Research On Several Issues Of Secure Multi-party Computing

The rapid development of information technology promotes other technologies such as big data,cloud computing,networking,block chain to burgeon,and further makes information transfer more convenient.While brings human great convenience,information security problem is increasingly serious.Cryptography is an important means to ensure information security.Secure multiparty computation,an important tool to protect privacy in private data ap-plications,attracts more and more scholars to study it to design efficient secure multiparty computation protocols.Secure multiparty computation is a research fo-cus in the international cryptographic community.Secure multiparty computation has been applied to electronic voting,secret auction,data mining,secret inquiry,scientific computing,data statistics etc.Studying secure multiparty computation is of both theoretical and practical significance.Many secure multiparty computation protocols have been proposed,but their efficiency needs to be further improved.Furthermore,there are many secure multi-party computing problems that need to be studied.We first propose new protocols for the following problems:the comparison problem,the socialist Millionaires' prob-lem,the secure sorting problem.Then,we put forward protocols for problems such as secure three-party computation of geometry problems,secure computation of ba-sic elementary functions,of singular value,eigenvalue and norm of a matrix.Our contributions are as follows:(1)We first introduce an encoding method to encode a number into a vector to facilitate secure computation.Then based on the encoding method,we propose two efficient comparison protocols of which one is constructed using the Paillier additively homomorphic encryption,another one is based on the Goldwasser-Micali XOR homomorphic encryption.Both protocols can securely compare two numbers in one round.Secondly,we propose protocols to compare rational numbers.Then,we study the socialist Millionaires' Problem and apply it to determine whether two matrices are equal,and combining with the Godel number,propose a protocol to privately determine whether two matrices are equal.(2)Based on the Paillier encryption scheme and secret cutting,we propose two secure multiparty sorting protocols,one for sorting datum that are all distinct,and another one for any datum.We analyze the computational complexities and communication complexities of the protocols and show the efficiency of the protocols on a PC,and prove that they are secure in the semi-honest model and that they can resist collusion attack of n-2 players.These protocols are practical.(3)Using bilinear pairs,we propose secure multiparty computation protocols for the following geometric problem:whether a given point is on a line,whether three points are collinear,whether three lines intersect at one point,and whether three vectors are in the same plane.We analize the correctness of these protocols.The protocols are secure in the semi-honest model.They can resist collusion attack of n-1 players.Supplements the secure three-party computational geometry research.Our study does a little bit to secure multiparty computation and is of practical significance.