Abstract: The Zero-Knowledge Proof(ZKP)is a powerful tool which can be used and already be used for many cryptographic applications and ECommerce. But all existing Zero-Knowledge Proofs are iterative in nature, it increases the communication traffic of in interactive bilateral, and makes difficult in practice．This thesis proposes a new ZKP protocol which runs in oneround while ensure the completeness property， and the soundness property, and decreases the communication traffic in the maximum extent. The scheme is based on the Paillier Cryptosystem， and ascribes security to it. 

Key words: zero knowledge proofs, Carmiehael theory, Paillier cryptosystem, one-round ZKP protocol