Paper 2018/303

21 - Bringing Down the Complexity: Fast Composable Protocols for Card Games Without Secret State

Bernardo David, Rafael Dowsley, and Mario Larangeira

Abstract

While many cryptographic protocols for card games have been proposed, all of them focus on card games where players have some state that must be kept secret from each other, e.g. closed cards and bluffs in Poker. This scenario poses many interesting technical challenges, which are addressed with cryptographic tools that introduce significant computational and communication overheads (e.g. zero-knowledge proofs). In this paper, we consider the case of games that do not require any secret state to be maintained (e.g. Blackjack and Baccarat). Basically, in these games, cards are chosen at random and then publicly advertised, allowing for players to publicly announce their actions (before or after cards are known). We show that protocols for such games can be built from very lightweight primitives such as digital signatures and canonical random oracle commitments, yielding constructions that far outperform all known card game protocols in terms of communication, computational and round complexities. Moreover, in constructing highly efficient protocols, we introduce a new technique based on verifiable random functions for extending coin tossing, which is at the core of our constructions. Besides ensuring that the games are played correctly, our protocols support financial rewards and penalties enforcement, guaranteeing that winners receive their rewards and that cheaters get financially penalized. In order to do so, we build on blockchain-based techniques that leverage the power of stateful smart contracts to ensure fair protocol execution.