One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
On hardness of one-way functions
Information Processing Letters
Complexity classes without machines: on complete languages for UP
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
SIAM Journal on Computing
Upward separation for FewP and related classes
Information Processing Letters
Definability on finite structures and the existence of one-way functions
Methods of Logic in Computer Science
Defying upward and downward separation
Information and Computation
Characterizing the existence of one-way permutations
Theoretical Computer Science
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Polynomial reducibilities and complete sets.
Polynomial reducibilities and complete sets.
The cpa's responsibility for the prevention and detection of computer fraud.
The cpa's responsibility for the prevention and detection of computer fraud.
The NP-completeness column: Finding needles in haystacks
ACM Transactions on Algorithms (TALG)
Quantum cryptography: A survey
ACM Computing Surveys (CSUR)
Query-monotonic Turing reductions
Theoretical Computer Science
Other complexity classes and measures
Algorithms and theory of computation handbook
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
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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 P ≠ UP ∩ 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 SAT ∈ SelfNP, and, under standard complexity-theoretic assumptions, SelfNP ≠ NP.