The great thing about creating lotteries using cryptocurrencies is that there will be no need for any collateral from players participating in the lottery. Previous cryptocurrency lottery protocols needed a security deposit that is presentable via the formula
O(N2) the bet amount
where N represents the number of players.
The “N-player commitment lottery” protocol, which we will present throughout this article, will utilize the tournament bracket construction that requires only O(log N) rounds to be successfully completed. Consequently, this protocol represents great improvement, because it allows players to participate in the lottery with little amounts of money while omitting the need for collateral deposits.
The Outline of N-Player Commitment Lottery Protocol Using Bitcoin or Ethereum:
Let’s overview the outlines of the N-player commitment lottery protocol utilization via bitcoin or ethereum.
Security properties of the cryptocurrency lottery protocol:
Let’s propose a standard lottery environment comprising a set of N players, that can include “deceiving” players or others controlled by a specific adversary. The lottery protocol will rely on bitcoin’s or ethereum’s blockchains to keep track of the amount of cryptocurrencies in the lottery pot (for this example, the amount of cryptocurrency in the lottery pot will be denoted in Bitcoin B). The following security properties will be used in implementation of the N-party coin flip lottery protocol:
– Ideal setting: considering all parties are honest, then each will have a probability of 1 – 1/N to earn an amount of B(-1) and a probability of 1/N to earn an amount equal to B(N – 1).
– Completed successfully in finite time: If any of the participating players is honest, then the protocol will be successfully completed in some time window Tfinal , after which all rewards will be paid.
– Commit/abort decision: The protocol ensures that during a shorter time window Tcommit, the protocol will be “committed” or “aborted”. If the protocol “aborts”, then each honest player will immediately receive a payout of 0 as any paid money is repaid by Tcommit.
– Payoff is stochastically dominant: whenever the protocol is successfully committed, each player will receive a payoff of P’ , at the end of Tfinal , that is stochastically dominant to Pideal, Stochastic dominance guarantees a fair payoff to all lottery players.
– Minimal collateral: although the protocol is designed to constrain the payout available for each player, it may also require players to contribute additional upfront money (in the form of a collateral deposit), which would be paid back to honest parties.
2 Party Commitment Based Lottery:
Within the context of a 2 player commitment based lottery, the 2 players, A and B, will commit to 2 random values; a and b respectively. After registration of both players’ commitments, the commitments will be opened. The revealed values are formulated to determine a pseudorandom string, via XOR mod 2, so that if either player selects randomly a value, the output will be also random. The commitment is deployed via utilization of a hash function.
N Player Commitment Lottery Tournament:
The protocol will use a binary tree structure to transform a 2-player lottery into a lottery tournament with an unlimited number of players. Let’s assume that N number of players have participated in the lottery tournament. Along the tournament’s first level, each 2 players, e.g. player i and player i+1, will be pitted against each other with N/2 instances of the aforementioned 2 player lottery within settings called “matches”. Afterwards, the winners of each and every level of the tournament will be pitted against each other in pairs again. The process will continue on until the final level reaches a value of log2 N which will determine the final winner(s). The protocol will be secure against history reversal attacks because it will deploy the blockchain protocol, of either bitcoin or ethereum.
The following diagram shows an Ethereum lottery tournament built using a tournament tree.
Using cryptocurrency to create lotteries will not only promote zero collateral lottery tournaments, but will also provide secure platforms for lottery enthusiasts, especially after the recent hacking attacks that compromised tens of thousands of lottery accounts. More anonymity and security can be provided via combining the blockchain technology with darknet in building lottery tournaments.
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