Atomic-scale physical unclonable functions in solids.

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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Adv . 2026 Mar 18;12(12):eaed3987. doi: 10.1126/sciadv.aed3987 Search in PMC Search in PubMed View in NLM Catalog Add to search Atomic-scale physical unclonable functions in solids Zihua Chai Zihua Chai 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Validation, Visualization, Writing - original draft, Writing - review & editing Find articles by Zihua Chai 1 , Zeyu Gao Zeyu Gao 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. Data curation, Validation, Visualization Find articles by Zeyu Gao 1 , Mengqi Wang Mengqi Wang 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. 2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China. Resources Find articles by Mengqi Wang 1, 2 , Jingyang Zhou Jingyang Zhou 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. Validation Find articles by Jingyang Zhou 1 , Pei Yu Pei Yu 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. Resources Find articles by Pei Yu 1 , Xu Zhou Xu Zhou 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. 3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China. Formal analysis Find articles by Xu Zhou 1, 3 , Junyu Guan Junyu Guan 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. 2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China. Formal analysis Find articles by Junyu Guan 1, 2 , Pei Zhang Pei Zhang 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. Data curation Find articles by Pei Zhang 1 , Ya Wang Ya Wang 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. 2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China. 3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China. Conceptualization, Funding acquisition, Resources, Visualization Find articles by Ya Wang 1, 2, 3 , Kangwei Xia Kangwei Xia 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. 3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China. Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing - review & editing Find articles by Kangwei Xia 1, 3, * Author information Article notes Copyright and License information 1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China. 2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China. 3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China. * Corresponding author. Email: [email protected] Roles Zihua Chai : Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Validation, Visualization, Writing - original draft, Writing - review & editing Zeyu Gao : Data curation, Validation, Visualization Mengqi Wang : Resources Jingyang Zhou : Validation Pei Yu : Resources Xu Zhou : Formal analysis Junyu Guan : Formal analysis Pei Zhang : Data curation Ya Wang : Conceptualization, Funding acquisition, Resources, Visualization Kangwei Xia : Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing - review & editing Received 2025 Oct 30; Accepted 2026 Feb 17; Collection date 2026 Mar 20. Copyright © 2026 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license , which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited. PMC Copyright notice PMCID: PMC12998501  PMID: 41849614 Abstract The rapid development of the Internet of Things and the digital information era has intensified the demand for secure hardware and information systems. Physical unclonable functions (PUFs) provide a hardware-based approach by exploiting fabrication-induced randomness to generate unique, unclonable labels. Concurrently, advances in deterministic nanofabrication increasingly challenge the unclonability of conventional micro- and nanoscale PUFs, motivating the exploration of more fundamental sources of physical randomness. Here, we demonstrate an atomic-scale PUF architecture that leverages intrinsic randomness in solids through lattice and defect engineering. The resulting PUFs exhibit both three-dimensional spatial variability and atomic-scale configurational complexity, yielding extraordinary encoding space and uniqueness. For a characteristic feature size of 1 nanometer, the Shannon entropy is estimated at 17.49, underscoring the encoding capacity. Moreover, the embedded structure ensures intrinsic unclonability and robustness against environmental perturbations. These results establish atomic-scale PUFs as a fundamentally secure and scalable platform for next-generation hardware and information security. Atomic-scale physical randomness enables fundamental hardware and information security. INTRODUCTION The rapid expansion of the Internet of Things (IoT) has intensified the demand for robust hardware and information security. Concurrently, advances in manufacturing and computational capabilities have enabled adversarial techniques, escalating the threats of cloning, tampering, and reverse engineering ( 1 – 4 ). To address the challenges, physical unclonable functions (PUFs) provide a