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A Toolbox for Mental Card Games

Christian Schindelhauer

Published Jan 1, 1998• 2 citations
OpenAlex

Abstract

Mental card games are played without a trusted party and without cards. It is well known that the problem of mental card games can be solved in principle. But the schemes known so far are too messy to be used in practice. Only for the mental poker game a suitable solution is known [Cr'ep 87] that achieves security against player coalition and complete confidentiality of a player's strategy. Here, we present a general-purpose scheme that may be used as basic toolbox for straight-forward implementations of card games. We present a data structure for cards and decks that is secure against player coalitions and enables standard operations like picking up a card, opening it, and (re-)mixing stacks. Futhermore, we introduce tools for special operations like inserting a card into the deck, splitting the deck, parting the game. The correctness of all operations is testified by zeroknowledge proofs. Finally, we discuss security problems that are typical for mental card games and suggest solutio...

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Mental card games are played without a trusted party and without cards. It is well known that the problem of mental card games can be solved in principle. But the schemes known so far are too messy to be used in practice. Only for the mental poker game a suitable solution is known [Cr'ep 87] that achieves security against player coalition and complete confidentiality of a player's strategy. Here, we present a general-purpose scheme that may be used as basic toolbox for straight-forward implementations of card games. We present a data structure for cards and decks that is secure against player coalitions and enables standard operations like picking up a card, opening it, and (re-)mixing stacks. Futhermore, we introduce tools for special operations like inserting a card into the deck, splitting the deck, parting the game. The correctness of all operations is testified by zeroknowledge proofs. Finally, we discuss security problems that are typical for mental card games and suggest solutio...
Abstract: There are many wonderful protocols in cryptography which are still waiting for their realization. Here we consider efficient solutions for secure electronic card games. Our contribution seems to be the first known practical implementation that requires no trusted third-party and simultaneously keeps the players ’ strategies confidential. The provided open source library LibTMCG can be used for creating secure peer-to-peer games and furthermore for some unusual applications, e.g., secure multiparty computation or simple electronic voting schemes.
An efficient and secure mental poker scheme is proposed in this paper. It is based on multiple encryption and decryption of individual cards. The protocol satisfies all major security requirements of a real mental poker. It gets rid of the Card Salesman and guarantees minimal effect due to collusion of players. The protocol is secure and more efficient compared with other known protocols. The strategies of players can be kept confidential with the introduction of a Dealer. The protocol is suitable to be implemented in an on-line card game.
Abstract. In this paper, we present a fast and secure mental poker protocol. The basic structure is the same as Barnett & Smart's and Castellà-Roca's protocols but our encryption scheme is different. With this alternative encryption scheme, our shuffle is not only twice as fast, but it also has different security properties. As such, Barnett & Smart's and Castellà-Roca's security proof cannot be applied to our protocol directly. Nevertheless, our protocol is still provably secure under the DDH assumption. The only weak point of our protocol is that reshuffling a small subset of cards might take longer than Barnett & Smart's and Castellà-Roca's protocols. Therefore, our protocol is more suitable for card games such as bridge, most poker games, mahjong, hearts, or black jack, which do not require much partial reshuffling.
Abstract Card-based cryptography started with the “five-card trick” designed by Den Boer (EUROCRYPT 1989); it enables Alice and Bob to securely evaluate the AND value of their private bits using a physical deck of five cards. It was then shown that the same task can be done with only four cards, i.e., Mizuki et al. proposed a four-card AND protocol (ASIACRYPT 2012). These two AND protocols are simple and easy even for non-experts, such as high school students, to execute. Their only common drawback is the need to prepare a customized deck consisting of red and black cards such that all cards of the same color must be identical. Fortunately, several existing protocols are based on a standard deck of playing cards (commercially available). Among them, the state-of-the-art AND protocol was constructed by Koch et al. (ASIACRYPT 2019); it uses four playing cards (such as ‘A, J, Q, K’) to securely evaluate the AND value. The protocol is elaborate, while its possible drawback is the need to repeat a shuffling operation six times (in expectation), which makes it less practical. This paper aims to provide the first practical protocol working on a standard deck of playing cards. We present an extremely simple AND protocol that terminates after only one shuffle using only four cards; our proposed protocol relies on a new operation, called the “half-open” action, whereby players can check only the suit of a face-down card without revealing the number on it. We believe that this new operation is easy-to-implement, and hence, our four-card AND protocol working on a standard deck is practical. We formalize the half-open action to present a formal description of our proposed protocol. Moreover, we discuss what is theoretically implied by introducing the half-open action and show that it can be applied to efficiently solving Yao’s Millionaires’ problem with a standard deck of cards.
Online gambling allows users to participate in mental games and bet over the Internet. It can open new opportunities for casinos to make more money; however, at the same time, there are a lot of security challenges. In this paper, we describe our scheme for secure online gambling and secure mental poker protocols over the Internet based on our previous researches. Our scheme provides both the fairness of online gambling processes and secure linking of the online gambling with payment. A unique link between payments and gambling outcome is provided so that the winner can be ensured to get the payment. The gambling games are generic in our fair online gambling scheme. Mental poker is one of most popular games of online gambling. In this paper, efficient and secure mental poker protocols are provided. These mental poker protocols are based on multiple encryption and decryption of individual cards. These protocols satisfy all major security requirements of a real mental poker. The card salesman has been got rid of and the minimal effect due to collusion has been guaranteed. These protocols are more efficient compared with other known protocols. The strategies of players can be kept confidential with the introduction of a dealer. These mental poker protocols are suitable for implementation in an online card game.