Verifying correctness of inner product of vectors in cloud computing

Abstract

Inner product computation of vectors has been extensively applied in a number of computer application fields. Many applications with inner product of vectors as the fundamental operation have been deployed on the cloud computing platform. As the service provider of the cloud computing may not be completely trustworthy, it is necessary for the client to verify the correctness of the returned computation results of inner product of vectors. In this paper, we present an effective and efficient correctness verification mechanism for the inner product of vectors, which is named aggregate verification vector and constructed on the algebraic properties of the inner product of vectors. The aggregate verification vector is constructed secretly by the data owner, shared with the client, and kept secretly from the service provider. On the basis of the aggregate verification vector, we propose a novel verification scheme, which enables the client to check whether the returned computation results are correct or not. We make exhaustive security analysis of the proposed verification scheme and show that the scheme provides strong probabilistic guarantees on the correctness of the computation results of inner product between vectors. Extensive experiments demonstrate the performance efficiency of our proposed verification scheme.