I have a conundrum to solve but am not knowledgeable enough about cryptography to know whether it's possible to do, and if so, what method to use.
I am a Provider and my task is to prove to some outside Verifier the existence of a Connection to some device, beyond some reasonable probability $\epsilon$. The Verifier and the Prover have a communication channel and can ask each other questions. As a Prover, I could lie at any point, and pretend the Connection exists when it doesn't, or vice versa. I need a protocol that is secure in such a way that the Verifier can establish the Connection is genuinely there.
Question 1: Is there any such protocol that could do with with communication and computation on the Prover side alone?
Question 2: In case the former isn't possible, if the Device could do some computation (i.e. do (modular) arithmetic etc.) and the Connection could be used for that, would that make this possible?
I feel there are some cryptographic algorithms out there that are designed for this, but I don't quite know what they are. I have looked into Zero-Knowledge proofs, but all the examples I find aren't quite suitable to this kind of issue.
