We show that a class of optical physical unclonable functions (PUFs) can be efficiently PAC-learned to arbitrary precision with arbitrarily high probability, even in the presence of intentionally injected noise, given access to polynomially many challenge-response pairs, under mild and practical assumptions about the distributions of the noise and challenge vectors. We motivate our analysis by identifying similarities between the integrated version of Pappu’s original optical PUF design and the post-quantum Learning with Errors (LWE) cryptosystem. We derive polynomial bounds for the required number of samples and the computational complexity of a linear regression algorithm, based on size parameters of the PUF, the distributions of the challenge and noise vectors, and the desired accuracy and probability of success of the regression algorithm. We use a similar analysis to that done by Bootle et al. [“LWE without modular reduction and improved side-channel attacks against BLISS,” in Advances in Cryptology – ASIACRYPT 2018], who demonstrated a learning attack on poorly implemented versions of LWE cryptosystems. This extends the results of Rührmair et al. [“Optical PUFs reloaded,” Cryptology ePrint Archive, 2013], who presented a theoretical framework showing that a subset of this class of PUFs is learnable in polynomial time in the absence of injected noise, under the assumption that the optics of the PUF were either linear or had negligible nonlinear effects. (Rührmair et al. also included an experimental validation of this technique, which of course included measurement uncertainty, demonstrating robustness to the presence of natural noise.) We recommend that the design of strong PUFs should be treated as a cryptographic engineering problem in physics, as PUF designs would benefit greatly from basing their physics and security on standard cryptographic assumptions. Finally, we identify future research directions, including suggestions for how to modify an LWE-based optical PUF design to better defend against cryptanalytic attacks.
We show that a class of optical physical unclonable functions (PUFs) can be efficiently PAC-learned to arbitrary precision with arbitrarily high probability, even in the presence of intentionally injected noise, given access to polynomially many challenge-response pairs, under mild and practical assumptions about the distributions of the noise and challenge vectors. We motivate our analysis by identifying similarities between the integrated version of Pappu’s original optical PUF design and the post-quantum Learning with Errors (LWE) cryptosystem. We derive polynomial bounds for the required number of samples and the computational complexity of a linear regression algorithm, based on size parameters of the PUF, the distributions of the challenge and noise vectors, and the desired accuracy and probability of success of the regression algorithm. We use a similar analysis to that done by Bootle et al. [“LWE without modular reduction and improved side-channel attacks against BLISS,” in Advances in Cryptology – ASIACRYPT 2018], who demonstrated a learning attack on poorly implemented versions of LWE cryptosystems. This extends the results of Rührmair et al. [“Optical PUFs reloaded,” Cryptology ePrint Archive, 2013], who presented a theoretical framework showing that a subset of this class of PUFs is learnable in polynomial time in the absence of injected noise, under the assumption that the optics of the PUF were either linear or had negligible nonlinear effects. (Rührmair et al. also included an experimental validation of this technique, which of course included measurement uncertainty, demonstrating robustness to the presence of natural noise.) We recommend that the design of strong PUFs should be treated as a cryptographic engineering problem in physics, as PUF designs would benefit greatly from basing their physics and security on standard cryptographic assumptions. Finally, we identify future research directions, including suggestions for how to modify an LWE-based optical PUF design to better defend against cryptanalytic attacks.
Physical Unclonable Functions (PUFs) provide hardware-level security by exploiting intrinsic randomness to produce device-unique responses. However, machine learning and side-channel attacks increasingly undermine their classical assumptions, calling for new approaches to ensure unforgeability. Quantum mechanics naturally supports this goal through intrinsic randomness and the no-cloning theorem, motivating the study of Quantum Physical Unclonable Functions (QPUFs). Yet, existing QPUF models often assume ideal unitary dynamics, neglecting non-unitary effects such as decoherence and dissipation that arise in real quantum devices. This work introduces a new class of non-unitary QPUFs that leverage open quantum system dynamics as a foundation for security. Three architectures are proposed: the Dissipative QPUF (D-QPUF), which uses amplitude damping as an entropy source; the Measurement-Feedback QPUF (MF-QPUF), which employs mid-circuit measurements and conditional unitaries; and the Lindbladian QPUF (L-QPUF), which models Markovian noise via the Lindblad master equation and Trotter-Suzuki decomposition. Simulation results show that these non-unitary designs achieve strong uniqueness, uniformity, and unforgeability, with controllable reliability trade-offs from stochastic noise. The L-QPUF, in particular, exhibits exponential modeling resistance under limited challenge-response access. By reframing environmental noise as a constructive resource, this work establishes a framework for noise-aware quantum hardware authentication and highlights non-unitary evolution as a viable foundation for post-quantum security.
Physically unclonable functions (PUFs) have emerged as a promising hardware security primitive, and recent years have seen growing interest in realizing PUFs on photonic integrated circuits (PICs). We classify existing PIC-based PUFs into electrically configured and optically encoded designs. Notably, security properties remain insufficiently analyzed, with mathematical unclonability often assumed without supporting argument. To illustrate this issue, we introduce a modeling attack against the subclass of optically encoded PUFs that operate in a linear optical regime. We show that, for a representative simulated PUF construction, observing as few as 200 challenge-response pairs allows learning the challenge-response mapping. Under canonical modeling assumptions, linear optically encoded PUFs are therefore mathematically clonable, calling for a careful assessment of their suitability for authentication protocols that rely on mathematical unclonability.
