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One-way functions and the nonisomorphism of NP-complete sets
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Associative one-way functions: a new paradigm for secret-key agreement and digital signatures
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Methods of Logic in Computer Science
An observation on associative one-way functions in complexity theory
Information Processing Letters
Journal of Computer and System Sciences
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Theoretical Computer Science
Foundations of Cryptography: Basic Tools
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The cpa's responsibility for the prevention and detection of computer fraud.
The cpa's responsibility for the prevention and detection of computer fraud.
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One-way permutations and self-witnessing languages
Journal of Computer and System Sciences
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Journal of Computer and System Sciences
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Theoretical Computer Science
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
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IEEE Transactions on Information Theory
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Rabi and Sherman [M. Rabi, A. Sherman, An observation on associative one-way functions in complexity theory, Information Processing Letters 64 (5) (1997) 239-244; M. Rabi, A. Sherman, Associative one-way functions: A new paradigm for secret-key agreement and digital signatures, Tech. Rep. CS-TR-3183/UMIACS-TR-93-124, Department of Computer Science, University of Maryland, College Park, MD, 1993] proved that the hardness of factoring is a sufficient condition for there to exist one-way functions (i.e., p-time computable, honest, p-time noninvertible functions; this paper is in the worst-case model, not the average-case model) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve the sufficient condition to PNP. More generally, in this paper we completely characterize which types of one-way functions stand or fall together with (plain) one-way functions-equivalently, stand or fall together with PNP. We look at the four attributes used in Rabi and Sherman's seminal work on algebraic properties of one-way functions (see [M. Rabi, A. Sherman, An observation on associative one-way functions in complexity theory, Information Processing Letters 64 (5) (1997) 239-244; M. Rabi, A. Sherman, Associative one-way functions: A new paradigm for secret-key agreement and digital signatures, Tech. Rep. CS-TR-3183/UMIACS-TR-93-124, Department of Computer Science, University of Maryland, College Park, MD, 1993]) and subsequent papers-strongness (of noninvertibility), totality, commutativity, and associativity-and for each attribute, we allow it to be required to hold, required to fail, or ''don't care''. In this categorization there are 3^4=81 potential types of one-way functions. We prove that each of these 81 feature-laden types stands or falls together with the existence of (plain) one-way functions.