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.
Supported in part by grants NSF-CCR-9322513 and NSF-INT-9815095/DAAD-315-PPP-gü-ab. Work done in part while visiting Julius-Maximilians-Universität Würzburg.
Supported in part by grant NSF-INT-9815095/DAAD-315-PPP-gü-ab and a Heisenberg Fellowship of the Deutsche Forschungsgemeinschaft. Work done in part while visiting the University of Rochester.
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Hemaspaandra, L.A., Pasanen, K., Rothe, J. (2001). If P ≠ NP then Some Strongly Noninvertible Functions Are Invertible. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_17
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DOI: https://doi.org/10.1007/3-540-44669-9_17
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