Modelling trust in random wireless networks

We present an analysis of the probability that a set of devices capable of communicating wirelessly can form a fully connected, trusted network. The network model that is used accounts for the geometric properties of the physical network boundaries, the statistical nature of the propagation environment, and the notion that both trustworthy and untrustworthy devices may occupy the network domain. Two local (pairwise) trust models are explored in the context of this model: proximity-based trust, where trust between two devices is a function of the distance between them, and experience-based trust, where trust is dependent upon the outcomes from prior inter-device interactions. Both models are probabilistic, a condition that is motivated by our interest in the steady state or average behaviour of the network as well as several practical applications, including sensor and device-to-device (D2D) networks for disaster relief, public safety, and peer-to-peer file sharing in 5G cellular systems. Our analysis illustrates a clear and simple mathematical relationship between the local trust probabilities and the underlying physics of the system, thus pointing to a need for trust protocols that are tailored to specific deployments.