Finding min-cut is a fundamental operation in graph theory. It has been widely used in many applications such as image segmentation and network partition. However, solving the min-cut problem is time-consuming for resource-constrained devices, especially when the graph is large and dense. In this paper, we explore how to securely solve the min-cut problem in the cloud environment, and propose two secure outsourcing schemes for the min-cut of undirected edge-weighted graphs. The first scheme is based on two non-colluded untrusted cloud servers, and the second one is under the single untrusted cloud server model. In the designed schemes, we develop a new technique that contains merging vertices and edges, inserting fake vertices and edges, shuffling vertices and randomizing weights of edges to protect the privacy of graphs. In order to realize the checkability of result from a single untrusted cloud server, we design a novel verification mechanism by outsourcing the min-cut of two related graphs. Besides, we also provide security analysis and the experimental evaluation. To the best of our knowledge, it is the first research on secure outsourcing of graph algorithm.

中文翻译：

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如何安全地外包找到无向边加权图的最小切除

查找最小割是图论中的基本操作。它已被广泛用于许多应用中，例如图像分割和网络分区。但是，对于资源受限的设备，解决最小切割问题非常耗时，尤其是当图形较大且密集时。在本文中，我们探索了如何安全地解决云环境中的最小割问题，并针对无向边加权图的最小割提出了两种安全的外包方案。第一个方案基于两个非冲突的不可信云服务器，第二个方案在单个不可信云服务器模型下。在设计的方案中，我们开发了一种新技术，其中包括合并顶点和边，插入伪顶点和边，对顶点进行混洗以及对边的权重进行随机化以保护图形的隐私。为了实现来自单个不受信任的云服务器的结果的可检查性，我们通过将两个相关图的最小割点外包来设计一种新颖的验证机制。此外，我们还提供安全性分析和实验评估。据我们所知，这是图算法安全外包的第一项研究。