That is correct. Any proof that digital signatures are secure on classical computers would imply P != NP. Further, it is known that BQP (bounded error quantum

That is correct. Any proof that digital signatures are secure on classical computers would imply P != NP. Further, it is known that BQP (bounded error quantum polynomial time. The quantum computer equivalent of P) is contained in PSPACE. However P=PSPACE is still an open question. This means that we still do not have any theoretical proof that quantum computers are more powerful that classical computers.