Computing in Social Networks

Abstract

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 $f:\ V \rightarrow U$ 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 $\mathcal{O}(\sqrt{n}\cdot {\rm polylog}{n})$. 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 ³-computes a class of aggregation functions, that is that can be expressed as a commutative monoid operation on U: f(x ₁,...,x _n) = x ₁ ⊕ ... ⊕ x _n, assuming the number of faulty participants is at most $\sqrt{n}/{\rm log}^2n$. 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.