Unformatted text preview: ol can allow two infinitely powerful parties to flip a fair coin. Alice and Bob were in trouble until they received a letter from an obscure graduate student in cryptography. The information in the letter was too theoretical to be of any earthly use to anyone, but the envelope the letter came in was extremely handy. The next time Alice and Bob wished to flip a coin, they played a modified version of the original protocol. First, Bob decided on a bit, but instead of announcing it immediately, he wrote it down on a piece of paper and placed the paper in the envelope. Next, Alice announced her bit. Finally, Alice and Bob took Bob’s bit out of the envelope and computed the random bit. This bit was indeed truly random whenever at least one of them played honestly. Alice and Bob had a working protocol, the cryptographer’s dream of social relevance was fulfilled, and they all lived happily ever after. Those envelopes sound a lot like bit-commitment blobs. When Manuel Blum introduced the problem of flipping a fair coin over a modem , he solved it using a bit-commitment protocol: (1) Alice commits to a random bit, using any of the bit-commitment schemes listed in Section 4.9. (2) Bob tries to guess the bit. (3) Alice reveals the bit to Bob. Bob wins the flip if he correctly guessed the bit. In general, we need a protocol with these properties: — Alice must flip the coin before Bob guesses. — Alice must not be able to re-flip the coin after hearing Bob’s guess. — Bob must not be able to know how the coin landed before making his guess. There are several ways in which we can do this. Coin Flipping Using One-Way Functions
If Alice and Bob can agree on a one-way function, this protocol is simple: (1) Alice chooses a random number, x. She computes y = f(x), where f(x) is the one-way function. (2) Alice sends y to Bob. (3) Bob guesses whether x is even or odd and sends his guess to Alice. (4) If Bob’s guess is correct, the result of the coin flip is heads. If Bob’s...
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- Fall '10
- Cryptography, Bruce Schneier, Applied Cryptography, EarthWeb, Search Search Tips