Abstract

Authentication of encoded information is a popular current trend in optical security. Recent research has proposed the production of secure unclonable ID tags and devices with the use of nanoscale encoding and thin-film deposition fabrication techniques, which are nearly impossible to counterfeit but can be verified using optics and photonics instruments. Present procedures in optical encryption provide secure access to the information, and these techniques are improving daily. Nevertheless, a rightful recipient with access to the decryption key may not be able to validate the authenticity of the message. In other words, there is no simple way to check whether the information has been counterfeited. Metallic nanoparticles may be used in the fabrication process because they provide distinctive polarimetric signatures that can be used for validation. The data is encoded in the optical domain, which can be verified using physical properties with speckle analysis or ellipsometry. Signals obtained from fake and genuine samples are complex and can be difficult to distinguish. For this reason, machine-learning classification algorithms are required in order to determine the authenticity of the encoded data and verify the security of unclonable nanoparticle encoded or thin-film-based ID tags. In this paper, we review recent research on optical validation of messages, ID tags, and codes using nanostructures, thin films, and 3D optical codes. We analyze several case scenarios where optically encoded devices have to be authenticated. Validation requires the combined use of a variety of multi-disciplinary approaches in optical and statistical techniques, and for this reason, the first five sections of this paper are organized as a tutorial.

© 2017 Optical Society of America

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2017 (1)

A. Carnicer, I. Juvells, B. Javidi, and R. Martínez-Herrero, “Optical encryption in the axial domain using beams with arbitrary polarization,” Opt. Lasers Eng. 89, 145–149 (2017).
[Crossref]

2016 (9)

T. Matsumoto, N. Yoshida, S. Nishio, M. Hoga, Y. Ohyagi, N. Tate, and M. Naruse, “Optical nano artifact metrics using silicon random nanostructures,” Sci. Rep. 6, 32438 (2016).
[Crossref]

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]

M. Wainberg, B. Alipanahi, and B. Frey, “Are random forests truly the best classifiers?” J. Mach. Learn. Res. 17, 1–5 (2016).

E. Medina, E. Bel, and J. Suñé, “Counterfeit medicines in Peru: a retrospective review (1997–2014),” BMJ Open 6, e010387 (2016).
[Crossref]

F. Goudail and M. Boffety, “Optimal configuration of static polarization imagers for target detection,” J. Opt. Soc. Am. A 33, 9–16 (2016).
[Crossref]

A. Carnicer, I. Juvells, B. Javidi, and R. Martínez-Herrero, “Optical encryption in the longitudinal domain of focused fields,” Opt. Express 24, 6793–6801 (2016).
[Crossref]

A. Markman, A. Carnicer, and B. Javidi, “Security authentication with a three-dimensional optical phase code using random forest classifier,” J. Opt. Soc. Am. A 33, 1160–1165 (2016).
[Crossref]

R. M. A. Azzam, “Stokes-vector and Mueller-matrix polarimetry [Invited],” J. Opt. Soc. Am. A 33, 1396–1408 (2016).
[Crossref]

A. Carnicer, O. Arteaga, J. M. Suñé, and B. Javidi, “Authentication of gold nanoparticle encoded pharmaceutical tablets using polarimetric signatures,” Opt. Lett. 41, 4507–4510 (2016).
[Crossref]

2015 (4)

2014 (11)

A. Markman and B. Javidi, “Full-phase photon-counting double-random-phase encryption,” J. Opt. Soc. Am. A 31, 394–403 (2014).
[Crossref]

O. Arteaga, M. Baldrís, J. Antó, A. Canillas, E. Pascual, and E. Bertran, “Mueller matrix microscope with a dual continuous rotating compensator setup and digital demodulation,” Appl. Opt. 53, 2236–2245 (2014).
[Crossref]

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

S. K. Rajput and N. K. Nishchal, “An optical encryption and authentication scheme using asymmetric keys,” J. Opt. Soc. Am. A 31, 1233–1238 (2014).
[Crossref]

S. A. Goorden, M. Horstmann, A. P. Mosk, B. Skoric, and P. W. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1, 421–424 (2014).
[Crossref]

K. Dégardin, Y. Roggo, and P. Margot, “Understanding and fighting the medicine counterfeit market,” J. Pharm. Biomed. Anal. 87, 167–175 (2014).
[Crossref]

S. Kovacs, S. E. Hawes, and S. N. Maley, “Technologies for detecting falsified and substandard drugs in low and middle-income countries,” PLoS One 9, e90601 (2014).
[Crossref]

T. Matsumoto, M. Hoga, Y. Ohyagi, M. Ishikawa, M. Naruse, K. Hanaki, R. Suzuki, D. Sekiguchi, N. Tate, and M. Ohtsu, “Nano-artifact metrics based on random collapse of resist,” Sci. Rep. 4, 6142 (2014).
[Crossref]

M. Fernández-Delgado, E. Cernadas, S. Barro, and D. Amorim, “Do we need hundreds of classifiers to solve real world classification problems?” J. Mach. Learn. Res. 15, 3133–3181 (2014).

