FMPC: Secure Multiparty Computation from Fourier Series and Parseval's Identity

TL;DR

FMPC introduces a secure multiparty computation protocol leveraging Fourier series and Parseval's identity, enabling multiplication of secrets with constant online latency and minimal communication, suitable for low-depth arithmetic circuits.

Contribution

It generalizes Parseval's identity for multiple inputs and presents a protocol that performs secret multiplication with no online communication, differing from traditional circuit garbling methods.

Findings

Supports secure multiplication with no online communication

Operates efficiently on low-depth arithmetic circuits

Uses offline preprocessing similar to SPDZ

Abstract

FMPC is a novel multiparty computation protocol of arithmetic circuits based on secret-sharing, capable of computing multiplication of secrets with no online communication; it thus enjoys constant online communication latency in the size of the circuit. FMPC is based on the application of Fourier series to Parseval's identity, and introduces the first generalization of Parseval's identity for Fourier series applicable to an arbitrary number of inputs. FMPC operates in a setting where users wish to compute a function over some secret inputs by submitting the computation to a set of nodes, but is only suitable for the evaluation of low-depth arithmetic circuits. FMPC relies on an offline phase consisting of traditional preprocessing as introduced by established protocols like SPDZ, and innovates on the online phase that mainly consists of each node locally evaluating specific functions. FMPC paves the way for a new kind of multiparty computation protocols capable of computing multiplication of secrets as an alternative to circuit garbling and the traditional algebra introduced by Donald Beaver in 1991.