The analogy between Bob's Cave and the Fiat-Shamir protocol is not entirely accurate. In the Fiat-Shamir protocol, Bob knows which value of e will force Alice to use the secret value S, assuming Alice follows the protocol. That is, if Bob chooses e = 1, then Alice must use the secret value S to construct the correct response in message three, but if Bob chooses e = 0, then Alice does not use S. As noted in the text, Bob must choose e at random to prevent Trudy from breaking the protocol. In the Bob's Cave analogy, Bob does not know whether Alice was required to use the secret phrase or not (again, assuming that Alice follows the protocol).
a. Modify the cave analogy so that Bob knows whether Alice used the secret phrase or not, assuming that Bob is not allowed to see which side Alice actually chooses. Bob's New-and-Improved Cave protocol must still resist an attack by someone who does not know the secret phrase.
b. Does your new cave analogy differ from the Fiat-Shamir protocol in any significant way?
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