Unformatted text preview: nds them back to Alice. Alice decrypts the messages and sends them back to Bob, who decrypts them to determine his hand. He then chooses five more messages at random and sends them back to Alice as he received them; she decrypts these and they become her hand. During the game, additional cards can be dealt to either player by repeating the procedure. At the end of the game, Alice and Bob both reveal their cards and key pairs so that each can be assured that the other did not cheat. Mental Poker with Three Players
Poker is more fun with more players. The basic mental poker protocol can easily be extended to three or more players. In this case, too, the cryptographic algorithm must be commutative. (1) Alice, Bob, and Carol each generate a public-key/private-key key pair. (2) Alice generates 52 messages, one for each card in the deck. These messages should contain some unique random string, so that she can verify their authenticity later in the protocol. Alice encrypts all the messages with her public key and sends them to Bob. EA(Mn) (3) Bob, who cannot read any of the messages, chooses five at random. He encrypts them with his public key and sends them back to Alice. EB(EA(Mn)) (4) Bob sends the other 47 messages to Carol. EA(Mn) (5) Carol, who cannot read any of the messages, chooses five at random. She encrypts them with her public key and sends them to Alice. EC(EA(Mn)) (6) Alice, who cannot read any of the messages sent back to her, decrypts them with her private key and then sends them back to Bob or Carol (depending on where they came from). DA(EB(EA(Mn))) = EB(Mn) DA(EC(EA(Mn))) = EC(Mn) (7) Bob and Carol decrypt the messages with their keys to reveal their hands. DB(EB(Mn)) = Mn DC(EC(Mn)) = Mn (8) Carol chooses five more messages at random from the remaining 42. She sends them to Alice. EA(Mn) (9) Alice decrypts the messages with her private key to reveal her hand. DA(EA(Mn)) = Mn (10) At the end of the game Alice, Bob, and Carol all reveal their hands and all of their keys so...
View Full Document
- Fall '10
- Cryptography, Bruce Schneier, Applied Cryptography, EarthWeb, Search Search Tips