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Privacy-preserving data mining has recently become an attractive research area, mainly due to its numerous applications. Within this area, privacy-preserving association rule mining has received considerable attention, and most algorithms proposed in the literature have focused on the case when the database to be mined is distributed, usually horizontally or vertically. In this paper, we focus on the case when the database is distributed vertically, and propose an efficient multi-party protocol for evaluating item-sets that preserves the privacy of the individual parties. The proposed protocol is algebraic and recursive in nature, and is based on a recently proposed two-party protocol for the same problem. It is not only shown to be much faster than similar protocols, but also more secure. We also present a variant of the protocol that is resistant to collusion among parties.