Creating quantum-resistant classical-classical OWFs from quantum-classical OWFs

TL;DR

This paper shows how quantum-classical one-way functions can be transformed into classical-classical ones, providing a new approach to constructing quantum-resistant cryptographic primitives.

Contribution

It introduces a method to derive classical-classical OWFs from quantum-classical OWFs, ensuring quantum resistance and expanding the theoretical framework of cryptography.

Findings

Quantum-classical OWFs imply classical-classical OWFs if they exist.

A domain-shifting technique converts quantum-classical OWFs into classical-classical OWFs.

The resulting classical-classical OWFs are resistant to quantum adversaries.

Abstract

One-way functions (OWF) are one of the most essential cryptographic primitives, the existence of which results in wide-ranging ramifications such as private-key encryption and proving $P \neq NP$. These OWFs are often thought of as having classical input and output (i.e. binary strings), however, recent work proposes OWF constructions where the input and/or the output can be quantum. In this paper, we demonstrate that quantum-classical (i.e. quantum input, classical output) OWFs can be used to produce classical-classical (i.e. classical input, classical output) OWFs that retain the one-wayness property against any quantum polynomial adversary (i.e. quantum-resistant). We demonstrate this in two ways. Firstly, we propose a definition of quantum-classical OWFs and show that the existence of such a quantum-classical OWF would imply the existence of a classical-classical OWF. Secondly, we take a proposed quantum-classical OWF and demonstrate how to turn it into a classical-classical OWF. In summary, this paper showcases another possible route into proving the existence of classical-classical OWFs (assuming intermediate quantum computations are allowed) using a "domain-shifting" technique between classical and quantum information, with the added bonus that such OWFs are also going to be quantum-resistant.