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Lecture 8:
Coin Flipping by Telephone
Wayne Patterson
SYCS 654
Spring 2010
Coin Flipping by
• 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 133--137. IEEE, 1982.
• Blum was Rene Peralta’s thesis advisor
• Rene is a colleague who is now
responsible for security in electronic
voting at NIST
As Rene Posed the
• 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 don’t trust each
other …
Alice and Bob Agree on a
Secure One-Way Function
• For example, the function could
be ax (mod p), for an agreedupon large prime number p and
an agreed-upon primitive root a.
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
• Alice chooses x (the flip) and
announces to Bob the computation y
= ax mod p.
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 = ax 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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