Quantum Commitments from Complexity Assumptions

TL;DR

This paper explores complexity-theoretic assumptions that enable the construction of quantum bit-commitment schemes, providing new links between complexity classes and cryptographic primitives.

Contribution

It introduces new quantum commitment schemes based on complexity assumptions like QSZK not in QMA and QIP not in QMA, expanding the theoretical foundations of quantum cryptography.

Findings

QSZK not in QMA implies a secure quantum commitment scheme

Quantum advice-based schemes depend on QIP not in QMA

Existence of a quantum oracle separating QSZK and QCMA

Abstract

Bit commitment schemes are at the basis of modern cryptography. Since information-theoretic security is impossible both in the classical and the quantum regime, we need to look at computationally secure commitment schemes. In this paper, we study worst-case complexity assumptions that imply quantum bit-commitment schemes. First, we show that QSZK not included in QMA implies a computationally hiding and statistically binding auxiliary-input quantum commitment scheme. Additionally, we give auxiliary-input commitment schemes using quantum advice that depend on the much weaker assumption that QIP is not included in QMA (which is weaker than PSPACE not included in PP). Finally, we find a quantum oracle relative to which honest-verifier QSZK is not contained in QCMA, the class of languages that can be verified using a classical proof in quantum polynomial time.