We study the problem of privacy-preserving computation of functions of data that belong to users in a social network under the assumption that users are willing to share their private data with trusted friends in the network. We demonstrate that such trust relationships can be exploited to significantly improve the trade-off between the privacy of users’ data and the accuracy of the computation. Under a one-hop trust model we design an algorithm for partitioning the users into circles of trust and develop a differentially private scheme for computing the global function using results of local computations within each circle. We quantify the improvement in the privacy--accuracy trade-off of our scheme with respect to other mechanisms that do not exploit inter-user trust. We verify the efficiency of our algorithm by implementing it on social networks with up to one million nodes. Applications of our method include surveys, elections, and recommendation systems.