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Brief Full Advanced Search Search Tips (Publisher: John Wiley & Sons, Inc.) Author(s): Bruce Schneier ISBN: 0471128457 Publication Date: 01/01/96 Search this book:
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----------- 4.10 Fair Coin Flips
It’s story time with Joe Kilian : Alice and Bob wanted to flip a fair coin, but had no physical coin to flip. Alice offered a simple way of flipping a fair coin mentally. “First, you think up a random bit, then I’ll think up a random bit. We’ll then exclusive-or the two bits together, ” she suggested. “But what if one of us doesn’t flip a coin at random?” Bob asked. “It doesn’t matter. As long as one of the bits is truly random, the exclusive-or of the bits should be truly random, ” Alice replied, and after a moment’s reflection, Bob agreed. A short while later, Alice and Bob happened upon a book on artificial intelligence, lying abandoned by the roadside. A good citizen, Alice said, “One of us must pick this book up and find a suitable waste receptacle.” Bob agreed, and suggested they use their coin-flipping protocol to determine who would have to throw the book away. “If the final bit is a 0, then you will pick the book up, and if it is a 1, then I will, ” said Alice. “What is your bit?” Bob replied, “1.” “Why, so is mine, ” said Alice, slyly, “I guess this isn’t your lucky day.” Needless to say, this coin-flipping protocol had a serious bug. While it is true that a truly random bit, x, exclusive-ORed with any independently distributed bit, y, will yield a truly random bit, Alice’s protocol did not ensure that the two bits were distributed independently. In fact, it is not hard to verify that no mental protoc...
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