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Miller, A., Bentov, I..  2017.  Zero-Collateral Lotteries in Bitcoin and Ethereum. 2017 IEEE European Symposium on Security and Privacy Workshops (EuroS PW). :4–13.

We present cryptocurrency-based lottery protocols that do not require any collateral from the players. Previous protocols for this task required a security deposit that is O(N2) times larger than the bet amount, where N is the number of players. Our protocols are based on a tournament bracket construction, and require only O(logN) rounds. Our lottery protocols thus represent a significant improvement, both because they allow players with little money to participate, and because of the time value of money. The Ethereum-based implementation of our lottery is highly efficient. The Bitcoin implementation requires an O(2N) off-chain setup phase, which demonstrates that the expressive power of the scripting language can have important implications. We also describe a minimal modification to the Bitcoin protocol that would eliminate the exponential blowup.