A Protocol for a Private Set-Operation

A new private set-operation problem is proposed. Suppose there are nparties with each owning a secret set. Let one of them, say P, be theleader, S be P's secret set, and t (less than n-1) be athreshold value. For each element w of S, if w appears morethan t times in the rest parties' sets, then P learns whichparties' sets include w, otherwise P cannot know whether wappears in any party's set. For this problem, a secure protocol isproposed in the semi-honest model based on semantically securehomomorphic encryption scheme, secure sharing scheme, and thepolynomial representation of sets. The protocol only needsconstant rounds of communication.