Random fractal-enabled physical unclonable functions with dynamic AI authentication

Anti-fake labels face increasing security challenges, with counterfeiting causing large economic losses and safety risks. Many current labels are vulnerable because they are fabricated deterministically. Physical unclonable functions (PUFs) are attractive identifiers because their intrinsic randomness yields high complexity and encoding capacity, making duplication nearly impossible. Prior PUFs include: (i) graphical PUFs from random micro/nanostructures (wrinkling/buckling/folding, evaporative patterns, random particles); (ii) spectral PUFs requiring analytical readout (random luminescence, SERS patterns, speckle patterns, chaotic photonic devices); and (iii) electronic PUFs leveraging disorder in devices (graphene/CNT FETs, memristors). Graphical tags are convenient due to simple optical imaging and can tune complexity via area and feature size. However, flexible material-based tags can suffer from low robustness under heat, humidity, water, or oxygen. Thus, ideal graphical PUF carriers combining high environmental stability and flexibility are needed. Random fractal structures exhibit intrinsic randomness and self-similarity; fractal-guided percolation networks are known in thin films. Thermal annealing of Au films drives evolution from rupture to ramified percolation networks below the percolation threshold, which are inherently unpredictable and durable due to Au’s stability, making them promising PUF carriers. Higher-security labels can benefit from multiple responses; combining chemistry (e.g., stimuli-responsive molecules) with PUFs adds orthogonal information. Plasmonic nanostructures provide stable localized surface plasmon resonance (LSPR) for electromagnetic enhancement and chemical signal amplification, but nanoparticle-based approaches face challenges (unpredictable hotspots, aggregation, stability, and nonuniform distribution). A homogeneous, inherent plasmonic platform independent of synthesized nanoparticles is desirable. Efficient, reliable authentication is essential. Traditional image processing can be slow and sensitive to orientation/quality. Deep learning (DL) can validate keys with high efficiency and tolerance but training with large databases is time-consuming, motivating improved back-end strategies. In this study, we develop an anti-counterfeiting system based on random fractal Au-network PUFs and AI authentication. Multiple tags are integrated via one-step annealing; network complexity is configurable by film thickness. An effective encoding capacity of about 10^34 is achieved. The Au network surface is nanoscale-roughened to enable SERS-based chemical encoding, providing multi-level security. A smartphone-readable, fast (6.36 s) and reliable (0% false positives) DL-based authentication system with a dynamic database update strategy is proposed, supporting mass production and environmental stability.

The paper surveys three main classes of PUFs: (i) graphical PUFs formed by random micro/nanostructures such as wrinkles, folds, evaporative patterns, and randomly arranged particles; (ii) spectral PUFs requiring instrumentation, including stimulated luminescence, SERS, speckle patterns from disordered textures, and chaotic photonic devices; and (iii) electronic PUFs leveraging material/device disorder in graphene/CNT FETs and memristors. Graphical tags are easily imaged and tunable in complexity but often lack robustness when made from flexible polymers, which age or degrade under temperature, humidity, water, or oxygen. Spectral tags and plasmonic nanoparticle-based systems can increase security via orthogonal chemical signatures, but suffer from unpredictable hotspot locations, aggregation, indirect bonding, instability, and nonuniform surface coverage, complicating authentication. Prior AI-based authentication enhances robustness and speed over traditional image processing but requires substantial training time for large databases. The authors position fractal-guided thin-film evolution (e.g., percolation/dewetting of metals) as a universal route to unique, durable PUFs, and propose a dynamic DL database strategy to mitigate retraining time.

