Paper 2023/309

Practical Construction for Secure Trick-Taking Games Even With Cards Set Aside

Abstract

Trick-taking games are traditional card games played all over the world. There are many such games, and most of them can be played online through dedicated applications, either for fun or for betting money. However, these games have an intrinsic drawback: each player plays its cards according to several secret constraints (unknown to the other players), and if a player does not respect these constraints, the other players will not realize it until much later in the game. In 2019, X. Bultel and P. Lafourcade proposed a cryptographic protocol for Spades in the random oracle model allowing peer-to-peer trick-taking games to be played securely without the possibility of cheating, even by playing a card that does not respect the secret constraints. However, to simulate card shuffling, this protocol requires a custom proof of shuffle with quadratic complexity in the number of cards, which makes the protocol inefficient in practice. In this paper, we improve their work in several ways. First, we extend their model to cover a broader range of games, such as those implying a set of cards set aside during the deal (for instance Triomphe or French Tarot). Then, we propose a new efficient construction for Spades in the standard model (without random oracles), where cards are represented by partially homomorphic ciphertexts. It can be instantiated by any standard generic proof of shuffle, which significantly improves the efficiency. We demonstrate the feasibility of our approach by giving an implementation of our protocol, and we compare the performances of the new shuffle protocol with the previous one. Finally, we give a similar protocol for French Tarot, with comparable efficiency.