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Physically Unclonable Functions (PUFs) are introduced to remedy the shortcomings of traditional methods of secure key storage and random key generation on Integrated Circuits (ICs). Due to their effective and low-cost implementations, intrinsic PUFs are popular PUF instances employed to improve the security of different applications on reconfigurable hardware. In this work we introduce a novel laser fault injection attack on intrinsic PUFs by manipulating the configuration of logic cells in a programable logic device. We present two fault attack scenarios, where not only the effectiveness of modeling attacks can be dramatically increased, but also the entropy of the targeted PUF responses are drastically decreased. In both cases, we conduct detailed theoretical analyses by considering XOR arbiter PUFs and RO PUFs as the examples of PUF-based authenticators and PUF-based random key generators, respectively. Finally we present our experimental results based on conducting laser fault injection on real PUFs, implemented on a common complex programmable logic device manufactured in 180 nm technology.