[bobbiechen]

Thank you!!

If I understand correctly:

* The prover commits to a starting value (public input)

* Instead of waiting for an interactive challenge, they hash it and use the resulting hash output as if it were a challenge

If we believe the hash is a random oracle (as we do for cryptographic hash functions), then it is hard for the prover to manipulate the challenges. Is that it?

[MatteoFrigo]

You got it. There are a few nuisances, e.g. the "theorem statement" must be hashed as well so that proving that name=Mickey has a different oracle than proving that name=Goofy, but your basic understanding is correct.