Improvements on "Multi-Party Quantum Summation without a Third Party based on $d$-Dimensional Bell States"

TL;DR

This paper identifies security loopholes in Wu et al.'s multi-party quantum summation protocol using d-dimensional Bell states and proposes improvements to enhance security against colluding dishonest participants.

Contribution

The paper introduces modifications to Wu et al.'s protocol to fix identified security loopholes, strengthening its resistance to participant collusion.

Findings

Loophole allows dishonest participants to conspire and reveal honest inputs.

Proposed improvements close the security gap and prevent collusion attacks.

Enhanced protocol maintains efficiency while improving security.

Abstract

In 2021, Wu et al. presented a multi-party quantum summation scheme exploiting the entanglement properties of d-dimensional Bell states (Wu et al. in Quantum Inf Process 20:200, 2021). In particular, the authors proposed a three-party quantum summation protocol and then extended their work to a multi-party case. It is claimed that their protocol is secure against outside and participants' attacks. However, this work points out that Wu's protocol has a loophole, i.e., two or more dishonest participants who meet a specific location relationship can conspire to obtain the private inputs of some honest participants without being detected. Accordingly, improvements are proposed to address these issues.