Secure outsourcing of large matrix determinant computation

Cloud computing provides the capability to connect resource-constrained clients with a centralized and shared pool of resources, such as computational power and storage on demand. Large matrix determinant computation is almost ubiquitous in computer science and requires large-scale data computation. Currently, techniques for securely outsourcing matrix determinant computations to untrusted servers are of utmost importance, and they have practical value as well as theoretical significance for the scientific community. In this study, we propose a secure outsourcing method for large matrix determinant computation. We employ some transformations for privacy protection based on the original matrix, including permutation and mix-row/mix-column operations, before sending the target matrix to the cloud. The results returned from the cloud need to be decrypted and verified to obtain the correct determinant. In comparison with previously proposed algorithms, our new algorithm achieves a higher security level with greater cloud efficiency. The experimental results demonstrate the efficiency and effectiveness of our algorithm.