彩票系統在全世界各個國家皆有運行，其中又以樂透彩券最為大家所熟知，藉由玩家選號並基於一定規則進行抽獎的遊戲方式，最早能夠溯源到西元13世紀，直至今日依舊盛行於世界各地。彩票系統的運作需要一筆龐大的資金做為信用保障以及獎金使用，使得彩票系統大多都由龐大的企業、金融業、政府所舉辦。這種系統被單一組織機構所掌控稱為中心式架構系統，在彩票系統這種需要公開規則、公開詳細資訊並講求公平性的博弈產業來說，中心式架構具有一定的風險存在；民眾無法對政府、龐大企業要求有效的稽核方法，確定遊戲過程沒有作弊行為。因此彩票系統憑藉著區塊鏈技術興起，在區塊鏈平台上建立了去中心化的彩票系統，其中又以公有區塊鏈「比特幣」 [1]、「以太坊」 [2]為主要開發平台。但是在公有區塊鏈上，每秒交易數量(TPS)因為共識決議程序，而被限定在一定數值之內，以「以太坊」為例，每秒交易數量約為每秒10筆交易，如此的限制將會影響彩票系統的使用人數，以台灣彩券 [3]每期、每三日約有200萬比投注來計算，將會佔據70% 以太坊區塊鏈頻寬，更不用說美國MegaMillions Lottery [4]每期、每三日約1000萬筆投注，將會使區塊鏈造成嚴重壅塞。
因此我們提出了基於以太坊區塊鏈智能合約，並搭配鏈下遊戲供應商的遊戲方式，能夠負荷超過千萬筆投注，且能進行遊戲資訊稽核、自動賠償機制卻只會占據約十萬分之一區塊鏈頻寬的彩票系統，達成更有效且可實踐的區塊鏈彩票系統。

The gambling system operates in various countries around the world, among which lottery tickets are the most well-known. The game method of lottery which is select numbers by player and following some special rules, it can be traced back to the 13th century AD as early as today and is still popular in the world now. The operation of the lottery system requires a large amount of funds for credit protection and bonus use, making the lottery system mostly organized by huge enterprises, financial industries, and governments. Such a system is called a centralized architecture system controlled by a single organization. In the lottery system, a game industry that requires open rules, detailed information, and fairness, the centralized architecture has certain risks; the public cannot require government or huge enterprises to provide an effective auditing methods to ensure that there is no cheating in the game. Therefore, with the rise of blockchain technology, the lottery system has established a decentralized lottery system on the blockchain platform. Among them, the public blockchains "Bitcoin" [1] and "Ethereum" [2] are the main ones. However, on the public blockchain, the number of transactions per second (TPS) is limited to a value due to the consensus resolution process. Taking Ethereum as an example, the number of transactions per second is about 10 transactions per second. The limit will affect the number of users of the lottery system. Based on the Taiwan lottery [3], there are about 2 million bets per period in three days, which will occupy 70% of the Ethereum blockchain bandwidth, not to mention the US MegaMillions. Lottery [4] about 10 million bets per period in three days, that will cause serious congestion on the blockchain.
Therefore, we propose a smart contract based on the Ethereum blockchain and a game method with an off-chain game provider, which can load more than 10 million bets, and can perform game information audit and automatic compensation mechanism, but only occupy about 1 in 100,000 blockchain bandwidth, that achieve a more effective and practical blockchain lottery system.

[1] S. Nakamoto, Bitcoin: A Peer-to-Peer Electronic Cash System, 2008.
[2] D. G. WOOD, ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER, 2014.
[3] “台灣彩券,” [線上]. Available: https://www.taiwanlottery.com.tw/.
[4] “Mega Millions,” [線上]. Available: https://www.megamillions.com/.
[5] Encyclopædia Britannica.
[6] ETtoday新聞雲, “樂透「億元頭獎」真有人中？　台彩主管爆：職業背景都假的！,” 2017. [線上]. Available: https://www.ettoday.net/news/20170424/910546.htm.
[7] “Blockchain,” [線上]. Available: https://en.wikipedia.org/wiki/Blockchain.
[8] V. Buterin, A Next-Generation Smart Contract and Decentralized Application Platform, 2017.
[9] Gwan-Hwan Hwang, Pei-Chun Tien, Yi-Hsiang Tang , Blockchain-based Automatic Indemnification Mechanism Based on Proof of Violation for Cloud Storage Services, ICBCT'20, 2020.
[10] Jiasheng Li ; Zijian Zhang ; Meng Li, BanFEL: A Blockchain Based Smart Contract for Fair and Efficient Lottery Scheme.
[11] “Euler–Lagrange equation,” [線上]. Available: https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation.
[12] “Quanta White Paper,” [線上]. Available: https://www.quantaplc.im/.
[13] “Transaction Positioned Merkle Tree,” [線上]. Available: https://itrustmachines.com/.
[14] Gwan-Hwan Hwang ; Wei-Sian Huang ; Jenn-Zjone Peng, Real-Time Proof of Violation for Cloud Storage, IEEE, 2014.
[15] M. Calderbank, The RSA Cryptosystem: History, Algorithm, Primes, 2007.
[16] P. K. C. f. t. F. S. I. American National Standard X9.62-2005, The Elliptic Curve Digital Signature Algorithm (ECDSA), 2005.
[17] “IPFS,” [線上]. Available: https://docs.ipfs.io/.
[18] “KRYO,” [線上]. Available: https://github.com/EsotericSoftware/kryo.
[19] E. B. Sasson et al., “Zerocash: Decentralized Anonymous Payments from Bitcoin,” IEEE Symposium on Security and Privacy, San Jose, CA, 2014.