Secure and efficient outsourcing computation on large-scale linear regressions

Abstract

Solving large-scale linear regression (LR) becomes more and more prevalent in theoretical research and engineering application, which however is too expensive to solve for limited-resource clients. To meet this challenge, more and more clients shift their expensive computations to powerful clouds in practice. The previous works on secure outsourcing LR usually possess heavy workloads, some of which even have potential limitations. In this paper, we first reveal several limitations in the state-of-the-arts. To overcome these shortcomings, we then propose a novel protocol for securely outsourcing large-scale LR. In our design, a client only utilizes two random vectors to encrypt his/her LR problem and decrypt the solution returned from the cloud, which is quite simple. In addition, the proposed protocol only involves with several vector-vector operations, two matrix-vector multiplications and one matrix-matrix subtraction, which thus achieves high efficiency. We also demonstrate that the proposed protocol can accomplish correctness guarantee, privacy protection and cheating resistance under the assumption of a malicious cloud. At last, extensive theoretical analysis and experimental results are provided to further validate the superiority of the proposed protocol.