New Combinatorial Complete One-Way Functions
Arist Kojevnikov, Sergey I. Nikolenko
TL;DR
This paper introduces two new combinatorial complete one-way functions based on string rewriting and the Post Correspondence Problem, providing proofs of their completeness and discussing properties for such functions.
Contribution
It presents novel one-way functions based on semi-Thue systems and the Post Correspondence Problem, along with an alternative proof of Levin's original result.
Findings
Two new complete one-way functions are proposed and proven.
An alternative proof of Levin's 2003 result is provided.
Discussion on properties necessary for combinatorial problems to be complete one-way functions.
Abstract
In 2003, Leonid A. Levin presented the idea of a combinatorial complete one-way function and a sketch of the proof that Tiling represents such a function. In this paper, we present two new one-way functions based on semi-Thue string rewriting systems and a version of the Post Correspondence Problem and prove their completeness. Besides, we present an alternative proof of Levin's result. We also discuss the properties a combinatorial problem should have in order to hold a complete one-way function.
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