If P ≠ NP then some strongly noninvertible functions are invertible

Abstract

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 ([RS93,RS97] attribute this to Rivest and Sherman) and digital signatures [RS93,RS97]-that strongly noninvertible functions would be 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 large, unexpected consequence: Unless P = NP, some strongly noninvertible functions are invertible.