On one-way functions and the average time complexity of almost-optimal compression

TL;DR

This paper establishes a fundamental equivalence between the existence of one-way functions and the difficulty of achieving almost-optimal compression on average for certain distributions, linking cryptography and data compression.

Contribution

It proves that one-way functions exist if and only if almost-optimal compression is hard on average relative to some efficient distribution, combining prior theorems in the field.

Findings

One-way functions are equivalent to the hardness of almost-optimal compression on average.

The result connects cryptographic assumptions with data compression complexity.

The proof synthesizes existing theorems by Ilango, Ren, Santhanam, Bauwens, and Zimand.

Abstract

We show that one-way functions exist if and only if there exists an efficient distribution relative to which almost-optimal compression is hard on average. The result is obtained by combining a theorem of Ilango, Ren, and Santhanam and one by Bauwens and Zimand.