Privacy preserving authentication has become one of the most important needs in the contemporary digital systems where the verification of identity should be done without disclosing any sensitive information about the user. This paper describes a zero-knowledge-proof (ZKP)-authentication system that can achieve secure and anonymous verification of user identity. The presented model mathematically states the authentication problem in terms of cryptographic relations and builds the statements of proofs with a witness representation that is efficient. A lightweight protocol that incorporates ZKP in the authentication process is developed, which includes key-generation mechanisms, credential issuance mechanisms, and non-interactive proof verification mechanisms. Performance analysis proves that it has low overhead in communication, high efficiency in verification and high replay and impersonation resistance. Compared to traditional authentication schemes, the framework compares well in terms of privacy assurance and performance, which is why it is applicable to distributed and resource-limited environment.