Well-known authentication mechanisms such as Public-key Infrastructure (PKI) and Identity-based Public-key Certificates (ID-PKC) are not suitable to integrate with the peer-to-peer (P2P) network environment. The reason is the difficulty in maintaining a centralized authority to manage the certificates. The authentication becomes even harder in an anonymous environment. We present three authentication protocols such that the users can authenticate themselves in an anonymous P2P network, without revealing their identities. Firstly, we propose a way to use existing ring signature schemes to obtain anonymous authentication. Secondly, we propose an anonymous authentication scheme utilizing secret sharing schemes. Finally, we propose a zero-knowledge-proof-based anonymous authentication protocol. We provide security justifications of the three protocols in terms of anonymity, completeness, soundness, resilience to impersonation attacks, and resilience to replay attacks. We hope our article will open up a useful topic for further research in the field of communication.