Locally verifiable approximate multi-member quantum threshold aggregation digital signature scheme

Locally verifiable aggregate signature primitives can reduce the complexity of aggregate signature verification by computing locally open algorithms to generate auxiliary parameters. However, the breakthrough results of quantum computers at this stage indicate that it will be possible for quantum computers to break through the security of traditional hardness-based aggregated signature schemes. In order to solve the above problems, this paper proposes for the first time a new locally verifiable class of multi-member quantum threshold aggregated digital signature scheme based on the property that the verification of quantum coset states is a projection on the trans-subspace. Combined with the idea of auxiliary parameter generation in traditional locally verifiable aggregated signatures, it makes the current stage of threshold quantum digital signatures realize the aggregated features, and reduces the complexity of the verification of aggregated signatures while realizing post-quantum security. In addition, the verification of the signature key (quantum state) of the signature members does not require measurement operations, and the generated signatures are classical, so the communication between the trusted third center (TC), the set of signature members, the classical digital signature verifier (CV), and the third-party trusted aggregation generator (TA) are all classical, simplifying the communication model. In the performance analysis we make this quantum aggregation signature scheme more flexible as well as less quantum state preparation compared to other schemes.