Preserving Data-Privacy with Added Noises: Optimal Estimation and Privacy Analysis

摘要

Networked system often relies on distributed algorithms to achieve a globalcomputation goal with iterative local information exchanges between neighbornodes. To preserve data privacy, a node may add a random noise to its originaldata for information exchange at each iteration. Nevertheless, a neighbor nodecan estimate other's original data based on the information it received. Theestimation accuracy and data privacy can be measured in terms of $(\epsilon,\delta)$-data-privacy, defined as the probability of $\epsilon$-accurateestimation (the difference of an estimation and the original data is within$\epsilon$) is no larger than $\delta$ (the disclosure probability). How tooptimize the estimation and analyze data privacy is a critical and open issue.In this paper, a theoretical framework is developed to investigate how tooptimize the estimation of neighbor's original data using the local informationreceived, named optimal distributed estimation. Then, we study the disclosureprobability under the optimal estimation for data privacy analysis. We furtherapply the developed framework to analyze the data privacy of theprivacy-preserving average consensus algorithm and identify the optimal noisesfor the algorithm.