Classical Communication Coset State (t,n) Threshold Quantum Digital Signature

In the field of quantum communication, classical communication processes have become a central open problem, especially in quantum threshold signature schemes. However, the existing quantum threshold signature schemes do not solve this problem well, and the signature verification process is relatively complicated. Therefore, the aim of this study is to propose a novel quantum threshold digital signature scheme that aims to realize classical communication and simplify the quantum threshold digital signature communication model while ensuring the security of the signature. Our approach constructs a binary linear secret-sharing matrix based on the properties of the coset states in the quantum state to share the master secret value and distribute the quantum tokens of the members. Unlike traditional schemes, our verification operation does not require the intervention of an arbitrator, thus simplifying the signature-verification process. In addition, we propose a novel reuse quantum-token protocol based on the length of the hash message to-be-signed to enable single-member signatures over multiple bits. This scheme has other potential applications, including eavesdropper identification, quantum threshold proxy signatures, and more flexible quantum threshold schemes. In addition, complex measurement operations are not required to verify the signatures, thus fulfilling the requirements of practical applications. In this paper, we present an innovative approach for solving the classical communication problem in quantum threshold signature schemes, which successfully solves the central open problem in this field by transforming the measurements of quantum states into classical communication. We believe that this approach will provide a more feasible solution for secure communication.