Imagine a group of citizens willing to collectively contribute their personal data for the common good to produce socially useful information, resulting from data analytics or machine learning computations. Sharing raw personal data with a centralized server performing the computation could raise concerns about privacy and a perceived risk of mass surveillance. Instead, citizens may trust each other and their own devices to engage into a decentralized computation to collaboratively produce an aggregate data release to be shared. In the context of secure computing nodes exchanging messages over secure channels at runtime, a key security issue is to protect against external attackers observing the traffic, whose dependence on data may reveal personal information. Existing solutions are designed for the cloud setting, with the goal of hiding all properties of the underlying dataset, and do not address the specific privacy and efficiency challenges that arise in the above context. In this paper, we define a general execution model to control the data-dependence of communications in user-side decentralized computations, in which differential privacy guarantees for communication patterns in global execution plans can be analyzed by combining guarantees obtained on local clusters of nodes. We propose a set of algorithms which allow to trade-off between privacy, utility and efficiency. Our formal privacy guarantees leverage and extend recent results on privacy amplification by shuffling. We illustrate the usefulness of our proposal on two representative examples of decentralized execution plans with data-dependent communications
