Information theoretically secure multi party set intersection re-visited

We re-visit the problem of secure multiparty set intersection (MPSI) in information theoretic settings. In [15], Li et.al have proposed a protocol for MPSI with n =3t+1 parties, that provides information theoretic security, when t out of those n parties are corrupted by an active adversary having unbounded computing power. In [15], the authors have claimed that their protocol takes six rounds of communication and communicates 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 [15] is much more than what is claimed in [15]. We then propose a novel information theoretically secure protocol for MPSI with n ≥ 1, which significantly improves the "actual" round and communication complexity of the protocol of [15]. Our protocols employ several tools which are of independent interest. © 2009 Springer-Verlag Berlin Heidelberg.