中文摘要：

目前,关于几何图形的相似问题仅限于多边形的相似,而一般几何图形相似的问题还没有研究.本文利用单向散列函数首先设计了保密判断两个数是否相等的协议、保密矩阵和向量是否相等的协议;最终,利用矩阵和向量相等的协议设计了保密判断图形是否同构和图形是否相似的协议.给出了以上协议的安全性证明、仿真实验与效率分析,实验数据表明本文保密的图形相似判定协议效率是两个多边形相似协议效率的889倍.图形相似的保密判定问题是一个全新的安全多方计算几何问题,本文研究成果可应用在分子生物学、机械工程和地形匹配等领域.

英文摘要：

At present,graphical similarity is limited to polygonal similarity,but the problem of general graphical similarity has not been studied. We first present protocols for privately determining whether two numbers,matrices or vectors are equal based on one-way hash function. Finally,we design protocols to privately determine whether two special graphics are isomorphic,and whether two graphics are similar. We prove the security of the protocols,implement them on a personal computer and analyze their efficiency. The simulation shows that the protocol of two similar graphics is 889 times as fast as the protocol of two similar polygons. Privately determining whether two graphs are similar is completely a newsecure multiparty computation problem. It has application prospects in the field of the molecular biology,mechanical engineering and terrestrial matching,etc.