Private Sample Alignment for Vertical Federated Learning: An Efficient and Reliable Realization

Sample alignment is recognized as a vital component of vertical federated learning, which facilitates the integration of differential samples and high-quality model training. In this trend, providing Private Sample Alignment (PSA) among multi-clients becomes naturally necessary for preventing unauthorized sample access and client privacy exposure. However, exiting PSA protocols mainly focus on two-party scenarios and cannot be directly adapted to the multi-client delegated computing scenarios required for vertical federated learning. Besides, these studies fail to address the need for protocol robustness in practical federated Learning network environments. Therefore, we aim to design an efficient and reliable PSA protocol in multi-client vertical federated learning. In this work, we present the first practical PSA protocol for vertical federated learning, allowing multi-clients to efficiently identify common samples without revealing additional information. Toward this direction, our PSA protocol first explores the Learning With Errors (LWE) problem to create a lightweight delegated Private Set Intersection (PSI) scheme, enabling efficient sample intersection among multiple clients. To achieve the reliability of the PSA protocol, we devise a multi-client vector aggregation algorithm that securely delegates the server to calculate the sample intersection. Building on this foundation, we develop an efficient Threshold-based Private Sample Alignment (T-PSA) protocol that allows multiple clients to determine the intersection of their input samples only if the intersection size surpasses a specific threshold. We implement a prototype and conduct a thorough security analysis. Comprehensive evaluation results confirm the efficiency and practicality of our design.