Abstract

Optical techniques have boosted a new class of cryptographic systems with some remarkable advantages, and optical encryption not only has spurred practical developments but also has brought a new insight into cryptography. However, this does not mean that it is elusive for the opponents to attack optical encryption systems. In this paper, for the first time to our knowledge, we experimentally demonstrate the machine-learning attacks on interference-based optical encryption. Using machine-learning models that are trained by a series of ciphertext-plaintext pairs, an unauthorized person is capable to retrieve the unknown plaintexts from the given ciphertexts without the usage of various different optical encryption keys existing in interference-based optical encryption. In comparison with conventional cryptanalytic methods, the proposed machine-learning-based attacking method can estimate transfer function or point spread function of interference-based optical encryption systems without subsidiary conditions. Simulations and optical experiments demonstrate feasibility and effectiveness of the proposed method, and the proposed machine-learning-based attacking method provides a versatile approach to analyzing the vulnerability of interference-based optical encryption.

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

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References

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

2015 (3)

X. Liu, J. Wu, W. He, M. Liao, C. Zhang, and X. Peng, “Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding,” Opt. Express 23(15), 18955–18968 (2015).
[Crossref] [PubMed]

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

A. Surekha, P. R. Anand, and I. Indu, “E-Payment Transactions Using Encrypted QR Codes,” Int. J. Appl. Eng. Res. 10(77), 461 (2015).

2014 (1)

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

2013 (3)

2012 (1)

L. Deng, “The MNIST database of handwritten digit images for machine learning research [best of the web],” IEEE Signal Process. Mag. 29(6), 141–142 (2012).
[Crossref]

2010 (4)

2009 (2)

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

2008 (1)

2007 (3)

N. M. Nasrabadi, “Pattern recognition and machine learning,” J. Electron. Imaging 16(4), 049901 (2007).
[Crossref]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15(24), 16067–16079 (2007).
[Crossref] [PubMed]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[Crossref]

2006 (3)

2005 (1)

2004 (1)

2002 (1)

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4–6), 277–285 (2002).
[Crossref]

2000 (4)

G. Unnikrishnan and K. Singh, “Double random fractional Fourier domain encoding for optical security,” Opt. Eng. 39(11), 2853–2859 (2000).
[Crossref]

P. C. Mogensen and J. Glückstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173(1–6), 177–183 (2000).
[Crossref]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
[Crossref] [PubMed]

E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39(14), 2313–2320 (2000).
[Crossref] [PubMed]

1999 (3)

1997 (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

1995 (1)

1978 (1)

R. C. Merkle, “Secure communications over insecure channels,” Commun. ACM 21(4), 294–299 (1978).
[Crossref]

Abuturab, M. R.

M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51(3), 317–324 (2013).
[Crossref]

Ahmad, M. A.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Alfalou, A.

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

Anand, P. R.

A. Surekha, P. R. Anand, and I. Indu, “E-Payment Transactions Using Encrypted QR Codes,” Int. J. Appl. Eng. Res. 10(77), 461 (2015).

Anderson, R. J.

F. A. Petitcolas, R. J. Anderson, and M. G. Kuhn, “Information hiding-a survey,” Proc. IEEE 87(7), 1062 (1999).
[Crossref]

Arcos, S.

Barrera, J. F.

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Brosseau, C.

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

Carnicer, A.

Chen, L.

Chen, W.

Chen, X.

Clemente, P.

Dai, J.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Deng, L.

L. Deng, “The MNIST database of handwritten digit images for machine learning research [best of the web],” IEEE Signal Process. Mag. 29(6), 141–142 (2012).
[Crossref]

Durán, V.

Gao, Q.

Glückstad, J.

P. C. Mogensen and J. Glückstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173(1–6), 177–183 (2000).
[Crossref]

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]

X. Liu, J. Wu, W. He, M. Liao, C. Zhang, and X. Peng, “Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding,” Opt. Express 23(15), 18955–18968 (2015).
[Crossref] [PubMed]

Hinton, G.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Indu, I.

A. Surekha, P. R. Anand, and I. Indu, “E-Payment Transactions Using Encrypted QR Codes,” Int. J. Appl. Eng. Res. 10(77), 461 (2015).

Javidi, B.

Joseph, J.

Juvells, I.

Kuhn, M. G.

