Secure and Efficient Outsourcing of Matrix Multiplication based on Secret Sharing Scheme using only One Server

In this paper, we propose secure and efficient outsourcing of matrix multiplication based on secret sharing scheme and using only one server. Matrix multiplication has been widely used in the field of machine learning, including deep learning. However, as the size of a matrix becomes larger, the computational complexity becomes more enormous (e.g., matrix multiplication between two m × $m$ matrices can be done with O($m$ 3) complexity). Because of the limited performance or storage on the device, it is impossible for an individual to perform such large-scale computations. To solve this problem, the technology that enables the consumer as a client to outsource computation securely to a high-performance server in the cloud, namely, secure outsourcing computation is studied. Our method is realized by multiplying some shares of a secret by different random numbers. The proposed method removes the disadvantage of secret sharing scheme that needs multiple servers to perform operations of less computational complexity than those of the method based on homomorphic encryption. We prove the security of our method against not only passive but also active adversaries. In addition, we show that our method is more efficient than existing methods of secure outsourcing computation.