Cyberdice: Peer-to-Peer Gambling in the Presence of Cheaters

We describe a simple gambling game in which n participants each put down a xed amount of money and one of them, selected at random, wins and takes it all. We describe how this game can be operated in cyberspace, without knowing anything about the other participants except for the bit strings they transmit. We show how the genuine winner can convert the bit strings back into money, without any other gambler or eavesdropper being able to do so before her. We also show that it is possible to have con dence in the fair running of the game even if all the other participants, including the dealer, are crooked and are prepared to manipulate the protocol to their advantage. The paper initially develops a naïve protocol for running the game, and shows various ways in which a gambler can cheat by ceasing to send messages once it is clear that she is losing. We incrementally build this up into a protocol that resists drop-outs, collusion and dishonesty from all players, by relying on the honest behaviour of some non-gambling `issuers' whose role is to convert currency into bit strings and vice versa.