O. Arteaga, “Useful Mueller matrix symmetries for ellipsometry,” Thin Solid Films 571, 584–588 (2014).
[Crossref]

A. Markman, B. Javidi, and M. Tehranipoor, “Photon-counting security tagging and verification using optically encoded QR codes,” IEEE Photon. J. 6, 1–9 (2014).
[Crossref]

2013 (6)

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (2013).
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Figures (30)

Figure 1
Figure 1

(a) Q(x,y,0), reversed QR code encoding the message 0034934021143. (b) Propagated irradiance IQ(x,y,z)=|Q(x,y,z)|2.

Figure 2
Figure 2

(a) Irradiance of the propagated field IR(x,y,z)=|R(x,y,z)|2. (b) Irradiance of the propagated field IC(x,y,z)=|C(x,y,z)|2.

Figure 3
Figure 3

Histograms of (a) irradiance of the propagated phase mask IR(x,y,z) and (b) irradiance of the propagated phase-encoded image IC(x,y,z).

Figure 4
Figure 4

Sketch of 4f double random phase encryption system.

Figure 5
Figure 5

Poincaré sphere displaying some states of polarization.

Figure 6
Figure 6

Sketch of (a) four photoelastic modulators Mueller matrix polarimeter and (b) Mueller matrix imaging ellipsometer. PEMs are photoelastic modulators. Reprinted with permission from [46]. Copyright 2016 Optical Society of America.

Figure 7
Figure 7

Two-class SVM: margin hyperplanes and support vectors.

Figure 8
Figure 8

Combined dataset X. Ellipses indicate a random selection of data (yellow ellipses) and features (blue ellipses) for generating a random tree.

Figure 9
Figure 9

Example of a complete decision tree. The red box indicates a random selection of nodes and conditions, i.e., a random tree.

Figure 10
Figure 10

(a) AuNP (gold) QR code (sample A), (b) platinum QR code (sample B), and (c) AuNP (gold) structure without QR code (sample C). Reprinted with permission from [44]. Copyright 2015 Optical Society of America.

Figure 11
Figure 11

Optical setup for authentication of codes produced with gold nanoparticles. Reprinted with permission from [44]. Copyright 2015 Optical Society of America.

Figure 12
Figure 12

Propagated QR codes: (a) sample A, (b) sample B, and (c) sample C (see Fig. 10 for details). Reprinted with permission from [44]. Copyright 2015 Optical Society of America.

Figure 13
Figure 13

Histograms of the three samples in Figs. 12(a)12(c) for different directions of polarization (0°, 30°, 60°, 120°, and 150°). (d) Principal component analysis of the histograms. Red dots, sample A; green dots, sample B; blue dots, sample C. Reprinted with permission from [44]. Copyright 2015 Optical Society of America.

Figure 14
Figure 14

Propagated random phase-encoded QR codes: (a) sample A, (b) sample B, and (c) sample C. Reprinted with permission from [44]. Copyright 2015 Optical Society of America.

Figure 15
Figure 15

(a)–(c) Histograms of the three phase-encoded samples in Figs. 14(a)14(c) for different directions of polarization (0°, 30°, 60°, 120°, and 150°). (d) Principal component analysis for the phase-encoded samples. Red dots, sample A; green dots, sample B; blue dots, sample C. Reprinted with permission from [44]. Copyright 2015 Optical Society of America.

Figure 16
Figure 16

(a) QR code encoding the message “0034934021143.” (b) High-contrast thin film used as the lithographic mask. (c) Ta2O5 QR (left) code and Cr QR (right). Reprinted with permission from [45]. Copyright 2015 Optical Society of America.

Figure 17
Figure 17

Mueller matrix images for samples (a) Cr and (b) Ta2O5. Reprinted with permission from [45]. Copyright 2015 Optical Society of America.

