Accessibility of covariance information creates vulnerability in Federated Learning frameworks

Federated Learning approaches are becoming increasingly relevant in various fields. These approaches promise to facilitate an integrative data analysis without sharing the data, which is highly beneficial for applications with sensitive data such as healthcare. Yet, the risk of data leakage caused by malicious attacks needs to be assessed carefully. In this study, we consider a new attack route and present an algorithm that depends on being able to compute sample means, sample covariances, and construct known linearly independent vectors on the data owner side. We show that these basic functionalities, available in several established Federated Learning frameworks, suffice to reconstruct privacy-protected data. Moreover, the attack algorithm is robust to defence strategies that build on random noise. We demonstrate this limitation of existing frameworks and discuss possible defence strategies. The novel insights will facilitate the improvement of Federated Learning frameworks.