If P \neq NP then Some Strongly Noninvertible Functions are Invertible
<|reference_start|>If P \neq NP then Some Strongly Noninvertible Functions are Invertible: 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.<|reference_end|>
@article{hemaspaandra2000if,
    title={If P \neq NP then Some Strongly Noninvertible Functions are Invertible},
    author={Lane A. Hemaspaandra, Kari Pasanen, and J"org Rothe},
    journal={arXiv preprint arXiv:cs/0010011},
    year={2000},
    archivePrefix={arXiv},
    eprint={cs/0010011},
    primaryClass={cs.CC}
}