Physically unclonable functions (PUFs) convert microscopic manufacturing noise inside a chip into a device-specific hardware fingerprint, but delay-based designs fall to machine-learning modelling once an adversary collects enough challenge-response pairs (CRPs). This article reports an empirical study of six machine-learning attacks — logistic regression, least-squares regression, a multilayer perceptron, an LMN feature-lifting model, a denoising autoencoder, and a compact Transformer encoder — against Arbiter OR-AND-XOR PUFs (AOX-PUFs), simulated with pypuf on the University of Sheffield's Stanage high-performance computing cluster across CRP budgets from 2,500 to 1.9 million. The attacks exploit the Arbiter PUF's linear-additive delay model, and the defence under test is a BB84-inspired encoding wrapper motivated by the Quantum Lock forging-probability bound. Classical AOX-PUFs were modelled with 95–99% accuracy within tens of thousands of CRPs, while BB84-inspired encoding capped every attacker at a flat ceiling of roughly 0.85–0.90 that did not rise within either batch, even at close to two million CRPs. Decomposing the encoding pipeline shows that this ceiling tracks the simulated measurement-success probability rather than a genuine basis-secrecy effect: disclosing the encoding basis altered outcomes by less than a percentage point. An illustrative calculation based on the Quantum Lock bound shows that a genuine quantum advantage should decay the forging probability exponentially as the number of encoded output qubits grows, a prediction the flat empirical ceiling does not fulfil. The results corroborate prior architectural-hardening findings for AOX-PUFs while diverging from the CRP-inflation behaviour the Quantum Lock model predicts.
The hallmark of the information age is the ease with which information is stored, accessed, and shared throughout the globe. This is enabled, in large part, by the simplicity of duplicating digital information without error. Unfortunately, an ever-growing consequence is the global threat to security and privacy enabled by our digital reliance. Specifically, modern secure communications and authentication suffer from formidable threats arising from the potential for copying of secret keys stored in digital media. With relatively little transfer of information, an attacker can impersonate a legitimate user, publish malicious software that is automatically accepted as safe by millions of computers, or eavesdrop on countless digital exchanges. To address this vulnerability, a new class of cryptographic devices known as physical unclonable functions (PUFs) are being developed. PUFs are modern realizations of an ancient concept, the physical key, and offer an attractive alternative for digital key storage. A user derives a digital key from the PUF’s physical behavior, which is sensitive to physical idiosyncrasies that are beyond fabrication tolerances. Thus, unlike conventional physical keys, a PUF cannot be duplicated and only the holder can extract the digital key. However, emerging machine learning (ML) methods are remarkably adept at learning behavior via training, and if such algorithms can learn to emulate a PUF, then the security is compromised. Unfortunately, such attacks are highly successful against conventional electronic PUFs. Here, we investigate ML attacks against a nonlinear silicon photonic PUF, a novel design that leverages nonlinear optical interactions in chaotic silicon microcavities. First, we investigate these devices’ resistance to cloning during fabrication and demonstrate their use as a source of large volumes of cryptographic key material. Next, we demonstrate that silicon photonic PUFs exhibit resistance to state-of-the-art ML attacks due to their nonlinearity and finally validate this resistance in an encryption scenario.
In this paper we reconsider Physical Unclonable Functions based on the traditional approach of optical scattering to randomly disordered optical media. These devices have the major advantage of utilization of simple and very low-cost technology and therefore the potential to be installed all over the network providing critical cybersecurity operations such authentication, real time cryptographic key generation and generation of trues random sequences. To comply with the requirements of the aforementioned operations, critical issues must be resolved. We propose and implement algorithms for the generation of an almost unlimited number of uncorrelated optical challenges. We show experimentally that the uncorrelated challenges result in optical speckle which, after the proper numerical processing, produce true random sequences. Moreover, we determine the optimal illumination conditions to achieve the best possible performance in terms of robustness and unpredictability. Last but not least, we studied the resilience of the PUF against machine learning attacks. We conclude experimentally that under certain illuminating conditions and using the aforementioned uncorrelated challenges, the network cannot predict the responses even after being trained with a very large number of challenge responses (24,000 pairs).
Random number generators (RNG) are fundamental to cryptographic systems, requiring high entropy, unpredictability, and resistance to cloning attacks. This work proposes RNG based on optical physical unclonable function (PUF) that uses random scattering of structured vortex beams through rough surface. The inherent disorder of the scattering medium with tunable beam parameters like vortex order, provides a rich source of physical randomness. The generated speckle patterns are processed using a post processing algorithm to produce random sequences at a rate of 1.42 Gbps. The statistical quality of the sequences is evaluated using the NIST SP 800-22, AIS-31, and Dieharder test suites, which meet the required randomness criteria. Further assessment using entropies and Kolmogorov complexity shows high entropy and algorithmic randomness. The physical unclonability and uniqueness are verified through inter-device hamming distances, Pearson correlation of sequences obtained from different spatial regions and vortex orders, revealing negligible correlations. To assess resilience against data based adversaries, machine learning modeling attacks are performed. The prediction accuracies remain close to random guessing, showing resistance to learning based cloning and response prediction attacks. These results establish the proposed optical PUF method as a high speed, physically unclonable, and machine learning resistant source of random numbers for secure cryptographic applications.