Let Me Prove It to You: RO PUFs Are Provably Learnable

The last decade has witnessed a major change in the methods of Integrated Circuit (IC) fingerprinting and random key generation.The invention of Physically Unclonable functions (PUFs) was a milestone in the development of these methods. Ring-oscillator (RO) PUFs are one of the popular intrinsic PUF instances in authentication and random number generation applications. Similar to other types of PUFs, unpredictability and unclonability are the key requirements for the security of RO-PUFs. However, these requirements cannot be perfectly met for RO-PUFs, as demonstrated by studies investigating different attacks against RO-PUFs. In addition to semi-invasive attacks, modeling attacks have been proposed that aim to predict the response to an arbitrarily chosen challenge. To this end, the adversary collects only a small number of challenge response pairs (CRPs), and then attempts to constitute a model of the challenge-response behavior of the PUF. Nevertheless, it is not ensured that a model will be delivered after learning the seen CRPs, whose number is solely estimated instead of being properly proved. Aiming to address these issues, this paper presents a Probably Approximately Correct (PAC) learning framework enabling the learning of an RO-PUF for arbitrary levels of accuracy and confidence. Indeed, we prove that a polynomial-size Decision List (DL) can represent an RO-PUF. Thus, an arbitrarily chosen RO-PUF can be PAC learned by collecting only a polynomial number of CRPs. The “hidden” polynomial size of the respective representation of an RO-PUF therefore accounts for the success of the previously proposed (heuristic) attacks. However, our proposed bound is provably better, when comparing the number of CRPs required for our attack with already existing bounds calculated by applying heuristic techniques. Finally, by conducting experiments we complement the proof provided in our PAC learning framework.