# 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}
}
• Published in Theor. Comput. Sci. 6 October 2000
• Mathematics
16 Citations
Enforcing and Defying Associativity, Commutativity, Totality, and Strong Noninvertibility for One-Way Functions in Complexity Theory
• Mathematics
ICTCS
• 2005
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
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
Low Ambiguity in Strong, Total, Associative, One-Way Functions
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
• Mathematics, Computer Science
IACR Cryptol. ePrint Arch.
• 2006
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
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
• Computer Science, Mathematics
The 11th IEEE International Conference on Networks, 2003. ICON2003.
• 2003
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
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
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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