Research On Application Protocols Of Secure Multi-Party Geometry And Sets Computation

As an important part of cryptography,SMC has become focus in the international cryptographic community.It breaks the traditional "partnership" relationship,and achieves the seemingly impossible win-win dialogue between opponents through the way of privacy-preserving computation.Early,the researchers paid more attention to the general method of secure multi-party computation.However,for specific application problems,the general method is not efficient or costly.Therefore,the customized SMC protocol is more in line with the requirements of the participants.Now,SMC is developing towards high availability and high security.So,it has become a hot topic for how to design a SMC application protocol with efficiency and security.In this paper,we focus on the application of secure multi-party geometric and set computation,including secure position relation judgment,secure spatial geometry computation,secure sets computation,secure more data/sets comparison.And we propose a series of solutions with safe,efficient and expandable.The main innovative works are as follows:1.Based on Paillier homomorphic encryption and wedge segmentation principle,a new privacy-preserving point-in-polygon protocol is proposed under semi-honest model.First,using 1-out-of-n oblivious transfer and geometric properties of the vector,general point-line protocol is extended to an oblivious secure point-line relationship protocol.Then,an new privacy-preserving point-in-polygon protocol is proposed based on wedge-shaped segmentation and secure binary search protocol.The basis of new protocol is the oblivious secure point-line protocol.The security of the protocol is proved.The validity and the complexity of the protocol is analyzed.The results show that this protocol has better efficiency and extenbility than the existing ones.2.Based on cloud platform and Boneh encryption,secure Euclidean distance square computation are designed.This protocol can resist the collusion between users and untrusted cloud platform and effectively protect users' privacy information.Using the above protocol as a building block,we provide a secure solid triangular area computation protocol.Combined with the geometric properties of the cayley-menger determinant,the protocol converts calculation of solid triangular areas into the calculation of determinant,and effectively solve the problem of privacy-preserving triangle area computation.Then we provide the solid tetrahedral volumes.Then,a secure two-square space tetrahedron volume calculation protocol is proposed,which has the same construction idea as the secure triangle area computation protocol.In addition,the protocol is used to solve the secure problem of the distance between points and lines,distance between points and surfaces and other secure multi-party spatial geometry problems,which broadens the solution ideas of secure spatial geometry problems.3.A secure two-party sets computation protocol based on cloud server outsourcing is proposed.The protocol realizes the privacy protection of privacy sets of participants with the combination of the point value calculations of polynomial and Boneh encryption system.During protocol execution,the calculation of each participant is completely independent without any form of data interaction.It allows multiple participants to storage their private data to the cloud server independently without having to upload copies multiple times.The correctness,security and performance of protocol is proved,and the result of experimental analysis show that the calculation cost of the protocol is better.4.A secure two-party sets comparison protocol is proposed based on the NTRU encryption.First,In semi-honest model,a security two-party sets comparison equality protocol is proposed.The protocol converts multi-data equality comparison to polynomials equality comparison and effectively solves the fully equality problem of multi-data.The protocol does not require pairwise comarisons between set elements.And the results show that our protocol has lower complexity.Then a secure multi-party multi-data equality comparison protocol is proposed.This protocol can solve the problem of security multi-party equality without the help of the third party.We provides this protocol is collusion-resistance security.