Unformatted text preview: d and keys. Alice can confirm that the cards are legitimate by checking her random strings. She can also confirm that the cards are the ones dealt by encrypting the cards with the winner’s public key and verifying that they are the same as the encrypted messages she received in step (3) or (5). This protocol isn’t secure against collusion among malicious players. Alice and another player can effectively gang up on the third and together swindle that player out of everything without raising suspicion. Therefore, it is important to check all the keys and random strings every time the players reveal their hands. And if you’re sitting around the virtual table with two people who never reveal their hands whenever one of them is the dealer (Alice, in the previous protocol), stop playing. Understand that while this is all interesting theory, actually implementing it on a computer is an arduous task. A Sparc implementation with three players on separate workstations takes eight hours to shuffle a deck of cards, let alone play an actual game [513]. Attacks against Poker Protocols
Cryptographers have shown that a small amount of information is leaked by these poker protocols if the RSA publickey 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. This property can be used to “mark” some cards—all the aces, for example. This does not reveal much about the hands, but in a game such as poker even a tiny bit of information can be an advantage in the long run. Shafi Goldwasser and Silvio Micali [624] developed a twoplayer mentalpoker protocol that fixes this problem, although its complexity makes it far more theoretical than practical. A general n player poker protocol that eliminates the problem of information leakage was developed in [389]. Other research on poker protocols can be found in [573, 1634, 389]. A complicated protocol that allows players to...
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 Fall '10
 ALIULGER
 Cryptography, Bruce Schneier, Applied Cryptography, EarthWeb, Search Search Tips

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