Secure & efficient delegation of system of linear equation to a malicious cloud server

Cloud computing offers an economical solution to the computationally weak clients. It enables the client to execute large computations beyond their computation capacity by outsourcing their computation load to the massive cloud servers. However, outsourcing of data and the computation to a third-party cloud server bring many security and privacy concern. In this paper, we are addressing the problem of system of linear equation (LE), which is a basic engineering and scientific problem that has application in various areas. We are employing efficient linear transformation technique using the concepts of linear algebra. The proposed algorithm transform the dataset to some other form to hide the original dataset. The algorithm provides a non-interactive proof of solution therefore, the algorithm executes with an optimal one round of communication. The proposed algorithm also employs an efficient result verification method to perceive deceitful server behavior with an optimal probability, thus preserving the data integrity. The result verification method is very efficient and run with modest overhead. The proposal has been verified through theoretical and experimental analysis to demonstrate the practical usability of the proposed algorithm.