Communication-Efficient Secure Federated Statistical Tests from Multiparty Homomorphic Encryption

The power and robustness of statistical tests are strongly tied to the amount of data available for testing. However, much of the collected data today is siloed amongst various data owners due to privacy concerns, thus limiting the utility of the collected data. While frameworks for secure multiparty computation enable functions to be securely evaluated on federated datasets, they depend on protocols over secret shared data, which result in high communication costs even in the semi-honest setting.In this paper, we present methods for securely evaluating statistical tests, specifically the Welch’s t-test and the χ2-test, in the semi-honest setting using multiparty homomorphic encryption (MHE). We tested and evaluated our methods against real world datasets and found that our method for computing the Welch’s t-test and χ2-test statistics required 100× less communication than equivalent protocols implemented using secure multiparty computation (SMPC), resulting in up to 10× improvement in runtime. Lastly, we designed and implemented a novel protocol to perform a table lookup from a secret shared index and use it to build a hybrid protocol that switches between MHE and SMPC representations in order to calculate the p-value of the statistics efficiently. This hybrid protocol is 1.5× faster than equivalent protocols implemented using SMPC alone.