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Unlike gambling, lottery games can exist in a lawful form to raise funds for charitable institutions. Owing to the expeditious development of network technology, lotteries over the Internet have become an inevitable trend. Since the Internet allows people to communicate with each other without direct contact, it is more difficult to guarantee the security and fairness of online lotteries than for conventional lottery games. However, electronic lottery methods can also provide something that conventional lottery mechanisms cannot: they allow players to purchase tickets at any time and in any place where they can access the Internet. The authors propose an online lottery mechanism that can confirm the propositions of general lottery games. Specifically, this novel method not only allows players to make t-out-of-n numbers in lotteries without iterative selection but also preserves the privacy of players' choices, making the system more similar to traditional lottery games.