Figure 18
Figure 18

Phase-only correlation: (a) |ρCrρCr| and (b) |ρCrρTa2O5|. Reprinted with permission from [45]. Copyright 2015 Optical Society of America.

Figure 19
Figure 19

Mueller matrix images for samples with adhesive tape: (a) Cr and (b) Ta2O5. Reprinted with permission from [45]. Copyright 2015 Optical Society of America.

Figure 20
Figure 20

Histograms (x axis, gray levels; y axis, frequency) of the four Stokes components distributions for class Cr: (a) S0, (b) S1, (c) S2, and (d) S3. Reprinted with permission from [45]. Copyright 2015 Optical Society of America.

Figure 21
Figure 21

Histograms (x axis, gray levels; y axis, frequency) of the four Stokes components distributions for class Ta2O5: (a) S0, (b) S1, (c) S2, and (d) S3. Reprinted with permission from [45]. Copyright 2015 Optical Society of America.

Figure 22
Figure 22

Principal component analysis for the phase-encoded samples Cr (red dots) and Ta2O5 (green dots): (a) S0, (b) S1, (c) S2, and (d) S3.

Figure 23
Figure 23

Produced tablets used in the experiments.

Figure 24
Figure 24

Mueller matrix components as a function of the wavelength. The wavelength and the Mueller components range from 280 to 700 nm and [1, 1], respectively. For the sake of clarity, the y scale of the graphs is adapted to the dynamic range for each component. Two tablets of each class were used. Black, tablets without nanoparticles; red, tablets with 4 nm AuNP; green, tablets with 12 nm AuNP; blue, tablets with 25 nm AuNP. Reprinted with permission from [46]. Copyright 2016 Optical Society of America.

Figure 25
Figure 25

DoP as a function of the wavelength for several input states of polarization: S=(1,0,0,0), S=(1,1,0,0), S=(1,1,0,0), S=(1,0,1,0), S=(1,0,1,0), and S=(1,0,0,1). Two tablets of each class were used. Black, tablets without nanoparticles; red, tablets with 4 nm AuNP; green, tablets with 12 nm AuNP; blue, tablets with 25 nm AuNP. Reprinted with permission from [46]. Copyright 2016 Optical Society of America.

Figure 26
Figure 26

Averaged DoP as a function of the polarization angle ψ. Two tablets of each class were used. Black, tablets without nanoparticles; red, tablets with 4 nm AuNP; green, tablets with 12 nm AuNP; blue, tablets with 25 nm AuNP. Reprinted with permission from [46]. Copyright 2016 Optical Society of America.

Figure 27
Figure 27

3D phase-encoded codes: (a) two-layer 3D code (code A), (b) four-layer s3D code (code B), and (c) five-layer 3D code (code C). Reprinted with permission from [56]. Copyright 2016 Optical Society of America.

Figure 28
Figure 28

(a) Conventional QR code printed on transparency film, (b) two-layer 3D code (class A), and (c) optical setup. Reprinted with permission from [56]. Copyright 2016 Optical Society of America.

Figure 29
Figure 29

Recorded speckle distributions and the corresponding histograms for d=110  mm. Gamma distributions fitted to match the histograms are depicted in red: (a) 3D code class A, (b) 3D code class B, and (c) 3D code class C. Reprinted with permission from [56]. Copyright 2016 Optical Society of America.

Figure 30
Figure 30

Classification errors as a function of the number of trees used. Reprinted with permission from [56]. Copyright 2016 Optical Society of America.

Tables (7)

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Table 1. Propagation Variables

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Table 2. SVM Results, Three-Class Problem

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Table 3. Phase-Only Cross-Correlation Maximaa

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Table 4. K-NN Classification Mean Accuracy, k=1

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Table 5. Pharmaceutical Tablets and Coating Components

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Table 6. Camera Specifications

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Table 7. Twelve Classes Considered

Equations (43)

