Secure Outsourcing Of Matrix Computations To The Cloud

The emergence of massive data can cause large scale system of computing task(e.g., more complex data mining, statistical and scientific computations), whose computational overhead and resource consumption is constantly increasing. And then, the outsourced computing model(outsourcing data to a third party to compute and get the return results) supported by cloud computing technology came into being. Matrix computations are widely used in scientific computing, image encryption, 3D image processing and so on. Outsourcing of matrix computations is identified as an important application of cloud computing outsourcing.However, most of the schemes tackle such problem by cryptography and secure multiple party techniques, which is more secure but leads to low efficiency and is not impractical.Taking into account the efficiency problem, secure outsourcing scheme for complex computational problem based on diagonal matrix multiplicative perturbation privacy has attracted considerable attention. Which avoiding the low efficiency problem caused by the computation of the cipher text. However, the promising algorithm has some security deficiency. We aim to design complex linear transformation algorithm to disguise the original data of the client, and propose three protocols for secure outsourcing of common matrix computation problems. Including linear equations, matrix determinant, and linear regression. Our protocol has improved the security of previous scheme. The main contents and contributions of this paper are given as follows:(1) We introduce data segmentation privacy protection techniques. During the investigation, the original matrix elements are preprocessed to protect the privacy of the client. We propose a secure outsourcing protocol for large scale of linear equations. Our protocol has improved the security. And make sure our protocols fulfill the basic goals of high efficiency and result verification.(2)We propose a secure outsourcing protocol for matrix determinant. We introduce mutil-cloud nodes model which is assume to be non-colluding, and outsource complex disguising computations to cloud servers. It can reduce the computation cost for client and keep privacy of client’s original data during the protocol. At same time, complex disguise transformations can make our protocol achieving formal security.(3) Based on the former studies, we propose a secure outsourcing protocol for linear regression. We introduce an ingenious linear conversion techniques enable client do complex linear transformation on original problem, meanwhile, keep client high efficiency. Our protocol solve the security flaws in the existing scheme, and can improve the security. Theoretical and experimental analysis validate the practicability of our protocols.