Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps

TL;DR

This paper introduces privacy-preserving verifiable computation schemes for polynomial evaluation and matrix multiplication using multilinear maps, enabling secure and private outsourcing of computations with proof verification.

Contribution

It develops novel VC schemes with input and function privacy based on multilinear maps, extending their application to private information retrieval.

Findings

Achieved input privacy for polynomial evaluation and matrix multiplication.

Extended schemes to also provide function privacy.

Applicable to private information retrieval (PIR) systems.

Abstract

{\em Verifiable computation} (VC) allows a computationally weak client to outsource the evaluation of a function on many inputs to a powerful but untrusted server. The client invests a large amount of off-line computation and gives an encoding of its function to the server. The server returns both an evaluation of the function on the client's input and a proof such that the client can verify the evaluation using substantially less effort than doing the evaluation on its own. We consider how to privately outsource computations using {\em privacy preserving} VC schemes whose executions reveal no information on the client's input or function to the server. We construct VC schemes with {\em input privacy} for univariate polynomial evaluation and matrix multiplication and then extend them such that the {\em function privacy} is also achieved. Our tool is the recently developed {mutilinear maps}. The proposed VC schemes can be used in outsourcing {private information retrieval (PIR)}.