Straightness And Ellipse, Straight Line And Hyperbolic Position Relationship Between The Security Decision Protocol

With the rapid development of modern information society, there are more and more people communicating with each other through the Internet frequently. During the communication process of information, people have seen a lot of advantages, such as the convenience and speediness. But at the same time, they also realized an important issue, called Information Safety. There are many kinds of information safety problems, for example, network intrusion, personal information disclosure and so on. To solve these problems, we need to use a series of technologies. Because of the progress of Internet society, it makes secure multi-party computation possible. In the process of multi-party computation, each party needs to protect its personal information from disclosure, but they still want to get the result. For that reason, secure multi-party computation exists as an important field. Now secure multi-party computation has become a major issue in code educational circles. It has also been used in many fields, privacy preserving computational geometry is one of them.There is an example of secure multi-party computation at the beginning. Then the concept, research background, current situation and significance of secure multi-party computation is introduced. Some basic concepts and protocols about secure multi-party computation are described, and some geometry issues are discussed and analyzed.The four protocols presented in this thesis are all based on semi-honest model:The first protocol is designed for protocol two and protocol four. It mainly uses the privacy-preserving dot product protocol to compute d2.The second protocol, the position determination protocol of line and ellipse with privacy preserving is used for determining the position of line and ellipse without the disclosure of their private information. It is mainly based on the first protocol and privacy-preserving point-line relation determination protocol.There are more kinds of positions in the determination of line and hyperbola than that in the determination of line and ellipse. So it is more complicated and difficult to determine the position of line and hyperbola. Protocol three and protocol four are designed in different ways to solve this issue. Protocol three is based on algebraic method. It gets the discriminant of simultaneous equation of line and hyperbola, and then determines the position with the result of the discriminant.Protocol four, using the same geometry method as protocol two, computes the slope and intercept of line and asymptote. Then it gets d2by protocol one and compares d2and4a2by millionaires’ protocol. Protocol three and four are also compared in method and computing complexity.At last, four protocols are analyzed and compared in their objectives and computing complexity. Protocol two is taken as a example to analyze its computing complexity with different privacy-preserving dot product protocol and millionaires’ protocol.