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Physically unclonable functions (PUFs) which are robust to modeling attacks, usually have a complex, high-dimensional, nonlinear relationship between challenges and responses. Often, it is difficult to derive closed-form analytical expressions for these relationships. Consequently, it becomes difficult to compare PUF variants with regard to their robustness to modeling attacks. In this article, we apply a data-driven empirical metric termed the intrinsic dimension (ID), to estimate the inherent complexity of the relationship between the challenges and responses of a given PUF variant. This metric is computed from the linear projection layer of a deep neural network (DNN) aimed at modeling the PUF and has a unique advantage that it is independent of the architectural details and chosen hyperparameters of the DNN. It also does not require the knowledge of the structural and functional details of the PUF. The proposed approach is evaluated using two well-known ID estimation methods based on the nearest neighbor method and the full correlation integral (FCI). Through detailed experimental results, we demonstrate that the numerical values of the FCI-based ID metric for different types of PUFs have consistently high positive correlation with the perceived difficulty of modeling several common PUF variants. We also show that the ID metric provides deep insight about various subtleties that affect the robustness of PUFs to modeling attack and provides a convenient mechanism to perform a systematic comparison between different PUF compositions. [ABSTRACT FROM AUTHOR]

XOR arbiter PUF (XOR APUF), where the outputs of multiple arbiter PUF (APUFs) are XOR-ed, has proven to be more robust to machine learning-based modeling attacks. The reported successful modeling attacks for XOR APUF either employ auxiliary side-channel or reliability information, or require enormous computational effort. This robustness is primarily due to the difficulty in learning the unknown internal delay parameter terms in the mathematical model of a XOR APUF, and the robustness increases as the number of APUFs being XOR-ed increases. In this article, we employ a novel machine learning-based modeling technique called efficient CANDECOMP/PARAFAC-tensor regression network (CP-TRN), a variant of CP-decomposition-based tensor regression network, to reduce the computational resource requirement of model building attacks on XOR APUF. We theoretically prove the reduction in computational complexity, as well as give supporting experimental results. In addition, our proposed technique does not require any auxiliary information, and is robust to noisy training data. The proposed technique allowed us to successfully model 64-bit 8-XOR APUF and 128-bit 7-XOR APUF on a single desktop workstation, with high prediction accuracy. Further, we extend the proposed modeling attack technique to XOR APUF variants, e.g., lightweight secure PUF (LSPUF), which rely on input challenge transformation. The modeling accuracy results obtained by us for the LSPUF are comparable with those obtained by applying other state-of-the-art techniques, while requiring less training data. [ABSTRACT FROM AUTHOR]