Low cost pervasive devices such as RFID (radio-frequency identification) tags and sensor nodes are increasingly becoming part of the fabric of life. Using these pervasive devices to store and collect data securely is becoming a challenge because stringent requirements on power and area constrain the implementation of standard cryptographic mechanisms. In this paper, we propose a secure and lightweight authentication protocol for resource scarce pervasive devices built upon a physical unclonable function (PUF) primitive termed Obfuscated PUF (OB-PUF) and a variant of a parameter-based authentication protocol. This protocol sends obfuscated challenges to an OB-PUF where the subsequent recovery of the obfuscated challenges by a server (verifier) is guaranteed. In particular, our approach exploits server (verifer) aided computations to reduce the hardware complexity on the pervasive device while still maintaining a high level of security and taking advantage of the known vulnerability of PUFs to model building attacks. Most importantly, the unclonability of the OB-PUF is preserved and, consequently, OB-PUF based pervasive devices are resilient to cloning. We also show through statistical analysis and model building attacks the infeasibility of constructing a model of our proposed OB-PUF by an adversary.