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In this paper, we address the problem of multi-party privacy-preserving matching (PPM) over the encrypted data. We firstly construct an efficient identity-based re-encryption scheme like ElGmal (IBR-ElGmal) using combined public keys, which not only ensures the privacy of the information during the transmission process but also holds perfect multiplicative homomorphic property. Then we construct a multi-party identity-based symmetric privacy-preserving matching (M-IBSPM) protocol based on IBR-ElGmal scheme in cloud environments, which realizes the privacy-preserving matching among multiple different parties as well as getting the symmetric output. Furthermore, with our M-IBSPM protocol, most of the computation costs are taken over by cloud service provider without leaking any privacy, and our protocol achieves perfect security and privacy in the semi-honest model. Finally, we analyze the …