In our modern information society, many subjects related to computer networks are studies. The electronic bidding system based on cryptology is one of such subjects. In this study, we focus upon the bidding system used in the internet electronically. The electronic bidding system compared to the older version is time consuming and cost efficient in the process of bidding. However, there are many issues, that connected with the safety and the equality, to be resolved before the system can be applied in practice. Therefore, in this paper, we consider with the problems and requirements of the electronic bidding system and analyze the conventional electronic bidding systems based on the requirements. Also we propose the new secure efficient electronic bidding system that satisfies all requirments.