User rey - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T22:22:08Z http://mathoverflow.net/feeds/user/10827 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22624/example-of-a-good-zero-knowledge-proof/46007#46007 Answer by Rey for Example of a good Zero Knowledge Proof. Rey 2010-11-14T02:52:07Z 2010-11-14T02:52:07Z <p>An easy ZKP-based authentication scheme is one that uses a deck of shuffled playing cards and a paper bag:</p> <p>Suppose Alice and Bob want to authenticate using the secret number "27". Alice takes the deck of cards, places her hands (with the cards) inside the bag and begins drawing card after card until she has reached the 27th card. She pulls this one card out of the bag and reveals it to herself and Bob.</p> <p>Alice places the cards back on the deck in the same order she drew them (not destroying the original order).</p> <p>Now it's Bob's turn. He is handed the deck of cards and hides his hands (and the counting of cards) in the paper bag. If he knows the secret number (27) then he should draw down to the 27th card and reveal the same card Alice did.</p> <p>If Alice and Bob draw different cards then they did not draw the same number of cards.</p> <p>One more:</p> <p>Suppose Alice and Bob want to authenticate using the secret number of "27" but don't want to reveal it to one another. In this scenario they use a third party, Charlie.</p> <p>Charlie randomly comes up with a number (any number will do) -- we'll say 15 -- and whispers it to Alice. Alice then adds the secret number (27) to Charlie's number (15) and whispers the total (42) to Bob.</p> <p>Bob subtracts the secret number (27) from the total (42) and whispers the result (15) to Charlie.</p> <p>If Charlie is read back his own number (15) then he can declare Alice and Bob have successfully authenticated.</p> http://mathoverflow.net/questions/22624/example-of-a-good-zero-knowledge-proof/46007#46007 Comment by Rey Rey 2010-11-17T00:41:12Z 2010-11-17T00:41:12Z It's assumed that Alice and Bob are, in the first scenario, authenticating in a face-to-face manner as to make sure no slight of hand or cheating is occurring. You're right, though, in that it is not a tamper proof system.