Efficient Byzantine-Robust Privacy-Preserving Federated Learning via Dimension Compression

Federated Learning (FL) allows collaborative model training across distributed clients without sharing raw data, thus preserving privacy. However, the system remains vulnerable to privacy leakage from gradient updates and Byzantine attacks from malicious clients. Existing solutions face a critical trade-off among privacy preservation, Byzantine robustness, and computational efficiency. We propose a novel scheme that effectively balances these competing objectives by integrating homomorphic encryption with dimension compression based on the Johnson-Lindenstrauss transformation. Our approach employs a dual-server architecture that enables secure Byzantine defense in the ciphertext domain while dramatically reducing computational overhead through gradient compression. The dimension compression technique preserves the geometric relationships necessary for Byzantine defence while reducing computation complexity from $O(dn)$ to $O(kn)$ cryptographic operations, where $k \ll d$. Extensive experiments across diverse datasets demonstrate that our approach maintains model accuracy comparable to non-private FL while effectively defending against Byzantine clients comprising up to $40\%$ of the network.