Achieving differentially private computations in decentralized settings poses significant challenges, particularly regarding accuracy, communication cost, and robustness against information leakage. While cryptographic solutions offer promise, they often suffer from high communication overhead or require centralization in the presence of network failures. Conversely, existing fully decentralized approaches typically rely on relaxed adversarial models or pairwise noise cancellation, the latter suffering from substantial accuracy degradation if parties unexpectedly disconnect. In this work, we propose IncA, a new protocol for fully decentralized mean estimation, a powerful primitive in data-intensive processing. Our protocol, which enforces differential privacy, requires no central orchestration and employs low-variance correlated noise, achieved by incrementally injecting sensitive information into the computation. First, we theoretically demonstrate that, when no parties permanently disconnect, our protocol achieves accuracy comparable to that of a centralized setting—already an improvement over most existing decentralized differentially private techniques. Second, we empirically show that our use of low-variance correlated noise significantly mitigates the accuracy loss experienced by existing techniques in the presence of dropouts.

Recent advances in recommender systems have shown that relying on graph filters, such as the normalized item-item adjacency matrix and the ideal low-pass filter yields competitive performance and scales better than Graph Convolutional Networks-based solutions. However, these solutions require centralizing user data, which raises concerns over data privacy, security, and the monopolization of user data by a few actors. To address those concerns, we propose PriviRec and PriviRec-k, two complementary recommendation frameworks. In PriviRec, we show that it is possible to decompose widely used filters so that they can be computed in a distributed setting using Secure Aggregation and a distributed version of the Randomized Power Method, without revealing individual users contributions. PriviRec-k extends this approach by having users securely aggregate low-rank projections of their contributions, enabling a tunable balance between communication overhead and recommendation accuracy. We demonstrate theoretically as well as experimentally on Gowalla, Yelp2018, and Amazon-Book that our methods achieve performance comparable to centralized state-of-the-art recommender systems and superior to decentralized ones, while preserving confidentiality and low communication and computational overheads.

The primary promise of decentralized learning is to allow users to engage in the training of machine learning models in a collaborative manner while keeping their data on their premises and without relying on any central entity. However, this paradigm necessitates the exchange of model parameters or gradients between peers. Such exchanges can be exploited to infer sensitive information about training data, which is achieved through privacy attacks (e.g., Membership Inference Attacks - MIA). In order to devise effective defense mechanisms, it is important to understand the factors that increase/reduce the vulnerability of a given decentralized learning architecture to MIA. In this study, we extensively explore the vulnerability to MIA of various decentralized learning architectures by varying the graph structure (e.g., number of neighbors), the graph dynamics, and the aggregation strategy, across diverse datasets and data distributions. Our key finding, which to the best of our knowledge we are the first to report, is that the vulnerability to MIA is heavily correlated to (i) the local model mixing strategy performed by each node upon reception of models from neighboring nodes and (ii) the global mixing properties of the communication graph. We illustrate these results experimentally using four datasets and by theoretically analyzing the mixing properties of various decentralized architectures. We also empirically show that enhancing mixing properties is highly beneficial when combined with other privacy-preserving techniques such as Differential Privacy. Our paper draws a set of lessons learned for devising decentralized learning systems that reduce by design the vulnerability to MIA.

In this paper we study verifiable sampling from probability distributions in the context of multi-party computation. This has various applications in randomized algorithms performed collaboratively by parties not trusting each other. One example is differentially private machine learning where noise should be drawn, typically from a Laplace or Gaussian distribution, and it is desirable that no party can bias this process. In particular, we propose algorithms to draw random numbers from uniform, Laplace, Gaussian and arbitrary probability distributions, and to verify honest execution of the protocols through zero-knowledge proofs. We propose protocols that result in one party knowing the drawn number and protocols that deliver the drawn random number as a shared secret.