Cryptanalysis and improvement of a (t, n) threshold group signature scheme

Recently, a (t, n) threshold group signature scheme is present in Qin et al. (Quantum Inf Process 19(2):71, 2020). In this paper, we point out that it is not a threshold signature scheme, namely any number of members can generate a valid signature. By introducing a secret sharing scheme, we show how to improve the original scheme to a threshold signature scheme. In the original scheme, the key for the one-time pad encryption is used more than once, which makes the verifier recover the key and fabricate any signature at his will. We show how to close this security loophole. And we also show how to add a round for checking the honesty of the arbitrator, and thus the trust put on the arbitrator can be reduced.