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Lecture 8: Coin Flipping by Telephone Wayne Patterson SYCS 654 Spring 2010

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Coin Flipping by Telephone Originally presented by Manuel Blum, then at UC Berkeley (now at Carnegie-Mellon): M. Blum. Coin flipping by telephone. In Proceedings of IEEE Spring Computer Conference, pages IEEE, Blum was Rene Peraltas thesis advisor Rene is a colleague who is now responsible for security in electronic voting at NIST

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As Rene Posed the Problem Alice and Bob have decided to divorce. They are in different cities, want to decide who gets the (house, car, dog, …) They decide to flip a coin Naturally they dont trust each other …

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Alice and Bob Agree on a Secure One-Way Function For example, the function could be a x (mod p), for an agreed- upon large prime number p and an agreed-upon primitive root a.

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Alice Will Flip the Coin The act of flipping is the choice of a secret x, 1 < x < p-1. x is either odd or even (i.e. heads or tails) Alice chooses x (the flip) and announces to Bob the computation y = a x mod p.

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What Does Bob Do? Bob receives y, and guesses that x is odd or even (heads or tails). Bob sends his guess to Alice. Alice verifies the result, whether Bob guessed right or wrong, and proves her decision by sending x to Bob. Bob can verify that Alice did not lie by performing the same computation y = a x mod p. If Alice lied about the value of x, Bob can prove the lie by the fact that the y he computes will not be the same y he had received.

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