If P≠NP then some strongly noninvertible functions are invertible

Rabi, Rivest, and Sherman alter the standard notion of noninvertibility to a new notion they call strong noninvertibility, and show—via explicit cryptographic protocols for secret-key agreement (Rabi and Sherman attribute this protocol to Rivest and Sherman) and digital signatures (Rabi and Sherman)—that strongly noninvertible functions are very useful components in protocol design. Their definition of strong noninvertibility has a small twist (“respecting the argument given”) that is needed to ensure cryptographic usefulness. In this paper, we show that this small twist has a consequence: unless P=NP, some strongly noninvertible functions are invertible.