Secure Multi-Key Homomorphic Encryption with Application to Privacy-Preserving Federated Learning

Multi-Key Homomorphic Encryption (MKHE), proposed by Lopez-Alt et al. (STOC 2012), allows for performing arithmetic computations directly on ciphertexts encrypted under distinct keys. Subsequent works by Chen and Dai et al. (CCS 2019) and Kim and Song et al. (CCS 2023) extended this concept by proposing multi-key BFV/CKKS variants, referred to as the CDKS scheme. These variants incorporate asymptotically optimal techniques to facilitate secure computation across multiple data providers. In this paper, we identify a critical security vulnerability in the CDKS scheme when applied to multiparty secure computation tasks, such as privacy-preserving federated learning (PPFL). In particular, we show that CDKS may inadvertently leak plaintext information from one party to others. To mitigate this issue, we propose a new scheme, SMHE (Secure Multi-Key Homomorphic Encryption), which incorporates a novel masking mechanism into the multi-key BFV and CKKS frameworks to ensure that plaintexts remain confidential throughout the computation. We implement a PPFL application using SMHE and demonstrate that it provides significantly improved security with only a modest overhead in homomorphic evaluation. For instance, our PPFL model based on multi-key CKKS incurs less than a 2\times runtime and communication traffic increase compared to the CDKS-based PPFL model. The code is publicly available at https://github.com/JiahuiWu2022/SMHE.git.