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E(x,y,z)=FT1[FT[E(x,y,0)]H(u,v,z)],H(u,v,z)=exp(i2πλz1λ2u2λ2v2).
α=λu,β=λv,γ=1α2β2=1λ2u2λ2v2.
E(x,y,z)=FT1[FT[E(x,y,0)]exp(2πλz1λ2u2λ2v2)].
E(x,y,z)=exp(ikz)FT1[FT[E(x,y,0)]exp(iπλz(u2+v2))].
p(I)=(n0I)n0In01exp(In0/I)Γ(n0),
p(I)=(n0I)n0In01exp(In0/I)Γ(n0).
x,y[log(IC(x,y,z))log(IQ(x,y,z))]>0.
Nln[1Γ(n0C)(n0CIC)n0e]+(n0C1)x,ylnIC(x,y,z)n0CICx,yIC(x,y,z)Nln[1Γ(n0Q)(n0QIQ)n0]+(n0Q1)x,ylnIQ(x,y,z)n0QIQx,yIQ(x,y,z)>0.
E(x,y,4f)=FTλf[M2FTλf[QM1]],
Q=|FTλf[M2*FTλf[E]]|,
S0=Ex*Ex+Ey*Ey,S1=Ex*ExEy*Ey,S2=Ex*Ey+Ey*Ex,S3=i[Ey*ExEx*Ey],
Ei*Ej=1TTEi*Ejdt.
S=S0(1,cos2ψcos2ε,sin2ψcos2ε,sin2ε),
P=1S0S12+S22+S32,
S=S0(1,Pcos2ψcos2ε,Psin2ψcos2ε,Psin2ε).
M0°=12(1100110000000000)M±45°=12(10±100000±10100000),M90°=12(1100110000000000)MQWP=(1000010000010010).
R(θ)=(10000cosθsinθ00sinθcosθ00001)and
Mθ=R(θ)M0°R(θ).
S0=I0°,0+I90°,0,S1=I0°,0I90°,0,S2=I45°,0I45°,0,S3=I45°,π/2I45°,π/2.
S0=M0°·S+M90°·S=(S0,S1,0,0),S1=M0°·SM90°·S=(S1,S0,0,0),S2=M45°·SM45°·S=(S2,0,S0,0),S3=M45°·MQWP·SM45°·MQWP·S=(S3,0,S0,0).
MI=(1N00N10000CS00SC),
N=cos(2Ψ),C=sin(2Ψ)cosΔ,S=sin(2Ψ)sinΔ.
ρ=rpprss=tanΨexp(iΔ).
L=(0l01l02l03l010l12l13l02l120l23l03l13l230).
ρ=1KT[cosT2+(l01il23)sinT2],ρps=1KT[l12+l02i(l03+l13)sinT2],ρsp=1KT[l12l02i(l03l13)sinT2],
K=1T[cosT2(l01il23)sinT2]andT=(l23+il01)2+(l13+il02)2+(l12il03)2.
MPEM=(1000010000cosδ(t)sinδ(t)00sinδ(t)cosδ(t)).
SS=MSR(θ2)MPEM1R(θ1)R(θ0)MPEM0R(θ0)R(θP1)MP1R(θP1)(1000),
SD=R(θP2)MP2R(θP2)R(θ3)MPEM1R(θ3)R(θ2)MPEM1R(θ2)SS,
SD=M1MRC1MSMRC0M0SS,
MRC=(10000cos22θ+cosδsin22θcos2θsin2θ(1cosδ)sin2θsinδ0cos2θsin2θ(1cosδ)sin22θ+cosδcos22θcos2θsinδ0sin2θsinδcos2θsinδcosδ).
x=1Ni=1Nxi,σ2=1N1i=1N(xix)2,s^(x)=N(N1)N21Ni=1N(xix)3(1Ni=1N(xix)2)3,k^(x)=3+N1(N2)(N3)((N+1)1Ni=1N(xix)4(1Ni=1N(xix)2)23(N1)),
H(x)=i=1Npilog2pi.
X=(x11x12x13x1mx21x22x23x2mx31x32x33x3mxn1xn2xn3xnm)y=(y1y2y3yn).
Sy=1M1YYT.
Sy=1M1YYT=1M1(PX)(PX)T=1M1PXXTPT=1M1PAPT,
SY=1M1PAPT=1M1PPTDPPT=1M1D.
yi(w·xi+b)1  fori=1,,n.
minimize|w|2withconditions  yi(w·xi+b)1  fori=1,,n.
min[|w|2+Ciξi]withconditionsyi(w·xi+b)1ξi  andξi0  fori=1,,n,
min[|w|2+Ciξi]withconditionsyi(w·ϕ(xi)+b)1ξi  andξi0  fori=1,,n.
K(xi,xj)=ϕ(xi)·ϕ(xj)=Cexp(γ|xixj|2)  withγ>0.
ρCrρTa2O5=|FT1[FT[ρCr]|FT[ρCr]|FT[ρTa2O5]*]|,

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