两个凸包相交检测的安全两方计算协议
A Secure Two-Party Computation Protocol for Intersection Detection between Two Convex Hulls
摘要：
三维物体之间的相交检测在计算机图形学、视频游戏开发、机器人技术以及军事工业中具有各种应用。在某些方面，实体不想披露关于它们自己的敏感信息，包括它们的位置。在本文中，我们提出了一个安全的两方协议，以确定实体之间的交集的存在。本文提出的协议允许在三维空间中的几何相交检测。我们的方法是使用两个空间之间的相交平面来确定它们的分离或相交。为此，我们引入了一个计算几何协议，以确定相交平面的存在。本文首先利用Minkowski差分将两个空间问题化为一个空间问题。然后，得到分离集，并根据中心点的包含情况确定两个形状的分离度。然后，我们通过修改分离集计算方法作为一个隐私保护和改变Minkowski差分方法来实现这一目标的协议安全。所提出的协议适用于任何形式的凸三维形状。实验成功地找到了一种安全的两个凸包之间的相交检测协议的几何形状，如金字塔和长方体。
英文摘要：
Intersection detection between three-dimensional bodies has various applications in computer graphics, video game development, robotics as well as military industries. In some respects, entities do not want to disclose sensitive information about themselves, including their location. In this paper, we present a secure two-party protocol to determine the existence of an intersection between entities. The protocol presented in this paper allows for intersection detection in three-dimensional spaces in geometry. Our approach is to use an intersecting plane between two spaces to determine their separation or intersection. For this purpose, we introduce a computational geometry protocol to determine the existence of an intersecting plane. In this paper, we first use the Minkowski difference to reduce the two-space problem into one-space. Then, the separating set is obtained and the separation of two shapes is determined based on the inclusion of the center point. We then secure the protocol by modifying the separating set computation method as a privacy-preserver and changing the Minkowski difference method to achieve this goal. The proposed protocol applies to any form of convex three-dimensional shape. The experiments successfully found a secure protocol for intersection detection between two convex hulls in geometrical shapes such as the pyramid and cuboid.
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