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Unformatted text preview: nt. Their waiter informs them that arrangements have been made with the maître d‘hôtel for the bill to be paid anonymously. One of the cryptographers might be paying for the dinner, or it might have been the NSA. The three cryptographers respect each other’s right to make an anonymous payment, but they wonder if the NSA is paying. How do the cryptographers, named Alice, Bob, and Carol, determine if one of them is paying for dinner, while at the same time preserving the anonymity of the payer? Chaum goes on to solve the problem: Each cryptographer flips an unbiased coin behind his menu, between him and the cryptographer to his right, so that only the two of them can see the outcome. Each cryptographer then states aloud whether the two coins he can see—the one he flipped and the one his left-hand neighbor flipped—fell on the same side or on different sides. If one of the cryptographers is the payer, he states the opposite of what he sees. An odd number of differences uttered at the table indicates that a cryptographer is paying; an even number of differences indicates that NSA is paying (assuming that the dinner was paid for only once). Yet, if a cryptographer is paying, neither of the other two learns anything from the utterances about which cryptographer it is. To see that this works, imagine Alice trying to figure out which other cryptographer paid for dinner (assuming that neither she nor the NSA paid). If she sees two different coins, then either both of the other cryptographers, Bob and Carol, said, “same” or both said, “different.” (Remember, an odd number of cryptographers saying “different” indicates that one of them paid.) If both said, “different, ” then the payer is the cryptographer closest to the coin that is the same as the hidden coin (the one that Bob and Carol flipped). If both said, “same, ” then the payer is the cryptographer closest to the coin that is different from the hidden coin. However, if Alice sees two coins that are the same, then either Bob said,...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
- Fall '10