A study and implementation of large-scale log-determinant computation to cloud.

Logarithm of a square matrix is a factor that clearly affects the quality or result of something. Logarithms are used to maintain exactitude in many numerical computations than the determinant. At present cloud computing is an emerging topic to perform this kind of operations. Cloud computing qualifies resource-awkward clients to solve their immense computational workloads through a cloud server that provides heavy computational power and it is also less expensive. This rising computing paradigm undoubtedly introduces new challenges and security concerns such as security, correctness, competency and result verifiability. Matrix log-determinant is a quite simple scientific, engineering and machine learning application. It inspired us to plan a protocol that satisfies all the concerns for the outsourcing of LDC to a cloud which is malicious in this paper. The primary concept to save privacy is to put in some changes on the original matrix for encryption and send the encrypted matrix to the cloud. The cloud then uses any LU decomposition algorithm on the encrypted matrix and divide the matrix for calculating the log-determinant. After returning from the cloud some transformations are applied to the returned result to get the accurate log-determinant of the original matrix. [ABSTRACT FROM AUTHOR]