# Signature scheme against an unbounded rival

And I've read the following theorem:

Theorem (Lamport, GMR, Naor-Yung, Rompel, Goldreich) If one-way functions exist then there are signature schemes which are existentially unforgeable under chosen plaintext attacks.

I was wondering if this implies, that given an unbounded rival, no signature scheme exists that this rival can't break. This is due to the fact that the rival can inverse the 'OWF'.

Any thoughts? Corrections?