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.
翻译:即将到来的量子计算迫使我们重新检查人们使用的加密系统。 我们正在对现代信息安全和未来对超级计算机和量子计算机袭击的加密应用地貌编码的图形颜色。 这里引入的许多技术都与许多数学猜想和NP问题相关联。 我们将引入一组 W- constraint (k, d) 总计颜色和算法, 以在某类图表中实现这些颜色, 用于快速制作公用钥匙和私用钥匙的颜色总和。 这些( k, d) 总颜色是: 优雅( k, d) 总颜色, 和谐( k, d) 总颜色, (k, d) 和NP- 问题。 我们将引入一组 W- constrain( k, d) 总计颜色总颜色总和色彩总和算, 用于在某类图表中快速制作公共钥匙和私用钥匙, 这些( k, d) 总颜色总颜色总和颜色总和颜色总配对调。 我们使用的一种有用的工具被称作“ Topcodecodealal-rial ”, 其元素可以全部被从图像中定义为最上面的颜色定的颜色定序。