Abstract

A desirable property of one-way functions is that they be total, one-to-one, and onto—in other words, that they be permutations. We prove that one-way permutations exist exactly if PaUP-coUP: This provides the first characterization of the existence of one-way permutations based on a complexity-class separation and shows that their existence is equivalent to a number of previously studied complexity theoretic hypotheses. We study permutations in the context of witness functions of nondeterministic Turing machines. A language is in PermUP if, relative to some unambiguous, nondeterministic, polynomial-time Turing machine accepting the language, the function mapping each string to its unique witness is a permutation of the members of the language. We show that, under standard complexity-theoretic assumptions, PermUP is a strict subset of UP. We study SelfNP, the set of all languages such that, relative to some nondeterministic, polynomial-time Turing machine that accepts the language, the set of all witnesses of strings in the language is identical to the language itself. We show that SATASelfNP; and, under standard complexity-theoretic assumptions, SelfNP /= NP:

Publication Date

2003

Comments

Journal of Computer and System Sciences article.Please see www.ScienceDirect.com for the complete article.Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

Center for Advancing the Study of CyberInfrastructure

Campus

RIT – Main Campus

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