Achievable Rate of Private Function Retrieval from MDS Coded Databases

TL;DR

This paper introduces an optimal scheme for private function retrieval in distributed MDS coded databases, achieving the theoretical capacity and ensuring privacy of the linear combination coefficients.

Contribution

It proposes a new achievable scheme for MDS coded private function retrieval that matches the known capacity, advancing privacy-preserving data retrieval methods.

Findings

Achieves the capacity for MDS coded private function retrieval.

Provides a scheme that is tight in some special cases.

Ensures no information about the linear coefficients is leaked.

Abstract

We study the problem of private function retrieval (PFR) in a distributed storage system. In PFR the user wishes to retrieve a linear combination of $M$ messages stored in non-colluding $(N,K)$ MDS coded databases while revealing no information about the coefficients of the intended linear combination to any of the individual databases. We present an achievable scheme for MDS coded PFR with a rate that matches the capacity for coded private information retrieval derived recently, $R=(1+R_c+R_c^2+\dots+R_c^{M-1})^{-1}=\frac{1-R_c}{1-R_c^M}$, where $R_c=\frac{K}{N}$ is the rate of the MDS code. This achievable rate is tight in some special cases.