Secure Trick-Taking Game Protocols

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

“…Since such cheating is possible with a physical deck of cards, the classical cryptographic card game protocols do not prevent it. In [6], Bultel and Lafourcade introduce the secure trick-taking game protocols, which allows to detect when a player does not respect the rules of the game, without learning anything from its cards. Such protocols have the following properties: Unpredictability: the cards are dealt at random.…”

“…Hand and game privacy: players do not know the hidden cards of their adversaries at the beginning of the game, then at each step of the game, the protocol does not reveal anything else than the cards that have been played. Unfortunately, the security model from [6] cannot be applied to games in which not all cards are used by the players, because the challenger deduces the opponent's hand from the knowledge of the honest players' hands, which is not possible if cards are discarded. This excludes some very famous games, such as the well-known French Tarot, the Skat game, considered as the national card game of Germany, as well as one of the oldest trick-taking games, Triomphe, which dates back to the 15 th century and is at the origin of both the word trump and many other games, like Écarté and Euchre.…”

“…Furthermore, the card distribution mechanism of the protocol in [6] suffers from two drawbacks inherent to its design. In a nutshell, each player chooses a secret key sk and computes the corresponding public key pk for each of its cards.…”

“…At the end of this step, each generator/key pair is assigned a random card thanks to a random value the players need to agree on. The first issue is that this approach is highly dependent on the random oracle model, the second is that the shuffle proof proposed in [6] is not efficient since its complexity is in O(n 2 ) in the number of cards, which is 32, 54, 78 or even 104 cards depending on the game.…”

“…Contributions. In this paper, we first extend the security model from [6] to cover the French Tarot (see Section 4). French Tarot being the most complex of the games with Cards Set Aside, it is easy to simplify our model to adapt it to other games having this property.…”