Differentially Private Aggregation Of Distributed Time-series With Transformation And Encryption

Abstract

We propose the first differentially private aggregation algorithm for distributed time-series data that offers good practical utility without any trusted server. This addresses two important challenges in participatory data-mining applications where (i) individual users collect temporally correlated time-series data (such as location traces, web history, personal health data), and (ii) an untrusted third-party aggregator wishes to run aggregate queries on the data. To ensure differential privacy for time-series data despite the presence of temporal correlation, we propose the Fourier Perturbation Algorithm (FPA<i>_k</i>). Standard differential privacy techniques perform poorly for time-series data. To answer <i>n</i> queries, such techniques can result in a noise of Θ(<i>n</i>) to each query answer, making the answers practically useless if <i>n</i> is large. Our FPA<i>_k</i> algorithm perturbs the Discrete Fourier Transform of the query answers. For answering <i>n</i> queries, FPA<i>_k</i> improves the expected error from Θ(<i>n</i>) to roughly Θ(<i>k</i>) where <i>k</i> is the number of Fourier coefficients that can (approximately) reconstruct all the <i>n</i> query answers. Our experiments show that <i>k</i> << <i>n</i> for many real-life data-sets resulting in a huge error-improvement for FPA<i>_k</i>. To deal with the absence of a trusted central server, we propose the Distributed Laplace Perturbation Algorithm (DLPA) to add noise in a distributed way in order to guarantee differential privacy. To the best of our knowledge, DLPA is the first distributed differentially private algorithm that can scale with a large number of users: DLPA outperforms the only other distributed solution for differential privacy proposed so far, by reducing the computational load per user from <i>O</i>(<i>U</i>) to <i>O</i>(1) where <i>U</i> is the number of users.