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Journal of Jishou University

Secure Two-Party Scientific Computations

Li Xiang

Published Jan 1, 2003• 1 citation
OpenAlex

Abstract

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.

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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.
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.
Abstract. Linear algebra plays an important role in computer science, especially in cryptography.Numerous cryptog-raphic protocols, scientific computations, and numerical computations are based on linear algebra. Many linear algebra tasks can be reduced to some core problems, such as matrix multiplication, determinant of matrix and the characteristic polynomial of matrix. However, it is difficult to execute these tasks independently for client whose computation abilities are weaker than polynomial-time computational ability. Cloud Computing is a novel eco-nomical paradigm which provides powerful computational resources that enables resources-constrained client to outsource their mass computing tasks to the cloud. In this paper, we propose a new verifiable and secure outsourcing protocol for the problem of computing the characteristic polynomial and eigenvalues of matrix. These protocols are not only effi-cient and secure, but also unnecessary for any cryptographic assumption.
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.
We propose several practical SMC protocols for privacy-preserving cooperative scientific computations. We consider two important scientific computations which involve linear equations: the linear systems of equations problem and the linear least-square problem. The protocols proposed in this paper achieve acceptable security in the sense of Du-Zhan's paradigm and t-wise collusion-resistance, and their communication complexity is O(tm), where t is a security parameter and m is the total number of participants. The complexity of our protocol is significantly better than the previous result O( m2/μm^2/{\mu}m2/μ ) of [4], in which the oblivious transfer protocol is used as an important building block.
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.