关键词: 云计算, 外包计算, 矩阵行列式, 矩阵相乘, 矩阵的逆

Abstract: The large-scale MMC (matrix multiplication computation), MIC (matrix inversion computation) and MDC (matrix determinant computation) algorithm in secure outsourcing computing is widely researched and applied, while its existing problems are also increasingly highlighted. The problem of hiding the number of zero elements in the original matrix is one of them. However, there are few researches on it, and the existing researches can only protect the position of zero elements. There is no encryption method aiming at protecting the number of zero elements and at the same time achieving high efficiency, which is very unsafe in the cloud computing. To solve this problem, from the perspective of algorithm, the encryption method of permutation matrix is improved, and a new algorithm of secure outsourcing MMC, MIC and MDC is designed. The algorithm extends the algebraic structure to the finite domain. Firstly, the initial matrix is permuted randomly, then transformed by the unimodular matrix, and the encrypted matrix is sent to the cloud server. The cloud computes it and returns the results to the client. The client decrypts and verifies it. Through theoretical proof, the algorithm not only protects the number of zero elements of the original matrix, but also achieves the purposes of correctness, privacy and verifiability. Finally, experiments show that the encryption method based on unimodular matrix is efficient.

Key words: cloud computing, outsourcing computing, matrix determinant, matrix multiplication, inversion of matrix