Perfectly Private Over-the-Air Computation

TL;DR

This paper demonstrates that perfect privacy and accurate over-the-air computation can be simultaneously achieved by combining real-field and modulo operations, resolving a fundamental privacy-accuracy dilemma.

Contribution

It introduces a novel approach leveraging the interplay of real-field and modulo operations to attain perfect privacy in AirComp.

Findings

Perfect privacy does not conflict with accurate AirComp.

A method combining real-field and modulo operations enables private aggregation.

The approach achieves both privacy and accuracy simultaneously.

Abstract

This paper studies a key research question: how to achieve perfect privacy in over-the-air computation (AirComp)? The problem is particularly intriguing due to a dilemma. Real-field operations can ensure invertibility but generally introduce statistical dependence, resulting in inevitable privacy leakage. In contrast, modulo operations can decorrelate the output from the original message, but suffer from the ill-posed invertibility when applied over non-prime groups (e.g., the real field). This raises a subtle yet fundamental question: Does perfect privacy intrinsically conflict with AirComp? We show that the answer is no. By carefully leveraging the interplay between real-field and modulo operations, perfect privacy and accurate computation can, in fact, be achieved simultaneously, enabling perfectly private aggregation.