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Cross-silo federated learning (FL) enables multiple clients tocollaboratively train a machine learning model without sharing training data,but privacy in FL remains a major challenge. Techniques using homomorphicencryption (HE) have been designed to solve this but bring their ownchallenges. Many techniques using single-key HE (SKHE) require clients to fullytrust each other to prevent privacy disclosure between clients. However, fullytrusted clients are hard to ensure in practice. Other techniques usingmulti-key HE (MKHE) aim to protect privacy from untrusted clients but lead tothe disclosure of training results in public channels by untrusted thirdparties, e.g., the public cloud server. Besides, MKHE has higher computationand communication complexity compared with SKHE. We present a new FL protocolESAFL that leverages a novel efficient and secure additively HE (ESHE) based onthe hard problem of ring learning with errors. ESAFL can ensure the security oftraining data between untrusted clients and protect the training resultsagainst untrusted third parties. In addition, theoretical analyses present thatESAFL outperforms current techniques using MKHE in computation andcommunication, and intensive experiments show that ESAFL achieves approximate204 times-953 times and 11 times-14 times training speedup while reducing thecommunication burden by 77 times-109 times and 1.25 times-2 times compared withthe state-of-the-art FL models using SKHE.

ESAFL: Efficient Secure Additively Homomorphic Encryption for Cross-Silo Federated Learning