Privacy homomorphisms for e-gambling and mental poker

Abstract

Abstract —With the development of computer networks, situ-ations where a set of players remotely play a game ( e-gaming )have become usual. Often players play for money ( e-gambling ),which requires standards of security similar to those in physicalgambling. Cryptographic tools have been commonly used so farto provide security to e-gambling. Homomorphic encryption isan example of such tools.In this paper we review the mental poker protocols, whereplayers are assumed to remotely play poker. We focus on the keyadvantage of using cryptosystems with homomorphic properties( privacy homomorphisms ) because they offer the possibility ofmanipulating cards in encrypted form. Index Terms —Cryptography, privacy homomorphism, mentalpoker I. I NTRODUCTION The growth of computer networks has allowed many activ-ities that used to require physical presence to become doableover the network. One example is e-gambling. In this paper wefocus on mental poker, i.e. a poker game played among playersthat are not physically together but communicate throughcomputer networks.A mental poker system needs to provide protocols togenerate a deck of cards, shuffle it and confidentially dealthe cards to players. Naive approaches assume the existenceof a trusted third party (TTP), who performs some or all ofthe aforementioned operations [1].Since the assumption on all players trusting this central nodeis not always realistic, research on solutions not requiringa trusted party has become a hot topic [2]–[5]. To ensurethe players a fair play, standards of security similar to thosein physical gambling must be guaranteed. For instance, it isgood for trust generation that all players participate in thecomputation of the shuffled deck of cards. Current proposalsin the literature are based on a paradigm consisting of thefollowing steps:1) The players generate the deck of 52 face-up cards