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It is shown that a class of optical physical unclonable functions (PUFs) canbe learned to arbitrary precision with arbitrarily high probability, even inthe presence of noise, given access to polynomially many challenge-responsepairs and polynomially bounded computational power, under mild assumptionsabout the distributions of the noise and challenge vectors. This extends theresults of Rh\"uramir et al. (2013), who showed a subset of this class of PUFsto be learnable in polynomial time in the absence of noise, under theassumption that the optics of the PUF were either linear or had negligiblenonlinear effects. We derive polynomial bounds for the required number ofsamples and the computational complexity of a linear regression algorithm,based on size parameters of the PUF, the distributions of the challenge andnoise vectors, and the probability and accuracy of the regression algorithm,with a similar analysis to one done by Bootle et al. (2018), who demonstrated alearning attack on a poorly implemented version of the Learning With Errorsproblem.

Polynomial Bounds for Learning Noisy Optical Physical Unclonable Functions and Connections to Learning With Errors