma, “PCANet: A simple deep learning baseline for image classification,” inProceedings of IEEE transactions on image processing (IEEE, 2015), 5017–5032.
[Crossref]

Maria, J. Y.

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

Matoba, O.

Meng, X. F.

Ozcan, A.

Peng, X.

Qin, W.

Refregier, P.

Ren, S.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2016), 770–778.

Ren, Z.

Rivenson, Y.

Shen, X. X.

Sinha, A.

Situ, G.

Sun, J.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2016), 770–778.

Teng, D.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Wang, H.

H. Wang, M. Lyu, and G. Situ, “eHoloNet: a learning-based end-to-end approach for in-line digital holographic reconstruction,” Opt. Express 26(18), 22603–22614 (2018).
[Crossref] [PubMed]

Y. Rivenson, Z. Gorocs, H. Günaydın, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
[Crossref]

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

Wang, W.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

Wang, Y.

Z. Zhang, Q. Liu, and Y. Wang, “Road extraction by deep residual u-net,” inProceedings of IEEE Geoscience and Remote Sensing Letters (IEEE, 2018), 749–753.

Wang, Y. R.

Wei, H.

Wei, Z.

Wu, Y.

Xu, X. F.

Xu, Z.

Yu, B.

Zamrani, W.

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

Zeng, Z.

T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma, “PCANet: A simple deep learning baseline for image classification,” inProceedings of IEEE transactions on image processing (IEEE, 2015), 5017–5032.
[Crossref]

Zhang, G.

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35(9), 2506–2512 (1996).
[Crossref]

Zhang, H.

Zhang, J.

Zhang, L. B.

J. Chen, Y. Zhang, J. Li, and L. B. Zhang, “Security enhancement of double random phase encoding using rear-mounted phase masking,” Opt. Eng. 101(2), 51–59 (2018).
[Crossref]

Zhang, P.

Zhang, X.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2016), 770–778.

Zhang, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

J. Chen, Y. Zhang, J. Li, and L. B. Zhang, “Security enhancement of double random phase encoding using rear-mounted phase masking,” Opt. Eng. 101(2), 51–59 (2018).
[Crossref]

Y. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Gunaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5(6), 704–710 (2018).
[Crossref]

Y. Rivenson, Z. Gorocs, H. Günaydın, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
[Crossref]

Zhang, Z.

Z. Zhang, Q. Liu, and Y. Wang, “Road extraction by deep residual u-net,” inProceedings of IEEE Geoscience and Remote Sensing Letters (IEEE, 2018), 749–753.

Appl. Opt. (1)

Light Sci. Appl. (1)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Opt. Eng. (3)

B. Javidi, G. Zhang, and J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35(9), 2506–2512 (1996).
[Crossref]

A. Esmail, W. Zamrani, N. Azami, A. Lizana, J. Campos, and J. Y. Maria, “Optical triple random-phase encryption,” Opt. Eng. 56(11), 113–114 (2017).

J. Chen, Y. Zhang, J. Li, and L. B. Zhang, “Security enhancement of double random phase encoding using rear-mounted phase masking,” Opt. Eng. 101(2), 51–59 (2018).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

Optica (4)

Sci. Rep. (2)

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

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(1), 41789 (2017).
[Crossref] [PubMed]

Other (9)

M. Lyu, H. Wang, G. Li, and G. Situ, “Exploit imaging through opaque wall via deep learning,” arXiv, 1708, 07881 (2017).

T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma, “PCANet: A simple deep learning baseline for image classification,” inProceedings of IEEE transactions on image processing (IEEE, 2015), 5017–5032.
[Crossref]

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2016), 770–778.

B. Schneier, Applied cryptography: protocols, algorithms, and source code in C. 2nd ed. Hoboken: John Wiley and Sons (1996).

