Information Theoretically Secure Multi Party Set Intersection Re-visited

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Abstract

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 \({\cal O}(n^4m^2)\) 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 ≥ 3t + 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.