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

$f:\ V \rightarrow U$

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.