Cryptology ePrint Archive: Report 2014/442

Secure Outsourced Computation of the Characteristic Polynomial and Eigenvalues of Matrix

Xing Hu and Chunming Tang

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 economical 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 efficient and secure, but also unnecessary for any cryptographic assumption.

Category / Keywords: Cloud Computing;Outsourced computation;Matrix;Characteristic polynomial;Eigenvalues

Date: received 8 Jun 2014, last revised 12 Jun 2014

Contact author: ctang at gzhu edu cn

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Version: 20140613:045239 (All versions of this report)

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