Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
On hardness of one-way functions
Information Processing Letters
Structural complexity 1
SIAM Journal on Computing
One-way functions and the nonisomorphism of NP-complete sets
Theoretical Computer Science
Introduction to the theory of complexity
Introduction to the theory of complexity
Associative one-way functions: a new paradigm for secret-key agreement and digital signatures
Associative one-way functions: a new paradigm for secret-key agreement and digital signatures
An observation on associative one-way functions in complexity theory
Information Processing Letters
Journal of Computer and System Sciences
Characterizing the existence of one-way permutations
Theoretical Computer Science
The complexity theory companion
The complexity theory companion
If P != NP Then Some Strongly Noninvertible Functions Are Invertible
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
On Sets with Easy Certificates and the Existence of One-Way Permutations
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
A Note on Cryptography and NP$\cap$ CoNP-P
A Note on Cryptography and NP$\'cap$ CoNP-P
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.
Information and Computation
One-way permutations and self-witnessing languages
Journal of Computer and System Sciences
Tight lower bounds on the ambiguity of strong, total, associative, one-way functions
Journal of Computer and System Sciences
A digital cash protocol based on additive zero knowledge
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
If P ≠ NP then some strongly noninvertible functions are invertible
Theoretical Computer Science
Quantum cryptography: A survey
ACM Computing Surveys (CSUR)
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Rabi and Sherman [RS97,RS93] 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) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve the sufficient condition to P ≠ NP. 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 P ≠ NP. We look at the four attributes used in Rabi and Sherman’s seminal work on algebraic properties of one-way functions (see [RS97,RS93]) 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 34 = 81 potential types of one-way functions. We prove that each of these 81 feature-laden types stand or fall together with the existence of (plain) one-way functions.