空间位置关系的安全多方计算及其应用

空间位置关系的保密计算属于安全多方计算中的空间几何问题，在机密性商业、工程、军事等方面有着重要的意义。但目前大多数空间几何问题都是通过转化为距离或数据对应成比例问题解决的，计算复杂性较高，且应用范围受限。针对这些问题，该文先将原问题转化为一个点是否为一个方程的解，再利用一种简单高效的内积协议一次性解决了点线、点面、线线、线面、面面等5种空间位置关系的判定，并利用模拟范例证明了协议的安全性。该文方案并没有利用任何公钥加密算法，取得了信息论安全；并且由于问题的巧妙转化，使得能解决的问题更加广泛，效率也相对较高。

Secure Multi-party Computation of Spatial Relationship and Its Application

Privacy-preserving determination of spatial relationship belongs to spatial geometry problem in secure multiparty computation, which is significant to confidential business, engineering, military, etc. However, most existing schemes transform the original problem into the distance problem or the correspondingly proportional data problem, which makes the computation complexity high and the application range being limited. To deal with these problems, first, the original problem is transformed into whether a point is the solution of equation. Based on the technique, a simple and efficient scalar product protocol is adopted to determine five spatial relationships all at once: point and line, point and plane, line and line, line and plane, and plane and plane. In addition, the security of the proposed protocol is proved with simulation paradigm. The proposed scheme does not employ any public key encryption algorithm so as to achieve the information security. The analysis indicates the trick transformation makes the proposed scheme higher efficient and more applicable than the known schemes.