Commitments from Quantum One-Wayness

TL;DR

This paper demonstrates that quantum one-way state generators can be used to realize quantum cryptographic primitives like bit commitments and multiparty computation, bridging a gap between quantum assumptions and cryptographic applications.

Contribution

It proves that quantum one-way state generators with pure states imply quantum bit commitments and secure multiparty computation, introducing the intermediate primitive of quantum one-way puzzles.

Findings

Quantum one-way state generators imply quantum bit commitments.

Quantum one-way state generators imply secure multiparty computation.

Introduction of quantum one-way puzzles as an intermediate primitive.

Abstract

One-way functions are central to classical cryptography. They are both necessary for the existence of non-trivial classical cryptosystems, and sufficient to realize meaningful primitives including commitments, pseudorandom generators and digital signatures. At the same time, a mounting body of evidence suggests that assumptions even weaker than one-way functions may suffice for many cryptographic tasks of interest in a quantum world, including bit commitments and secure multi-party computation. This work studies one-way state generators [Morimae-Yamakawa, CRYPTO 2022], a natural quantum relaxation of one-way functions. Given a secret key, a one-way state generator outputs a hard to invert quantum state. A fundamental question is whether this type of quantum one-wayness suffices to realize quantum cryptography. We obtain an affirmative answer to this question, by proving that one-way state generators with pure state outputs imply quantum bit commitments and secure multiparty computation. Along the way, we build an intermediate primitive with classical outputs, which we call a (quantum) one-way puzzle. Our main technical contribution is a proof that one-way puzzles imply quantum bit commitments.