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.

翻译：多密钥同态加密（MKHE）由Lopez-Alt等人（STOC 2012）提出，允许直接对使用不同密钥加密的密文执行算术运算。Chen和Dai等人（CCS 2019）以及Kim和Song等人（CCS 2023）的后续研究通过提出多密钥BFV/CKKS变体（称为CDKS方案）扩展了这一概念。这些变体采用渐近最优技术，以促进跨多个数据提供方的安全计算。本文发现，当CDKS方案应用于多方安全计算任务（如隐私保护联邦学习（PPFL））时，存在关键的安全漏洞。具体而言，我们证明CDKS可能无意中将一方的明文信息泄露给其他方。为缓解此问题，我们提出一种新方案SMHE（安全多密钥同态加密），该方案在多密钥BFV和CKKS框架中引入了一种新颖的掩蔽机制，以确保明文在整个计算过程中保持机密性。我们使用SMHE实现了一个PPFL应用，并证明其在同态评估中仅需适度开销即可显著提升安全性。例如，与基于CDKS的PPFL模型相比，我们基于多密钥CKKS的PPFL模型运行时和通信流量增加不到2倍。代码公开于https://github.com/JiahuiWu2022/SMHE.git。