A fundamental property of Physical Unclonable Functions (PUFs) is uniqueness, which results from the intrinsic characteristics of each PUF instance. However, PUF architectures employ elements whose physical characteristics and behavior may be very similar among different instances, thus leaking unwanted information. We explore the consequences of this effect by mounting Template Attacks over XOR Arbiter PUFs. In the attack, Challenge-Respose Pairs (CRPs) are profiled in one FPGA instance of the PUF to predict responses of a different FPGA instance, obtaining up to 80