Designing an efficient and secure authentication technique to detect fraudulent behavior is a very important subject in mobile network systems. However, treating each transaction as a suspect seems to contradict the fact that most communication behaviors are honest. Based on this fact, it is reasonable to design a more efficient authentication protocol despite its loss of efficiency in dishonest communication situations. In such a way, an overall cost-effective solution can be obtained. In this paper, the BGSW protocol is redesigned under the concept and a cost-effective solution is shown. However, we have to emphasize that main purpose of this paper is not to improve the BGSW protocol, but to show the new idea that it is reasonable to design a more efficient authentication protocol despite its loss efficiency in dishonest communication situation.