Abstract

Herein, we propose a new security enhancing method that employs wavefront aberrations as optical keys to improve the resistance capabilities of conventional double-random phase encoding (DRPE) optical cryptosystems. This study has two main innovations. First, we exploit a special beam-expander afocal-reflecting to produce different types of aberrations, and the wavefront distortion can be altered by changing the shape of the afocal-reflecting system using a deformable mirror. Then, we reconstruct the wavefront aberrations via the surface fitting of Zernike polynomials and use the reconstructed aberrations as novel asymmetric vector keys. The ideal wavefront and the distorted wavefront obtained by wavefront sensing can be regarded as a pair of private and public keys. The wavelength and focal length of the Fourier lens can be used as additional keys to increase the number of degrees of freedom. This novel cryptosystem can enhance the resistance to various attacks aimed at DRPE systems. Finally, we conduct ZEMAX and MATLAB simulations to demonstrate the superiority of this method.

© 2017 Optical Society of America

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References

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2015 (1)

2014 (2)

2013 (2)

2012 (1)

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (1)

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

2007 (1)

2006 (3)

2004 (1)

2000 (5)

1995 (1)

1982 (1)

Alfalou, A.

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

Barrera, J. F.

Brosseau, C.

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

Cai, J.

Castro, A.

Chen, L.

Chen, W.

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

Chen, X.

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

Chen, Y.

Cho, M.

Dai, C.

Dou, S.

Fienup, J. R.

Frauel, Y.

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]

Javidi, B.

Joseph, J.

Kumar, P.

Lei, M.

Lin, C.

Liu, S.

Liu, W.

Liu, Z.

Matoba, O.

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]

Naughton, T. J.

Nomura, T.

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[Crossref] [PubMed]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
[Crossref]

Peng, X.

Pérez-Cabré, E.

Qin, W.

Refregier, P.

Shen, X.

Singh, K.

Situ, G.

Tajahuerce, E.

Torroba, R.

Unnikrishnan, G.

Verrall, S. C.

Wang, X.

X. Wang, Y. Chen, C. Dai, and D. Zhao, “Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform,” Appl. Opt. 53(2), 208–213 (2014).
[Crossref] [PubMed]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

Wei, H.

Yu, B.

Zhang, J.

Zhang, P.

Zhao, D.

Adv. Opt. Photonics (2)

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

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

Appl. Opt. (4)

Opt. Commun. (2)

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

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

Opt. Eng. (1)

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
[Crossref]

Opt. Express (2)

Opt. Lett. (11)

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38(10), 1651–1653 (2013).
[Crossref] [PubMed]

J. Cai, X. Shen, M. Lei, C. Lin, and S. Dou, “Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition,” Opt. Lett. 40(4), 475–478 (2015).
[Crossref] [PubMed]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
[Crossref] [PubMed]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
[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]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[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]

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]

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

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[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]

Other (4)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed (Roberts & Company Publishers., 2004).

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 7th expanded ed. (Cambridge University, New York, 1999).

R. K. Tyson, Principles of adaptive optics (CRC, 2011).

V. N. Mahajan, “Zernike Polynomial and Wavefront Fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley- Interscience, 2007), pp. 498–546.

Supplementary Material (1)

NameDescription
» Data File 1: CSV (0 KB)      The fringe Zernike coefficients corresponding to wavefront aberrations in paper

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Figures (8)

Fig. 1
Fig. 1

Wavefront aberration and the ray aberration.

Fig. 2
Fig. 2

Schematic cryptosystem based on distorted wavefront beam illumination and DRPE.

Fig. 3
Fig. 3

(a) Ideal wavefront for measuring the optical path; (b) Distorted wavefront for measuring the optical path.

Fig. 4
Fig. 4

When λ = 537.8nm, f = 100mm: (a) Ideal wavefront point array; (b) Distorted wavefront point array; (c) Ideal wavefront map; (d) Distorted wavefront map. See Data File 1.

Fig. 5
Fig. 5

For λ = 537.8nm and f = 100mm: (a) Wavefront aberration map; (b) Wavefront aberration decryption map; (c) Wavefront aberration surface shadow in XY plane; (d) Wavefront aberration decryption surface shadow in XY plane.

