Inverse multiserver parallel outsourcing computing scheme based on three-step decomposition matrix

With the rapid development of information technology such as cloud computing and Internet of Things, outsourcing computing has received more and more attention. Outsourcing computing provides a way for resource-constrained clients to solve complex computing problems. Matrix inversion is a basic mathematical operation widely used in scientific and engineering fields. However, there are some problems in the existing matrix inversion outsourcing computing, such as privacy security challenges, the limitation of parallel computing in multi-server mode and poor verification efficiency. In order to solve these problems, we propose a three-step decomposition based matrix inversion multi-server parallel computing algorithm, and designs a corresponding matrix inversion multi-server security verifiable computing scheme. In this scheme, the matrix partitioning and matrix 𝐿𝑈 decomposition techniques are used to decompose the matrix inversion process into three steps: matrix LU decomposition, triangular matrix inversion and triangular matrix multiplication. At the same time, the number of servers is extended from two to multiple, which improves the efficiency of server parallel computation. Security analysis and simulation experiments show that the proposed scheme can improve the efficiency of outsourcing computation while meeting the security goals.