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Privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union secretly, meaning that any information other than union is not revealed. We propose efficient PPMU protocols, using multiplicative homomorphic cryptosystem. The novelty of our protocol is to directly encrypt a polynomial by representing it by an element of an extension field. The resulting protocols consist of constant rounds and improve communicationdoi:10.4134/bkms.2013.50.6.1799 fatcat:mrni5fintbeijivd2wkqvowpoa