拓扑编码中图的参数化着色与标号
Parameterized Colorings And Labellings Of Graphs In Topological Coding
摘要：
即将到来的量子计算迫使我们重新审视人们使用的密码系统。我们正在将拓扑编码的图着色应用到现代信息安全和未来密码学中，以对抗未来的超级计算机和量子计算机攻击。这里介绍的许多技术都与许多数学猜想和NP问题有关。我们将介绍一组W-约束（k，d）-全染色以及在某些图中实现这些染色的算法，它们用于快速生成公钥和私钥，这些（k，d）-全染色是：优美（k，d）-全染色，协调（k，d）-全染色，（k，d）-边幻全染色，（k，d）-全差全染色和（k，d）-适宜差全染色。我们使用的有用工具之一是Topcode矩阵，元素可以是各种各样的东西，例如，集合，图形，基于数字的字符串。大多数参数化的图形着色/标记都是由Topcode矩阵代数定义的。从应用的角度来看，我们的许多着色技术都是由算法给出的，很容易转换成程序。
英文摘要：
The coming quantum computation is forcing us to reexamine the cryptosystems people use. We are applying graph colorings of topological coding to modern information security and future cryptography against supercomputer and quantum computer attacks in the near future. Many of techniques introduced here are associated with many mathematical conjecture and NP-problems. We will introduce a group of W-constraint (k,d)-total colorings and algorithms for realizing these colorings in some kinds of graphs, which are used to make quickly public-keys and private-keys with anti-quantum computing, these (k,d)-total colorings are: graceful (k,d)-total colorings, harmonious (k,d)-total colorings, (k,d)-edge-magic total colorings, (k,d)-graceful-difference total colorings and (k,d)-felicitous-difference total colorings. One of useful tools we used is called Topcode-matrix with elements can be all sorts of things, for example, sets, graphs, number-based strings. Most of parameterized graphic colorings/labelings are defined by Topcode-matrix algebra here. From the application point of view, many of our coloring techniques are given by algorithms and easily converted into programs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
