Verifying Outsourced Inner Product Computation via Vector Aggregation in Cloud Computing

Outsourced computation has been extensively studied in a number of computer application fields with the increasing prevalence of cloud computing. As the basis and the fundamental operation, inner product computation of vectors, has also been put forwarded. As the service provider of the cloud computing may not be trustworthy, the correctness of the computation results can be corrupted if the service provider is with random fault or not honest (e.g., lazy, malicious, etc). Therefore, it is necessary for the client to verify the correctness of inner product of vectors. Existing verification mechanisms are almost built on the Merkle tree structure and signature chain mechanism, which lack efficiency on both storage and computation aspects. The existing aggregate verification scheme based on algebraic properties is able to ease such problem, however, there exist some serious design defects and lack important details. In order to solve such problems, in this paper we propose the sound inner product verification schemes based on the algebraic properties. Specifically, we first propose the simple aggravate framework, then we analyze its serious defects under smart cloud attack. Furthermore, we design the local aggregate and random aggregate framework to solve the problems respectively. Finally, we provide analysis of the proposed verification schemes in this paper.