2.1.

Working Principle

Figure 1(a) illustrates the plasmonic PUF array integrated onto a quartz substrate. By partitioning the substrate into an $M\times N$ array, the boundaries of each PUF label can be clearly defined. Compared with other noble metals, gold possesses excellent chemical stability and oxidation resistance, ensuring the reliability of the PUFs over the long term. As shown in Fig. 1(b), considering both the field of view of the experimental platform and the need for efficient PUF integration, the dimensions of each PUF label were set at $\sim 0.3\mathrm{mm}\times 0.25\mathrm{mm}$. This allows for the mass integration of hundreds of units onto a single chip. In contrast to conventional lithography-based approaches and bottom-up syntheses, the adopted template-assisted deposition offers an efficient route to the mass production of large-scale plasmonic nanostructures integrated on a chip (see Appendix: Experimental Section). Here, one key control knob is the deposition angle $\alpha$ determining the gradience in the structures and the optical responses. Compared with the deposition at a normal incidence angle, shadow deposition results in an overall decrease in the sizes of nanoparticles and clusters and hence alters the morphology-dependent localized surface plasmon resonance (LSPR).

Fig. 1

Plasmonic PUF arrays empowered by a multi-dimensional expanding strategy. (a) Schematic of a plasmonic PUF system featuring gold nanostructures partitioned into 2D pixelized zones as an $M$-by-$N$ array of PUF labels. The PUF labels with different $N$ reveal a varying deposition angle $\alpha$ between 8 and 16 deg, corresponding to a significant variation in responses of transmission images and PUF responses. (b) Schematic of a zoomed-in view of one PUF label. (c) Schematics with the top view (top) and cross-sectional view (bottom) showing clusters and closely packed nanoparticles. (d) Schematic presenting a raw transmitted image (top) and an extracted PUF key with $30\times 30$ elements (bottom). (e) Schematic of two schemes to expand the CRP space, namely, wavelength-based expansion of one PUF label with channels $1-i$ (left) and polarization-based expansion of one PUF label with channels $1-j$ (right).

The randomness and local defects in the nanoporous membrane template, which were often considered detrimental in applications, such as surface-enhanced Raman scattering (SERS)⁴² and plasmon-enhanced fluorescence (PEF),⁴³ are advantages to generating unclonable anticounterfeiting labels.³⁶ Via deposition, the size, shape, and distributions of deposited gold nanoparticles vary significantly between each PUF label. The deposited metal structures can be mainly divided into two types [see Fig. 1(c)]: the small (sub-100 nm) particles defined by the pore size of the template and the big clusters with a size of several hundred nanometers to several micrometers due to the local defects in the template.

Owing to the LSPRs of gold nanostructures in the visible wavelength range and the resulting strong absorption and scattering, the spatial inhomogeneity in the densely packed plasmonic pattern can be easily extracted simply by transmission imaging,⁴⁴ which differs from the common readout scheme using dark-field microscopy in previously reported plasmonic PUFs.^11,12 Here, transmission images can be captured by an objective lens and recorded using a top-view image sensor (see Appendix: Experimental Section). Figure 1(d) schematically visualizes the image from a PUF label, in which the dark spots represent the effect of randomly distributed clusters, and the background signal is determined by the density and size condition of nanoparticles.

Notably, both the spatial and spectral responses are highly sensitive to the morphological disorders of each PUF label. As a result, it is, in principle, impractical to duplicate them with identical ones accurately. The images can be binarized and processed using a perceptual hash (pHash) algorithm (see Appendix: Experimental Section) and consequently form a PUF key. The output sequence generated by the pHash algorithm is generally robust against noise-related variations in the raw images. As a result, a transmission image captured at an arbitrary probe wavelength ${\lambda }_p$ and a specific polarization state can form a PUF key, serving as a unique fingerprint for each PUF label. In addition, the PUF key becomes scalable by adjusting the frequency range used in the encoding process. In this study, the wavelength and polarization as two inherent properties of the excitation light can be employed for the reconstruction of PUF keys [see Fig. 1(e)], which can be essential in expanding the space of CRPs and also building databases with higher security.

2.2.

