This novel methodology develops a Pseudo Trust in Peer-to-Peer networks using Lagrange Interpolation and Zero-Knowledge Protocol and creates a non-forgeable pseudonym. Authentication of a peer can be done without disclosing any sensitive information by using Zero-Knowledge Protocol. Each node in a peer maintains a unique I.D. It is not necessary to reveal the credential information at the time of verification. The implementation of distributed trust model is done incrementally in P2P networks. This proposed methodology generates different polynomials at the source and destination, respectively. After creating polynomials, authentication is performed using a challenge-based system (Zero-Knowledge Protocol) by exchanging pseudo-random numbers. Source and destination generate the same polynomial without exchanging any secret information. This polynomial can be used for encryption and decryption. The proposed algorithm is analysed by considering three parameters of network Throughput, the number of packets dropped and the number of packets delivered. These results measure the performance of the proposed algorithm applied in Peer-to-Peer networks over public networks.