Abstract: In the paper,a four round interactive protocol of the random self reducibility is constructed,which doesn’t rely on any complex assumption or any power of prover.The protocol is applied in wider areas including quadratic residues,discrete logarithms and graph isomorphism and is optimal with the round complexity.The protocol satisfies some properties of the knowlege and the language membership interactive proof systems such as the completeness and the perfect zero knowledge,but does not satisfy the soundness.A new definition of soundness is given,and the definition is reasonable in practice.The protocol is practically sound,which can be used to a cryptographic identification scheme.