Vupsi: Verifiable Unbalanced Private Set Intersection Based on Homomorphic Encryption

Abstract

Unbalanced private set intersection (UPSI), a cryptographic technique for securely computing set intersections in asymmetrical setups while preserving privacy, has been extensively studied. However, existing protocols often require clients with small sets to participate in computations, are highly interactive, and lack result verifiability. In this paper, we propose VuPSI, a verifiable unbalanced PSI scheme designed to overcome the limitations of existing protocols. VuPSI offloads the computational burden to the server, reducing client-side processing and simplifying the overall workflow. In addition, VuPSI incorporates an efficient zero-knowledge verification mechanism that allows clients to efficiently verify the correctness of intersection results with minimal computational overhead. This approach significantly improves the reliability of PSI outcomes. Our design implements a low-interaction protocol that ensures scalability and efficiency, especially for large-scale dynamic datasets. Experimental evaluations show that VuPSI is both efficient and practical. Specifically, VuPSI can process 1,024 client-side items and 1,000,000 server-side items within seconds using 32 threads, achieving 40×  the communication efficiency of comparable protocols such as DiPSI. Its lower computational overhead and faster data preprocessing make it well-suited for real-time, dynamic server environments.