Private Sum Computation: Trade-Offs between Communication, Randomness, and Privacy

TL;DR

This paper investigates the trade-offs between communication, randomness, and privacy in distributed sum computation, establishing fundamental limits and linking it to secret sharing for privacy guarantees.

Contribution

It characterizes the minimal communication and randomness needed for private sum computation and connects it to secret sharing techniques.

Findings

Minimum communication bounds are established.

Minimum randomness requirements are characterized.

Secret sharing is necessary for local randomness generation.

Abstract

Consider multiple users and a fusion center. Each user possesses a sequence of bits and can communicate with the fusion center through a one-way public channel. The fusion center's task is to compute the sum of all the sequences under the privacy requirement that a set of colluding users, along with the fusion center, cannot gain more than a predetermined amount $\delta$ of information, measured through mutual information, about the sequences of other users. Our first contribution is to characterize the minimum amount of necessary communication between the users and the fusion center, as well as the minimum amount of necessary randomness at the users. Our second contribution is to establish a connection between private sum computation and secret sharing by showing that secret sharing is necessary to generate the local randomness needed for private sum computation, and prove that it holds true for any $\delta \geq 0$.