VOLE-CPSI Meets Paillier Aggregation: Practical Private Intersection Cardinality with Linear-Scale Performance
Private set intersection (PSI) and its circuit variant (Circuit-PSI, CPSI) are core tools for privacy-preserving analytics. Unlike plain PSI that directly reveals intersecting elements, CPSI outputs secret shares of intersection indicators (and associated-value shares), which can be reused in subsequent MPC tasks without disclosing element-level membership. This paper presents a practical two-stage framework for secure intersection cardinality: we instantiate CPSI following VOLE-PSI, then compute |X ∩Y| via Paillier-based homomorphic aggregation over CPSI indicator shares. The contribution is primarily a systems-oriented composition and analysis of these building blocks, with element-level privacy preserved and only the final aggregate cardinality revealed to the receiver.We provide a complete protocol description, a correctness argument, a complexity analysis, and a semi-honest simulation-based security discussion. We further present an experimental evaluation covering protocol breakdown, scalability, and several clearly labeled derived/estimated scenario tables. The results show clear scaling up to 220-level set sizes and identify the main practical bottlenecks, including ciphertext expansion and communication-aware batching. Overall, the framework offers an implementable and extensible solution for privacy-preserving cardinality analytics in realistic two-party settings.