Public-Key Quantum Authentication and Digital Signature Schemes Based on the QMA-Complete Problem

TL;DR

This paper introduces a quantum public-key authentication and digital signature scheme based on QMA-complete problems, eliminating the need for trusted third parties and ensuring security against quantum adversaries.

Contribution

It presents a novel quantum cryptographic protocol leveraging QMA-complete problems for public-key authentication, with rigorous security proof and practical verification analysis.

Findings

Protocol is unforgeable against quantum attacks

Security reduces to solving a QMA-complete problem

Verification efficiency is analyzed via quantum state tomography

Abstract

We propose a quantum authentication and digital signature protocol whose security is founded on the Quantum Merlin Arthur~(QMA)-completeness of the consistency of local density matrices. The protocol functions as a true public-key cryptography system, where the public key is a set of local density matrices generated from the private key, a global quantum state. This construction uniquely eliminates the need for trusted third parties, pre-shared secrets, or authenticated classical channels for public key distribution, making a significant departure from symmetric protocols like quantum key distribution. We provide a rigorous security analysis, proving the scheme's unforgeability against adaptive chosen-message attacks by quantum adversaries. The proof proceeds by a formal reduction, demonstrating that a successful forgery would imply an efficient quantum algorithm for the QMA-complete Consistency of Quantum Marginal Problem~(QMP). We further analyze the efficiency of verification using partial quantum state tomography, establishing the protocol's theoretical robustness and outlining a path towards practical implementation