Exploring the topological graph encoding implementation of integer grids(探索整数格的拓扑图编码实现)

In the post quantum era, lattice cryptography is featured as an interdisciplinary and diversified research method, and is most likely to become post quantum cryptography. The graphic lattice in topological coding is the product of interdisciplinary study. Graphs in graphic lattices are stored by matrices and run in the computer, the main theoretical technology of topological coding is originated from mathematical disciplines such as discrete mathematics, number theory and algebra. Because topological coding contains a lot of mathematical conjectures and NP-problems, the number-based strings generated by topological coding possess irreversibility and computational security. Some new labelings and colorings are defined in this paper, and the algorithms to realize these labelings and colorings are given, and the classes of graphs admitting these new labelings and colorings are determined. We establish graphic lattices based on graph operations and graphic lattice bases, for asymmetric cryptography, and show connections among caterpillar-graphic lattices, their complementary graphic lattices and integer lattices. The technical methods in this paper are shown by effective and feasible algorithms.(在后量子时代，格密码具有多学科交叉性且研究方法多样性的特点，极有可能成为后量子密码。拓扑编码中的图格是多学科交叉的产物，其中的图通过矩阵进行存储并在计算机中运行，其主要理论来自离散数学、数论、代数学等数学学科。由于拓扑编码含有大量的数学猜想和计算NP-问题，因此其产生的数字串具有不可逆性和计算安全性。本文定义了新的标号和着色，并给出了实现这些标号和着色的算法，确定了承认这几种标号和着色的图类。同时，建立了毛毛虫树图格及其互补图格，探讨了这些图格与传统的整数格之间的关系。所用技术方法均基于有效且可行的算法实现。)