Poker Protocols

Abstract

The situation is quite serious. After four years of research, there has been no satisfactory way for a group of card sharks to play poker over the phone. Until now. In this paper, we present a new method for playing 'mental poker,' discuss its significance, and mention some of the further questions it r a b s. Ante up. The rules for mental poker are just like regular poker, except that players communicate over the phone, and there are no physical cards. The hard part of mental poker is dealing the cards. Hands must be random and disjoint, and players should not be able to claim to have any cards but those dealt (a sleeve will hold as many 'virtual cards' as angels will fit on the head of a pin). Playing mental poker is a difficult problem for a number of reasons. The foremost reason is that it is impossible, a result due to Shamir, Rivest and Adleman.['l Of course, this is an information-theoretic result, and the same reference presents a method for playing mental poker that relies on the difficulty of inverting certain cryptographic transformations. Unfortunately, a cryptographic flaw allows players to determine the color of each other's cards.['] This set the stage for a new implementation devised by Goldwasser and Micali, which was proven to hide all partial information (up to an explicit cryptographic assumption) ,[31 Unfortunately, this implementation works only for two players, which is a very restricted kind of poker. Next, Barany and Furedi devised a protocol that permits three or more players to play poker,[41 but only if players are not permitted to form coalitions. If two players conspire, they can learn the contents of everyone else's hands. The following section discusses this history of mental poker in more detail, outlining the key ideas, contributions and limitations of this earlier work. This paper presents a new way of playing mental poker. Unlike earlier solutions, it is secure against coalitions, permits any number of players, and uses inexpensive, highly secure cryptographic techniques. The protocol does require the participation of a trusted party to shuffle the cards. However, thereafter the trusted party does not participate in the protocol. The protocol can be easily adapted to play almost

Applied cryptography: Protocols, algorithms, and source code in C

“…Cryptographers have shown that a small amount of information is leaked by these poker protocols if the RSA public-key algorithm is used [453,573]. Specifically, if the binary representation of the card is a quadratic residue (see Section 11.3), then the encryption of the card is also a quadratic residue.…”

“…Other research on poker protocols can be found in [573,1634,389]. A complicated protocol that allows players to not reveal their hands can be found in [390].…”

Efficient TTP-free mental poker protocols

“…Mental poker is one of the most popular games of online gambling and the fairness of the involved players is challenging from the view point of data security. Mental poker was firstly proposed by Shamir et al [13] in 1979 and many attempts have been made to achieve protocols that would allow people to play mental poker [8,14,9,1,15,4,5,6].…”

“…Mental poker protocols with a TTP [10,8,1] are normally simple and efficient. However, the assumption of a fully trusted TTP is not tolerable in online gambling.…”

A fast mental poker protocol

“…However, it is not easy to design a fast enough protocol to satisfy practical needs. Despite many protocols have been proposed ( [2,3,7,9,8,16,15,18,20,21,23,25,27,28,29]), online poker rooms are still based on client-server architectures. Therefore, online players are assumed to trust the server.…”