Asklemmy

Coin flipping

Suppose Alice and Bob want to resolve some dispute via coin flipping. If they are physically in the same place, a typical procedure might be:

Alice "calls" the coin flip,
Bob flips the coin,
If Alice's call is correct, she wins, otherwise Bob wins.

If Alice and Bob are not in the same place a problem arises. Once Alice has "called" the coin flip, Bob can stipulate the flip "results" to be whatever is most desirable for him. Similarly, if Alice doesn't announce her "call" to Bob, after Bob flips the coin and announces the result, Alice can report that she called whatever result is most desirable for her. Alice and Bob can use commitments in a procedure that will allow both to trust the outcome:

Alice "calls" the coin flip but only tells Bob a commitment to her call,
Bob flips the coin and reports the result,
Alice reveals what she committed to,
Bob verifies that Alice's call matches her commitment,
If Alice's revelation matches the coin result Bob reported, Alice wins.
For Bob to be able to skew the results to his favor, he must be able to understand the call hidden in Alice's commitment. If the commitment scheme is a good one, Bob cannot skew the results. Similarly, Alice cannot affect the result if she cannot change the value she commits to.