Abstract of the diploma thesis: We consider mental poker, i.e. a game of poker played without the aid of physical cards, most commonly on the internet. A special branch of cryptography deals with ensuring fairness and security in such online games even if not all the players are well-intentioned. The problem becomes particularly interesting if we wish to dispose of a centralized trusted server which would conduct the game (deal the cards and similar) without itself participating as an active player. Such a server, if present in the game, has complete control over its proceedings and therefore represents a natural and vulnerable target for various attacks. A greater part of this thesis deals with steps involved in constructing a cryptographic scheme for playing poker without a central server of this kind. We first formally identify the background of the problem and its security requirements. We then proceed to describe those mathematical and cryptographic tools that typically play an important role in constructing mental poker protocols. Building on that, we present three solutions which satisfy the identified security constraints to varying degrees. The most interesting of these solutions satisfies all the constraints while maintaining reasonable performance. Lastly, we comment on the role of online poker in today's society and consider the potential of using advanced decentralized solutions like the ones described in everyday games of online poker.
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Math. subj. class (2000):