Abstract

There are a number of scenarios where users wishing to communicate, share a weak secret. Often, they are also part of a common social network. Connections (edges) from the social network are represented as shared link keys between participants (vertices). We propose several mechanisms that utilise the graph topology of such a network, to increase the entropy of weak pre-shared secrets. Our proposals are based on using random walks to efficiently identify a chain of common acquaintances between Alice and Bob, each of which contribute entropy to the final key. Our mechanisms exploit one-wayness and convergence properties of Markovian random walks to, firstly, maximize the set of potential entropy contributors, and second, to resist any contribution from dubious sources by exploiting the community information characteristically present in real world network topologies.