Parameterized Colorings And Labellings Of Graphs In Topological Coding

TL;DR

This paper introduces a new class of graph colorings and labelings based on topological coding, aiming to enhance cryptographic security against quantum attacks through novel algorithms and mathematical frameworks.

Contribution

It presents parameterized (k,d)-total colorings and algorithms using Topcode-matrix algebra for cryptography, addressing quantum-resistant key generation methods.

Findings

Developed (k,d)-total colorings with cryptographic applications

Created algorithms for efficient coloring realization in graphs

Proposed Topcode-matrix as a versatile tool for graph labeling

Abstract

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.