A Study Of Secure Multiparty Computation Protocol For Two Geometry Problems

The collaborative computation of network users has become more and more common with the development of information technology.Secure Multi-party Computation expands the scope of traditional distributed computation and information security,and provides a new computing model for network collaborative computation.It is of great significance to solve the problem of information security in the network environment.At present,Secure Multi-party Computation has important applications in many aspects and has become an indispensable part of Cryptography.This paper studies the confidential computation of Manhattan distance and the confidential determination of the positional relationship between points and polygons or between points and polyhedrons.The main research contents are as follows:(1)For the confidential computation of Manhattan distance,the protocol in this paper uses the nature of the absolute value of the difference between two numbers and the Paillier homomorphic encryption scheme to cleverly solve the problem of confidential computation of absolute value,and extends it to the confidential computation of Manhattan distance protocol of n-dimensional vectors.In addition,this paper proposes a new encoding method,which converts the data into a natural array form on the basis of the corpus,and constructs an protocol to compute the Manhattan distance confidentially.The important thing is that the protocols in this paper can be applied to the range of rational numbers.This paper uses the simulator view simulation method to analyze the security of the protocol,and the results show that the protocols in this paper is safe under the semi-honest model.Through theoretical efficiency analysis and comparison,the protocols in this paper is efficient.(2)Regarding the confidential determination of the positional relationship between point and polygon or polyhedron,this paper analyzes the current research status of this problem,summarizes its advantages and disadvantages,and proposes a new scheme for determining the positional relationship between point and triangle.This scheme transforms the problem of the position relationship between point and triangle into the problem of the position relationship between point and interval,and constructs a secure protocol.On the basis of solving the problem of the positional relationship between point and triangle,this paper solves the positional relationship problem between point and polygon or between point and polyhedron.Through the theoretical analysis and comparison of the efficiency of this protocol and the existing results,the efficiency of this protocol has been greatly improved.