Perfectly Private Over-the-Air Computation

2026-04-30

AI Summary

This work investigates the simultaneous achievement of information-theoretic perfect privacy, high-accuracy aggregation, and invertibility in over-the-air computation (AirComp). Addressing the inherent tension between real-number invertibility and the decorrelation properties of modular arithmetic, the authors propose a hybrid mechanism that integrates real-valued linear encoding with modular operations. By co-designing signal representation and privacy-preserving perturbations, the framework eliminates statistical dependencies between the aggregated output and individual input messages while ensuring exact invertibility of the aggregation result. This approach establishes, for the first time, that perfect privacy and accurate AirComp can coexist, thereby overcoming fundamental theoretical limitations of existing methods.

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.

Problem

• perfect privacy
• over-the-air computation
• AirComp
• privacy leakage
• invertibility

Innovation

• Over-the-Air Computation
• Perfect Privacy
• Modulo Operation
• Real-Field Operation
• Private Aggregation