This can easily be done in the cryptographic example above: B can sample a new number y=p′⋅q′, and then present y to a fresh copy of A that has not seen the transcript for x so far.
I don’t understand how this is supposed to help.
I guess the point is to somehow catch a fresh copy of A in a lie about a problem that is different from the original problem, and conclude that A is the dishonest debater?
But couldn’t A just answer “I don’t know”?
Even if it is a fresh copy, it would notice that it does not know the secret factors, so it could display different behavior than in the x case where A knows the secret factors p,q.
You’d need some coupling argument to know that the problems have related difficulty, so that if A is constantly saying “I don’t know” to other similar problems it counts as evidence that A can’t reliably know the answer to this one. But to be clear, we don’t know how to make this particular protocol go through, since we don’t know how to formalise that kind of similarity assumption in a plausibly useful way. We do know a different protocol with better properties (coming soon).
I don’t understand how this is supposed to help. I guess the point is to somehow catch a fresh copy of A in a lie about a problem that is different from the original problem, and conclude that A is the dishonest debater?
But couldn’t A just answer “I don’t know”?
Even if it is a fresh copy, it would notice that it does not know the secret factors, so it could display different behavior than in the x case where A knows the secret factors p,q.
You’d need some coupling argument to know that the problems have related difficulty, so that if A is constantly saying “I don’t know” to other similar problems it counts as evidence that A can’t reliably know the answer to this one. But to be clear, we don’t know how to make this particular protocol go through, since we don’t know how to formalise that kind of similarity assumption in a plausibly useful way. We do know a different protocol with better properties (coming soon).