A Secure and Efficient Federated Learning Scheme Based on Homomorphic Encryption and Secret Sharing
Caimei Wang, Zhipeng Sun, Jianhao Lu · 2024
Federated Learning (FL) is a decentralized machine learning framework that enables collaborative model building without exposing client data. However, FL faces the risk of client data leakage. Homomorphic Encryption (HE) is a solution, providing ciphertext computability to safeguard client data in FL. Existing HE-based FL research primarily focuses on achieving secure training under semi-honest models. Nevertheless, there are two problems in combining the practical application of secret sharing: Client provides wrong subkey, which may cause decryption error and training failure. The computational overhead of HE is high, leading to inefficient training. To address these, we propose a secure and efficient FL scheme (SEAFL). Firstly, we propose a Fingerprint-based Subkey Verification Algorithm (FKM) to generate unique fingerprints for each subkey. This allows clients to authenticate subkeys, preventing decryption errors and training failures caused by malicious client attacks. Secondly, we design a Gradient Protection Scheme that combines an elliptic curve encryption algorithm with preprocessing (SM2-GPM). In the preprocessing phase, a mapping table is constructed by mapping plaintext space values to points on an elliptic curve. When encrypting gradients, the complexity of point operations on elliptic curves is used to achieve higher security levels with shorter keys and reduce encryption overhead. Decryption of gradients is expedited through a comparison of ciphertext with the mapping table. The experimental demonstrates a significant 45 times reduction in training time compared to existing schemes.