Skefl: Single-Key Homomorphic Encryption for Secure Federated Learning

Abstract

Homomorphic encryption (HE) is widely adopted in untrusted environments such as federated learning. A notable limitation of conventional single-key HE schemes is the stringent security assumption regarding collusion between the parameter server and participating clients: Adversary clients are assumed not to collude with the server, as otherwise, the parameter could transmit the ciphertext of one client \(C_0\) to another client \(C_1\), who shares the same private key and could recover the local model of \(C_0\). One plausible solution to alleviate this strong assumption is multi-key HE schemes, which, unfortunately, prove impractically slow in production systems. In this work, we propose a new protocol that achieves the balance between security and performance: We extend single-key HE schemes with efficient secret sharing, ensuring that collusion between the parameter server and any compromised clients cannot reveal any local model. We term this protocol Skefl: Single-key homomorphic encryption for secure federated learning. The key idea behind Skefl is the secret-sharing of homomorphic \textit{ciphertexts} generated by multiple clients using the same pair of secret and public keys. We will substantiate the security claims of the proposed protocol using the well-known simulation framework in cryptography. Additionally, we will report on the practical performance of the Skefl protocol.