# Is it possible to have a zero knowledge proof with a P Prover?

In the literature, when reading about zero knowledge proofs, the prover (prover/verifier) is always given an unlimited computational power or just capacity to solve NP.

Is it necessary for the prover to have higher computational power than the verifier?

If it is, is there any variant that does not need this property?

If any of the answers is yes can you give me references?

If the prover has the same power as the verifier, then the verifier can simulate the entire interaction himself, which makes the interactive proof unnecessary. For example, if we have an interactive proof with a probabilistic polynomial verifier and a polynomial prover for some language $$L$$, then $$L\in BPP$$. When dealing with interactive proof systems with a polynomial verifier it suffices to consider PSPACE provers, since a PSPACE prover can find and send the messages that maximize the verifier's acceptance probability.