Multi-party semiquantum key distribution with multi-qubit GHZ states

In this paper, we first put forward a four-party semiquantum key distribution (SQKD) scheme by using three-qubit GHZ states, which can establish three different private keys shared by one quantum user and three semiquantum users simultaneously. It doesn’t need a third party, and employs three-qubit GHZ states as the initial quantum resource. It requires the quantum user to perform the \(Z\) $Z$ basis (i.e., \(\left\{ {\left| 0 \right\rangle ,\left| 1 \right\rangle } \right\}\) $\left\{\left|0\right.〉,\left|1\right.〉\right\}$ ) measurements and the GHZ basis measurements, and needs the semiquantum users to implement the \(Z\) $Z$ basis measurements. It adopts none of Pauli operations, Hadamard gate or quantum entanglement swapping, and doesn’t require the semiquantum users to use any quantum memory. Detailed security proof shows that this four-party SQKD scheme is secure against different kinds of attack from an outside eavesdropper. Finally, we generalize the four-party SQKD scheme into the counterpart of \(M + 1\) $M+1$ -party.