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 << 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. Our approach also demonstrates substantial improvements in computational and communication efficiency. Experimental evaluation shows that the dimension compression technique achieves 25× ~ 35× reduction in computational overhead and 17× reduction in communication overhead compared to our non-compression version. When compared to state-of-the-art methods like ShieldFL [1], our approach demonstrates order-of-magnitude improvements in both computational and communication efficiency while maintaining equivalent privacy guarantees and achieving superior Byzantine robustness comparable to FLTrust [2]. These substantial efficiency enhancements make secure FL practical for deployment in large-scale neural networks with millions of parameters.