Private Computation of Systematically Encoded Data with Colluding Servers

TL;DR

This paper introduces a private computation scheme that handles colluding servers, coded data, and non-linear functions, achieving optimal rates and extending previous PIR schemes to more complex data storage and function types.

Contribution

It presents a novel private computation scheme for colluding, coded data that supports arbitrary functions, including non-linear ones, and generalizes star-product PIR schemes.

Findings

Achieves PIR capacity for replicated data with collusion.

Explicitly computes rates for polynomial functions on encoded data.

Extends PIR schemes to non-linear functions and coded data scenarios.

Abstract

Private Computation (PC), recently introduced by Sun and Jafar, is a generalization of Private Information Retrieval (PIR) in which a user wishes to privately compute an arbitrary function of data stored across several servers. We construct a PC scheme which accounts for server collusion, coded data, and non-linear functions. For data replicated over several possibly colluding servers, our scheme computes arbitrary functions of the data with rate equal to the asymptotic capacity of PIR for this setup. For systematically encoded data stored over colluding servers, we privately compute arbitrary functions of the columns of the data matrix and calculate the rate explicitly for polynomial functions. The scheme is a generalization of previously studied star-product PIR schemes.