Who started this rumor? Quantifying the natural differential privacy guarantees of gossip protocols
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Gossip protocols, also called rumor spreading or epidemic 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 one indeed start a gossip and safely hide in the crowd? This paper is the first to study gossip protocols using 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 sensors, we derive matching lower and upper bounds on the differential privacy parameters. Crucially, our results show that gossip protocols can naturally guarantee some privacy without the need for additional perturbations, and reveal that asynchronous protocols provide a different and stronger type of privacy guarantees than their synchronous counterparts. Furthermore, while the optimal privacy guarantees are attained at the cost of a drastic reduction of the dissemination speed, we show that one can devise gossip protocols achieving both fast spreading time and near-optimal privacy.
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