Identity-based matchmaking encryption is a new cryptographic primitive that allows both the receiver and the sender to specify each other’s identity and communicate with each other only when the identities match. Meanwhile, it provides a non-interactive secret handshake protocol to get rid of real-time interaction and further improve participant privacy. This study proposes an identity-based matchmaking encryption (IB-ME) scheme in prime-order groups under symmetric external Diffie-Hellman (SXDH) assumption under the standard model. Realizing short parameters and reducing the matchmaking times during decryption are the most efficient identity-based matchmaking encryption scheme. Additionally, this study also puts forward the first inner product with equality matchmaking encryption (IPE-ME) scheme under the SXDH assumption in the standard model. Technically, it first constructs two schemes in composite-order groups, then simulates them with dual pairing vector space (DPVS) into prime-order groups, and further reduces the parameter size by decreasing the required dimension of dual basis. Finally, for the proposed IPE-ME scheme, this study replaces the equality policy in the first layer of an IB-ME scheme with inner-product policy.