Belief Peaks Clustering （BPC） algorithm is a new variant of Density Peaks Clustering （DPC） algorithm based on fuzzy perspective. It uses fuzzy mathematics to describe the distribution characteristics and correlation of data. However， BPC algorithm mainly relies on the information of local data points in the calculation of belief values， instead of investigating the distribution and structure of the whole dataset. Moreover， the robustness of the original allocation strategy is weak. To solve these problems， a fuzzy Clustering algorithm based on Belief Subcluster Cutting （BSCC） was proposed by combining belief peaks and spectral method. Firstly， the dataset was divided into many high-purity subclusters by local belief information. Then， the subcluster was regarded as a new sample， and the spectral method was used for cutting graph clustering through the similarity relationship between clusters， thus coupling local information and global information. Finally， the points in the subcluster were assigned to the class cluster where the subcluster was located to complete the final clustering. Compared with BPC algorithm， BSCC has obvious advantages on datasets with multiple subclusters， and it has the ACCuracy （ACC） improvement of 16.38 and 21.35 percentage points on americanflag dataset and Car dataset， respectively. Clustering experimental results on synthetic datasets and real datasets show that BSCC outperforms BPC and the other seven clustering algorithms on the three evaluation indicators of Adjusted Rand Index （ARI）， Normalized Mutual Information （NMI） and ACC.

Convolutional Neural Network （CNN） is sensitive to the local features of data due to the complex classification boundaries and too many parameters. As a result， the accuracy of CNN model will decrease significantly when it is attacked by adversarial attacks. However， the Topological Data Analysis （TDA） method pays more attention to the macro features of data， which naturally can resist noise and gradient attacks. Therefore， an image classification algorithm named MCN （Mapper-Combined neural Network） combining topological data analysis and CNN was proposed. Firstly， the Mapper algorithm was used to obtain the Mapper map that described the macro features of the dataset. Each sample point was represented by a new feature using a multi-view Mapper map， and the new feature was represented as a binary vector. Then， the hidden layer feature was enhanced by combining the new feature with the hidden layer feature extracted by the CNN. Finally， the feature-enhanced sample data was used to train the fully connected classification network to complete the image classification task. Comparing MCN with pure convolutional network and single Mapper feature classification algorithm on MNIST and FashionMNIST data sets， the initial classification accuracy of the MCN with PCA （Principal Component Analysis） dimension reduction is improved by 4.65% and 8.05%， the initial classification accuracy of the MCN with LDA （Linear Discriminant Analysis） dimensionality reduction is improved by 8.21% and 5.70%. Experimental results show that MCN has higher classification accuracy and stronger anti-attack capability.

At present, most of the existing certificateless signcryption schemes proven secure are proposed in the random oracle. Concerning the problem that this kind of schemes usually can not construct the corresponding instance in the practical application, a certificateless signcryption scheme was designed in the standard model. By analyzing several certificateless signcryption schemes in the standard model, it was pointed out that they were all insecure. Based on Aus scheme (AU M H, LIU J K, YUEN T H, et al. Practical hierarchical identity based encryption and signature schemes without random oracles. http://eprint.iacr.org/2006/368.pdf), a new proven secure certificateless signcryption scheme was proposed in the standard model by using bilinear pairing technique of elliptic curves. In the end, it is proved that the scheme satisfies indistinguishability against adaptive chosen ciphertext attack and existential unforgeability against adaptive chosen message and identity attack under the complexity assumptions, such as Decisional Bilinear Diffie-Hellman (DBDH) problem. Therefore, the scheme was secure and reliable.