On Real-Valued Total Colorings Towards Topological Authentication In Topological Coding

In order to deal with the attack of decoding equipped with AI or even quantum computers, we develop uncountable topological codes by means of techniques from real functions and topological coding. We introduce four C-edge-magic real-valued total colorings first, where ‘C-edge-magic’ is one of edge-magic, difference edge-magic, mixed-edge-magic, graceful edge-magic. These real-valued total colorings help us to design public-key sets and private-key sets for topological authentication problems, since these sets contains non-countable graphs with real-valued total colorings. We introduce ‘real-valued Topcode-matrices', which can produce huge numbers of more complex text-based passwords with longer bytes in order to ba applied in real network security, and some algebraic skills on real-valued Topcode-matrices.