中文摘要：

目前安全多方几何计算问题都是在传统模式下依靠参与方交互完成,文中首次将安全多方几何计算问题转移到云计算平台下借助不可信第三方云服务器参与完成,这为安全多方计算提供了一个新的研究方向.传统模式下空间位置关系的保密判定已存方案,大多是把原问题转化为距离问题或数据对应成比例问题,造成了用户计算成本过大,或能判断的位置关系有限,而且这些方法只能由参与方相互交互完成,因此在云计算平台下并不适用.针对这些问题,文中首先将原问题转化为夹角问题,接着设计了适用于云外包计算的内积协议,然后基于此内积协议在云平台下解决了点线、线线、点面、线面、面面五种空间位置关系的保密判定,并用模拟范例证明了协议的安全性.最后的分析和比较显示,文中不但首次设计了云计算平台下空间位置关系的保密判断协议,并且设计的方案能判断的位置关系更加广泛,也为用户节省了更多的计算成本.此外,我们设计的内积协议可以作为一种新的云计算技术的基础协议,可以被其他协议调用.

英文摘要：

Up to now, all secure multi-par ty geometric computation problems are conducted underthe conditional pattern, which is handled only by the interaction of participants. In this paper, we first transform this traditional pattern into the cloud computing pattern, which allows the untrusted third party （i. e. , the cloud server） involved in the procedure of calculation. This manner provides a new research direction for secure multi-party computation. The most existing schemes about privacy-preserving determination of spatial location-relation transform the original problem into either the distance problem or the correspondingly proportional data problem and solve it with traditional pattern. These approaches burden the user’ s computation overhead or limit the range of determining location-relation, moreover, with which the participants accomplish the computation task only by their interactive with each other. It is not suitable for secure mult- party computation in cloud computing. Aiming at these problems, we first transform the original problem into the included angle problem, then design a novel protocol of scalar product available for cloud computing, and further determine the five spatial location-relation： point and line, point and plane, line and line, line and plane, and plane and plane in cloud computing. Lastly, we prove the security of our protocols with simulation paradigm. The analysis indicates it is the first that we design the protocol for preserving-privacy determination of spatial location-relation in cloud computing, which can not only save more computation cost for users but also determine more location-relation than the known schemes. In addition, the proposed scalar protocol in this work as the new technique of cloud computing can be used a building-block, which can be invoked by other schemes.