Privacy amplification with social networks

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 mechanisms that utilise the graph topology of such a network, to increase the entropy of weak pre-shared secrets. Our proposal is based on using random walks to 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 such as Sybill sub-networks. © 2010 Springer-Verlag.