Quantum (t, n) threshold group signature based on Bell state

Quantum group signature is an important branch of quantum signature. Most of the existing quantum group signature schemes require that all the signatories must be present to generate a valid signature, and this property may limit their application in practice. In this paper, we will propose a quantum (t, n) threshold group signature scheme. In our scheme, n signatories compose a group, and any t out of these n signatories can generate a valid signature on behalf of the group. The t signatories use the quantum-controlled-not operations to expand the quantum message into t-particle entangled states, and then use the entanglement swapping to transmit the quantum message to the receiver. The receiver performs the single-particle measurements and unitary operations to recover the initial quantum message, and then verifies the signature with the help of the arbitrator. Compared to the existing quantum group signature schemes, our (t, n) threshold scheme will be more flexible in practice.