hardware-based foundation for anti-counterfeiting, authentication, and cryptography. By leveraging the limits of manufacturing techniques and the intrinsic stochasticity of fabrication processes, PUFs generate unique, device-specific responses that are infeasible to replicate or predict ( 5 – 8 ). A wide range of PUF platforms has been explored, incorporating stochastic two-dimensional (2D) particle distributions and structural variations at micro- to nanoscale dimensions on heterogeneous substrates. These architectures yield distinct optical, electrical, or magnetic features, demonstrating strong uniqueness and versatility ( 9 – 21 ). In parallel, continuous progress in nanolithography and nanofabrication has extended the limits of controllable patterning at the nanoscale, thus motivating the exploration of more fundamental sources of uniqueness to intrinsically reinforce unclonability ( 22 – 24 ). Atoms, as the fundamental building blocks of matter, provide an unexplored degree of freedom for securing information, offering a higher level of intrinsic uniqueness. Stochastic atomic-scale features such as vacancies, impurities, and isotopic variations in materials naturally embed randomness throughout the 3D volume ( 25 , 26 ). Harnessing this randomness enables atomic-scale PUFs that overcome the dimensional constraints of micro- and nanoscale PUFs while introducing a fundamental level of unclonability. Replicating such atomic configurations would require atom-by-atom engineering, a task limited not only by current technological capabilities but also by the probabilistic nature of quantum mechanics and atomic-level complexity ( 27 ). Furthermore, as these entropy sources are inseparably embedded within the host material, the PUFs are inherently protected and benefit from the stability of the underlying lattice ( 28 ). By harnessing the irreducible randomness of atomic configurations, atomic-scale PUFs combine superior uniqueness, long-term robustness, and intrinsic unclonability, thereby establishing a distinct paradigm that extends the scope of PUFs for reliable hardware-based security. In this work, we propose an atomic-scale PUF architecture and experimentally demonstrate the PUFs with optically active color centers through defect engineering in diamond. Across the 3D lattice volume, the combined variability of color centers and isotopic distributions induces atomic-scale (1 nm) randomness and complexity, thereby fundamentally enhancing both single-pixel entropy and overall encoding capacity. Consequently, these atomic-scale PUFs are intrinsically resistant to cloning with any currently available technology. Furthermore, owing to diamond’s exceptional mechanical, chemical, and electromagnetic robustness ( 29 ), the embedded PUFs exhibit long-term stability and resilience under extreme conditions. Beyond hardware authentication, the atomic-scale PUFs also support cryptographic key generation and secure data encryption, positioning them as a versatile platform for next-generation information security. RESULTS The conceptual framework of atomic-scale PUFs is illustrated in Fig. 1 . Defect-engineering techniques, such as electron irradiation and ion implantation, enable the stochastic generation of color centers throughout solids ( Fig. 1A ). The resulting fluorescence patterns exhibit micro- to nanoscale spatial randomness that can be probed across multiple layers, yielding 3D optical PUFs in which volumetric disorder substantially expands the encoding space ( N ) and increases encoding capacity ( C ). Building on these spatially random distributions, the intrinsic crystallographic anisotropy of solids further diversifies color-center properties, such as orientation ( Fig. 1B ). These anisotropic optical responses increase the dimensionality ( R ) for each fluorescence pixel, extending encoding from binary to multilevel schemes within each layer and thereby strengthening resistance to cloning. At the atomic limit, each fluorescence pixel further incorporates spin degrees of freedom through the interplay between engineered color centers and the intrinsic disorder of the host lattice, giving rise to a quantum system with extreme configurational complexity and abundant entropy sources ( Fig. 1C ). The spin-based multilevel encoding provides an exponential increase in response dimensionality R , approaching the fundamental limits of unclonability in hardware security ( Fig. 1D ). The system can be robustly authenticated through optical, magnetic, and spectroscopic techniques, manifested as dynamically modulated fluorescence. In our demonstration, the framework is realized using engineered nitrogen-vacancy (NV) centers in bulk diamond, whose exceptional optical and spin properties ( 30 ), together with the stochastic distribution of 13 C isotopes in the host lattice, provide an ideal platform for the stepwise realization of atomic-scale PUFs. Fig. 1. Schematic