  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.
