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.

翻译：研究表明，在噪声和挑战向量分布的温和假设下，即使存在噪声，一类光学物理不可克隆函数（PUF）在获取多项式数量的挑战-响应对且计算能力多项式有界时，能够以任意精度和任意高概率被学习。该结论扩展了Rhūramir等人（2013）的研究成果——他们证明在无噪声条件下，若PUF光学系统为线性或非线性效应可忽略，该类PUF的子集可在多项式时间内被学习。我们基于PUF的尺寸参数、挑战与噪声向量的分布、以及回归算法的概率与精度，推导了线性回归算法所需样本数量与计算复杂度的多项式边界，其分析思路与Bootle等人（2018）针对低效实现版带错误学习问题的学习攻击类似。