diagram of atomic-scale PUFs based on color center systems in solids. Open in a new tab ( A ) Multilayer encoding enabled by the 3D spatial randomness of engineered color centers. ( B ) Optical multilevel encoding arising from anisotropic responses of fluorescence emitters. ( C ) Atomic-scale multilevel encoding based on spin quantum systems formed by coupled color centers, isotopes, and other intrinsic defects. ( D ) Estimation of the number of responses per pixel ( R ) contributed by different sources of randomness. To realize multilayer optical PUFs, vacancies were first uniformly introduced into bulk diamond by electron irradiation, as schematically shown in Fig. 2A . These vacancies subsequently paired with substitutional nitrogen impurities, resulting in the stochastic generation of NV centers throughout the diamond lattice. Upon excitation with a laser at 532 nm, the color centers emit fluorescence across the 3D volume. A representative subregion ( Fig. 2B ) highlights the spatial randomness of the emitters. For the construction of multilayer PUFs, a total of 48 fluorescence images were acquired from three vertically stacked layers as PUF labels (16 labels per layer), each separated by 10 μm in depth and covering a 25 μm–by–25 μm area. An example PUF label taken at a depth of 28 μm is presented in Fig. 2C . For binary encodings, the PUF labels were thresholded and binarized into 25 × 25 pixel binary keys ( Fig. 2D ), where pixels with high or low fluorescence intensity correspond to binary “1” or “0,” respectively. Fig. 2. Multilayer encoding based on color centers in diamond. Open in a new tab ( A ) Schematic of electron irradiation and generation of NV centers across diamond. e − , electron. ( B ) 3D fluorescence image of a subregion within the diamond substrate. Scale bar, 5 μm. ( C ) Fluorescence image of an area of 25 μm by 25 μm, located at a depth of 28 μm. ( D ) Binary key derived from the fluorescence image in (C), where dark and bright pixels are assigned values of 0 and 1, respectively. ( E ) The inter- and intra-Hamming distances of the binary keys generated from 48 PUF labels across three distinct layers. ( F ) Pairwise comparison of the binary keys. The notation Z 1-3 denotes the three layers, and indices “i” and “ii” indicate pre- and posttreatment measurement results of the labels, respectively. ksps, kilo-counts per second. Quantitative evaluation of the PUF performance was conducted through standard metrics (see the Supplementary Materials section I for details). Uniqueness was assessed by calculating the inter-Hamming distance among different binary keys, yielding an average value of 0.4984, which is in close agreement with the theoretical value of 0.5, confirming statistical randomness and uniqueness ( Fig. 2E ). Subsequently, robustness was evaluated under harsh environmental conditions by immersing the diamond substrate in a strongly oxidizing triacid mixture of sulfuric acid (95% H 2 SO 4 ), nitric acid (65% HNO 3 ), and perchloric acid (70% HClO 4 ), followed by heating for 7.5 hours. Comparative fluorescence imaging before and after the treatments revealed negligible changes in both spatial emission profiles and intensities (see the Supplementary Materials section II for details). The average intra-Hamming distance between pre- and posttreatment binary keys was 0.0849 ( Fig. 2E ), demonstrating excellent stability and reliability under extreme environments. Furthermore, analysis of the key similarity ( Fig. 2F ) showed minimal cross-correlation, confirming the absence of spatial cross-talk among stacked layers ( Z 1-3 ) and verifying the effectiveness of the multilayer encoding scheme. Owing to the macroscopic thickness of the substrate (0.5 mm), more than a dozen layers can be used for PUF labels (see the Supplementary Materials section VI for details). This substantially enlarges the encoding space compared to conventional 2D PUF architectures and thereby increases overall capacity. Collectively, these results establish 3D optical PUFs as a scalable and highly reliable platform, offering superior uniqueness, environmental resilience, and encoding capacity. In addition to bulk fabrication by electron irradiation, PUF labels were also engineered through controlled implantation of nitrogen ions (N + ) beneath the diamond surface, enabling customizable architectures. A polymethyl methacrylate (PMMA) mask was first patterned to confine the implantation regions with nanoscale precision ( Fig. 3A ). Each region comprised a 50 × 50 aperture array, where the aperture dimensions and spacing were tailored to ensure uniformity and independence among individual doping sites while optimizing the encoding density (see Materials and Methods for details). Due to the moderate conversion yield rate during the ion-implantation processes ( 31 ), the number of color centers generated among the doping sites varied stochastically, resulting