Characterizations of Plasmonic PUFs

Figure 2(a) shows the fabricated plasmonic chip incorporating an 18-by-18 array of PUF labels (see Appendix: Experimental Section and Fig. S1 in the Supplementary Material). For PUF labels aligned along with the transverse axis ($x$ axis, i.e., with the same $N$ but different $M$), the value of the deposition angle $\alpha$ is almost identical. Hence, the uniqueness of PUFs can be quantified among $M$ devices under the same fabrication configuration. Figures 2(b) and 2(c) reveal the clusters as random defects embedded in the densely packed nanoparticles that were transferred from the defect in the template induced during the template preparation.^45–47 For PUF labels aligned along with the longitudinal axis ($y$ axis), the dimensions of clusters and nanoparticles differ significantly due to varying $\alpha$ between 8 and 16 deg [see Fig. 2(c)]. Figure S2 in the Supplementary Material provides the histograms of nanoparticle size with $\alpha =8$ and 16 deg. Such a difference can also be discerned using dark-field microscopy (see Fig. S3 in the Supplementary Material), in which the relatively large particle size upon $\alpha =8\mathrm{deg}$ is ascertained by stronger scattering signals than those upon a larger $\alpha$.

Fig. 2

Characterizations of the heterogeneous plasmonic nanostructures. (a) Picture of the PUF chip. (b) Scanning electron microscopy (SEM) image showing fine nanostructures in a PUF label on a silicon substrate. (c) Zoomed-in-view of SEM image of panel (b) showing a cluster and its vicinity. (d) Schematic of the home-built hyperspectral imaging setup. BBS, broadband source; LP, linear polarizer; HWP, half-wave plate; RM, reflection mirror; OB, objective lens; BS, beam splitter; LED, light-emitting diode. (e) Extinction spectra for PUF labels with $\alpha =8\mathrm{deg}$ (top) and 16 deg (bottom). The resonance wavelengths ${\lambda }_{\mathrm{res}}$ are denoted at the resonance peaks. SEM images of PUF labels fabricated with $\alpha =8\mathrm{deg}$ (f) and 16 deg (g) show the distinct sizes of nanoparticles.

Due to the ultrahigh density of close-packed nanoparticles ($\sim 1.5\times {10}^{10}{\mathrm{cm}}^{-2}$), the PUF response can be read out by easy transmission imaging. The spectral responses have been characterized using a home-built hyperspectral imaging setup [Fig. 2(d)]. As revealed in the measured extinction spectra in Fig. 2(e), the change $\alpha$ results in modification of the particle sizes and subsequently alters the LSPR effect (see Figs. S4–S6 in the Supplementary Material). For a small $\alpha$, an intensified LSPR with increased optical absorption and scattering strength is obtained, which is attributed to the overall large size of the packed nanoparticles and narrow interparticle spacing [see Fig. 2(f)]. In contrast, these effects are weakened upon a large $\alpha$ [see Fig. 2(g) and Fig. S7 in the Supplementary Material for details]. Besides, the blueshift of resonance wavelength ${\lambda }_{\mathrm{res}}$ from $\sim 592$ to $\sim 577\mathrm{nm}$ in Fig. 2(e) also verifies the strong dependence between ${\lambda }_{\mathrm{res}}$ and the particle size, according to the LSPR theory.^48,49

Figure 3(a) presents the raw transmission image captured by a CMOS camera at ${\lambda }_p$ of 580 nm. One can identify local spots as well as winkle-like patterns in a nonuniform background, which are attributed to the heterogeneity of the nanostructures (see Fig. S6 in Supplementary Material for results of a PUF label with $\alpha =16\mathrm{deg}$). The image was processed using the pHash algorithm (see Appendix: Experimental Section) to extract the inherent randomness, forming a $1000\times 800$ matrix. One key merit here is that the encoding capacity is not dominated by the size of the raw image but becomes scalable by choosing the proper frequency range. The theoretical encoding capacity of a single PUF key becomes $L^s$, where $L$ represents the bit states and $s$ represents the size of bit sequences in the frequency domain. For proof-of-concept demonstrations, we first employ binary matrices of $30\text{pixel}\times 30\text{pixel}$ for authentication, representing the key feature at the lower-frequency range [see Fig. 3(b)].

