Local Differential Privacy with Correlated Noise Achieves Central-DP Optimal Cost

2026-05-28

AI Summary

This work addresses the fundamental challenge of achieving efficient and highly accurate estimation of the sum of user data under local differential privacy (LDP) in the honest-but-curious server model. The authors propose a novel correlated noise mechanism that, within a pure LDP framework, injects carefully designed correlated noise at the user side and leverages a distributed summation protocol to enable privacy-preserving computation. This approach is the first to demonstrate that LDP with correlated noise can attain estimation error arbitrarily close to the theoretical lower bound achievable in the centralized differential privacy setting. By doing so, it overcomes the well-known utility limitations of traditional LDP mechanisms that rely on independent noise, achieving near-optimal accuracy with only an arbitrarily small, tunable gap from the centralized lower bound.

Abstract

We study privately estimating the sum of $n$ user-held values in the presence of an honest-but-curious server. This motivates requiring privacy not only at data release but also throughout server-side computation. We therefore adopt the local (pure) differential privacy model, in which each user transmits a noise-perturbed value. It is well known that independent local noise typically incurs a substantial utility loss compared to the centralized model, where noise is added only after aggregation. We show that this gap is not fundamental. By carefully designing correlations among the locally added noise variables, we construct $\varepsilon$-DP mechanisms whose estimation cost matches the optimal cost achievable in the centralized setting, up to an arbitrarily small error.

Problem

• Local Differential Privacy
• Correlated Noise
• Private Sum Estimation
• Utility Loss
• Centralized Differential Privacy

Innovation

• Local Differential Privacy
• Correlated Noise
• Optimal Estimation Cost
• Sum Estimation
• Privacy-Utility Tradeoff