in variations in the detected photon count rates across the array. A representative fluorescence image of one PUF label is shown in Fig. 3B , with the statistical distribution of photon count rates summarized in Fig. 3C . The observed site populations (44.4, 37.6, 14.0, and 4.0%) follow a Poisson distribution (λ = 0.7, k = 0,1,2 …), confirming the discrete and probabilistic nature of color-center formation. Fig. 3. Multilevel encoding based on color centers in diamond. Open in a new tab ( A ) Schematic of ion implantation and generation of NV centers near the surface of diamond. ( B ) Fluorescence image of an ion-implantation region of 50 μm by 50 μm. ( C ) Distribution of fluorescence intensities across all ion-implantation sites within the region in (B). ( D ) The bit uniformity across 16 binary keys. ( E ) Binary key corresponding to the region shown in (B). Pixels with index 1 denote the sites with at least one color center. ( F ) The inter- and intra-Hamming distance (inter-HD and intra-HD) of the binary keys. ( G ) Fluorescence response of four representative sites under applied magnetic fields B → 0 with directions D 1-4 . The count rate ratio is defined as the photon count rate with the magnetic field applied relative to that at zero field. ( H ) Multilevel key corresponding to the region shown in (B). Pixels with indices 1 to 4 denote sites containing single color centers with orientations D 1-4 , respectively. Index 5 represents sites with at least two color centers. ( I ) The inter- and intra-Hamming distance of the multilevel keys. ( J ) Pairwise comparison of the multilevel keys. “i” and “ii” represent the measurement results of the labels before and after acid treatments, respectively. ( K ) Photon count rates versus excitation polarization (controlled with a rotating half-wave plate). Single-emitter sites (blue and orange) show distinct crystallographic orientations, while dual-emitter sites (yellow, purple, and green) reflect different orientation combinations. Light blue indicates a site with three emitters. This intrinsic spatial randomness provides a direct entropy source for encoding PUF labels. For binary encoding, sites containing color centers were assigned a binary value of 1, while the empty sites were assigned 0. Consequently, the fluorescence image of the PUF label ( Fig. 3B ) was converted into a binary key (50 × 50 pixels), as illustrated in Fig. 3E . To evaluate the performance of ion-implanted PUFs, a set of 16 labels was randomly sampled across the substrate. Through precise control of the implantation dose and energy, the generated binary keys exhibited excellent average bit uniformity with an average value of 0.5048 ( Fig. 3D ), closely matching the ideal value of 0.5 and thereby maximizing the Shannon entropy of binary keys to 1 (see the Supplementary Materials section IV for details). The average inter-Hamming distance among these binary keys was calculated as 0.4999 ( Fig. 3F ), in agreement with the theoretical expectation of 0.5, confirming the statistical uniqueness. The spatial independence of the pixels eliminates spatial cross-talk common in conventional optical PUFs, consequently maximizing the effective encoding capacity. For a 50 × 50 pixels binary key, the encoding capacity was estimated as 2 2500 (10 753 ). These results demonstrate ion implantation as a complementary and highly flexible method for fabricating near-surface PUFs with independently addressable regions and customizable spatial architectures. Multilevel encoding extends the encoding capacity of PUFs beyond the limitations of binary schemes by increasing the number of responses per pixel, thereby enhancing system uniqueness. In diamond, the intrinsic lattice anisotropy introduces atomic-scale structural variability in color centers, enabling optical multilevel encoding strategies. NV centers have a symmetry axis aligned along one of four crystallographic orientations in the diamond lattice, [111], [ 1 ¯ 1 ¯ 1 ] , [ 1 1 ¯ 1 ¯ ] , and [ 1 ¯ 1 1 ¯ ] , which are denoted as D 1-4 , respectively. The orientation features can be identified through the photodynamics of color centers under magnetic fields ( 32 ). When the orientation aligns with the applied magnetic field B → 0 , the fluorescence intensity remains comparable to the zero-field case. In contrast, misalignment between the orientation and B → 0 results in fluorescence suppression. Figure 3G presents the orientation-dependent fluorescence responses of different sites under magnetic fields applied along the four crystallographic directions D 1-4 , confirming unambiguous identification of orientation information. To highlight the utility of orientation-dependent features in multilevel encoding, ion-implanted PUF labels were further analyzed. Pixels containing single color centers were reindexed from 1 to 4 according to their respective crystallographic orientations, while pixels with two or