What do you mean by the line about zkps? We have perfectly-hiding proofs that reveal no information about the secret information, no matter how powerful the adversary is.
Yes, but they're not proofs in the mathematical sense, since there's always an (exponentially-shrinking) chance that the answers were only correct due to coincidence.
Exactly, practically it makes no different that the method could be fooled with a very tiny probability, but when making these counterintuitive statements I think it is important to be precise.
Ideally the reader should fully understand the statement and still feel amazed, rather than doubting the statement for a valid reason: perfect zero knowledge proof systems (which do not fail sometimes) are impossible and a reader would be right to think so