Fig. 3

Scalable PUF keys and verifications of their key performances. (a) Captured 2D image of a PUF label with $\alpha =8\mathrm{deg}$. (b) A 2D code generated via the pHash algorithm. Inset: the adopted $30\times 30$ PUF key with features in the lower-frequency range. (c) Bit uniformity in 15 keys generated from labels with the same $N$. (d) Summary of statistical NIST tests using binary sequences generated from 15 PUF keys. (e) Pairwise match of 15 PUF keys with the same $N$ and different $M$ to examine uniqueness. The color bar shows the extracted HD. (f) Distributions of interdevice and intradevice HDs for PUF labels prepared with $\alpha =8\mathrm{deg}$. (g) The extracted relationship between the encoding capacity and the adopted size of the PUF key. Inset: a $150\times 150$ PUF key. (h) Summary of $\mu$ and $\sigma$ of interdevice HD as a function of $\alpha$. (i) Distributions of interdevice and intradevice HDs for PUF labels prepared with $\alpha =0\mathrm{deg}$.

Here, we evaluate the statistical properties of 15 PUFs ($M=1$ to 15, $N=1$) integrated on the same chip. The bit uniformity (i.e., the number of 0 or 1 bits in a binary sequence) metric is calculated using the following equation:^1,50

In practice, PUF labels need to be authenticated repeatedly, requiring good reproducibility between readouts of the same label and distinctiveness among different labels. Herein, we adopt normalized Hamming distance (HD) to quantify both the uniqueness (via interdevice HD) and the reproducibility (via intradevice HD). In an ideal PUF system, the interdevice HD of 0.5 means perfect uniqueness, and the intradevice HD of 0 means perfect reproducibility. Figure 3(e) presents the 2D correlation of 15 PUF labels ($M=1$ to 15, see Fig. S8 in the Supplementary Material for details). Via a Gaussian fit $P(x)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{(x-\mu {)}^2}{2{\sigma }^2}}$ of the probability density histogram of the interdevice HD [Fig. 3(f)], a mean value $\mu$ of 0.494 and a variance $\alpha$ of 0.017 are obtained, indicating the stochastic genesis of our PUF labels. The intradevice HD is examined based on 15 repeated challenge–response cycles for the same PUF (see Fig. S9 in the Supplementary Material). A Gaussian fit of the histogram returns $\mu =0.0051$ and $\sigma =0.0017$ [Fig. 3(f)]. As presented in Fig. 3(f), the threshold for discrimination is set as $\sim 0.03$. For practical applications, the stabilities of the anticounterfeiting keys are essential. We have therefore characterized the robustness of the PUF chip against environmental fluctuations. Through a test under the relative humidity change over 40% to 70% and a long-term test over 1 week, the PUF keys suggest a fluctuation of intradevice HD of less than 0.03 (see Fig. S10 in the Supplementary Material), indicating the resilience of these plasmonic PUFs in real-world scenarios.

The distribution of interdevice HDs can be modeled with an equivalent binomial distribution $B(N,p)$ and hence can be fitted by a Gaussian function in the limit of “degree of freedom,” i.e., the number of independent bits $N_c$. The number of mutually independent bits (i.e., degrees of freedom) is defined as $N_c=\frac{\mu (1-\mu )}{{\sigma }^2}$. For PUF labels with $\alpha =8\mathrm{deg}$, an extracted $N_c$ of $\sim 875.12$ results in an encoding capacity of $2^{N_{\mathrm{c}}}=2^{875}$. Notably, such a capacity can be readily scalable by expanding the frequency range (see Fig. S11 in the Supplementary Material). As presented in Fig. 3(g), the encoding capacity increases up to $2^{43401}$ by adopting a $210\times 210\text{-}\text{bit}$ PUF key with $\alpha =8\mathrm{deg}$. In addition, one should also note that there is a trade-off between the PUF key size and the reproducibility (see Fig. S11 in the Supplementary Material).

