1. I've read the sections twice over and am still having trouble understanding how exactly Peggy can use square roots of factors of x to show Victor that she has factored n. How is showing Victor x[1] or x[2] the same as showing Victor that she has factored n? Isn't she giving him enough information so that he can actually deduce what s is, or for that matter what the factors of n are? I think I'm getting lost in the labeling of variables somehow.
2. If Peggy were to mis-choose which numbers to send to Victor as proof, wouldn't there be worse consequences than Victor knowing that Peggy didn't find a factor of n? Wouldn't Victor know that for some reason Peggy was just shooting in the dark, hoping to find some secret information or get something out of Victor? How does this apply to the example of crooks trying to steal sensitive information?
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