Information Theoretically Secure Multi Party Set Intersection Re-visited

We re-visit the problem of secure multiparty set intersection in information theoretic settings. In [16], Li et.al have proposed a protocol for multiparty set intersection problem with n parties, that provides information theoretic security, when t < n 3 parties are corrupted by an active adversary having unbounded computing power. In [16], the authors claimed that their protocol takes six rounds of communication and communicates O(nm) field elements, where each party has a set containing m field elements. However, we show that the round and communication complexity of the protocol in [16] is much more than what is claimed in [16]. We then propose a novel information theoretically secure protocol for multiparty set intersection with n > 3t, which significantly improves the ”actual” round and communication complexity (as shown in this paper) of the protocol given in [16]. To design our protocol, we use several tools which are of independent interest.