Together with the morphology of the template, the deposition angle $\alpha$ is a key parameter shaping the heterogeneity of the plasmonic nanostructures and can be regarded as a control knob for optimizing the PUF response and the security level. Figure 3(h) summarizes the extracted values of $\mu$ and $\sigma$ of the interdevice HD for PUF labels with different $\alpha$. In addition, as $\alpha$ gets adjusted, the clear evolution of the interdevice HD can be discerned. Upon an increased $\alpha$, the degraded uniqueness featuring an increased $\sigma$ is attributed to the potentially reduced probability of cluster formation and suppressed heterogeneity. Consequently, the estimated $N_c$ is degraded from $\sim 875$ to $\sim 720$ upon an increased $\alpha$ (see Fig. S12 in the Supplementary Material). Here, control experiments on an additional PUF chip deposited at a normal angle ($\alpha =0\mathrm{deg}$) were carried out. PUFs made by shadow deposition, in general, result in elevated uniqueness compared with those made at $\alpha =0\mathrm{deg}$ [$\mu =0.4860$, $\sigma =0.0200$; see Fig. 3(i)]. Meanwhile, as revealed in Fig. 3(g), the extracted encoding capacity at $\alpha =0\mathrm{deg}$ (e.g., $2^{N_{\mathrm{c}}}=2^{638}$ at $m=15$) is scalable, yet in general, degraded compared with those at $\alpha =8\mathrm{deg}$.

2.3.

Multidimensional Expanding Strategy

Given the wavelength and polarization-sensitive response of the heterogeneous plasmonic nanostructures, these two inherent properties of light can be exploited to generate unpredictable and distinct responses. Such a multidimensional expanding strategy meets the quest for expanded space of CRPs and circumvents the precision spatial or spectral encoding processes. As presented in Fig. 4(a), three representative responses of one single PUF label upon different ${\lambda }_p$ were studied, namely, one away from resonance (500 nm), one around the resonance (540 nm), and one aligned at the LSPR peak wavelength (580 nm). A hash function compresses an arbitrary-length input to a fixed-length output, featuring an avalanche behavior wherein at least half of the bits are flipped by a minor change in the input. Therefore, the fine changes in patterns result in distinct cryptographic keys. Considering the tolerance of PUF authentication for sufficient robustness, the channel spacing between each challenge was set as 40 nm. Hence, the single PUF would yield at least seven CRPs leveraging the flexibility of the probe wavelength in the visible range. In Fig. 4(b), the interkey HDs spanning 0.31 to 0.45 are sufficiently separated from the intrakey HD ($\mu$ of 0.015), indicating a nice uniqueness of each.

Given the anisotropic nature of the on-chip nanostructures, polarization emerges as another degree of freedom. Figure 4(c) presents three representative responses of the same PUF label upon excitation of linearly polarized light with a switched polarization angle $\theta$. Similar to the process in the wavelength-expanding strategy, here, the channel spacing between each challenge was set as 30 deg, leading to six CRPs from one single PUF. Figure 4(d) examines the uniqueness by characterizing the interkey HDs between 0.40 and 0.52; the distribution histogram of the HDs also shows a clear separation between the intrakey and interkey HDs. As the overall expanding space is dependent on the number of CRPs, here, these two alternative channels provide a significant expansion of PUF capacity.

Fig. 4

Wavelength and polarization-enabled expanding strategies. (a) Top: captured raw image (left) and contrast images (middle and right) for three different ${\lambda }_p$. Bottom: their corresponding PUF keys. (b) Distributions of interkey and intrakey HDs using the wavelength-expanded strategy. The threshold was set to 0.05 when the PUF key size $m$ is $150\times 150$. Inset: pairwise match of seven PUF keys upon different ${\lambda }_p$. (c) Top: contrast images for three different $\theta$. ${\lambda }_p$ is fixed at 580 nm. Bottom: their corresponding PUF keys. (d) Distributions of interkey and intrakey HDs using the polarization-expanded strategy. Inset: pairwise match of seven PUF keys upon different $\theta$. One should note that the last one ($\theta =180\mathrm{deg}$) is a control test (essentially the same as $\theta =0\mathrm{deg}$) examining repeatability.

2.4.

