Summary
Federated learning is a method where many computers work together to train AI without sharing their private data. To protect privacy, a technique called Secure Aggregation combines information so individual data stays hidden. The authors show that when this method is used in decentralized settings with limited connections, some participants can gather enough clues to uncover others’ private updates. They developed a mathematical attack that uses tools from cryptography to recover hidden data from these partial views. This means that just using Secure Aggregation is not always enough to keep data private in decentralized learning setups.
Federated LearningSecure AggregationDecentralized networksPrivacy attackLattice-based cryptographyHidden Subset Sum ProblemModel updateSparse topologyReconstruction attackSemi-honest nodes
Authors
Wenrui Yu, Changlong Ji, Johannes Bjerva, Qiongxiu Li
Abstract
Secure Aggregation (SA) is widely regarded as a strong defense against model-update leakage in Federated Learning (FL), as it reveals only aggregate results while hiding individual updates. In Decentralized Federated Learning (DFL), SA is commonly instantiated as local neighborhood aggregation, where each node obtains a weighted aggregate over its neighbors. We show that this locality creates a structural leakage surface: sparse decentralized topologies provide colluding semi-honest nodes with asymmetric aggregate views, exposing multiple hidden linear combinations of honest participants' private states. Reconstructing private states from these aggregate views is fundamentally challenging, as both the private states and the aggregation coefficients are hidden. We tackle this challenge by establishing a formal connection to the Hidden Subset Sum Problem, a long-studied problem in cryptography. Building on this formulation, we design a lattice-based reconstruction approach that combines lattice reduction with structural filtering to reconstruct protected model states. We evaluate our attack on image, tabular, and text tasks under sparse DFL topologies. Our results show that colluding semi-honest nodes can recover the original local updates of honest nodes, enabling downstream reconstruction of private training data. These findings demonstrate that SA alone does not guarantee privacy in DFL when local aggregation induces asymmetric observations.