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Journal of Beijing Electronic Science and Technology Institute

Analysis and Improvement of a Multi-Party Protocol for Finding the Eigenvalues of Matrices

Yiqi Dai

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

LUO et al. presented a multi-party protocol of finding eigenvalues of matrix in a secure multi-party computation situation and studied the security of it. The authors of this paper points out that the protocol is insecure in most cases of scientific computation and technological applications. A new protocol solving the same problem and the discussion of its security are also given.

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Secure Two-Party Computation is Practical.

Benny Pinkas B, Thomas H. Schneider, Nigel Paul Smart +1 more

Abstract. Secure multi-party computation has been considered by the cryptographic community for a number of years. Until recently it has been a purely theoretical area, with few implementations with which to test various ideas. This has led to a number of optimisations being proposed which are quite restricted in their application. In this paper we describe an implementation of the two-party case, using Yao’s garbled circuits, and present various algorithmic protocol improvements. These optimisations are analysed both theoretically and empirically, using experiments of various adversarial situations. Our experimental data is provided for reasonably large circuits, including one which performs an AES encryption, a problem which we discuss in the context of various possible applications. 1

•Jan 1, 2009•1 citation
LUO et al. presented a multi-party protocol of finding eigenvalues of matrix in a secure multi-party computation situation and studied the security of it. The authors of this paper points out that the protocol is insecure in most cases of scientific computation and technological applications. A new protocol solving the same problem and the discussion of its security are also 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.
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.
Abstract. Secure multi-party computation has been considered by the cryptographic community for a number of years. Until recently it has been a purely theoretical area, with few implementations with which to test various ideas. This has led to a number of optimisations being proposed which are quite restricted in their application. In this paper we describe an implementation of the two-party case, using Yao’s garbled circuits, and present various algorithmic protocol improvements. These optimisations are analysed both theoretically and empirically, using experiments of various adversarial situations. Our experimental data is provided for reasonably large circuits, including one which performs an AES encryption, a problem which we discuss in the context of various possible applications. 1