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arXiv · 2506.16904

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

Le-Ran Liu·Min-Quan He·Dan-Bo Zhang·Z. D. Wang
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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

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Le-Ran Liu, Min-Quan He, Dan-Bo Zhang, Z. D. Wang. 2025-06-20. Public-Key Quantum Authentication and Digital Signature Schemes Based on the QMA-Complete Problem. https://arxiv.org/abs/2506.16904

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