Differential Privacy and Prediction Uncertainty of Gossip Protocols in General Networks

Recent advances in social media and information technology have enabled much faster dissemination of information, while at the same time raise concerns about privacy leakage after various privacy breaches. Therefore, the privacy guarantees of information dissemination protocols have attracted increasing research interests, among which the gossip protocols assume vital importance in various information exchange applications. Very recently, the rigorous framework of differential privacy has been introduced to measure the privacy guarantees of gossip protocols in the simplified complete network scenario. In this work, we extend the study to general networks. First, lower bounds of the differential privacy guarantees are derived for the gossip protocols in general networks in both synchronous and asynchronous settings. The prediction uncertainty of the source node given a uniform prior is also determined. It is found that source anonymity is closely related to some key network structure parameters in the general network setting. Then, we investigate information spreading in wireless networks with unreliable communications, and quantity the tradeoff between differential privacy guarantees and information spreading efficiency. Finally, considering that the attacker may not be present in the beginning of the information dissemination process, the scenario of delayed monitoring is studied and the corresponding differential privacy guarantees are evaluated.