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

TL;DR

This paper demonstrates that certain optical PUFs can be learned accurately even with noise, using polynomially many samples and computational resources, connecting physical security to learning theory and LWE problems.

Contribution

It extends previous noiseless PUF learnability results to noisy settings, providing polynomial bounds and a regression-based learning method under mild assumptions.

Findings

Optical PUFs are learnable with noise using polynomial resources.

Polynomial bounds are derived for sample complexity and computational effort.

The approach relates PUF learning to the Learning With Errors problem.

Abstract

It is shown that a class of optical physical unclonable functions (PUFs) can be learned to arbitrary precision with arbitrarily high probability, even in the presence of noise, given access to polynomially many challenge-response pairs and polynomially bounded computational power, under mild assumptions about the distributions of the noise and challenge vectors. This extends the results of Rh\"uramir et al. (2013), who showed a subset of this class of PUFs to be learnable in polynomial time in the absence of noise, under the assumption that the optics of the PUF were either linear or had negligible nonlinear effects. 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 probability and accuracy of the regression algorithm, with a similar analysis to one done by Bootle et al. (2018), who demonstrated a learning attack on a poorly implemented version of the Learning With Errors problem.