Y. LeCun, Y. Bengio, and G. Hinton, Deep Learning (MIT, 2015).

V. Badrinarayanan, A. Kendall, and R. Cipolla, “A deep convolutional encoder-decoder architecture for image segmentation,” inProceedings of IEEE transactions on pattern analysis and machine intelligence (IEEE, 2017), 2481–2495.
[Crossref]

Z. Zhang, Q. Liu, and Y. Wang, “Road extraction by deep residual u-net,” inProceedings of IEEE Geoscience and Remote Sensing Letters (IEEE, 2018), 749–753.

H. Xiao, K. Rasul, and R. Vollgraf, “Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms,” arXiv, 1708, 07747 (2017).

L. Deng, “The MNIST database of handwritten digit images for machine learning research,” in Proceedings of IEEE Signal Processing Magazine (IEEE, 2012), 141–142.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Scheme setup of triple random phase encoding.
Fig. 2
Fig. 2 Schematic diagram of the DecNet neural network for optical cryptanalysis.
Fig. 3
Fig. 3 Convergence curve during the training process: (a) mean absolute error, (b) CC correlation coefficient. The blue and green line represent DRPE and TRPE scheme, respectively.
Fig. 4
Fig. 4 Original data set (fashion-MNIST test data) reconstruction that DecNet deciphered (a) DRPE and (b) TRPE: (i) testing ciphertext images, (ii) ground truth (original plaintext images), (iii) the deciphered plaintext images by trained DecNet.
Fig. 5
Fig. 5 New-type data set (MNIST, which have never been trained) reconstruction that DecNet deciphered (a) DRPE and (b) TRPE: (i) testing ciphertext images, (ii) ground truth (original plaintext images), (iii) the deciphered plaintext images using DecNet trained by fashion-MNIST.
Fig. 6
Fig. 6 Robustness test against shear: (a), (b) and (c) are ciphertexts with a shear ratio of 20%, 40%, and 60%, respectively; (d), (e) and (f) are corresponding deciphered images.
Fig. 7
Fig. 7 Robustness test against additive noise: (a), (b), and (c) are ciphertexts with additive noise weight of 0.25, 0.5 and 1, respectively; (d), (e) and (f) are corresponding deciphered images.
Fig. 8
Fig. 8 Robustness test against multiplicative noise: (a), (b), and (c) are ciphertexts with multiplicative noise weight of 0.25, 0.5 and 1, respectively; (d), (e) and (f) are corresponding deciphered images.
Fig. 9
Fig. 9 Reconstruction results when using only the amplitude of ciphertext: (a) the amplitude of ciphertext, (b) ground truth plaintexts, and (c) the retrieved plaintext images.
Fig. 10
Fig. 10 Diagram of the experimental setup: SF, spatial filter; SLM, spatial light modulator; L1, L2, L3, lenses; M1, M2, M3, random phase masks; P1, P2, polarizers.
Fig. 11
Fig. 11 Experimental results: (a) the amplitude of ciphertext, (b) ground truth plaintexts, and (c) the retrieved plaintext images.

Equations (8)

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

E D R P E ( x , y ) = IFT { FT { P ( x , y ) M 1 ( x , y ) } M 2 ( u , v ) }
E T R P E ( x , y ) = IFT { FT { P ( x , y ) M 1 ( x , y ) } M 2 ( u , v ) } M 3 ( x , y )
h D R P E ( x , y ) = IFT { F T { δ ( 0 , 0 ) M 1 ( x , y ) } M 2 ( u , v ) } = IFT { F T { M 1 ( 0 , 0 ) } M 2 ( u , v ) } = IFT { M 2 ( u , v ) }
h T R P E ( x , y ) = IFT { F T { δ ( 0 , 0 ) M 1 ( x , y ) } M 2 ( u , v ) } M 3 ( x , y ) = IFT { F T { M 1 ( 0 , 0 ) } M 2 ( u , v ) } M 3 ( x , y ) = IFT { M 2 ( u , v ) } M 3 ( x , y )
M A E = 1 w h i = 1 w j = 1 h | O ( i , j ) P ( i , j ) |
C C = m n ( P P ¯ ) ( O O ¯ ) [ m n ( P P ¯ ) 2 ] [ m n ( O O ¯ ) 2 ]
E 1 = E × ( 1 + r × p )
E 2 = E × r × p

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