Fed-Cor: Federated Correlation Test with Secure Aggregation

In this paper, we propose the first federated correlation test framework compatible with secure aggregation, namely Fed-Cor. In Fed-Cor, correlation tests are recast as frequency moment estimation problems. To estimate the frequency moments, the clients collaboratively generate a shared projection matrix and then use stable projection to encode the local information in a compact vector. As such encodings can be linearly aggregated, secure aggregation can be applied to conceal the individual updates. We formally establish the security guarantee of Fed-Cor by proving that only the minimum necessary information (i.e., the correlation statistics) is revealed to the server. The evaluation results show that Fed-Cor achieves good accuracy with small client-side computation overhead and performs comparably to the centralized correlation test in several real-world case studies.