Research On The Scheme Of Verifiable And Secure Cloud Computation Outsourcing Of Square Matrix Power

Computing the high power of huge-dimension square matrix is a hard job for those entities(clients) with limited compute capability, therefore, a verifiable and secure cloud computing outsourcing scheme of square matrix power is designed based on the cloud computing platform. In the scheme, two different cloud computing outsourcing protocols are involved. One is the verifiable and secure cloud computing outsourcing protocol of square matrix power based on single cloud outsourcing model(S-SMP), and the other is the verifiable and secure cloud computing outsourcing protocol of square matrix power based on double cloud outsourcing model(D-SMP).In the S-SMP protocol, the client firstly constructs a random permutation and generates a secret key which includes a non-singular square matrix and its inverse matrix by combining the permutation with the Kronecker function. Secondly, the original square matrix is encrypted with the secret key by the client, and then the encrypted matrix is sent to the cloud along with the original exponent. After completing the calculation of the encrypted square matrix power, the cloud returns the result to the client. On receiving the returned result, the client decrypts it with the secret key and compares the elements that are randomly chosen by the client with the accurate values computed by the client himself correspondingly to verify the correctness of the result.In the D-SMP protocol, the client firstly constructs two groups of secret keys using the same method as in S-SMP protocol and each group contains a non-singular square matrix and its inverse. Secondly, the original square matrix is encrypted separately with the different secret key by the client, and then the result matrices of the encryption are dispatched to two different clouds along with the original exponent. After completing the calculation of the encrypted square matrix power, each cloud returns the result to the client. On receiving the returned results, the client decrypts them with the corresponding secret key and compares the elements of the decryption results correspondingly to verify the correctness of the result.Theoretical analysis shows that the protocol meets the requirements of outsourcing protocol well, which includes correctness, security, verifiability and high efficiency. In the simulation experiments of S-SMP protocol and D-SMP protocol, square matrix power are divided into two aspects: dimension fixed exponent changing and exponent fixed dimension changing. At the same time, the computation of square matrix power are conducted in two ways: the definition method and the dichotomy method. Finally, the experiment result illustrates that outsourcing computation of both cases of square matrix power, compared with the client completing the original job himself, can substantially reduce the time consumption of the client and derive a desirable outsourcing performance under each protocol of S-SMP and D-SMP. Except the single cloud outsourcing of square matrix power with dimension fixed exponent changing using dichotomy method, the cloud computation outsourcing performance of the others becomes better with the increase of dimension and exponent.