Optimal capacity region for PUF-based authentication with a constraint on the number of challenge-response pairs

In this work we consider the problem of a PUF-based authentication model with a generated secret key. The considered scenario is that after an enrollment phase, where for several challenge-response pairs a secret key and helper data is generated, the decoder will choose one of the challenges uniform at random for authentication, this time the PUF provides a noisy version of the original response; we use the helper data to reconstruct the formerly calculated secret key. We will give an optimal capacity region for the model with respect to the number of generated challenge-response pairs, and the rate of communicated helper data, the amount of privacy leakage, the size of the secret key, and the distribution of the secret key, for each challenge index. For each challenge index we also minimize the probability of falsely rejecting a legitimate party, and the knowledge an adversary can gain about the secret key. This work provides further insights into the work in [1], using a similar model but different security criteria while additionally providing an optimal upper bound on the total number of challenge-response pairs that can be maintained by this model.