more color centers were assigned index 5. The resulting multilevel key, shown in Fig. 3H , was derived from the same PUF label in Fig. 3B , demonstrating enhanced encoding dimensionality. Consequently, the interdevice uniqueness is substantially improved. The average inter-Hamming distance among the multilevel keys was promoted to 0.6998, in close agreement with the theoretical value of 0.6944 expected from a random orientation distribution of the color centers (see the Supplementary Materials section I for details). Based on the experimentally measured frequency distribution, the average Shannon entropy per site was calculated to be 2.14 (theoretical value, 2.13), corresponding to an effective encoding capacity of ~2 2.14 × 2500 (10 1611 ) for a single PUF label (see the Supplementary Materials section IV for details). The robustness of both binary and multilevel keys was evaluated under harsh chemical conditions by immersing and boiling the diamond substrate in the triacid mixture for 13 hours. In both cases, the average intra-Hamming distances (0.0136 and 0.0415) remained near the theoretical expectation (0), as presented in Fig. 3F and Fig. 3I , respectively. The detailed pairwise comparison of the multilevel keys is further illustrated in Fig. 3J . The minor deviations from the theoretical expectation are attributed primarily to photon shot noise during readout. Considering the shallow implantation depth (≈20 nm), these results highlight the robustness and stability of diamond PUFs at nanometer-scale depths. Further stabilization of the charge state of near-surface color centers can be achieved through surface engineering, for example, by applying graphene coatings to suppress surface charge noise ( 33 ). In parallel, higher-energy ion implantation can be used to generate deeper PUF labels, thereby effectively mitigating surface-related perturbations. Besides the magnetic field–dependent photodynamics, the orientations of color centers can also be characterized through polarization-dependent fluorescence. As illustrated in Fig. 3K , photon count rates from different sites exhibited distinct modulation with varying excitation polarization. These modulations revealed both individual and clustered color centers with mixed orientations, providing a complementary approach for multilevel PUF verification. Collectively, the site-to-site orientation variability and stochastic population of color centers establish a robust basis for constructing multilevel optical PUFs with high uniqueness and reliable authentication. The encoding capability of classical optical PUFs is fundamentally constrained by the microscale feature size of the structures and the optical diffraction limit. In contrast, the intrinsic atomic disorder originating from defects and isotopic variations gives rise to complex and stochastic quantum systems, which naturally compose atomic-scale PUFs, as illustrated in Fig. 4A . The atomic randomness can be resolved with subnanometer precision through quantum sensing, which leverages the coherent control of the central electron spins of NV center ( S = 1). For instance, coupling between nuclear spins of 13 C isotopes ( I = 1 / 2 ) and the electron spin induces characteristic hyperfine splittings ( Fig. 4B ). Strongly coupled nuclear spins give rise to distinct and resolvable electronic spectral features, enabling lattice site–specific identification of the atomic environments (see the Supplementary Materials section III for details) ( 34 ). Representative spectra obtained from three different positions within the PUF label of Fig. 3B are shown in Fig. 4 (C to E), each reflecting a distinct atomic configuration in the diamond lattice and generating a spin-derived code for multilevel encoding. These couplings with nuclear spins thus provide an extra entropy source across color centers even with identical optical responses, thereby further enhancing the uniqueness of PUFs. Fig. 4. Atomic-scale PUFs based on spin quantum systems. Open in a new tab ( A ) Enlarged fluorescence image from Fig. 3B with schematic of the diamond lattice. Yellow spheres represent randomly distributed 13 C isotopes; those within the dashed circle are strongly coupled to the NV electron spin, while distant ones are weakly coupled. ( B ) Energy-level diagram of the electron-nuclear spin system. Strongly coupled nuclear spins manifest as resolvable spectral splittings, whereas weakly coupled nuclear spins are detectable through dynamical decoupling spectroscopy. ( C to E ) Representative spectra of strongly coupled spin systems with distinct local atomic configurations. The coordinates correspond to the sites of the array in (A). ( F ) Characterization of weakly coupled spin systems with dynamical decoupling spectroscopy ( N p = 32, B 0 = 738 Gs). Left: Resonance dips identify individual electron-nuclear spin interactions. Right: Spatial positions of the corresponding 13 C