Research On Geometric Problem Of Security-oriented Multi-party Computation

At present,the information transmission and feedback of people are becoming more and more rapid and frequent because of the increasing prosperity of Internet technology in the network environment.As a platform for people to exchange and interact in every day life,the network brings us convenience and shortcut,but also leaks our privacy.That is called information safety.Cryptography is the cornerforce to protect information security.As a result of the diversity of encryption methods,encryption technology is also improving and moving towards all aspects of people's lives,which provides a strong guarantee for users' privacy data not being leaked.Secure multi-party compution is a hot topic in the field of cryptography.Nowadays,secure multiparty computation is widely applied in the fields of data security and privacy protection,data mining,scientific compution and computational geometry.The computational geometry of privacy protection is a novel secure multiparty compution problem.In accordance with the special needs of life,it abstracts specific problems into computational geometric models,and designs special protocols according to the computational geometry model.Nowadays,the computational geometry of privacy preserving is of great theoretical value and strong practical application prospects in secure image processing,scientific compution engineering,geolocation and national defense construction.At present,scholars have not only achieved great achievements in plane geometry,but also made amazing achievements in space geometry for the computational geometry of privacy preserving.Based on the semi-honest model,we study the problems of spatial distance and security decision,and put forward new secure multi-party computation protocols.The main contents are as follows:(1)Oblivious transfer protocol is usually adopted in secure multi-party computation,but the efficiency is low and the computation complexity is high.To solve this problem,new privacy protection protocols are proposed.The first protocol(SSTS protocol): the distance calculation protocol between two parallel lines in three-dimensional space under standard form.The second protocol(PHEA protocol): the distance calculation protocol between two parallel lines in three-dimensional space under intersection form.The two protocols can effectively reduce the computational complexity and communication complexity of the two parallel straight line distance problem in three-dimensional space.Besides,the correctness of SSTS protocol and PHEA protocol is calculated and deduced respectively.The security of SSTS protocol and PHEA protocol is proved by simulation example.(2)A new security decision protocol is proposed aiming the position relationship between the straight line and the two degree curve.Since the protocol is based on homomorphic encryption algorithm,this protocol effectively reduces the computation complexity and communication complexity of location relation between straight line and two degree curve.In addition,the correctness of this protocol is calculated and deduced,and the security of the protocol is proved by the simulation example.