Computing in Social Networks

This paper defines the problem of Scalable Secure Computing in a Social network: we call it the S-3 problem. In short, nodes, directly reflecting on associated users, need to compute a function f : V -> U of their inputs in a set of constant size, in a scalable and secure way. Scalability means that the message and computational complexity of the distributed computation is at most O(root n . polylog n). Security encompasses (1) accuracy and (2) privacy: accuracy holds when the distance from the output to the ideal result is negligible with respect to the maximum distance between any two possible results; privacy is characterized by how the information disclosed by the computation helps faulty nodes infer inputs of non-faulty nodes.