高效安全向量计算及其推广

安全多方计算是密码学的一个重要研究方向，也是目前国际密码学界的研究热点.因为许多实际问题都可以用向量来描述，研究向量的保密计算具有重要的理论与实际意义.目前，关于向量保密计算问题大多是在整数集上进行研究，关于有理数向量问题的研究很少.在此主要研究有理数域上向量的安全多方计算问题，包括向量点积、向量相等、向量优势等问题，设计了安全高效的计算协议，扩大了向量保密计算的应用范围.对这些协议的安全性分析和效率分析表明，它们在安全性和效率方面与现有协议相比具有明显优势.并且利用所设计的协议解决了一些新的向量问题和计算几何问题.

Efficient Secure Vector Computation and Its Extension

Secure multiparty computation is an important research topic of cryptography and focus of the international cryptographic community. Many practical problems can be described using vectors. Therefore, it is of important theoretical and practical significance to study secure multiparty vector computation. Existing secure vector computation protocols are for integer vectors, and there are few works on rational vectors. To fill the gap, the secure multiparty computation is studied for rational vectors, including computing the dot product of two vectors, determining whether two vectors are equal, and whether one vector dominates another. The efficient protocols are proposed for these problems and the application of secure vector computation is extended. It is also proved that these new protocols are secure. The efficiency analysis shows that the proposed protocols outperform existing protocols. Finally, these new protocols are applied to solve some new vector computation problems and some computational geometric problems.