We propose a novel protocol for computing a circuit which implements the multi-party private set intersection functionality (PSI). Circuit-based approach has advantages over using custom protocols to achieve this task, since many applications of PSI do not require the computation of the intersection itself, but rather specific functional computations over the items in the intersection. Our protocol represents the pioneering circuit-based multi-party PSI protocol, which builds upon and optimizes the two-party SCS \cite{huang2012private} protocol. By using secure computation between two parties, our protocol sidesteps the complexities associated with multi-party interactions and demonstrates good scalability. In order to mitigate the high overhead associated with circuit-based constructions, we have further enhanced our protocol by utilizing simple hashing scheme and permutation-based hash functions. These tricks have enabled us to minimize circuit size by employing bucketing techniques while simultaneously attaining noteworthy reductions in both computation and communication expenses.

翻译：我们提出了一种新型协议，用于计算实现多方私有集合交集功能（PSI）的电路。基于电路的方法相比使用自定义协议完成此任务具有优势，因为许多PSI应用并不需要计算交集本身，而是需要针对交集中的元素进行特定的功能性计算。我们的协议代表了开创性的基于电路的多方PSI协议，它建立在两方SCS协议\cite{huang2012private}之上并进行了优化。通过采用两方之间的安全计算，我们的协议规避了与多方交互相关的复杂性，并展现出良好的可扩展性。为了减轻基于电路构造带来的高开销，我们进一步利用简单哈希方案和基于置换的哈希函数增强了协议。这些技巧使我们能够通过桶化技术最小化电路规模，同时在计算和通信开销方面实现显著降低。