Physical unclonable functions (PUFs), as hardware security primitives, exploit manufacturing randomness to extract hardware instance-specific secrets. One of most popular structures is time-delay based Arbiter PUF attributing to large number of challenge response pairs (CRPs) yielded and its compact realization. However, modeling building attacks threaten most variants of APUFs that are usually employed for strong PUF-oriented application---lightweight authentication---without reliance on the securely stored digital secrets based standard cryptographic protocols. In this paper, we investigate a reconfigurable latent obfuscation technique endowed PUF construction, coined as OB-PUF, to maintain the security of elementary PUF CRPs enabled authentication where a CRP is never used more than once. The obfuscation---determined by said random patterns---conceals and distorts the relationship between challenge-response pairs capable of thwarting a model building adversary needing to know the exact relationship between challenges and responses. A bit further, the obfuscation is hidden and reconfigured on demand, in other words, the patterns are not only invisible but also act as one-time pads that are only employed once per authentication around and then discarded. As a consequence, the OB-PUF demonstrates significant resistance to the recent revealed powerful Evaluation Strategy (ES) based modeling attacks where the direct relationship between challenge and response is even not a must. The OB-PUF's uniqueness and reliability metrics are also systematically studied followed by formal authentication capability evaluations.