Commitments from Quantum One-Wayness

• URL: http://arxiv.org/abs/2310.11526v4
• Date: Mon, 29 Jan 2024 18:47:50 GMT
• Title: Commitments from Quantum One-Wayness
• Authors: Dakshita Khurana (UIUC) and Kabir Tomer (UIUC)
• Abstract summary: This work studies one-way state generators, a natural quantum relaxation of one-way functions. A fundamental question is whether this type of quantum one-wayness suffices to realize quantum cryptography. We prove that one-way state generators with pure state outputs imply quantum bit commitments and secure multiparty computation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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