  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.
