On one-way functions and polynomial-time isomorphisms☆

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Abstract

It is shown that if one-way functions exist, then there are sets A and B such that A and B are equivalent under one-one and length-increasing polynomial-time reductions, and such that A is not polynomial-time isomorphic to B. Furthermore, sets A and B can be constructed such that they are polynomial-time truth-table complete for the class of exponential-time computable sets.

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A preliminary version of this paper has appeared in the Proceedings of the 18th ACM Symposium on Theory of Computing, 1986.

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The research of the first author was supported in part by NSF Grants MCS-8103479A01 and DCR-8501226

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Part of this work was done while the second author was at New Mexico State University

Copyright © 1986 Published by Elsevier B.V.