The wireless medium contains domain-specific information that can be used to complement and enhance traditional security mechanisms. In this paper we propose ways to exploit the fact that, in a typically rich scattering environment, the radio channel response decorrelates quite rapidly in space. Specifically, we describe a physical-layer algorithm that combines channel probing (M complex frequency response samples over a bandwidth W) with hypothesis testing to determine whether current and prior communication attempts are made by the same user (same channel response). In this way, legitimate users can be reliably authenticated and false users can be reliably detected. To evaluate the feasibility of our algorithm, we simulate spatially variable channel responses in real environments using the WiSE ray-tracing tool; and we analyze the ability of a receiver to discriminate between transmitters (users) based on their channel frequency responses in a given office environment For several rooms in the extremities of the building we considered, we have confirmed the efficacy of our approach under static channel conditions. For example, measuring five frequency response samples over a bandwidth of 100 MHz and using a transmit power of 100 mW, valid users can be verified with 99% confidence while rejecting false users with greater than 95% confidence.