Electric commerce system based on distributed mobile on object such as mobile agents need both precise identification and secure authentication scheme on remotemobile entities. In this paper, existing discrete logarithm based Schnorr like entity authentication schemes are improved by the analysis of performance and security on the bi-directional interactive proofs. And ElGamal like schemes are also proposed. Then, there are enhanced with oblivious transfer based mono-directional authentication schemes based on trusted third party for applying to the mobile agent based computing systems. Therefore, proposed schemes provide compatible performance and safety on mobile entity authentication process.