If P neq NP then some strongly noninvertible functions are invertible

@inproceedings{Hemaspaandra2006IfPN,
  title={If P neq NP then some strongly noninvertible functions are invertible},
  author={Lane A. Hemaspaandra and Kari Pasanen and J{\"o}rg Rothe},
  booktitle={Theor. Comput. Sci.},
  year={2006}
}
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16 Citations
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Enforcing and Defying Associativity, Commutativity, Totality, and Strong Noninvertibility for One-Way Functions in Complexity Theory
TLDR
This paper completely characterize which types of one- way functions stand or fall together with (plain) one-way functions—equivalently, stand orFall together with P ≠ NP.
Invertible calculation's non-invertibility
TLDR
It is argued that while a logical operation that maps its input state to the output state unchanged can be computed efficiently, the computation of its inverse cannot be computed efficient because undoing the computational path of this sort of correspondence violates a most important principle of nature: the second law of thermodynamics.
Non-Invertibility in Invertible Systems
In cryptosystem theory, it is well-known that a logical mapping that returns the same value that was used as its argument can be inverted with a zero failure probability in linear time. In this…
Tight lower bounds on the ambiguity of strong, total, associative, one-way functions
Low Ambiguity in Strong, Total, Associative, One-Way Functions
TLDR
It is proved that if standard, unambiguous, one-way functions exist, then there exist strong, total, associative, one -way functions that are $\mathcal{O}(n)$-to-one, which puts a reasonable upper bound on the ambiguity.
A New Cryptosystem Based On Hidden Order Groups
  • A. Saxena, B. Soh
  • Mathematics, Computer Science
    IACR Cryptol. ePrint Arch.
  • 2006
TLDR
This work exploits a ``gap'' to construct a cryptosystem based on hidden order groups and presents a practical implementation of a novel cryptographic primitive called an \emph{Oracle Strong Associative One-Way Function} (O-SAOWF).
Double Blind Comparisons using Groups with Infeasible Inversion
TLDR
This paper shows how Double Blind Comparisons can be implemented using a Strong Associative One-Way Function (SAOWF), making an additional assumption that the SAOWF is implemented on a Group with Infeasible Inversion (GII).
A new paradigm for group cryptosystems using quick keys
  • A. Saxena, B. Soh
  • Computer Science, Mathematics
    The 11th IEEE International Conference on Networks, 2003. ICON2003.
  • 2003
TLDR
A new approach to group key agreement is introduced based on the idea of an associative one way function (AOWF) and it is illustrated how such functions can be used to perform highly dynamic and fully contributory multiparty key agreement in group-oriented cryptosystems.
Some facets of complexity theory and cryptography: A five-lecture tutorial
  • J. Rothe
  • Computer Science, Mathematics
    CSUR
  • 2002
TLDR
This tutorial discusses the notion of one-way functions both in a cryptographic and in a complexity-theoretic setting, and considers interactive proof systems and some interesting zero-knowledge protocols.
Quantum one-way permutation over the finite field of two elements
TLDR
Levin’s one-way permutation is provably secure because its output values are four maximally entangled two-qubit states, and whose probability of factoring them approaches zero faster than the multiplicative inverse of any positive polynomial poly(x) over the Boolean ring of all subsets of x.
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References

SHOWING 1-10 OF 14 REFERENCES
One-way functions in worst-case cryptography: algebraic and security properties are on the house
TLDR
Until recently, it was an open question whether one- way functions having the algebraic and security properties that these protocols require could be created from any given one-way function, and recently, Hemaspaandra and Rothe resolved this open issue in the affirmative, by showing that one-Way functions exist if and only if strong, total, commutative, associative one-ways exist.
Creating Strong, Total, Commutative, Associative One-Way Functions from Any One-Way Function in Complexity Theory
TLDR
It is proved that if P?NP then strong, total, commutative, associative one-way functions exist.
Associative one-way functions: a new paradigm for secret-key agreement and digital signatures
TLDR
This work proposes associative one-way functions as a new cryptographic paradigm for exchanging secret keys and for signing digital documents and constructively proves that they exist if and only if P 6 = NP.
Low Ambiguity in Strong, Total, Associative, One-Way Functions
TLDR
It is proved that if standard, unambiguous, one-way functions exist, then there exist strong, total, associative, one -way functions that are $\mathcal{O}(n)$-to-one, which puts a reasonable upper bound on the ambiguity.
On Some Natural Complete Operators
  • K. Ko
  • Mathematics
    Theor. Comput. Sci.
  • 1985
An Observation on Associative One-Way Functions in Complexity Theory
Introduction to the theory of complexity
TLDR
1. Mathematical Preliminaries, Elements of Computability Theory, and Space-Complexity Classes: Algorithms and Complexity Classes.
Structural Complexity I
TLDR
This volume is written for undergraduate students who have taken a first course in Formal Language Theory and presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory.
Complexity Measures for Public-Key Cryptosystems
A general theory of public-key cryptography is developed that is based on the mathematical framework of complexity theory. Two related approaches are taken to the development of this theory, and th...
Structural complexity 1
...
...