Zero-Collateral Lotteries in Bitcoin and Ethereum

TL;DR

This paper introduces cryptocurrency lottery protocols that eliminate collateral requirements, significantly reducing security deposit sizes and improving efficiency, with practical implementations on Ethereum and Bitcoin.

Contribution

The paper proposes novel zero-collateral lottery protocols based on tournament structures, reducing collateral needs from quadratic to logarithmic in the number of players.

Findings

Ethereum implementation is highly efficient.

Bitcoin implementation has exponential setup complexity.

A minimal Bitcoin protocol modification can remove exponential overhead.

Abstract

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 $O(N^2)$ 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 $O(\log N)$ 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 $O(2^N)$ 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.