In this paper we study key exchange protocols in a model where the key exchange takes place between devices with limited displays that can be compared by a human user. If the devices display the same value then the human user is convinced that the key exchange terminated successfully and securely, and if they do not then the user knows that it came under attack. The main result of this paper is a rigorous proof that the numeric comparison mode for device pairing in Bluetooth version 2.1 is secure, under appropriate assumptions regarding the cryptographic functions used. Our proof is in the standard model and in particular does not model any of the functions as random oracles. In order to prove our main result, we present formal definitions for key exchange in this model and show our definition to be equivalent to a simpler definition. This is a useful result of independent interest that facilitates an easier security analysis of protocols in this model.