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

Cross-silo federated learning (FL) enables multiple clients to collaboratively train a machine learning model without sharing training data, but privacy in FL remains a major challenge. Techniques using homomorphic encryption (HE) have been designed to solve this but bring their own challenges. Many techniques using single-key HE (SKHE) require clients to fully trust each other to prevent privacy disclosure between clients. However, fully trusted clients are hard to ensure in practice. Other techniques using multi-key HE (MKHE) aim to protect privacy from untrusted clients but lead to the disclosure of training results in public channels by untrusted third parties, e.g., the public cloud server. Besides, MKHE has higher computation and communication complexity compared with SKHE. We present a new FL protocol ESAFL that leverages a novel efficient and secure additively HE (ESHE) based on the hard problem of ring learning with errors. ESAFL can ensure the security of training data between untrusted clients and protect the training results against untrusted third parties. In addition, theoretical analyses present that ESAFL outperforms current techniques using MKHE in computation and communication, and intensive experiments show that ESAFL achieves approximate <inline-formula><tex-math notation="LaTeX">$204\times$</tex-math></inline-formula>−<inline-formula><tex-math notation="LaTeX">$953\times$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$11\times$</tex-math></inline-formula>−<inline-formula><tex-math notation="LaTeX">$14\times$</tex-math></inline-formula> training speedup while reducing the communication burden by <inline-formula><tex-math notation="LaTeX">$77\times$</tex-math></inline-formula>−<inline-formula><tex-math notation="LaTeX">$109\times$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$1.25\times$</tex-math></inline-formula>−<inline-formula><tex-math notation="LaTeX">$2\times$</tex-math></inline-formula> compared with the state-of-the-art FL models using SKHE.