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Designing such a challenge is Impossible. If we assume that having a connection is equal to being able to exchange any piece of knowledge at any given time then the proof of impossibility of such challenge is as follows: Proof. First assume that there is such a challenge and Alice is capable of querying such a challenge to correctly determine whether the ...


Yes! Here is one such scheme. Let $s=\mathcal S(x)$ be what that the question's tiny device produces for 64-bit input $x$, and $\mathcal V(s,x)$ the public verification function for that, which outputs $1$ if $s$ matches $x$, $0$ otherwise. I'll assume this resists existential forgery under adaptive chosen message attack, and we want to extend it to ...

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