On Verifiable And Secure Outsourcing Protocols For Matrix Operations

With the development of cloud computing, cloud computation outsourcing service has found tremendous applications. However, the security issue is the bottleneck to restrict the further applications of cloud outsourcing services in real life practice.Large-dimensional matrix operations often requires a large amount of computing resources. So the matrix outsourcing computing schemes will heavily reduce the computational overheads for the users. However, the existing matrix outsourcing computing schemes are confronted with the following security drawbacks: fail to obtain a relatively high level of security in the single-server model, or be vulnerable to the colluding attacks under the multi-server models. The contributions of this dissertation are as follows.1. Verifiable and secure outsourcing computing protocol for matrix multiplications.The protocol firstly splits the secret matrix into two parts and then disguises the split matrices by utilizing permutation matrices to achieve the input and output privacy. It is illustrated that the protocol is immune from the colluding attacks in the double-server model. The returned results of the protocol can be fast verified by using the redundancy computations of the servers. Comparisons with other schemes and the experiment results show that the proposed outsourcing protocol is secure, efficient and practical.2. Verifiable and secure outsourcing computing protocol for matrix determinant. A secure computation outsourcing protocol for determining the determinant of square matrices is proposed based on the matrix multiplication outsourcing protocol in this dissertation. The protocol can ensure the input and output privacy as well as the verifiability of the returned results. It is also shown that the proposal can resist colluding attacks in the double-server model. Analysis demonstrates that the proposed protocol is secure, efficient and practical.3. Verifiable and secure outsourcing computing protocol for system of linear equations.The protocol randomly splits the constant vector into two vectors and then encrypts the constants and the coefficients with permutation matrices, and thus the input and output privacy is obtained. The protocol is shown to be invulnerable to colluding attacks under the double-server model, and can verify the results with the redundancy computations of the servers. Comparisons and analysis reveal that the proposed outsourcing protocol is secure, efficient and practical.