论文标题
拓扑编码中的图固定色和超图
Graph Set-colorings And Hypergraphs In Topological Coding
论文作者
论文摘要
为了使拓扑编码制作更复杂的基于数量的字符串，以防御配备量子计算的智能攻击并为量子计算时代提供有效的保护技术，我们将介绍固定的图表，以承认固定颜色，这些图是相当大的隐态意义，尤其是与超图相关的。我们使用图形的集合颜色来反映元素的相交，并添加其他约束要求，以表达集合之间的更多连接（如超级杂货）。 Since we try to find some easy and effective techniques based on graph theory for practical application, we use intersected-graphs admitting set-colorings defined on hyperedge sets to observe topological structures of hypergraphs, string-type Topcode-matrix, set-type Topcode-matrix, graph-type Topcode-matrix, hypergraph-type Topcode-matrix, matrix-type topcode-matrix \ emph {etc}。我们将表明，每个连接的图都是某些超图的相互作用，并研究了超图的连接性，超图形的着色，超图同质性，超核，超核网络，无标度网络发生器，具有与角度相交图的化合物超透明图为高维扩展图（用于高维扩展图）。自然地，我们会得到各种图形晶格，例如边缘配合的相交晶格，顶点胶状的相交格晶格，边缘 - 汉密顿图形晶格，超图形晶格和相交的网络网络晶格。本文中的许多技术都可以转化为多项式算法，因为我们的目标是将超图和图设定色应用于同态加密和非对称加密仪。
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will introduce set-colored graphs admitting set-colorings that has been considerable cryptanalytic significance, and especially related with hypergraphs. We use the set-coloring of graphs to reflect the intersection of elements, and add other constraint requirements to express more connections between sets (as hyperedges). Since we try to find some easy and effective techniques based on graph theory for practical application, we use intersected-graphs admitting set-colorings defined on hyperedge sets to observe topological structures of hypergraphs, string-type Topcode-matrix, set-type Topcode-matrix, graph-type Topcode-matrix, hypergraph-type Topcode-matrix, matrix-type Topcode-matrix \emph{etc}. We will show that each connected graph is the intersected-graph of some hypergraph and investigate hypergraph's connectivity, colorings of hypergraphs, hypergraph homomorphism, hypernetworks, scale-free network generator, compound hypergraphs having their intersected-graphs with vertices to be hypergraphs (for high-dimensional extension diagram). Naturally, we get various graphic lattices, such as edge-coincided intersected-graph lattice, vertex-coincided intersected-graph lattice, edge-hamiltonian graphic lattice, hypergraph lattice and intersected-network lattice. Many techniques in this article can be translated into polynomial algorithms, since we are aiming to apply hypergraphs and graph set-colorings to homomorphic encryption and asymmetric cryptograph.
