Focused on the problems of no protection for the number of zero elements in original matrix and no verification for the result returned by cloud in outsourcing algorithm of matrix full rank decomposition, a verifiable and secure outsourcing scheme of matrix full rank decomposition was proposed. Firstly, in the phase of encryption, a dense invertible matrix was constructed by using the Sherman-Morrison formula for encryption. Secondly, in the phase of cloud computing, the cloud computing of the full rank decomposition for the encryption matrix was required. And when the results of full rank decomposition for encryption matrix (a column full rank matrix and a row full rank matrix) were obtained, the cloud computing of the left inverse of the column full rank matrix and the right inverse of the row full rank matrix was required respectively. Thirdly, in the phase of verification, the client not only needed to verify whether these two matrices returned by cloud are row-full-rank or column-full-rank respectively, but also needed to verify whether the multiplication of these two matrices is equal to the encryption matrix. Finally, if the verification was passed, the client was able to use the private key to perform the decryption. In the protocol analysis, the proposed scheme is proved to satisfy correctness, security, efficiency, and verifiability. At the same time, when the dimension of the selected original matrix is 512×512, with different densities of non-zero elements in the matrix, the entropy of the encryption matrix calculated by this scheme is identically equal to 18, indicating that the scheme can protect the number of zero elements effectively. Experimental results show the effectiveness of the proposed scheme.

Focused on the problems of multiple expression variations, multiple pose variations as well as varying-degree missing face point cloud data in Three-Dimensional (3D) faces, 3D point cloud face data was exploratively applied to PointNet series classification networks, and the recognition results were compared and analyzed, then a new network framework named HFN (Hierarchical Feature Network) was proposed. First, the point cloud with fixed points was randomly sampled after data preprocessing. Second, the point fixed point cloud was input into SA (Set Abstraction) module in order to obtain the centroid points and neighborhood points of the local areas, and extract the features of the local areas, then the point cloud spatial structural features extracted from DSA (Directional Spatial Aggregation) module based on multi-directional convolution were mosaicked. Finally, the full connection layer was used to perform the classification of 3D faces, so as to realize the 3D face recognition. The results on CASIA database show that the average recognition rate of the proposed method is 96.34%, which is better than those of classification networks such as PointNet, PointNet++, PointCNN and Spatial Aggregation Net (SAN).

Aiming at the problem of low reconstruction quality of the existing Compressed Sensing Magnetic Resonance Imaging (CSMRI) algorithms at low sampling rates, an imaging method combining deep priors and non-local similarity was proposed. Firstly, a deep denoiser and Block Matching and 3D filtering (BM3D) denoiser were used to construct a sparse representation model that can fuse multiple priori knowledge of images. Secondly, the undersampled k-space data was used to construct a compressed sensing magnetic resonance imaging optimization model. Finally, an alternative optimization method was used to solve the constructed optimization problem. The proposed algorithm can not only use the deep priors through the deep denoiser, but also use the non-local similarity of the image through the BM3D denoiser to reconstruct the image. Compared with the reconstruction algorithms based on BM3D, experimental results show that the proposed algorithm has the average peak signal-to-noise ratio of reconstruction increased about 1 dB at the sampling rates of 0.02, 0.06, 0.09 and 0.13. Compared with the existing MRI algorithm WaTMRI (Magnetic Resonance Imaging with Wavelet Tree sparsity),DLMRI (Dictionary Learning for Magnetic Resonance Imaging), DUMRI-BM3D (Magnetic Resonance Imaging based on Dictionary Updating and Block Matching and 3D filtering), etc, the images reconstructed by the proposed algorithm contain a lot of texture information, which are the closest to the original images.

In view of the subjective arbitrariness of objective weight in multi-objective decision making based on Vague sets and the monotong problem of evaluation function, a novel approach to multi-objective decision making based on entropy weighted-Vague sets was presented. Firstly, the decision matrix was transformed into the objective-grade-membership matrix. Then the objective weight of each objective was calculated by entropy coefficient method, and the weight vector interval of each objective was obtained by considering objective weight and subjective weight. Next the Vague evaluation was obtained by computing the sets of objectives being in favor, against and neutral. Finally, a new evaluation function was defined to sort the alternatives and select the optimal scheme. The rationality and effectiveness of the method were verified by an example.

To effectively control large-scale outbreak, the propagation properties of the leeching P2P (Peer-to-Peer) botnet was studied using dynamics theory. Firstly, a delayed differential-equation model was proposed according to the formation of the botnet. Secondly, the threshold expression of controlling botnet was obtained by the explicit mathematical analysis. Finally, the numerical simulations verified the correctness of theoretical analysis. The theoretical analysis and experimental results show that the botnet can be completely eliminated if the basic reproduction number is less than 1. Otherwise, the defense measures can only reduce the scale of botnet. The simulation results show that decreasing the infection rate of bot programs or increasing the immune rate of nodes in the network can effectively inhibit the outbreak of botnet. In practice, the propagation of bot programs can be controlled by some measures, such as uneven distribution of nodes in the network, timely downloading patch and so on.

The arithmetic correlation function is a new method for studying the cryptographic properties of Boolean functions. Based on the basic definitions of addition and multiplication of multi-2-adic integer, the study constructed a new algebraic ring and realized the arithmetic or “with-carry” analogs of classic correlation functions. In this paper the definition of arithmetic autocorrelation function was introduced. The arithmetic correlation value of symmetric Boolean functions was studied. The results show that the arithmetic autocorrelation function of symmetric Boolean functions is a real symmetric function with at most n1 values.