In this letter, we delve into a scenario where a user aims to compute polynomial functions using their own data as well as data obtained from distributed sources. To accomplish this, the user enlists the assistance of $N$ distributed workers, thereby defining a problem we refer to as privacy-preserving polynomial computing over distributed data. To address this challenge, we propose an approach founded upon Lagrange encoding. Our method not only possesses the ability to withstand the presence of stragglers and byzantine workers but also ensures the preservation of security. Specifically, even if a coalition of $X$ workers collude, they are unable to acquire any knowledge pertaining to the data originating from the distributed sources or the user.

翻译：本文探讨了一种场景：用户希望利用自身数据以及从分布式来源获取的数据来计算多项式函数。为实现此目标，用户借助$N$个分布式工作节点的协助，由此定义了一个我们称之为“面向分布式数据的隐私保护多项式计算”的问题。为应对这一挑战，我们提出了一种基于拉格朗日编码的方法。该方法不仅能够抵御滞后节点和拜占庭节点的存在，还能确保安全性。具体而言，即使有$X$个工作节点结盟共谋，它们也无法获取任何关于分布式来源或用户数据的信息。