The Tale of One-way Functions

TL;DR

This paper explores the fundamental problem of one-way functions in computer theory, providing new insights, clarifying subtleties in definitions, and introducing the first combinatorial complete one-way function.

Contribution

It introduces the first combinatorial complete one-way function and offers a unified approach to clarify subtleties in the definitions of one-way functions.

Findings

First combinatorial complete one-way function introduced

Clarification of subtleties in basic definitions

Unified approach to the concept of one-way functions

Abstract

The existence of one-way functions is arguably the most important problem in computer theory. The article discusses and refines a number of concepts relevant to this problem. For instance, it gives the first combinatorial complete owf, i.e., a function which is one-way if any function is. There are surprisingly many subtleties in basic definitions. Some of these subtleties are discussed or hinted at in the literature and some are overlooked. Here, a unified approach is attempted.