Private Set Intersection (PSI) enables secure computation of set intersections while preserving participant privacy, standard PSI existing protocols remain vulnerable to data integrity attacks allowing malicious participants to extract additional intersection information or mislead other parties. In this paper, we propose the definition of data integrity in PSI and construct two authenticated PSI schemes by integrating Merkle Trees with state-of-the-art two-party volePSI and multi-party mPSI protocols. The resulting two-party authenticated PSI achieves communication complexity $\mathcal{O}(n \lambda+n \log n)$, aligning with the best-known unauthenticated PSI schemes, while the multi-party construction is $\mathcal{O}(n \kappa+n \log n)$ which introduces additional overhead due to Merkle tree inclusion proofs. Due to the incorporation of integrity verification, our authenticated schemes incur higher costs compared to state-of-the-art unauthenticated schemes. We also provide efficient implementations of our protocols and discuss potential improvements, including alternative authentication blocks.

翻译：私有集合交集（PSI）能够在保护参与者隐私的前提下安全计算集合交集，然而现有标准PSI协议仍面临数据完整性攻击的威胁，恶意参与者可能借此提取额外交集信息或误导其他参与方。本文提出了PSI中数据完整性的定义，并通过将Merkle树与最先进的两方volePSI协议及多方mPSI协议相结合，构建了两种认证PSI方案。所得的两方认证PSI方案实现了$\mathcal{O}(n \lambda+n \log n)$的通信复杂度，与当前最优的非认证PSI方案持平；而多方构造方案为$\mathcal{O}(n \kappa+n \log n)$，该方案因包含Merkle树的存在证明而引入了额外开销。由于完整性验证机制的引入，我们的认证方案相较于最先进的非认证方案产生了更高的成本。我们还提供了协议的高效实现，并讨论了包括替代认证模块在内的潜在改进方向。