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Chinese Journal of Computers

The Secure Multi-Party Protocol of Matrix Product and Its Application

Luo Wen

Published Jan 1, 2005• 8 citations
OpenAlex

Abstract

Wenliang Du has been studied some secure two-party scientific computation problems [4] : Linear systems of equations problems, Linear least squares problems and Linear programming problems. And he point to: (1)There are some other interesting scientific computation problems that need to be studied, such as how secure compute eigenvalues of matrix. (2)Extension to the secure multi-party computation problem, and thought extension secure two-party computation protocols to the secure multi-party computation protocols is not trivial. In this paper, authors disscuss two scientific computation problems: eigenvalues of matrix in secure multi-party computation situation, and give some secure multi-party scientific computation protocols.

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Wenliang Du has been studied some secure two-party scientific computation problems [4] : Linear systems of equations problems, Linear least squares problems and Linear programming problems. And he point to: (1)There are some other interesting scientific computation problems that need to be studied, such as how secure compute eigenvalues of matrix. (2)Extension to the secure multi-party computation problem, and thought extension secure two-party computation protocols to the secure multi-party computation protocols is not trivial. In this paper, authors disscuss two scientific computation problems: eigenvalues of matrix in secure multi-party computation situation, and give some secure multi-party scientific computation protocols.
Dr.W.DU has studied three secure two-party scientific computation problems: Linear systems of equations problems,Linear least squares problems and Linear programming problems.And he points out:there are some other interesting scientific computation problems that need to be studied,such as secure compute eigenvalues,eigenvales,eigenvectors,determinants,conditions,and factorization of a matrix.In this paper,the authors have been studied two scientific computation problems:eigenvalues and eigenvectora of matrix in secure two-party computation situation.Some secure two-party scientific computation protocols are given.
Secure Multi-party Computation(SMC) about which people have got some research findings at home and abroad has been a research focus in international cryptographic community recently,and this paper proposes a new protocol for the inverse of n×n matrices by using Oblivious Transfer 1 out of p protocol in the secure two-party computation environment.The protocol can be used to solve the problem securely and more efficiently.Then gives a new protocol for secure two-party linear system of equations based on it.
Considering constant-round protocols for generating random shared values, for secure multiplication and for addition of shared values, etc are available and can be met by known techniques in all standard models of communication. Protocols are presented allowing the players to securely solve standard computational problems in linear algebra. In particular, securely, efficiently and in constant-round compute determinant of matrices product, rank of a matrix, and determine similarity between matrices. If the basic protocols (addition and multiplication, etc) are unconditionally secure, then so are our protocols. Furthermore our protocols offer more efficient solutions than previous techniques for secure linear algebra.
It is well known that, in theory, the general secure multi-party computation problem is solvable using circuit evaluation protocols. However, the communication complexity of the resulting protocols depend on the size of the circuit that expresses the functionality to be computed and hence can be impractical. Hence special solutions are needed for specific problems for efficiency reasons. The point inclusion problem in computational geometry is a special multiparty computation and has got many applications. Previous protocols for the secure point inclusion problem are not adequate. In this paper we modify some known solutions to the point inclusion problem in computational geometry to the frame work of secure two-party computation.
A secure two-party hamming distance computing protocol is proposed based on the secure two-party matrix product protocol; a secure four-party addition protocol, a secure three-party addition protocol and a secure two-party number protocol are proposed based on the additive homomorphic encryption and secure two-party compare protocol. A secure multi-party closest string protocol is presented based on the secure two-party hamming distance computing protocol and a secure multi-party addition protocol. These protocols are based on semi-honest model.