Title: FED-$\chi^2$: Secure Federated Correlation Test. Abstract: In this paper, we propose the first secure federated $\chi^2$-test protocol, FED-$\chi^2$. We recast $\chi^2$-test as a problem of the second moment estimation and use stable projection to encode the local information in a short vector. Due to the fact that such encodings can be aggregated with summation, secure aggregation can smoothly be applied to conceal the individual updates. We formally establish the security guarantee of FED-$\chi^2$ by demonstrating that the joint distribution is hidden in a subspace containing exponentially possible distributions. Our evaluation results show that FED-$\chi^2$ achieves good accuracy with small client-side computation overhead. FED-$\chi^2$ performs comparably to the centralized $\chi^2$-test in several real-world case studies. The code for evaluation is in the supplementary material.