Fabrication of Au network PUFs: A Si/SiO2 (300 nm oxide) wafer was diced (1.5 cm × 1.5 cm), cleaned (acetone, ethanol, DI water), spin-coated with photoresist (Ar-3110, 3000 rpm, 1 min), and baked (90 °C, 1 min). Circular areas (120 µm diameter) were exposed by laser direct writing (405 nm, 83 mW peak, 2000 ns pulse, 100 Hz raster), developed 100 s, followed by Au deposition by DC magnetron sputtering (50 W, Ar 23 sccm). Film thicknesses: 30, 50, 70, 90 nm achieved by 540, 900, 1440, 1800 s deposition, respectively. Lift-off in acetone yielded Au circles. Annealing in air (muffle furnace) induced depercolation and network formation: 30 nm film annealed 30 min at 500 °C; 50 nm at 700 °C for 90 min; 70 nm at 800 °C for 90 min; 90 nm at 900 °C for 90 min. Networks formed via thermally driven rupture and edge retraction below the percolation threshold, producing ramified, fractal-like meshes. Optionally, a protective PMMA layer was spin-coated (5500 rpm, 40 s). Shapes beyond circles (e.g., squares, triangles, pentagons, stars) were defined using laser lithography; macroscopic patterns (letters, QR code) were fabricated by mask-assisted UV lithography (hard contact, 48 s exposure), Au deposition (70 nm), and annealing (800 °C, 90 min). Configurable encoding and modeling: The network wavelength and amplitude were tuned via film thickness, guided by a critical wavelength model λc = √(ho/(4π^3σ/A)), where ho is film thickness, σ surface tension (temperature-dependent), and A Hamaker constant. Thicker films yielded sparser networks (larger wavelength). Fractal dimensions were quantified by box-counting (ImageJ/FracLac), showing higher D for thinner films. Plasmonic roughening and chemical encoding: To activate nanoscale LSPR hotspots, the annealed Au network surface was roughened via oxygen plasma cleaning (HM-Plasma5L, 70 W, 210 s), generating dense nanoscale convexities (~1.5 nm height fluctuation by AFM). Rhodamine 6G (R6G) in ethanol (1 mM, 10 µL) was drop-cast, dried, then rinsed for SERS tests. Electromagnetic field distributions were simulated using Lumerical FDTD (120 × 120 × 60 nm domain, 0.5 nm mesh, 514 nm p-polarized plane wave). Environmental stability tests: Optical microscopy benchmarked tags before/after exposure to harsh conditions: low temperature (−40 °C, 60 h); high temperature (600–775 °C, 10 h at each step; stable up to 750 °C); aqueous corrosion/sonication (PMMA-coated, DI water, 40 kHz, 10 min); mechanical abrasion (PMMA-coated, rubbed on frosted desktop ×10); dust/stain exposure (sand and organic contamination; cleaned with alcohol-dipped cloth). Chemical encoding photostability was assessed by repeating Raman measurements after six months under ambient exposure. Characterization: Bright/dark-field optical microscopy (Olympus BX53M, 50×) for morphology; 3D confocal microscopy (Olympus LEXT-OLS4000, 50×) for topography; step profiler (DEKTAK 6 M) for thickness and height verification; XRD (D8 ADVANCE) for crystallinity; AFM (Bruker Dimension Icon) for nanoscale roughness; HRSEM (Hitachi S-8200) for surface morphology; Raman spectroscopy/mapping (Renishaw inVia plus, 514 nm, 1.4 mW, 50×, 10 s, 1 accumulation). Smartphone readout used a Huawei nova 6 with a portable mini-microscope. Deep learning-based authentication: Images were preprocessed (PUF center localization via Otsu’s method; grayscale stretch via custom algorithm; resizing; added random Gaussian noise). Data augmentation used rotations (training: 0–330° in 30° steps, 12 images per pattern; validation: 1–359° in 2° steps, 180 images per pattern). Base dataset: 1100 PUFs, total 211,200 images (13,200 training; 198,000 validation). A ResNet50 classifier (PyTorch), initialized with ImageNet-pretrained weights, was trained for 2500 epochs (51.4 s/epoch; ~35 h total), selecting the best validation accuracy model (99.63% at epoch 2250). For database expansion, a dynamic strategy updated only the final classification layer when adding new PUF classes; both original and new classes were included during updates, stopping when validation accuracy ≥0.95. Training speed for expansion was ~0.137 s/epoch (e.g., 40 epochs in 5.48 s when the fifth new PUF was added). Authentication pipeline: smartphone-captured image uploaded; DL model retrieves top candidates; FSIM computes similarity against candidates; if top similarity ≥ threshold (0.5), authenticated and traced; otherwise, user is prompted to recapture with better quality. Testing used 26,000 images from 1300 in-database PUFs under varied conditions and 11,000 images from 550 out-of-database PUFs.

