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

Jiahui Wu, Tiecheng Sun, Fucai Luo, Haiyan Wang, Weizhe Zhang

TL;DR

This paper identifies a critical security vulnerability in the CDKS scheme when applied to multiparty secure computation tasks, such as privacy-preserving federated learning (PPFL), and proposes 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.

Abstract

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.

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

TL;DR

This paper identifies a critical security vulnerability in the CDKS scheme when applied to multiparty secure computation tasks, such as privacy-preserving federated learning (PPFL), and proposes 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.

Abstract

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.

Paper Structure

This paper contains 26 sections, 2 theorems, 34 equations, 4 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Challenges and Contributions
  3. Related Work
  4. Preliminaries
  5. Ring Learning with Errors
  6. Multi-Key Homomorphic Encryption
  7. Gadget Decomposition
  8. Overview of Prior Work
  9. Foundational Construction of CDKS
  10. Security Vulnerability of CDKS
  11. New Multi-Key Variants of CKKS and BFV
  12. A Masking Scheme for CKKS and BFV
  13. SMHE Construction
  14. Security of SMHE
  15. Correctness of Homomorphic Evaluation
  16. ...and 11 more sections

Key Result

Theorem 1

Under the RLWE assumption and the semantic security of CKKS and the masking mechanism in Section ssec:maskingScheme, the SMHE-based PPFL protocol securely realizes $\mathcal{F}_{\mathsf{Agg}}$ in the semi-honest model: for any PPT adversary $\mathcal{A}$ corrupting $\mathcal{S}$ and any subset $\mat

Figures (4)

  • Figure 1: FL system model.
  • Figure 2: High-level overview of privacy-preserving federated learning.
  • Figure 3: Runtime breakdown comparison of PPFL models using different HEs , where "idle" denotes the duration during which the clients/server remain inactive while waiting for other parties to complete their operations. For CDKS and THE, "train&enc" represents the time spent on local model training and encryption. For MKGSW and SMHE, this stage additionally includes the time for masking generation.
  • Figure 4: Comparison of final model accuracy under different client elimination rates using SMHE/CDKS/THE scheme, where the models are all trained for $10,000$ iterations.

Theorems & Definitions (11)

  • Definition 1: Correctness
  • Definition 2: Simulation-Based Security
  • Definition 3: Gadget Decomposition
  • Definition 4: Gadget Encryption
  • Definition 5: External Product
  • Definition 6: Simulation-based security target
  • Theorem 1: One-round PPFL security, semi-honest
  • proof : Proof sketch with hybrids
  • Corollary 1: Server + subset collusion
  • Remark 1: On inference from functionality leakage
  • ...and 1 more