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Linear Regression (LR) is a classical machine learning algorithm which hasmany applications in the cyber physical social systems (CPSS) to shape andsimplify the way we live, work and communicate. This paper focuses on the dataanalysis for CPSS when the Linear Regression is applied. The training processof LR is time-consuming since it involves complex matrix operations, especiallywhen it gets a large scale training dataset In the CPSS. Thus, how to enabledevices to efficiently perform the training process of the Linear Regression isof significant importance. To address this issue, in this paper, we present asecure, verifiable and fair approach to outsource LR to an untrustworthycloud-server. In the proposed scheme, computation inputs/outputs are obscuredso that the privacy of sensitive information is protected against cloud-server.Meanwhile, computation result from cloud-server is verifiable. Also, fairnessis guaranteed by the blockchain, which ensures that the cloud gets paid only ifhe correctly performed the outsourced workload. Based on the presentedapproach, we exploited the fair, secure outsourcing system on the Ethereumblockchain. We analysed our presented scheme on theoretical and experimental,all of which indicate that the presented scheme is valid, secure and efficient.

Machine Learning on Cloud with Blockchain: A Secure, Verifiable and Fair Approach to Outsource the Linear Regression for Data Analysis