保护私有信息几何对象的相对位置计算

摘要

Privacy-preserving computational geometry is an interesting topic in relation to the secure multi-party computation problem. This paper studies the relative position calculation protocols for two spatial geometric objects in a privacy-preserving situation. Based on a semi-honest model and scalar product protocol, a vector-included angle protocol and a vector-subtracted ratio protocol were presented. On that basis, distance measurements for two line segments and intersection angle calculations among the line and plane in space were developed. Its correctness, security, and efficiency were analyzed. The analysis results show that the new protocols are more efficient than current protocol for it calls less scalar product and privacy comparison calculations, and can be used to solve various privacy-preserving computational geometry problems. They also further the development of secure multi-party computation in computational geometry.%为了探讨在保护参与方隐私前提下,空间几何对象之间的相对位置计算问题,该文在半诚实模型下,基于点积协议,提出了向量夹角协议和向量差比值协议,在此基础上,给出了判定线、线相对位置的新方法,构建了空间线、面夹角计算协议及线、线距离计算协议.给出了协议的正确性证明,并对其安全性和复杂度进行了理论分析.分析结果表明,所提方法调用点积运算和秘密比较运算的次数少于现有方法,有效降低了协议计算复杂度,可用于解决其他更多的安全多方计算几何问题.