论文标题
拓扑编码的图形晶格和基质晶格
Graphic Lattices and Matrix Lattices Of Topological Coding
论文作者
论文摘要
基于晶格的密码学被认为具有经典计算机的特征和量子攻击性。我们将根据图理论和拓扑编码的知识设计各种图形晶格和矩阵晶格，因为图理论的许多问题可以通过（彩色）星形 - 图形晶格表示或说明。将引入一对新的叶片分割操作和叶子涂的操作，我们将图形色素和图形标记结合起来，以设计特定的合适的总彩物作为构建各种图形晶格，图形同构晶格，图形组晶格和topode-matcode-matrix lattices。图形组晶格和（定向）top-matrix晶格使我们能够在传统晶格和图形晶格之间建立连接。我们提出了研究图形晶格中遇到的数学问题，一些问题是：树拓扑认证，将图形分解为hanzi graphs，数字字符串分解问题，$（p，s）$ - 优雅的总数。
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 many problems of graph theory can be expressed or illustrated by (colored) star-graphic lattices. A new pair of the leaf-splitting operation and the leaf-coinciding operation will be introduced, and we combine graph colorings and graph labellings to design particular proper total colorings as tools to build up various graphic lattices, graph homomorphism lattice, graphic group lattices and Topcode-matrix lattices. Graphic group lattices and (directed) Topcode-matrix lattices enable us to build up connections between traditional lattices and graphic lattices. We present mathematical problems encountered in researching graphic lattices, some problems are: Tree topological authentication, Decompose graphs into Hanzi-graphs, Number String Decomposition Problem, $(p,s)$-gracefully total numbers.