isotopes. m s denotes the spin magnetic quantum number. a.u., arbitrary units. Beyond the proximate strongly coupled 13 C spins, the detection volume of the central electron spin encompasses a larger number of weakly coupled 13 C spins with more intricate atomic configurations. These weakly coupled nuclear spins were resolved using dynamical decoupling spectroscopy (see the Supplementary Materials section III for details) ( 35 ), where resonances in the coherence spectrum correspond to the coupled evolutions of individual nuclear spins. A representative spectrum is shown in Fig. 4F (left), where four distinct resonances reveal the existence of four weakly coupled 13 C nuclei. By modeling the hyperfine interactions as dipole-dipole couplings, the spatial positions of these nuclei were reconstructed ( Fig. 4F , right), yielding a unique configuration at the atomic scale (1 nm). The stochastic distribution of such isotopes within the sensing volume gives rise to 673056 possible local configurations, corresponding to a Shannon entropy of 17.49 (see the Supplementary Materials section V for details). This configurational randomness ensures that each spin system inherently constitutes a multilevel atomic-scale PUF. Owing to the uniform distribution of 13 C isotopes across the diamond lattice, such atomic-scale PUFs are intrinsically abundant across the material. At the device level, PUF labels defined over planar areas of 50 μm by 50 μm host ~1875 NV centers per label ( Fig. 3 ), yielding an estimated encoding capacity on the order of 2 17.49 × 1875 (10 9869 ). Extending from planar regions to the full 3D lattice further enlarges the encoding space, markedly amplifying capacity and scalability. Replicating these configurations is fundamentally infeasible with current technologies, which are limited both by the exponential configurational complexity and by the practical impossibility of fabrication, thereby ensuring the unclonability and long-term security of atomic-scale PUFs. Thus far, we have demonstrated the atomic-scale PUFs that exploit the quantum discretization features of both engineered color centers and the intrinsic atomic environments. Meanwhile, various classical properties that are commonly explored in broader PUFs research can serve as encoding parameters in parallel, such as the wavelength of the zero-phonon line, fluorescence lifetime, spectra contrast, and linewidth. Incorporating these dimensions further increases the encoding capacity and highlights color centers in solids as multimodal platforms for PUF-based identification and secure information systems. In parallel with the high-capacity atomic-scale PUFs that exploit the randomness of individual NV center systems, the deterministic engineering of ensemble GR1 centers inside the bulk diamond provides high-density and robust optical data storage against environmental perturbations ( 36 ). The integration of both stochastic and deterministic defect species thus enables unified cryptographic and storage applications, with diamond serving as a multifunctional substrate. As a demonstration, PUF labels were first used as true random number generators to generate both optical and spin-based encryption keys. Encrypted information was ASCII-encoded and deterministically written in diamond through patterned GR1 centers laser writing ( Fig. 5A ), with bright and dark fluorescence units denoting binary 1 and 0, respectively. An example decryption process is shown in Fig. 5B , where the encrypted information was recovered using an XOR operation with an optical PUF key extracted from the bottom left corner of Fig. 3E , restoring the plaintext “USTC.” For enhanced security, a dual-layer encryption scheme further incorporates the embedded spin keys derived from the same PUF labels ( Fig. 5C ). Here, pixels containing strongly coupled electron-nuclear spin systems (coupling strength of ≥3 MHz) were assigned a binary 1, while the others were labeled 0. In this scheme, recovery of the plaintext “SPIN” requires XOR decryption with both the optical and spin keys. This atomic-scale encryption protocol demonstrates the feasibility of integrating quantum systems with engineered material platforms for high-security information storage. Meanwhile, the atomic-scale PUFs can also serve as an authentication layer, thereby reinforcing the overall security architecture of optical data storage and hardware identification. Fig. 5. Information encryption and decryption based on atomic-scale PUFs. Open in a new tab ( A ) Encrypted data storage in diamond realized through deterministic engineering of GR1 centers. Bright and dark fluorescence units encode binary 1 and 0, respectively. ( B ) Decryption with optical PUF keys (red) extracted from the bottom left corner of Fig. 3E . XOR operations between the encrypted data and the optical key recover the plaintext message “USTC.” ( C ) Dual-layer decryption with combined optical