A private mutual authentication, or unlinkable secret handshake, originally allows two members from the same organisations to anonymously authenticate each other. In this paper, a new privacy-preserving mutual authentication protocol is constructed to achieve fuzzy private matching. The proposed protocol supports more flexible threshold-based appropriate matching under the multiple-groups environment, which is not limited to authenticate between members from the same groups. Our new protocol is constructed from the fuzzy identity-based encryption scheme and constant-size group signature. Without using the random oracle, the new protocol is proved secure by assuming the intractability of the decisional bilinear Diffie-Hellman problems. Compared with previous works, our proposed protocol can adapt to many different applications.