Semi-quantum private comparison protocol of size relation with d-dimensional GHZ states

A novel efficient semi-quantum private comparison protocol based on the d-dimensional GHZ states is proposed. With the assistance of semi-honest third party, two classical participants can compare the size relation of their secrets without any information leakage. To reduce the consumption of quantum devices, the qubit efficiency of our protocol is improved by introducing the semi-quantum conception via the existing semi-quantum private comparisons. Furthermore, it is unnecessary to prepare the secure classical authentication channel among participants in advance. It is shown that our protocol is not only correct and efficient, but also free from external and internal attacks.