Research On Serval Computational Geometry Protocols Of Secure Multi-Party Computational

Secure Multi-Party Computation refers to the problem which two or more parties want to jointly compute a task based on their private inputs, while no party is willing to disclose their privacy to any other. The problem is proposed firstly by A.C.Yao in 1982, has generated a lot of research directions, such as data mining, computational geometry, statistical analysis, electronic voting ect. This paper mainly researches the problems of Privacy-Preserving Computational Geometry. Specifically focuses on the following four aspects:Firstly, we studied the problem of closest-pair of points. Atallah and Du Proposed the issue in 2001, but they did not give the specific implementation methods. So far, the relevant research literature is very less. This paper analysised the problem and constructed a protocol which can solve the privacy-preserving closest-pair of points with homomorphic encryption schemes. About complexity and security, the protocol is more efficient than the current protocols.Secondly, we study the problem of set intersection. It can be applied in many fields, such as commerce and military field. It has important significance of new, safe and fair sharing of database information to research it. We presented currently research and the deficiency of existing protocols. Protocols we proposed can solve the bipartite set intersection and the tripartite set intersection. Then we illustrate the correctness of these protocols and make a precise analysis of complexity and security.Thirdly, we studied the problem of relative position calculation of geometric objects. Luo proposed the problem and gived the specific implementation methods, but they only studied the judgement of relative position of the point, line, surface. We studied the angle of beeline and plane, the distance of beelines, then proposed the solution of the problem.Finally, we studied the problem of collaborative compution of geometric objects. Currently, most of the computation geometry involving only two parties, here we extended to the case of multi-party participation, more generally. We constructed the protocols which solve the privacy-preserving question of triangle's shape, triangle's area and tetrahedron's volume.