Secure Multi-party Computation of Differentially Private Median

In this work, we consider distributed private learning. For this purpose, companies collect statistics about telemetry, usage and frequent settings from their users without disclosing individual values. We focus on rank-based statistics, specifically, the median which is more robust to outliers than the mean. Local differential privacy, where each user shares locally perturbed data with an untrusted server, is often used in private learning but does not provide the same accuracy as the central model, where noise is applied only once by a trusted server. Existing solutions to compute the differentially private median provide good accuracy only for large amounts of users (local model), by using a trusted third party (central model), or for a very small data universe (secure multi-party computation). We present a multi-party computation to efficiently compute the exponential mechanism for the median, which also supports, e.g., general rank-based statistics (e.g., pth percentile, interquartile range) and convex optimizations for machine learning. Our approach is efficient (practical running time), scaleable (sublinear in the data universe size) and accurate, i.e., the absolute error is smaller than comparable methods and is independent of the number of users, hence, our protocols can be used even for a small number of users. In our experiments we were able to compute the differentially private median for 1 million users in 3 minutes using 3 semi-honest computation parties distributed over the Internet.