Cryptanalysis and improvement on two party quantum private comparison based on seven-qubit and eight-qubit states

Ji et al. [Mod. Phys. Lett. A 34, 1950229 (2019)] and Fan et al. [Mod. Phys. Lett. A 37, 2250026 (2022)] proposed two-party quantum private comparison (QPC) protocols based on 7-qubit and 8-qubit states, respectively. However, these two QPC protocols did not consider third-party (TP) attacks. Therefore, this study focuses on TP attacks and demonstrates that the property of a 7-qubit or 8-qubit entanglement state is useless in this attack situation; that is, the participant wastes resources to maintain the qubits. For the same assumption environment proposed by Ji et al. and Fan et al., this study proposes an improvement and simplification protocol that allows participants to reach the goal of private comparison by using only classical computation and the classical communication channel without any entanglement state.