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In order to justify such an assumption, we need to rely on digital interface computation that to some extent remains confidential\u2014otherwise, information about PUF challenge\u2013response pairs leak with which the adversary can train a prediction model for the PUF. We introduce a theoretical framework that allows the adversary to have a prediction model (with a typical accuracy of 75% for predicting response bits for state-of-the-art silicon PUF designs). We do not require any confidential digital computing or digital secrets, while we can still prove rigorous statements about the bit security of a system that interfaces with the PUF. 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