In this paper, we present a secure multiparty computation (SMC) protocol for least common multiple (LCM) based on Shor's quantum period-finding algorithm (QPA). Our protocol is based on the following principle: the connection of multiple periodic functions is also a periodic function whose period is exactly the least common multiple of all small periods. Since QPA is a probabilistic algorithm, we also propose a one-vote-down vote protocol based on the existing secure multi-party quantum summation protocol, which is used to verify the results of the proposed LCM protocol. Security analysis shows that under the semi-honest model, the proposed protocol is secure with high probability, while the computational consumption remains at polynomial complexity. The protocol proposed in this paper solves the problem of efficient and secure multiparty computation of LCM, demonstrating quantum computation potential.

翻译：本文提出了一种基于Shor量子周期搜索算法（QPA）的安全多方计算（SMC）协议，用于求解最小公倍数（LCM）。该协议基于以下原理：多个周期函数的复合仍为周期函数，其周期恰好等于所有小周期的最小公倍数。由于QPA属于概率性算法，我们进一步基于现有安全多方量子求和协议提出了一种一票否决投票协议，用于验证所提LCM协议的计算结果。安全性分析表明，在半诚实模型下，本协议以高概率实现安全性，同时计算复杂度保持多项式级别。本文提出的协议解决了高效安全计算LCM的多方问题，展现了量子计算的应用潜力。