The underlying variability in the ReRAM device operation, while undesired in many applications, can be advantageous for hardware security primitives. ReRAM devices also come with the advantage of having non-linear multi-state operation. By comparison with previous reported ReRAM PUFs, which utilized spatial variations in the devices' binary ON/OFF states, we proposed to use sneak path currents and device / network nonlinearity as its main source of randomness to implement robust, reconfigurable and dense security primitives. In particular, in this work we present an in-depth discussion of how device non-linearity is affected by the read bias and the thermal stresses applied to the ReRAM crossbar. For the experimental demonstration, we used a three-dimensional stack of two 10×10 Al2O3/TiO2−x-based ReRAM crossbars with good uniformity for the memristors in both crossbar layers. The results highlight the utility of device non-linearity to extract more complex and more reliable one-way functions from relatively small ReRAM crossbar arrays.