Three participants Quadratic polynomial, one cheater. The Cheater discloses a false (x,y) pair I need to prove that any one of the truth-telling participants can't tell which of the others is the liar. I do realize that any pair of participants have a linear subspace of possible solutions since they don't know the secret they can't tell if it is a member of their subspace, but I don't think it is a proof just an intuition as to why this claim is true.
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What's a "cheater"? – fkraiem Dec 30 '17 at 08:50
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Hey, there are three participants each holds a secret pair (x,y) one of the participants disclose a false pair he is the "cheater". they try to reconstruct the secret and find out they have a false result. I need to prove that it is impossible the find the lying participant. – Nitzan Ben-Hur Dec 30 '17 at 09:16
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Related: How do you find a cheater in Shamir Secret Sharing? – e-sushi Jan 10 '18 at 19:14
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You could use the fact that having two of three pairs does not reveal any information about the secret (polynomial). Also see the Wikipedia article on Shamir's secret sharing: it provides you with a nice graphical answer to your question.
