A Distributed Secure Outsourcing Scheme for Solving Linear Algebraic Equations in Ad Hoc Clouds

The emerging ad hoc clouds form a new cloud computing paradigm by leveraging untapped local computation and storage resources. An important application of ad hoc clouds is to outsource computational intensive problems to nearby cloud agents. Specifically, for the problem of solving a linear algebraic equation (LAE), an outsourcing client assigns each cloud agent a subproblem, and then all involved agents apply a consensus-based algorithm to obtain the correct solution of the LAE in an iterative and distributed manner. However, such a distributed collaboration paradigm suffers from cyber security threats that undermine the confidentiality of the outsourced problem and the integrity of the returned results. In this paper, we identify a number of such security threats in this process, and propose a secure outsourcing scheme which not only preserves the privacy of the LAE parameters and the final solution from the participating agents, but also guarantees the correctness of the final solution. We prove that the proposed scheme has low computation complexity at each agent, and is robust against the identified security attacks. Numerical and simulation results are presented to demonstrate the effectiveness of the proposed method.