Practical Authentication of PUF Labels

In practical authentication, to avoid replay-based attacks, each CRP can be only used once. Therefore, authentication processes for multiple purposes require a sufficiently large CRP space.²³ Here, 12 PUF keys generated via the multidimensional expanding strategy were applied as “identifiers” to a single binary image challenge pattern using a simple exclusive-OR (XOR) operation. The identifiers and the single challenge are binary images of size $150\text{pixel}\times 150\text{pixel}$, as shown in Fig. 5(a) (see Fig. S13 in the Supplementary Material for sources). As depicted in Fig. 5(b), the different responses exhibit high discernibility. The averaged HD of $\sim 0.41\pm 0.11$ is sufficiently far away from the preset threshold of 0.05 [see Fig. 5(c)]. Therefore, these nanoidentifiers offer sufficiently distinguishable responses in a single challenge–different PUFs and, hence, suggest a pathway to secure and reliable authentication.

Fig. 5

Practical authentication of PUF labels using the multidimensional expanding strategy. (a) Schematic showing a series of CRPs generated with the same challenge of the logo of Harbin Institute of Technology ($150\text{pixel}\times 150\text{pixel}$) using XOR operation. Each corresponding pixel is compared, resulting in a value of 0 if they are the same and 1 if they are different. (b) Pairwise match of responses from a single challenge–different PUF operation. Items 1 to 6 adopt keys obtained at varied ${\lambda }_p$ and fixed $\theta =0\mathrm{deg}$, whereas items 7 to 12 adopt keys obtained at varied $\theta$ and fixed ${\lambda }_p=580\mathrm{nm}$. (c) Histogram of HDs for 66 CRPs. (d) Conceptual schematic of the multipurpose authentication flow of products using the plasmonic PUF chip with a multidimensional expanding strategy.

Figure 5(d) illustrates the multipurpose authentication flow of products using our proposed plasmonic PUF chips. The PUF chips can be mass-produced on low-cost flexible substrates with good transparency⁴² and seamlessly integrated with the packaging of cosmetics, pharmaceuticals, and other products by the manufacturers. Consequently, they can be distributed across commodity circulation networks, potentially undergoing multiple rounds of authentication, thanks to the working principle obviating the need for spectrally resolved measurements and complex spatial encoding strategies. The multidimensional expansion can be performed by users at different phases (e.g., shipping, retail, or end-use) using compact filters and polarizers. Although the key database in the cloud can be built up by the manufacturers, users can access specific channels to read out a label and upload the key to the database for decoding and authentication.

4.1.

Fabrication of Chip-Scale Plasmonic PUFs

Laser direct writing was used to define pixelized zones on a single quartz substrate with a total area of $\sim 10\mathrm{mm}\times 10\mathrm{mm}$. Each individual PUF was designed with dimensions of $0.3\mathrm{mm}\times 0.3\mathrm{mm}$ and spaced $\sim 200\mu \mathrm{m}$ apart. Nanomembranes of porous AAO were employed as a template for deposition⁵³ (see Section S1 in the Supplementary Material). The film thickness and averaged pore size of the AAO membranes were $\sim 270$ and $\sim 80\mathrm{nm}$, respectively. To engineer the heterogeneity of deposited gold nanoparticles, angle-resolved shadow evaporation was employed. The deposition angle $\alpha$ ranging from 8 to 16 deg was obtained by adjusting the lateral offset between the center aligned with the source and the AAO-integrated substrate. Upon a large deposition angle, some atoms are blocked by the pore walls of the nanomembrane template, resulting in a reduced amount of the atoms being deposited onto the substrate, and hence an overall gradience of particle size. As a reference study, PUF samples were also fabricated with $\alpha =0\mathrm{deg}$. The electron-beam (Beijing Technol Science Co., Ltd., Beijing, China) deposition rate is $0.5\mathrm{nm}{\mathrm{s}}^{-1}$ at ${10}^{-4}\mathrm{Pa}$. The estimated thickness at normal deposition is $\sim 60\mathrm{nm}$. SEM inspections (FEI Inspect F50) were performed on samples fabricated on silicon substrates with the same configuration.

4.2.