Fig. 6
Fig. 6

(a) Input plaintext (Townlet, 256 × 256 pixels); Only wavefront-aberration keys are used; (b) f = 100mm, λ = 441.6nm, the ciphertext; (c) f = 100mm, λ = 537.8nm, the ciphertext; (d) f = 100mm, λ = 632.8nm, the ciphertext; (e) f = 200mm, λ = 537.8nm, the ciphertext; (f) f = 300mm, λ = 537.8nm, the ciphertext.

Fig. 7
Fig. 7

(a) Input plaintext (Townlet, 256 × 256 pixels); (b) Encryption with two encryption keys; (c) Two decryption keys are both wrong; (d) False double-random phase decryption keys and true wavefront aberration decryption keys; (e)True double-random phase decryption keys and false wavefront aberration decryption keys; (f) Two decryption keys are both true.

Fig. 8
Fig. 8

(a) SSEs of phase-key retrieval versus the number of iterations for the WA-DRPE and DRPE; (b) Retrieved result of the proposed scheme; (c) Retrieved result of the DRPE scheme.

Equations (21)

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

Φ K =[ Q ¯ Q]=[ P 0 Q][ P 0 Q ¯ ],
ξ η W(ξ,η) = i Φ i ,
kW(ξ,η)=Δϕ=ϕ(ξ,η) ϕ 0 (ξ,η).
P(ξ,η)={ exp[jkW(ξ,η)] ξ 2 + η 2 D pupil 2 0 ξ 2 + η 2 > D pupil 2 .
o(x',y')=IFT{FT[f(x,y)n(x,y)]B(μ,ν)},
o'(x',y')=o(x',y')h(x',y'),
h(x',y')=c P(ξ,η) exp[j k d (x'ξ+y'η)]dξdη. =c'FT{P(λd f ξ ,λd f η )}
H 1 ( f ξ , f η )=FT[h(x',y')]=c'P(λd f ξ ,λd f η )=exp[jkW(λd f ξ ,λd f η )],
o'(x',y')=IFT{FT[f(x,y)n(x,y)]B(μ,ν)exp[jkW(λdμ,λdν)]},
ψ(μ,ν)=FT{f(x,y)exp[jϕ(x,y)]}exp[jφ(μ,ν)]exp[jkW(λdμ,λdν)].
exp[jφ(μ,ν)]= ψ(μ,ν) FT{f(x,y)exp[jϕ(x,y)]}exp[jkW(λdμ,λdν)] .
ψ(μ,ν)=FT[f(x,y)n(x,y)]B(μ,ν)exp[jkW(λdμ,λdν)] =FT[δ(x,y)n(x,y)]B(μ,ν)exp[jkW(λdμ,λdν)] =n(0,0)B(μ,ν)exp[jkW(λdμ,λdν)],
ψ'(μ,ν)=n(i,j)B(μ,ν)exp[jkW(λdμ,λdν)].
n'(x,y)= ψ'(μ,ν) ψ(μ,ν) ,
n'(x,y)= n(x,y) n(0,0) ,
ψ 2 (μ,ν)=FT[ f 2 (x,y)n(x,y)]B(μ,ν)exp[jkW(λdμ,λdν)].
ψ 2 (μ,ν)=FT[ f 2 (x,y)n'(x,y)]B'(μ,ν)exp[jkW(λdμ,λdν)],
B'(μ,ν)= ψ 2 (μ,ν) FT[ f 2 (x,y)n'(x,y)]exp[jkW(λdμ,λdν)] .
NMSE= i=1 M j=1 N [f(i,j) f ' (i,j)] 2 i=1 M j=1 N [f(i,j)] 2 ,
NSNR=-10 log 10 { i=1 M j=1 N [f(i,j) f ' (i,j)] 2 i=1 M j=1 N [f(i,j)] 2 }=-10 log 10 (NMSE).
SSE=10 log 10 { [f(i,j) f N (i,j)] 2 f (i,j) 2 },

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