Security Analysis of the Quantum (t, m, n) Threshold Group Blind Signature Scheme and its Improvement

Abstract

Recently, a threshold group blind quantum signature scheme has been proposed. Compared to other similar schemes, this scheme has flexibility in the number of signers and the original message is blind. However, our analysis revealed two security vulnerabilities in this scheme. First, some of the shared secret keys have issues with leakage to other participants. Second, the blindness of the original message is partially invalidated for the signer and the third-party. In this paper, we proved these two vulnerabilities and proposed an improved scheme also based on entanglement swapping. In the improved scheme, a trusted third-party is responsible for generating the threshold key, the sender is responsible for blinding the original message, at least \(\varvec{t}\) signers collaborate to generate the signature, and the third-party and verifier jointly perform the verification. The improved scheme not only overcomes the vulnerabilities of the old scheme but also has relatively better efficiency. In addition, this scheme has unforgeability and undeniability, the number of signers remains flexible and it satisfies threshold security.