Hardware-intrinsic security primitives employ instance-specific and process-induced variations in electronic hardware as a source of cryptographic data. Among various emerging technologies, memristors offer unique opportunities in such security applications due to their underlying stochastic operation. Here we show that the analogue tuning and nonlinear conductance variations of memristors can be used to build a basic building block for implementing physically unclonable functions that are resilient, dense, fast and energy-efficient. Using two vertically integrated 10 × 10 metal-oxide memristive crossbar circuits, we experimentally demonstrate a security primitive that offers a near ideal 50% average uniformity and diffuseness, as well as a minimum bit error rate of around 1.5 ± 1%. Readjustment of the conductances of the devices allows nearly unique security instances to be implemented with the same crossbar circuit.