If P \neq NP then Some Strongly Noninvertible Functions are Invertible

TL;DR

This paper proves that if P ≠ NP, then some functions that are strongly noninvertible in cryptography are actually invertible, revealing a surprising link between complexity theory and cryptographic function properties.

Contribution

It demonstrates that under the assumption P ≠ NP, the notion of strong noninvertibility does not necessarily imply noninvertibility, challenging previous cryptographic assumptions.

Findings

If P ≠ NP, some strongly noninvertible functions are invertible.

The small twist in the definition of strong noninvertibility has significant implications.

The result links complexity theory to cryptographic function properties.

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.