and spin keys (yellow) derived from the bottom left corner of Fig. 3E . Spin keys are defined by pixels hosting strongly coupled electron-nuclear spin systems, which are assigned a binary 1. XOR operations with both key layers yield the plaintext “SPIN.” a.u., arbitrary units. DISCUSSION In this work, we demonstrated atomic-scale PUFs that harness the intrinsic randomness of color center systems in solids. Leveraging the exceptional mechanical, chemical, and optical properties of diamond, these PUFs exhibited robust performance, spatial multilayer encoding, and quantum-enhanced multimodal encoding capabilities arising from complex atomic-scale configurations distributed across the crystal lattice. The Shannon entropy was estimated at 17.49 within a characteristic feature size of 1 nm, while a planar area of 50 μm by 50 μm yielded an encoding capacity on the order of 10 9869 , underscoring the exceptional uniqueness. We further implemented these PUFs in a proof-of-concept information encryption scheme, enabling a complete storage-encryption process entirely within the same platform. Beyond NV centers, a variety of color centers can be engineered in parallel ( 37 – 39 ), allowing simultaneous exploitation of their diverse optical and spin characteristics to realize multiplex atomic-scale PUFs. While diamond served as the model system in this study, the atomic-scale PUF architecture is applicable to various material platforms, including semiconductors such as silicon carbide ( 40 , 41 ), gallium nitride ( 42 ), and silicon ( 43 ), as well as rare earth–doped crystals ( 44 , 45 ). The intrinsic atomic-scale randomness across a variety of platforms offers a pathway toward next-generation and high-security PUFs, with broad applications including semiconductor device authentication, secure tagging, and encryption technologies. MATERIALS AND METHODS Experimental setup The atomic-scale diamond PUFs were demonstrated with a homebuilt confocal microscope under ambient conditions. A continuous wave 532-nm laser (CNI Optoelectronics Technology, MGL-III-532) was used for optical pumping. An air objective lens (Olympus, MPLAPON50X) was used for the excitation and fluorescence collection of color centers, while a long-pass optical filter (Semrock, BLP01-633R-25) was used to suppress residual laser scattering. The same confocal setup was also used for the readout of optical data stored with GR1 centers. The microwave signal used to obtain the optically detected magnetic resonance spectra of electron spins was generated by a microwave signal source. For the detection of weakly coupled nuclear spins, the microwave control sequences were generated by an arbitrary wave generator (Keysight, M8190A). PUF fabrication The diamond substrates used in this work were commercial single-crystal [100]-oriented diamond plates. The substrates contained a natural 13 C abundance of 1.1% and a nitrogen concentration of <5 parts per billion, with dimensions of 2 mm by 2 mm by 0.5 mm. For electron-irradiated PUF labels, the entire substrate was irradiated by an electron beam with an energy of 2.3 MeV and a dose of 0.30 mA·s, generating vacancies across the crystal lattice. These vacancies subsequently combined with substitute nitrogen atoms to form optically active color centers throughout the lattice. For ion-implanted PUF labels, hundreds of labels were fabricated in parallel on a single diamond substrate. To exhibit configurable implantation patterns, a PMMA layer was first spin coated on the substrate surface as a doping mask. Aperture arrays with a radius of 15 nm and nearest-neighbor spacing of 1 μm were precisely fabricated in the PMMA layer using electron-beam lithography. Nitrogen ions ( 14 N + ) were then implanted with an energy of 15 keV and a dose of 1.5 × 10 12 /cm 2 , ensuring ion penetration exclusively through the predefined apertures while being blocked elsewhere by the mask. On average, ~10 ions were implanted into the diamond substrate per aperture. After ion implantation, the PMMA mask was removed with acetone. To facilitate the formation of color centers, both electron-irradiated and ion-implanted substrates were subsequently annealed at 1000°C in vacuum. Acknowledgments We thank Q. Zhang for helpful discussions. Funding: This work is supported by the National Natural Science Foundation of China (grant nos. T2325023, 12274400, 12504594, 12474500, 92265204, and 92565304), the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302200), and the Fundamental Research Funds for the Central Universities (grant no. WK2030000076). Author contributions: K.X. and Z.C. conceived the idea and designed the experiments. Z.C. and Z.G. performed the experiments. M.W., J.Z., and P.Y. prepared the samples. Z.C., Z.G., X.Z., J.G., P.Z., and K.X. analyzed the data. Z.C., K.X., and Y.W. wrote the manuscript. K.X. supervised the project. 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