If P ≠ NP then some strongly noninvertible functions are invertible

Authors:
Lane A. Hemaspaandra;Kari Pasanen;Jörg Rothe
Affiliations:
Department of Computer Science, University of Rochester, Rochester, NY and Julius-Maximilians-Universität W¨rzburg and Heinrich-Heine-Universität Düsseldorf;Starnet Systems, Jyväskylä, Finland and University of Jyväskylä and Nokia Networks, Jyväskylä, Finland;Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany and University of Rochester
Venue:
Theoretical Computer Science
Year:
2006

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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 (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.