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 α 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 30×30 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).

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 α=8deg (top) and 16 deg (bottom). The resonance wavelengths λres are denoted at the resonance peaks. SEM images of PUF labels fabricated with α=8deg (f) and 16 deg (g) show the distinct sizes of nanoparticles.

Fig. 3. Scalable PUF keys and verifications of their key performances. (a) Captured 2D image of a PUF label with α=8deg. (b) A 2D code generated via the pHash algorithm. Inset: the adopted 30×30 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 α=8deg. (g) The extracted relationship between the encoding capacity and the adopted size of the PUF key. Inset: a 150×150 PUF key. (h) Summary of μ and σ of interdevice HD as a function of α. (i) Distributions of interdevice and intradevice HDs for PUF labels prepared with α=0deg.

Fig. 4. Wavelength and polarization-enabled expanding strategies. (a) Top: captured raw image (left) and contrast images (middle and right) for three different λp. 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 150×150. Inset: pairwise match of seven PUF keys upon different λp. (c) Top: contrast images for three different θ. λp 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 θ. One should note that the last one (θ=180deg) is a control test (essentially the same as θ=0deg) examining repeatability.

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 (150pixel×150pixel) 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 λp and fixed θ=0deg, whereas items 7 to 12 adopt keys obtained at varied θ and fixed λp=580nm. (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.