Privacy concerns have been persistently afflicting individuals within online social networks (OSNs), rendering privacy-preserving communications over the Internet with authentication especially important. Unfortunately, the guarantees of privacy and authenticity are not always provided in OSNs. Individuals are still facing the challenges of being deceived or exploited. To mitigate these issues, anonymous social networks (ASNs) have emerged as a remedy for OSNs, facilitating individuals to connect with others anonymously and authentically. Despite the existence of numerous and remarkable cryptographic primitives, there are no formal solutions for ASNs except for matchmaking encryption (ME), since ME can simultaneously provide various key functionalities, i.e. bilateral access control, identity anonymity, and message authentication, to address the requirements of ASNs. In this paper, we design a system for ASNs by adopting fuzzy identity-based matchmaking encryption (fuzzy IB-ME), and the proposed scheme in this work is highly efficient. The scheme also realizes adaptive security in generic group model (GGM), which is generally adopted in pairing-based cryptography. The proposed ASNs system offers various advantages compared to the previous solutions, including 1) bilateral access control, 2) enhanced security, 3) high scalability, and 4) high efficiency. In addition to theoretical evaluations, we conduct extensive experiments to evaluate our scheme’s computational and storage efficiency. These evaluations indicate that our solution outperforms previous solutions and as well as preserves many desired functionalities.