Physical unclonable functions (PUFs) have emerged as a promising hardware security primitive, but existing CMOS PUFs suffer from issues related to reliability and susceptibility to modeling attacks. Memristors, leveraging nanotechnology fabrication process and highly nonlinear behavior, pose as an interesting alternative. In this paper, we report the first demonstration of memristor based PUFs. The six memristors we fabricated show a 50% uncertainty of PUF response and high reliability upon repeated interrogation. A physics based circuit model of memristors was also implemented to accurately determine the simulation time required for randomly selected polyominoes from a 3-D array of memristors. The proposed model provides higher degree of complexity and results in seven orders of increase in simulation time for an attacker than that reported by Rajendran <etal/>, 2012.