If P != NP Then Some Strongly Noninvertible Functions Are Invertible

Authors:
Lane A. Hemaspaandra;Kari Pasanen;Jörg Rothe
Affiliations:
-;-;-
Venue:
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Year:
2001

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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 ([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.