• Random, fractal-guided Au network PUFs were fabricated via lithography, sputtering, and thermal annealing, producing unique, unclonable network morphologies with controllable complexity by film thickness.
• Configurability: Network wavelength and amplitude increased with film thickness; fractal dimension D increased as thickness decreased (from ~1.52 at 90 nm to ~1.75 at 30 nm). Shape and size of tags are freely designable via lithography.
• Uniqueness: Cross-correlation (FSIM) among 600 patterns (two scans each) showed a strong diagonal in the heat map and clearly separated intra- vs inter-correlation distributions, confirming uniqueness across and within batches.
• Encoding capacity: With practical grayscale levels (~140 usable levels) and a 750 × 750 px image, effective encoding capacity was estimated at ~10^34, exceeding basic benchmarks (~10^20). Capacity scales with pattern area and feature density; can be tuned by coverage area and filling ratio.
• Plasmonic platform and SERS encoding: Post-roughening produced nanoscale convexities (~1.5 nm height fluctuation by AFM) that supported enhanced electromagnetic hotspots (FDTD simulations). SERS of R6G was significantly enhanced on roughened networks versus substrate/pristine networks; Raman mapping demonstrated spatially robust, orthogonal chemical readout.
• Environmental stability: Tags remained unchanged after −40 °C for 60 h and stable up to 750 °C for 10 h (changes at 775 °C). PMMA-coated tags withstood sonication in water (10 min, 40 kHz), mechanical rubbing (×10), and contamination (dust/stains) with clean recovery.
• AI authentication performance: Base DL model (ResNet50) achieved 99.63% validation accuracy. In deployment testing with 26,000 in-database and 11,000 out-of-database images (varied brightness/rotation/noise), setting a similarity threshold of 0.5 yielded 0% false positives and ~5% false negatives. End-to-end authentication time was 6.36 s per tag.
• Dynamic database updates: Only the final layer was retrained when adding new PUFs, achieving fast updates (e.g., 40 epochs in 5.48 s; ~0.137 s/epoch), maintaining performance while scaling the database.
• Practical readout: Smartphone plus mini-microscope successfully captured PUFs for authentication; macroscopic patterns (e.g., logo, QR code) composed of microscopic unique units demonstrated multi-scale labeling.

The study addresses the core challenge in PUFs of balancing configurability (code flexibility) with environmental stability. Fractal-guided depercolation of Au thin films produces intrinsically random, unique network structures whose complexity is tunable via film thickness while leveraging gold’s chemical and thermal robustness. The capacity (~10^34) and clear separation of intra- vs inter-pattern similarity confirm strong uniqueness and practical encoding potential. By nanoscale roughening, the same network serves as a homogeneous plasmonic platform supporting SERS, enabling orthogonal chemical encoding for multi-level security without relying on unstable nanoparticle assemblies. The proposed AI authentication pipeline combines a robust ResNet50 classifier with an FSIM-based final similarity check, achieving 0% false positives and rapid verification (6.36 s), even under variations in rotation, brightness, and noise. The dynamic database strategy mitigates the retraining bottleneck by updating only the final layer when adding new tags, enabling scalable deployment. Collectively, these results demonstrate a comprehensive anti-counterfeiting system that is unique, configurable, stable, mass-producible, and efficiently authenticated, with potential extensions to other materials and integration into electronics.

This work introduces a universal, fractal-guided annealing approach to fabricate random Au network PUFs with on-demand complexity and high environmental stability. The system achieves high encoding capacity (~10^34), robust uniqueness, and multi-level security via SERS-enabled chemical encoding. A practical AI-based authentication pipeline, featuring a dynamic database update strategy, delivers reliable (0% false positives), rapid (6.36 s) verification using smartphone-acquired images. Future directions include: expanding fractal-guided strategies to other materials and scales (e.g., diffusion-limited aggregation, electrochemical deposition, metal-induced crystallization, evaporation-driven crystallization); integrating network tags via rapid thermal annealing for wafer-scale microelectronic compatibility; enhancing multi-dimensional chemical encoding and leveraging handheld high-speed Raman for convenient spectral readout; and further optimizing database management and model efficiency for large-scale deployments.

• Encoding capacity, while very high, is not necessarily dominant compared to some wrinkling/crumpling systems with dynamic grayscale or tags with multiple stimuli-responsive responses.
• Multidimensional chemical encoding via SERS currently requires surface roughening and molecular probes, plus specialized Raman readout, which can increase readout time and impose operational constraints (though handheld Raman devices are improving).
• The base deep learning model training is time-consuming (~35 h for 2500 epochs), although mitigated by transfer learning and dynamic last-layer updates for database expansion.
• Original (unroughened) micron-scale Au networks exhibit weaker LSPR; plasmonic enhancement depends on the roughening process.
• While robust across tested conditions, generalizability to all real-world environments and long-term aging beyond reported tests requires further validation; the current design leaves room for optimization for electronics and diverse product fields.