In this paper, we propose the first secure federated $chi^2$-test protocol Fed-$chi^2$. To minimize both the privacy leakage and the communication cost, we recast $chi^2$-test to the second moment estimation problem and thus can take advantage of stable projection to encode the local information in a short vector. As such encodings can be aggregated with only summation, secure aggregation can be naturally applied to hide the individual updates. We formally prove the security guarantee of Fed-$chi^2$ that the joint distribution is hidden in a subspace with exponential possible distributions. Our evaluation results show that Fed-$chi^2$ achieves negligible accuracy drops with small client-side computation overhead. In several real-world case studies, the performance of Fed-$chi^2$ is comparable to the centralized $chi^2$-test.
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