Computing the determinant of large matrix is a time-consuming task, which is appearing more and more widely in science and engineering problems in the era of big data. Fortunately, cloud computing can provide large storage and computation resources, and thus, act as an ideal platform to complete computation outsourced from resource-constrained devices. However, cloud computing also causes security issues. For example, the curious cloud may spy on user privacy through outsourced data. The malicious cloud violating computing scripts, as well as cloud hardware failure, will lead to incorrect results. Therefore, we propose a secure outsourcing algorithm to compute the determinant of large matrix under the malicious cloud mode in this paper. The algorithm protects the privacy of the original matrix by applying row/column permutation and other transformations to the matrix. To resist malicious cheating on the computation tasks, a new verification method is utilized in our algorithm. Unlike previous algorithms that require multiple rounds of verification, our verification requires only one round without trading off the cheating detectability, which greatly reduces the local computation burden. Both theoretical and experimental analysis demonstrate that our algorithm achieves a better efficiency on local users than previous ones on various dimensions of matrices, without sacrificing the security requirements in terms of privacy protection and cheating detectability.
New Algorithms for Secure Outsourcing of Large-Scale Systems of Linear Equations