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.

翻译：本文研究一个关键问题：如何在空中计算（AirComp）中实现完美隐私？该问题因一个两难困境而尤为引人入胜。实域运算可确保可逆性，但通常会引入统计依赖性，导致不可避免的隐私泄露。相比之下，模运算能使输出与原始消息去相关，但在非质数群（如实域）上应用时面临病态可逆性问题。这引出一个微妙而根本的疑问：完美隐私是否与空中计算本质上存在冲突？我们证明答案是否定的。通过精心利用实域运算与模运算之间的相互作用，完美隐私与精确计算实际上可以同时实现，从而达成完美私密聚合。