A Secure Multiparty Quantum Least Common Multiple Computation Protocol

Abstract: 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.