Computing in Social Networks

This paper defines the problem of Scalable Secure Computing in a Social network: we call it the S 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(√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. We present AG-S3, a protocol that S-computes a class of aggregation functions, that is that can be expressed as a commutative monoid operation on U : f(x1, . . . , xn) = x1 ⊕ · · · ⊕ xn, assuming the number of faulty participants is at most √ n/ log n. Key to our protocol is a dedicated overlay structure that enables secret sharing and distributed verifications which leverage the social aspect of the network: nodes care about their reputation and do not want to be tagged as misbehaving.