A Protocol for a Private Set-Operation

Rong-Hua Li, Chuan-Kun Wu

Abstract: A new private set-operation problem is proposed. Suppose there are n parties with each owning a secret set. Let one of them, say P, be the leader, S be P’s secret set, and t (less than n − 1) be a threshold value. For each element w of S, if w appears more than t times in the rest parties’ sets, then P learns which parties’ sets include w, otherwise P cannot know whether w appears in any party’s set. For this problem, a secure protocol is proposed in the semi-honest model based on semantically secure homomorphic encryption scheme, secure sharing scheme, and the polynomial representation of sets. The protocol only needs constant rounds of communication.