Private computation with shared randomness over broadcast channel

Abstract

In this paper we introduce a new model for private computation, the Shared Randomness over Broadcast Channel model (SRoBC for short). Following the classical model for private computation [2,4], we consider a set of n computationally unbounded honest but curious players P1,…, Pn with private inputs x1, x2,…, xn. The players wish to compute a function f of their inputs in a private way. Unlike in the classical model, no private channel is available to the players but all the communication takes place using a broadcast channel. Moreover, the only available source of randomness is a shared random string. We show that even in this minimal setting private computation is possible: we present a protocol for computing the sum modulo 2 in a t-private way in the SRoBC model. The protocol uses n(t+1)/2 random bits. We show that this is the optimal randomness complexity in the case each random bit is shared between two players (low-contention protocols). We further show that, in the case t = 1, this protocol is optimal with respect to the randomness complexity regardless of the contention of the protocol.