Secure Distributed Outsourcing of Large-scale Linear Systems

Solving the system of linear algebraic equations (LAE) is the most well known and probably the most important of all numerical computations involving real numbers. Researchers have been committed to developing distributed algorithms to solve such systems for a long time. However, traditional distributed algorithms have serious security risks when the coefficients and the solution are of great value. To address the privacy issue, we propose a new secure distributed outsourcing protocol for solving large-scale LAE systems. Specifically, we give an algorithm for generating a generic repeatedly jointly strongly connected sequence, for the first time as far as we know. Then we embed the matrix masking technique in our distributed system requiring multiple rounds of iteration while keeping the correctness of convergence. In addition, for the first time, we give a method for discriminating by the agents under masking whether the plaintext approximate solution corresponding to the current masked solution satisfies a predetermined constraint. Finally, we give the experimental result to show the practicality of our new protocol.