Cryptanalysis and improvement of the quantum private comparison protocol based on Bell entangled states

TL;DR

This paper analyzes a quantum private comparison protocol based on Bell states, identifies a critical security flaw allowing a third party to learn secrets, and proposes an improved, more secure, and efficient version using decoy photons.

Contribution

It reveals a security loophole in Liu et al.'s protocol and introduces a simplified, more secure protocol with reduced resource consumption.

Findings

Original protocol has a fatal security loophole.

The improved protocol prevents third-party eavesdropping.

Resource usage is reduced in the new protocol.

Abstract

Recently, Liu et al. [Commun. Theor. Phys. 57, 583, 2012] proposed a quantum private comparison protocol based on entanglement swapping of Bell states, which aims to securely compare the equality of two participants' information with the help of a semi-honest third party (TP). However, this study points out there is a fatal loophole in this protocol, i.e., TP can obtain all of the two participants secret inputs without being detected through making a specific Bell-basis measurement. To fix the problem, a simple solution, which uses one-time eavesdropper checking with decoy photons instead of twice eavesdropper checking with Bell states, is demonstrated. Compared with the original protocol, it also reduces the Bell states consumption and simplifies the steps in the protocol.