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A mathematical topology with matrix is a natural representation of a coding relational structure that is found in many fields of the world. Matrices are very important in computation of real applications, s ce matrices are easy saved in computer and run quickly, as well as matrices are convenient to deal with communities of current networks, such as Laplacian matrices, adjacent matrices in graph theory. Motivated from convenient, useful and powerful matrices used in computation and investigation of todays networks, we have introduced Topcode-matrices, which are matrices of order $3times q$ and differ from popular matrices applied in linear algebra and computer science. Topcode-matrices can use numbers, letters, Chinese characters, sets, graphs, algebraic groups emph{etc.} as their elements. One important thing is that Topcode-matrices of numbers can derive easily number strings, since number strings are text-based passwords used in information security. Topcode-matrices can be used to describe topological graphic passwords (Topsnut-gpws) used in information security and graph connected properties for solving some problems coming in the investigation of Graph Networks and Graph Neural Networks proposed by GoogleBrain and DeepMind. Our topics, in this article, are: Topsnut-matrices, Topcode-matrices, Hanzi-matrices, adjacency ve-value matrices and pan-Topcode-matrices, and some connections between these Topcode-matrices will be proven. We will discuss algebraic groups obtained from the above matrices, graph groups, graph networking groups and number string groups for encrypting different communities of dynamic networks. The operations and results on our matrices help us to set up our overall security mechanism to protect networks.
Information-theoretic security is considered in the paradigm of network coding in the presence of wiretappers, who can access one arbitrary edge subset up to a certain size, also referred to as the security level. Secure network coding is applied to
In the two-part paper, we consider the problem of secure network coding when the information rate and the security level can change over time. To efficiently solve this problem, we put forward local-encoding-preserving secure network coding, where a
In this paper we introduce Neural Network Coding(NNC), a data-driven approach to joint source and network coding. In NNC, the encoders at each source and intermediate node, as well as the decoder at each destination node, are neural networks which ar
Topological Coding consists of two different kinds of mathematics: topological structure and mathematical relation. The colorings and labelings of graph theory are main techniques in topological coding applied in asymmetric encryption system. Topsnut
Lattice-based Cryptography is considered to have the characteristics of classical computers and quantum attack resistance. We will design various graphic lattices and matrix lattices based on knowledge of graph theory and topological coding, since ma