VPAFL: Verifiable Privacy-Preserving Aggregation for Federated Learning Based on Single Server

Federated Learning (FL) has emerged as a promising distributed machine learning paradigm that enables multi-party collaborative training while eliminating the need for raw data sharing. However, its reliance on a server introduces critical security vulnerabilities: malicious servers can infer private information from received local model updates or deliberately manipulate aggregation results. Consequently, achieving verifiable aggregation without compromising client privacy remains a critical challenge. To address these problem, we propose a reversible data hiding in encrypted domains (RDHED) scheme, which designs joint secret message embedding and extraction mechanism. This approach enables clients to embed secret messages into ciphertext redundancy spaces generated during model encryption. During the server aggregation process, the embedded messages from all clients fuse within the ciphertext space to form a joint embedding message. Subsequently, clients can decrypt the aggregated results and extract this joint embedding message for verification purposes. Building upon this foundation, we integrate the proposed RDHED scheme with linear homomorphic hash and digital signatures to design a verifiable privacy-preserving aggregation protocol for single-server architectures (VPAFL). Theoretical proofs and experimental analyses show that VPAFL can effectively protect user privacy, achieve lightweight computational and communication overhead of users for verification, and present significant advantages with increasing model dimension.