Optical Characterizations

For capturing transmitted images and generation of PUF keys, optical characterizations were performed using a home-built hyperspectral microscopy setup. The wavelength of probe light was swept from 400 to 700 nm (step of 1 nm) using a monochromator (PLGL-021, PL OPTICS) coupled to a broadband source (OSL2, Thorlabs, Newton, New Jersey, United States). For polarization-dependent studies, a linear polarizer (LPVISC, Thorlabs) and a half-wave plate (AHWP10M-980, Thorlabs) were mounted onto motorized rotation stages (PRM1/MZ8, Thorlabs) to adjust the polarization state of the incident light. The ellipticity of the excitation beam was examined using a polarimeter (PAX1000, Thorlabs). The collimated linearly polarized light beam was focused onto the sample using an objective lens (PLCN20X, 20×, NA: 0.28, WD: 10.6 mm, Olympus, Tokyo, Japan). The excitation power is $\sim 0.12\mathrm{mW}$. The transmitted image response was recorded by a long-working-distance objective lens (MPLAN APO 378-803-3, 20×, NA: 0.25, WD: 34 mm, Mitutoyo, Kawasaki, Japan) and a monochrome CMOS Camera (MQ013MG-ON, XIMEA, $1280\text{pixel}\times 1024\text{pixel}$, frame rate: 2.8 frame/s). The exposure time for capturing all images was set to 15 ms. The extinction spectra were extracted based on the stack of hyperspectral images using MATLAB.

4.3.

Algorithms for Data Processing

To avoid potential defects near the edge areas, the captured images were first cropped into a size of $1000\text{pixel}\times 800\text{pixel}$. To mitigate the effect of image jitter, a locating algorithm was implemented.⁵⁴ For each PUF label, the central region of the first image (with a size of $100\text{pixel}\times 100\text{pixel}$) is used as a reference. The optimal cross-correlation value between the processed image and the reference was evaluated. Judging from the value, the region of interest was adjusted to correct any potential spatial offsets. Such a correction ensures precise alignment between the series of images and the reference image for fair evaluations.

The extraction of PUF labels was performed through perceptual hash based on the type II discrete cosine transform.⁵⁵ The information in the frequency domain was extracted using the dct2 function in MATLAB, and the frequency domain matrix of $1000\times 800$ was generated. Select a fixed value $m$, the dominant low-frequency coefficients from 1 to $m^2$ ($m=30$ to 200) were included in each PUF label. The high-frequency components correlating with minor details hardly reflect the key variation of the images and therefore can be neglected. By setting a threshold of 0, the $m\times m$ low-frequency coefficients get transformed into a binary matrix (i.e., a PUF key). Therefore, the PUF key becomes scalable by adopting different values of $m$.

Intradevice HDs were evaluated according to the following definition:

Interdevice HDs were evaluated according to the following definition:

4.4.

NIST tests

For evaluations of randomness in the generated cryptographic key, the NIST SP 800-22 (National Institute of Standards and Technology Special Publication 800-22) statistical test suite was adopted. A set of images was obtained from 15 PUFs on a chip and processed to form a cryptographic key sequence with a length of 13,500 bits ($15\text{bits}\times 30\text{bits}\times 30\text{bits}$). The first 12,800 bits were selected and divided into 100 groups of 128 bits each. The $P$-values were calculated for seven tests (frequency, block frequency, cumulative sums, runs, longest run, approximate entropy, and serial). Certain tests, such as binary matrix rank, discrete Fourier transform, and nonoverlapping template matching, were omitted due to their requirement of a minimum bit length of ${10}^6$ for a single test and ${10}^8$ for the complete set of 100 trials.³⁵ The number of bits ($l$) in the stream being tested was set to 128, and the number of bits in a substring (block) size was set to 16. For each round of the test, the significance level ($\epsilon$) was 0.01, and a pass was granted if the $P$-value was greater than $\epsilon$. The range of acceptable proportions was determined using the confidence interval defined as $\omega \pm 3\sqrt{\frac{\omega (1-\omega )}{l}}$, where $\omega =1-\epsilon$, and $l$ is the sample size.²¹ The calculated threshold to pass is 0.9602.