[betterunix2]

Technically that is not "zero knowledge" since the definition of ZK requires interaction (so there is no "publishing" of a proof). What you described sounds like this construction of "non-interactive ZK:"

https://en.wikipedia.org/wiki/Fiat%E2%80%93Shamir_heuristic

NIZK is a very different concept from ZK, because the verifier does learn something, in the sense that the verifier has received a string it could not compute on its own. In ordinary ZK the verifier cannot compute anything after running the protocol that it could not have computed beforehand (so it gains nothing from the interaction).

[andromeduck]

I'm not quite sure I follow. What does the verifier learn after NIZK? Isn't it the point that the verifier learns nothing other than the prover has some secret knowledge? Seems to me like it's just the same information rescheduled with the help of a PRF.

[betterunix2]

The verifier learns the NIZK itself; i.e. the verifier could not have computed the NIZK independently.