Due to the mature of networks and communication technologies, electronic commerce is growing up rapidly and many advanced applications in electronic commerce are developed recently, such as on-line shopping, on-line bidding, and on-line gambling. There are numerous types of gambling like typical lottery, sport lottery, and poker gambling where our research will focus on the lottery games. Because of some special characteristics of the lottery games such as fairness and anonymity, it is hard to design a perfect electronic lottery protocol. The transaction mechanism in an electronic lottery protocol is an important issue since it will affect the benefits of customers if it is not fair or secure. The generating of random winning numbers in a lottery game has been discussed in many papers, but the fairness and anonymity for purchasing tickets and claiming the prizes are only discussed in few papers where these previous results cannot completely cope with the problems of fairness and anonymity. In the thesis, we will propose two electronic lottery protocols that can achieve the fairness and perfect anonymity simultaneously.