F. A. Petitcolas, R. J. Anderson, and M. G. Kuhn, “Information hiding-a survey,” Proc. IEEE 87(7), 1062 (1999).
[Crossref]

Lancis, J.

LeCun, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Li, H.

Li, Q.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Li, T.

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]

X. Liu, J. Wu, W. He, M. Liao, C. Zhang, and X. Peng, “Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding,” Opt. Express 23(15), 18955–18968 (2015).
[Crossref] [PubMed]

Liu, S.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[Crossref]

Liu, X.

Liu, Z.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[Crossref]

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]

Matoba, O.

Merkle, R. C.

R. C. Merkle, “Secure communications over insecure channels,” Commun. ACM 21(4), 294–299 (1978).
[Crossref]

Mira, A.

Mogensen, P. C.

P. C. Mogensen and J. Glückstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173(1–6), 177–183 (2000).
[Crossref]

Montes-Usategui, M.

Nasrabadi, N. M.

N. M. Nasrabadi, “Pattern recognition and machine learning,” J. Electron. Imaging 16(4), 049901 (2007).
[Crossref]

Peng, X.

Petitcolas, F. A.

F. A. Petitcolas, R. J. Anderson, and M. G. Kuhn, “Information hiding-a survey,” Proc. IEEE 87(7), 1062 (1999).
[Crossref]

Refregier, P.

Sheppard, C. J.

Shi, Y.

Singh, K.

G. Unnikrishnan and K. Singh, “Double random fractional Fourier domain encoding for optical security,” Opt. Eng. 39(11), 2853–2859 (2000).
[Crossref]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
[Crossref] [PubMed]

Singh, N.

N. Singh and A. Sinha, “Chaos based multiple image encryption using multiple canonical transforms,” Opt. Laser Technol. 42(5), 724–731 (2010).
[Crossref]

Sinha, A.

N. Singh and A. Sinha, “Chaos based multiple image encryption using multiple canonical transforms,” Opt. Laser Technol. 42(5), 724–731 (2010).
[Crossref]

Situ, G.

Sun, X.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Surekha, A.

A. Surekha, P. R. Anand, and I. Indu, “E-Payment Transactions Using Encrypted QR Codes,” Int. J. Appl. Eng. Res. 10(77), 461 (2015).

Tajahuerce, E.

Tanno, N.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4–6), 277–285 (2002).
[Crossref]

Tao, R.

Torres-Company, V.

Torroba, R.

Unnikrishnan, G.

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
[Crossref] [PubMed]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier domain encoding for optical security,” Opt. Eng. 39(11), 2853–2859 (2000).
[Crossref]

Verrall, S. C.

Wang, B.

Wang, Y.

Wei, H.

Wu, J.

Xin, Y.

Yu, B.

Zhang, C.

Zhang, J.

Zhang, P.

Zhang, S.

Zhang, Y.

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[Crossref] [PubMed]

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4–6), 277–285 (2002).
[Crossref]

Zhao, D.

Zheng, C. H.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4–6), 277–285 (2002).
[Crossref]

Adv. Opt. Photonics (2)

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

Appl. Opt. (2)

Commun. ACM (1)

R. C. Merkle, “Secure communications over insecure channels,” Commun. ACM 21(4), 294–299 (1978).
[Crossref]

IEEE Signal Process. Mag. (1)

L. Deng, “The MNIST database of handwritten digit images for machine learning research [best of the web],” IEEE Signal Process. Mag. 29(6), 141–142 (2012).
[Crossref]

Int. J. Appl. Eng. Res. (1)

A. Surekha, P. R. Anand, and I. Indu, “E-Payment Transactions Using Encrypted QR Codes,” Int. J. Appl. Eng. Res. 10(77), 461 (2015).

