This document proposes an Identity-Based Private Matching (IBPM) scheme that enables private matching operations on outsourced encrypted datasets in identity-based cryptosystems. The IBPM scheme allows a privileged cloud server to perform matching without leaking private data through rigorous security proofs. Analysis shows the IBPM scheme has linear complexity to the dataset size and is more efficient than existing works. The IBPM scheme can also build efficient identity-based fuzzy private matching and multi-keyword fuzzy search schemes.