One Way Function Candidate based on the Collatz Problem

TL;DR

This paper proposes a new one way function based on the Collatz problem's branching structure, analyzing its mathematical complexity and the relationship between branching and computational cost.

Contribution

It introduces a novel one way function construction leveraging the Collatz problem's conditional branching, highlighting its potential cryptographic applications.

Findings

Mathematical inaccessibility of the Collatz problem explained

Exponential relationship between branching and running cost established

Potential cryptographic utility of the proposed function suggested

Abstract

The one way function based on the Collatz problem is proposed. It is based on the problem's conditional branching structure which is not considered as important even the 3x+1 question is quite famous. The analysis shows why the problem is mathematically so inaccessible and how the algorithm conditional branching structure can be used to construct one way functions. It also shows exponential dependence between algorithm's conditional branching and running cost of algorithm branch-less reductions.