Characterizations of the Existence of Partial and Total One-Way Permutations

Joerg Rothe; Lane A. Hemaspaandra

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arXiv · cs/9907040

Characterizations of the Existence of Partial and Total One-Way Permutations

Joerg Rothe·Lane A. Hemaspaandra

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Abstract

In this note, we study the easy certificate classes introduced by Hemaspaandra, Rothe, and Wechsung, with regard to the question of whether or not surjective one-way functions exist. This is an important open question in cryptology. We show that the existence of partial one-way permutations can be characterized by separating P from the class of UP sets that, for all unambiguous polynomial-time Turing machines accepting them, always have easy (i.e., polynomial-time computable) certificates. This extends results of Grollmann and Selman. By Grädel's recent results about one-way functions, this also links statements about easy certificates of NP sets with statements in finite model theory. Similarly, there exist surjective poly-one one-way functions if and only if there is a set L in P such that not all FewP machines accepting L always have easy certificates. We also establish a condition necessary and sufficient for the existence of (total) one-way permutations.

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Joerg Rothe, Lane A. Hemaspaandra. 1999-07-26. Characterizations of the Existence of Partial and Total One-Way Permutations. https://arxiv.org/abs/cs/9907040

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