J. Electron. Imaging (1)

N. M. Nasrabadi, “Pattern recognition and machine learning,” J. Electron. Imaging 16(4), 049901 (2007).
[Crossref]

Nature (1)

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Opt. Commun. (4)

P. C. Mogensen and J. Glückstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173(1–6), 177–183 (2000).
[Crossref]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[Crossref]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282(8), 1536–1540 (2009).
[Crossref]

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4–6), 277–285 (2002).
[Crossref]

Opt. Eng. (1)

G. Unnikrishnan and K. Singh, “Double random fractional Fourier domain encoding for optical security,” Opt. Eng. 39(11), 2853–2859 (2000).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

N. Singh and A. Sinha, “Chaos based multiple image encryption using multiple canonical transforms,” Opt. Laser Technol. 42(5), 724–731 (2010).
[Crossref]

Opt. Lasers Eng. (1)

M. R. Abuturab, “Color image security system based on discrete Hartley transform in gyrator transform domain,” Opt. Lasers Eng. 51(3), 317–324 (2013).
[Crossref]

Opt. Lett. (12)

L. Chen and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31(23), 3438–3440 (2006).
[Crossref] [PubMed]

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[Crossref] [PubMed]

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(13), 1644–1646 (2005).
[Crossref] [PubMed]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31(22), 3261–3263 (2006).
[Crossref] [PubMed]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[Crossref] [PubMed]

W. Chen, X. Chen, and C. J. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[Crossref] [PubMed]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[Crossref] [PubMed]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 Schematic setup for interference-based optical encryption. SLM: spatial light modulator; BS: beam splitter; CCD: charge-coupled device; M: random mask.
Fig. 2
Fig. 2 Schematic of the designed CNN architecture for attacking interference-based optical encryption. The inputs (i.e., ciphertexts) are resized from 512×512pixels to 100×100pixels to lower computational load. After two convolutions and two pooling layers, the input is reshaped and fully connected to the ground truth. Using sufficient pairs of ciphertexts and plaintexts fed to the learning model, the CNN model is trained to predict unknown plaintexts from the given ciphertexts. (a) Training phase: pairs of ciphertexts and plaintexts obtained from interference-based optical encryption are respectively fed to the inputs and outputs of a designed CNN model. (b) Testing phase: typical examples show that the trained CNN model can be used in real time to predict the unknown plaintexts from the given ciphertexts.
Fig. 3
Fig. 3 Simulation results of the proposed learning attack on interference-based optical encryption. Testing phase: (a), (c), (e), (g), (i), (k), (m), (o) and (q) the ciphertexts obtained by using the interference-based optical encoding (further sent to the trained learning model). (b), (d), (f), (h), (j) and (l) The unknown plaintexts retrieved by using the trained learning model respectively corresponding to (a), (c), (e), (g), (i) and (k). (n), (p) and (r) The retrieved plaintexts (i.e., from different databases) obtained by using the learning model trained by the MNIST database.
Fig. 4
Fig. 4 Experimental results of the proposed machine-learning attacks to the interference-based optical encryption. Testing phase: (a), (c), (e), (g), (i), (k), (m), (o) and (q) ciphertexts recorded by using interference-based optical encryption setup. (b), (d), (f), (h), (j), (l), (n), (p) and (r) The unknown plaintexts retrieved by using the trained learning model respectively corresponding to (a), (c), (e), (g), (i), (k), (m), (o) and (q).
Fig. 5
Fig. 5 Experimental setup for interference-based optical encryption with cascaded random masks at the object beam arm.
Fig. 6
Fig. 6 Experimental results of the proposed machine-learning attacks on the interference-based optical encryption. Testing phase: (a), (c), (e), (g), (i), (k), (m), (o) and (q) ciphertexts recorded by using the interference-based optical encryption system. (b), (d), (f), (h), (j), (l), (n), (p) and (r) The unknown plaintexts retrieved by using the trained learning model respectively corresponding to (a), (c), (e), (g), (i), (k), (m), (o) and (q).
Fig. 7
Fig. 7 Experimental setup for interference-based optical encryption with cascaded random masks at the reference beam arm.
Fig. 8
Fig. 8 Experimental results of the proposed machine-learning attacks on interference-based optical encryption. Testing phase: (a), (c), (e), (g), (i), (k), (m), (o) and (q) ciphertexts recorded by using the interference-based optical encryption system. (b), (d), (f), (h), (j), (l), (n), (p) and (r) The unknown plaintexts retrieved by using the trained learning model respectively corresponding to (a), (c), (e), (g), (i), (k), (m), (o) and (q).

Equations (2)

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H(μ,ν)= FrT d,λ [f(x,y) M 1 (x,y)]+ FrT d,λ [ M 2 (x,y)],
I(μ,ν)= | FrT d,λ [f(x,y) M 1 (x,y)]+ FrT d,λ [ M 2 (x,y)] | 2 .

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