Comment on "Fault-Tolerate Quantum Private Comparison Based on GHZ States and ECC"

TL;DR

This paper critically analyzes a fault-tolerant quantum private comparison scheme using GHZ states, identifies a security loophole under a specific attack, and proposes an improved method with permutation operators to enhance security.

Contribution

It reveals a security flaw in an existing fault-tolerant quantum comparison protocol and introduces a permutation-based enhancement to prevent the identified attack.

Findings

The original scheme is vulnerable to a twice-Hadamard-CNOT attack.

Applying a permutation operator effectively prevents the specific attack.

The improved protocol enhances the security of quantum private comparison schemes.

Abstract

A two-party quantum private comparison scheme using GHZ states and error-correcting code (ECC) was introduced in Li et al.'s paper [Int. J. Theor. Phys. 52: 2818-2815, 2013], which holds the capability of fault-tolerate and could be performed in a none-ideal scenario. However, this study points out there exists a fatal loophole under a special attack, namely the twice-Hadamard-CNOT attack. A malicious party may intercept the other's particles, firstly executes the Hadamard operations on these intercepted particles and his (her) own ones respectively, and then sequentially performs twice CNOT operations on them and the auxiliary particles prepared in advance. As a result, the secret input will be revealed without being detected through measuring the auxiliary particles. For resisting this special attack, an improvement is proposed by applying a permutation operator before TP sends the particle sequences to all the participants.