Who started this rumor? Quantifying the natural differential privacy guarantees of gossip protocols

TL;DR

This paper rigorously analyzes gossip protocols using differential privacy to quantify how well they protect the source's identity, revealing a trade-off between privacy and dissemination speed and identifying parameters that optimize both.

Contribution

It introduces a mathematical framework for differential privacy in gossip protocols and identifies protocol parameters that balance privacy guarantees with rapid information spreading.

Findings

Standard push protocol lacks differential privacy in large graphs.

Muting parameter s=0 achieves optimal privacy but slows spreading.

Certain s values provide a good balance between privacy and speed.

Abstract

Gossip protocols are widely used to disseminate information in massive peer-to-peer networks. These protocols are often claimed to guarantee privacy because of the uncertainty they introduce on the node that started the dissemination. But is that claim really true? Can the source of a gossip safely hide in the crowd? This paper examines, for the first time, gossip protocols through a rigorous mathematical framework based on differential privacy to determine the extent to which the source of a gossip can be traceable. Considering the case of a complete graph in which a subset of the nodes are curious, we study a family of gossip protocols parameterized by a ``muting'' parameter $s$: nodes stop emitting after each communication with a fixed probability $1-s$. We first prove that the standard push protocol, corresponding to the case $s=1$, does not satisfy differential privacy for large graphs. In contrast, the protocol with $s=0$ achieves optimal privacy guarantees but at the cost of a drastic increase in the spreading time compared to standard push, revealing an interesting tension between privacy and spreading time. Yet, surprisingly, we show that some choices of the muting parameter $s$ lead to protocols that achieve an optimal order of magnitude in both privacy and speed. We also confirm empirically that, with appropriate choices of $s$, we indeed obtain protocols that are very robust against concrete source location attacks while spreading the information almost as fast as the standard (and non-private) push protocol.