A Byzantine Client Detection Method for Federated Learning Based on Encrypted Repeated Median Linear Regression

Federated learning is an emerging distributed machine learning technology that allows participants to jointly train machine learning models locally without the need for large-scale data transmission and sharing, thereby greatly improving data security. However, some Byzantine clients may intentionally tamper with local model parameter updates with the intention of manipulating the global model's update direction, which can lead to a decline in the overall performance of federated learning. Besides, existing Byzantine client detection research is conducted in plain text, which will lead to the leakage of private information. To solve the above issues, we propose a Byzantine client detection method for federated learning based on encrypted repeated median linear regression. Specifically, it combines the repeated median linear regression algorithm with homomorphic encryption, which can detect and eliminate clients with Byzantine behavior in the ciphertext state, ensuring the security and reliability of the parameters in the entire federated learning process. Additionally, we also designed an adaptive gradient clipping method based on historical iteration to clip the gradient to a reasonable range, which can not only reduce communication and computing overhead, but also improve the convergence speed and stability of the model. Experiments show that the proposed method can maintain high accuracy under the influence of malicious behavior of Byzantine clients.