Paper 2017/899

Kaleidoscope: An Efficient Poker Protocol with Payment Distribution and Penalty Enforcement

Bernardo David, Rafael Dowsley, and Mario Larangeira

Abstract

The research on secure poker protocols without trusted intermediaries has a long history that dates back to modern cryptography's infancy. Two main challenges towards bringing it into real-life are enforcing the distribution of the rewards, and penalizing misbehaving/aborting parties. Using recent advances on cryptocurrencies and blockchain technologies, Andrychowicz et al. (IEEE S\&P 2014 and FC 2014 BITCOIN Workshop) were able to address those problems. Improving on these results, Kumaresan et al. (CCS 2015) and Bentov et al. (ASIACRYPT 2017) proposed specific purpose poker protocols that made significant progress towards meeting the real-world deployment requirements. However, their protocols still lack either efficiency or a formal security proof in a strong model. Specifically, the work of Kumaresan et al. relies on Bitcoin and simple contracts, but is not very efficient as it needs numerous interactions with the cryptocurrency network as well as a lot of collateral. Bentov et al. achieve further improvements by using stateful contracts and off-chain execution: they show a solution based on general multiparty computation that has a security proof in a strong model, but is also not very efficient. Alternatively, it proposes to use tailor-made poker protocols as a building block to improve the efficiency. However, a security proof is unfortunately still missing for the latter case: the security properties the tailor-made protocol would need to meet were not even specified, let alone proven to be met by a given protocol. Our solution closes this undesirable gap as it concurrently: (1) enforces the rewards' distribution; (2) enforces penalties on misbehaving parties; (3) has efficiency comparable to the tailor-made protocols; (4) has a security proof in a simulation-based model of security. Combining techniques from the above works, from tailor-made poker protocols and from efficient zero-knowledge proofs for shuffles, and performing optimizations, we obtain a solution that satisfies all four desired criteria and does not incur a big burden on the blockchain.