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Unformatted text preview: “same” and Carol said, “different, ” or Bob said, “different” and Carol said, “same.” If the hidden coin is the same as the two coins she sees, then the cryptographer who said, “different” is the payer. If the hidden coin is different from the two coins she sees, then the cryptographer who said, “same” is the payer. In all of these cases, Alice needs to know the result of the coin flipped between Bob and Carol to determine which of them paid. This protocol can be generalized to any number of cryptographers; they all sit in a ring and flip coins among them. Even two cryptographers can perform the protocol. Of course, they know who paid, but someone watching the protocol could tell only if one of the two paid or if the NSA paid; they could not tell which cryptographer paid. The applications of this protocol go far beyond sitting around the dinner table. This is an example of unconditional sender and recipient untraceability. A group of users on a network can use this protocol to send anonymous messages. (1) The users arrange themselves into a circle. (2) At regular intervals, adjacent pairs of users flip coins between them, using some fair coin flip protocol secure from eavesdroppers. (3) After every flip, each user announces either “same” or “different.” If Alice wishes to broadcast a message, she simply starts inverting her statement in those rounds corresponding to a 1 in the binary representation of her message. For example, if her message were “1001, ” she would invert her statement, tell the truth, tell the truth, and then invert her statement. Assuming the result of her flips were “different, ” “same, ” “same, ” “same, ” she would say “same, ” “same, ” “same, ” “different.” If Alice notices that the overall outcome of the protocol doesn’t match the message she is trying to send, she knows that someone else is trying to send a message at the same time. She then stops sending the message and wa...
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- Fall '10