Security analysis and improvement of a semi-quantum private comparison protocol with three-particle G-like states

Semi-quantum private comparison (SQPC) allows two parties with limited quantum capability to compare their private secrets for equality with the assistance of a quantum third party (TP). Recently, Yan et al. presented an efficient SQPC protocol by using three-particle G-like states as the resource state (Quantum Inf Process 20(6): 17, 2021). However, we discover a design flaw in the protocol and show how it can make the protocol vulnerable to the double CNOT attack, through which a malicious participant can acquire each secret bit of the other honest party with probability 1/2 without being detected. Then, we propose an improved SQPC protocol and show that it can be secure against similar types of attack that can be avoided in the original SQPC protocol and also the double CNOT attack.