The interactive version works not because the verifier is making the queries, but because the prover is not. The intuition behind making an interactive protocol

The interactive version works not because the verifier is making the queries, but because the prover is not. The intuition behind making an interactive protocol non-interactive is use unbiasable queries that can be predicted ahead of time used hashes for pseudo-randomness. https://en.m.wikipedia.org/wiki/Fiat%E2%80%93Shamir_heuristic https://en.m.wikipedia.org/wiki/Fiat%E2%80%93Shamir_heuristi...