Efficient Privacy-Preserving Federated Learning via Homomorphic Encryption-Enabled Over-the-Air Computation

Federated Learning (FL) enables collaborative model training across devices, but data exchanges pose privacy risks. Homomorphic Encryption (HE) is widely used to enhances privacy in FL but incurs significant communication and computation latency. Prior work reduced this latency using compressions, but sacrificed learning accuracy and overlooked the impact of the number of participating devices on latency. Over-the-air computation (AirComp) leverages wireless channels' superposition property to achieve high spectral efficiency and efficient aggregation irrespective of device number. In this paper, we propose HEAirFed, integrating AirComp with the state-ofthe-art HE scheme CKKS for efficient privacy-preserving FL. In HEAirFed, we develop a ciphertext-oriented wireless communication module to ensure homomorphic operations leverage AirComp's superposition property, enabling correct decryption. We further build a rigorous error analysis model, derive the worst-case upper bound of approximation error, and characterize this bound's impact on the convergence guarantee of HEAirFed, measured by the optimality gap with bounded approximation error. Then, we minimize this gap and derive a near-optimal solution in semi-closed form. Extensive experimental results on real-world datasets validate the ciphertext-oriented design's necessity, the error analysis's correctness, and demonstrate that HEAirFed achieves a substantial reduction in communication and aggregation latency compared to baseline, with minimal learning accuracy loss.