中文摘要：

近年来，随机化算法因其优良的性能吸引了大批学者的关注。在很多问题的求解中，随机化算法常有着惊人的效率，它通常是最快或者是最简单的算法，有时甚至二者兼备。讨论随机化算法在求解最小外接圆中的应用，介绍一个基于随机增量式的递归式算法，对该算法的思想进行详细的叙述，从理论上分析其性能，并结合实验验证，说明该随机化算法具有良好的性能。引入安全性要求，探讨如何在安全多方计算的环境下求解最小外接圆。

英文摘要：

In recent years, randomized algorithm attracts lots of scholars＇ attention, because of its excellent performance. In many problems, randomized algorithms often have stupendous efficiency, they generally are the fastest or simplest algorithms, even both. Discusses the application of the randomized algorithms in finding the minimal circumscribed circle, introduces a recursive algorithm which is based on the randomized incremental algorithm, and depicts the thinking of the algorithm in detail, proves that it has good performance by analyzing its performance in theory and validating it experimentally. At last, oonsider the security requirement, research the problem of the minimal eireurmcribed circle under the environment of secure multi - party computation.