高维空间平行四边形面积的多方保密计算

Secure multi-party computation of high-dimensional spatial parallelogram area

几何问题的安全多方计算在保密位置判断、保密数据查询等方面有着重要的应用价值。但目前大多数几何问题的研究主要集中在平面几何,很少涉及空间几何。文章从一个军事实际问题出发,首先利用两方置换协议和同态加密算法保密计算了空间几何中2个高维向量差的范数,并用模拟范例证明了此方案的安全性。接着,利用此方案设计了空间几何中平行四边形面积的保密计算协议。不同于以往的方案,协议使用了一个有关安全两方置换问题的转化技巧,避免了以往方案中出现的高次模指数运算,因此效率较高;由于方案不局限于三维向量,适合于任何高维向量,更具有普遍意义。

Secure multi-party computation of the geometric problems is significant to privacy-preserving location estimation,data query,etc. But most of the existing literatures of geometric problems have focused on plane geometry,while few have addressed spatial geometry. In this paper,motivated from a military problem,we first compute securely the norm of high-dimensional vector difference using homomorphic encryption and secure two-party permutation protocol,and further prove the security of this scheme with simulation paradigm. Then,we design the privacy-preserving protocol of the area of parallelogram in spatial geometry using this scheme,so as to solve our real problem. Unlike the previously known,our scheme adopts a technique of conversion about secure two-party permutation protocol,which avoids highorder modular exponentiation in other known schemes. It makes our scheme efficient; In addition,our scheme is suitable for any high-dimensional vector except three-dimensional one,which makes our scheme more universal than others.