安全多方计算中空间位置关系的保密判定

Privacy-Preserving Determination of Spatial Location-Relation in Secure Multi-Party Computation

保密判断空间位置关系属于安全多方计算中的几何问题,在军事、商业等领域有着广泛的应用前景.针对空间中位置关系问题,首先将该问题转化为平行四边形面积问题,接着设计了保密计算两向量张成的平行四边形面积协议,然后基于此协议解决了空间中三点共线和点线面位置关系的保密判定问题,最后,利用模拟范例证明了协议的安全性.分析和比较显示：与已有的方案相比,本文的方案避免了多个基础协议的调用,不但提高了效率,而且适用范围更加广泛.此外,由于我们的方案没有使用任何公钥加密算法,因此达到了信息论安全.

Privacy-preserving determination of spatial location-relation is classified as geometry problem in secure multiparty computation,and it is widely applied in business and military service.Aiming at spatial location-relation issue,we first transform this problem into the area problem of parallelogram,and then design a protocol to compute the area of the parallelogram formed by the two vectors.Furthermore,based on this protocol,the protocols of the three points collinear,and the location-relation of point line and plane in space are designed.Lastly,we prove the security of our protocols with simulation paradigm.Compared with the existed schemes,our protocols avoids the invoking of multiple basic protocols,and it not only improves the efficiency but also extends the scope of application.In addition,the proposed scheme does not employ any public key encryption algorithm to make our protocols achieve the information security.